Simulation of the temperature distribution in automotive head lamps Dr. sc. techn. Christian Mielke, Dr.-Ing. Stepan Senin, Andreas Wenzel, Dr. Carsten Horn, Merkle & Partner, Heidenheim, Germany Johannes Scheuchenpflug, Audi AG, Ingolstadt, Germany Summary: The design of head lamps plays an important part in the development process of modern cars as it contributes significantly to the first impression of a car. However, beyond the design aspect technical requirements have to be fulfilled. These are foremost the lighting properties, the quality of the product and its lifetime. In this respect, the knowledge of the maximum temperature of different components of the head lamp is of great importance during the development process, as the temperature limits of the various materials are not to be exceeded. Therefore, numerical simulation is an important tool for the prediction of temperature distributions in head lamps during the development process. The heat transfer in an automotive head lamp is a complicated process, as different mechanisms have to be taken into account. These are the conduction in the solid parts and the transport due to convection by the air, respectively. Furthermore, heat transport due to thermal radiation plays a dominant role. Together with Audi AG, Merkle & Partner has investigated a method to predict the temperature distribution in a head lamp by means of numerical simulation. Therefore we use Star-CD for the computation of the convective flow field and the software AURA for the calculation of the radiation heat transfer. Both codes are coupled by user-subroutines. Within this presentation we want to briefly describe the methodology of the process. As an example a simplified model of an automotive head lamp is investigated. The influence of the different heat transfer mechanisms is described. Keywords: Head lamps, convection, radiation, conduction, temperature.
1 Introduction The look of the head lamps is a distinct design feature in modern cars. Therefore, the design of the head lamps is already investigated in the early development phases of a car. Beyond the design of the head lamps, the technical requirements have also to be fulfilled. These are primarily the lighting characteristics, the lifetime and the quality of the product. Here the information about the temperatures of the different parts is of special interest. The maximum temperature has an important role in the decision which plastic material is used for the different components. For this task numerical simulation is an indispensable tool in support of the development of head lamps, especially for the choice of the materials used. The simulation has to predict the temperature distribution with the necessary accuracy long before a prototype is tested. Nolte [1] has described a method for the simulation of temperature and flow distribution in lighting equipment. This method consists of the coupling of a commercial CFD-Code with a CAL (Computer Aided Lighting)-Program to take account of the radiative heat transport. This method has been extended to the simulation of fogging and de-fogging simulation of vehicle head lamps by Maschkio [2]. A study by Senin [3] describes the coupling of a commercial CFD-Code with an in-house ray tracing program (Forward Ray Tracing). Merkle & Partner has performed numerous investigations on the simulation of the temperature field in head lamps. These investigations resulted in a method to simulation the temperature distribution in head lamps. First we want to describe the model used for the investigation. In the following we briefly want to describe the influence of the different transport mechanisms, e.g. convection and radiation. The model is a simplified head lamp consisting of the relevant parts, for which also experimental investigations exist. 2 Geometrical model A typical head lamp of a modern car has a quite complicated geometry with a lot of different parts inside. For these investigations we used a simplified model of a head lamp, the so called reflector box. This model consists of the important components of a head lamp. The geometry of the reflector box model is shown in Figure 1 below. reflector glass plate housing with insulation cap bulb Figure 1: Geometry of the reflector box model. With this reflector box different physical phenomena of heat transfer can be easily investigated experimentally as well as numerically. Due to the simplicity only the main physical heat transport mechanisms are present. In a realistic head lamp additionally disturbing phenomena would appear, like for example the heat loss in electrical components. Hence with the reflector box model we can investigate isolated phenomena under controlled conditions. Another advantage of the reflector box is its geometrical simplicity, resulting in small mesh sizes and therefore in short computation times. 3 Physical model The heat transfer in a head lamp is a complex process, as all heat transfer mechanisms, e.g. convection and radiation have an important influence on the resulting temperature distribution. The
bulb receives surface temperatures in the range of T = 700 K in steady state operation for a given heat loss of Q = 15 W. The resulting heat has to be distributed to the other parts by means of radiation and convection. Since the air volume in car head lamps is constantly reduced, due to more complex parts like adaptive light systems, radiation is going to play an ever increasing role in the overall heat transfer process. For the numerical simulation we want to use as little assumptions as possible. In our process we usually prescribe the resulting heat flux at the surface of the bulb. The distribution of the resulting heat flux between radiation and convection has to be done by the numerical model. The other parameters prescribed in advance are only the material properties. Here also difficulties can appear as especially the radiation properties of the different components of the head lamp are not known in advance. In the following we briefly describe the numerical model and the software used. 4 Numerical model The geometrical complexity of modern head lamps and the requirements to the computation of the radiation exceeds the possibility of most commercially available codes. The numerical model of a typical head lamp consists of roughly 400.000 to 600.000 radiation patches. Using commercial software this grid size would result in computation times of several weeks. Hence for the computation of the radiation the code AURA (Audi-Radiation) was developed. This code was developed under the control of Audi AG to solve large radiation problems as they appear in the automotive development. The advantage of AURA is a panel clustering technique where several radiation patches are grouped according to their distance and view field. This technique provides a considerable speedup when compared to other codes. Unfortunately more details cannot be given due to a secrecy agreement. Other examples for the use of AURA are engine cooling and passenger comfort simulations. Using AURA we need about two to three days to solve a typical simulation of an automotive head lamp. Our simplified reflector box model as described above results in smaller mesh sizes for both the radiation and the CFD part. Hence the simulations run faster and we easily can run parameter studies. The heat transfer in a head lamp is dominated by radiation and by convection processes, as already described. The radiation part is computed by AURA and the convective flow field is calculated with Star-CD. To get a correct distribution of the total heat flux in radiation and convection we have to couple both codes. The coupling between Star-CD and AURA is done by user subroutines. AURA delivers surface temperatures to Star-CD, while Star-CD delivers local fluid temperatures and heat transfer coefficients to AURA, respectively. The conduction within the solid materials is done by AURA. Figure 2: Computational domain for the reflector box and cross-section of the computational mesh. Figure 2 shows the numerical model used for our investigations. The AURA model consists of all radiation patches of the reflector box. The CFD-model is a two-fluid-model with one fluid inside the reflector box and an outer fluid surrounding the reflector box to take the external free convection into account. For both fluids the Boussinesq approximation ( = (T)) is assumed. The meshes consist of approximately 100.000 radiation patches (triangles) in AURA and 850000 fluid cells. The fluid mesh is a hybrid mesh. A real head lamp is a complex geometry, with respect to the development times it is impossible to spend a lot of time in creating an optimal mesh with prism layers
on all parts. Hence the mesh was obtained using ICEM-CFD Tetra with a conversion of Tetra to Hexa. A prism layer was created only on the glass plate, as this is of special interest. To prepare all the geometry for prism-layers would need too much time. The mesh has an aspect ratio of larger than 0.3 for the tetrahedral elements and a determinant of larger than 0,3 for the hexahedra which is good enough for convergence of the CFD run. The AURA surface grid has an aspect ratio of larger than 0.1. A comparison with a mesh with overall prism layers did not show any significant difference in the resulting temperature distribution but it took much more effort in mesh generation. The simulations were run until a steady state solution was obtained. AURA is a pure unsteady code which was run for a total simulation time of t = 8480 s with a time step of 1 s and an update interval of 10 s with constant boundary conditions. This means that AURA and Star-CD exchange their results every 10 s. As Star-CD was run in steady state mode we took 100 Iterations between each coupling with AURA. Smaller time steps and coupling intervals were also investigated but did not show any difference in the resulting temperature distribution, while much larger intervals will lead to different results. 5 Results 5.1 Experimental study The reflector box was build up as an experimental model at Technical University Illmenau, where the measurements were performed. Unfortunately, no data are available for the temperature distribution inside of the reflector box. By infrared measurement the temperature distribution on the outer side of the glass plate was determined, which is shown in Figure 3. The results show a maximum temperature of T HotSpot = 34.1 C located in the upper region of the glass plate. From this distribution we can assume, that both radiation as well as free convection have an important influence and none of them can be neglected. The slightly asymmetric temperature distribution can be explained by the asymmetric shape of the reflector geometry. T in C T hot spot = 34.1 C Figure 3: Experimental results These experimental results are what we want to hit with our numerical simulation in a robust, safe and accurate method which additionally is fast enough to go ahead with the development process. 5.2 Numerical study To determine the influence of the different heat transfer mechanisms we performed several numerical studies. By evacuating the reflector box we can eliminate the influence of the free convection within the reflector box. The heat transport from the bulb to the glass plate is only performed by radiation.
Hence this model results in a pure radiation computation without coupling to Star-CD. However, convective transport to the surroundings is taken into account by lumped heat transfer coefficients. Figure 4: Temperature distribution on the reflector and the outer glass plate (only radiation) In this computation the bulb heats up the cap and the reflector by radiation. The temperate distribution on the reflector is smeared due to the cross conduction, as can be seen in figure 4. Further the reflector radiates towards the glass plate. The hot spot appears in the lower region of the glass plate in the optical axis of the reflector, as one would expect. The maximum temperature on the outer side of the glass plate reaches a value of T = 32 C which is a little bit lower than the measured value of T = 34.1 C. In a second study we investigated the influence of pure convection (heat transport to the environment is modelled by boundary conditions with a prescribed heat transfer resistance). The radiation was turned off. In Figure 5 the velocity and temperature distributions in the symmetry plane are shown. Figure 5: Velocity and temperature distribution in the symmetry plane for the case without radiation. (only convection) The results in this case show clearly that due to convection the temperature level in the upper part of the box rises and hence the temperature on the front plate is considerably higher than measured. This also indicates that a substantial amount of heat has to be transmitted into the environment by radiation in order to achieve the measured temperature level. As neither pure radiation nor pure convection can predict the temperature distribution with the necessary accuracy a coupled simulation was performed, taking into account both effects. The results are shown in the following. The most interesting result is the comparison of the temperature distribution on the outer side of the glass plate. Do the numerical results match the experimental measurements? A comparison is shown in the Figure 6 below.
T in C T hot spot = 34,1 C Figure 6: measured and computed temperature distribution on the outer side of the glass plate (coupled simulation). The levels of the colour bands on the right have been adapted to resemble those from the measurement. As we can see from Figure 6, the location of the hot spot as well as the temperature in the hot spot is predicted quit well with a temperature deviation of T = 1K. In the lower part of the glass plate there appears a larger temperature deviation. The reasons for this cannot be clearly explained, as a lot of parameters may be responsible for it. Up to now we don t know if the reflector box is positioned in the experiment exactly horizontally. Especially the boundary conditions in the surrounding of the reflector box are not documented in the experimental study. The surface temperatures in the reflector box are shown in Figure 7. Already in these figures we can see the influence of the convective flow field. The temperature distribution on the reflector surface differs to the almost symmetric distribution shown in Figure 4 for the pure radiation computation. A hot air streak is rising from the bulb leading to a temperature rise in the upper half of the reflector. The footprint of this streak can also be seen on the temperature distribution of the inner surface of the housing. Figure 7: Surface temperature distribution in the reflector box AURA-results (coupled simulation)
Figure 8: Temperature distribution in the air inside the reflector box with different scaling (coupled simulation) The temperature distribution in the fluid in Figure 8 shows clearly, that the air is heated up around the bulb and then rises to the top of the housing. Additionally the air is heated at the rear side of the reflector. This side is heated up by conduction from the inner side. At the top of the reflector box the hot air is cooled down by the glass plate and as seen in the velocity distribution in Figure 9 at the glass plate the air flow is directed downward. Hence the hot bulb induces a vortical flow field in the reflector box. Figure 9: Velocity distribution in the reflector box (coupled simulation) According to [3] a discrimination of the effective heat transfer mechanisms (radiation, convection) can be made by plotting the vertical temperature distribution on the front plate. Figure 10 shows such a plot for the current simulation results (radiation, convection and coupled simulation). Herein height and temperature are expressed as dimensionless quantities. The dimensionless height is the ratio of distance from the top of the plate to the plate diameter. The dimensionless temperature is expressed as (T T ) λ A / (P el L S ) This analysis further confirms the assertion that the temperature on the front plate of the reflector box is to a great extent determined by convective heat transfer. However, if the radiation heat transfer was neglected the temperature level would be considerably overestimated. An interesting feature of the plot is the appearance of a second 'shoulder' for the convection simulation at a height of about 0.3. This indicates that there exists a secondary convective roll cell in front of the reflector. This can be seen to a lesser extent in the case of the coupled simulation.
Dimensionless temperature (-) 0.014 0.012 Coupled Radiation Convection 0.01 0.008 0.006 0.004 0.002 0 0 0.2 0.4 0.6 0.8 1 Dimensionless height (-) Figure 10: Vertical temperature distribution on the front plate (coupled / radiation / convection) 6 Summary Within this article the temperature field in an automotive head lamp was investigated by means of numerical simulation. For the temperature transport all three transport mechanisms are important. The study has shown that the current method is robust enough and delivers the necessary accuracy needed during the development process of a new car. 7 References [1] Nolte, S.: "Eine Methode zur Simulation der Temperatur- und Strömungsverteilung in lichttechnischen Geräten, Cuvillier Verlag, Göttingen, 2007 [2] Maschkio, T.: "CFD-Simulation der Be- und Enttauungsprozesse in Kfz-Scheinwerfern, Dissertation Universität Paderborn, 2007 [3] Senin, S.: "Numerische und experimentelle Untersuchungen zum Wärmetransport in einem Automobilscheinwerfer, Dissertation TU Illmenau, 2007 8 Nomenclature λ A L S P el T T conductivity of the air area of the front plate distance between lamp and front plate electric power of the lamp temperature temperature of the surrounding