Transcription of CAE 「数値流体力学」輪講 第3章：乱流とそのモデリング(3) …
1 3 (3) [ 75] 1 2013 11 10 14:00 ESI@ CAE @ 2013/11/10 4 2013/11/10 2 4 ( ) openfoam 2013/11/10 3 4 2 H. K. Versteeg & W. Malalasekera 2011 7 9975 544 ( ) 2013/11/10 4 4 3 75 ( ) 69 2013/11/10 5 4 - (RANS) ( 69) ( 68) 2013/11/10 6 4 - (RANS) ( 69) ( 68) 2013/11/10 7 4 wikipedia u t ( ) 2013/11/10 8 4 ( ) ( )
2 4/13 dl ( ld) ld (1) 2013/11/10 9 4 (Direct Numerical Simulation: DNS) (Large Eddy Simulation: LES) - (Reynolds-Averaged Navier-Stokes equation: RANS) (2) 2013/11/10 10 4 u t ( ) DNS RANS LES DNS LES RANS 2013/11/10 11 4 - (RANS) ( 69) ( 68) 2013/11/10 12 4 u, v uuu vvv TudtTu01)0(10 TvdtTv 0'1'0 TdtuTu0'1'0 TdtvTv ( 8 ) 2013/11/10 13 4 u v u v 0 vu 0 vu ( 8 ) ( ) 0 (1) 2013/11/10 14 4 ( 8 )
3 Y u 0 u1 u2 y1 y2 v = 0 S: y u u 2 v 2 u 1 v 1 y ( ) x )'(uuu y SvvSvV)'( S=1 v=0 'vV (2) 2013/11/10 15 4 ( 8 ) y u 0 u1 u2 y1 y2 v = 0 S: y u u 2 v 2 u 1 v 1 y ( ) y (x ) ')'(vuuVu TTdtvuuTVdtuT00')'(1 '''''00vudtvuTdtvTuTT (3) 2013/11/10 16 4 ( 8 ) y u 0 u1 u2 y1 y2 v = 0 S: y u u 2 v 2 u 1 v 1 y2 y y v (>0) x u u2 y2 x u2 (<0) u v u v u v ''vuxy (4) 2013/11/10 17 4 xy 2 wwvwuwwvvvuvwuvuuuzzzyzxyzyyyxxzxyxx uvvu uwwu vwwv yxxy zxxz zxxz (1) 2013/11/10 18 4 ( )j, y jj yy j, y ( ) 0 yj 0jj sss jj dsdsdsjj yjyj 0 j )(jjyjjyyjjy ))((yj 0 yj (2) 2013/11/10 19 4 a aAa Aaadivdivdiv aAaa jjjdiv)div(div)div()div(grad)div(grad j - (RANS) (1)
4 2013/11/10 20 4 )div(grad1)div(uxputu u0div u)div(grad1)div(vypvtv u)div(grad1)div(wzpwtw u ( ) - u=(u, v, w): (x, y, z) t: : ( ) p: : ( ) - (RANS) (2) 2013/11/10 21 4 u=(u, v, w) p uUu wvuWVUwvu pPp , 0div U)div(grad1)div()div(UxPuUtU uU)div(grad1)div()div(VyPvVtV uU)div(grad1)div()div(WWzPwtW uU - (RANS) - (RANS) (3) 2013/11/10 22 4 )div(grad1)div(UxPUtU U)div(grad1)div(VyPVtV U)div(grad1)div(WWzPtW U - (RANS) 0div U xzxyxxzyx 1 yzyyyxzyx 1 zzzyzxzyx 1 2013/11/10 23 4 RANS ( )j jj St)div()graddiv(1)div(uUj ( ) (1) 2013/11/10 24 4 RANS RANS - )div()div()
5 Div()()(uuU uuUutUt )div(gradUxP 0)div()div()( uU t ( ) (2) 2013/11/10 25 4 Morkovin 5 ( ) x xx ~ - (1) 2013/11/10 26 4 )~graddiv(~)~~div(~UxPUtU U)~graddiv(~)~~div(~VyPVtV U)~graddiv(~)~~div(~WzPWtW U - (RANS) 0~div U tMxSwuzvuyuux )()()( MySwvzvvyuvx )()()( MzSwwzvwyuwx )()()( - (2) 2013/11/10 27 4 )~graddiv()~~div(~Wt U Swzvyux)()()(j j j 2013/11/10 28 4 3 75 ( ))
