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INTRODUCTIONAutomobile air conditioning is more difficult than building HVAC (heating, ventilation, and air condition) problems in that, it is more susceptible to outside environment conditions. To better control automobile air conditioning, a better modeling of the associated thermal dynamics is needed, which, however, is a complex problem.
Several models on varying degree of system modeling accuracy have been proposed. Black-box method that represents input-output relations by fitting measurements was used; [1] studied ATC control strategy by modern control theory based on a simplified third order matrix by statistical identification method. As opposed to this black-box method that only depends on measurement data, the grey-box modeling approach is based on theoretical considerations and parameters obtained from measurements; [2] uses this grey-box approach to control air-handing units (AHUs) for constant air volume systems.
The objective of this study is to develop a climate environment model for the air distribution system and then to analyze its climatic characteristic affected by certain main operational parameters. In particular, this paper studies the dynamics of temperature and humidity of air in car compartment, especially their relationship to HVAC control variables of: fresh air ratio, hot air mix ratio, and flow rate of supply air in the circulation.
As a physical property that measures heat content of substances, enthalpy [3] [4] is used to estimate the amount of heat involved during air-conditioning processes. The concept of enthalpy is especially useful in the setting of automobile air conditioning where the thermal load in the car compartment is time-varying. Viewing automobile air
This work is supported in part by National Science Council, Taiwan under Grant NSC 96-2221-E-011-125 and in part by the Ministry of Education, Taiwan under Grant MOE 96-E-01-297
conditioning in the framework of enthalpy reduces the otherwise complexity involved in precise modeling. The changing thermal load in the space can be treated as the change of air enthalpy, which is properly determined by dry-bulb temperature and relative humidity.
The contribution of this study is to present an automobile climate environment model based on the air distribution system, which is used for investigating the air-conditioning process including cooling, dehumidification, heating and so on. Based on energy balance and mass conservation, the air-conditioning process can regarded as the change of specific enthalpy on the psychrometric chart. To be more precise, the difference of specific enthalpy between two thermal states of moist air can be separated into sensible heat change and latent heat change. As such, this property can be formulated as two mathematical equations for temperature as well as humidity ratio respectively. Then, by utilizing constant enthalpy and constant temperature properties, an evaluation for the two equations is performed within a computer simulation environment.
From the simulation results, there is an agreement on the two equations or the proposed automobile climate environment model. Furthermore, different control strategies can alternatively be slotted into such model so as to evaluate its cooling results.
This paper is organized as follows. In section 2, the characterization of an automobile air-conditioning system and its thermodynamic properties are introduced. The equilibrium condition for an exchange of heat is interpreted in section 3 and then the equation for a car climate environment is presented. Simulation results in section 4 shows the validation of the proposed model under two thermodynamic conditions.
Modeling of automobile air conditioning systems
Chung-Lun Li1, Shung-Luen Chung1, and Jing-Nang Lee2
1. Department of Electrical Engineering, National Taiwan University of Science and Technology, Taiwan E-mail: [email protected] [email protected]
2. Department of Refrigeration, Air Conditioning and Energy Engineering, National Chin-Yi University of Technology, Taiwan E-mail: [email protected]
Abstract: This paper studies the dynamics of temperature and humidity of air in a car compartment by the concept of enthalpy in analyzing the heat exchange involved. With heat change decomposed into sensible heat and latent heat, we are able to derive dynamics of temperature and humidity of the car compartment after taking into account of the difference of ASHF (apparatus sensible heat factor) and RSHF (room sensible heat factor). These two formulas are used in conjunction with two control strategies on flow rates of supply air to simulate the intended controlled car compartment at constant enthalpy and of constant temperature. The contribution of this work is to provide a framework for automobile air-conditioning analysis and simulation.
Key Words: automobile air-conditioning, enthalpy, HVAC
978-1-4244-2723-9/09/$25.00 c 2009 IEEE 985
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Characterization of an automobile HVAC systemThis section first examines the construct of an automobile air-conditioning. Special emphasis is elaborated on the working mechanism of various processes during a complete air-conditioning circulation cycle. Enthalpy changes corresponding to the different processes within a circulation cycle, especially their relation to the three control variables of: fresh air ratio, hot air mix ratio, and air flow rate, are explained in the context of thermal equilibrium state.
2.1 Automobile air-condition system
A typical automobile air-conditioning system composed of air-conditioning equipment, a passenger compartment, sensors, and an automobile temperature controller (ATC).
Fig. 1 the equipments of automobile air-conditioning system In order to maintain the climate in the car comfortable to passengers within the car compartment, three controls are installed: The first is the outside air intake control β ruling the percentage of fresh air and total air. The second is air mixing control α whose purpose is to get Ts by adjusting the air damper accordingly to mix heater temperature T with apparatus dew point temperature H T . E The last one is the air mass control that m (a kg sec) will alter automatically with several fan speed levels, depending on the degree of the thermal distribution behind the car compartment. In practice, β takes value of either 0.3 or 0.7; α ranges from 0 (no mix with hot air) to 1 (full percentage of hot air); and air flow rate m is variable air a amount.
To better illustrate the air-conditioning circulation process, Fig. 1 sketches a typical automobile air-conditioning system which is composed of a refrigeration system above and an air distribution system below. Six important positions during the air-conditioning process are particularly identified:
O: the source of outside fresh air suffering from the changeable weather.
M: the mixed air with outside air and re-circulated air E: the chilled air from evaporator
H: the hot air from heater sourced from a heat exchange of an engine
S: the supplying air prepared to enter the passenger compartment
R: the circulated air returned from the conditioned compartment
The refrigeration system chiefly consists of the following four components: an evaporator, a compressor, a condenser, and an expansion valve. The output of the evaporator (position E) is the chilled air that is prepared to mix with the hot air (position H) to obtain a suitable supplying air. The conditioned air, as the input of air distribution system, will then be supplied to the compartment. The supplying air will alter the temperature of the compartment, which is also subject to external disturbances such as the radiation of the sun and the convection around the passenger compartment. Under the influence of heat exchange, the resultant cooling effect causing at the air distribution system is the temperature difference between outlet (position S) and inlet air (position M).
2.2 Enthalpy
Enthalpy is used to measure the heat content of substances.
Het content can be divided into sensible heat and latent heat: roughly speaking, sensible heat reflects the temperature difference in the air; latent heat reflects the humidity change of the moisture in the air. To be more precise, according to ASHRAE fundamental handbook [4], the specific enthalpy of moist air h (kJ kg) equals to the sum of specific enthalpy of dir air hda and water vapor hv, as shown in (1).
( )
1.006 2501 1.805
da v
h h h
T T
ω ω
= + ×
= + + (1)
where ω is humidity ratio ( kg kg ).
We now determine the amount of exchanged heat of each process during a full cycle of air-conditioning circulation.
Based on the analysis here, we will derive the dynamics of temperature and humidity of the air in the car compartment in the next section.
The framework of the air distribution system, show as the solid rectangular box in Fig. 1, is redrawn in Fig. 2.
Fig. 2 air distribution system
The specific enthalpy difference hΔ of the mixed air provided by the air-conditioning equipments is the specific enthalpy change between position M and position S shown in Fig. 2, which can be written as equation (2).
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M S
h h h
Δ = − (2)
Equation (2) can be re-written as (3), using linear algebraic calculations with mass conservation and energy conservation.
( ) ( ) ( )
M S R E E H O R
h −h = h −h +α h −h +β h −h (3) Equation (3) shows that the specific enthalpy difference is determined by the given values of β and α , the percentage of outside air flow rate and the percentage of heating air flow rate in Fig. 1. In other words, the desired specific enthalpy difference hΔ can be obtained by adjusting the opening percentage of the dampers
( )
α β, .In terms of the cooling capacity provided by an HVAC mechanism, it is the product of the specific enthalpy difference hΔ and the air mass flow rate m . We call a Q e (kJ/ sec) the cooling capacity of the given HVAC system, as defined by equation (4).
( )
( ) ( )
( )
e a
a M S
a R E E H O R
Q m h
m h h
m h h α h h β h h
= × Δ
= × −
= ×
− + − + −
(4)
2.3 Psychrometric chart
To facilitate the enthalpy analysis, psychrometric chart [4]
is utilized, which a graphic tool expressing various properties of moist air under different combination of humidity ratio and dry-bulb temperature, as shown in Fig.
3-(a). With the psychrometric chart, it is easy to visualize how enthalpy changes for various processes during an air-conditioning cycle, such as heating or cooling processes, on the chart, as shown in Fig. 3-(b). Sometimes two or more of these processes are required to bring the air to a desired temperature and humidity ratio level, as shown in Fig. 4. The following discussions will focus on the interpretation of the change on specific enthalpy in the various processes involved in a complete circulation cycle, using a psychrometric chart.
Fig. 3 schematic for a psychrometric chart and air-conditioning processes
With back reference to the six positions in Fig. 2, we now discuss how enthalpy changes at these positions during a complete cycle of air-conditioning process in Fig. 4-(a). In the beginning, outside air sourcing from position O is mixed with the re-circulated air sourcing from position R to get the mixed air (position M). The percentage of
mixing outside air is β . With the cooling and dehumidification (process M-E) process, the mixed air will be chilled and the specific enthalpy also will be decreased from hM to h . This process can be simplified into a E simple line of approximation, called ASHF (apparatus sensible heat factor).
In general, cooling capacity of the automobile air-conditioning equipment is sufficient, so this process always makes the air to reach a saturation temperature (at position E, at 4ć DB and 100% RH). When the chilled air is too cool to be supplied directly into the car compartment, it needs to be mixed with hot air or go through a heating process, parameterized by the percentage of heating air flow rate α , and then get the supplying air (position S). If the value of α doesn’t equal to zero, as shown in Fig.
4-(a), the heating process (process E-S) is represented by a horizontal line on the psychrometric chart since the humidity ratio remains unchanged. Finally, the supplying air into the car compartment will absorb heat and humidity so as to complete an air-conditioning cycle, which is the process S-R. Process S-R can be simplified into another line of approximation, RSHF (room sensible heat factor), and will be shown in Fig. 4-(b) and discussed later.
Fig. 4-(a) can be used to explain the continuing cooling process as long as the car compartment temperature T is R higher than the setting temperature TSS. With the initial cooling process starting at O, on the psychrometric chart, the initial cycle is completed when it traverses through R-M-E-S-R. With the expectation that R is getting closed to T at each cycle of circulation, the process will R continue until T gets closed enough to R TSS. While doing so, various parameters, such as T , R T , ASHF and S RSHF , are expected to be adjust and slightly different from previous cycle. At the end, the value of T almost R equals to that of TSS, which is the desired result of the air-conditioning procedure, as shown in Fig. 4-(b).
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Modeling of temperature and humidity in a car compartmentWe now analyze the equilibrium state of a circulation cycle where the cooling capacity Q of the HVAC cancels out e all the heat gains Qroom (kJ/ sec) added into the car compartment. In particular, balancing sensible heat between Qroom and Q leads to the dynamic modeling of e temperature of the air in the car compartment; similar balancing on latent heat leads to that of humidity. Validity of the derived dynamics formula is then checked by air flow rates derived by constant specific enthalpy and by constant temperature.
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Fig. 4 the air-conditioning analysis of Fig. 2 on the psychrometric chart
Fig. 5 a schematic diagram for heat transfer balance Suppose that the air-conditioning circulation reaches an equilibrium, or steady-state condition, as show in Fig. 5.
Given that the product of air flow rate and the difference of specific enthalpy equals to power, we conclude that the sensible, latent, and total power capacities of the circulation cycle are proportional to the differences in temperature, humidity ratio, and specific enthalpy, shown in Fig. 5. In particular, for sensible heat, the extracted sensible heat (TSH) by Q equals to the total sensible heat e gains by Qroom: sensible heater (SH), room (RSH), and ventilation (OSH), as expressed in (5). Similarly, as shown in (6), the extracted latent heat (TLH) equals to the sum of latent heat gains from room (RLH) and ventilation (OLH).
Table 1 shows their corresponding definitions.
TSH =SH +RSH+OSH (5)
TLH =RLH+OLH (6)
At equilibrium point, after a complete circulation, the temperature TRand humidity ω in the car compartment R will remain the same. However, variations on temperature TRand humidity ω will occur, if such equilibrium state R
is not attained: imbalance between the cooling capacity Q and heat gains e Qroom on either or both of sensible and latent heat gains.
Table 1 the definitions of symbols in Fig. 5
item Description scale
TSH total extracted
sensible heat
( )
( )
M E
a
M E
a p
ASHF m h h
m c T T
× −
= −
TLH total extracted
latent heat
( ) ( )
( )
1 a M E
M E
a fg
ASHF m h h
m h ω ω
− × −
= −
RSH room sensible heat
RSHF× Qroom
RLH room latent heat
(
1−RSHF)
× QroomOSH sensible heat gain
from ventilation
( )
( )
a p M R
a p O R
m c T T
m c T T
β
−
= −
OLH latent heat gain
from ventilation
( )
( )
a fg M R
a fg O R
m h m h
ω ω
β ω ω
−
= −
SH sensible heat gain
from heater
( )
( )
a p S E
a p H E
m c T T
m c T T
α
−
= −
where c is specific heat capacity of air p kJ (kg C , 0 ) hfg is specific enthalpy of vapor at saturation (kJ kg)
To facilitate our discussion, let’s assume that the total extracted sensible heat (TSH) exceeds that of the sensible heat gains, i.e., TSH >SH+RSH+OSH, then T will R decrease. On the other hand, if the total extracted latent heat (TSL) is more than that of latent heat gain, then ω R will decrease. To sum up, the variation of T can be R obtained from the relationship of sensible heat exchange, regardless of the latent heat exchange. Similarly, the
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variation of ωR is only depends upon the latent heat exchange. This conclusion will be utilized in the following discussion so as to formulate the two inherent characteristics of a car: T and R ωR.
The variation of T can be re-written as the following R equation (7): the item of m ca p
(
TR−TE)
represents the effective cooling capacity of Q at the given e( )
α β,combination. The effective cooling capacity is to offset the room sensible heat gains (RSHF× Qroom) and the sensible heat gain from heater (αm ca p
(
TH −TE)
). By the same token, the variation ofω
R can be re-written as equation (8). The two equations, (7) and (8), together model the thermal dynamics of the car compartment model.R
4
Modeling verificationTo verify a model formulated by equation (7) and (8), this section runs simulations under two different air flow rates m : one at constant enthalpy and the other at constant a
temperature. The simulation results shown next confirm the validity of the proposed dynamics for temperature and humidity, while revealing the difference between the two properties and constitute a conclusion for m . a
4.1 Derivation of air flow rates
The total heat transfer can be represented as the change of specific enthalpy between two states on the psychrometric chart. As shown in Fig. 5, the extracted heat can be expressed in terms of the mass flow rate m and the a decreased specific enthalpy (from state M to state E).
Meanwhile, the total heat gains correspond to the increased specific enthalpy which is contributed from heater (from state E to state S), room (from state S to state R), and ventilation (from state R to state M). At constant enthalpy, equations (5) and (6) are added together, and m a can be determined, as shown in (9):
( ) ( ) ( )
On the other hand, in order to main constant temperature, sensible heat transfer needs to be balanced, and m can be a derived from equation (5) to yield equation (10) below.
( )
4.2 Simulation results
Under the same initial simulation parameters, Fig. 6 and Fig. 7 show simulation results using constant enthalpy condition and constant temperature condition for m , a respectively. For the case of constant enthalpy, Fig. 6-(a) is the trajectory of the (temperature, humidity) state. Fig.
6-(d) shows that the specific enthalpy is kept at almost a constant. However, the compartment temperature T R keeps increasing, as shown in Fig. 6-(b). It is because, as shown in Fig. 6-(f), the extracting sensible heat capacity is not enough to remove the sensible heat gains: (RSHF×Qroom> ASHF×Q ). e
In contrast, if m is replaced with the one in equation (10) a to keep T constant, it is shown in Fig. 7-(a) and (b) that R the temperature T is kept approximately at a constant. R Moreover, as shown in Fig. 7-(c), the rate of extracting sensible heat capacity (ASHF× ) is greater than that of Qe sensible heat gains ( RSHF× Qroom ), so that the temperature T is maintained at approximately constant. R
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(a) simulation result (b) car compartment temperature T R (c) humidity ratio ωR
(d) specific enthalpy hR (e) total heat exchange (f) sensible heat exchange Fig. 6 the simulation results for equation (9)
(a) simulation result (b) car compartment temperature T R (c) sensible heat exchange Fig. 7 the simulation results for equation (10)
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ConclusionThe contribution of this work is to provide a framework for automobile air-conditioning analysis and simulation. With the temperature and humidity dynamics derived, effects of air conditioning under different control policies can be simulated in the proposed simulation environment and compared directly on psychrometric chart. Future work is to find an effective control strategy that will bring an arbitrary (temperature, humidity) state of the air in the car compartment to a desirable comfortable zone. In particular, when the car compartment temperature T is R not equal to the desired setting temperature TSS , the difference translates into an extra cooling load QΔ on the system.
REFERENCES
[1] T. Tabe, K. Matsui, T. Kakehi, and M. Ohba, Automotive climate control, IEEE Contorl Systems Magazine, Vol. 6, No. 5, 20-24, Oct.
1986.
[2] C. Ghiaus, A. Chicinas, and C. Inard, Grey-box identification of air-handling unit elements, Control Engineering Practive, Vol. 15, No. 4, 421-433, 2007.
[3] C.-M. Chu, T.-L. Jong, and Y.-W. Huang, A study of thermal comfort control using least enthalpy estimator on HVAC system, Proceeding of the American Control Conference, Vol. 5, 3665-3670, 2005.
[4] ASHRAE, ASHRAE Handbook-Fundamentals, Atlanta American Society of Heating, Refrigerating and Air Conditioning Engineers, Inc., 2005.
990 2009 Chinese Control and Decision Conference (CCDC 2009)
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