# modeling of a reversible air conditioning-heat pump system for electric vehicles.

by：NULITE
2019-08-20

Abstract: This paper presents a simulation model of reversible air conditioning and heat pump system for electric vehicles.

The system consists of a variable speed compressor, three micro-channel heat exchangers, an accumulator and two electronic expansion valves.

Solved by discrete the heat exchanger into a battery.

The compressor and Accumulator models are developed by fitting the data with physical insight.

The expansion valve is modeled by an equal enthalpy process.

System performance is calculated by connecting all parts in the same way as the physical system and solving them iteratively.

According to the experimental data of the individual experimental study, the model is verified reasonably.

Future improvements need to take into account the poor distribution in the outdoor heat exchanger working as an evaporator in HP mode.

Further research is also needed for component analysis.

Quote: Feng, L. and Hrnjak, P.

, \"Modeling of reverse air conditioning-

Heat pump system for electric vehicles, \"SAE Int. J. Passeng. Cars -Mech. Syst. 9(1):68-74, 2016.

Electric vehicles (EV)

It has become more and more popular in the past few years.

The waste heat generated by electric vehicles is not as good as the traditional internal combustion engine (ICE)cars.

Therefore, other heat sources need to meet the heating requirements of the cabin air.

Temperature coefficient ratio (PTC)

The heater, heat pump has a higher second law efficiency and can provide more heating capacity for the cabin by consuming the same power.

In addition, the heat pump function can be realized by adding only a few pumping parts to the mobile air conditioning system, which is usually installed on electric vehicles.

At present, some electric vehicle models, including Nissan Leaf, Renault Zoe, Kia Soul and BMW i3, are using heat pumps for cabin heating.

In a separate experimental study, a desktop heat pump system was built in the laboratory by using the same heat exchanger and system configuration as the Nissan Leaf heat pump system.

Figure 1 shows the system configuration and two working modes, and Figure 2 shows the component photos.

The performance of the system under various operating conditions, especially the heating function, is studied.

However, in the actual vehicle application, the heat pump system is operated in a large parameter space, and the detailed experimental cost covering the entire parameter space is high, and the time is tight. consuming.

Simulation tools based on existing experimental data can help to understand System Physics, performance under different operating conditions and system design modification to a large extent.

In this study, a steady-state simulation model was established to predict the system performance under different operating conditions.

The programming language used is the engineering equation solver (EES)

Built-

A function used to calculate the thermodynamic and transport properties of different operating fluids.

The refrigerant used is R134a.

The system model includes the compressor model, the accumulator model and the micro-channel heat exchanger model. The expansion valve is modeled by a simple isoenthalpy process and the supercooling of the condensate outlet is set to input.

The compressor model is a curve fitting based on the volume and isoentropy efficiency obtained from the experimental data.

The accumulator model is established to predict the suction steam quality of the compressor when there is liquid accumulation in the accumulator.

In the current state of study, the accumulator model was disabled due to the lack of good charge retention prediction in the assembly, and on the contrary, the suction mass of the compressor was arbitrarily set to 0.

The situation that represents reality.

A micro-channel heat exchanger model was established based on finite capacity built.

The heat exchanger is divided into small parts and calculated continuously with finite volume method.

In the system model, all components are connected with the pressure and enthalpy as the parameters of the connected state.

The exit attribute of the upstream component becomes the input attribute of the downstream component.

Iterative algorithm based on Newton-Newton

According to the Raphson method and stop criteria, the system is solved iteratively until no further modifications are required for all connection states.

In the literature, the term \"Compressor Model\" comes from a variety of different types of models, from pure physical models of compressor structural details to pure statistical models obtained entirely from experimental data, with no physical insight [1].

The physical model can better capture the properties of the compressor, but many details of the specific compressor need to be studied and cannot be easily promoted, so it is not suitable for the simulation of the refrigeration system.

The pure statistical model will be valuable for understanding how the system works.

In this study, a compressor model was established with statistical curve fitting based on a certain degree of physical understanding.

The following equation is used to correlate the volume efficiency of the compressor with the pressure ratio between discharge and suction.

The gap volume ratio and the compressed multi-party index are obtained by curve fitting.

Under the given suction state and the volume efficiency obtained, the refrigerant mass flow rate in the entire refrigeration circuit can be calculated. [

Mathematical expressions that cannot be reproduced in ASCII](1)

Another characteristic that the compressor model needs to determine is the discharge enthalpy of the compressor, which can be calculated with an appropriate isoentropy efficiency equation.

Compressor manufacturers usually provide equal entropy efficiency in the form of curve fitting.

In this study, the manufacturer equation was not available, whereas a large database was produced in the relevant experimental study.

Therefore, the isoentropy efficiency curve fitting is obtained from this database.

It is found that the linear curve fitting between the compression pressure ratio and the ratio of isoentropy efficiency to volumetric efficiency gives the best result.

Based on these two efficiency curve fittings, the refrigerant mass flow rate and compressor discharge state can be determined using the suction state and discharge pressure as input variables.

When implementing the system model, the discharge pressure needs to be given through the condenser model, which has an arbitrary outlet cooling level.

The original Nissan Leaf system of the accumulator model uses an accumulator at comprescycle to store additional refrigerant charges, especially in the heating mode, as it is found that the system\'s demand for charge is much lower than the cooling mode.

From the experimental study, in the heating mode, j-

The tube inside the accumulator is almost always soaked in the liquid, not only returning the oil to the compressor for suction, but also bringing some liquid to the compressor.

Through the heat loss of the calibrated compression casing, the inlet quality of the experimental compressor is obtained.

In order to model the accumulator, the liquid flow of the refrigerant and oil mixture is by J-tube.

There are three components of this differential pressure: dynamic pressure drop, friction pressure drop, and hydraulic pressure difference, as shown in the equation (2). [DELTA]P = [DELTA][P. sub. dyn]+ [DELTA][P. sub. f]+[DELTA][P. sub. hydr](2)

Dynamic terms calculated in the equation (3)

The difference between static pressure and dynamic pressure.

Since the liquid score is usually very low, this is through J-

Calculate the tube with total refrigerant mass flow. [

Mathematical expressions that cannot be reproduced in ASCII](3)

The friction term is obtained by using Churchill\'s single-phase friction coefficient Association [2]In the equation (4)and (5).

An improved Churchill association can be found in the literature3]

, And will be implemented in future studies to improve the prediction of evaporation pressure drop. [

Mathematical expressions that cannot be reproduced in ASCII](4)[

Mathematical expressions that cannot be reproduced in ASCII](5)

The hydraulic differential pressure is generated by the liquid level above the small hole in the accumulator and calculated by formula (6). [DELTA][P. sub. hydr]= [[rho]. sub. ref*f]g[h. sub. ll](6)

In the case of determining the total differential pressure, then by the balance between the viscous shear stress and the differential pressure in the equation, the liquid refrigerated mass flow rate through the small hole is calculated (7)

Let\'s assume a stable distribution of parabolic velocity.

Please note that when there is no liquid refrigerant gathering in the accumulator, or the liquid level is not high enough to reach J-

Tube, then in principle there will be no liquid into the compressor suction. [

Mathematical expressions that cannot be reproduced in ASCII](7)

The equation can now be used (8). [

Mathematical expressions that cannot be reproduced in ASCII](8)

Micro-channel heat exchanger model limited volume is the mainstream method of micro-channel heat exchanger modeling at present.

The heat exchanger is divided into short sections along the refrigerant flow circuit.

Starting from the inlet of the heat exchanger, the local heat transfer coefficient and friction coefficient on the refrigerant side are calculated with the inlet refrigerant state of each section to calculate the local heat transfer and pressure drop.

The outlet State of the paragraph is then determined by the loss of heat and pressure transmitted.

This export status becomes the import status of the downstream segment.

The computer program calculates each segment continuously until the outlet State of the heat exchanger is determined.

The total heat transfer capacity is only the sum of the heat transfer capacity of all parts.

By using the air inlet state for local heat transfer calculation, the above procedure works normally on the single board heat exchanger.

However, for more

Air inlet status of the downstream flat plate on the air side flat plate heat exchanger (s)

Depending on the downstream channel of the refrigerant side (es).

Iteration is required for this case.

The iteration starts with the air inletstate of all elements set to the air inlet state of the heat exchanger.

After each calculation from the refrigerant side inlet to the outlet, the air inlet state of the element on the downstream plate of the air side (s)

Update with the air output status of the corresponding upstream element.

Finally, the iteration ends when the refrigerant outlet State stops changing.

In this study, a finite capacity method was used for all three heat exchangers.

The following assumptions were made: 1.

Steady flow and heat transfer; 2.

Or the thermodynamic equilibrium indicated in other ways; 3.

Uniform distribution between parallel pipes; 4.

Ignore the heat transfer and pressure drop of the collector box; 5.

Ignoring the thermal resistance transmitted through the wall; 6.

The lubricant effect is not included in the current study; 7.

At present, there is no study on dewetting in the current stage of research.

The external geometry of all three heat exchangers is known.

Indirect measurement of the internal geometry of micro-channel tubes for outdoor heat exchangers by cross analysissection.

Through the external measurement, the internal geometry of the micro-channel of the evaporator and the internal condenser is obtained, and the pipe wall thickness, Port barrier thickness and port number are reasonably guessed.

When the heat exchanger can be turned on for measurements, these fault measurements will be updated in the future.

Each heat exchanger is divided into several elements of equal length.

Determine the number of elements by sensitivity analysis.

By doubling this number, the change in heat exchange capacity should be less than 0. 5%.

Solve heat transfer in each element by using [epsilon]-

NTU method with equation (9), (10), (11),(12). Equation (11)

Applicable to two-phase regions and equations (12)

Single phase area. [C. sub. min]

Minimum value of heat capacity flow on refrigerant side and air side, C is the ratio [C. sub. max]to[C. sub. min]. [

Mathematical expressions that cannot be reproduced in ASCII](9)[

Mathematical expressions that cannot be reproduced in ASCII](10)[epsilon]= 1-exp(-NTU)(11)[

Mathematical expressions that cannot be reproduced in ASCII](12)In Equation (9)

Using empirical associations in the literature, the heat transfer coefficient of the air side and the refrigerant side was obtained.

For the air side, there are blinds on all three heat exchangers.

King Changde 1996 [:4]

Calculation of heat transfer coefficient on air side selected correlation [htc. sub. air].

Calculation of Fin efficiency by equation (13)

Where L is fin length (

Or half of the pipe interval)

, P is the circumference of the fin crossingsection, and [A. sub. c]is fincross-sectional area. [

Mathematical expressions that cannot be reproduced in ASCII](13)

Total surface efficiency through the equation (14), where[A. sub. fin]and [A. sub. tot]

The air side heat transfer area and the total air side heat transfer area of the fin surface are respectively expressed.

Both are determined by geometric measurements. [

Mathematical expressions that cannot be reproduced in ASCII](14)

The pressure drop on the air side is calculated according to the program _ Yingchang and Wang 1996 [5]and Chang et. al. 1994 [6].

For the refrigerant side, different associations are selected depending on single-phase or two-phase, evaporation or condensation.

Formula for correlation coefficient of single phase, Gnielinski and Petukhovfriction [7]

Adopted in a volatile area of full development, where [Re. sub. D]

> = 3000 as standard.

However, since the hydraulic diameter of the flow channel is usually 1mm or less, the Reynolds number usually falls in the olaminar area, especially when the refrigerant is in a liquid state. Hence,when [Re. sub. D]

The system consists of a variable speed compressor, three micro-channel heat exchangers, an accumulator and two electronic expansion valves.

Solved by discrete the heat exchanger into a battery.

The compressor and Accumulator models are developed by fitting the data with physical insight.

The expansion valve is modeled by an equal enthalpy process.

System performance is calculated by connecting all parts in the same way as the physical system and solving them iteratively.

According to the experimental data of the individual experimental study, the model is verified reasonably.

Future improvements need to take into account the poor distribution in the outdoor heat exchanger working as an evaporator in HP mode.

Further research is also needed for component analysis.

Quote: Feng, L. and Hrnjak, P.

, \"Modeling of reverse air conditioning-

Heat pump system for electric vehicles, \"SAE Int. J. Passeng. Cars -Mech. Syst. 9(1):68-74, 2016.

Electric vehicles (EV)

It has become more and more popular in the past few years.

The waste heat generated by electric vehicles is not as good as the traditional internal combustion engine (ICE)cars.

Therefore, other heat sources need to meet the heating requirements of the cabin air.

Temperature coefficient ratio (PTC)

The heater, heat pump has a higher second law efficiency and can provide more heating capacity for the cabin by consuming the same power.

In addition, the heat pump function can be realized by adding only a few pumping parts to the mobile air conditioning system, which is usually installed on electric vehicles.

At present, some electric vehicle models, including Nissan Leaf, Renault Zoe, Kia Soul and BMW i3, are using heat pumps for cabin heating.

In a separate experimental study, a desktop heat pump system was built in the laboratory by using the same heat exchanger and system configuration as the Nissan Leaf heat pump system.

Figure 1 shows the system configuration and two working modes, and Figure 2 shows the component photos.

The performance of the system under various operating conditions, especially the heating function, is studied.

However, in the actual vehicle application, the heat pump system is operated in a large parameter space, and the detailed experimental cost covering the entire parameter space is high, and the time is tight. consuming.

Simulation tools based on existing experimental data can help to understand System Physics, performance under different operating conditions and system design modification to a large extent.

In this study, a steady-state simulation model was established to predict the system performance under different operating conditions.

The programming language used is the engineering equation solver (EES)

Built-

A function used to calculate the thermodynamic and transport properties of different operating fluids.

The refrigerant used is R134a.

The system model includes the compressor model, the accumulator model and the micro-channel heat exchanger model. The expansion valve is modeled by a simple isoenthalpy process and the supercooling of the condensate outlet is set to input.

The compressor model is a curve fitting based on the volume and isoentropy efficiency obtained from the experimental data.

The accumulator model is established to predict the suction steam quality of the compressor when there is liquid accumulation in the accumulator.

In the current state of study, the accumulator model was disabled due to the lack of good charge retention prediction in the assembly, and on the contrary, the suction mass of the compressor was arbitrarily set to 0.

The situation that represents reality.

A micro-channel heat exchanger model was established based on finite capacity built.

The heat exchanger is divided into small parts and calculated continuously with finite volume method.

In the system model, all components are connected with the pressure and enthalpy as the parameters of the connected state.

The exit attribute of the upstream component becomes the input attribute of the downstream component.

Iterative algorithm based on Newton-Newton

According to the Raphson method and stop criteria, the system is solved iteratively until no further modifications are required for all connection states.

In the literature, the term \"Compressor Model\" comes from a variety of different types of models, from pure physical models of compressor structural details to pure statistical models obtained entirely from experimental data, with no physical insight [1].

The physical model can better capture the properties of the compressor, but many details of the specific compressor need to be studied and cannot be easily promoted, so it is not suitable for the simulation of the refrigeration system.

The pure statistical model will be valuable for understanding how the system works.

In this study, a compressor model was established with statistical curve fitting based on a certain degree of physical understanding.

The following equation is used to correlate the volume efficiency of the compressor with the pressure ratio between discharge and suction.

The gap volume ratio and the compressed multi-party index are obtained by curve fitting.

Under the given suction state and the volume efficiency obtained, the refrigerant mass flow rate in the entire refrigeration circuit can be calculated. [

Mathematical expressions that cannot be reproduced in ASCII](1)

Another characteristic that the compressor model needs to determine is the discharge enthalpy of the compressor, which can be calculated with an appropriate isoentropy efficiency equation.

Compressor manufacturers usually provide equal entropy efficiency in the form of curve fitting.

In this study, the manufacturer equation was not available, whereas a large database was produced in the relevant experimental study.

Therefore, the isoentropy efficiency curve fitting is obtained from this database.

It is found that the linear curve fitting between the compression pressure ratio and the ratio of isoentropy efficiency to volumetric efficiency gives the best result.

Based on these two efficiency curve fittings, the refrigerant mass flow rate and compressor discharge state can be determined using the suction state and discharge pressure as input variables.

When implementing the system model, the discharge pressure needs to be given through the condenser model, which has an arbitrary outlet cooling level.

The original Nissan Leaf system of the accumulator model uses an accumulator at comprescycle to store additional refrigerant charges, especially in the heating mode, as it is found that the system\'s demand for charge is much lower than the cooling mode.

From the experimental study, in the heating mode, j-

The tube inside the accumulator is almost always soaked in the liquid, not only returning the oil to the compressor for suction, but also bringing some liquid to the compressor.

Through the heat loss of the calibrated compression casing, the inlet quality of the experimental compressor is obtained.

In order to model the accumulator, the liquid flow of the refrigerant and oil mixture is by J-tube.

There are three components of this differential pressure: dynamic pressure drop, friction pressure drop, and hydraulic pressure difference, as shown in the equation (2). [DELTA]P = [DELTA][P. sub. dyn]+ [DELTA][P. sub. f]+[DELTA][P. sub. hydr](2)

Dynamic terms calculated in the equation (3)

The difference between static pressure and dynamic pressure.

Since the liquid score is usually very low, this is through J-

Calculate the tube with total refrigerant mass flow. [

Mathematical expressions that cannot be reproduced in ASCII](3)

The friction term is obtained by using Churchill\'s single-phase friction coefficient Association [2]In the equation (4)and (5).

An improved Churchill association can be found in the literature3]

, And will be implemented in future studies to improve the prediction of evaporation pressure drop. [

Mathematical expressions that cannot be reproduced in ASCII](4)[

Mathematical expressions that cannot be reproduced in ASCII](5)

The hydraulic differential pressure is generated by the liquid level above the small hole in the accumulator and calculated by formula (6). [DELTA][P. sub. hydr]= [[rho]. sub. ref*f]g[h. sub. ll](6)

In the case of determining the total differential pressure, then by the balance between the viscous shear stress and the differential pressure in the equation, the liquid refrigerated mass flow rate through the small hole is calculated (7)

Let\'s assume a stable distribution of parabolic velocity.

Please note that when there is no liquid refrigerant gathering in the accumulator, or the liquid level is not high enough to reach J-

Tube, then in principle there will be no liquid into the compressor suction. [

Mathematical expressions that cannot be reproduced in ASCII](7)

The equation can now be used (8). [

Mathematical expressions that cannot be reproduced in ASCII](8)

Micro-channel heat exchanger model limited volume is the mainstream method of micro-channel heat exchanger modeling at present.

The heat exchanger is divided into short sections along the refrigerant flow circuit.

Starting from the inlet of the heat exchanger, the local heat transfer coefficient and friction coefficient on the refrigerant side are calculated with the inlet refrigerant state of each section to calculate the local heat transfer and pressure drop.

The outlet State of the paragraph is then determined by the loss of heat and pressure transmitted.

This export status becomes the import status of the downstream segment.

The computer program calculates each segment continuously until the outlet State of the heat exchanger is determined.

The total heat transfer capacity is only the sum of the heat transfer capacity of all parts.

By using the air inlet state for local heat transfer calculation, the above procedure works normally on the single board heat exchanger.

However, for more

Air inlet status of the downstream flat plate on the air side flat plate heat exchanger (s)

Depending on the downstream channel of the refrigerant side (es).

Iteration is required for this case.

The iteration starts with the air inletstate of all elements set to the air inlet state of the heat exchanger.

After each calculation from the refrigerant side inlet to the outlet, the air inlet state of the element on the downstream plate of the air side (s)

Update with the air output status of the corresponding upstream element.

Finally, the iteration ends when the refrigerant outlet State stops changing.

In this study, a finite capacity method was used for all three heat exchangers.

The following assumptions were made: 1.

Steady flow and heat transfer; 2.

Or the thermodynamic equilibrium indicated in other ways; 3.

Uniform distribution between parallel pipes; 4.

Ignore the heat transfer and pressure drop of the collector box; 5.

Ignoring the thermal resistance transmitted through the wall; 6.

The lubricant effect is not included in the current study; 7.

At present, there is no study on dewetting in the current stage of research.

The external geometry of all three heat exchangers is known.

Indirect measurement of the internal geometry of micro-channel tubes for outdoor heat exchangers by cross analysissection.

Through the external measurement, the internal geometry of the micro-channel of the evaporator and the internal condenser is obtained, and the pipe wall thickness, Port barrier thickness and port number are reasonably guessed.

When the heat exchanger can be turned on for measurements, these fault measurements will be updated in the future.

Each heat exchanger is divided into several elements of equal length.

Determine the number of elements by sensitivity analysis.

By doubling this number, the change in heat exchange capacity should be less than 0. 5%.

Solve heat transfer in each element by using [epsilon]-

NTU method with equation (9), (10), (11),(12). Equation (11)

Applicable to two-phase regions and equations (12)

Single phase area. [C. sub. min]

Minimum value of heat capacity flow on refrigerant side and air side, C is the ratio [C. sub. max]to[C. sub. min]. [

Mathematical expressions that cannot be reproduced in ASCII](9)[

Mathematical expressions that cannot be reproduced in ASCII](10)[epsilon]= 1-exp(-NTU)(11)[

Mathematical expressions that cannot be reproduced in ASCII](12)In Equation (9)

Using empirical associations in the literature, the heat transfer coefficient of the air side and the refrigerant side was obtained.

For the air side, there are blinds on all three heat exchangers.

King Changde 1996 [:4]

Calculation of heat transfer coefficient on air side selected correlation [htc. sub. air].

Calculation of Fin efficiency by equation (13)

Where L is fin length (

Or half of the pipe interval)

, P is the circumference of the fin crossingsection, and [A. sub. c]is fincross-sectional area. [

Mathematical expressions that cannot be reproduced in ASCII](13)

Total surface efficiency through the equation (14), where[A. sub. fin]and [A. sub. tot]

The air side heat transfer area and the total air side heat transfer area of the fin surface are respectively expressed.

Both are determined by geometric measurements. [

Mathematical expressions that cannot be reproduced in ASCII](14)

The pressure drop on the air side is calculated according to the program _ Yingchang and Wang 1996 [5]and Chang et. al. 1994 [6].

For the refrigerant side, different associations are selected depending on single-phase or two-phase, evaporation or condensation.

Formula for correlation coefficient of single phase, Gnielinski and Petukhovfriction [7]

Adopted in a volatile area of full development, where [Re. sub. D]

> = 3000 as standard.

However, since the hydraulic diameter of the flow channel is usually 1mm or less, the Reynolds number usually falls in the olaminar area, especially when the refrigerant is in a liquid state. Hence,when [Re. sub. D]