Transient flow simulations

Transcription

1 Transient flow simulations Lecture 4 March 8, 2016 March 8, / 20

2 Table of Contents 1 Stationary and transient 2 Block structured meshes 3 Steps of the analysis through an example 4 Mesh refining March 8, / 20

3 Stationary and transient Transient (unsteady) Every real flow is transient in molecular sense Stationary (steady-state) flow refers to the condition where the fluid properties do not change over time all the time derivatives of a flow field are vanishing Re < 5 47 < Re < 3x < Re < 47 3x10 5 < Re March 8, / 20

4 Geometry L slip wall l d W inlet wall outlet slip wall March 8, / 20

5 Domain decomposition P12 P13 P14 P15 n yt P28 P29 P30 P31 B6 B7 B8 P24 P25 P26 P27 P8 n yc P20 P9 B4 P21 P10 P22 B5 P11 P23 P4 P5 P6 P7 n yb B1 B2 B3 P16 P17 P18 P19 P0 n xu P1 n xc P2 n xd P3 March 8, / 20

6 blockmeshdict - list of vertices Listing coordinates of the block vertices: Listing 1: vertices in blockmeshdict 1 converttometers 1.0; 2 3 vertices 4 ( 5 ( ) // P0 6 ( ) // P1 7 ( ) // P2 8 ( ) // P ); March 8, / 20

7 blockmeshdict - block definition Listing the blocks, ordered list of vertex labels and mesh size: Listing 2: blocks in blockmeshdict 1 blocks 2 ( 3 // vertex numbers, number of intervals, interval grading 4 hex ( ) ( ) simplegrading ( ) 5 hex ( ) ( ) simplegrading ( ) 6 hex ( ) ( ) simplegrading ( ) ); Listing edges (line, polyline, arc, simplespline, polyspline): Listing 3: edges in blockmeshdict 1 edges 2 ( 3 // edge type, labels of end vertices, coord. of interpolation point (s) 4 arc 5 6 ( ) 5 arc 6 10 ( 1 0-1) ); March 8, / 20

8 blockmeshdict - boundary definition Listing boundaries (type, vertices of the faces): 1 boundary 2 ( 3 inlet 4 { 5 type patch ; 6 faces 7 ( 8 ( ) 9 ( ) 10 ( ) 11 ); 12 } ); mergepatchpairs 18 ( 19 ); Listing 4: boundaries in blockmeshdict March 8, / 20

9 Steps of the numerical analysis - Domain and mesh March 8, / 20

10 Steps of the numerical analysis - Boundaries Inlet (Dirichlet BC for U, Neumann BC for p) fixed value for U (U = U in = 1 ms 1 ) zero gradient for p ( p/ n = 0) Outlet (Dirichlet BC for p, Neumann BC for U) zero gradient for U ( U/ n = 0) fixed value for p (p = p ref = 0 P a) Walls fixed value for U (U = 0) zero gradient for p Front and back sides of a 2D domain empty for both U and p Bottom and top sides slip wall for both U and p March 8, / 20

11 Steps of the numerical analysis - BC and IC for U Listing 5: boundaries in 0/U 1 dimensions [ ]; 2 internalfield uniform (1 0 0); 3 boundaryfield 4 { 5 inlet 6 { 7 type fixedvalue ; 8 value uniform (1 0 0); 9 } 10 outlet 11 { 12 type zerogradient ; 13 } 14 cylinderwall 15 { 16 type fixedvalue ; 17 value uniform (0 0 0); 18 } 19 topwall 20 { 21 type slip ; 22 } } March 8, / 20

12 Steps of the numerical analysis - BC and IC for p 1 dimensions [ ]; 2 internalfield uniform 0; 3 boundaryfield 4 { 5 inlet 6 { 7 type zerogradient ; 8 } 9 outlet 10 { 11 type fixedvalue ; 12 value uniform 0; 13 } 14 cylinderwall 15 { 16 type zerogradient ; 17 } 18 topwall 19 { 20 type zerogradient ; 21 } } Listing 6: boundaries in 0/p March 8, / 20

13 Steps of the numerical analysis - Numerical setup 1. 1 solvers 2 { 3 p 4 { 5 solver PCG ; 6 preconditioner DIC ; 7 tolerance 1e -05; 8 reltol 0; 9 } 10 U 11 { 12 solver PBiCG ; 13 preconditioner DILU ; 14 tolerance 1e -06; 15 reltol 0; 16 } 17 } 18 PISO 19 { 20 ncorrectors 2; 21 nnonorthogonalcorrectors 0; 22 prefcell 0; 23 prefvalue 0; 24 } Listing 7: fvsolution March 8, / 20

14 Steps of the numerical analysis - Numerical setup 2. Listing 8: fvschemes 1. 1 ddtschemes 2 { 3 default Euler ; 4 } 5 6 gradschemes 7 { 8 default Gauss linear ; 9 grad (p) Gauss linear ; 10 } divschemes 13 { 14 default none ; 15 div (phi,u) Gauss linear ; 16 } laplacianschemes 19 { 20 default Gauss linear orthogonal ; 21 } March 8, / 20

15 Steps of the numerical analysis - Numerical setup 3. 1 interpolationschemes 2 { 3 default linear ; 4 } 5 6 sngradschemes 7 { 8 default orthogonal ; 9 } fluxrequired 12 { 13 default no; 14 p ; 15 } Listing 9: fvschemes 2. March 8, / 20

16 Steps of the numerical analysis - Simulation March 8, / 20

17 Steps of the numerical analysis - Simulation March 8, / 20

18 Steps of the numerical analysis - Simulation March 8, / 20

19 Steps of the numerical analysis - Refined mesh March 8, / 20

20 Steps of the numerical analysis - Fine simulation March 8, / 20