Numerical Simulation of Effusion Cooling through Porous Media

Transcription

1 Sonderforschungsbereich/Transregio 4 Annual Report Numerical Simulation of Effusion Cooling through Porous Media By W. Dahmen, V. Gerber, T. Gotzen AND S. Müller Institut für Geometrie und Praktische Mathematik, RWTH Aachen University Templergraben 55, 5256 Aachen Effusion cooling using ceramic matrix composite (CMC) materials is an innovative concept for cooling rocket thrust chambers. Numerical simulations of a carbon/carbon material mounted in the side wall of a hot gas channel have been performed. The coolant (air) is driven through the by a pressure difference between the coolant reservoir and the turbulent hot gas flow. A finite volume solver for the compressible Reynolds averaged Navier Stokes equations is coupled with a porous media solver. The results at Mach number Ma=.5 and hot gas temperature T hg = 54K for different blowing ratios are compared with experiments. 1. Introduction In future space transportation systems the reduction of heat loads at the wall is an important design parameter. Since passive cooling techniques, such as radiation cooling, are limited and non-adjustable during flight, active solutions, e.g. effusion cooling might offer a promising alternative. In particular, such a technology would allow one to reduce the weight of the structural component. The basic idea of film cooling is to inject a coolant through boreholes or slots in the wall, such that the temperature boundary layer thickens and a coolant film develops. This leads to a significant reduction of the heat load at the wall. However, establishing a continuous cooling film significantly depends on the topology and size of the boreholes or slits and their spatial distribution, see Linn et al. [1, 2]. In this regard, effusion cooling, where the coolant is injected into the hot gas flow through a, might offer advantages for the formation of stable films. Appropriate materials are currently under investigation [3]. Experiments with different coolants in a hypersonic wind tunnel have been performed by Gülhan et al. [4]. Langener [5] and Langener et al. [6] investigated effusion cooling with CMC materials, in particular composite carbon/carbon (C/C) materials at sub- and supersonic speeds. In the present work we focus on the numerical simulation of cooling-gas injected through a in a flat plate into a turbulent, subsonic flow field. For this configuration experimental data are available from Langener et al. [6]. The simulations are carried out using separate solvers for the hot gas flow and the flow in the porous medium, respectively, that are directly coupled with each other through alternating data exchange at the interface. The coupling is realized in a weak sense, i.e., the two flow fields are evolved in time applying the two solvers alternately. In particular, no fix point problem is solved for a given instance of time. Concerning the hot gas flow, we use the adaptive parallel solver Quadflow [7], which

2 2 W. Dahmen, V. Gerber, T. Gotzen & S. Müller solves the Reynolds-averaged Navier Stokes equations using the Menter SST model [8]. The core ingredients are: (i) the flow solver concept based on a finite-volume discretization [9], (ii) the grid adaptation concept based on wavelet techniques [1], and (iii) the grid generator based on B-spline mappings [11]. These three constituents are not just viewed as black boxes communicating only via interfaces, but are intertwined. The porous media flow is modeled using a one-dimensional finite difference scheme for the continuity equation, the Darcy-Forchheimer equation and two temperature equations for both fluid and solid material. The main purpose is to validate both, numerical solvers and the coupling, with the aid of experimental results. In the following, we will refer to the two solvers as the flow solver and the porous medium solver, respectively. The present paper is structured as follows: first, the governing equations for modeling the porous media flow are presented in Sec. 2. Then the basic concepts of the numerical method are briefly summarized in Sec. 3. In Sec. 4.1 we first validate the porous media solver by performing a stand-alone computation of the flow inside the porous material. The results are compared with experimental results from Langener et al. [6]. Then the porous media solver is coupled with the flow solver Quadflow and the injection through the into the turbulent flow field is simulated. We conclude with a summary of the main results and give an outlook to future work. 2. Mathematical Model for porous media flow For the simulation of a pressure-driven flow of a cooling gas in a porous medium we take into account the compressibility of the fluid, the velocity of the fluid and the heat conduction in the fluid as well as in the solid. The continuum model thus consists of the continuity equation, the Darcy-Forchheimer equation and two heat equations. In particular, we are interested in transport effects and non-equilibrium temperature effects. In the following we briefly summarize the model. A detailed discussion can be found in [12] and references cited therein. In contrast to pure fluids we have to account for the porosity ϕ of the porous medium in our continuum model. This is defined as the ratio of void space and the total volume of the medium. Here we assume that all the void space is connected. Averaging the fluid velocity over a volume V f consisting of fluid only we obtain the intrinsic average velocity V. This is related to the Darcy velocity (seepage velocity, filtration velocity, superficial velocity) v, i.e., the average velocity with respect to a volume element V m incorporating both solid and fluid material, by the porosity as v=ϕv. The continuity equation for the fluid density then reads ϕ ρ f t + (ρ fv)=. (2.1) For the momentum we take quadratic drag into account which leads to the Darcy- Forchheimer equation ρ f ( 1 v ϕ t + 1 µ ϕ 2(v )v)= p v ρ f v v. (2.2) K D K F Here µ denotes the dynamic viscosity of the fluid, K D the permeability of the medium and K F the Forchheimer coefficient. The pressure p is determined by the ideal gas law with the specific gas constant R. p=ρ f T f R (2.3)

3 Effusion Cooling through Porous Media 3 FIGURE 1. Configuration of coupled fluid-porous medium problem. The temperature of the solid and the fluid are assumed to be in non-equilibrium. We therefore need two heat equations for both the solid and the fluid, respectively. In the solid we neglect convection resulting in (1 ϕ)(ρc p ) s T s t =(1 ϕ) (k s T s )+h(t f T s ), (2.4) where k s is the heat conduction coefficient, ρ s the constant density and c p the specific heat capacity at constant pressure of the solid. Since the fluid is in contact to the solid and both the fluid and the solid radiate heat, the exchange of heat is accounted for by the heat transfer coefficient h to be determined by experiments. Since the fluid is moving in the medium we have to take into account convection in the heat equation for the fluid ϕ(ρc p ) f ( T f t + 1 ϕ v T f)=ϕ (k f T f )+h(t s T f ) (2.5) with k f the heat conduction coefficient and c p the specific heat capacity at constant pressure of the fluid. For the boundaries we have to distinguish the inflow boundary Γ R and the outflow boundary Γ HG of the porous medium where the cooling gas enters from the reservoir or is leaving into the hot gas flow, respectively, as well as the solid walls Γ W bordering the porous medium, see Figure 1. At the inflow boundary we choose p=p c, v n =, T s=t s,r, T f =T c on Γ R, (2.6) where p c and T c denotes the reservoir pressure and temperature and T s,r the temperature of the backside of the porous medium. On the hot gas side we prescribe p=p HG, v n =, T s=t s,hg, T f n = on Γ HG (2.7) with the hot gas pressure p HG and the temperature T s,hg of the porous medium at the hot gas side. The bordering walls are assumed to be isothermal and we impose no-slip conditions, i.e., p n =, v=, T s=t w, T f n = on Γ W. (2.8) where T w denotes the temperature of the wall. Note that the fluid density ρ f can be computed by the ideal gas law (2.3).

4 4 W. Dahmen, V. Gerber, T. Gotzen & S. Müller 3. Numerical method Since the flow in the porous medium is driven by the gradient between the high reservoir pressure and the lower fluid pressure in the boundary layer of the hot gas, the flow is at this stage assumed to be essentially one-dimensional. Therefore we consider the model (2.1) (2.5) only on an intervali=[,l] using a uniform discretization x=l/m, i.e., x i = i x, i=,...,m. Here the cooling gas enters the porous medium at the left side and exits to the main flow at the right interval end. First applying finite difference approximations to the spatial derivatives we obtain a nonlinear system of ordinary differential equations (ODE) for the interior discretization points x i, i=1,...,m 1: d(ρ f ) i dt dv i dt = 1 (ρ f ) i v i (ρ f ) i 1 v i 1, (3.1) ϕ x ϕr (ρ f ) i+1 (ρ f ) i 1 (T f ) i+1 (T f ) i 1 = ((T f ) i +(ρ f ) i µv i ) (ρ f ) i 2 x 2 x RK D d(t s ) i dt d(t f ) i dt = = ϕv2 i v i v i v i 1, (3.2) K F ϕ x 1 (T s ) i+1 2(T s ) i +(T s ) i 1 (k s + h (ρc p ) s x 2 1 ϕ ((T f) i (T s ) i )), (3.3) 1 (ρ f ) i (c p ) f (k f (T f ) i+1 2(T f ) i +(T f ) i 1 x 2 + h ϕ ((T s) i (T f ) i )) v i(t f ) i (T f ) i 1. (3.4) ϕ x Here the pressure gradient in the Darcy-Forchheimer equation (2.2) is approximated by first applying the chain rule to the equation of state (2.3) and then discretizing the temperature and density gradient by symmetric finite differences of second order. The Laplacians in the temperature equations (2.4) and (2.5) are approximated by secondorder symmetric finite differences. For the convection terms in equations (2.1), (2.2) and (2.5) we use a first order upwind discretization where we assume that due to the pressure gradient the fluid moves from left to right. Introducing the vector U=(ρ f,v,t f,t s ) the ODE system can be written as du i =L(U i 1,U i,u i 1 ) L i, (3.5) dt Due to the diffusive terms this ODE system is stiff and, hence, requires an implicit time discretization. Here we use the θ-scheme U n+1 i tθl n+1 i =U n i t(1 θ)l n i. (3.6) For the choice of the parameter θ we distinguish between the unsteady and the steady state problem. In case of the transient flow through the porous medium we want to be time-accurate and therefore choose θ =.5 corresponding to the implicit Crank- Nicholson scheme For a steady state problem, where we are not interested in the transient behavior, time is considered an iteration parameter only. Here a fully implicit first order time discretization is used, i.e., θ = 1 corresponding to the backward Euler scheme. In both cases this results in a nonlinear system for the unknowns U i, i=1,...,m 1. Note that fori=1andi=m 1 the vectorsu andu M are determined by the boundary conditions (2.6) and (2.7), respectively, using either constant values (Dirichlet) or the

5 Effusion Cooling through Porous Media 5 blowing ratio F.3 mass flux coolant m c.15kg/s hot gas temperature T HG 535K reservoir temperature T c K backside temperature T s,r 375.7K frontside temperature T s,hg 425.4K reservoir pressure p c 4489Pa hot gas pressure p HG 956Pa TABLE 1. List of experimental parameters. porosity ϕ.113 density ρ s 1.14kg/m 3 spec. heat capacity c p,s 622J/(kgK) eff. heat conductivity k s 1.97W/(mK) TABLE 2. List of porous media parameters. spec. heat capacity c p,s 11J/(kgK) eff. heat conductivity k s 1.4W/(mK) dynamic viscosity µ Ns/m 2 permeability K D m 2 Forchheimer coeff. K F /m TABLE 3. List of coolant parameters (air). values inside the porous medium (von Neumann). This system is solved by Newton s method. In each Newton step we have to solve a linear system of equations where the Jacobi matrix is a block-tridiagonal matrix that can be efficiently solved by a direct solver. The Newton iteration is terminated if the residual drops below 1 8 or after 25 iterations. 4. Results First of all we validate the porous medium model and its discretization described in Section 2 and Section 3 by a stand-alone computation for the flow inside the porous medium. Then we consider a coupled fluid-porous medium problem Validation of porous medium model In Langener et al. [6] experiments have been performed using C/C ceramics measuring temperatures in different depths of the material. We perform numerical simulations using material parameters and conditions from the experiment listed in Tab Initial conditions are determined by a linear pressure distribution between the pressure in the reservoir and the hot gas. The initial temperatures for coolant and solid are taken as constants from the reservoir and the backside of the porous medium, respectively. By the equation of state we then compute the initial density distribution. The initial velocity is then computed from the cooling gas mass flux measured in the experiment. The has a thickness of L = 15mm and is discretized by M = 48

6 6 W. Dahmen, V. Gerber, T. Gotzen & S. Müller Temperature [K] x T_f (h=5) T_s (h=5) T_f (h=1) T_s (h=1) T_f (h=3) T_s (h=3) Exp x x x x x x x y/l [ - ] FIGURE 2. Temperatures of solid and coolant, comparison of simulations with different heat transfer coefficients h with experiments. equidistant grid points. Since we are interested in the steady state solution, we apply the backward Euler time discretization. The time iteration is performed until the maximum time residual drops below 1 7. For the time discretization t we use t=cfl x λ max (4.1) with λ max =(v max /ϕ)+ RT f,max the maximum characteristic speed determined by the hyperbolic part in eqns. (2.1), (2.2), (2.4) and (2.5). The CFL number evolves with each subsequent time step n according to CFL=1.5 n, (4.2) starting with CFL min = 1, until we reach CFL max = 1 6. Less than 5 time steps are necessary for convergence to steady state. In Fig. 2 we compare the temperatures measured in the experiment with our simulation. Here, the coordinatey is made dimensionless by the thicknesslof the material. As stated in [6], the thermocouples used for measuring the temperature in the experiment are glued with the tip to the C/C wall. Hence, it is assumed that they are not in contact with the gaseous phase. Therefore, we can directly compare them to the temperature of the solid taken from our simulation. As mentioned before in Sec. 5 the choice of the heat transfer coefficient h is difficult, because it has not been determined by experiments so far. Therefore we performed simulations with different heat transfer coefficients. We notice that for h=5w/(m 3 K) and h=1w/(m 3 K), the temperature of the solid is in very good agreement with the experimental results. A larger value for h results in a lower temperature of the solid and a less linear behaviour, as more heat is transferred to the coolant. For h=3w/(m 3 K), the temperature of the solid is noticeably too low. The temperature of the coolant exhibits a linear behavior in all three cases, but the slope becomes larger with increasing h.

7 Effusion Cooling through Porous Media 7 p [Pa] y/l [ - ] FIGURE 3. Pressure and velocity of coolant (simulation with h=1w/(m 3 K)) v [m/s] The pressure of the coolant decreases as shown in Fig. 3, whereas the coolant s velocity is accelerated significantly near the outflow boundary of the porous medium. More details on the discretization and the implementation of the porous medium model and further results on stand-alone computations can be found in [13] Experimental setup 4.2. Effusion cooling through porous medium For the experiments, the has been mounted into the sidewall of the plenum of a subsonic wind tunnel. On the backside of the CMC material, a coolant reservoir has been attached. The experimental setup is shown in Fig. 4. The test section is 1.32m long with the CMC material beginning.58m downstream from the entrance, the height is 9mm and the width 6mm. In the hot gas channel, the pressure is measured on the opposite side of the CMC material. The temperature distribution on the surface of the are monitored by infrared thermography. Additionally, the temperature of the solid phase of the at different depths is measured by thermocouples. The condition of the coolant in the reservoir is monitored as well. The experiments are described in detail by Langener et al. [6]. The turbulent inflow conditions are summarized in Tab. 4. The boundary layer in the channel has been estimated using pitot elements. The boundary layer thickness is about δ =.2 m. The parameters concerning the CMC material and the coolant (air) have already been listed in Tab. 2 and 3, respectively Numerical setup For the numerical simulation, we apply a weak coupling of the finite volume solver Quadflow, which has been used for the simulation of cooling gas injection before, see Dahmen et al. [14], with the one-dimensional porous media solver described in Sec. 3. On the hot gas side, we solve the two-dimensional flow through a channel. A sketch of the computational domain can be seen in Fig. 5.

8 8 W. Dahmen, V. Gerber, T. Gotzen & S. Müller (a) Hot gas channel (b) Sample integration FIGURE 4. Experimental setup by Langener et al. [6]. Mach number Ma.5 density ρ HG.65kg/m 3 total temperature T t,hg 525K pressure p HG 956Pa TABLE 4. List of inflow conditions. Dealing with the boundary conditions of the porous media solver, p HG in (2.7) is determined by averaging the pressure in the hot gas flow on the porous media part (Γ HG ) of the lower wall. The remaining boundary conditions for the porous media simulation are taken from the experiment and listed in Tab. 5. Concerning the flow solver, the injection of the coolant is modeled by a subsonic inflow boundary condition: p n =, u=, v=v c, T=T c, on Γ HG. (4.3) Here,uandv denote the velocity components andv c andt c are the coolant velocity and temperature extrapolated from the interior of the porous media domain. Note that after one time step of the flow solver we solve only one single one-dimensional problem in the porous medium that is used as input for the flow solver for all cells attached to Γ HG. To gain such a thick boundary layer as measured in the experiment, on the inflow boundary Γ I of the channel the velocity and temperature profile are prescribed using the law of the wall. The pressure is extrapolated from the interior by imposing a homogeneous

9 Effusion Cooling through Porous Media 9 solid wall Γ W Γ I Γ O Γ W ΓHG Γ W solid wall Γ R porous medium solid wall FIGURE 5. Computational domain of coupled fluid-porous medium problem in a channel. blowing ratio F [ ] reservoir pressure p c [Pa] coolant temperature T c [K] solid temperature reservoir side T s,r [K] solid temperature hot gas side T s,hg [K] TABLE 5. List of porous media boundary conditions. Neumann boundary condition. At the outflow boundary Γ O, the pressure is prescribed whereas density and velocity are extrapolated from the interior of the flow domain. The computational domain measures[,1.12] [,.6]m 2 and is discretized using a coarse structured grid with 19 grid points. The grid lines are denser towards the walls and the region of the cooling gas injection. The coarse grid is refined during the computation using 5 additional refinement levels. The initial grid and data are taken from the reference computation without coolant injection. Grid adaptation is performed five times every 5 time steps. After the last adaptation the computation continues until the averaged residual of the density has dropped by five orders of magnitude. The final adaptive grid consists of about 15 grid points (depending on the blowing ratio), which is a significant reduction compared to the fully refined grid consisting of grid points. For the temporal discretization of the flow solver, an implicit Euler backward scheme is used with a local time step determined by the same CFL evolution strategy as described in Eq. (4.2). Here, the minimum and maximum CFL number are set to 1 and 1, respectively. The CFL number is computed accordingly to Eq. (4.1) with maximal characteristic speed given in [9] Results First, we compare the simulated temperature distributions at different depths of the with experiments for different blowing ratios, see Fig. 6. As expected the temperatures for both solid and coolant are decreasing with increasing coolant mass flux. Accordingly, the coolant is cooler in the instance of the injection into the hot gas flow. Therefore, the cooling film downstream from the injection has a higher cooling potential. The overall agreement with the experimental results is quite good. Except for F =.3, the temperature of the solid is slightly underestimated by the simulation in those regions above the measurements are subject to higher uncertainties. Probably the choice of the heat transfer coefficient, which is currently just guessed, is too high. In Fig. 7 the wall normal momentum above the injection is shown for different blowing

10 1 W. Dahmen, V. Gerber, T. Gotzen & S. Müller (a) F=.1, F=.2 (b) F=.3, F=.1 FIGURE 6. Comparison of temperature distribution in the with experiments for different blowing ratios (solid - T s, dashed - T f, symbols - T s from experiment). ratios. As expected, the momentum of the injection is very small for smaller blowing ratios and becomes larger with increasing blowing ratios. For F =.1, see Fig. 7(c), a spot with high normal momentum occurs at the leading edge of the. Here the larger injected mass flux interacts with the hot gas flow. Considering the turbulent kinetic energy, see Fig. 8, the same behavior shows up. For small blowing ratios there is almost no disturbance of the main flow by the injection. For F=.1, see Fig. 8(c), there is a significant increase in turbulence triggered at the leading edge of the. Regarding the temperature distribution in Fig. 9, the thickness of the coolant film varies with the injected mass flux as well. Furthermore, as shown in Fig. 6, the temperature of the coolant in the instance of the injection into the hot gas flow depends strongly on the blowing ratio. Finally, the variation of the pressure at the upper wall of the hot gas channel normalized by the total pressure for different blowing ratios is shown in Fig. 1. As mentioned in Section 4.2.2, in the simulation of the hot gas flow, the pressure is fixed at the outflow boundary. Without blowing, the pressure distribution between inflow and outflow is linear, as expected. Downstream the the pressures produced by the simulations with blowing are very close to that straight line. With higher blowing ratio, the pressure drop above the rises as well. 5. Conclusions The direct coupling of a finite volume flow solver for the hot gas flow and a onedimensional finite difference solver for the simulation of a flow through has been used for the simulation of an effusion cooling testcase. The comparison with experiments confirms that the porous media solver adequately reproduces the temperature distribution and the mass flow through the. Nevertheless, there is a strong dependence on parameters like the heat exchange coefficients, which have yet to be determined by experiments. Compared with film cooling approaches using for example slots or holes the injection

11 Effusion Cooling through Porous Media 11 rho*v_y: (a) F =.1 rho*v_y: (b) F =.3 rho*v_y: (c) F =.1 F IGURE 7. Wall normal momentum in the channel for different blowing ratios with zero level. of a coolant through a tends to promote more the cooling of the structure itself rather than the development of a film on the surface of the wall downstream from the injection. Therefore, blowing ratios are smaller and the interaction with the hot gas flow is weaker. For such investigations, the correct temperature boundary conditions for both the hot gas flow and the become an important topic. In contrast to shock tube

12 12 W. Dahmen, V. Gerber, T. Gotzen & S. Müller rho*k: (a) F =.1 rho*k: (b) F =.3 rho*k: (c) F =.1 F IGURE 8. Turbulent kinetic energy in the channel for different blowing ratios. experiments, the wind tunnel cannot be modeled with a low isothermal wall temperature. Otherwise, it is not adiabatic either. We used an isothermal temperature determined by the experiments for both the solid wall and the. This means, at this point we cannot compute the cooling effect yet, but only reproduce the temperature measurements in the from the experiments. In accordance with other authors we made the assumption that the pressure is con-

13 Effusion Cooling through Porous Media 13 T: (a) F=.1 T: (b) F=.3 T: (c) F=.1 FIGURE 9. Temperature distribution in the channel for different blowing ratios. tinuous across the interface between the flow domain and the. Nield and Bejan [12] pointed out that this is the case on the microscopic scale, but this might not hold on the macroscopic scale. There can be a relevant pressure difference in a thin layer around the interface that cannot easily be resolved in numerical computations. Furthermore, the weakly coupled simulations in this work has been done without performing a fixed point iteration at the interface between the and the hot

14 14 W. Dahmen, V. Gerber, T. Gotzen & S. Müller.96 F = F =.1 F =.2 F =.3 F =.1 p_s,hg / p_t,hg [-] FIGURE 1. Normalized pressure on the upper wall of the channel for different blowing ratios. Dashed lines indicate the location of the injection. gas flow. A more thorough investigation whether the weak coupling is sufficient is still in progress. The assumption that the flow and the temperature distribution in the is more or less one-dimensional is valid in most parts of the material. However, considering a thin region around the interface between hot gas and, the one-dimensional approach is no longer adequate. To resolve this, as a next step a two-dimensional porous medium solver will be implemented and applied to the problem. In order to further improve the model we will employ in the future homogenization techniques to determine effective boundary conditions for porous medium injection. This will allow us to take small scale effects into account that are caused by the roughness of the porous medium surface which in turn cannot be directly resolved. For incompressible, laminar flow results are reported in [15]. Acknowledgments Financial support has been provided by the German Research Foundation (Deutsche Forschungsgemeinschaft DFG) in the framework of the Sonderforschungsbereich Transregio 4. References [1] LINN, J. AND KLOKER, M. J. (28). Numerical investigations of Film Cooling and its influence on the Hypersonic Boundary-Layer Flow. In: Gülhan, A. (Ed.), RESPACE Key Technologies for Reusable Space Systems, NNFM, 98, Springer, [2] LINN, J., KELLER, M. AND KLOKER, M. J. (21). Effects of Inclined Blowing on Effusion Cooling in a Mach-2.67 Boundary Layer. SFB/TRR 4 Annual Report 21,

15 Effusion Cooling through Porous Media 15 [3] SELZER, M., LANGENER, T., HALD, H. AND VON WOLFERSDORF, J. (29). Production and Characterization of Porous C/C Material. SFB/TRR 4 Annual Report 29, [4] GÜLHAN, A. AND BRAUN, S. (211). An experimental study on the efficiency of transpiration cooling in laminar and turbulent hypersonic flows. Exp. Fluids 5(3), [5] LANGENER, T. (211). A Contribution to Transpiration Cooling for Aerospace Applications Using CMC Walls. Diss Univ. Stuttgart. [6] LANGENER, T., VON WOLFERSDORF, J., SELZER, M. AND HALD, H. (212). Experimental investigations of transpiration cooling applied to C/C material. Intl. J. Thermal Sc. 54, [7] BRAMKAMP, F., LAMBY, PH. AND MÜLLER, S. (24). An adaptive multiscale finite volume solver for unsteady and steady state flow computations. J. Comp. Phys., 197(2), [8] MENTER, F. R. (1994). Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications. AIAA J., 32(8), [9] BRAMKAMP, F. (23). Unstructured h-adaptive Finite-Volume Schemes for Compressible Viscous Fluid Flow. Diss. RWTH Aachen. [1] MÜLLER, S. (23). Adaptive Multiscale Schemes for Conservation Laws. Lecture Notes on Computational Science and Engineering, 27, 1st edition, Springer Verlag. [11] LAMBY, PH. (27). Parametric Multi-Block Grid Generation and Application to Adaptive Flow Simulations. Diss. RWTH Aachen. [12] NIELD, D. A. AND BEJAN, A. (26). Convection in Porous Media. Springer, 3rd edition, USA. [13] GERBER, V. (212). Modellierung und Simulation von Strömungen in porösen Medien. Bachelor thesis, RWTH Aachen, to be submitted September 212. [14] DAHMEN, W., GOTZEN, T., MELIAN-FLAMAND, S. S. AND MÜLLER, S. (212). Numerical simulation of cooling gas injection using adaptive multiscale techniques. Submitted to Computers and Fluids. [15] JÄGER, W. AND MIKELIC, A. (21). On the roughness-induced effective boundary conditions for a viscous flow. J. Diff. Eq., 17,