1. For an inviscid flow, the momentum equation for a Newtonian flow can be written as:...
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1. For an inviscid flow, the momentum equation for a Newtonian flow can be written as: (pu) + (pu,u,) + Ox P =0 ax where p is the density and p is the pressure. (1) (a) In order to characterise a turbulent flow by the mean values of flow properties, apply thebasic concepts of time-averaging along with the basic concepts of Reynolds averaging rule: = a=a; a+=a+; a=a a=+a''; as = Jads = fds Os (b) Based on the definition of the mass-weighted mean property : and along with the basic concepts of Reynolds averaging rule above, derive the Favre- Averaged form of equation (1). Identify each term in the derived equation. (c) Assuming incompressible flows and constant properties, briefly comment on the difference between the Reynolds-Averaged and Favre-Averaged form of equation (1). 1. For an inviscid flow, the momentum equation for a Newtonian flow can be written as: (pu) + (pu,u,) + Ox P =0 ax where p is the density and p is the pressure. (1) (a) In order to characterise a turbulent flow by the mean values of flow properties, apply thebasic concepts of time-averaging along with the basic concepts of Reynolds averaging rule: = a=a; a+=a+; a=a a=+a''; as = Jads = fds Os (b) Based on the definition of the mass-weighted mean property : and along with the basic concepts of Reynolds averaging rule above, derive the Favre- Averaged form of equation (1). Identify each term in the derived equation. (c) Assuming incompressible flows and constant properties, briefly comment on the difference between the Reynolds-Averaged and Favre-Averaged form of equation (1).
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a Applying timeaveraging to equation 1 we have ddxoverlinehooverlineu overlinehooverlinev 0 Where overlineho is the timeaveraged density overlineu is ... View the full answer
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