Strömungs- und passive Skalarfluss- Vorgänge in komplexen turbulenten Prallströmungen

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1 ProcessNet-Fachausschuss Wärme und Stoffubertragung (2008) DECHEMA Strömungs- und passive Skalarfluss- Vorgänge in komplexen turbulenten Prallströmungen Naseem Uddin 1, S. Olaf Neumann 1, Bassam A. Younis 2, Bernhard Weigand 1 1 Pfaffenwaldring Department of Civil & Environmental Engineering University of California, Davis Davis, CA95616

2 Impinging jet: Applications 1. Cooling. 2. Drying. 3. Vertical take-off & landing aircrafts.

3 Impinging jet Applications Gas turbine blade cooling

4 Impinging jet Applications Electronic component cooling

5 Impinging jet Applications Vertical takeoff & landing aircrafts

6 Turbulent impinging jet Free shear layer/ Jet core region Stagnation region Wall jet region

7 Complexity of jet impingement Popiel & Trass, Smoke Wire Visualisation

8 Impinging Jet Test Case Experimental data Cooper et al. (1993) ERCOFTAC Test Case for turbulence models [C25].

9 Computational Domain & Conditions Re=23000 H/D=2

10 FASTEST3D Flow Analysis Solving Transport Equations Simulating Turbulence 3 Dimensional The second-order central differencing scheme is used for spatial discretization. Time discretization is done by applying the second order implicit Crank-Nicolson method. The SIMPLE algorithm is used for coupling the velocity and pressure fields. The computations were performed on the CRAY Opteron Cluster, Höchstleistungsrechenzentrum (HLRS),, Germany. Total 20 processors are used for 47 blocks

11 Large Eddy Simulation (LES) Top hat filtering is used. Dynamic Smagorinsky model proposed by Germano et al. is used (1991). Inflow conditions used are proposed by Klein et al. (2003).

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15 Uddin ITLR The Ring Vortex visualised via Iso-pressure surfaces

16 Radial Distribution of the Nusselt number at the target wall

17 Prediction of heat transfer through RANS based turbulence model Scalar flux is modelled via turbulent Prandtl number.

18 Distribution of Turbulent Prandtl Number in wall normal direction at different radial positions

19 Exact scalar-flux transport equation

20 Explicit scalar-flux model

21 The first term represent the gradient transport model The second term represent the Daly & Harlow model. The last two terms represent the scalar-flux transport via surface pressure fluctuations, modelled according to Dakos & Gibson model.

22 Daly & Harlow Model Coefficient original C θ1 = r/d

23 original C θ2 = Abe & Suga Model Coefficient r/d

24 0.4 Younis et. al Model Coefficients r/d C 1 C 2 C 3 C 4

25 Budgets of turbulent kinetic energy close to wall Loss Gain 0.15 Convection Production Turbulent Diffusion 0.10 Molecular Diffusion Pressure Diffusion 0.05 Dissipation r/d

26 Mechanical time scale Thermal time scale

27 Results from the Models in CFX+standard Prt standard Prandtl-Number approach SST BSL RST SSG RST EXP 300 Nu r/d

28 Results from the Models implemented in CFX 150 BSL RST (CFX) +younis Dietz +younis 100 younis approach Nu r/d

29 140 Younis Model Abe & Suga Daly & Harlow Exp Y Axis Title X Axis Title

30 Giovannini & Kim (2006) Younis et al. model CFX-11- sp1 Baseline RSM model Nu r/d

31 Conclusion The Younis et al. model is found to be more realistic in its representation of the impinging jet phenomenon & prediction. The inclusion of different mechanical & heat time scales in future scalar flux models for RANS may give better results. The better representation of the pressure driven scalar flux transpot in models is required. LES is capable to predict accurately the location & madnitude of secondary peak in radial distribution of Nusselt number, in impinging jet cases.

32 References 1. D. Cooper, D. C. Jackson, B. E. Launder, G. X. Liao, 1993, Impinging jet studies for turbulence model assessment- I. Flow field experiments, Int. J. Heat and Mass Transfer, Vol 36, No. 10, M. Germano, U. Piomelli, P. Moin, W. H. Cabot, 1991, A dynamic subgrid-scale eddy viscosity model, Phy. Fluid A 3 (7), M. Klein, A. Sadiki, J. Janicka, 2003, A digital filter based generation of inflow data for spatially direct numerical or large eddy simulations, J. of Comp. Physics 18, B. A. Younis, C. G. Speziale, T. T. Clark, 2005, A rational model for turbulent scalar fluxes, Proceedings of the Royal Society A, 461,

33 5. T. Dakos, M.M. Gibson, 1987, On modelling the pressure terms of the scalar flux equations, 7-18, Turbulent Shear flows 5, Springer. 6. K. Abe, K. Suga, 2001, Towards the development of a Reynolds-averaged algebraic turbulent scalar-ux model, Int. J. Heat and Fluid Flow, 22, B. J. Daly, F. H. Harlow, 1970, Transport equations in turbulence, Phy. Fluids, Vol. 13, No. 11,