# an extension of a steady-state model for fin-and-tube heat exchangers to include those using capillary tubes for flow control.

Tube heat exchanger (MPHX)

Widely used for refrigeration or air-

Adjusting the application, the refrigerant distribution in the path is very important for the performance of the heat exchanger.

Inappropriate refrigerant distribution in the evaporator may result in drying

Outside the circuit, it eventually leads to poor heat transfer and wastes the heat transfer area, while the inappropriate cooling distribution in the condenser may result in an area of reduced heat transfer due to high liquid load.

In addition, inappropriate refrigerant distribution may result in a high temperature difference between adjacent tubes, resulting in reverse heat conduction through the fins and reducing the performance of the heat exchanger (Romero-Mendez et al. 1997; Wang etal. 1999).

In order to obtain a suitable refrigerant distribution, the method of changing the mode of the refrigerant circuit (Romero-Mendez etal. 1997; Wang et al. 1999; Liang et al. 2000, 2001)

And change the geometry of the thermal distributor (Jiao et al. 2003)have been used.

In addition to these two methods, adding a capillary tube to the path is an effective way to regulate the distribution of refrigerant in different paths of MPHX, which is low cost, especially for pair-guided regulation

Therefore, the simulation study of MPHX should include the study of flow control using a capillary tube.

Many models and algorithms of MPHX are proposed, but they ignore the refrigerant distribution between paths (

Martins and Parris 1993Jia et al. 1999;

Judge and Radermacher 1997; Lee et al. 2003)

Or just consider the refrigerant distribution between paths without a capillary (Domanski 1991;

Li and Domanski 1997; Bensafiet al. 1997; Liang et al. 2001).

We put forward a general stability. statemodel (GSSM)

For MPHX with any refrigerant loop (Liu et al. 2004)

In order to simultaneously evaluate the influence of the distribution of refrigeration between paths in any refrigerant circuit, with continuous fins, air-

Sidemaldistribution, etc.

, But it still does not consider the cold storage distribution between the MPHX paths using a capillary for flow control.

As for the capillary, the mathematical model of a single capillary used as a throttling device in refrigeration or air

The development of air conditioning system is relatively perfect, such as Zhang and Ding (2004)

, Bansal and Rupasinghe (1996)

Bit and bit (1996), Chung(1998), Garcia-

Valladares, etc. (2002), etc.

But the model on TV

Tube flow or MPHX using a capillary tube for flow control is not available.

However, if we extend GSSM directly to MPHX for flow control using a capillary tube, simply add a model of a single catheter, due to the blocking properties of the catheter, an incorrect result or an abnormal termination of the simulation process may occur.

Therefore, measures must be taken to extend GSSM toMPHX using a capillary tube for flow control.

The main difficulty in extending the GSSM of MPHX to GSSM using a capillary for flow control is to solve the refrigeration distribution between the paths containing the capillary.

GSSM solves the refrigerant distribution between paths by using iterative calculations.

Since the capillary has a blocking property, flow control using a capillary is used, additional constraints on the maximum refrigerant mass flow rate are introduced in the refrigerant distribution equation of MPHX.

The simulation process may terminate abnormally or output results that are obviously incorrect, if during the iteration the assumed value of the flow of refrigerant in one capillary is greater than the maximum value.

Therefore, in the process of solving the equation of cold storage distribution between MPHX paths using capillary flow control, the selection properties of capillary should be considered at the same time.

The purpose of this paper is to extend GSSM to MPHX using capillary tubes for flow control.

This paper first gives a description of the simulation object and an analysis of the flow control problem of applying GSSM directly to MPHX using a capillary tube, and then gives an extended GSSM.

Finally, the experimental verification and conclusion are given.

Description of the simulation object considered in this paper is MPHX using a capillary tube for flow control.

The capillary can be added on several or all of the inlet paths of the MPHX, and the MPHX can have refrigerant paths of any divergence or convergence.

All the geometric parameters of the simulated object and the inlet state of bothrefrigerant and air are known.

The goal of the simulation is to obtain the general performance of the simulation object and the temperature and air state of each part of the simulation object.

All paths of the simulated object are simply divided into two types--the main path (MP)

Subpath (SP)--

To describe the distribution of refrigerant conveniently.

MP refers to a set of paths with the same inlet tube and the same outlet tube, and theSP refers to a subpath in a MP.

All MPs in MPHXare are encoded [MP. sub. i]([M. sub. r,out], [p. sub. r,out],[h. sub. r,out], and [M. sub. r,1j](

Zhang, Ding 2004

This shows that the calculated deviation and temperature of the cooling capacity-

Calculation deviation of side pressure drop of MPHXusing R-GSSM

22 fewer [+ or -]10% and [+ or -]

20%, and the deviation of the single capillary model is within [range]+or -]15%.

Therefore, this paper does not verify the two models, only verifies the effect of the integrated model and algorithm in the extended GSSM.

In order to verify the extended GSSM of MPHX using capillary tubes for flow control, an experimental platform was set up and a series of experiments were designed and carried out.

The schematic diagram of the experimental device and the refrigerant circuit of the test coil are shown in figure 5.

The experimental conditions are shown in Table 1. [

Figure 5 Slightly]

The test system consists of four subsystems: wind tunnel, refrigerant circuit, air and refrigerant performance control system and data acquisition system. A variable-

The speed blower is used to control the airflow speed.

Control the temperature and humidity of the air in the temperature and humidity control room.

Measure the mass flow rate of air with a standard nozzle.

Measure the temperature of the air and refrigerator with T-type thermocouple.

The temperature measurement system was calibrated with a standard platinum resistance thermometer, and the uncertainty was [+ or -]0.

For the entire temperature range of 173, 05 K. 15-473. 15 K.

Mass flow speed of refrigerant measured with mass flowmeter with maximum error less [+ or -]0.

Within the full range of 0-12%200 kg. [h. sup. -1].

Refrigerant pressure is measured using an absolute pressure sensor with an error of less [+ or -]0.

0-full range 12%5 MPa.

The mass flow rate of refrigerant is regulated by pulse-

Electric expansion valve controller (EEV).

The enthalpy of the coil inlet refrigerant is determined by the measured pressure and temperature of the EEV inlet.

In order to prevent heat exchange with the surrounding environment, the air duct and connecting pipe are well insulated.

The cooling capacity is measured by the air enthalpy method, and the maximum error is less [+ or -]

0-full range 4%5 kW.

Experimental data in the air-side dry-

Bulbtemperature and wet

The bulb temperature of the enthalpy potential system reaches steady state.

By using the data acquisition system, the experimental data is collected every five minutes, and each group is collected in total.

So the average of 7-time-

The collected data is used as the actual experimental data.

The validation results of the extended GSSM compare the experimental data with the simulation results of the extended GSSM using the relationship between heat transfer and pressure drop in table 2.

The simulation results are compared with the experimental results.

Comparison of refrigeration capacity and refrigerant

Figure 6 and figure 7 respectively show the side pressure drop between the simulation and the experimental data, indicating that the difference between the calculated cooling capacity and the experimental cooling capacity is less [+ or -]

5%, while the difference between calculated refrigerants

The ratio of side pressure drop and experiment [small]+or -]15%. [

Figure 6 slightly][

Figure 7 Slightly]

Table 3 lists the calculated mass flow rate of refrigerant in each of the four test cases to demonstrate the difference between equal distribution cases modeled only for Heat Exchangers, and uneven conditions of heat exchangers using capillary tubes for flow control.

In four test cases, case 1 does not use test tubes, case 2 and case 3 use different capillary tubes on different paths, and the same total mass flow rate is the same as the case 1 and case 4. The refrigerant uses the same capillary as the case 3, and the total mass flow ratio of the refrigerant is 3.

In Table 3, the calculation results of Case 1 show that the refrigerant distribution in the heat exchanger is equal without using a capillary tube.

The calculation results of case 2 and case 3 show that changing the length or inner diameter of the capillary on different paths can control the refrigerant distribution between paths, the degree of uneven distribution of refrigerant decreases with the increase of capillary inner diameter.

The calculation results of case 3 and case 4 show that the degree of poor distribution of refrigerant increases with the increase of total mass flow of refrigerant.

Therefore, engineering designers can flexibly use extended GSSM to control the refrigerant distribution in MPHX by using different kinds of capillary tubes by considering the influence of capillary tubes on the distribution of refrigerant in the path.

Conclusion of solving heat equation by introducing two auxiliary equations

GSSM developed before (Liu et al. 2004)

For MPHX without capillary tubes, an improved MPHX model and algorithm for flow control using capillary tubes were developed.

The models and algorithms developed are suitable not only for MPHX capillary tubes for flow control, but also for MPHX without capillary tubes.

An experimental platform was established and a series of experiments were carried out on the heat transfer and pressure drop properties of the capillary heat exchanger used for flow control to evaluate the model and algorithm developed.

The evaluation results show that the difference between the calculated cooling capacity and the experimental cooling capacity is less [+ or -]

5%, while the difference between calculated refrigerants

The ratio of side pressure drop to experiment [small]+ or -]15%.

Using different capillary tubes on different paths helps to control the refrigerant distribution between MPHX paths.

This study theoretically helps to model MPHX using capillary tubes for flow control and other multi-online systems such as multi-Online home refrigeration systems.

In Engineering Practice, relevant software allows users and designers to flexibly analyze the performance of MPHX using a capillary tube for flow control, and analyze the performance of traditional non-capillary MPHX. NOMENCLATURE [A. sub. o]

= Total surface area of air side ,[m. sup. 2][A. sub. i]

= Surface area of inner tube ,[m. sup. 2]

Therefore, it is assumed that the refrigerant flow in the capillary has not cooled.

Calculate the mass flow rate of blocked refrigerant based on the following criteria :[dL. sub. cap]/[dp. sub. r,cap]= 0 (A1)-d[p. sub. r,cap]= [G. sub. r,out,cap. sup. 2](1/[[rho]. sub. r,out,cap]-1/[[rho]. sub. r,in,cap])+[[[f. sub. m][G. sub. r,out,cap. sup. 2]/[2d. sub. cap][[rho]. sub. r,m,cap]]]d[L. sub. cap](A2)

The refrigerant flow in the tube is considered 1-

The axial flow of the dimension and the axial conduction along the tube are ignored.

The energy conservation equation of refrigerant flow in the tube is as follows :[Q. sub. 1r]= [Q. sub. 2r](A3)Where [Q. sub. 1r]= [M. sub. r]([h. sub. r,in]-[h. sub. r,out])(A4)[Q. sub. 2r]= [[alpha]. sub. r][A. sub. i]([[T. sub. r,in]+[T. sub. r,out]]/2 -[T. sub. wall])(A5)where [[alpha]. sub. r]

Calculated based on selected empirical correlations.

The continuity equation of refrigerant flow in the tube is as follows :[G. sub. r,out]= [G. sub. r,in](A6)

The momentum conservation equation of refrigerant flow in the tube is as follows :[[DELTA][p. sub. r,tube]]= [[DELTA][p. sub. r,f]]+[[DELTA][p. sub. r,acc]](A7)where [p. sub. r,f]and [p. sub. r,acc]

Calculated based on the selection correlation.

The energy conservation equation of air is as follows :[Q. sub. 1a]= [Q. sub. 2a](A8)Where [Q. sub. 1a]= [M. sub. a]. ([h. sub. a,in]-[h. sub. a,out])(A9)[Q. sub. 2a]= [[alpha]. sub. a][A. sub. o][[eta]. sub. o]([[[T. sub. a,in]+[T. sub. a,out]]/2]-[T. sub. wall])(A10)

[Where is the air quality flow]M. sub. a]

Calculation based on the upstream control volume of the front row; [[alpha]. sub. a]

Calculated from selected empirical correlations.

The continuity equation of air is as follows :[G. sub. a,out]= [G. sub. a,in](A11)

The momentum conservation equation of air is as follows :[[DELTA]p. sub. a]]= [[DELTA]p. sub. a, fin]]+ [[DELTA]p. sub. a,tube]](A12)where [p. sub. a,fin]is the air-

Decreased side pressure due to surface reasons; [p. sub. a,tube]is the air-

Side pressure is down due to tubesurface.

Energy conservation equation of finsand-

The tube is as follows :【Q. sub. 1r]+ [Q. sub. 1a]+ [Q. sub. cond]= 0 (A13)[Q. sub. cond]= [Q. sub. front]+ [Q. sub. back]+ [Q. sub. top]+[Q. sub. bottom](A14)where [Q. sub. cond]

Is the total heat conduction of fins; [Q. sub. front], [Q. sub. back], [Q. sub. top], and [Q. sub. bottom]

Heat conduction from the nearest front, rear, upper and following fins, respectively.

For coils with divergence or convergence, in order to determine the inlet state parameters of refrigerant in the downstream branch, the governing equation of divergence or convergence point is required.

No equations 10, 12, 13 are used.

After replacing \"1\" with \"I\", I divergent flow, the following equation is used for No

I confluence :[M. sub. r,i]= [m. [Sum up (