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Old   June 6, 2001, 02:56
Default pipe flow calculations
  #1
arup kumar biswas
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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
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Old   June 6, 2001, 03:11
Default Re: pipe flow calculations
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John C. Chien
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(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.
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Old   June 6, 2001, 03:37
Default Re: pipe flow calculations
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arup kumar biswas
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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
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Old   June 6, 2001, 03:52
Default Re: pipe flow calculations
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John C. Chien
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(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.
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Old   June 6, 2001, 05:20
Default Re: pipe flow calculations
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arup kumar biswas
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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
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Old   June 6, 2001, 12:03
Default Re: pipe flow calculations
  #6
John C. Chien
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(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.
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Old   June 7, 2001, 00:59
Default Re: pipe flow calculations
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arup kumar biswas
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whom should i contact or any book???
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Old   July 7, 2001, 12:01
Default Re: pipe flow calculations
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Ramaprakash B
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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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