汪志明版流体力学英文版chap7.ppt

Chapter 7 Turbulent Flow of Viscous Fluid § Characters of turbulent flow When Reynolds Number of flow exceed the critical value, the flow is turbulent. So the inertial force is dominant comparing with viscous force in turbulent flow. It is observed that the instantaneous values of flowing variables, such as velocity, pressure etc. are pulsant and holding in a range near a averaged value in turbulent flow. Turbulent flow has greater effect of translating mass, momentum etc. than laminar flow. § Characters of turbulent flow ? The pulsant phenomenon of flowing variables: § Characters of turbulent flow ? To simplify dealing with instantaneous value, it is written as sum of averaged and pulsant values. ? Define the averaged value about time for function: ????????? t'ppp t??),(trF t? dttrFt trFtrF ttt t???? 0),( 1),(),( 0???§ Characters of turbulent flow ? The rules of averaged calculate: 0),( '?trF ? ttttGFGF???x Fx F tt?????x Fx F tt????? 22x Fax aF tt?????t Ft F tt?????''GFGFGF tttt?????§ Reynolds Equation ? The turbulent equations are results of averaged calculating about time based on the fluid mechanical equations. 1) Averaged Continuity Equation Put the instantaneous velocity into continuity equation and take averaged calculation, then averaged continuity equation is : 0?????????z wy vx u § Reynolds Equation 2) Reynolds Equation Similarly, take averaged calculating to N-S equation, gaining Reynolds equation: where is additional paring with N-S equation. Call as Reynolds stress. ???''??????????????????)( 1)(????????????????pgt??'''''' ji ijuu or T?????????????§ Reynolds Equation 3) K á rm án Similitude Ká rm án Number is defined as: It is based on the similar between inertial force and apparent turbulent stress. 22*)( )( Ka???????????????????§ Mixing Length Theorem ? Prandtl hyp