Discussion on thermodynamic analysis of compression/jet mixing refrigeration cycle

0 Preface

The circulating structure widely used in refrigeration systems is: compressor → condenser → throttle valve → evaporator → compressor structure type, the suction pressure of the compressor is equal to the evaporation pressure, and the exhaust pressure is equal to the condensation pressure. The loss of this type of refrigeration cycle is mainly composed of three parts: (1) loss due to non-isentropic of the compression process; (2) loss of heat transfer temperature difference between the condenser and the evaporator; and (3) throttling loss of the throttle valve. The non-isentropic loss of the compression process in these three losses is directly related to the manufacturing process of the compressor. The reduction of the heat transfer temperature difference loss can increase the heat transfer coefficient of the heat exchanger on the one hand, and increase the heat exchange coefficient on the other hand. The thermal area, the reduction in these two losses is limited. The throttling loss causes the useful energy of the refrigerant to be wasted, and these energy can be recovered by appropriate measures. The calculation shows that the throttling loss caused by the throttling process exceeds 10% of the total loss of the refrigeration system [1]. If this part of energy can be recovered by measures, the refrigeration efficiency of the refrigeration system can be greatly improved. It is generally believed that in the throttling process of the vapor compression refrigeration cycle, the refrigerant is in the two-phase region, and the energy recovery device is easily damaged, and the recovery is not worth the loss.

The injector is simple in construction, low in cost, has no moving parts, and is suitable for use in any flow pattern including two-phase flow. The ejector has long been used in heat-driven refrigeration systems [2, 3, 4], and Kornhauser [5] has proposed a compression/injection hybrid vapor compression refrigeration cycle, which makes it possible to recover throttling energy losses. Many studies have shown that the use of injectors in refrigeration systems can indeed improve the refrigeration performance of refrigeration units [6, 7, 8].

The theoretical analysis methods for compression/jet mixing vapor compression refrigeration cycle are also introduced in the literature [9,10], which is generally related to the structure of the injector and is difficult to be used for pure thermodynamic analysis. This paper refers to the literature [9,10]. Combined with the basic equation of the injector, a pure thermodynamic analysis method for the compression/jet mixing vapor compression theoretical refrigeration cycle is proposed.

1 Thermodynamic analysis of compression/jet mixing vapor compression refrigeration cycle

Fig.1 Flow chart of compression/jet mixing vapor compression refrigeration cycle and its representation on LgP-h diagram

Figure 2 Schematic diagram of the injector

The connection of the components of the compression/injection hybrid vapor compression refrigeration cycle and its representation on the LgP-h diagram are shown in Figure 1, and the structure of the injector is shown in Figure 2. Compared with the traditional vapor compression refrigeration cycle, the difference between Zui is that the high-temperature and high-pressure liquid refrigerant from the condenser directly enters the nozzle of the injector, accelerates the pressure reduction in the nozzle, converts the pressure energy into velocity energy, and sprays it from the nozzle. The speed usually exceeds the speed of sound and the pressure drops to the evaporation pressure. The low-pressure high-speed refrigerant sprayed from the nozzle is injected and mixed with the low-pressure low-temperature gas refrigerant from the evaporator, and then decelerated and boosted in the diffuser chamber of the injector, so that the speed energy can be converted into pressure energy, thereby making the pressure from the evaporator The refrigerant pressure rises, and after gas-liquid separation in the gas-liquid separator, the gaseous refrigerant enters the compressor, and the liquid refrigerant enters the evaporator. There are two loops in the refrigerant, the loop 1:1 '-2'-3-5-6-7-1', and the loop 2: 8-9-1-6-7-8. This allows the suction pressure to enter the compressor to be higher than the evaporation pressure, thereby increasing the efficiency of the refrigeration system.

1.2 Thermodynamic analysis of compression/jet mixing vapor compression refrigeration cycle

1.2.1 Model assumptions

To facilitate calculations and analysis, we have made assumptions about certain aspects of the compression/injection hybrid vapor compression refrigeration cycle, including:

(1) Ignore resistance losses such as pipes, condensers, and evaporators.

(2) The refrigerant leaving the evaporator is a saturated vapor phase, and the refrigerant leaving the condenser is a saturated liquid phase.

(3) After the refrigerant is ejected from the nozzle, the pressure is reduced to the evaporation pressure, and the refrigerant is mixed in the ejector to be equal pressure mixing under the evaporation pressure.

(4) The refrigerant is in a quasi-equilibrium state from time to time, and the refrigerant is in an entropic process during the acceleration process of the nozzle and the compression process in the diffusion chamber, regardless of the friction loss.

(5) Ignore the kinetic energy of the nozzle inlet, evaporator outlet, and injector outlet.

1.2.2 Calculation of thermal parameters

1) Thermal calculation of traditional refrigeration cycle

The representation of the conventional refrigeration cycle on the LgP-h diagram is shown in Figure 1-2-3-4-1, and the cooling capacity per unit refrigerant mass flow is:

(1)

Compressor power consumption per unit refrigerant mass flow:

(2)

Refrigeration coefficient of the refrigeration cycle:

(3)

2) Thermal calculation of compression/jet mixing vapor compression refrigeration cycle

According to Figure 1, the cooling capacity of the compression/injection hybrid vapor compression refrigeration cycle is:

(4)

The power consumption of the compressor:

(5)

In the formula: - Mainstream refrigerant flow and ejector refrigerant flow, respectively.

Refrigeration coefficient of the refrigeration cycle:

(6)

1.2.3 Determination of injection coefficient and injector outlet pressure

It can be seen from equations (4) and (5) that in the calculation of cooling capacity and compressor power consumption, with It is unknown because the injector's injection coefficient and injector outlet pressure are unknown. The injection coefficient is defined as the ratio of the flow rate of the ejector fluid to the flow rate of the mainstream fluid, ie:

(7)

The process of generating refrigerant in the ejector is ideal, that is, the ejector can meet the need for throttling loss recovery. The mainstream refrigerant is ejected from the nozzle, in a state of 5, mixed with the ejector refrigerant (state 1), reaches state 6, and reaches state 7 after isentropic compression. The control body between the sections A-A and B-B of Fig. 2 has the following relationship:

Conservation by quality:

(8)

In the formula: - the mass flow rate for the injector mixing chamber

Conservation by momentum:

(9)

which is: (10)

Conservation of energy by:

(11)

then: (12)

The main flow rate can be obtained by the expansion process 3-5 in the nozzle:

(13)

From 6 o'clock pressure to evaporation pressure , the entropy of 6 points can be obtained according to the refrigerant property equation

(14)

The refrigerant can be regarded as an isentropic compression process in the ejector expansion chamber, ie From this, you can get 7 points:

(15)

The pressure at 7 points from the physical property equation is:

(16)

In the above formulas, there is still an unknown quantity, which is the injection coefficient. In the process of analyzing the refrigerant in the gas-liquid separator, it can be seen that in order to make the circulation loop 1:1'-2'-3-5-6-7-1' and the circulation loop 2:8-9-1- 6-7-8 can be maintained, and the conditions of mass balance must also be met. That is, for processes 7-8 and 7-1', [10] must be satisfied:

(17)

Injection coefficient Must meet:

(18)

At this point, as long as the evaporation pressure and the condensing pressure are known, an ideal thermodynamic cycle analysis can be performed on the injection/compression hybrid refrigeration cycle.

2 Calculation results and discussion

According to equations (1) to (18), the theoretical refrigeration performance of the compression/injection hybrid refrigeration cycle of nine common refrigerants was analyzed. The results are shown in Figs. 3 to 8.

Figure 3 and Figure 6 show the variation of the injection coefficient of the injector with the evaporation temperature. It can be seen from the figure that as the evaporation temperature increases, the injection coefficient of the injector increases, as can be seen by comparing Figure 5 and Figure 6, with As the condensation temperature increases, the injection coefficient decreases.

Figure 3 The injection coefficient varies with evaporation temperature

Fig. 4 Variation of compression ratio of compression/injection mixing cycle and conventional cycle cooling coefficient with evaporation temperature

Figure 5 The injection coefficient varies with evaporation temperature

Fig.6 Variation of the ratio of the compression coefficient of the compression/injection mixing cycle to the conventional cycle cooling coefficient as a function of the evaporation temperature

Figures 4 and 6 the ratio of compression / injection mixing cycle refrigeration coefficient (COP) and the conventional refrigerating cycle refrigeration coefficient (COP ₀₎ of the curve with the evaporation temperature, it can be seen from the figure, with the increase of the evaporation temperature The increase in the coefficient of refrigeration (COP) is gradually reduced. Taking R404A as an example, the refrigeration coefficient (COP) ratio is reduced from 1.54 at an evaporation temperature of -30 °C to 1.32 at an evaporation temperature of 5 °C at a condensation temperature of 50 °C. Comparing Fig. 4 and Fig. 6, it can be seen that as the condensing temperature increases, the ratio of the refrigeration coefficient increases.

Comparing different refrigerants, it can be seen that for different refrigerants, the compression/injection hybrid refrigeration cycle is different due to the difference in thermophysical properties, and the magnitude of the improvement of the refrigeration coefficient is different. It can be seen from the above calculations that in the conventional refrigerant, the refrigeration coefficient of the R404A is increased by the compression/injection hybrid refrigeration cycle, and the cooling coefficient of the NH ₃ is reduced by the compression/injection hybrid refrigeration cycle. The comparison of the refrigerant, the refrigeration coefficient of increase in order was: R404A, R410A, R290, R407C , R134a, R600a, R12, R22, NH 3. Moreover, comparing the injection coefficient, it can be seen that the refrigerant having a larger increase in the coefficient of refrigeration has a smaller injection coefficient. From the above analysis, it can be concluded that R404A is more suitable for compression/injection hybrid refrigeration cycle. At 50 °C condensation temperature, when the evaporation temperature is -30 °C, the refrigeration coefficient can be increased by more than 50%, and the R410A can only be followed. Increase by about 36%, far more than other refrigerants.

3 Conclusion

The compression/injection mixing cycle can recover the throttling loss caused by the throttling of the refrigeration system, so that the refrigeration coefficient of the refrigeration cycle can be increased. The injection coefficient of the compression/injection mixing cycle and the compression ratio of the refrigerant from the evaporator are not arbitrarily determined. The variables are determined for certain cooling conditions.

The theoretical analysis of the refrigeration performance of the compression/injection hybrid refrigeration cycle of nine common refrigerants shows that the lower the evaporation temperature, the higher the condensation temperature, and the more the refrigeration coefficient of the compression/injection hybrid refrigeration cycle is increased compared with the conventional refrigeration cycle. . For the different refrigerants commonly used, the compression coefficient of the compression/injection hybrid refrigeration cycle system is different. The R404A increases the zui, and the refrigeration coefficient increases when the condensation temperature is 50 °C and the evaporation temperature is -30 °C. 50%; NH ₃ zui is low, which can be increased by about 13%. Common refrigerants, the refrigeration coefficient of increase in descending order was: R404A, R410A, R290, R407C , R134a, R600a, R12, R22, NH 3.

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