FLOW STRUCTURES AND HEAT TRANSFER IN A CAR CABINBY APPLICATION OF HUMAN THERMOREGULATION

S. Knochenhauer1, R. Kewitz1, J. Turnow1 and N. Kornev1

1 Institute of Modeling and SimulationDepartment of Mechanical Engineering and Shipbuilding

University of Rostockstefan.knochenhauer@uni-rostock.de

Abstract The heating, ventilation and air-conditioning device have become a favoured feature ofcustomers in automotive. Nowadays the challenge offurther development is not only the generation of a bet-ter comfortable climate in the passenger compartment.It has to collateral with the optimisation of energy ef-ficiency. Therefore, a better insight of the flow char-acteristics considering heat transfer in the car cabin isessential. A numerical approach (CFD) to this sub-ject can support the challenge of optimisation. Thesolutions of numerical simulations are analysed andpresented. For that the defrost- and panel-mode ofventilation for a car cabin are regarded. To considerreal conditions of heat transfer the heat emission bythe driver is simulated by the model of Fiala. As aresult different flow structure with a varying tempera-ture distribution can be observed. These induce a localvariation of the human skin temperature.

1 IntroductionThe subject of heating, ventilation and air-

conditioning (HVAC) of passenger compartments han-dles two crucial aspects, the aspect of traffic safety andthe aspect of passengers thermal comfort. Main pri-ority is the aspect of traffic safety. First of all, legalregulations have to be followed, which applies the de-frosting and defogging of the windshield. Secondly,thermal load of the driver shall be avoided to ensureroadworthiness, whereby this point also refers to theaspect of thermal comfort.

Thermal comfort is defined in ISO 7330 as the feel-ing, which represents contentment with the environ-ment. Thus it represents an equilibrium state betweenheat production of the human organism and the heatemission to its surrounding. However, thermal com-fort is a subjective feeling, which depends on the in-dividual state of acclimatization. Hence, a quantita-tive assessment is not that simply. However, the in-vestigation of Fanger [1973] show, that there are cli-matic states, which are perceived as being comfortableat 95% of the probands with the same physical stress.Even so thermal comfort is a subjective feeling, theinvestigation of Fanger shows that a uniform climatecondition, which represents thermal comfort can be es-

tablished.The improvement of occupant’s thermal comfort

has visibly gained in importance in the automotive sec-tor. Innovative solutions for best thermal comfort ofpassengers have already been developed early on in thesegment of luxury cars1. Today the automobile manu-facturers are looking for well thoughtful solutions evenfor city cars1. On the one hand for the purpose of mar-keting and on the other to satisfy the needs of the cus-tomers.

Below the vehicle segment of executive cars1 de-velopers are confronted with a comparatively lower in-stallation space. For constructive measures of air ven-tilation and additional HVAC systems the space supplyis very limited.

Additional systems lead to rising costs, both eco-nomic and ecological. Costs for acquisition and main-tenance are very important when it comes to decidefor the purchase of a car. Hence, additional systemsare not allowed to have an adverse impact on the pur-chase decision. From an ecological point of view maythe reduced pollutant emission due to the continualdevelopment of the combustion engines and the after-treatment of exhaust gases not be used up and possiblyinjured legal requirements.

In electric cars, i.e. purely battery-powered ve-hicles, the inconvenience of exhaust emissions doesnot exist, but instead the problem of power capac-ity. The small energy density of batteries in com-parison to fuels permit the operation of additionalenergy-consuming systems only in a minor extent. Anincreased consumption of electric energy inevitablyleads to a loss of range.

Wiebelt and Wawzyniak [2013] report about thethermo management of electric cars. To ensure anoptimum operation of the used batteries and to avoidtechnical defects or a reduction of the life cycles, theoperation of batteries must take place in a narrow tem-perature range. This requires possibly heating or cool-ing of the respective batteries. Thus the challenge liesin the development of a low energy air-conditioningsystem, which satisfies both the requirement to thepreparation of a thermal cosiness state in the car cabinand the optimum operation of the batteries.

1European Commission classification

This brings up the question, where to find an ap-proach for optimum dimensioning of ventilation andair-conditioning systems, regardless of the differentinitial conditions for vehicles operated by fuel or elec-tricity. One approach is an understanding of the cli-matic conditions in the vehicle passenger compart-ment. Essentially this includes the velocity and tem-perature distribution together with consideration of theheat transfer between the masses inside the car cabin.

To determine the required data two options are wellknown, the experimental methods and the numericalsimulation. Particularly in an early design stage exper-imental methods are too complex and too cost inten-sive. Due to scaling effects and the complex geometryof the interior the use of scale models is unsuitable (seeLombardi et al. [2007] and Lee et al. [2011]). Herenumerical simulations offer a time- and cost-effectivealternative. This way boundary conditions can be sim-ply varied and constructive measure to the geometricmodel can be made with little effort.

This study indicates an analysis of the flow con-ditions considering the heat transfer in the car cabin.For that two different ventilation conditions will betreated. In order to consider the heat emission of theoccupants, the human thermoregulation is simulatedby the model of Fiala. Thereby the human and his en-vironment (here the passenger compartment) are cou-pled in a numerical way. The solution of this simula-tion is the human skin temperature, which representsthe temperature boundary condition.

2 The Fiala ModelTo predict passengers thermoregulatory responses

to environmental conditions (temperature, air circu-lation, radiation, relative humidity) the Fiala modelhas been chosen. It is composed of two interactingsystems: An active central nervous system controlingshivering, sweating and vasomotion. A multisegmen-tal human body construction with separated tissue lay-ers (bones, muscles, fat, skin) forming the passive sys-tem. Based on Pennes bioheat equation (Eq. (1)) thepassive system predicts heat generation and accumula-tion, as well as heat transfer by conduction and bloodcirculation in and between the tissue layers. The heatexchange with the environment takes into account con-vective and radiative heat transfer, as well as heat lossby evaporation and respiration. Fiala has extensivelyvalidated his model against data from numerous inde-pendent experiments.

The human body model considered in Fiala’s ap-proach is composed of cylindrical and spherical ele-ments (e.g. arms, legs, neck, head, ...) To enable asym-metric heat conduction due to environmental condi-tions each element is separated into spatial sectors.

The heat conduction inside of each body elementis considered only in radial direction and described by

where, ρ (kg m−3) is tissue density, c (J kg−1 K−1) tissueheat capacitance, T (°C) tissue temperature, t (s) time, k(W m−1 K−1) tissue conductivity, r (m) radius, ω is ageometry factor (ω=1 for polar co-ordinates, ω=2 forspheres), Tbla (°C) arterial blood temperature, ρbl (kg m

−3)density of blood, wbl (m

3 s−1 m−3) blood perfusion rate, cbl(J kg−1 K−1) heat capacitance of blood, and qm (W m

−3)metabolism.

In the numerical model, each tissue layer is discre-tised as one or more tissue nodes (see Fig. 1, sectionA-A”) totalling 187 nodes for the body as a whole. Tominimise numerical error, tissue nodes are spaced unequal-ly in radial direction with a denser spacing towards outer

body regions where the steepest temperature gradientsoccur.

A finite-difference scheme is employed to discretise Eq. 1in the numerical model. The partial derivatives with radiusare modelled using the central difference method. The partialderivative for temporal changes in tissue temperature isapproximated using the Crank-Nicholson scheme (ΩCN Tr),which is constituted by averaging the explicit (ΩExTr) andthe implicit (ΩImTr) method defined for the current time-step(t) and the ‘future’ time-step (t+1), respectively:

4CNTðtÞr ¼

1

24ExT

ðtÞr þ 4ImT tþ1ð Þr

� �ð2Þ

Table 1 Body geometry parameters

Body element Length (m) Outer radius (m) Central angle (deg) Surface area (m2) Spatial sectors - angle (deg)

Anterior Posterior Inferior Superior

Head 0.1040 180.0 0.068 16.0 164.0

Face 0.0984 0.0780 210.0 0.028 98.0 112.0

Neck 0.0842 0.0567 360.0 0.030 58.0 80.0 222.0

Shoulders 0.3200 0.0460 130.0 0.033 130.0

Thorax 0.3060 0.1290 360.0 0.248 165.0 149.0 46.0

Abdomen 0.5520 0.1260 360.0 0.230 133.0 131.0 96.0

Upper arms 0.6380 0.0430 360.0 0.172 77.0 76.0 52.0 155.0

Lower arms 0.6360 0.0404 360.0 0.161 44.0 59.0 128.0 129.0

Hands 0.6200 0.0226 360.0 0.088 183.0 177.0

Upper legs 0.7020 0.0584 360.0 0.258 95.0 79.0 83.0 103.0

Lower legs 0.6880 0.0511 360.0 0.221 68.0 99.0 89.0 104.0

Feet 0.4800 0.0350 360.0 0.106 239.0 121.0

Fig. 1 Schematic diagram ofthe UTCI-Fiala model

Int J Biometeorol (2012) 56:429–441 431

Figure 1: The passive system [D.Fiala, UTCI-multinodemodel of human heat transfer and temperature reg-ulation. 2010]

Pennes bioheat equation:

ρcp∂T

∂t− 1rω

∂

∂r

(rωk

∂T

∂r

)=

qm + ρblcblwbl (Tbl,a − T )(1)

with temperature T , density ρ, thermal capacity cp,thermal conductivity k, blood perfusion rate wbl andarterial blood temperature Tbl,a of the tissue layers,density ρbl and thermal capacity cbl of blood and heatgeneration qm due to activity and shivering (for cylin-drical elements ω = 1, for spherical elements ω = 2).The last term on the right hand side reflects the convec-tive heat transfer due to blood circulation which linksall body elements.

The active system regulates the human thermalstate through e.g. changing the blood perfusion rateswbl (vasomotion) or the heat generation qm (shivering)in response to environmental conditions. Fiala deter-mined control equations to predict shivering, sweatingand vasomotion. The main input quantities for the ac-tive system are mean skin temperature, hypothalamustemperature and a weighted time derivative of meanskin temperature.

The Fiala model has been (re)implemented and dy-namically coupled with CFD-solvers in OpenFOAM.Local heat flow rates on the human body surface andenvironmental temperatures are determined in Open-FOAM. Based on these data an external solver predictsthe body’s thermoregulatory responses and reports theupdated skin surface temperatures.

The heat exchange with the environment due toevaporation and radiation is only considered in the ex-ternal solver but not directly coupled with CFD calcu-lations.

A finite volume scheme is used to discretize thebioheat equation (1) and a direct solver has been devel-oped which takes into account the the sparse structureof the matrix system.

3 MethodologyFor the study of the flow with consideration of heat

transfer in an car cabin the framework OpenFOAM isused. Next the assumptions made for the numericalsimulation will be described.

Model assumptions

• The flow is regarded as steady-state.

• The flow is regarded as incompressible. To con-sider buoyancy forces caused by differences indensity the Boussinesq approximation is used.

• The flow is viscous and turbulent. The numericalcalculation is done by using the RANS methodapplying the k − ω−SST model.

• The drivers heat emission is simulated by themodel of Fiala. The heat transfer across the carbody and the car windows results by indirect cou-pling between the car cabin and the external en-vironment.

• Thermal radiation in the passenger compartmentis not considered.

Governing Equations and Numerical MethodsTo determine the velocity and the temperature dis-

tribution the Reynolds-Averaged continuity equation(Eq. (2)), the Navier-Stokes equations (Eq. (3)) andthe temperature transport equation for the steady-state,incompressible case will be solved numerically (seeBergman et al. [2011]:

∂ui∂xi

= 0 (2)

uj∂ui∂xj

= − ∂p∂xi− g + ν ∂

2ui∂x2j

+∂u′iu

′j

∂xj︸ ︷︷ ︸Reynoldsstresses

(3)

uj∂T

∂xj=

(ν

Pr+

νtPrt

)∂2T

∂x2j(4)

The Boussinesq approximation is:

(ρ∞ − ρ) ≈ ρβ(T − T∞

)(5)

and is applicable to the condition β(T − T∞

)�

1. For equation (3) follows:

uj∂ui∂xj

= gβ(T − T∞

)+ ν

∂2ui∂x2j

+∂u′iu

′j

∂xj(6)

To solve the well-known closure problem of theRANS equations the k − ω−SST Modell by Menter[2001] is used.

Geometry and Computational GridThe geometric model of the car cabin with its di-

mensions and arrangements is based on a small familycar1. The length overall in x direction is 2.6m, thewidth in y direction is 1.5m and the height in z di-rection is 1.2m. The level of detail is restricted to asurface representation of the main device such as carbody and windows, seats, etc. Figure 2 shows the posi-tion of the inlet and outlet vents. There arrangementsare also based on the real car. Interior elements likedoor panels or the covering of the pillar, which possi-bly influences the flow are not represented in the CAD-model.

Figure 2: Arrangements of the inlets and outlet.

The geometry of the passenger is also modelled asa CAD-model. Its body size is 1.75m and its entirebody surface is 1.85m2. The position and posture isthat of the driver, i.e. sitting with legs stretched to thepedals and arms stretched out to the steering wheel.According with the requirements of the Fiala modelthe CAD-model is divided into body sectors within therespective area, figure 3. These sectors are handled asinterface patches in the numerical simulation to coupleOpenFOAM with the Fiala model.

Figure 3: Segmentation of manikin.

On basis of the CAD-models the numerical grid isgenerated with an optimized snappyHexMesh ver-sion, which has a size of 12.1 million cells, figure 4.The mesh is progressively refined in direction to thewall area. Furthermore, an inflation layer of five lay-ers is generated at the car body, windows and driverinclude the seat, figure 5. So the dimensionless dis-tance between the wall face and the corresponding

cell-center is y+ < 1. The reason behind is to solvethe boundary layer without using wall functions.

Figure 4: Numerical grid.

Figure 5: Refinement areas and inflation layer.

Boundary ConditionsThe boundary conditions for the inlet velocity and

the inlet temperature are listed in the table 1. Two ven-tilation modes are considered, the defrost mode andthe panel mode. They differ in the choice of the inletvelocities. The maximum inlet velocity correspondsto the fan level one like for manually controlled heat-ing and ventilation systems. As mentioned previouslythe patch temperature of the driver is controlled by theFiala model.

Inlet Mode

Defrost-vent Panel-vent

red |U | = 1.5ms |U | = 0.2ms

ϑ = 15◦C ϑ = 15◦C

blue |U | = 0.2ms |U | = 1.5ms

ϑ = 15◦C ϑ = 15◦C

green closed closed

Table 1: Inlet boundary conditions

With regard to the heat transfer across the car bodyand windows the ambient temperature and the roomtemperature of the car cabin are indirectly coupled.Input parameters for the respective patch is the out-side temperature Tout, the heat transfer coefficient h

for the outer environment and the thermal conductiv-ity κi with the corresponding thickness δi of the singlematerial layer.

From the heat transfer coefficient and the accumu-lated thermal resistance δiκi a heat transfer coefficienthp is determined. The value fraction is than given by:

w =hp

hp +κairδ

(7)

Here κair is the thermal conductivity of the fluidinside the car and δ the distance between the boundarycell face and its cell center. The temperature Tp of thecell face is determined with the temperature of its cellcenter Tc by:

Tp = w (Tout − Tc) + Tc (8)

In contrast to a fixed value boundary condition oftemperature or heat flux a more realistic picture of theinhomogeneous heat transfer between the environmentand the car cabin is given. The outside temperature forthe simulation is set to ϑout = 30◦C.

It is not possible to keep the required dimension-less wall distance y+ for using wall functions, causedby the inhomogeneous distribution of velocity andtemperature. Hence the boundary layer will be solvedwith the k−ω−SST model as a Low-Reynolds modelwith adapted boundary conditions for k and ω.

4 Results and discussionThe residuals of the mean velocity components

converge to a value of 2 · 10−4 by using the upwindscheme for the divergence term. They show slight os-cillations which indicates unsteady effects. The aver-age velocity in the passenger compartment is 0.1ms .Local velocity fluctuations are low, so they only showvery small visible effects.

Flow structure and heat transfer by the defrost-mode

Figure 6: Streamlines from the defrost-vent nozzle.

Figure 6 depicts the streamlines for the defrost-mode. The flow is directed along the windshield andcar top to the rear window of the car. In the rear the

flow separates from the car top caused by loss of ki-netic energy. Thereby the velocity increases in the rearseat, figure 7.

Figure 7: Velocity field at the driver’s side centre plane -defrost-mode.

The velocity vectors on the driver’s side point to-wards the negative y-axis, i.e. in the direction of thecar body or window (for the passenger side vice versatowards positive y-axis), figure 8. Along the car bodythe flow gets back to the front area. As a result the airfrom the front of the car cabin and rear is mixed.

In addition the figure 8 depicts the velocity vectorsalong the driver’s body. They are directed upwardsin the positive z-axis and represent the natural convec-tion, due to temperature differences between the driverand his surrounding.

Figure 8: Velocity vector field at the driver’s side centreplane - defrost-mode.

All in all an inhomogeneous velocity distributionoccurs. This is created by the free jet from theducts and the flow-influencing geometric and thermalmasses inside the car cabin.

Figure 9 represents the temperature distribution atthe driver’s side centre plane. The average temper-ature in the passenger compartment for the defrost-mode is 21.8◦C. Between the average temperatureson the vehicle floor and the car top there is a differenceof 6.1◦C. From the physical point of view the temper-ature distribution depicted in figure 9 is realistic. Socold air collects on the bottom and warm air at the cartop. Nevertheless, as a result of the inlet temperaturelocal minima occurs in front of the roof.

Figure 9: Temperature field at the driver’s side centre plane- defrost-mode.

In spite of the driver’s heat emission the tempera-tures in the front of the car is higher than in the rear(fig. 7). This is caused by the heat transfer of theforced convection along the car top. In addition thepresence of low speed flow in the area of the back shelfsupports the heat transfer from the car body and rearwindow through heat conduction with increasing tem-peratures. In contrast, the forced convection along thewindshield supports the heat transfer through convec-tion with decreasing temperature.

Flow structure and heat transfer by the panel-mode

Figure 10: Streamlines from the panel-vent nozzle.

Figure 10 depicts the streamlines for the panel-mode. A varied flow arises as a logical consequenceof the changed inlet velocities. The jet flow from themiddle panel-vent nozzles are directed to the rear. Thejet flow from the outer panel-vent nozzles is directedalong the car body and windows towards the rear. Inboth cases the jet flows along the driver’s hands andarms.

The velocity distribution depicted in figure 11shows a brisker air movement in comparison to thedefrost-mode (fig. 7) in the car cabin.

The velocity vectors at the rear seat are also di-rected to the corresponding side, figure 12. But theflow is not redirected to the front like in the previ-ous vent mode. Through the interaction of the mid-dle and outer jet flow a recirculation behind the front

Figure 11: Velocity field at the driver’s side centre plane -panel-mode.

seats is formed. A part of the jet flow from the middlepanel-vent nozzle is redirected under the front seat tothe front.

Figure 12: Velocity vector field at the driver’s side centreplane - panel-mode.

In figure 12 pronounced upward (positive z-axis)directed velocity vectors along the head and thorax canbe seen. They do not result form the natural convec-tion but through superposition with the redirected jetstream on the driver’s thorax.

Figure 13: Temperature field at the driver’s side centre plane- panel-mode.

Figure 13 represents the temperature distributionfor the panel defrost-mode. The average temperaturein the passenger compartment is 21◦C. Between vehi-cle floor and car top the difference is 7.8◦C.

The recirculation behind the front seat ensureslower temperature in the rear. In difference to the de-frost mode the velocities on the back shelf are higherdue to the ventilation flow over the back seat. This sup-ports the heat transfer through convection from the carbody and rear window so the temperatures decreaseand vice versa in the region of the windshield. How-ever the temperatures in front of the driver’s torso arelower compared with the defrost mode. The reason canbe described with the previous explanation, meaninginlet flow along arm and thorax and also the redirectedflow under the front seat.

Effect of the flow structure to the human skin tem-perature

There is no extraordinarily difference in the aver-aged temperature between the defrost and panel mode.Therefore, the maximum discrepancy of the skin tem-perature between the two modes is only 0.3◦C. Thisdifference is located on the hands, arms and thorax dueto a varying heat transfer coefficient.

The velocity and temperature distribution in theheight of the lower arms are is shown in figure 14 and15.

(a) Velocity field

(b) Temperature field

Figure 14: Distribution around the lower arm - defrost-mode.

Since the flow velocity and the temperature aroundthe body sectors differ between the two vent modes,the reaction through the human thermoregulation is adifferent one. So an alter skin temperature set in tokeep the balance between human heat production andheat emission.

(a) Velocity field

(b) Temperature field

Figure 15: Distribution around the lower arm - panel-mode.

The opposite is shown in figure 16 and 17. A sim-ilar velocity and temperature distribution can be seenfor both vent modes. As a result the skin temperaturesof the head do not differ much and is about 36.1◦C.

5 ConclusionIn this study the framework for a numerical analy-

sis of the flow in a car cabin associated with heat trans-fer is presented. The numerical solution shows a phys-ical realistic representation of the velocity and temper-ature distribution for both vent modes. The same ap-plies for the coupling between the human thermoregu-lation and the environment.

In both vent-modes the averaged velocity and tem-perature in the car cabin conform approximately withthe engineer standard of thermal comfort in livingrooms. But due to strong local variations of velocityand temperature along the driver’s body a determina-tion of thermal comfort only on basis of averaged val-ues is not expedient. With regard to partial high veloc-ity along the human body the influence of shear stresson the human surface has been taken into account forthermal comfort.

By indirect coupling of the passenger compartmentand outer environment the inhomogeneous heat trans-fer along the car body and windows is determined. Thespecification of the outer heat transfer coefficient al-lows to compute the heat transfer as a function of thevehicle speed.

With the visualization of the numerical solution a

(a) Velocity field

(b) Temperature field

Figure 16: Distribution around the head - defrost-mode.

(a) Velocity field

(b) Temperature field

Figure 17: Distribution around the head - panel-mode.

detailed representation can be obtained in terms of ve-locity and temperature distribution. This underlinesthe usability to make qualitative statements. To reducethe quantitative failures thermal radiation between themasses inside the car cabin must be considered. Cou-pled simulations usind CFD solver and Fiala modelshows excellent capabilities for thermal comfort anal-ysis. In summary, the results clearly demonstrate thatthere is a high potential to ensure thermal comfort us-ing numerical simulations in combination with a ther-mal regulation model for the human body.

ReferencesFanger P. O. (1973). Thermal Comfort. McGraw-Hill.Wiebelt A. and Wawzyniak (2013). Thermomanag-ment im Elektrifizierten Antrieb, MTZ - MotortechnischeZeitschrift, Vol. 74, pp. 592-598.Lombardi G., Maganzi M., Cannizzo F. and Solinas G(2007). The use of CFD to improve the Thermal Comfortin Automotive field, EACC - 3rd European AutomotiveCFD Conference, pp. 233-235.Lee J. P., Kim H. L. and Lee S. J. (2011). Large-scalePIV measurements of ventilation flow inside the passen-ger compartment of a real car, Journal of Visualization,Vol. 14, Issue 4, pp. 321-329.Fiala D., Havenith G., Bröde P., Kampmann B. and Jen-dritzky, G. (2012), UTCI-Fiala multi-node model of hu-man heat transfer and temperature regulation, Int. J.Biometeorology, Vol. 56, pp. 429-441.Fiala D. (1998) , Dynamic simulation of human heat trans-fer and thermal comfort. PhD thesis, De Montford Univer-sity, UK.Bergman T. L., Lavine A. S., Incropera F. P. and DewittD. P. (2011). Introduction to Heat Transfer. John Wiley &Sons.Menter F. and Esch T. (2001). Elements of Industrial HeatTransfer Prediction, 16th Brazilian Congress of Mechani-cal Engineering (COBEM).