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April 16, 2007, 18:44 
Relationship between velocity and pressure drop

#1 
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Hi, guys
Suppose that velocity field is available in a domain divided with polyhedral meshes, I want to calculate pressure drop in each polyhedron according the existing velocity profile. Is there any relation/formula available? I would appreciate your suggestion. Regards, Harry 

April 17, 2007, 02:36 
Re: Relationship between velocity and pressure dro

#2 
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Just a thought (I had never tried it myself).
If the velocity field is known, you can isolate grad(p) in the NavierStokes equation and explicitly calculate it by numerical differentiation. In this way you may get the local value of grad(p) at any point. If then you wish to get a pressure drop in a certain direction, you can integrate grad(p) along a path. 

April 17, 2007, 02:39 
Re: Relationship between velocity and pressure dro

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I think this way costs too much calculations.


April 17, 2007, 03:08 
Re: Relationship between velocity and pressure dro

#4 
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I see 'Harry' is having fun again


April 17, 2007, 04:19 
Re: Relationship between velocity and pressure dro

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As long as you losses are not significant so that your total pressure can be assumed constant it should be a fairly simple operation to calculate grad(p) from a known velocity field. You will of course have to specify the absolute pressure in one point, but then the velocity field should give you the pressure in the whole field. If total pressure is not constant you need more information than just the velocity field to compute the static pressure.


April 17, 2007, 06:36 
Re: Relationship between velocity and pressure dro

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I have never tried this, but I think if you write the NS equations for a control volume, you can get the p at each point directly from the known velocity field. at worst you will have to invert a matrix for p. this way errors from differentiation and integration can be avoided. Also you ensure local conservation of momentum.


April 17, 2007, 09:52 
Re: Relationship between velocity and pressure dro

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If the flow is incompressible then if you know the velocity field you know the pressure field apart for the constant background pressure. Taking the divergence of the momentum equation and solving the resulting Poisson equation should give you something that is consistent with your differencing.
If the flow is compressible then you would also need to know the other thermodynamic property and, probably, the value of pressure and/or the fluid state at the boundary. 

April 17, 2007, 18:19 
Re: Relationship between velocity and pressure dro

#8 
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Thanks. In fact, according to manuals of Fluent/CFX, I guess there should some formula to describe this matter. Here is the reason. Sometimes, pressure field is bad, but velocity seems normal. this inevitably happens in the solution of a transient multiphase flow. In such case, we'd better use velocity to calculate particle forces associated with pressure drop,or the robustness of code would be extremely week. You can check the related formation in Fluent/CFX in the part about DPM model (discrete particle model), especially pressure gradient force model. I would appreciate your further comment.


April 19, 2007, 01:16 
To andy

#9 
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the possion equation preserves the same form in all situations for incompressible flow, is it right?


April 19, 2007, 07:51 
Re: To andy

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I do not understand your question but since you are performing multiphase simulations I am not sure it is answerable without understanding the details of what is being done.


April 19, 2007, 18:06 
Re: To andy

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Hi,andy
Is it possible for me to contact you by email as I need write some formula to elucidate this problem. Regards, Harry 

April 22, 2007, 10:57 
Re: To andy

#12 
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Sorry but no. I am just chatting on a CFD forum when taking a break.


April 22, 2007, 16:22 
Re: To andy

#13 
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it's ok. I have found the answer in a paper. It is a little complicated. the pressure drop can be related to fluid acceleration.


May 8, 2007, 06:39 
Re: Relationship between velocity and pressure dro

#14 
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pls show a mathematical relationship between pressure and velocity


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