Instantaneous Turbulent Flow Equations Consider turbulent flow of an incompressible fluid with constant property, no heat generation, no body force, and negligible viscous dissipation. This flow is governed by the following continuity, momentum and temperature equations: ди + + ду д = 0 дх ду д ди du +u ди ди 1 др du du du v- +W == +V + at dx ду Əz P ox Ox2 y2 Oz² dv Ov dv 1 др a²v av av +u. +v +w = +u +V +W Ot Ox ду Əz Ow Ow Ow Ow at Ox ду Əz p dz от от от от +u. +v- +wa at dx ду Əz ax² dy2 a²T T T + + Oy² Oz² +V + ρον Ox dy² az² 1 др aw aw aw + + + Oz2 Time-Averaged Turbulent Flow Equations The time-averaged continuity, momentum and energy equations are + בו શશશશ Ox दा ди dy + ди от д dx dy ди 1 др дл Pox Ov 1 др = ду Əz ρον Ow Ow Ow +V +w = - дх ду Əz +V + Əz 0 u u u + du² du'v' du'w' Ox² ay² az² дх ду Əz Ou'v' v2 v'w' + + dx ду Əz Ou'w' v'w' w2 1 др Poz +V Ox2 y2 Oz² www + + Ox² dy² dz² дх ду Əz a²T T T Ou'T 'T' Ow'T' от от от = a + Ox ду Əz Ox2 y2 Oz2 dx ду Əz These are five equations for 14 unknowns including the arguments of the last three terms in momentum and energy equations; this is called closure problem. The science of developing additional information to close this problem is called turbulent modeling.