The Use of CFD to Improve the Thermal Comfort in the Automotive Field Lombardi G., Maganzi M. Department of Aerospace Engineering of Pisa, Italy

Cannizzo F., Solinas G. Ferrari S.p.A. – Maranello (Mo), Italy

ABSTRACT

The general aspects of thermal comfort are discussed in order to define a thermal comfort index. In this way, a more rational approach to the problem, moving from a “qualitative” evaluation to a “quantitative” one, is obtained. Aerodynamic evaluations are required, in particular the velocity and temperatures fields. From this point of view, an experimental approach appears difficult and the real car must be tested. Obviously, testing a real car using experimental methods presents problems in terms of making modifications to improve comfort. Therefore, a CFD approach, using FLUENT, appears to represent a significant improvement. The more important aspects related to the evaluation of the thermo-fluidodynamics field in the cockpit, taking into account thermal exchanges, convection, conduction, radiation and solar load, are described. Finally, the CFD results are compared with a dedicated experimental campaign. Results appear satisfactory, both for the flow characteristics and the indices evaluation. The use of thermal comfort indices appears a powerful tool to improve car thermal comfort, and, by using CFD, it can be applied to any phase of the design.

1. INTRODUCTION

Thermal comfort is now an important feature for customers when choosing a car. It has assumed a crucial role in automotive design, which has influenced Ferrari to conduct research in this area. Many disciplines are involved in this area of research, but aerodynamics is the fundamental one. The first part of the research, in cooperation with the Department of Physiology at the University of Pisa, has been devoted to the general aspects of thermal comfort, in order to define one or more, comfort indices. The definition of these indices leads to a more rational approach to the problem - the aim being to shift the consideration of thermal comfort from a qualitative standpoint to a quantitative one by the definition of a numerical comfort index. The fundamental aspects of the index definition are related to aerodynamics; in particular, the velocity and temperatures fields must be evaluated. An experimental approach is very

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difficult because of the low velocities and small variations in temperature that have to be measured, and, mainly, because these fields are highly related to Reynolds number and geometric details. Therefore, it is not possible to use a scale model; instead it is necessary to test a real car. Obviously, using an experimental approach, it could be very difficult to make modifications to improve comfort. A CFD approach in the design phase, using FLUENT, appears to represent a significant improvement on experimental methods. In the paper described, the more important aspects related to the evaluation of the thermo-fluidodynamic field in the cockpit, taking into account thermal exchanges, convection, conduction, radiation and solar load. Finally, the CFD results are compared with a dedicated experimental campaign, carried out in the thermal Wind Tunnel on the Ferrari 599.

2. THE APPROACH TO THERMAL COMFORT

Comfort is not a measurable quantity, but a subjective perception, different for each person, that is a response to objective situations. Therefore, it is evident that a rigorous definition of comfort cannot be given. There are several qualitative definitions for comfort; “a state of mental satisfaction related to a corrected psychophysical equilibrium”, for instance, gives a clinical representation of the problem. The European standard rules give a precise, but qualitative, definition of thermal comfort: “psychological satisfaction status relating to the thermal environment” (Ref. 1). In literature there are many papers about thermal comfort, mainly derived by the Fanger theory (Ref. 2), but related to civil situations (offices, theatres, airports, etc.). The specific problem of thermal comfort in the cockpit has been seldom treated. Fanger defines an acceptable thermal condition as a situation in which thermal discomfort is not felt, and this definition can be assumed as a reference, taking into account that the discomfort level in a car cockpit cannot be as low as in a civil environment. Thermal comfort is a result of physiological behaviour, even if the thermo-aerodynamic aspects are preponderant for a quantitative evaluation. A scheme of the problem is shown in Fig. 1.

Fig. 1 – Scheme of thermal comfort aspects

2.1 Physiological aspects The aspects of thermal comfort related to the physiological responses to the environmental situation were analysed with the Department of Physiology at the University of Pisa (Ref. 3). This activity has been devoted to the general aspects of thermal comfort, in order to define one, or more, comfort indices, as shown in the following arguments.

Environment

Man

Judgment

Stimuli

PhysiologyCOMFORT

INDEX

Aerodynamic

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The psychophysics is currently based on Stevens theory: “the correlation between the stimulus intensity and sensation intensity in the human sensorial can be described by an exponential law”, of the type:

ak 0 (1)

where k is a constant depending on the stimulus scale, is the stimulus level, 0 is the stimulus threshold level and a is an exponent depending on sensorial and stimulation conditions. Furthermore, according to the “theory of adaptation level”, the exposition produces an adaptation level, and the “score” is not referred to as an absolute level, but to the adapted one: obviously, this aspect increases the complexity of a quantitative representation of comfort. The temperature of the human body is kept constant by means of the equilibrium between the production and dispersion of heat. In equilibrium conditions, the heat production related to the metabolism must be equal to the heat flux from the body surface to the environment. The energy balance of the human body can be deduced by the first principle of thermodynamics in its application to the typical situation of a car. It runs as follows:

M - CRES - ERES – C – R – S - ED = (2)

where: M = Metabolic energy CRES = Heat dissipated in the respiration phase ERES = Energy dissipated by evaporation in the respiration phase C = Heat by convection on the body surface (with the clothes) R = Heat by irradiation on the body surface (with the clothes) S = Heat exchanged by means of transpiration ED = Energy dissipated by evaporation from the skin (diffusion)

= Energy unbalance

Thermal sensors are the thermal interface between the human body and the external environment: cold spots for the lower temperature and warm spots for the higher temperature. An important aspect is that their surface density is different for different zones of the skin; an indicative distribution is reported in Table 1, derived from Hensel (Ref. 4), Strughold and Porz (Ref. 5) and Rein (Ref. 6).

Spots SpotsHuman skin Warm Cold Human skin Warm ColdForehand 5,5-8,0 Back of Hand 7,4 0,5 Nose 8 1 Palm of Hand 1,0-5,0 0,4 Lips 16,0-19,0 Finger Dorsal 7,0-9,0 1,7 Other Parts of Face 8,5-9,0 1,7 Finger Ventral 2,0-4,0 1,6 Chest 9,0-10,2 0,3 Thigh 4,5-5,2 0,4 Abdomen 8,0-12,5 Calf 4,3-5,7 Back 7,8 Back of Foot 5,6 Upper Arm 5,0-6,5 Sole of Foot 3,4 Forearm 6,0-7,5 0,3-0,4

Table 1 - Number of warm and cold spots per square centimetre in human skin

From the data of Tab. 1 and the typical surface area of each element, it is possible to obtain the thermal sensitivity factor for the different part of the human body. Data (from Crawshaw, Ref. 7) are presented in Tab. 2, showing the area, the sensitivity to both warming and cooling, and the thermal sensitivity mean value, TSK.

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Clearly, clothes modify these basic values. The thermal characteristics of clothes can be obtained by measurements on articulated mannequins using thermally controlled cameras (data are shown, for instance, in Ref. 8).

Area weight Sensitivity to warming

Sensitivity to cooling TSK

Face 0,07 0,21 0,19 0,20 Chest 0,09 0,10 0,08 0,09 Upper Back 0,09 0,11 0,09 0,10 Abdomen 0,18 0,17 0,12 0,145 Upper Legs 0,16 0,15 0,12 0,135 Lower Legs 0,16 0,08 0,15 0,115 Upper Arm 0,13 0,12 0,13 0,125 Lower Arm 0,12 0,06 0,12 0,09 Total 1 1 1 1

Table 2 – mean skin temperature TSK weighting factors

2.2 Aerodynamic aspects From the aerodynamic point of view it is necessary to evaluate the flow characteristics, in terms of velocity and temperature fields, in the car cockpit, taking into account that some aspects appear particularly important and critical to evaluate:

Large glazing surfaces Important heat exchange with the external field Direct solar irradiance Small volume of the cockpit Important, hot or cold, air flow in the cockpit, originating from a limited number of

small surfaces It is clear that an experimental approach in a scale wind tunnel is practically impossible, because of the complexity of correctly simulating the thermo-aerodynamic flow in the cockpit. Indeed, the flow is characterized by low values of the velocities and important thermal effects, and both these aspects are highly dependent on the Reynolds number and geometrical details. Furthermore, the thermal characteristics of the different elements, in term of material (glass, plastic, alloy, etc.) and dimensions, can strongly affect the thermo-aerodynamic aspect of the flow. Therefore, an experimental evaluation of the required thermo-aerodynamic quantities can be obtained only by testing a real car, with a completely defined representation of the air inlet system and of the geometric details of the elements in the cockpit. Clearly, this is possible only when a car prototype is available, at the end of the design phase. This aspect reduces the capability of the proposed approach, since only a final evaluation seems possible and, at this point, it would be very difficult to propose some modifications to improve the quality of the thermal aspects at this point. In order to highlight the capabilities offered by the present approach a CFD analysis is therefore required. In this way, in fact, the evaluation of the thermal comfort characteristics can be carried out in each phase of the design, giving the possibility: a) to modify the elements of the air system following the indications of the numerical evaluation, and b) to test and optimise the thermal design of the cockpit of the car. It is evident that for a corrected evaluation it is necessary to consider all the involved aspects: flow field, thermal aspects in terms of conductivity, conductibility, irradiation and solar load. The code FLUENT, currently used both at DIA and Ferrari, is able to take into account all these aspects. Therefore, it was decided to analyse the capabilities of FLUENT to evaluate the quantities involved in thermal comfort and to verify the accuracy of the results, in order to define a numerical procedure for the evaluation of the comfort index, defined in paragraph 3. This part of the activity will be described in paragraph 4.

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3. DEFINITION OF THE COMFORT INDEX

The definition of an index to quantify thermal comfort in the cockpit is a quite complex matter. In fact, it is necessary to take into account several quantities influencing thermal comfort. Furthermore, these quantities are not homogeneous, giving the problem of correlating quantities of different dimensions, physical meanings and impact levels on thermal comfort. In the present paper, according to the indications of literature and the experiences in Ferrari, the index is considered to be a derivative of the following four fundamental contributions:

The global thermal equilibrium of the body (IE) The discomfort related to the draught (IG); The vertical gradient of temperature (IVT); The horizontal gradient of temperature (ILT);

The single indices are evaluated on a scale from 0 to 10 (see the following paragraphs for a more complete description of the single indices). To determine each single index two conditions are considered:

Optimum thermal comfort level I = 10 (3.a) Sufficient thermal comfort level I = 6 (3.b)

The value of the single index is then determined, following Eq. 1, by an exponential law. The global thermal comfort index, IT, is then evaluated by means of a weighted mean:

IT = ( K1 IE + K2 IG + K3 IVT + K4 ILT ) / 4 (4)

where the weights ki arise from the analysis, based on experiences on existing cars, of the correlation between the single contribution index and thermal comfort.It is worth noting that both the definition of the control conditions (Eqs. 3) and the weightings (Eq. 4) could be changed for different conditions and cars; this is clearly an advantage, because the contributions to the general comfort of the fundamental aspects can be different for different operative conditions (season, car “mission”, passengers’ expectations, etc) or for different cars. It is also important to observe that the analysis of the results in terms of comfort index cannot be based only on the value of the global index IT: in fact, to have a satisfactory behaviour, all the four basic indices must be “sufficient”, and a low value in the standard deviation of the four single indices is preferred. In the following paragraphs a brief description of the four basic indices will be given.

3.1 The global thermal equilibrium of the body (IE)By assuming for an “optimal” condition (Eq. 3.a) the equilibrium condition, =0, and for a “sufficient” condition (Eq. 3.b) the condition corresponding at non equilibrium condition with an energy flux =15 W/m2, following Eq. 1, we obtain the exponential law:

IE = 10 exp ( - 0.034065 ) (5)

Represented, as an example of a single index, in Fig. 2.

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30 40 50 60 70 80 90 100

I E

Fig. 2 –Values of the energy equilibrium index for the assumed condition

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Eq. 2 expresses the energy balance of the human body. The terms in this equation can be evaluated (from Refs. 1, 9 and 10, see Ref. 2 for a deeper analysis) with the following relations:

)641,0885,056,28(00152,0 AaRES ptMC (6) )63,1153,034,59(00127,0 AaRES ptME (7)

AclclC ttfhC (8) clmrclr ftthR (9) 15,5842.0 MS (10)

)99,65733(1005,3 3AD pME (11)

while the metabolic term, M, can be obtained by Tab. 3 (Ref. 11):

Driven activity W m-2

Car in Relax 60 Car in Heavy Traffic 115 Heavy Truck 185

Tab. 3 – Typical metabolic energy for driving activity

3.2 The discomfort related to the draught (IG)The discomfort related to the draught is, in effect, caused by the temperature variation produced by the guests. The thermal energy lost depends on the temperature, the mean velocity, the turbulence level and the frequencies involved. Furthermore, higher turbulence levels produce higher discomfort, also with the same energy lost. The standard European rules (Ref. 1) give, based on statistical evaluations, the percentage of unsatisfied people (DR):

14,337,005,034 62,0 TuvvtDR AiAiAii (12.a) Tu = 100 * SD/va (12.b)

where ta is the air temperature [°C], va is the mean velocity [m/s] and SD is the Standard Deviation of the velocity. The measurement is on a period of 3 minutes. Obviously, the gust related to an airflow is evaluated in relation to the more critical zones of passengers, usually those without the protection of clothing. The values are weighted, for the different zones, following the data of Tab. 2. Clearly, zero number of unsatisfied people is assumed as the optimum condition and, following Ref. 1, DR=15% is assumed as the sufficient value. By these values it is possible to obtain the exponential law for the draught index IG.

3.3 The vertical gradient of temperature (IVT)The control points for the vertical gradient of temperature are usually assumed at the lower and higher positions, that being the ankles and face. From the European standard rules (Ref. 1) 95% of people are satisfied within a temperature difference of 3°C. Therefore, a difference of 3°C is assumed as the sufficient condition and, obviously, a zero difference is assumed as the optimum condition. By these values it is possible to obtain the exponential law for the vertical gradient of temperature index IVT.

3.4 The horizontal gradient of temperature (ILT)The control points for the horizontal gradient of temperature are assumed to be the seat edges. The same gradient determined in par. 3.3 is assumed as the sufficient condition and,

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again, a zero difference is assumed as the optimum condition. By these values is possible to obtain the exponential law for the vertical gradient of temperature index IHT.

4. THE AERODYNAMICS EVALUATION

In a preliminary phase of the research the capabilities offered by FLUENT (version 6.2.16) have been analysed, and the problems related to the evaluation of the flow characteristics in the car cockpit, both without and with thermal effects, have been studied. The results of this activity, described in Ref. 12, were satisfactory, and give the fundamental information about the set-up of the thermo-fluid dynamic evaluations. The quantities involved in the thermal comfort index are the velocity, the temperature (air and surfaces) and the irradiation temperature.

4.1 The Hardware The computer, a Linux Cluster made of 32 “AMD Opteron 280 Dual Core” nodes, each node having 8 Gb of RAM, has been supported by AMD. This configuration gives the capability of solving the complex thermo-aerodynamic problems with a reasonable computer time (about 10 hours for 20.000 iterations).

4.2 The numerical procedure The numerical procedure is described in detail in Ref. 13. In order to reduce the complexity of the numerical problem, in this phase of the project only the cockpit is represented. Therefore, the thermal effects related to the external flow are lost. The considered car is the Ferrari 599: in Fig. 3-a the cockpit is represented, while in Fig. 3-b a CAD representation (Questa imagine è di GAMBIT) of the cockpit is shown, with the mannequin used seated in the driving position.

a) the real car b) the CAD representation

Fig. 3 – The cockpit of Ferrari 599

The grid is non-structured, with about 3.4 million tethrahedrical elements. The mean skewness is 0.333, with a maximum value of 0.874. The grid is divided into 18 elements, in order to impose different conditions in terms of material characteristics and boundary conditions.

The steady solution is obtained with the coupled-implicit approach. After a sensitivity analysis (Ref. 14) a k- �turbulence model is used, with a non-equilibrium wall function treatment. As to the conduction effects, the material properties are assigned as alloy for the car faces, glass for the windows, plastic for the dashboard and leather for the seats. The convection is activated on the windows. For the radiation problem, five different models can be found in FLUENT. They were analysed in Ref. 13, and the DO Radiation Model was considered suitable for the present problem, coupled with DO Irradiation Solar Load Model for the solar

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load. Inlet conditions are imposed at the outlets of the air-conditioning ducts (in yellow in Fig. 4-a) in terms of mass flow rate and temperature. These values can be obtained by experimental data (as for the evaluations discussed in the following) or by a specific numerical analysis on the flow in the ducts (Ref. 15). A pressure outlet condition is given at the exhaust holes (in red in Fig. 4-b).

a) Inlet b) outlet

Fig. 4 – The air inlet and outlet in the cockpit of Ferrari 599

4.3 Experimental verification A dedicated experimental campaign was carried out in the air-conditioned Ferrari wind tunnel. It is essentially used for thermal tests on the car components (brakes, radiator, air duct, etc) and to evaluate the air conditioning system. The main characteristics are reported in Tab. 4.

Test section 3.2 x 1.7 m Dynamometer For front, rear, four- wheel drive

Air Speed 0 – 180 Km/h Rollers Diameter 1.9 m Fan Power 460 Kw Max Speed 400 Km/h Temperature Range 5 – 55 °C Max Power 595 Kw Relative Humidity 30 – 95 % Pressure Channels 96 Velocity Distribution ± 1% Temperature Channels 173 Temperature Uniformity ± 0.3 °C Simulated Solar Load up to 1300 W/m2

Tab. 4 – Ferrari Air-conditioned Wind Tunnel characteristics

The car is a Ferrari 599, with the driver on the right side. Two conditions were analysed (Tab. 5): a warming and a cooling condition. For the latter the solar load in the wind tunnel was activated.

Test Warming condition Cooling condition Car Speed 60 km/h 60 km/h External Temperature 10° C 30° C Solar Load NO 900 W/m^2 Required Temperature 22° C 18° C

Tab. 5 – Test Conditions

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As previously indicated, an important advantage of CFD is the knowledge of the complete fields. As an example, the velocity field for warming conditions is represented in Fig. 5. It is plain to see how important this type of information is: it becomes possible to obtain a clear idea of the flow typology, as well as indications as to the problems and their solution, too.

Fig. 5 – CFD flow field in the cockpit of Ferrari 599

By analysing Fig. 5, for instance, it is evident that the velocities are low; the velocities are characterised by high gradients and important variation in their direction. Therefore, it is difficult to compare experimental and CFD results in terms of velocity: the experimental measurements are critical, and characterised by a low level of accuracy.

4.3.1 Warming condition As an example, the temperatures evaluated by CFD are represented in Fig. 6 for two planes.

a) cross plane b) horizontal plane

Fig. 6 – Temperature field in the cockpit (°K, warming condition)

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The comparison with the experimental results is shown in Tab. 6.

Car elements CFD Exp. Driver CFD Exp. Left fore window 285.6 286.7 Head 291.9 293.0 Right fore window 287.9 287.6 Right shoulder 290.5 294.8 Left rear window 286.3 286.6 Left shoulder 291.7 294.9 Right rear window 286.3 287.2 Right knee 289.1 290.6 Windshield (left side) 284.5 285.2 Left knee 288.9 290.3 Windshield (right side) 286.2 286.2 Right foot 289.2 290.5 Left door 287.0 293.3 Left foot 289.0 290.0 Right door 288.0 294.0 Chest 290.0 292.0 Car top 290.5 293.3

Tab. 6 – CFD versus Experimental temperatures (°K, warming condition)

By analysing Tab. 6 it appears there is a satisfactory correlation (though not definitely adequate) between experimental and numerical data. This correlation could be considered satisfactory because of the problem presented by the high gradient, causing a strong influence of the position of the measurement points. Nevertheless, significant differences appear for the elements of the car that are alloy: this is probably caused by the presence, in the experiment, of thermal panelling, something not considered in the CFD evaluation. Another aspect to take into account is that the external flow is not represented. This could represent a source of uncertainty. The velocities in the same planes are represented in Fig. 7. It is worth noting the high values in the zones corresponding to the air inlets.

a) cross plane b) horizontal plane

Fig. 7 – Velocity field in the cockpit (warming condition)

4.3.2 Cooling condition This is the most critical condition. A direct irradiation is present, and the solar model must be considered in the CFD evaluation. The temperatures evaluated by CFD are represented in Fig. 8 for the same two planes.

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a) cross plane b) horizontal plane

Fig. 8 – Temperature field in the cockpit (cooling condition)

The comparison with the experimental results is shown in Tab. 7. In this condition the correlation appears to be less satisfactory. This could be related to the “glasshouse effect”, which is present in the experiment and not well represented in the numerical model used. The velocities in the same planes are represented in Fig. 9. It is interesting to note the high values in the zones corresponding to the air inlets, and the important curvature of the flow around the head of the driver.

Car elements CFD Exp. Driver CFD Exp. Left Fore Window 296.5 296.0 Head 286.4 290.4Right Fore Window 296.4 297.3 Right Shoulder 285.6 287.5Left Rear Window 297.0 296.0 Left Shoulder 285.8 288.5Right Rear Window 296.8 297.3 Right Knee 288.5 290.0Windshield (Left Side) 298.7 298.0 Left Knee 288.8 290.2Windshield (Right Side) 298.6 300.2 Right Foot 292.2 293.7Left Door 287.4 291.2 Left Foot 291.8 294.0Right Door 286.8 290.5 Chest 287.0 289.0Car Top 287.0 294.8

Tab. 7 – CFD versus experimental temperatures (°K, cooling condition)

a) cross plane b) horizontal plane

Fig. 9 – Velocity field in the cockpit (°K, cooling condition)

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5. EVALUATION OF THE THERMAL COMFORT INDEX

The thermal comfort index can now be evaluated, from both the experimental and numerical data. By applying the procedure described in par. 3, the results shown in Tab. 8 are obtained. At this stage of the study, the contribution of the different terms is assumed in Eq. 4, K1= K2= K3= K4=1.

Warming Cooling Exp. CFD Exp. CFD Global Thermal Equilibrium of the Body, IE 6.72 6.16 6.87 7.93 Discomfort Related to the Draught, IG 4.46 6.08 3.96 3.87 Vertical Gradient of Temperature, IVT 6.31 6.88 5.42 5.42 Horizontal Gradient of Temperature, ILT 9.76 7.47 9.53 7.84 Global Thermal Comfort Index, IT 6.81 6.64 6.26 6.44 St. Dev. 1.90 0.57 1.67 1.96

Tab. 8 – Thermal comfort indices

The correlation between experimental and numerical data appears satisfactory, with more significant differences in the local indices, related to the difficulty in the gradient evaluation, especially from experimental data.

From the design standpoint, data indicates a sufficient thermal comfort in general terms, but some effects appear to suggest a level of discomfort. This aspect is related to the particular setting of the air inlet, and thermal comfort has been significantly improved with a different set-up.Clearly, the analysis of the comfort level from the indices will be significantly improved when a database with a large number of different cars and conditions will be available.

6. CONCLUSION

The definition of thermal comfort indices leads to a more rational approach to the problem, shifting the approach from a “qualitative” evaluation (the tester’s subjective opinion) to a “quantitative” one (the numerical value of the index). The fundamental aspects of the index definition are related to the aerodynamic situation; in particular, the velocity and temperatures fields must be evaluated. An experimental approach is very difficult, because small variations and low levels of phenomena such as temperature and flow velocities have to be measured, and, mainly, because these fields are highly related to the Reynolds number and geometrical details. Therefore, it is not possible to use a scale model since a real car must be tested. Obviously, using this method it could be very difficult to make modifications to improve the comfort. The comparison of CFD results with experimental ones shows a satisfactory correlation, but the accuracy of the numerical results could probably be improved. In particular, it seems necessary to have more accurate results and to take into account also the external flow, that is not represented in the present evaluations. This could represent a source of uncertainty, and, in the next phase of the project a full evaluation will be done. Furthermore, the solar load model and the thermal characteristics of the isolation panels could be better represented. The defined procedure, by using CFD, gives important indications about thermal comfort from the initial phase of the design, and it can now be considered an important tool for the optimal design of the internal flow systems.

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ACKNOWLEDGEMENTS

The authors would like to express their gratitude to AMD for providing the cluster, M. Davini and A. Ciampa for their support during the project, Doct. Santarcangelo and Doct. Sebastiani for the fundamental support in the physiology aspects.

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