RU2244267C2 - Method of measuring gas consumption factor at flowing gas through slit channel in working chamber of volumetric action machine - Google Patents

Abstract

FIELD: experimental gas dynamics.

SUBSTANCE: reciprocal piston is placed inside air-tight working cylinder (working chamber) in such a manner that two working cavities are formed above and beneath the piston. Cavities communicates with each other through slit channel. Instant values of current values of pressure P, gas temperature T, geometrical volume V of working cavity and through cross-section area f of slit channel are measured in small equal time gaps Δτ. Mass consumption M of gas is calculated from measured values P, V, T and Δτ. Instant consumption factor α is calculated from relation which includes current values of area f and variable pressure P at the entrance and exit of slit channel for any preset measurement.

EFFECT: improved precision of measurement.

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Description

The invention relates to the field of experimental gas dynamics, and more specifically to methods for determining the gas flow coefficient during flow through the slotted channel in the working chamber of a volumetric machine and can be used to study the working process in volumetric machines.

A known method for determining the mass flow rate through the slotted channel by static blowing [1].

The method consists in the fact that in machines of volumetric action, a slit channel is installed having a fixed gap with a passage area f. The purges are carried out at constant pressures P ₁ , P ₂ , and temperatures T ₁ , T ₂ , before and after the slotted channel. The gas flow passing through the slotted channel is measured using known devices, for example a rotameter or diaphragm [2]. Then from the formula [1]:

get the formula for determining the flow coefficient α:

where M is the mass flow rate through the slotted channel, kg / s;

P ₁ , P ₂ - gas pressure before and after the slotted channel, Pa;

ρ ₁ - gas density in front of the slotted channel, kg / m ³ ;

f is the area of the passage section of the slotted channel, m ² ;

ε _p is the compressibility coefficient.

The disadvantage of this method is that not all factors accompanying the gas flow through the slotted channel in a working volumetric machine are taken into account to determine the flow coefficient, namely: a rapid change in pressure and temperature before and after the channel; the mobility of the channel walls and the rapid change in its bore, which, for example, takes place in the flow part of the valves or in the gap between the piston and the cylinder. Therefore, the results of static purges do not give exact results in terms of M and α, which occur in actual, non-stationary processes.

The closest known method is to determine the gas flow through the slotted channel with moving walls of the channel [3]. The method consists in placing a reciprocating moving piston in the working chamber of a volumetric machine, providing constant pressure on both sides of the piston, measuring the values of these constant pressures and average flow rate using a diaphragm, then the flow coefficient can be determined by the formula (2) .

The disadvantage of this method is that in the studied machines the volumetric effects of pressure above and below the piston are constant, which does not correspond to the actual picture of the unsteady gas flow that takes place in the working chamber under rapidly changing gas parameters and the passage area of the slot channel, so it is impossible to obtain accurate results for determining instantaneous flow rate.

The objective of the invention is to determine the coefficient of gas flow at short intervals when it flows through the slotted channel in the working chamber of a volumetric machine under the conditions of mobility of the channel walls, changing values of the passage area and pressures at the entrance and exit of the slotted channel.

The objective of the invention is achieved in that a double-acting reciprocating piston is placed in a sealed working chamber in such a way that two working cavities are formed, communicating with each other either through a slotted channel between the piston and the cylinder, or through a self-acting valve mounted on the piston. Then, in each working cavity, instantaneous values of current values are measured at small equal time intervals Δτ: temperature T, gas pressure P, geometric volume V at each moment of time and area f of the passage section of the slotted channel, and the mass flow rate M is determined by the formula:

where R is the gas constant, J / kg · K;

P _i is the gas pressure measured at the i-th step in one of the working cavities, Pa;

P _i-1 is the gas pressure measured at the i-1st step in the same working cavity as P _i , Pa;

T _i - gas temperature measured at the i-th step, in the same working cavity as P _i , K;

T _i-1 is the gas temperature measured at the i-1st step in the same working cavity as P _i , K;

V _i - the geometric volume of the working cavity at the i-th step, in which the measurements of P _i , T _i , m ³ ;

V _i-1 is the geometric volume of the working cavity at the i-1-th step, in which measurements were taken P _i-1 , T _i-1 , m ³ ;

where N≥360 is the number of measurements per cycle;

υ is the frequency of the duty cycle of a volumetric machine, and the instantaneous gas flow rate α is determined by the formula:

The proposed method for determining the instantaneous gas flow rate can be implemented by a device, a diagram of which is shown in the drawing. The device comprises: a working chamber 1, a reciprocating moving piston 2, located in the working chamber 1 and dividing the working chamber 1 into two working cavities 3 and 4, which communicate with each other through a slot channel 5 between the piston 2 and the wall of the working chamber 1. The stuffing box 6, to maintain the tightness of the working chamber 1, instantaneous pressure sensors 7 and 8, instantaneous temperature sensors 9 and 10, placed in cavities 3 and 4, a piston displacement sensor 11 and a slot channel measuring sensor 12, to amplify the signal, an amplifier 13, analog -digit a new converter (ADC) 14 - for converting the signal to digital, a computer 15 - for processing a digital signal received from the ADC 14.

The method itself is implemented as follows. The piston 2 reciprocates in the working chamber 1 and changes the geometric volumes V of the cavities 3 and 4, which are determined using the piston displacement sensor 11, while the area f of the passage section of the slotted channel 5 formed by the walls of the working chamber 1 and the side surface of the piston 2 , defined as the difference between the cross-sectional areas of the cylinder 1 and the cross-section of the piston 2.

where δ is the width of the slotted channel, m;

D _C - diameter of the working chamber, m;

D _P - piston diameter, m

When the volume V in the working cavities 3 and 4 changes, the instantaneous pressures P are measured by instantaneous pressure sensors 7 and 8, and the instantaneous temperatures T are measured by instantaneous temperature sensors 9 and 10. The movement of the piston L is measured by the displacement sensor 11, and the area of the slot channel f during the movement of the piston measured by a sensor measuring the width of the slotted channel 12. All these measurements are made in both working cavities on each i-th dimension, which are made by the total number of N measurements. The signals from the sensors are continuously fed to the input of the amplifier 13, and then to the ADC 14, after the ADC 14, the converted signal is transmitted in digital digital form to the computer 15, where this data is generated in the form of an array, and their discreteness is determined by a small time interval Δτ. Next, this array is processed with a special program. The method for calculating the instantaneous gas flow rate coefficient α is as follows: after a short period of time Δτ, pressures P, temperatures T, piston displacement L are measured and the volume of the working cavity is determined by the formula

where F is the piston area, m ² .

Next, determine the mass flow rate of gas M in the working cavity. To do this, use the well-known equation of state [4]

where t is the mass of gas, kg;

R is the gas constant, J / (kg · K);

P is the pressure, Pa;

V is the volume occupied by gas, m ³ ;

T is the temperature of the gas, K.

follows from it

Then the mass flow rate M is defined as the difference of the gas mass Δm in the considered working cavity between the ith and i-1st measurements over the time interval Δτ

where Δm is the difference in gas mass between the i-th and i-1-th dimension, kg;

- масса газа в рассматриваемой рабочей полости вычисленная на i-ом шаге, кг;

- the mass of gas in the considered working cavity calculated at the i-th step, kg;

- масса газа в рассматриваемой рабочей полости, вычисленная на i-1-м шаге, кг;

- the mass of gas in the considered working cavity, calculated at the i-1st step, kg;

Substituting m _i and m _i-1 in the expression (8) get the mass flow rate of gas:

where P _i , T _i , V _i and P _i-1 , T _i-1 , V _i-1 - pressure, temperature and volume of the working cavity for a small time interval Δτ;

Thus, to determine the mass flow rate M, measurements of instantaneous values of the above values (P, T, V) in one of the working cavities taken from a computer-generated array for adjacent measurements i and i-1 are used.

R is the gas constant, J / (kg · K).

To determine M, either of the two cavities can be considered.

Next, find the instantaneous gas flow rate in the ith dimension when it flows through the slotted channel in the working chamber of the volumetric machine through the mass flow rate M:

where f is the area of the passage section of the slotted channel, in the i-th dimension, m ² ;

ε _p - compressibility coefficient, on the i-th dimension, is determined by the known relation [1]:

p ₁ , P ₂ - instantaneous gas pressure before and after the slot channel, on

i-th dimension, i.e. instantaneous gas pressure on the i-th dimension in both cavities. Pa;

- плотность газа на входе в щелевой канал [4], кг/м³.

- gas density at the entrance to the slotted channel [4], kg / m ³ .

T ₁ - gas temperature in front of the slotted channel in the i-th dimension, K.

The obtained flow coefficient can be used to study and calculate non-stationary mass transfer processes in the working cavities of volumetric machines.

Sources of information

1. Plastinin P.I. Theory and calculation of reciprocating compressors. M .: VO Agropromizdat, 1987 .-- 271 p.

2. Kremlin P.P. Flow meters and quantity counters. - L .: Mechanical Engineering, 1975 .-- 776 p.

3. Kazakov A.A., Klibanov E.L., Bezhanishvili E.M., Dzottsev A.B. Calculation of pressing elements for non-metallic piston rings // Refrigeration. -1984. - No. 11. - S. 36-39.

4. Kirillin V.A. et al. Technical Thermodynamics: A Textbook for High Schools. - M .: Energy, 1974.- 448 p.

Claims (1)

A method for determining the gas flow coefficient during its flow through the slotted channel in the working chamber of a volumetric machine, including measuring the pressure in the working cavities above and below the reciprocating piston and calculating the gas flow coefficient by the formula:

where M is the mass gas flow through the slotted channel, kg / s; P ₁ , P ₂ - gas pressure in the working cavities before and after the slotted channel, Pa; ρ ₁ - gas density in front of the slotted channel, kg / m ³ ; f is the area of the passage section of the slotted channel, m ² ; ε _p is the compressibility factor, characterized in that in working cavities isolated from the environment, measurements are made of the instantaneous values of current values of gas pressures P, gas temperatures T, geometric volumes of cavities V and the area of the passage section of the slotted channel f at small equal time intervals Δτ, and the mass flow rate of gas M determined by the formula:

where R is the gas constant, J / kg · K; P _i is the gas pressure measured at the i-th step in one of the working cavities, Pa; P _i-1 is the gas pressure measured at the i-1st step in the same working cavity as P _i , Pa; T _i - gas temperature, measured at the i-th step, in the same working cavity as P _i , K; T _i-1 - gas temperature, measured at the i-1st step, in the same working cavity as P _i , K; V _i - the geometric volume of the working cavity at the i-th step, in which the measurements of R _i , T _i , m ³ ; V _i-1 is the geometric volume of the working cavity at the i-1st step, in which measurements were taken P _i-1 , T _i-1 , m ³ ;

where N≥360 is the number of measurements per cycle; ν is the frequency of the duty cycle of the machine volumetric action.