CN108197407B - Frequency conversion air supplement compressor performance calculation method based on local linearization theory - Google Patents

Frequency conversion air supplement compressor performance calculation method based on local linearization theory Download PDF

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CN108197407B
CN108197407B CN201810084138.2A CN201810084138A CN108197407B CN 108197407 B CN108197407 B CN 108197407B CN 201810084138 A CN201810084138 A CN 201810084138A CN 108197407 B CN108197407 B CN 108197407B
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胡海涛
孙浩然
丁国良
吴静玮
李�浩
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Shanghai Jiaotong University
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Abstract

The invention relates to the field of performance calculation of compressors, and discloses a method for calculating the performance of a variable-frequency air supply compressor based on a local linearization theory, which comprises the following specific steps of: a. acquiring the nameplate parameters of the air supply compressor, including the air displacement and the rated operating frequency of the air suction cylinder and the air supply cylinder; b. acquiring test experiment data and fitting model coefficients; c. inputting running parameters of the air-supplementing compressor, including running frequency, suction and air-supplementing refrigerant states and exhaust pressure; d. calculating the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor according to the operation frequency and the state of the refrigerant; e. calculating the input power of the air supply compressor according to the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor; f. and calculating the exhaust temperature of the air make-up compressor according to the flow and the input power of the air make-up compressor. The invention saves the calculation time and cost of the model, and has high accuracy and high calculation speed.

Description

Frequency conversion air supplement compressor performance calculation method based on local linearization theory
Technical Field
The invention relates to the field of performance calculation of compressors, in particular to a method for calculating the performance of a variable-frequency air supply compressor based on a local linearization theory.
Background
Inverter compressors are widely used in residential heat pumps and air conditioners due to their advantages of sustainable control, high efficiency, etc. However, when the heat pump system is operated in a low temperature environment, the mass flow rate of the system and the efficiency of the compressor are reduced due to a low suction temperature and a high compression ratio, with the consequent deterioration of the system COP. In recent years, in order to avoid the decrease of system COP of a heat pump in a low-temperature environment, an inverter compressor with air compensation is widely used. Compared with the conventional compressor, the inverter compressor with air compensation has two additional parameters: the intermediate pressure and the temperature of the supply air, and these two parameters are coupled to each other to influence the performance of the compressor. The analysis and prediction of compressor performance directly affects the system design and selection. Therefore, the quick calculation method for establishing the frequency conversion compressor with air supplement has very important significance for the control and model selection design of the compressor with air supplement.
In the calculation model, in order to improve the calculation precision of the model and widen the application range, the model is based on a theoretical mechanism; in order to increase the computation speed of the theoretical model, the display expression should be used for solving computation so as to avoid the iterative process required for solving the implicit expression. Therefore, there is a need for a theoretical-based explicit calculation model to predict the performance of inverter compressors with air make-up. For an explicit calculation model of the compressor, the existing research is mainly focused on the traditional compressor without air make-up, and the research on the compressor with air make-up is lacked. In the research results of the conventional compressor, the mass flow is a second-order polynomial function related to the ratio of the operation frequency and the rated frequency; the input power is significantly influenced by the compressor speed and the condensing pressure. However, for the compressor with the make-up air, there are additional make-up air and secondary compression processes, and the mass flow rate and the input power are affected by the intermediate pressure and the make-up air temperature, so that the conventional compressor model cannot correctly reflect the characteristics thereof.
Currently, there are two models of calculation for inverter compressors with air compensation, namely an explicit model based on data fitting (teleo-inquiry, f.m. navorro-per, e., Gonz a lvez-Maci, j.new characteristics simulation method for fluctuation-injection control system, 2017,74: 528. 539.) and an implicit model based on mass-energy balance theory (choo, i.y., Ko, s.b., Kim, y.optimization injection in symmetry and actual control system with fluctuation-injection in balance, international simulation of simulation, 35(4): 850. 860, france, l, local simulation, map, simulation, injection, 2012, and simulation, and simulation, 35(4), simulation, model, simulation. In the existing data fitting explicit model, the mass flow and the input power are both polynomial functions of the gas supply temperature and the intermediate pressure. The data fitting model has the advantages of simple expression and good precision under experimental conditions, but the accuracy of the model may become unacceptable outside the experimental conditions due to lack of physical significance, and the expansibility is poor. In the implicit model based on mass-energy balance theory, mass flow and power are expressed as a series of nonlinear equations derived from energy conservation and mass conservation, and are solved by iteration, but the calculation speed and stability in the solving process are limited. However, the existing model directly derived from the mass energy balance theory is a nonlinear implicit equation without an analytic solution, so that the existing theoretical model and the explicit expression are combined, and the explicit model with physical significance cannot be directly obtained.
Therefore, those skilled in the art are devoted to develop a method for calculating the performance of the inverter air compressor based on the local linearization theory.
Disclosure of Invention
In view of the above defects in the prior art, the technical problem to be solved by the present invention is to improve the model calculation accuracy, widen the application range, and improve the calculation speed and stability of the theoretical model.
In order to achieve the purpose, the invention provides a performance calculation method of the variable-frequency air supplement compressor based on the local linearization theory, which can quickly and accurately establish a performance calculation prediction model of the variable-frequency compressor with air supplement, saves the calculation time and cost of the model, and has high accuracy and high calculation speed.
In the preferred embodiment of the present invention, the specific steps are:
a. acquiring the nameplate parameters of the air supply compressor, including the air displacement and the rated operating frequency of the air suction cylinder and the air supply cylinder;
b. acquiring test experiment data and fitting model coefficients;
c. inputting running parameters of the air-supplementing compressor, including running frequency, suction and air-supplementing refrigerant states and exhaust pressure;
d. calculating the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor according to the operation frequency and the state of the refrigerant;
e. calculating the input power of the air supply compressor according to the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor;
f. and calculating the exhaust temperature of the air supply compressor according to the air suction flow of the compressor, the air supply flow of the compressor, the exhaust flow of the compressor and the input power of the air supply compressor.
Further, in the step b, a least square fitting method is specifically adopted to perform regression analysis on the compressor experimental data to obtain a regression coefficient required in the calculation equation.
Further, in the step c, the state of the sucked and replenished refrigerant includes the pressure, temperature or enthalpy of the refrigerant, and can be determined by the operating states of the upstream and downstream components.
Further, in step d, the inspiratory flow equation is expressed as a function of the normalized volumetric efficiency:
Figure BDA0001561902070000031
η＝kv·ηv,ref (2)
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000032
is the inspiratory flow;
Figure BDA0001561902070000033
is the displacement of the suction cylinder per revolution; n is the rotation speed (rps); v. ofsucIs the specific volume of the inspiratory flow; η is the volumetric efficiency; k is a radical ofvIs the normalized volumetric efficiency; etav,refIs the volumetric efficiency at the nominal frequency.
In step d, the overall calculation process of the compressor suction flow rate may be represented as:
Figure BDA0001561902070000034
in the formula (f)rIs the ratio of the rotational frequency to the nominal frequency; pinjIs the air supply pressure; psucIs the suction pressure; a is1-a5Is the flow of inspirationThe fitting coefficients in the equation can be obtained in step b above.
In the step d, the calculation of the polytropic process in the air supply flow equation adopts a second-order taylor expansion to carry out local linearization treatment, and the method can regress the polytropic coefficient through a linear equation:
Figure BDA0001561902070000035
in the formula, TcomIs the temperature of the compressed refrigerant; t issucIs the suction temperature; σ is a high order infinitesimal quantity; n issucThe polytropic coefficient of the polytropic process in the air suction cylinder can be obtained through the step b after linearization, and b6-b8And c, obtaining a fitting coefficient of the air supply mass flow through the step b.
In the step d, the overall calculation process of the compressor make-up air flow may be represented as:
Figure BDA0001561902070000036
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000037
is the flow of the air supply;
Figure BDA0001561902070000038
is the displacement of the suction cylinder per revolution; v. ofinjIs the specific volume of the air supply flow; pdisIs the discharge pressure; t issucIs the suction temperature; b1-b8Is a fitting coefficient, and can be obtained by the above step b.
In step d, the overall calculation process of the compressor discharge flow rate may be represented as:
Figure BDA0001561902070000039
Figure BDA0001561902070000041
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000042
is the exhaust flow rate.
Further, in the step e, the total input power equation is linearized by a second-order taylor expansion method, wherein the polytropic coefficient can be obtained by the step b:
Figure BDA0001561902070000043
in the step e, the overall calculation process of the input power of the air make-up compressor can be represented as:
Figure BDA0001561902070000044
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000045
is the total input power of the air make-up compressor, c1-c3,d1-d5,e1-e4Is a dimensionless fitting coefficient and can be obtained by the above step b.
Further, in the step e, dimensionless factors are used
Figure BDA0001561902070000047
To reflect the influence of the leakage enthalpy on the discharge enthalpy in the model, which can be regressed by experimental data, and can be obtained by the step b.
Further, in the step f, the overall calculation process of the discharge temperature of the make-up air compressor may be represented as:
Tdis＝Func(Pdis,hdis) (9)
in the formula, TdisIs the exhaust temperature; h isdisIs the enthalpy of exhaust;func represents an explicit function of the thermodynamic properties of the refrigerant.
Further, the exhaust enthalpy hdisCan be expressed as:
Figure BDA0001561902070000046
compared with the prior art, the invention develops a method for quickly calculating the performance of the variable-frequency air-replenishing compressor based on the local linearization theory, and can be used for quickly predicting the performance parameters of the air-replenishing compressor, including air suction and air-replenishing mass flow rates, total input power and exhaust temperature. All calculation formulas are explicit expressions based on theoretical derivation, and calculation speed can be improved while calculation accuracy is guaranteed. Compared with other methods, the method can improve the calculation speed by 10 on the premise of ensuring the same precision2-103And (4) doubling.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a schematic diagram of a compressor with variable frequency and air supply according to a preferred embodiment of the present invention;
FIG. 2 is a parameter chart of the inverter compressor for supplying air according to the preferred embodiment of the present invention;
FIG. 3 is a flow chart of the calculation of a preferred embodiment of the present invention.
Detailed Description
The technical contents of the preferred embodiments of the present invention will be more clearly and easily understood by referring to the drawings attached to the specification. The present invention may be embodied in many different forms of embodiments and the scope of the invention is not limited to the embodiments set forth herein.
In the drawings, structurally identical elements are represented by like reference numerals, and structurally or functionally similar elements are represented by like reference numerals throughout the several views. The size and thickness of each component shown in the drawings are arbitrarily illustrated, and the present invention is not limited to the size and thickness of each component. The thickness of the components may be exaggerated where appropriate in the figures to improve clarity.
As shown in fig. 3, the method comprises the following specific steps:
a. acquiring the nameplate parameters of the air supply compressor, including the air displacement and the rated operating frequency of the air suction cylinder and the air supply cylinder;
b. acquiring test experiment data and fitting model coefficients;
c. inputting running parameters of the air-supplementing compressor, including running frequency, suction and air-supplementing refrigerant states and exhaust pressure;
d. calculating the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor according to the operation frequency and the state of the refrigerant;
e. calculating the input power of the air supply compressor according to the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor;
f. and calculating the exhaust temperature of the air supply compressor according to the air suction flow of the compressor, the air supply flow of the compressor, the exhaust flow of the compressor and the input power of the air supply compressor.
In the step a, the nameplate parameters of the air supply compressor can be imported by a third party in a mode of csv files, dll files and the like, and the model can automatically acquire related parameters.
In the step b, a least square fitting method is specifically adopted to carry out regression analysis on the compressor experimental data to obtain a regression coefficient required in the calculation equation.
In step c, the state of the sucked and replenished refrigerant comprises the pressure, temperature or enthalpy of the refrigerant, and can be determined by the working states of the upstream and downstream components.
As shown in fig. 1 and 2, in said step d, the inspiratory flow equation is expressed as a function of the normalized volumetric efficiency:
Figure BDA0001561902070000051
η＝kv·ηv,ref (2)
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000052
is the inspiratory flow;
Figure BDA0001561902070000053
is the displacement of the suction cylinder per revolution; n is the rotation speed (rps); v. ofsucIs the specific volume of the inspiratory flow; η is the volumetric efficiency; k is a radical ofvIs the normalized volumetric efficiency; etav,refIs the volumetric efficiency at the nominal frequency.
As shown in fig. 1 and 2, in the step d, the overall calculation process of the compressor suction flow rate can be represented as:
Figure BDA0001561902070000061
in the formula (f)rIs the ratio of the rotational frequency to the nominal frequency; pinjIs the air supply pressure; psucIs the suction pressure; a is1-a5Is the fitting coefficient in the inspiratory flow equation and can be obtained through the step b.
As shown in fig. 1 and fig. 2, in the step d, the calculation of the polytropic process in the make-up air flow equation adopts a second-order taylor expansion to perform local linearization, and the method can regress the polytropic coefficients through a linear equation:
Figure BDA0001561902070000062
in the formula, TcomIs the temperature of the compressed refrigerant; t issucIs the suction temperature; σ is a high order infinitesimal quantity; n issucThe polytropic coefficient of the polytropic process in the air suction cylinder can be obtained in the step b after linearization, and b6-b8And c, obtaining a fitting coefficient of the air supply mass flow through the step b.
As shown in fig. 1 and fig. 2, in the step d, the overall calculation process of the compressor make-up air flow rate can be represented as:
Figure BDA0001561902070000063
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000064
is the flow of the air supply;
Figure BDA0001561902070000065
is the displacement of the suction cylinder per revolution; v. ofinjIs the specific volume of the air supply flow; pdisIs the discharge pressure; t issucIs the suction temperature; b1-b8Is a fitting coefficient, and can be obtained by the step b.
As shown in fig. 1 and 2, in the step d, the overall calculation process of the compressor discharge air flow rate can be represented as:
Figure BDA0001561902070000066
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000071
is the exhaust flow rate.
As shown in fig. 1 and fig. 2, in said step e, the total input power equation is linearized by a second-order taylor expansion method, wherein the polytropic coefficient can be obtained by said step b.
Figure BDA0001561902070000072
As shown in fig. 1 and fig. 2, in the step e, the overall calculation process of the input power of the make-up air compressor can be represented as:
Figure BDA0001561902070000073
in the formula (I), the compound is shown in the specification,
Figure BDA0001561902070000074
is the total input power of the air make-up compressor, c1-c3,d1-d5,e1-e4Is a dimensionless fitting coefficient and can be obtained by the step b.
In said step e, as shown in fig. 1 and 2, dimensionless factors are used
Figure BDA0001561902070000076
To reflect the effect of the enthalpy leak on the enthalpy of discharge in the model, which can be regressed by experimental data, and can be obtained by said step b.
As shown in fig. 1 and fig. 2, in the step f, the overall calculation process of the discharge temperature of the make-up air compressor can be represented as:
Tdis＝Func(Pdis,hdis) (9)
in the formula, TdisIs the exhaust temperature; h, hdisIs the enthalpy of exhaust; func represents an explicit function of the thermodynamic properties of the refrigerant. The exhaust enthalpy hdisCan be expressed as:
Figure BDA0001561902070000075
to verify the effectiveness of the method, the computational accuracy and computational speed of the Model are compared to the existing theoretical-based Model of a gas-filled variable-frequency compressor represented by implicit nonlinear equations, including the theoretical-based Model (Qiao, H.T., Aute, V.J., Radiograph, R.dynamic of flash compressor), which is expressed by the theoretical-based nonlinear equations, using experimental data in the literature (Dardene, L., Fraccari, E., Maggioni, A., Molina, L., Proserpio, L., Windin, E.S. semi-empirical modeling of a variable compressor with variable speed, 2015,54: 76-87), including the theoretical-based Model (Qiao, H.T., Aute, V., Radiograph, R.D., Model of a gas compressor), Model of variable compressor, P.S., P.P., Model, P.S. simulation, L., P.S. simulation, P.S. Model, P.S. 1. and P.S. simulation, Model, P.S. simulation, P.S. Model, P.S. 1. A., P.S. Model, P.S. sub.S. 1, P. simulation, P.S. 1, P. Model, P. 1, P. sub.S. Model, P. 1, P. sub.S. 1, P. Model, P. sub.S. Model, P. sub.S. 1, 2015,54:76-87.). The validation operation was performed using MATLAB on a computer with Intel core i3 for CPU and 8GB for RAM. The validation conditions of the model are shown in table 1.
Table 1 verification conditions of the model
Verification conditions Range
Rotation frequency-f (Hz) 40-120
Suction pressure-Psuc (kPa) 300-900
Pressure of Qi supplement-Pinj (kPa) 900-2000
Exhaust pressure-Pdis (kPa) 2000-4000
Degree of superheat of suction (K) 5-10
Air supplement superheat degree (K) 1-5
Table 2 lists the comparison of the computational accuracy of the explicit computational model proposed by the present invention with the existing models. The result shows that the calculation precision of the model is superior to that of a theoretical model and is equivalent to that of the existing semi-empirical model.
TABLE 2 comparison of model calculation accuracy
Figure BDA0001561902070000081
Table 3 lists the comparison of the explicit calculation model proposed by the present invention with the existing model calculation speed. The result shows that the calculation speed of the model is 10 times faster than that of the existing theoretical model2Times, 10 times faster than the semi-empirical model3And (4) doubling.
TABLE 3 comparison of model calculated speeds
Figure BDA0001561902070000082
According to the analysis, the invention establishes the frequency conversion air supplement compressor explicit calculation model based on the local linearization theory by adopting the local linearization method. In the present invention, the suction flow rate is expressed as a function of normalized volumetric efficiency; the flow of the air supplement is calculated by a local linearization method; the total input power is subjected to local linearization processing through a second-order Taylor expansion; the exhaust temperature equation adopts a heat leakage factor to avoid the calculation of the heat leakage of the compressor shell in the iterative calculation process, thereby realizing the accurate and rapid calculation of the performance parameters of the air supply compressor. The verification result shows that the calculation precision of the method is equivalent to that of the existing model, and the calculation speed is 10 times faster than that of the existing model2-103And the good effect is achieved.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.

Claims (2)

1. A method for calculating the performance of a frequency conversion air supply compressor based on a local linearization theory is characterized by comprising the following specific steps:
a. acquiring the nameplate parameters of the air supply compressor, including the air displacement and the rated operating frequency of the air suction cylinder and the air supply cylinder;
b. obtaining test experiment data, and fitting an explicit calculation model coefficient of the variable-frequency air supply compressor;
c. inputting running parameters of the air-supplementing compressor, including running frequency, suction and air-supplementing refrigerant states and exhaust pressure; the states of the air suction and air supply refrigerants comprise the pressure, the temperature or the enthalpy value of the refrigerants;
d. calculating the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor according to the operating frequency and the state of the refrigerant;
the step d comprises the following steps:
the compressor suction flow equation is expressed as a function of normalized volumetric efficiency:
Figure FDA0003000922160000011
η＝kv·ηv，ref；
wherein the content of the first and second substances,
Figure FDA0003000922160000012
is the flow rate of the intake air,
Figure FDA0003000922160000013
is the displacement of the suction cylinder per revolution, N is the rotation speed,
vsucis the specific volume of the suction flow, eta is the volumetric efficiency, kvIs the normalized volumetric efficiency of the fluid to be,
ηv，refis volumetric efficiency at nominal frequency;
the overall calculation process of the compressor suction flow is as follows:
Figure FDA0003000922160000014
wherein the content of the first and second substances,
fris the ratio of the rotational frequency to the nominal frequency;
Pinjis the air supply pressure; psucIs the suction pressure; a is1、a2、a3、a4、a5Is a fitting coefficient in the inspiratory flow equation;
the variable process calculation in the compressor air supply flow equation adopts a second-order Taylor expansion formula to carry out local linearization processing, and the variable coefficients are regressed through a linear equation:
Figure FDA0003000922160000015
Figure FDA0003000922160000021
wherein the content of the first and second substances,
Tcomis the temperature of the refrigerant being compressed and,
Tsucis the temperature of the air being sucked in,
a is a high-order infinitesimal quantity,
nsucis the polytropic coefficient of the polytropic process in the air suction cylinder,
b6、b7、b8is a fitting coefficient in the air supply flow equation;
the total calculation process of the air supply flow of the compressor comprises the following steps:
Figure FDA0003000922160000022
wherein the content of the first and second substances,
Figure FDA0003000922160000023
is the flow rate of the air supply,
Figure FDA0003000922160000024
is the displacement of the suction cylinder per revolution,
vinjis the specific volume of the air supply flow,
Pdisis the pressure of the exhaust gas,
Tsucis the temperature of the air being sucked in,
b1、b2、b3、b4、b5is a fitting coefficient in the air supply flow equation;
the overall calculation process of the compressor exhaust flow is as follows:
Figure FDA0003000922160000025
wherein the content of the first and second substances,
Figure FDA0003000922160000026
is the exhaust flow rate;
e. calculating the input power of the air supply compressor according to the air suction flow of the compressor, the air supply flow of the compressor and the exhaust flow of the compressor;
the step e comprises the following steps:
linearizing an input power equation of the air make-up compressor into:
Figure FDA0003000922160000031
the overall calculation process of the input power of the air supply compressor comprises the following steps:
Figure FDA0003000922160000032
wherein the content of the first and second substances,
Figure FDA0003000922160000033
is the total input power of the air make-up compressor,
c1、c2、c3、d1、d2、d3、d4、d5、e1、e2、e3、e4、e5is a dimensionless fitting coefficient;
f. calculating the exhaust temperature of the air supplement compressor according to the air suction flow of the compressor, the air supplement flow of the compressor, the exhaust flow of the compressor and the input power of the air supplement compressor;
the overall calculation process of the exhaust temperature of the air supply compressor is as follows:
Tdis＝Func(Pdis，hdis)；
wherein the content of the first and second substances,
Tdisis the temperature of the exhaust gas and,
hdisis the enthalpy of the exhaust gas,
func represents an explicit function of refrigerant thermodynamic properties;
performing regression analysis on the compressor experimental data by adopting a least square fitting method for the fitting model coefficients in the step b to obtain regression coefficients of the calculation equations in the step d and the step e, wherein the regression coefficients comprise c1、c2、c3、d1、d2、d3、d4、d5、e1、e2、e3、e4、e5、b1、b2、b3、b4、b5、b6、b7、b8；
H isdisComprises the following steps:
Figure FDA0003000922160000034
wherein the content of the first and second substances,
Figure FDA0003000922160000035
the method is a dimensionless factor and reflects the influence of the heat leakage enthalpy on the discharge enthalpy.
2. The method for calculating the performance of the frequency-conversion air-supplement compressor based on the local linearization theory as claimed in claim 1, wherein in the step a, the nameplate parameters of the air-supplement compressor are imported by a third party; and the third party imports modes comprising csv files and dll files.
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