# pipe flow calculations

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 June 6, 2001, 02:56 pipe flow calculations #1 arup kumar biswas Guest   Posts: n/a basically i am interrested to calculate the velocity field in entrance rigion of a pipe with the use of Navier stokes equn. how to discretise the euqn. in cilyndrical co-ord. system

 June 6, 2001, 03:11 Re: pipe flow calculations #2 John C. Chien Guest   Posts: n/a (1). In this particular case, I would suggest that you transform the governing equations into the classical stream function-vorticity equation formulation. (2). You should be able to find the finite-difference formulation in most cfd books related to the solutions of the stream function equation and the vorticity equation. (3). You can use the second order central difference for the stream function. For the vorticity transport equation, you can use the central difference for the diffusion term, and the upwind difference (or higher-order method) for the convection term. (4). With a non-uniform Cartesian mesh, you should be able get the solution quite easily. (5). For turbulent flow, you will have to solve the turbulence model equations.

 June 6, 2001, 03:37 Re: pipe flow calculations #3 arup kumar biswas Guest   Posts: n/a no ,i am interested to solve the problem by primitive variable methods.hoe could i do it ap tp=as ts+an tn+aw tw+ ae te.where t is a property.how to find ap,as,an,aw,ae by discretising the p.d.e in cylindrical coordinate system

 June 6, 2001, 03:52 Re: pipe flow calculations #4 John C. Chien Guest   Posts: n/a (1). Don't tell me that you are going to use staggered grid. (2). For example, dT/dx~ (T(i+1,j)-T(i-1,j))/deltaX/2., d(dT/dx)/dx~ (T(i+1,j)-2T(i,j)+T(i-1,j))/(deltaX*deltaX),...etc. (3). Repeat this for dT/dy, d(dT/dy)/dy,... in the same way. (4). Now you have the finite-difference equation written in terms of T(i+1,j), T(i,j), T(i-1,j), T(i,j+1), T(i,j-1). (5). If you collect all of these terms, you will get something like AE*T(i+1,j), AW*T(i-1,j), AN*T(i,j+1), AS*T(i,j-1), and (AE+AW+AN+AS)*T(i,j),...etc. Here you can call (AE+AW+AN+AS)=AP. (6). Naturally, you will have additional coefficients in front of the differential terms.

 June 6, 2001, 05:20 Re: pipe flow calculations #5 arup kumar biswas Guest   Posts: n/a yes , i am using staggered grid system. ok.it is all ok for catesian co-ordinate sytem, but i want the values of the co-efficinet for the cylindrical co-ordinate system

 June 6, 2001, 12:03 Re: pipe flow calculations #6 John C. Chien Guest   Posts: n/a (1). I don't use that method in staggered grid, so you will have to get someone else to help you for the cylindrical coordinates formulation.

 June 7, 2001, 00:59 Re: pipe flow calculations #7 arup kumar biswas Guest   Posts: n/a whom should i contact or any book???

 July 7, 2001, 12:01 Re: pipe flow calculations #8 Ramaprakash B Guest   Posts: n/a hello there .i am a final year mechanical engg student. i am interested in doing my MS degree in cfd.i do not have any idea about the scope or future of this subject.i just have an idea abou the beauty of the subject.please advice me at prakashbayadi@yahoo.co.in .i am sorry for writing such a letter whilst you might be expecting a technical one.please reply.thanking you, Ramaprakash B

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