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jj November 15, 2006 21:46

kinetic energy
 
Sir, how to find kinetic energy in the lid drivencavity problem. plz give me the formula..

amarnath November 16, 2006 00:56

Re: kinetic energy
 
Hai! i think u want the KE of each fluid partical in the cavity. if it is the case, i think u have to use the general formula (0.5*rho*V^2), where V is the total velocity of each individual partical

jj November 16, 2006 23:21

Re: kinetic energy
 
im using E(nxdelt)=SUM((u(i,j)^2+v(i,j)^2)^0.5) where n is the no. of time step. and delt is the relaxation time. im using steady state equation with pseduo transient. is this formula right

amarnath November 17, 2006 03:52

Re: kinetic energy
 
but what is SUM indicates! are u trying to find out the average velocity of all the particles, the u have to use the rms value. that formula u can get from kinetic theory of gases. and i want to know exactly what u r doing!

Jonas Holdeman November 17, 2006 07:31

Re: kinetic energy
 
Your formula is for the average velocity on a uniform mesh, or for the L2 norm of the velocity. KE is proportional to the velocity squared, so you need to remove the square root. For KE, you need to multiply by 1/2 and by the density if your equations are not scaled so that the density is 1.

For a non-uniform mesh, you must multiply (or weight) the velocity squared at each node by a volume associated with the node.

Some times mathematicians will refer to just the velocity squared as the kinetic energy, ignoring multiplicative constants, when establishing bounds on solutions.

M.Lipinski November 17, 2006 08:31

Re: kinetic energy
 
Jonas,

Why do you need to weight velocity with the volume? Taking half of the square of the magnitude of the velocity vector and multiplying it by the density gives you kinetic energy per unit volume so it does not need any scaling even if the mesh is non-uniform.

regards

M.Lipinski

Jonas Holdeman November 18, 2006 07:10

Re: kinetic energy
 
Re: M. Lipinski -- "Taking half of the square of the magnitude of the velocity vector and multiplying it by the density gives you kinetic energy per unit volume" gives the KE at a point. jj is summing over the nodes of the mesh and hence calculating the total KE over the domain. By dimensional analysis, one must multiply (KE/vol) by a volume to get KE.


M.Lipinski November 18, 2006 08:55

Re: kinetic energy
 
OK Jonas, I see your point. Though I think that the KE/Vol (KE per unit volume) is something that is more interesting than KE. E.g. it will give you a constant value, in regions where RHO and velocity are constant, independent of the element size. On the other side, KE involves mass that is clearly element size dependent.

regards

M.Lipinski


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