EP4664038A1

EP4664038A1 - Fault detection of an expansion valve

Info

Publication number: EP4664038A1
Application number: EP24182293.1A
Authority: EP
Inventors: Karl-Heinz Petry
Original assignee: Siemens Schweiz AG
Current assignee: Siemens Schweiz AG
Priority date: 2024-06-14
Filing date: 2024-06-14
Publication date: 2025-12-17
Also published as: US20250383133A1; CN121140254A

Abstract

Disturbances in refrigerant circuits. Detecting a disturbance in a refrigerant circuit (1), the circuit (1) comprising a valve (3) having an inlet and an outlet and a first sensor (7) for recording a thermodynamic state at the inlet, and a second sensor (8) for recording a thermodynamic at the outlet, the detection comprising: recording a first signal using the first sensor (7); recording a second signal using the second sensor (8); processing the first signal to determine an upstream pressure p_u ; processing the second signal to determine a downstream pressure p_d ; recording a position signal; processing the position signal to determine a position (12) of the valve (3); determining a discharge coefficient c_m based on the upstream pressure p_u, based on the downstream pressure p_d, wherein the coefficient c_m relates actual flow ṁ at the position to maximum flow ṁ at the position.

Description

Background

The present disclosure deals with disturbances in refrigerant circuits. More specifically, the instant disclosure pertains to fluctuations of pressure in closed circuits for heating and/or ventilation and/or air-conditioning (HVAC).
Installations for heating and/or ventilation and/or air-conditioning are commonly made up of a plurality of circuits. Each circuit comprises one or more terminal units to provide cooling and/or heating to various parts of a building. Terminal units can comprise cooling devices and/or heating devices. A terminal unit of a domestic heating system can be a thermal energy exchanger such as a radiator, a condenser or an evaporator.
HVAC installations such as installations for air-conditioning can also comprise one or more refrigerant circuits. These refrigerant circuits are made up of compressors, evaporators, (expansion) valves, and condensers. A compressor, an evaporator, an expansion valve such as an electronic expansion valve, and a condenser connect in series to form a refrigerant circuit. The circuit can provide additional sensors such as temperature sensors, pressure sensors, and/or power meters to monitor and to control operation of the circuit.
Fluctuations of pressure and of temperature can be caused by changes of the configuration of a HVAC circuit. In operation, refrigerant circuits are also prone to refrigerant loss. Those changes can impact on pressure and on temperature as well as on nominal flow through a circuit.
A loss of refrigerant from an installation for heating and/or ventilation and/or air-conditioning does not only harm the environment in terms of global warming. A loss of refrigerant can decrease process efficiency (COP).
What's more, a loss of refrigerant can cause additional wear of and/or damage to mechanical components such as compressors of the refrigerant circuit. For example, fluctuations and/or changes in pressure can impact on the boiling point of a refrigerant in a circuit. Ultimately, a refrigerant in liquid form can enter a compressor and cause the compressor to fail. To prevent such failures, the system operates with a safety margin and the refrigerant is typically superheated as it enters the compressor. That said, a superheated refrigerant lowers process efficiency.
The issue is further exacerbated because refrigeration systems leaking refrigerant can incur a risk of personnel injury. Certain refrigerants are known to be explosive especially when mixed with air. Systems leaking refrigerant can also affect a person's respiratory system and can cause suffocation and/or chemical burn.
Various approaches exist to control the flow of a medium regardless of pressure. In mechanical pressure-independent control valves, a pressure regulator comprises a valve that moves as a function of a differential pressure. The dependence of flow on differential pressure is thereby mitigated. Flow through this type of control valve is essentially constant so long as the differential pressure exceeds a threshold. The patent US9784375B2 discloses a pressure-independent control valve.
Pressure independent flow can also be achieved by means of closed-loop control. For example, the utility model CN201093671Y discloses a configuration having a flow sensor of the ultrasonic type, a control valve and a control unit. The control unit reads a signal from the flow sensor and adjusts the valve in accordance with this signal. However, flow sensors such as ultrasonic flow sensors have shortcomings. Ultrasonic flow sensors tend to be unpredictable in the regime between laminar flow and turbulent flow. Also, a concentration of solids or of bubbles above a lower limit is required for a Doppler flowmeter to ensure reliable, accurate operation.
Instead of ultrasonic flow meters, a signal related to flow can also be recorded using a pair of pressure nozzles. For example, the patent application CN1837996A discloses a first pressure nozzle upstream of a butterfly valve and a second pressure nozzle downstream of the butterfly valve. A differential pressure ΔP is recorded using the pair of pressure nozzles and an opening degree of the butterfly valve is adjusted in accordingly. Flow Q through the valve of CN1837996A can be calculated using Bernoulli's equation $Q \propto \sqrt{ΔP}$
This presupposes that Bernoulli's equations is applicable.
A solution harnessing a plurality of sensors to detect refrigerant loss is also known from the European patent EP4006454B1 . A sensor such as a temperature sensor is arranged upstream of or downstream of an expansion valve of the system of EP4006454B1 . Another sensor records a pressure at or near the outlet of the evaporator. The sensors are used to estimate a maximum capacity of the refrigerant circuit. An alarm will be generated whenever a ratio between a current capacity of the system and a maximum capacity of the system exceeds a threshold.
A German patent application DE102004019929A1 was filed by SIEMENS AG on 21 April 2004 . The application was published on 1 December 2005. DE102004019929A1 deals with an air conditioning system having an acoustic sensor coupled to a refrigerant circuit.
The acoustic sensor of DE102004019929A1 records a signal indicative of loss of a carbon dioxide refrigerant from the circuit. The acoustic sensor sends its signal to a signal processing circuit. The signal processing circuit employs a band-pass filter to extract frequencies that indicate leakages from the circuit. The filtered signal is then integrated, rectified, and compared to a threshold. If the experimentally determined threshold is exceeded, a signal indicative of a leakage will be produced.
A European patent application EP2499435A2 was filed by EMERSON RETAIL SERVICES INC on 11 November 2010 . The application was published on 19 September 2012. EP2499435A2 deals with refrigerant leak detection.
According to EP2499435A2 , a receiver is arranged in between the condenser and the evaporator. The receiver provides a refrigerant level indicator such as an ultrasonic sensor that detects a refrigerant level using an ultrasonic beam. The system also provides temperature and pressure sensors associated with a compressor rack. A model is selected based on data gathered from the temperature and pressure sensors and is employed to predict a level of refrigerant. The predicted level of refrigerant is compared to a reading obtained from the refrigerant level indicator. An alarm will be generated as soon as a deviation between the predicted level of refrigerant and the refrigerant level as indicated exceeds a threshold.
The instant disclosure deals with disturbances in a refrigerant circuit. The solution according to the present disclosure is applicable to a wide range of fluids such as perfect liquids, perfect gases, flashing liquids, single-phase fluids, and two-phase fluids.

Summary

The instant disclosure relies on a discharge coefficient c_m to estimate actual mass flow ṁ through at least one valve. Actual mass flow ṁ is estimated as a percentage of maximum achievable mass flow $\hat{\dot{m}}$ . The maximum achievable flow ih is the flow that can be achieved at a given position of the at least one valve.
The discharge coefficient c_m can be estimated and/or determined for various types of fluids such as perfect liquids, perfect gases, flashing liquids, single-phase fluids, and two-phase fluids. To that end, various sensors such as pressure sensors downstream and upstream of the at least one valve can be used. A temperature sensor and/or a vapour quality sensor can also be used to estimate and/or determine discharge coefficient c_m .
A characteristic curve of the at least one valve is then employed to estimate flow at a predetermined position. This characteristic curve describes flow through the at least one valve as a function of its opening degree. For example, a discharge coefficient c_m as estimated or determined at an opening degree of ten percent will lead to different value of flow when the at least one valve is fully open.
In other words, the flow ṁ as indicated by the discharge coefficient c_m is rescaled using the characteristic curve of the at least one valve. The flow ṁ as indicated by the discharge coefficient c_m is rescaled to a predetermined position. The predetermined position can, by way of non-limiting example, be a maximum position of the at least one valve.
The value of flow at the predetermined position can then be compared to an expected value. A difference between the expected value and the flow at the predetermined position can, by way of non-limiting example, be determined. A ratio between the expected value and the flow at the predetermined position can, by way of another non-limiting example, be determined.
It is envisaged that the expected value of flow is a nominal value of flow. It is also envisaged that the expected value of flow is a rated value of flow. The expected value of flow can depend on the type of fluid circulating inside the HVAC circuit.
If the deviation is bigger than a threshold value, the deviation will be considered as an indication of an anomaly and/or of a disturbance. For example, a deviation between the expected value and the flow at the predetermined position of more than ten percent can point to a disturbance. The anomaly and/or the disturbance can, by way of non-limiting example, be a loss of refrigerant or a change of the configuration of a HVAC circuit.

Brief description of the drawings

Various features will become apparent to those skilled in the art from the following detailed description of the disclosed non-limiting embodiments. The drawings that accompany the detailed description can be briefly described as follows:

FIG 1 schematically illustrates of a refrigerant circuit having a compressor, a condenser, a valve, and an evaporator.
FIG 2 schematically illustrates a controller of the valve.
FIG 3 schematically illustrates a controller of the valve and a sensor for vapour quality.
FIG 4 shows a linear valve curve.
FIG 5 shows an equal-percentage valve curve.

Detailed description

FIG 1 shows a refrigerant circuit 1. The refrigerant circuit 1 can, by way of non-limiting example, be a refrigerant circuit of an air-conditioning installation or system. The refrigerant circuit 1 can, by way of another non-limiting example, also be a refrigerant circuit of a HVAC installation or system.
The refrigerant circuit 1 has a condenser 2. The condenser 2 provides an outlet that leads to an inlet of the at least one valve 3. The at least one valve 3 can, by way of non-limiting example, be or comprise at least one expansion valve 3. A conduit can connect the outlet of the condenser 2 to the inlet of the at least one valve 3, thereby enabling fluid communication between the condenser 2 and the at least one valve 3. More specifically, a conduit can connect the outlet of the condenser 2 to the inlet of the at least one expansion valve 3, thereby enabling fluid communication between the condenser 2 and the at least one expansion valve 3.
According to an aspect of the present disclosure, the expansion valve 3 comprises an electronic expansion valve. More specifically, the expansion valve 3 can be an electronic expansion valve.
According to an aspect of the present disclosure, the expansion valve 3 comprises a control valve. More specifically, the expansion valve 3 can be a control valve.
The expansion valve 3 can comprise an electronic expansion valve and a control valve. The expansion valve 3 can still be an electronic expansion valve and a control valve.
Refrigerant leaves the at least one expansion valve 3 via its outlet and flows toward an inlet of the at least one evaporator 4. To that end, another conduit can be provided between the outlet of the at least one expansion valve 3 and the inlet of the at least one evaporator 4.
The at least one evaporator 4 is in fluid communication with at least one compressor 5 via an outlet of the at least one evaporator 4. The at least one evaporator 4 is also in fluid communication with at least one compressor 5 via an inlet of the at least one compressor 5. Yet another conduit can connect the outlet of the at least one evaporator 4 to the inlet of the at least one compressor 5. The refrigerant can thus flow from the at least one evaporator 4 to the at least one compressor 5.
The refrigerant when leaving the at least one compressor 5 via an outlet of the at least one compressor 5 flows toward the condenser 2. To that end, still another conduit connects the outlet of the at least one compressor 5 to an inlet of the at least one condenser 2. That conduit closes the circuit. It affords flow from the condenser 2 through the at least one valve 3 and through the at least one evaporator 4 and back to the condenser 2.
Disturbances such as fluctuations of pressure as described herein can be handled by a controller 6 of the at least one valve 3. Those disturbances can also be handled by a controller 6 of at least one expansion valve 3. The controller 6 advantageously comprises a microcontroller and/or a microprocessor. In an embodiment, the controller 6 is a microcontroller and/or is a microprocessor. The controller 6 preferably comprises a memory such as a non-volatile memory. That is, the controller 6 can comprise a microcontroller and a non-volatile memory. The controller 6 can also comprise a microprocessor and a non-volatile memory. The controller 6 can still be a microcontroller having a non-volatile memory. The controller 6 can also be a microprocessor having a non-volatile memory.
In an embodiment, the controller 6 is separate from the at least one valve 3. The controller 6 can still be separate from at least one expansion valve 3.
In another embodiment, the at least one expansion valve 3 has a housing such as a metallic housing. The controller 6 is secured relative to the housing of the at least one expansion valve 3. In special embodiment, the controller 6 is arranged inside the housing of the at least one expansion valve 3.
In still another embodiment, the controller 6 comprises a local controller such as a controller 6 of the at least one expansion valve 3. The local controller is or comprises an inexpensive, low-power system on a chip microcontroller having integrated wireless connectivity. In a special embodiment, the chip microcontroller has a memory not exceeding one mebibyte. The controller 6 also comprises a remote controller such as a cloud computer. The local controller and the remote controller are in operative communication.
The controller 6 is in operative communication with sensors 7, 8 arranged upstream of and downstream of the at least one valve 3. FIG 2 shows such sensors 7, 8. The sensors 7, 8 record signals indicative of thermodynamic states of the refrigerant at or near the inlet and at or near the outlet. The sensors 7, 8 advantageously are sensors 7, 8 of the refrigerant circuit 1. In a special embodiment, the sensors 7, 8 are sensors 7, 8 of the at least one expansion valve 3.
It is envisaged that the sensor 7 upstream of the at least one valve 3 comprises a pressure sensor. The pressure sensor is configured to sense a pressure of the refrigerant upstream of the at least one valve 3. In a special embodiment, the sensor 7 at or near the inlet of the at least one expansion valve 3 comprises a pressure transducer. In another special embodiment, the sensor 7 at or near the inlet of the at least one expansion valve 3 comprises a pressure nozzle.
It is still envisaged that the sensor 7 upstream of the at least one valve 3 is a pressure sensor. The pressure sensor is configured to sense a pressure of the refrigerant upstream of the at least one valve 3. In a special embodiment, the sensor 7 at or near the inlet of the at least one expansion valve 3 is a pressure transducer. In another special embodiment, the sensor 7 at or near the inlet of the at least one expansion valve 3 is a pressure nozzle.
The sensor 7 upstream of the at least one valve 3 can connect to the controller 6 via a signal line. The signal line can, by way of non-limiting examples, comprise an electric cable or a fibre-optic cable. Fibre-optic cables confer advantages in hazardous and/or explosive environments.
The signal originating from the sensor 7 can be an analog signal and the controller 6 can comprise an analog-to-digital converter. The analog-to-digital converter provides conversion of analog signals from the sensor 7 into (digital) measures. The analog-to-digital converter can be an integral part of the controller 6. To achieve compactness, the analog-to-digital converter and the controller 6 can be arranged on the same system-on-a-chip.
The signal originating from the sensor 7 can be an analog signal and the controller 6 can comprise a sigma-delta converter. The sigma-delta converter provides conversion of analog signals from the sensor 7 into (digital) measures. The sigma-delta converter can be an integral part of the controller 6 To achieve compactness, the sigma-delta converter and the controller 6 can be arranged on the same system-on-a-chip.
It is envisaged that the sensor 8 downstream of the at least one valve 3 comprises a pressure sensor. The pressure sensor is configured to sense a pressure of the refrigerant downstream of the at least one valve 3. In a special embodiment, the sensor 8 at or near the outlet of the at least one expansion valve 3 comprises a pressure transducer. In another special embodiment, the sensor 8 at or near the outlet of the at least one expansion valve 3 comprises a pressure nozzle.
It is still envisaged that the sensor 8 downstream of the at least one valve 3 is a pressure sensor. The pressure sensor is configured to sense a pressure of the refrigerant downstream of the at least one valve 3. In a special embodiment, the sensor 8 at or near the outlet of the at least one expansion valve 3 is a pressure transducer. In another special embodiment, the sensor 8 at or near the outlet of the at least one expansion valve 3 is a pressure nozzle.
The sensor 8 downstream of the at least one valve 3 can connect to the controller 6 via a signal line. The signal line can, by way of non-limiting examples, comprise an electric cable or a fibre-optic cable. Fibre-optic cables confer advantages in hazardous and/or explosive environments.
The signal originating from the sensor 8 can be an analog signal and the controller 6 can comprise an analog-to-digital converter. The analog-to-digital converter provides conversion of analog signals from the sensor 8 into (digital) measures. The analog-to-digital converter can be an integral part of the controller 6. To achieve compactness, the analog-to-digital converter and the controller 6 can be arranged on the same system-on-a-chip.
The signal originating from the sensor 8 can be an analog signal and the controller 6 can comprise a sigma-delta converter. The sigma-delta converter provides conversion of analog signals from the sensor 8 into (digital) measures. The sigma-delta converter can be an integral part of the controller 6 To achieve compactness, the sigma-delta converter and the controller 6 can be arranged on the same system-on-a-chip.
Preferably, the sensors 7, 8 at or near the inlet and at or near the outlet each comprise a pressure sensor. That is, a first sensor 7 of the sensors 7, 8 is configured to sense a pressure of the refrigerant upstream of the at least one valve 3. A second sensor 8 of the sensors 7, 8 is configured to sense a pressure of the refrigerant downstream of the at least one valve 3. In a special embodiment, the first sensor 7 comprises a pressure transducer and the second sensor 8 comprises a pressure transducer. In another special embodiment, the first sensor 7 comprises a pressure nozzle and the second sensor 8 comprises a pressure nozzle.
Ideally, the sensors 7, 8 at or near the inlet and at or near the outlet are pressure sensors. That is, a first sensor 7 of the sensors 7, 8 is configured to sense a pressure of the refrigerant upstream of the at least one valve 3. A second sensor 8 of the sensors 7, 8 is configured to sense a pressure of the refrigerant downstream of the at least one valve 3. In a special embodiment, the first sensor 7 is a pressure transducer and the second sensor 8 is a pressure transducer. In another special embodiment, the first sensor 7 is a pressure nozzle and the second sensor 8 is a pressure nozzle.
The at least one valve 3 comprises a constriction such as an adjustable orifice. More specifically, the at least one expansion valve 3 can comprise a constriction such as an adjustable orifice. A discharge coefficient c_m relates actual mass flow ṁ through the constriction to maximum achievable mass flow $\hat{\dot{m}}$ : $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}}$
If the fluid entering the at least one valve 3 is a perfect liquid, the discharge coefficient c_m will depend on a back pressure ratio r_b: $c_{m} = \sqrt{1 - r_{b}}$
The back pressure ratio r_b is defined as: $r_{b} = \frac{p_{d}}{p_{u}}$ where p_d denotes the pressure sensed by sensor 8 and p_u denotes the pressure sensed by sensor 7.
In other words, a sensor 7 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a sensor 8 at or near the outlet of the at least one valve 3 communicatively connects to the controller 6. The controller 6 is configured to:

read a first signal from the sensor 7 at or near the inlet of the at least one valve 3;
read a second signal from the sensor 8 at or near the outlet of the at least one valve 3;
process the first signal to determine an upstream pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the second signal to determine a downstream pressure p_d of the refrigerant at or near the outlet of the at least one valve 3;
determine a back pressure ratio r_b based on the upstream pressure p_u and based on the downstream pressure p_d ; and
determine a discharge coefficient c_m based on the back pressure ratio r_b.

In a special embodiment, the discharge coefficient c_m is determined exclusively based on the back pressure ratio r_b. That is, the discharge coefficient c_m exclusively depends on the back pressure ratio r_b.
More specifically, the controller 6 can be configured to:

read a first signal from the sensor 7 at or near the inlet of the at least one valve 3;
read a second signal from the sensor 8 at or near the outlet of the at least one valve 3;
process the first signal to determine an upstream pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the second signal to determine a downstream pressure p_d of the refrigerant at or near the outlet of the at least one valve 3;
calculate a back pressure ratio r_b as a ratio between the downstream pressure p_d and the upstream pressure p_u ; and
calculate a discharge coefficient c_m as a function of the back pressure ratio r_b.

In a special embodiment, the discharge coefficient c_m is calculated exclusively as a function of the back pressure ratio r_b. That is, the discharge coefficient c_m exclusively depends on the pressure ratio r_b.
It is envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one control valve.
If the fluid entering the at least one expansion valve 3 is a perfect gas, an isentropic expansion coefficient k needs to be factored in. The isentropic expansion coefficient k relates the pressure and the volume under isentropic conditions: $p \cdot V^{k} = const .$
The isentropic expansion coefficient k is a property of the gas and depends on pressure and on temperature. For example, the isentropic expansion coefficient k of ammonia (NH₃) at a temperature of 293 Kelvin and at a pressure of 1013 hPa is k = 1.32. The isentropic expansion coefficient k of ammonia (NH₃) at a temperature of 723 Kelvin and at a pressure of 1013 hPa is k = 1.20.
In other words, an additional sensor 9 will be required to sense temperature at or near the inlet of the at least one valve 3. More specifically, an additional sensor 9 can be required to sense temperature at or near the inlet of the at least one expansion valve 3.
The controller 6 is in operative communication with the additional sensor 9 arranged at or near the inlet of the at least one valve 3. More specifically, the controller 6 can be in operative communication with the additional sensor 9 arranged at or near the inlet of the at least one expansion valve 3. FIG 2 shows the additional sensor 9. The sensor 9 functions to record signals indicative of a thermodynamic state of the refrigerant at or near the inlet. The sensor 9 advantageously is a sensor 9 of the refrigerant circuit 1. In a special embodiment, the sensor 9 is a sensor 9 of the at least one expansion valve 3.
It is envisaged that the sensor 9 upstream of the at least one valve 3 comprises a temperature sensor. The temperature sensor is configured to sense a temperature of the refrigerant upstream of the at least one valve 3. In a special embodiment, the sensor 9 at or near the inlet of the at least one expansion valve 3 comprises a temperature transducer. In another special embodiment, the sensor 9 at or near the inlet of the at least one expansion valve 3 comprises a temperature nozzle.
It is still envisaged that the sensor 9 upstream of the at least one valve 3 is a temperature sensor. The temperature sensor is configured to sense a temperature of the refrigerant upstream of the at least one valve 3. In a special embodiment, the sensor 9 at or near the inlet of the at least one expansion valve 3 is a temperature transducer. In another special embodiment, the sensor 9 at or near the inlet of the at least one expansion valve 3 is a temperature nozzle.
The sensor 9 at or near the inlet of the at least one expansion valve 3 can connect to the controller 6 via a signal line. The signal line can, by way of non-limiting examples, comprise an electric cable or a fibre-optic cable. Fibre-optic cables confer advantages in hazardous and/or explosive environments.
The signal originating from the sensor 9 can be an analog signal and the controller 6 can comprise an analog-to-digital converter. The analog-to-digital converter provides conversion of analog signals from the sensor 9 into (digital) measures. The analog-to-digital converter can be an integral part of the controller 6. To achieve compactness, the analog-to-digital converter and the controller 6 can be arranged on the same system-on-a-chip.
The signal originating from the sensor 9 can be an analog signal and the controller 6 can comprise a sigma-delta converter. The sigma-delta converter provides conversion of analog signals from the sensor 9 into (digital) measures. The sigma-delta converter can be an integral part of the controller 6 To achieve compactness, the sigma-delta converter and the controller 6 can be arranged on the same system-on-a-chip.
According to a special aspect, the pressure sensor 7 and the temperature sensor 9 at or near the inlet are arranged in a combined sensor. That is, a combined sensor records signals indicative of pressure and signals indicative of temperature. The combined sensor can comprise a combined nozzle recording signals indicative of pressure and signals indicative of temperature. More specifically, the combined sensor can be a combined nozzle recording signals indicative of pressure and signals indicative of temperature. The combined sensor can also comprise a combined transducer recording signals indicative of pressure and signals indicative of temperature. More specifically, the combined sensor can be a combined transducer recording signals indicative of pressure and signals indicative of temperature.
The isentropic expansion coefficient k is factored into the discharge coefficient c_m as follows: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = \sqrt{\frac{k}{k - 1} \cdot (r_{a}^{\frac{2}{k}} - r_{a}^{\frac{k + 1}{k}})}$
The isentropic expansion coefficient depends on the degrees of freedom of the gaseous fluid and can approach unity: $k = 1$ and the discharge coefficient c_m reads: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = r_{a} \sqrt{\ln (\frac{1}{r_{a}})}$
The above relationships for the discharge coefficient c_m involve an application pressure ratio r_a . The application pressure ratio r_a is a maximum value selected from

a back pressure ratio r_b,
a critical pressure ratio r_c .

In other words, the controller 6 is configured to:

determine a back pressure ratio r_b ;
determine a critical pressure ratio r_c ;
compare the back pressure ratio r_b and the critical pressure ratio r_c to one another; and
determine an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c .

The application pressure ratio r_a is preferably determined as follows: $r_{a} = \max (r_{b}, r_{c})$
More specifically, the controller 6 can be configured to:

calculate a back pressure ratio r_b ;
calculate a critical pressure ratio r_c ;
compare the back pressure ratio r_b and the critical pressure ratio r_c to one another; and
calculate an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c .

The application pressure ratio r_a is ideally calculated as follows: $r_{a} = \max (r_{b}, r_{c})$
The back pressure ratio r_b relates the pressure p_u sensed by the sensor 8 to the pressure p_d sensed by the sensor 7: $r_{b} = \frac{p_{d}}{p_{u}}$
In other words, a sensor 7 at or near the inlet of the at least one valve 3 connects to the controller 6 and a sensor 8 at or near the outlet of the at least one valve 3 communicatively connects to the controller 6. The controller 6 is configured to:

read a first signal from the sensor 7 at or near the inlet of the at least one valve 3;
read a second signal from the sensor 8 at or near the outlet of the at least one valve 3;
process the first signal to determine an upstream pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the second signal to determine a downstream pressure p_d of the refrigerant at or near the outlet of the at least one valve 3; and
determine a back pressure ratio r_b based on the upstream pressure p_u and based on the downstream pressure p_d.

More specifically, the controller 6 can be configured to:

read a first signal from the sensor 7 at or near the inlet of the at least one valve 3;
read a second signal from the sensor 8 at or near the outlet of the at least one valve 3;
process the first signal to determine an upstream pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the second signal to determine a downstream pressure p_d of the refrigerant at or near the outlet of the at least one valve 3; and
calculate a back pressure ratio r_b as a ratio between the downstream pressure p_d and the upstream pressure p_u .

It is envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one control valve.
When the isentropic expansion coefficient k is different from unity $k \neq 1$ the critical pressure ratio r_c reads $r_{c} = {(\frac{2}{k + 1})}^{\frac{k}{k - 1}}$
When the isentropic expansion coefficient k equals unity $k = 1$ the critical pressure ratio r_c reads $r_{c} = \frac{1}{\sqrt{e}}$
The controller 6 preferably comprises a human-machine interface such that a user or an operator can choose a (gaseous) refrigerant. A human-machine interface according to this disclosure preferably comprises a display with a suitable resolution. Suitable resolutions include, but are not limited to 426 x 320 pixels, 470 x 320 pixels, 640 x 480 pixels, 960 x 720 pixels. In a preferred embodiment, the human-machine interface of this disclosure comprises a monochrome display or a colour display. The display can be a liquid-crystal display. The display can also comprise organic light-emitting diodes. The human-machine interface also provides input devices such as, by way of non-limiting examples, keyboards, buttons, touchscreens, capacitive touchscreens, voice recognition, track points etc. The human-machine interface further provides a memory such that physical layer data can be stored in the memory.
The controller 6 selects a (gaseous) refrigerant in response to the user's or the operator's choice. The controller 6 advantageously comprises a memory such as a non-volatile memory storing values of the isentropic expansion coefficient k at various pressures and temperatures. Ideally, one or more lookup tables with values of the isentropic expansion coefficient k at various pressures and at various temperatures are stored in the memory. The controller 6 can store a plurality of lookup tables for a plurality of gaseous refrigerants, wherein each lookup table applies to a particular gaseous refrigerant.
The controller 6 thus loads a lookup table that is applicable to the selected (gaseous) refrigerant from the memory. The controller 6 processes one or more signals from the pressure sensor 7 to obtain a pressure p_u of the refrigerant. The controller 6 also processes one or more signals from the temperature sensor 9 to obtain a temperature t_u of the refrigerant. The controller 6 uses the pressure p_u and the temperature t_u to look up a value of the isentropic expansion coefficient k of the selected gaseous refrigerant.
If the fluid entering the at least one valve 3 is a flashing liquid, a subcooled or a saturated liquid will enter the at least one valve 3. More specifically, a subcooled or a saturated liquid can enter a constriction inside the at least one valve 3. Also, a subcooled or a saturated liquid will enter the at least one expansion valve 3 in consequence of the fluid entering the at least one expansion valve 3 being a flashing liquid. A subcooled or a saturated liquid can then enter a constriction inside the at least one expansion valve 3.
A back pressure ratio r_b relates the pressure p_d sensed by the sensor 8 to the pressure p_u sensed by the sensor 7: $r_{b} = \frac{p_{d}}{p_{u}}$
In other words, a sensor 7 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a sensor 8 at or near the outlet of the at least one valve 3 communicatively connects to the controller 6. The controller 6 is configured to:

More specifically, the controller 6 can be configured to:

It is envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one control valve.
The subcooled or the saturated liquid has a saturation pressure p_s . Where the liquid is a subcooled liquid, the saturation pressure p_s will be less than the inlet pressure p_u . Where the liquid is saturated liquid, the saturation pressure p_s will equal the inlet pressure p_u .
The saturation pressure p_s can be determined from the temperature of the refrigerant at or near the inlet of the at least one expansion valve 3.
In other words, an additional sensor 9 will be required to sense temperature at or near the inlet of the at least one expansion valve 3. FIG 2 shows an additional temperature sensor 9 at or near the inlet of the at least one expansion valve 3. The additional temperature sensor 9 is preferably placed at the inlet of the at least one valve 3. The additional temperature sensor 9 is ideally placed at the inlet of the at least one expansion valve 3.
The temperature sensor 9 communicatively connects to the controller 6 such that the controller 6 is configured to:

read a signal from the sensor 9;
process the signal to determine a temperature t_u of the refrigerant at or near the inlet of the at least one valve 3.

The controller 6 advantageously comprises a memory storing a relationship between a temperature of the refrigerant and a saturation pressure p_s of the refrigerant and is configured to:

load the relationship from the memory; and
use the relationship and the temperature t_u of the refrigerant at or near the inlet of the at least one valve 3 to determine a saturation pressure p_s of the refrigerant at or near the inlet of the at least one valve 3.

In a special embodiment, controller 6 comprises a memory storing a relationship between a temperature of the refrigerant and a saturation pressure p_s of the refrigerant and is configured to:

load the relationship from the memory; and
use the relationship and the temperature t_u of the refrigerant at or near the inlet of the at least one valve 3 to calculate a saturation pressure p_s of the refrigerant at or near the inlet of the at least one valve 3.

It is envisaged that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the least one valve 3 comprises at least one control valve.
The aforementioned relationships are properties of the refrigerant. According to an aspect of the present disclosure, the controller 6 comprises a memory storing a plurality of relationships, wherein each relationship corresponds to a particular refrigerant. The controller 6 is thus configured to:

select a refrigerant as a function of a user's or of an operator's choice;
load a relationship of the plurality of relationships from the memory such that the loaded relationship corresponds to the selected refrigerant; and
use the loaded relationship and the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 to determine a saturation pressure p_s of the refrigerant at or near the inlet of the at least one expansion valve 3.

More specifically, the controller 6 can be configured to:

select a refrigerant as a function of a user's or of an operator's choice;
load a relationship of the plurality of relationships from the memory such that the loaded relationship corresponds to the selected refrigerant; and
use the loaded relationship and the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 to calculate a saturation pressure p_s of the refrigerant at or near the inlet of the at least one expansion valve 3.

A user's or an operator's choice of a refrigerant can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6.
The aforementioned relationships can comprise one or more formulas relating the temperature t_u of the refrigerant and the saturation pressure p_s of the refrigerant. More specifically, the aforementioned relationships can be one or more formulas relating the temperature t_u of the refrigerant and the saturation pressure p_s of the refrigerant. The aforementioned relationships can also comprise a plurality of points, wherein each point is defined by a temperature t_u of the refrigerant and by a saturation pressure p_s of the refrigerant. The saturation pressure p_s corresponding to the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 can then be determined by interpolating between the points. More specifically, the saturation pressure p_s corresponding to the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 can be calculated by interpolating between the points. It is still envisaged that the determination of the saturation pressure p_s involves a relationship comprising one or more formulas and a plurality of points, wherein each point is defined by a temperature t_u of the refrigerant and by a saturation pressure p_s of the refrigerant. It is yet further envisaged that the calculation of the saturation pressure p_s involves a relationship comprising one or more formulas and a plurality of points, wherein each point is defined by a temperature t_u of the refrigerant and by a saturation pressure p_s of the refrigerant.
When the saturation pressure p_s of the refrigerant at or near the inlet is known, a saturation pressure ratio r_s can be determined: $r_{s} = \frac{p_{s}}{p_{u}}$
More specifically, the saturation pressure ratio r_s can be calculated: $r_{s} = \frac{p_{s}}{p_{u}}$
Also, a liquid critical pressure ratio factor F_F can be determined: $F_{F} = 0.96 - 0.28 \cdot \sqrt{\frac{p_{s}}{p_{crit}}}$
More specifically, the liquid critical pressure ratio factor F_F can be calculated: $F_{F} = 0.96 - 0.28 \cdot \sqrt{\frac{p_{s}}{p_{crit}}}$
The liquid critical pressure ratio factor F_F depends on a (thermodynamic) critical pressure p _crit.
The (thermodynamic) critical pressure p _crit is a property of the refrigerant. According to an aspect of the present disclosure, the controller 6 comprises a memory storing a plurality of (thermodynamic) critical pressures p _crit, wherein each (thermodynamic) critical pressures p _crit corresponds to a particular refrigerant. The controller 6 is thus configured to:

select a refrigerant as a function of a user's or of an operator's choice;
load a (thermodynamic) critical pressure p _crit of the plurality of (thermodynamic) critical pressures p _crit from the memory such that the loaded (thermodynamic) critical pressure p _crit corresponds to the selected refrigerant; and
use the loaded (thermodynamic) critical pressure p _crit and the saturation pressure p_s to determine a liquid critical pressure ratio factor F_F .

More specifically, the controller 6 can be configured to:

select a refrigerant as a function of a user's or of an operator's choice;
load a (thermodynamic) critical pressure p _crit of the plurality of (thermodynamic) critical pressures p _crit from the memory such that the loaded (thermodynamic) critical pressure p _crit corresponds to the selected refrigerant; and
use the loaded (thermodynamic) critical pressure p _crit and the saturation pressure p_s to calculate a liquid critical pressure ratio factor F_F .

A user's or an operator's choice of a refrigerant can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6.
When the saturation pressure ratio r_s and the liquid critical pressure ratio factor F_F are known, a critical pressure ratio r_c can be determined: $r_{c} = 1 - F_{L}^{2} \cdot (1 - F_{F} \cdot r_{s})$
More specifically, a critical pressure ratio r_c can be calculated: $r_{c} = 1 - F_{L}^{2} \cdot (1 - F_{F} \cdot r_{s})$
The critical pressure ratio r_c depends on a liquid pressure recovery factor F_L . The liquid pressure recovery factor F_L is specific to the at least one valve 3. In a special embodiment, the liquid pressure recovery factor F_L is specific to the at least one expansion valve 3. The liquid pressure recovery factor F_L can also be specific to the at least one electronic expansion valve 3. The liquid pressure recovery factor F_L can still be specific to the at least one control valve 3.
The liquid pressure recovery factor F_L is generally less than or equal to unity: $F_{L} \leq 1$
According to an aspect of the present disclosure, the controller 6 comprises a memory storing a liquid pressure recovery factor F_L . The controller 6 is thus configured to:

load the liquid pressure recovery factor F_L from the memory; and
use the liquid pressure recovery factor F_L and the liquid critical pressure ratio factor F_F and the saturation pressure ratio r_s to determine a critical pressure ratio r_c .

More specifically, the controller 6 can be configured to:

load the liquid pressure recovery factor F_L from the memory; and
use the liquid pressure recovery factor F_L and the liquid critical pressure ratio factor F_F and the saturation pressure ratio r_s to calculate a critical pressure ratio r_c .

A user and/or an operator can, by way of non-limiting example, use the human-machine interface of the controller 6 to enter the liquid pressure recovery factor F_L of the at least one expansion valve 3. The controller 6 can thereafter store the entered liquid pressure recovery factor F_L in the memory. According to this aspect of the present disclosure, the controller 6 comprises an input device for receiving a signal indicative of a liquid pressure recovery factor F_L . The controller 6 is thus configured to:

receive a signal indicative of the liquid pressure recovery factor F_L from the input device;
process the signal received from the input device to determine the liquid pressure recovery factor F_L ;
use the determined liquid critical pressure ratio factor F_F and the determined liquid pressure recovery factor F_L and the determined saturation pressure ratio r_s to determine a critical pressure ratio r_c .

More specifically, the controller 6 can be configured to:

receive a signal indicative of the liquid pressure recovery factor F_L from the input device;
process the signal received from the input device to determine the liquid pressure recovery factor F_L ;
use the calculated liquid critical pressure ratio factor F_F and the determined liquid pressure recovery factor F_L and the calculated saturation pressure ratio r_s to calculate a critical pressure ratio r_c .

The signal indicative of the liquid pressure recovery factor F_L can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6. That is, the input device is part of the human-machine interface. Also, the controller 6 can comprise an interface. The interface receives the signal indicative of the liquid pressure recovery factor F_L . The signal is processed by the interface and then transmitted to the controller 6. In a special embodiment, the signal indicative of the liquid pressure recovery factor F_L can be transmitted to an arithmetic logic unit of the controller 6.
According to still another aspect of the present disclosure, the controller 6 comprises a memory storing a plurality liquid pressure recovery factors F_L , wherein each liquid pressure recovery factors F_L corresponds to a type of valve. The controller 6 is thus configured to:

select a type of a valve as a function of a user's or of an operator's choice;
load a liquid pressure recovery factor F_L of the plurality of liquid pressure recovery factors F_L from the memory such that the loaded liquid pressure recovery factor F_L corresponds to the selected type; and
use the determined liquid critical pressure ratio factor F_F and the loaded liquid pressure recovery factor F_L and the determined saturation pressure ratio r_s to determine a critical pressure ratio r_c .

More specifically, the controller 6 can be configured to:

select a type of a valve as a function of a user's or of an operator's choice;
load a liquid pressure recovery factor F_L of the plurality of liquid pressure recovery factors F_L from the memory such that the loaded liquid pressure recovery factor F_L corresponds to the selected type; and
use the calculated liquid critical pressure ratio factor F_F and the loaded liquid pressure recovery factor F_L and the calculated saturation pressure ratio r_s to calculate a critical pressure ratio r_c .

A user's or an operator's choice of a type of valve can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6.
The application pressure ratio r_a is then a maximum value selected from

the back pressure ratio r_b,
the critical pressure ratio r_c ,

In other words, the controller 6 is configured to:

determine the back pressure ratio r_b ;
determine the critical pressure ratio r_c ;
compare the back pressure ratio r_b and the critical pressure ratio r_c to one another; and
determine an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c .

calculate the back pressure ratio r_b ;
calculate the critical pressure ratio r_c ;
compare the back pressure ratio r_b and the critical pressure ratio r_c to one another; and
calculate an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c .

The pressure ratio r is ideally calculated as follows: $r_{a} = \max (r_{b}, r_{c})$
The discharge coefficient c_m relating actual mass flow ṁ through the constriction to maximum achievable mass flow $\hat{\dot{m}}$ can then be determined: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = \sqrt{1 - r_{a}}$
More specifically, the discharge coefficient c_m relating actual mass flow ṁ through the constriction to maximum achievable mass flow $\hat{\dot{m}}$ can be calculated: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = \sqrt{1 - r_{a}}$
If the fluid entering the at least one valve 3 is a single-phase fluid, the fluid will be in its liquid or in its gaseous phase or in a transcritical state. If the fluid entering the at least one expansion valve 3 is a single-phase fluid, the fluid will also be either in its liquid or in its gaseous phase.
A back pressure ratio r_b relates the pressure p_d sensed by the sensor 8 to the pressure p_u sensed by the sensor 7: $r_{b} = \frac{p_{d}}{p_{u}}$
In other words, a sensor 7 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a sensor 8 at or near the outlet of the at least one valve 3 communicatively connects to the controller 6. The controller 6 is configured to:

More specifically, the controller 6 can be configured to:

It is envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one control valve.
It can also be necessary to determine a saturation pressure p_s . The saturation pressure p_s can be determined from the temperature of the refrigerant at or near the inlet of the at least one valve 3. In a special embodiment, the saturation pressure p_s is determined from the temperature of the refrigerant at or near the inlet of the at least one expansion valve 3.
In other words, an additional sensor 9 will be required to sense temperature at or near the inlet of the at least one expansion valve 3. FIG 2 shows an additional temperature sensor 9 at or near the inlet of the at least one expansion valve 3. The additional temperature sensor 9 is preferably placed at the inlet of the at least one valve 3. The additional temperature sensor 9 is ideally placed at the inlet of the at least one expansion valve 3.
The temperature sensor 9 communicatively connects to the controller 6 such that the controller 6 is configured to:

read a signal from the sensor 9;
process the signal to determine a temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3.

The controller 6 advantageously comprises a memory storing a relationship between a temperature t_u of the refrigerant and a saturation pressure p_s of the refrigerant and is configured to:

load the relationship from the memory; and
use the relationship and the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 to determine a saturation pressure p_s of the refrigerant at or near the inlet of the at least one expansion valve 3.

In a special embodiment, controller 6 comprises a memory storing a relationship between a temperature t_u of the refrigerant and a saturation pressure p_s of the refrigerant and is configured to:

load the relationship from the memory; and
use the relationship and the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 to calculate a saturation pressure p_s of the refrigerant at or near the inlet of the at least one expansion valve 3.

The aforementioned relationships are properties of the refrigerant. According to an aspect of the present disclosure, the controller 6 comprises a memory storing a plurality of relationships, wherein each relationship corresponds to a particular refrigerant. The controller 6 is thus configured to:

More specifically, the controller 6 can be configured to:

A user's or an operator's choice of a refrigerant can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6.
The aforementioned relationships can comprise one or more formulas relating the temperature t_u of the refrigerant and the saturation pressure p_s of the refrigerant. More specifically, the aforementioned relationships can be one or more formulas relating the temperature t_u of the refrigerant and the saturation pressure p_s of the refrigerant. The aforementioned relationships can also comprise a plurality of points, wherein each point is defined by a temperature t_u of the refrigerant and by a saturation pressure p_s of the refrigerant. The saturation pressure p_s corresponding to the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 can then be determined by interpolating between the points. More specifically, the saturation pressure p_s corresponding to the temperature t_u of the refrigerant at or near the inlet of the at least one expansion valve 3 can be calculated by interpolating between the points. It is still envisaged that the determination of the saturation pressure p_s involves a relationship comprising one or more formulas and a plurality of points, wherein each point is defined by a temperature t_u of the refrigerant and by a saturation pressure p_s of the refrigerant. It is yet further envisaged that the calculation of the saturation pressure p_s involves a relationship comprising one or more formulas and a plurality of points, wherein each point is defined by a temperature t_u of the refrigerant and by a saturation pressure p_s of the refrigerant.
When the saturation pressure p_s of the refrigerant at or near the inlet is known, a saturation pressure ratio r_s can be determined: $r_{s} = \frac{p_{s}}{p_{u}}$
More specifically, the saturation pressure ratio r_s can be calculated: $r_{s} = \frac{p_{s}}{p_{u}}$
Also, a liquid critical pressure ratio factor F_F can be determined: $F_{F} = 0 .96 - 0.28 \cdot \sqrt{\frac{p_{s}}{p_{crit}}}$
More specifically, the liquid critical pressure ratio factor F_F can be calculated: $F_{F} = 0.96 - 0.28 \cdot \sqrt{\frac{p_{s}}{p_{crit}}}$
The liquid critical pressure ratio factor F_F depends on a (thermodynamic) critical pressure p _crit.
The (thermodynamic) critical pressure p _crit is a property of the refrigerant. According to an aspect of the present disclosure, the controller 6 comprises a memory storing a plurality of (thermodynamic) critical pressures p _crit, wherein each (thermodynamic) critical pressures p _crit corresponds to a particular refrigerant. The controller 6 is thus configured to:

select a refrigerant as a function of a user's or of an operator's choice;
load a (thermodynamic) critical pressure p _crit of the plurality of (thermodynamic) critical pressures p _crit from the memory such that the loaded (thermodynamic) critical pressure p _crit corresponds to the selected refrigerant; and
use the loaded (thermodynamic) critical pressure p _crit and the determined saturation pressure p_s to determine a liquid critical pressure ratio factor F_F .

More specifically, the controller 6 can be configured to:

select a refrigerant as a function of a user's or of an operator's choice;
load a (thermodynamic) critical pressure p _crit of the plurality of (thermodynamic) critical pressures p _crit from the memory such that the loaded (thermodynamic) critical pressure p _crit corresponds to the selected refrigerant; and
use the loaded (thermodynamic) critical pressure p _crit and the calculated saturation pressure p_s to calculate a liquid critical pressure ratio factor F_F .

A user's or an operator's choice of a refrigerant can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6.
In addition to the liquid critical pressure ratio factor F_F , a liquid pressure recovery factor F_L is needed to arrive at a liquid critical pressure ratio r_cl . The liquid pressure recovery factor F_L is specific to the at least one valve 3. In a special embodiment, the liquid pressure recovery factor F_L is specific to the at least one expansion valve 3. The liquid pressure recovery factor F_L can also be specific to the at least one electronic expansion valve 3. The liquid pressure recovery factor F_L can still be specific to the at least one control valve 3.
The liquid pressure recovery factor F_L is generally less than or equal to unity: $F_{L} \leq 1$
According to an aspect of the present disclosure, the controller 6 comprises a memory storing a plurality liquid pressure recovery factors F_L , wherein each liquid pressure recovery factors F_L corresponds to a type of valve. The controller 6 is thus configured to:

select a type of a valve as a function of a user's or of an operator's choice;
load a liquid pressure recovery factor F_L of the plurality of liquid pressure recovery factors F_L from the memory such that the loaded liquid pressure recovery factor F_L corresponds to the selected type of valve; and
use the determined liquid critical pressure ratio factor F_F and the loaded liquid pressure recovery factor F_L and the determined saturation pressure ratio r_s to determine a liquid critical pressure ratio r_cl .

Preferably, the liquid critical pressure ratio r_cl is determined as follows: $r_{c 1} = 1 - F_{L}^{2} \cdot (1 - F_{F} \cdot r_{s})$
More specifically, the controller 6 can be configured to:

select a type of a valve as a function of a user's or of an operator's choice;
load a liquid pressure recovery factor F_L of the plurality of liquid pressure recovery factors F_L from the memory such that the loaded liquid pressure recovery factor F_L corresponds to the selected type of valve; and
use the calculated liquid critical pressure ratio factor F_F and the loaded liquid pressure recovery factor F_L and the calculated saturation pressure ratio r_s to calculate a liquid critical pressure ratio r_cl .

Ideally, the liquid critical pressure ratio r_cl is calculated as follows: $r_{cl} = 1 - F_{L}^{2} \cdot (1 - F_{F} \cdot r_{s})$
A user's or an operator's choice of a type of valve can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6.
According to another aspect of the present disclosure, the controller 6 comprises an input device for receiving a signal indicative of a liquid pressure recovery factor F_L . The controller 6 is thus configured to:

receive a signal indicative of the liquid pressure recovery factor F_L from the input device;
process the signal received from the input device to determine the liquid pressure recovery factor F_L ;
use the determined liquid critical pressure ratio factor F_F and the determined liquid pressure recovery factor F_L and the determined saturation pressure ratio r_s to determine a liquid critical pressure ratio r_cl .

Preferably, the liquid critical pressure ratio r_cl is determined as follows: $r_{cl} = 1 - F_{L}^{2} \cdot (1 - F_{F} \cdot r_{s})$
More specifically, the controller 6 can be configured to:

receive a signal indicative of the liquid pressure recovery factor F_L from the input device;
process the signal received from the input device to determine the liquid pressure recovery factor F_L ;
use the calculated liquid critical pressure ratio factor F_F and the determined liquid pressure recovery factor F_L and the calculated saturation pressure ratio r_s to calculate a liquid critical pressure ratio r_cl .

Ideally, the liquid critical pressure ratio r_cl is calculated as follows: $r_{cl} = 1 - F_{L}^{2} \cdot (1 - F_{F} \cdot r_{s})$
The signal indicative of the liquid pressure recovery factor F_L can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6. That is, the input device is part of the human-machine interface. Also, the controller 6 can comprise a communication interface. The communication interface receives the signal indicative of the liquid pressure recovery factor F_L . The signal is processed by the communication interface and then transmitted to the controller 6. In a special embodiment, the signal indicative of the liquid pressure recovery factor F_L can be transmitted to an arithmetic logic unit of the controller 6.
A gaseous critical pressure ratio r_cg depends on an isentropic expansion coefficient k. The isentropic expansion coefficient k relates the pressure and the volume under isentropic conditions: $p \cdot V^{k} = const .$
The isentropic expansion coefficient k is a property of the gas and depends on pressure and on temperature. For example, the isentropic expansion coefficient k of ammonia (NH₃) at a temperature of 293 Kelvin and at a pressure of 1013 hPa is k = 1.32. The isentropic expansion coefficient k of ammonia (NH₃) at a temperature of 723 Kelvin and at a pressure of 1013 hPa is k = 1.20. The isentropic expansion coefficient k of carbon dioxide (CO₂) at a temperature of 307 Kelvin and at a pressure of 10 MPa is k = 7.7. The isentropic expansion coefficient k of carbon dioxide (CO₂) at a temperature of 312 Kelvin and at a pressure of 10 MPa is k = 4.6. The isentropic expansion coefficient k of carbon dioxide (CO₂) at a temperature of 322 Kelvin and at a pressure of 10 MPa is k = 1.8.
When the isentropic expansion coefficient k is different from unity $k \neq 1$ the gaseous critical pressure ratio r_cg reads $r_{cg} = {(\frac{2}{k + 1})}^{\frac{k}{k - 1}}$
When the isentropic expansion coefficient k equals unity $k = 1$ the gaseous critical pressure ratio r_cg reads $r_{cg} = \frac{1}{\sqrt{e}}$
The controller 6 preferably comprises a human-machine interface such that a user or an operator can choose a (gaseous) refrigerant. A human-machine interface according to this disclosure preferably comprises a display with a suitable resolution. Suitable resolutions include, but are not limited to 426 x 320 pixels, 470 x 320 pixels, 640 x 480 pixels, 960 x 720 pixels. In a preferred embodiment, the human-machine interface of this disclosure comprises a monochrome display or a colour display. The display can be a liquid-crystal display. The display can also comprise organic light-emitting diodes. The human-machine interface also provides input devices such as, by way of non-limiting examples, keyboards, buttons, touchscreens, capacitive touchscreens, voice recognition, track points etc. The human-machine interface further provides a memory such that physical layer data can be stored in the memory.
The controller 6 thus selects a (gaseous) refrigerant in response to the user's or the operator's choice. The controller 6 advantageously comprises a memory such as a non-volatile memory storing values of the isentropic expansion coefficient k at various pressures and temperatures. Ideally, one or more lookup tables with values of the isentropic expansion coefficient k at various pressures and at various temperatures are stored in the memory. The controller 6 can store a plurality of lookup tables for a plurality of gaseous refrigerants, wherein each lookup table applies to a particular gaseous refrigerant.
The controller 6 thus loads a lookup table that is applicable to the selected (gaseous) refrigerant from the memory. The controller 6 processes one or more signals from the pressure sensor 7 to obtain a pressure of the refrigerant. The controller 6 also processes one or more signals from the temperature sensor 9 to obtain a temperature of the refrigerant. The controller 6 uses the pressure and the temperature of the refrigerant to look up a value of the isentropic expansion coefficient k of the selected gaseous refrigerant.
The application pressure ratio r_a is a maximum value selected from

the back pressure ratio r_b,
the liquid critical pressure ratio r_cl ,
the gaseous critical pressure ratio r_cg.

In other words, the controller 6 is configured to:

determine the back pressure ratio r_b;
determine the liquid critical pressure ratio r_cl ;
determine the gaseous critical pressure ratio r_cg ;
compare the back pressure ratio r_b and the liquid critical pressure ratio r_cl and the gaseous critical pressure ratio r_cg to one another; and
determine an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the liquid critical pressure ratio r_cl and of the gaseous critical pressure ratio r_cg.

The application pressure ratio r_a is preferably determined as follows: $r_{a} = \max (r_{b}, r_{cl}, r_{cg})$
More specifically, the controller 6 can be configured to:

calculate the back pressure ratio r_b ;
calculate the liquid critical pressure ratio r_cl ;
calculate the gaseous critical pressure ratio r_cg ;
compare the back pressure ratio r_b and the liquid critical pressure ratio r_cl and the gaseous critical pressure ratio r_cg to one another; and
calculate an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the liquid critical pressure ratio r_cl and of the gaseous critical pressure ratio r_cg.

The application pressure ratio r_a is ideally calculated as follows: $r_{a} = \max (r_{b}, r_{cl}, r_{cg})$
The isentropic expansion coefficient k is eventually factored into the discharge coefficient c_m as follows: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = \sqrt{\frac{k}{k - 1} \cdot (r^{\frac{2}{k}} - r^{\frac{k + 1}{k}})}$
The isentropic expansion coefficient depends on the degrees of freedom of the gaseous fluid and can approach unity: $k = 1$ and the discharge coefficient c_m reads: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = r \sqrt{\ln (\frac{1}{r})}$
If the fluid entering the at least one expansion valve 3 is a two-phase fluid, the fluid will comprise a liquid fraction and a gaseous fraction. A back pressure ratio r_b relates the pressure p_d sensed by the sensor 8 to the pressure p_u sensed by the sensor 7: $r_{b} = \frac{p_{d}}{p_{u}}$
A discharge coefficient c_ml is then applicable to the liquid fraction and reads: $c_{ml} = \sqrt{1 - r_{b}}$
In other words, a sensor 7 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a sensor 8 at or near the outlet of the at least one valve 3 communicatively connects to the controller 6. The controller 6 is configured to:

read a first signal from the sensor 7 at or near the inlet of the at least one valve 3;
read a second signal from the sensor 8 at or near the outlet of the at least one valve 3;
process the first signal to determine an upstream pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the second signal to determine a downstream pressure p_d of the refrigerant at or near the outlet of the at least one valve 3;
determine a back pressure ratio r_b based on the upstream pressure p_u and based on the downstream pressure p_d ; and
determine a discharge coefficient c_ml of the liquid fraction based on the back pressure ratio r_b. In a special embodiment, the discharge coefficient c_ml of the liquid fraction is determined exclusively based on the back pressure ratio r_b. That is, the discharge coefficient c_ml of the liquid fraction exclusively depends on the back pressure ratio r_b.

More specifically, the controller 6 can be configured to:

read a first signal from the sensor 7 at or near the inlet of the at least one valve 3;
read a second signal from the sensor 8 at or near the outlet of the at least one valve 3;
process the first signal to determine an upstream pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the second signal to determine a downstream pressure p_d of the refrigerant at or near the outlet of the at least one valve 3;
calculate a back pressure ratio r_b as a ratio between the downstream pressure p_d and the upstream pressure p_u ; and
calculate a discharge coefficient c_ml of the liquid fraction as a function of the back pressure ratio r_b.

In a special embodiment, the discharge coefficient c_ml of the liquid fraction is calculated exclusively as a function of the back pressure ratio r_b. That is, the discharge coefficient c_ml of the liquid fraction exclusively depends on the back pressure ratio r_b.
It is envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the first sensor 7 comprises a first pressure sensor and the second sensor 8 comprises a second pressure sensor and that the least one valve 3 comprises at least one control valve.
A discharge coefficient c_mg is applicable to the gaseous fraction and depends on a gaseous critical pressure ratio r_cg. The gaseous critical pressure ratio r_cg depends on an isentropic expansion coefficient k. The isentropic expansion coefficient k relates the pressure and the volume under isentropic conditions: $p \cdot V^{k} = const .$
The isentropic expansion coefficient k is a property of the gas and depends on pressure and on temperature. For example, the isentropic expansion coefficient k of ammonia (NH₃) at a temperature of 293 Kelvin and at a pressure of 1013 hPa is k = 1.32. The isentropic expansion coefficient k of ammonia (NH₃) at a temperature of 723 Kelvin and at a pressure of 1013 hPa is k = 1.20. The isentropic expansion coefficient k of carbon dioxide (CO₂) at a temperature of 307 Kelvin and at a pressure of 10 MPa is k = 7.7. The isentropic expansion coefficient k of carbon dioxide (CO₂) at a temperature of 312 Kelvin and at a pressure of 10 MPa is k = 4.6. The isentropic expansion coefficient k of carbon dioxide (CO₂) at a temperature of 322 Kelvin and at a pressure of 10 MPa is k = 1.8.
When the isentropic expansion coefficient k is different from unity $k \neq 1$ the gaseous critical pressure ratio r_cg reads $r_{cg} = {(\frac{2}{k + 1})}^{\frac{k}{k - 1}}$
When the isentropic expansion coefficient k equals unity $k = 1$ the gaseous critical pressure ratio r_cg reads $r_{cg} = \frac{1}{\sqrt{e}}$
The controller 6 preferably comprises a human-machine interface such that a user or an operator can choose a (gaseous) refrigerant. A human-machine interface according to this disclosure preferably comprises a display with a suitable resolution. Suitable resolutions include, but are not limited to 426 x 320 pixels, 470 x 320 pixels, 640 x 480 pixels, 960 x 720 pixels. In a preferred embodiment, the human-machine interface of this disclosure comprises a monochrome display or a colour display. The display can be a liquid-crystal display. The display can also comprise organic light-emitting diodes. The human-machine interface also provides input devices such as, by way of non-limiting examples, keyboards, buttons, touchscreens, capacitive touchscreens, voice recognition, track points etc. The human-machine interface further provides a memory such that physical layer data can be stored in the memory.
The controller 6 thus selects a (gaseous) refrigerant in response to the user's or the operator's choice. The controller 6 advantageously comprises a memory such as a non-volatile memory storing values of the isentropic expansion coefficient k at various pressures and temperatures. Ideally, one or more lookup tables with values of the isentropic expansion coefficient k at various pressures and at various temperatures are stored in the memory. The controller 6 can store a plurality of lookup tables for a plurality of gaseous refrigerants, wherein each lookup table applies to a particular gaseous refrigerant.
The controller 6 thus loads a lookup table that is applicable to the selected (gaseous) refrigerant from the memory. The controller 6 processes one or more signals from the pressure sensor 7 to obtain a pressure of the refrigerant. The controller 6 also processes one or more signals from the temperature sensor 9 to obtain a temperature of the refrigerant. The controller 6 uses the pressure and the temperature of the refrigerant to look up a value of the isentropic expansion coefficient k of the selected gaseous refrigerant.
The isentropic expansion coefficient k is factored into the discharge coefficient c_mg of the gaseous fraction as follows: $c_{mg} = \sqrt{\frac{k}{k - 1} \cdot (r_{cg}^{\frac{2}{k}} - r_{cg}^{\frac{k + 1}{k}})}$
The isentropic expansion coefficient depends on the degrees of freedom of the gaseous fluid and can approach unity: $k = 1$
and the discharge coefficient c_mg of the gaseous fraction reads: $c_{mg} = r \sqrt{\ln (\frac{1}{r_{cg}})}$
When the discharge coefficients of the liquid fraction c_ml and of the gaseous fraction c_mg are known, the discharge coefficient c_m can be determined: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = \frac{1}{\sqrt{\frac{1 - q_{u}}{c_{ml}^{2}} \cdot \frac{v_{l}}{v_{u}} + \frac{q_{u}}{c_{mg}^{2}} \cdot \frac{v_{g}}{v_{u}}}}$
In this relationship,

q_u denotes a vapour quality,
v_g denotes a specific volume of the gaseous fraction,
v_l denotes a specific volume of the liquid fraction,
v_u denotes a specific volume at or near the inlet of the at least one valve 3.

It is envisaged that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the least one valve 3 comprises at least one control valve.
In a special embodiment, the discharge coefficient c_m is calculated as follows: $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}} = \frac{1}{\sqrt{\frac{1 - q_{u}}{c_{ml}^{2}} \cdot \frac{v_{l}}{v_{u}} + \frac{q_{u}}{c_{mg}^{2}} \cdot \frac{v_{g}}{v_{u}}}}$
In this relationship,

It is envisaged that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the least one valve 3 comprises at least one control valve.
In other words, an additional sensor 10 will be required to sense vapour quality at or near the inlet of the at least one expansion valve 3.
The controller 6 is in operative communication with the additional sensor 10 arranged at or near the inlet of the at least one expansion valve 3. FIG 3 shows the additional sensor 10. The sensor 10 functions to record signals indicative of a thermodynamic state of the refrigerant at or near the inlet. The sensor 10 advantageously is a sensor 10 of the refrigerant circuit 1. In a special embodiment, the sensor 10 is a sensor 10 of the at least one expansion valve 3.
It is envisaged that the sensor 10 at or near the inlet of the at least one expansion valve 3 comprises a vapour quality sensor. The vapour quality sensor is configured to sense a vapour quality of the refrigerant at nor near the inlet of the at least one expansion valve 3. In a special embodiment, the sensor 10 at or near the inlet of the at least one expansion valve 3 comprises a vapour quality transducer. In another special embodiment, the sensor 10 at or near the inlet of the at least one expansion valve 3 comprises a vapour quality nozzle.
It is still envisaged that the sensor 10 at or near the inlet of the at least one expansion valve 3 is a vapour quality sensor. The vapour quality sensor is configured to sense a vapour quality of the refrigerant at nor near the inlet of the at least one expansion valve 3. In a special embodiment, the sensor 10 at or near the inlet of the at least one expansion valve 3 is a vapour quality transducer. In another special embodiment, the sensor 10 at or near the inlet of the at least one expansion valve 3 is a vapour quality nozzle.
The sensor 10 at or near the inlet of the at least one expansion valve 3 can connect to the controller 6 via a signal line. The signal line can, by way of non-limiting examples, comprise an electric cable or a fibre-optic cable. Fibre-optic cables confer advantages in hazardous and/or explosive environments.
The sensor 10 can also be arranged at or near the outlet of the evaporator 4 and can comprise a vapour quality sensor. The vapour quality sensor is then configured to sense a vapour quality of the refrigerant at nor near the outlet of the evaporator 4. Advantageously, the sensor 10 is arranged at the outlet of the evaporator 4 and is a vapour quality sensor. The vapour quality sensor is then configured to sense a vapour quality of the refrigerant at the outlet of the evaporator 4. In a special embodiment, the sensor 10 at the outlet of the evaporator 4 is a vapour quality transducer. In another special embodiment, the sensor 10 at the outlet of the evaporator 4 is a vapour quality nozzle.
The sensor 10 at or near the outlet of the evaporator 4 can connect to the controller 6 via a signal line. The signal line can, by way of non-limiting examples, comprise an electric cable or a fibre-optic cable. Fibre-optic cables confer advantages in hazardous and/or explosive environments.
The signal originating from the sensor 10 can be an analog signal and the controller 6 can comprise an analog-to-digital converter. The analog-to-digital converter provides conversion of analog signals from the sensor 10 into (digital) measures. The analog-to-digital converter can be an integral part of the controller 6. To achieve compactness, the analog-to-digital converter and the controller 6 can be arranged on the same system-on-a-chip.
The signal originating from the sensor 10 can be an analog signal and the controller 6 can comprise a sigma-delta converter. The sigma-delta converter provides conversion of analog signals from the sensor 10 into (digital) measures. The sigma-delta converter can be an integral part of the controller 6 To achieve compactness, the sigma-delta converter and the controller 6 can be arranged on the same system-on-a-chip.
The specific volumes v_g, v_l, v_u and are determined as functions of the pressure p_u and of the temperature t_u at or near the inlet of the at least one valve 3. In other words, a pressure sensor 7 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a temperature sensor 9 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a vapour quality sensor 10 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6. The controller 6 comprises a memory and is configured to:

read a signal indicative of a pressure from the pressure sensor 7;
read a signal indicative of a temperature from the temperature sensor 9;
read a signal indicative of a vapour quality from the vapour quality sensor 10;
process the signal indicative of the pressure to determine a pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the signal indicative of the temperature to determine a temperature t_u of the refrigerant at or near the inlet of the at least one valve 3;
process the signal indicative of the vapour quality to determine a vapour quality q_u of the refrigerant at or near the inlet of the at least one valve 3;
select a refrigerant as a function of a user's or of an operator's choice;
load a gas fraction relationship between a specific volume v_g of a gaseous fraction of the refrigerant and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant from the memory, wherein the gas fraction relationship corresponds to the selected refrigerant;
use the gas fraction relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant to determine the specific volume v_g of the gaseous fraction of the refrigerant;
load a liquid fraction relationship between a specific volume v_l of a liquid fraction of the refrigerant and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant from the memory, wherein the liquid fraction relationship corresponds to the selected refrigerant;
use the liquid fraction relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant to determine the specific volume v_l of the liquid fraction of the refrigerant;
load an upstream relationship between a specific volume v_u at or near the inlet of the at least one valve 3 and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant from the memory, wherein the upstream relationship corresponds to the selected refrigerant; and
use the upstream relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant to determine the specific volume v_u of the refrigerant at or near the inlet of the at least one valve 3.

According to an aspect of the determinations of v_g, v_l, v_u, the memory of the controller 6 stores

a plurality of gas fraction relationships between the specific volume v_g of the gaseous fraction of the refrigerant and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant, wherein each gas fraction relationship corresponds to a particular refrigerant, and
a plurality of liquid fraction relationships between the specific volume v_l of the liquid fraction of the refrigerant and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant, wherein each liquid fraction relationship corresponds to a particular refrigerant, and
a plurality of upstream relationships between the specific volume v_u at or near the inlet of the at least one valve 3 and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant, wherein each upstream relationship corresponds to a particular refrigerant.

More specifically, the upstream relationship can relate the pressure p_u of the refrigerant and the temperature t_u of the refrigerant and the vapour quality q_u of the refrigerant to a specific volume v_u of the refrigerant at or near the inlet of the at least one valve 3. The controller 6 stores this relationship. The controller 6 uses the upstream relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant and the vapour quality q_u to determine the specific volume v_u at or near the inlet of the at least one valve 3. It is envisaged that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the least one valve 3 comprises at least one control valve.
The specific volumes v_g, v_l, v_u can also be calculated as functions of the pressure and of the temperature at or near the inlet of the at least one valve 3. In other words, a pressure sensor 7 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a temperature sensor 9 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6 and a vapour quality sensor 10 at or near the inlet of the at least one valve 3 communicatively connects to the controller 6. The controller 6 comprises a memory and is configured to:

read a signal indicative of a pressure from the pressure sensor 7;
read a signal indicative of a temperature from the temperature sensor 9;
read a signal indicative of a vapour quality from the vapour quality sensor 10;
process the signal indicative of the pressure to determine a pressure p_u of the refrigerant at or near the inlet of the at least one valve 3;
process the signal indicative of the temperature to determine a temperature t_u of the refrigerant at or near the inlet of the at least one valve 3;
process the signal indicative of the vapour quality to determine a vapour quality q_u of the refrigerant at or near the inlet of the at least one valve 3;
select a refrigerant as a function of a user's or of an operator's choice;
load a gas fraction relationship between a specific volume v_g of a gaseous fraction of the refrigerant and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant from the memory, wherein the gas fraction relationship corresponds to the selected refrigerant;
use the gas fraction relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant to calculate the specific volume v_g of the gaseous fraction of the refrigerant;
load a liquid fraction relationship between a specific volume v_l of a liquid fraction of the refrigerant and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant from the memory, wherein the liquid fraction relationship corresponds to the selected refrigerant;
use the liquid fraction relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant to calculate the specific volume v_l of the liquid fraction of the refrigerant;
load an upstream relationship between a specific volume v_u at or near the inlet of the at least one valve 3 and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant from the memory, wherein the upstream relationship corresponds to the selected refrigerant; and
use the upstream relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant to calculate the specific volume v_u of the refrigerant at or near the inlet of the at least one valve 3.

According to an aspect of the calculations of v_g, v_l, v_u, the memory of the controller 6 stores

More specifically, the upstream relationship can relate the pressure p_u of the refrigerant and the temperature t_u of the refrigerant and the vapour quality q_u of the refrigerant to a specific volume v_u of the refrigerant at or near the inlet of the at least one valve 3. The controller 6 stores this relationship. The controller 6 uses the upstream relationship and the pressure p_u of the refrigerant and the temperature t_u of the refrigerant and the vapour quality q_u to calculate the specific volume v_u at or near the inlet of the at least one valve 3. It is envisaged that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the least one valve 3 comprises at least one control valve.
When the discharge coefficient $c_{m} = \frac{\dot{m}}{\hat{\dot{m}}}$ is known, a ratio between actual mass flow ṁ and maximum mass flow $\hat{\dot{m}}$ is established for a given position of the at least one valve 3. A maximum flow through the at least one valve 3 at its maximum position still needs to be estimated and/or determined and/or calculated. More specifically, a ratio between actual mass flow ṁ and maximum mass flow $\hat{\dot{m}}$ can be established for a given position of the at least one expansion valve 3. A maximum flow through the at least one expansion valve 3 at its maximum position still needs to be established and/or determined and/or calculated.
This is where the valve curve of the at least one valve 3 needs to be factored in. The valve curve of the at least one valve 3 describes a relationship between a position of the at least one valve 3 and flow through the at least one valve 3. For example, a linear valve curve describes a linear relationship between the position and (mass) flow. FIG 4 illustrates a linear relationship 11 between the position 12 and flow 13 through the at least one valve 3. In an embodiment, the linear valve curve 11 is a linear characteristic curve 11. More specifically, the linear valve curve 11 of the at least one valve 3 can be a linear characteristic curve 11 of the at least one valve 3.
Unlike the linear curve, an equal-percentage curve describes an equal-percentage relationship between the position and (mass) flow. That is, the flow through the at least one valve 3 increases exponentially as the at least one valve 3 opens. FIG 5 illustrates an equal-percentage relationship 14 between the position 12 and flow 13 through the at least one valve 3. In an embodiment, the equal-percentage valve curve 14 is an equal-percentage characteristic curve 14. More specifically, the equal-percentage valve curve 14 of the at least one valve 3 can be an equal-percentage characteristic curve 14 of the at least one valve 3.
The valve curve of the at least one expansion valve 3 may also need to be factored in. The valve curve of the at least one expansion valve 3 describes a relationship between a position of the at least one expansion valve 3 and flow through the at least one expansion valve 3. For example, a linear valve curve describes a linear relationship between the position and (mass) flow. FIG 4 also illustrates a linear relationship 11 between the position 12 and flow 13 through the at least one expansion valve 3. More specifically, the linear valve curve 11 of the at least one expansion valve 3 can be a linear characteristic curve 11 of the at least one expansion valve 3.
Unlike the linear curve, an equal-percentage curve describes an equal-percentage relationship between the position and (mass) flow. That is, the flow through the at least one expansion valve 3 increases exponentially as the at least one expansion valve 3 opens. FIG 5 also illustrates an equal-percentage relationship 14 between the position 12 and flow 13 through the at least one expansion valve 3. More specifically, the equal-percentage valve curve 14 of the at least one valve 3 can be an equal-percentage characteristic curve 14 of the at least one expansion valve 3.
The controller 6 thus comprises a memory storing a plurality of valve curves 11, 14, wherein each valve curve 11, 14 corresponds to a type of valve. The controller 6 is configured to:

select a valve curve as a function of a user's or of an operator's choice;
load a valve curve 11, 14 of the plurality of valve curves 11, 14 from the memory such that the loaded valve curve 11, 14 corresponds to the selected curve;
read a signal indicative of a position 12 of the at least one valve 3;
process the signal indicative of the position 12 to determine the position 12 of the at least one valve 3; and
use the determined discharge coefficient c_m and the position 12 of the at least one valve 3 to estimate flow at a predetermined position of the at least one valve 3.

The controller 6 can also be configured to:

select a valve curve as a function of a user's or of an operator's choice;
load a valve curve 11, 14 of the plurality of valve curves 11, 14 from the memory such that the loaded valve curve 11, 14 corresponds to the selected curve;
read a signal indicative of a position 12 of the at least one valve 3;
process the signal indicative of the position 12 to determine the position 12 of the at least one valve 3; and
use the determined discharge coefficient c_m and the position 12 of the at least one valve 3 to determine flow at a predetermined position of the at least one valve 3.

The controller 6 can still be configured to:

select a valve curve as a function of a user's or of an operator's choice;
load a valve curve 11, 14 of the plurality of valve curves 11, 14 from the memory such that the loaded valve curve 11, 14 corresponds to the selected curve;
read a signal indicative of a position 12 of the at least one valve 3;
process the signal indicative of the position 12 to determine the position 12 of the at least one valve 3; and
use the calculated discharge coefficient c_m and the position 12 of the at least one valve 3 to calculate flow at a predetermined position of the at least one valve 3.

A user's or an operator's choice of a type of valve can, by way of non-limiting example, be obtained using the human-machine interface of the controller 6. The predetermined position of the at least one valve 3 preferably is the maximum position of the at least one valve 3. It is envisaged that the least one valve 3 comprises at least one expansion valve. It is still envisaged that the least one valve 3 comprises at least one electronic expansion valve. It is still further envisaged that the least one valve 3 comprises at least one control valve.
As described in detail herein, the present disclosure deals with a method of detecting and/or compensating a disturbance in a refrigerant circuit (1), the refrigerant circuit (1) comprising at least one valve (3) having an inlet port and an outlet port, the refrigerant circuit (1) also comprising a first sensor (7) for recording a signal indicative of a thermodynamic state of a refrigerant at the inlet port of the at least one valve (3), and a second sensor (8) for recording a signal indicative of a thermodynamic state of the refrigerant at the outlet port of the at least one valve (3), the method comprising the steps of:

recording a first signal using the first sensor (7);
recording a second signal using the second sensor (8);
receiving a position signal indicative of a position (12) of the at least one valve (3);
processing the first signal to determine an upstream pressure p_u ;
processing the second signal to determine a downstream pressure pj,
processing the position signal to determine the position (12) of the at least one valve (3);
determining a discharge coefficient c_m based on the upstream pressure p_u and based on the downstream pressure p_d, wherein the discharge coefficient c_m relates actual flow ṁ at the determined position (12) of the at least one valve (3) to maximum flow $\hat{\dot{m}}$ at the determined position (12) of the at least one valve (3);
using a valve curve (11, 14) of the at least one valve (3) and the discharge coefficient c_m and the determined position (12) to estimate a flow through the at least one valve (3) at a predetermined position of the at least one valve (3);
calculating a deviation measure as a function of the estimated flow through the at least one valve (3) at the predetermined position and as a function of a value of expected flow at the predetermined position;
comparing the deviation measure to a threshold value; and
if the deviation measure is greater than the threshold value:
producing a signal indicative of a disturbance in the refrigerant circuit (1).

The present disclosure also deals with any of the aforementioned methods, wherein the first sensor (7) comprises a first pressure sensor and the second sensor (8) comprises a second pressure sensor. The present disclosure still deals with any of the aforementioned methods, wherein the first sensor (7) is a first pressure sensor and the second sensor (8) is a second pressure sensor.
It is envisaged that the discharge coefficient c_m relates actual flow ṁ at the determined position (12) of the at least one valve (3) to maximum flow $\hat{\dot{m}}$ at the determined position (12) of the at least one valve (3). The valve curve (11, 14) of the at least one valve (3) and the discharge coefficient c_m and the determined position (12) can then be used to estimate a mass flow through the at least one valve (3) at a predetermined position. Also, a deviation measure is calculated as a function of the estimated mass flow through the at least one valve (3) at the predetermined position and as a function of a value of expected mass flow at the predetermined position.
According to an aspect of the present disclosure, mass flow means mass flow rate and flow means flow rate.
The present disclosure also pertains to any of the aforementioned methods, the method comprising the step of:
recording a position signal indicative of a position (12) of the at least one valve (3) from the at least one valve (3).
It is envisaged that the at least one valve (3) comprises an adjustable orifice and an actuator, wherein the actuator mechanically couples to the adjustable orifice. The position signal is advantageously received from the actuator of the at least one valve (3). The position signal is ideally recorded from the actuator of the at least one valve (3).
The instant disclosure also pertains to any of the aforementioned methods, the method comprising the steps of:

using a valve curve (11, 14) of the at least one valve (3) and the discharge coefficient c_m and the determined position (12) to determine a flow through the at least one valve (3) at a predetermined position of the at least one valve (3); and
calculating a deviation measure as a function of the determined flow through the at least one valve (3) at the predetermined position and as a function of a value of expected flow at the predetermined position.

The instant disclosure still pertains to any of the aforementioned methods, the method comprising the steps of:

using a valve curve (11, 14) of the at least one valve (3) and the discharge coefficient c_m and the determined position (12) to calculate a flow through the at least one valve (3) at a predetermined position of the at least one valve (3); and
calculating a deviation measure as a function of the calculated flow through the at least one valve (3) at the predetermined position and as a function of a value of expected flow at the predetermined position.

The instant disclosure still further pertains to any of the aforementioned methods, the method comprising the steps of:

using a valve curve (11, 14) of the at least one valve (3) and the discharge coefficient c_m and the determined position (12) to determine a mass flow through the at least one valve (3) at a predetermined position of the at least one valve (3); and
calculating a deviation measure as a function of the determined mass flow through the at least one valve (3) at the predetermined position and as a function of a value of expected mass flow at the predetermined position.

The instant disclosure yet further pertains to any of the aforementioned methods, the method comprising the steps of:

using a valve curve (11, 14) of the at least one valve (3) and the discharge coefficient c_m and the determined position (12) to calculate a mass flow through the at least one valve (3) at a predetermined position of the at least one valve (3); and
calculating a deviation measure as a function of the calculated mass flow through the at least one valve (3) at the predetermined position and as a function of a value of expected mass flow at the predetermined position.

The threshold value can, by way of non-limiting example, be set such that a deviation of more than ten percent between estimated flow and the value of expected flow will indicate a disturbance. The threshold value can, by way of another non-limiting example, be set such that a deviation of more than twenty percent between estimated flow and the value of expected flow will indicate a disturbance. In an embodiment, the controller (6) comprises a memory storing the threshold value. The threshold value can be a predetermined threshold value and the controller (6) can comprise a memory storing the predetermined threshold value. The predetermined threshold value can, by way of non-limiting example, be set such that a deviation of more than ten percent between estimated flow and the value of expected flow will indicate a disturbance. The predetermined threshold value can, by way of another non-limiting example, be set such that a deviation of more than twenty percent between estimated flow and the value of expected flow will indicate a disturbance.
The present disclosure also pertains to any of the aforementioned methods, the method comprising the step of:
determining the discharge coefficient c_m as an exclusive function of the upstream pressure p_u and of the downstream pressure p_d.
The instant disclosure also pertains to any of the aforementioned methods, the method comprising the step of:
calculating the discharge coefficient c_m as an exclusive function of the upstream pressure p_u and of the downstream pressure p_d.
An exclusive function does not accept arguments other than those specified.
The instant disclosure also pertains to any of the aforementioned methods not involving an exclusive determination based on upstream pressure p_u and on downstream pressure p_d, the refrigerant circuit (1) also comprising a third sensor (9) for recording a signal indicative of a thermodynamic state of the refrigerant at the inlet port of the at least one valve (3), the method comprising the steps of:

recording a third signal using the third sensor (9);
processing the third signal to determine an upstream temperature t_u ; and
determining the discharge coefficient c_m based on the upstream pressure p_u and based on the downstream pressure p_d and based on the upstream temperature t_u.

The present disclosure also deals with any of the aforementioned methods, wherein the third sensor (9) comprises a temperature sensor. The present disclosure still deals with any of the aforementioned methods, wherein the third sensor (9) is a temperature sensor.
The instant disclosure still deals with any of the aforementioned methods involving a third sensor (9), the method comprising the step of:
calculating the discharge coefficient c_m based on the upstream pressure p_u and based on the downstream pressure p_d and based on the upstream temperature t_u.
The present disclosure also deals with any of the aforementioned methods involving a third sensor (9), the method comprising the steps of:

receiving a choice signal indicative of a choice of a refrigerant;
processing the choice signal to determine the refrigerant;
determining a back pressure ratio r_b as a function of the downstream pressure p_d and of the upstream pressure p_u ;
determining a critical pressure ratio r_c as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
comparing the back pressure ratio r_b and the critical pressure ratio r_c to one another;
determining an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c ; and
determining the discharge coefficient c_m based on the application pressure ratio r_a .

This disclosure also discloses any of the aforementioned methods involving a choice signal, the method comprising the step of:
recording a choice signal indicative of a choice of a refrigerant from a user or from an operator.
The instant disclosure also discloses any of the aforementioned methods involving a choice signal, the method comprising the step of:
determining a critical pressure ratio r_c as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the chosen refrigerant.
The instant disclosure still deals with any of the aforementioned methods involving an application pressure ratio r_a , the method comprising the steps of:

calculating a back pressure ratio r_b as a function of the downstream pressure p_d and of the upstream pressure p_u ;
calculating a critical pressure ratio r_c as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
comparing the back pressure ratio r_b and the critical pressure ratio r_c to one another;
calculating an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c ; and
calculating the discharge coefficient c_m based on the application pressure ratio r_a .

It is envisaged that the back pressure ratio r_b is calculated as a ratio between the downstream pressure p_d and the upstream pressure p_u .
This disclosure also deals with any of the aforementioned methods involving a back pressure ratio r_b, the method comprising the steps of:

determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
determining the critical pressure ratio r_c as a function of the isentropic expansion coefficient k;
comparing the back pressure ratio r_b and the critical pressure ratio r_c to one another;
determining the application pressure ratio r_a as the maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c ; and
determining the discharge coefficient c_m based on the application pressure ratio r_a and based on the isentropic expansion coefficient k.

The present disclosure also deals with any of the aforementioned methods involving an isentropic expansion coefficient k, the method comprising the steps of:

determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
calculating the critical pressure ratio r_c as a function of the isentropic expansion coefficient k;
comparing the back pressure ratio r_b and the critical pressure ratio r_c to one another;
calculating the application pressure ratio r_a as the maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c ; and
calculating the discharge coefficient c_m as a function of the application pressure ratio r_a and of the isentropic expansion coefficient k.

The isentropic expansion coefficient k is preferably determined as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant using a lookup table. The lookup table comprises values of the isentropic expansion coefficient k as a function of pressure, of temperature, and of the refrigerant. In a special embodiment, the lookup table comprises values of the isentropic expansion coefficient k as a function of pressure, of temperature, and of a chemical composition of the determined refrigerant. More specifically, the lookup table can comprise values of the isentropic expansion coefficient k as a function of pressure, of temperature, and of a chemical composition of the chosen refrigerant.
This disclosure also deals with any of the aforementioned methods involving a back pressure ratio r_b, the method comprising the steps of:

receiving a numeric signal;
processing the numeric signal to determine a liquid pressure recovery factor F_L such that the liquid pressure recovery factor F_L is less than unity or equals unity;
determining a critical pressure p _crit based on the determined refrigerant;
determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant; and
using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to determine the critical pressure ratio r_c .

The numeric signal is preferably indicative of a real number that is less than unity or equal to unity.
The instant disclosure also discloses any of the aforementioned methods involving a numeric signal, the method comprising the step of:
recording a numeric signal from a user or from an operator.
The instant disclosure still discloses any of the aforementioned methods involving a numeric signal, the method comprising the step of:
recording a numeric signal from a user or from an operator, wherein the numeric signal is indicative of a real number that is less than unity or equal to unity.
The present disclosure still discloses any of the aforementioned methods involving a numeric signal, the method comprising the steps of:

determining a critical pressure p _crit based on the chosen refrigerant; and
determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the chosen refrigerant.

The instant disclosure still further discloses any of the aforementioned methods involving a numeric signal, the method comprising the steps of:

calculating a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant; and
using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to calculate the critical pressure ratio r_c .

The present disclosure yet further discloses any of the aforementioned methods involving a numeric signal, the method comprising the steps of:

determining a critical pressure p _crit based on the chosen refrigerant;
calculating a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the chosen refrigerant; and
using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to calculate the critical pressure ratio r_c .

This disclosure also deals with any of the aforementioned methods involving a saturation pressure ratio r_s, the method comprising the steps of:

determining a saturation pressure p_s based on the upstream temperature t_u and based on the determined refrigerant; and
determining the saturation pressure ratio r_s as a function of the saturation pressure p_s and of the upstream pressure p_u .

The present disclosure also deals with any of the aforementioned methods involving a saturation pressure p_s , the method comprising the steps of:

determining a liquid pressure ratio factor F_F as a function of the saturation pressure p_s and of the critical pressure p _crit; and
using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to determine the critical pressure ratio r_c .

The instant disclosure also deals with any of the aforementioned methods involving a saturation pressure p_s and a critical pressure ratio r_c , the method comprising the steps of:

determining a liquid pressure ratio factor F_F as an exclusive function of the saturation pressure p_s and of the critical pressure p _crit; and
exclusively using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to determine the critical pressure ratio r_c .

The present disclosure still deals with any of the aforementioned methods involving a saturation pressure p_s and a critical pressure ratio r_c , the method comprising the steps of:

calculating a liquid pressure ratio factor F_F as a function of the saturation pressure p_s and of the critical pressure p _crit; and
using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to calculate the critical pressure ratio r_c .

calculating a liquid pressure ratio factor F_F as an exclusive function of the saturation pressure p_s and of the critical pressure p _crit; and
exclusively using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to calculate the critical pressure ratio r_c .

The instant disclosure still deals with any of the aforementioned methods involving a third sensor (9), the method comprising the steps of:

receiving a choice signal indicative of a choice of a refrigerant;
receiving a numeric signal;
processing the choice signal to determine the refrigerant;
processing the numeric signal to determine a liquid pressure recovery factor F_L such that the liquid pressure recovery factor F_L is less than unity or equals unity;
determining a back pressure ratio r_b as a function of the downstream pressure p_d and of the upstream pressure p_u ;
determining a critical pressure p _crit based on the determined refrigerant;
determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to determine a liquid critical pressure ratio r_cl ;
determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
using the isentropic expansion coefficient k to determine a gaseous critical pressure ratio r_cg ;
comparing the back pressure ratio r_b and the liquid critical pressure ratio r_cl and the gaseous critical pressure ratio r_cg to one another;
determining an application pressure ratio r_s as a maximum value of the back pressure ratio r_b, of the liquid critical pressure ratio r_cl , and of the gaseous critical pressure ratio r_cg ; and
determining the discharge coefficient c_m based on the application pressure ratio r_a and based on the isentropic expansion coefficient k.

The instant disclosure also pertains to any of the aforementioned methods involving an upstream temperature t_u , the method comprising the steps of:

receiving a numeric signal;
processing the numeric signal to determine a liquid pressure recovery factor F_L such that the liquid pressure recovery factor F_L is less than unity or equals unity;
calculating a back pressure ratio r_b as a ratio between the downstream pressure p_d and the upstream pressure p_u ;
determining a critical pressure p _crit based on the determined refrigerant;
determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to calculate a liquid critical pressure ratio r_cl ;
determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
using the isentropic expansion coefficient k to calculate a gaseous critical pressure ratio r_cg ;
comparing the back pressure ratio r_b and the liquid critical pressure ratio r_cl and the gaseous critical pressure ratio r_cg to one another;
calculating an application pressure ratio r_a as a maximum value of the back pressure ratio r_b, of the liquid critical pressure ratio r_cl , and of the gaseous critical pressure ratio r_cg ; and
calculating the discharge coefficient c_m based on the application pressure ratio r_a and based on the isentropic expansion coefficient k.

The instant disclosure still discloses any of the aforementioned methods involving a saturation pressure p_s , the method comprising the step of:
using a lookup table to determine a saturation pressure p_s based on the upstream temperature t_u and based on the determined refrigerant.
The lookup table comprises values of the saturation pressure p_s as a function of temperature of the refrigerant. In a special embodiment, the lookup table comprises values of the saturation pressure p_s as a function of temperature and of a chemical composition of the determined refrigerant.
The instant disclosure still further discloses any of the aforementioned methods involving a saturation pressure p_s , the method comprising the step of:
using a lookup table to determine a saturation pressure p_s based on the upstream temperature t_u and based on the chosen refrigerant.
The lookup table comprises values of the saturation pressure p_s as a function of temperature and of the chosen refrigerant. In a special embodiment, the lookup table comprises values of the saturation pressure p_s as a function of temperature of a chemical composition of the chosen refrigerant.
The present disclosure still discloses any of the aforementioned methods involving a saturation pressure p_s , the method comprising the step of:
calculating the saturation pressure ratio r_s as a function of the saturation pressure p_s and of the upstream pressure p_u .
The present disclosure still further discloses any of the aforementioned methods involving a saturation pressure p_s , the method comprising the step of:
calculating the saturation pressure ratio r_s as a ratio between the saturation pressure p_s and the upstream pressure p_u .
The present disclosure also deals with any of the aforementioned methods involving a saturation pressure p_s and a liquid critical pressure ratio r_cl , the method comprising the steps of:

determining a liquid pressure ratio factor F_F as a function of the saturation pressure p_s and of the critical pressure p _crit; and
using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to determine the liquid critical pressure ratio r_cl .

The instant disclosure also deals with any of the aforementioned methods involving a saturation pressure p_s and a liquid critical pressure ratio r_cl , the method comprising the steps of:

determining a liquid pressure ratio factor F_F as an exclusive function of the saturation pressure p_s and of the critical pressure p _crit; and
exclusively using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to determine the liquid critical pressure ratio r_cl .

The present disclosure still deals with any of the aforementioned methods involving a saturation pressure p_s and a liquid critical pressure ratio r_cl , the method comprising the steps of:

calculating a liquid pressure ratio factor F_F as a function of the saturation pressure p_s and of the critical pressure p _crit; and
using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to calculate the liquid critical pressure ratio r_cl .

calculating a liquid pressure ratio factor F_F as an exclusive function of the saturation pressure p_s and of the critical pressure p _crit; and
exclusively using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to calculate the liquid critical pressure ratio r_cl .

The instant disclosure still deals with any of the aforementioned methods involving a third sensor (9), the refrigerant circuit (1) also comprising a fourth sensor (10) for recording a signal indicative of a thermodynamic state of the refrigerant at the inlet port of the at least one valve (3), the method comprising the steps of:

recording a fourth signal using the fourth sensor (10);
receiving a choice signal indicative of a choice of a refrigerant;
receiving a numeric signal;
processing the fourth signal to determine a vapour quality q_u ;
processing the choice signal to determine the refrigerant;
processing the numeric signal to determine a liquid pressure recovery factor F_L such that the liquid pressure recovery factor F_L is less than unity or equals unity;
determining a specific volume v_l of a liquid fraction of the refrigerant based on the upstream pressure p_u and based on the upstream temperature t_u and based on the determined refrigerant;
determining a specific volume v_g of a gaseous fraction of the refrigerant based on the upstream pressure p_u and based on the upstream temperature t_u and based on the determined refrigerant;
determining a critical pressure p _crit based on the determined refrigerant;
determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to determine a liquid critical pressure ratio r_cl ;
determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;
using the isentropic expansion coefficient k to determine a gaseous critical pressure ratio r_cg ; and
determining the discharge coefficient c_m based on the vapour quality q_u and based on the specific volume v_l of the liquid fraction and based on the specific volume v_g of the gaseous fraction and based on the liquid critical pressure ratio r_cl and based on the gaseous critical pressure ratio r_cg.

The present disclosure also deals with any of the aforementioned methods involving a fourth sensor (10), wherein the fourth sensor (10) comprises a vapour quality sensor. The present disclosure still deals with any of the aforementioned methods involving a fourth sensor (10), wherein the fourth sensor (10) is a vapour quality sensor.
The instant disclosure also deals with any of the aforementioned methods involving a specific volume v_l of a liquid fraction, the method comprising the steps of:

determining an upstream specific volume v_u of the refrigerant based on the specific volume v_l of the liquid fraction and based on the specific volume v_g of the gaseous fraction and based on the vapour quality q_u ; and
determining the discharge coefficient c_m based on the vapour quality q_u and based on the specific volume v_l of the liquid fraction and based on the specific volume v_g of the gaseous fraction and based on the upstream specific volume v_u of the refrigerant and based on the liquid critical pressure ratio r_cl and based on the gaseous critical pressure ratio r_cg.

The instant disclosure still deals with any of the aforementioned methods involving a specific volume v_l of a liquid fraction, the method comprising the steps of:

determining an upstream specific volume v_u of the refrigerant based on the specific volume v_l of the liquid fraction and based on the specific volume v_g of the gaseous fraction and based on the vapour quality q_u ; and
calculating the discharge coefficient c_m based on the vapour quality q_u and based on the specific volume v_l of the liquid fraction and based on the specific volume v_g of the gaseous fraction and based on the upstream specific volume v_u of the refrigerant and based on the liquid critical pressure ratio r_cl and based on the gaseous critical pressure ratio r_cg.

This disclosure also deals with a refrigerant circuit (1) comprising at least one condenser (2), at least one compressor (5), at least one evaporator (4), and at least one valve (3) having an inlet port and an outlet port, the refrigerant circuit (1) also comprising a first sensor (7) for recording a signal indicative of a pressure of a refrigerant at the inlet port of the at least one valve (3), a second sensor (8) for recording a signal indicative of a pressure of the refrigerant at the outlet port of the at least one valve (3), a third sensor (9) for recording a signal indicative of a temperature of the refrigerant at the inlet port of the at least one valve (3), a fourth sensor (10) for recording a signal indicative of a vapour quality at the inlet port of the at least one valve (3), and a controller (6) communicatively connected to the at least one valve (3), to the first sensor (7), to the second sensor (8), to the third sensor (9), and to the fourth sensor (10), wherein the controller (6) is configured to execute the steps of any of the aforementioned methods.
The instant disclosure still deals with an apparatus for air-conditioning, wherein the apparatus comprises any of the refrigerant circuits (1) as described above.
The instant disclosure still further deals with a heat pump, wherein the heat pump comprises any of the refrigerant circuits (1) as described above.
The instant disclosure also pertains to any of the aforementioned refrigerant circuits (1), wherein the at least one valve (3) comprises at least one expansion valve. The instant disclosure also pertains to any of the aforementioned refrigerant circuits (1), wherein the at least one valve (3) is at least one expansion valve.
This disclosure still deals with a computer program comprising instructions to cause the controller (6) of any of the aforementioned refrigerant circuits (1) to execute the steps of any of the aforementioned methods.
The present disclosure still deals with a computer program comprising instructions to cause any of the aforementioned refrigerant circuits (1) to execute the steps of any of the aforementioned methods.
This disclosure yet further deals with a computer-readable medium having stored thereon any of the aforementioned computer programs.
Any steps of a procedure according to the present disclosure can be embodied in hardware and/or in a software module executed by a processor. Any steps of such a procedure can also be embodied in a software module executed by a processor inside a container using operating system level virtualisation. Any steps of such a procedure can still be embodied in a cloud computing arrangement. It is envisaged that any steps of a procedure according to the present disclosure is implemented in a combination of the above embodiments. The software may include a firmware and/or a hardware driver run by the operating system and/or an application program. Thus, the disclosure also relates to a non-transitory computer program product for performing the operations presented herein. If implemented in software, the functions described may be stored as one or more instructions on a computer-readable and non-transitory medium. Storage media that can be used include, by way of non-limiting examples, random access memory (RAM) and/or read only memory (ROM) and/or flash memory. Storage media can, by way of non-limiting examples, also include EPROM memory and/or EEPROM memory and/or registers and/or a hard disk and/or a removable disk. Further storage media can, by way of non-limiting examples, include other optical disks and/or any available media that can be accessed by a computer. Storage media can still, by way of non-limiting example, include any other IT equipment and appliance.
It should be understood that the foregoing relates only to certain embodiments of the disclosure and that numerous changes can be made therein without departing from the scope of the disclosure as defined by the following claims. It should also be understood that the disclosure is not restricted to the illustrated embodiments and that various modifications can be made within the scope of the claims.
The controller (6) can also be in operative communication with a sensor (10) arranged at the outlet of the at least one evaporator (4). The sensor (10) functions to record one or more signal indicative of the thermodynamic states of the refrigerant at the outlet of the at least one evaporator (4). The sensor (10) advantageously is a sensor (10) of the refrigerant circuit (1). In a special embodiment, the sensor (10) is a sensor (10) of the at least one evaporator (4).
A circuit (1) having a plurality of indicators also disclosed. The indicators can indicate a fault in the refrigerant circuit (1) to maintenance personnel and/or to an operator. At least one indicator can, by way of non-limiting example, indicate a leakage. At least one indicator can, by way of another non-limiting example, indicate a disturbance.
The first signal indicative of the thermodynamic state advantageously comprises a pressure signal of the refrigerant.
The second signal indicative of the thermodynamic state advantageously comprises a pressure signal of the refrigerant.
The third signal indicative of the thermodynamic state advantageously comprises a temperature signal of the refrigerant.
F_L depends on the geometry of the at least one valve (3) such as the geometry of the at least one expansion valve. An inlet temperature T_u can ideally be recorded using the first sensor (7).
The present disclosure also deals with any of the aforementioned methods, wherein the refrigerant circuit (1) comprises a condenser (2). The condenser (2) advantageously is in fluid communication with the at least on valve (3). The condenser (2) advantageously is in fluid communication with the at least one compressor (5), too.
The fourth sensor (10) is advantageously different from the first sensor (7). The fourth sensor is ideally different from the third sensor (9). The fourth sensor (10) is advantageously different from the second sensor (8).
The instant disclosure also deals with any of the aforementioned methods, wherein the at least one valve (3) comprises a valve member, the valve member being movable between an open position which allows refrigerant flow through the at least one valve (3) and a closed position which obturates refrigerant flow through the at least one valve (3), the method comprising the step of:
recording from the at least one valve (3) a position signal indicative of the position (12) of the valve member.
The instant disclosure still deals with any of the aforementioned methods, wherein the at least one expansion valve (3) comprises a valve member, the valve member being movable between an open position which allows refrigerant flow through the at least one expansion valve (3) and a closed position which obturates refrigerant flow through the at least one expansion valve (3), the method comprising the steps of:

connecting to the at least one expansion valve (3); and
receiving from the at least one expansion valve (3) a position signal indicative of the position (12) of the valve member.

In an embodiment, the position (12) is determined from the position signal using analog-to-digital conversion. In another embodiment, the position (12) is determined from the position signal using delta-sigma modulation. In still another embodiment, the position (12) is determined from the position signal using analog-to-digital conversion and delta-sigma modulation.
According to an aspect of the present disclosure, the above methods involving a position signal comprise the steps of:

connecting to the at least one valve (3) via a communication bus; and
receiving from the at least one valve (3) and via the communication bus a position signal indicative of the position (12) of the valve member.

According to a special aspect of the present disclosure, the above methods involving a position signal comprise the steps of:

connecting to the at least one expansion valve (3) using a communication bus protocol; and
receiving from the at least one expansion valve (3) a position signal indicative of the position of the valve member using the communication bus protocol.

In an embodiment, the at least one expansion valve (3) comprises a valve member, the valve member being movable between an open position which enables flow of refrigerant through the at least one expansion valve (3) and a closed position which obturates flow of refrigerant through the at least one expansion valve (3).
The present disclosure also deals with any of the aforementioned methods, wherein the refrigerant circuit (1) comprises a visible indicator, the method comprising the step of:
if the deviation measure is greater than the threshold value:
activating the visible indicator.
The instant disclosure still deals with any of the aforementioned methods, wherein the refrigerant circuit (1) comprises a closed-loop control unit such as a proportional and/or integral closed-loop control unit and wherein the at least one valve (3) comprises an actuator, wherein the closed-loop control unit is communicatively coupled to the actuator and the method comprises the steps of:

the closed-loop control unit using the deviation measure to generate an actuation signal; and
the closed-loop control unit sending the actuation signal to the actuator of the at least one valve (3).

The instant disclosure further deals with any of the aforementioned methods, wherein the refrigerant circuit (1) comprises a closed-loop control unit such as a proportional and/or integral and/or derivative closed-loop control unit and wherein the at least one valve (3) comprises an actuator, wherein the closed-loop control unit is communicatively coupled to the actuator and the method comprises the steps of:

In the embodiment having a closed-loop control unit, the at least one valve (3) can comprise at least one expansion valve (3). More specifically, the at least one valve (3) can be at least one expansion valve (3).
The visible indicator advantageously comprises a light-emitting diode and/or a display. In a special embodiment, the visible indicator comprises a diode emitting red light. In another special embodiment, the visible indicator is a diode emitting red light.
It is envisaged that the refrigerant circuit (1) comprises a housing such as a metallic housing and that the visible indicator is secured relative to the housing of the refrigerant circuit (1). It is also envisaged that the refrigerant circuit (1) comprises a housing such as a metallic housing and that the visible indicator is mounted to the housing of the refrigerant circuit (1).
It is envisaged that the at least one valve (3) comprises a housing such as a metallic housing and that the visible indicator is secured relative to the housing of the at least one valve (3). It is also envisaged that the at least one valve (3) comprises a housing such as a metallic housing and that the visible indicator is mounted to the housing of the at least one valve (3).
It is envisaged that the at least one evaporator (4) comprises a housing such as a metallic housing and that the visible indicator is secured relative to the housing of the at least one evaporator (4). It is also envisaged that the at least one evaporator (4) comprises a housing such as a metallic housing and that the visible indicator is mounted to the housing of the at least one evaporator (4).
It is envisaged that the at least one compressor (5) comprises a housing such as a metallic housing and that the visible indicator is secured relative to the housing of the at least one compressor (5). It is also envisaged that the at least one compressor (5) comprises a housing such as a metallic housing and that the visible indicator is mounted to the housing of the at least one compressor (5).
The present disclosure also deals with a computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of any of the aforementioned methods.
The instant disclosure also deals with a computer program product comprising instructions which, when the computer program product is executed by a computer, cause the computer to carry out the steps of any of the aforementioned methods.
The present disclosure also deals with a computer-readable medium having stored thereon any one of the aforementioned computer program products.

Reference numerals

1 refrigerant circuit
2 condenser
3 expansion valve
4 evaporator
5 compressor
6 controller
7 - 10 sensors
11 linear characteristic
12 position
13 (mass) flow
14 equal-percentage characteristic

Claims

A method of detecting and/or compensating a disturbance in a refrigerant circuit (1), the refrigerant circuit (1) comprising at least one valve (3) having an inlet port and an outlet port, the refrigerant circuit (1) also comprising a first sensor (7) for recording a signal indicative of a thermodynamic state of a refrigerant at the inlet port of the at least one valve (3), and a second sensor (8) for recording a signal indicative of a thermodynamic state of the refrigerant at the outlet port of the at least one valve (3), the method comprising the steps of:
recording a first signal using the first sensor (7);

recording a second signal using the second sensor (8);

receiving a position signal indicative of a position (12) of the at least one valve (3);

processing the first signal to determine an upstream pressure p_u ;

processing the second signal to determine a downstream pressure pj,

processing the position signal to determine the position (12) of the at least one valve (3);

determining a discharge coefficient c_m based on the upstream pressure p_u and based on the downstream pressure p_d , wherein the discharge coefficient c_m relates actual flow m at the determined position (12) of the at least one valve (3) to maximum flow $\hat{\dot{m}}$ at the determined position (12) of the at least one valve (3);

using a valve curve (11, 14) of the at least one valve (3) and the discharge coefficient c_m and the determined position (12) to estimate a flow through the at least one valve (3) at a predetermined position of the at least one valve (3);

calculating a deviation measure as a function of the estimated flow through the at least one valve (3) at the predetermined position and as a function of a value of expected flow at the predetermined position;

comparing the deviation measure to a threshold value; and

if the deviation measure is greater than the threshold value:
producing a signal indicative of a disturbance in the refrigerant circuit (1).
The method according to claim 1, the method comprising the step of:
determining the discharge coefficient c_m as an exclusive function of the upstream pressure p_u and of the downstream pressure p_d.
The method according to claim 1, the refrigerant circuit (1) also comprising a third sensor (9) for recording a signal indicative of a thermodynamic state of the refrigerant at the inlet port of the at least one valve (3), the method comprising the steps of:
recording a third signal using the third sensor (9);

processing the third signal to determine an upstream temperature t_u ; and

determining the discharge coefficient c_m based on the upstream pressure p_u and based on the downstream pressure p_d and based on the upstream temperature t_u.
The method according to claim 3, the method comprising the steps of:
receiving a choice signal indicative of a choice of a refrigerant;

processing the choice signal to determine the refrigerant;

determining a back pressure ratio r_b as a function of the downstream pressure p_d and of the upstream pressure p_u ;

determining a critical pressure ratio r_c as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;

comparing the back pressure ratio r_b and the critical pressure ratio r_c to one another;

determining an application pressure ratio r_a as a maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c ; and

determining the discharge coefficient c_m based on the application pressure ratio r_a.
The method according to claim 4, the method comprising the steps of:
determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;

determining the critical pressure ratio r_c as a function of the isentropic expansion coefficient k;

comparing the back pressure ratio r_b and the critical pressure ratio r_c to one another;

determining the application pressure ratio r_a as the maximum value of the back pressure ratio r_b and of the critical pressure ratio r_c ; and

determining the discharge coefficient c_m based on the application pressure ratio r_a and based on the isentropic expansion coefficient k.
The method according to claim 4, the method comprising the steps of:
receiving a numeric signal;

processing the numeric signal to determine a liquid pressure recovery factor F_L such that the liquid pressure recovery factor F_L is less than unity or equals unity;

determining a critical pressure p _crit based on the determined refrigerant;

determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant; and

using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to determine the critical pressure ratio r_c .
The method according to claim 6, the method comprising the steps of:
determining a saturation pressure p_s based on the upstream temperature t_u and based on the determined refrigerant; and

determining the saturation pressure ratio r_s as a function of the saturation pressure p_s and of the upstream pressure p_u .
The method according to claim 7, the method comprising the steps of:
determining a liquid pressure ratio factor F_F as a function of the saturation pressure p_s and of the critical pressure p _crit; and

using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to determine the critical pressure ratio r_c .
The method according to claim 3, the method comprising the steps of:
receiving a choice signal indicative of a choice of a refrigerant;

receiving a numeric signal;

processing the choice signal to determine the refrigerant;

processing the numeric signal to determine a liquid pressure recovery factor F_L such that the liquid pressure recovery factor F_L is less than unity or equals unity;

determining a back pressure ratio r_b as a function of the downstream pressure p_d and of the upstream pressure p_u ;

determining a critical pressure p _crit based on the determined refrigerant;

determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;

using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to determine a liquid critical pressure ratio r_cl ;

determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;

using the isentropic expansion coefficient k to determine a gaseous critical pressure ratio r_cg ;

comparing the back pressure ratio r_b and the liquid critical pressure ratio r_cl and the gaseous critical pressure ratio r_cg to one another;

determining an application pressure ratio r_a as a maximum value of the back pressure ratio r_b, of the liquid critical pressure ratio r_cl , and of the gaseous critical pressure ratio r_cg ; and

determining the discharge coefficient c_m based on the application pressure ratio r_a and based on the isentropic expansion coefficient k.
The method according to claim 9, the method comprising the steps of:
determining a saturation pressure p_s based on the upstream temperature t_u and based on the determined refrigerant; and

determining the saturation pressure ratio r_s as a function of the saturation pressure p_s and of the upstream pressure p_u .
The method according to claim 10, the method comprising the steps of:
determining a liquid pressure ratio factor F_F as a function of the saturation pressure p_s and of the critical pressure p _crit; and

using the liquid pressure recovery factor F_L and the liquid pressure ratio factor F_F and the saturation pressure ratio r_s to determine the liquid critical pressure ratio r_cl .
The method according to claim 3, the refrigerant circuit (1) also comprising a fourth sensor (10) for recording a signal indicative of a thermodynamic state of the refrigerant at the inlet port of the at least one valve (3), the method comprising the steps of:
recording a fourth signal using the fourth sensor (10);

receiving a choice signal indicative of a choice of a refrigerant;

receiving a numeric signal;

processing the fourth signal to determine a vapour quality q_u ;

processing the choice signal to determine the refrigerant;

processing the numeric signal to determine a liquid pressure recovery factor F_L such that the liquid pressure recovery factor F_L is less than unity or equals unity;

determining a specific volume v_l of a liquid fraction of the refrigerant based on the upstream pressure p_u and based on the upstream temperature t_u and based on the determined refrigerant;

determining a specific volume v_g of a gaseous fraction of the refrigerant based on the upstream pressure p_u and based on the upstream temperature t_u and based on the determined refrigerant;

determining a critical pressure p _crit based on the determined refrigerant;

determining a saturation pressure ratio r_s as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;

using the liquid pressure recovery factor F_L and the critical pressure p _crit and the saturation pressure ratio r_s and the upstream pressure p_u to determine a liquid critical pressure ratio r_cl ;

determining an isentropic expansion coefficient k as a function of the upstream pressure p_u , of the upstream temperature t_u , and of the determined refrigerant;

using the isentropic expansion coefficient k to determine a gaseous critical pressure ratio r_cg ; and

determining the discharge coefficient c_m based on the vapour quality q_u and based on the specific volume v_l of the liquid fraction and based on the specific volume v_g of the gaseous fraction and based on the liquid critical pressure ratio r_cl and based on the gaseous critical pressure ratio r_cg.
A refrigerant circuit (1) comprising at least one condenser (2), at least one compressor (5), at least one evaporator (4), and at least one valve (3) having an inlet port and an outlet port, the refrigerant circuit (1) also comprising a first sensor (7) for recording a signal indicative of a pressure of a refrigerant at the inlet port of the at least one valve (3), a second sensor (8) for recording a signal indicative of a pressure of the refrigerant at the outlet port of the at least one valve (3), a third sensor (9) for recording a signal indicative of a temperature of the refrigerant at the inlet port of the at least one valve (3), a fourth sensor (10) for recording a signal indicative of a vapour quality at the inlet port of the at least one valve (3), and a controller (6) communicatively connected to the at least one valve (3), to the first sensor (7), to the second sensor (8), to the third sensor (9), and to the fourth sensor (10), wherein the controller (6) is configured to execute the steps of a method according to any of the claims 1 to 12.
A computer program comprising instructions to cause the controller (6) of the refrigerant circuit (1) of claim 13 to execute the steps of a method according to any of the claims 1 to 12.
A computer-readable medium having stored thereon the computer program of claim 14.