LES of Vortex Formation in a Spherical Dimple and Genetic Optimization of Heat Transfer Surfaces

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1 LES of Vortex Formation in a Spherical Dimple and Genetic Optimization of Heat Transfer Surfaces J.Turnow, N. Kornev, E. Hassel Department of Technical Thermodynamics University of Rostock Germany 5 th OpenFoam Workshop

2 LES of Vortex Formation in a Spherical Dimple and Genetic Optimization of Heat Transfer Surfaces 1. Vortex formation in a spherical dimple Motivation Numerical setup Results 2. Genetic optimization of heat transfer surfaces Introduction Method of optimization Results 3. Conclusion 2

3 Vortex formation in a spherical dimple Motivation Comparison of thermohydraulic efficiency Industrial applications Ligrani, et. al (2003) dimpled surfaces show best performance in respect to heat transfer enhancement by relative low pressure loss 3

4 Vortex formation in a spherical dimple Motivation Vortex structures inside dimples Ligrani P.M., Harrison J.L., Mahmood G.I., Hill M.L Physics of Fluids. Vol.13. N11.. (2001) Shukin A.V., Kozlov A.P., Agachev, Chudnovski Y.P. (2003) Kazan, Technical University Kazan, P The structure of vortices created within dimples remains not quite clear especially at large depth to diameter ratio of the dimple. 4

5 Vortex formation in a spherical dimple Numerical setup Standard case: t / D = 0.26 h / D = R = 0.0 Re = D h R Ū D k t Large Eddy Simulation incompressible temperature as passive scalar further improvements of SGS Model (momentum and scalar transport) Dynamic Mixed Model (Zang, Vreman) SGS 1 SGS 2 1 τij τkk δ ij = νt[2sij S kkδ ij] + Lij Lkkδ L ij ij = uiu j uiu j dynamic calculation of turbulent diffusion coefficient D SGS 5

6 Vortex formation in a spherical dimple Numerical setup 5 th OpenFoam Workshop due to single geometry and limited computational rescources blockstructured meshes by blockmeshtoolkit are favourable Easy copying and joining blocks together using of snappyhexmesh fails due to now feature line input in official version to get smooth blockstructered meshes around the sharp edge a deformationtool was implemented to stretch meshes onto a stl surface using mesh motion technique easy and fast deformation of meshes with smooth transition areas

7 Vortex formation in a spherical dimple Numerical setup precursor method works fine but requires many cells in this case of turbulent flow over a dimple using POD technique for inflow generation useful, but requires big data storage implementation of inflowgenerator proposed by Kornev et. al based on vortex methods shows main advantages - generation of turbulence with prescribed 2nd order statistics - grid independent / divergence free - anisotropic effects are taken into account - significant reduction of cells new version consists of feature to set the distribution of reynoldsstresses at the inlet generation of realistic turbulence

8 Vortex formation in a spherical dimple Results Vortex structures inside dimples URANS: steady asym. vortex inclined at ± 45 deg LES: unsteady asymmetric vortex switching between ± 45 deg (frequency: Hz) 8

9 Vortex formation in a spherical dimple Results Observation of opposite of phase motion R uu = u x ( x, t) u u x x ( x, t) u ( x + Δx, t) x ( x, t) 1 2 z. H =± U U Explanation of the effect: 9

10 Vortex formation in a spherical dimple Results Heat transfer Phaseaveraged Nusselt-number distribution Phaseaveraged vorticity distribution u u Formation of vortex axis increase heat transfer at downstream side of dimples Thermohydraulic efficiency ζ = 3 ( 1 = Nu/ Nuo ) ( f / f ) o

11 Vortex formation in a spherical dimple Results Proper Orthogonal Decomposition (POD) = Φ M a K ( t ) u(x,y,z,t) a K(t) k(x,y,z) Φ k k(x,y,z) time coefficients PODmodes decomposing a number of vector/scalar fields into a set of time independent orthogonal base functions and time coefficients reconstructed flow fields show main vortex movements extraction of modes which are responsible for high heat transfer implemented Galerkin projection method shows the energy transfer between POD modes Velocity Mode 1 Pressure Mode 1 11

12 Vortex formation in a spherical dimple Results Entropy Production Rates for evaluation of real heat transfer efficiency entropy production rates from velocity and temperature field are implemented..... Pro Pro Pro Pro Pro D T D' T' S = S + S + S + S main goal: using entropy criterium for optimization process

13 Genetic optimization of heat transfer surfaces Introduction idea: searching for an optimized heat transfer surface by genetic algorithm coupling of optimization process with CFD computational resources at time allow optimization of complex problems with many degrees of freedom OpenFOAM qualification: parallelization of code mesh motion technique adaptive solver algorithm control by bash / pyhton scripting 13

14 Genetic optimization of heat transfer surfaces Method of optimization Theory for simple technical devices by reproduction / inheritance the unknown target function F is found F( x) opt x [ ξ ( )] i i =1,2,..., N In case of heat transfer surfaces F( x) opt [ ξ ( x) ] i f = min Nu / / fo Nu o i = flow losses min heat transfer i 14

15 Genetic optimization of heat transfer surfaces Method of optimization Global function F( x) opt i x [ ξ ( )] x =1,2,..., N Parameters N =(0,,0) Parameters y i nodes optimized parameters: normal nodes displacement of the heat transfer surface 15

16 Genetic optimization of heat transfer surfaces Method of optimization Nodes displacement Displacement of node points in normal direction by PDF function (Gaussian distribution) P( a < X< b) μ σ μ μ+ σ t Enforced roughness avoided by smoothing function manipulated surface can adopt arbitrary shape 16

17 Genetic optimization of heat transfer surfaces Method of optimization displacement of node points using mesh motion technique by solving mesh diffusion equation ( γ u) =0 x = x +Δtu new old mesh quality controlled by checkmesh (bad mesh snappyhexmesh) no need to rebuild mesh for each shape RANS calculation of actual shape uses converged fields from previous solution fast iteration process 17

18 Genetic optimization of heat transfer surfaces Method of optimization Evolution algorithm Dimple standard case Mutation of surface Smoothing of surface Mesh deformation by mesh motion RANS Solution Best Performance Extraction of best realizations Optimized structure for heat transfer 18

19 Genetic optimization of heat transfer surfaces Results Optimized surface for heat transfer enhancement convergence process stable enhancement of thermohydraulic efficiency up to 16% surface structure after 800 generations 19

20 Conclusion LES / RANS simulation for heat transfer of turbulent flows over dimpled surfaces application of directmapped, POD and inflowgenerator to generate time resolved inlet conditions for les implementation of mesh deformation tool to generate blockstructured meshes with smooth transition areas entropy production rates as new way to determine heat exchanger efficiency POD modes and galerkin projection of flow field extract responsible structures for high heat transfer rates implementation of general genetic optimization process in openfoam using mesh motion technique 21

21 Thank you for your attention Johann Turnow University of Rostock Faculty of Mechanical Engineering and Naval Architecture Department of Technical Thermodynamics Albert Einstein Str Rostock Germany johann.turnow@uni-rostock.de Acknowledgement DFG HRLN Supercomputing Center Mr. H. Kroeger / Mr. M. Walter 22