# navier-stokes

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 February 22, 2005, 13:01 navier-stokes #1 queram Guest   Posts: n/a guys, does anyone know how should the navier-stokes equation for 1D unsteady compressible viscous fluid flow in the variable cross-section duct look like? I have tried to derive it by myself, but it doesn't look like the one I found on the web... thanks

 February 24, 2005, 07:37 Re: navier-stokes #2 Alexander Starostin Guest   Posts: n/a

 February 24, 2005, 07:56 Re: navier-stokes #3 Alexander Starostin Guest   Posts: n/a queram if you have velocity like (v(x),0,0) there v and x are oriented along with flow you will have stess tensor with non-zero xx,yy,zz component: Pxx=-p + m1 dv/dx + 2*m2 dv/dx; Pyy=-p + m1 dv/dx; Pzz=-p + m1 dv/dx; m1 and m2 - different viscosities but usually m1 = 2/3 m2. Further we have to put the tensor in Navier-Stokes there it turns to vector: (d(Pxx)/dx,0,0) Ask more if you need more complicated case. But actually in Cartesian coordinates general case with constant m1,m2 has very convinient form: (m1+m2)*grad div v + m2*Laplace v (*) In Cartesian you have: (m1+m2)*d( div v)/dx + m2*Laplace v (m1+m2)*d( div v)/dy + m2*Laplace u (m1+m2)*d( div v)/dz + m2*Laplace w But here comes a time for my question. I has to express (*) in cylindical coordinates. I started from Christofell symbols and obtained something very reliable (checked for incompressible) but I want be 100% sure. Does anybody know the source for the Navire-Stokes in cylindrical coordnates for compressible fluid?

 February 24, 2005, 11:11 Re: navier-stokes #4 Rami Guest   Posts: n/a The following classics have them: Bird, Stewart and Lightfoot, Transport Phenomena Anderson et al, Computational Fluid Mechanics & Heat Transfer Bachelor, An Intruduction to Fluid Mechanics

 February 24, 2005, 11:39 Re: navier-stokes #5 Alexander Starostin Guest   Posts: n/a Thank you, Rami, but what about URLs?

 February 25, 2005, 07:21 Re: navier-stokes #6 faber Guest   Posts: n/a mmmmmm.... look at my procedure: having NS for compressible 3D unsteady fluid flow in x direction in the form: du/dx=-1/ro*dp/dx+mu(d^2/dx^2+d^2/dy^2+d^2/dz^2)-mu/3*d/dx(du/dx+dv/dy+dw/dz) I have come to 1D unsteady compressible NS as: du/dt=-1/ro*dp/dx+2/3*mu*d^2u/dx^2 where u, v, w - velocity vectors ro - density mu - kin. viscosity x, y, z - coordinates

 February 25, 2005, 08:19 Re: navier-stokes #7 Alexander Starostin Guest   Posts: n/a Hi, faber I am afraid you have to change you code before its too late. m1=-2/3*m2 (looks like I've lost minus in the previous message) this done to keep physical sense of the pressure (pxx+pyy+pzz)/2=p. But it's only very common assumption. Originally Navier-Stoke's law contains two viscosities. For additional check you can look here http://www.efunda.com/formulae/fluids/navier_stokes.cfm Couldn't find any more relevant.

 February 25, 2005, 08:20 Re: navier-stokes #8 Alexander Starostin Guest   Posts: n/a (pxx+pyy+pzz)/2=p -> (pxx+pyy+pzz)/3=p

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