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Energy equation for compressible flow

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Old   June 20, 2012, 09:40
Default Energy equation for compressible flow
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Michal
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Hello,

I have a question about the energy equation (compressible flow - subsonic) in OF v 1.6-ext and 2.1.0 (there are some posts but still without answer).

The conservation of energy has the form:
\rho  \frac{D}{Dt} \left[\frac{u_{i}u_{i}}{2} +  e\right]  - \rho k_{i}u_{i} - \frac{\partial}{\partial  x_{j}}[\tau_{ji}u_{i}]  + \frac{\partial  q_{i}}{\partial x_{i}} = 0,
where \tau is the stress tensor:

\tau_{ij} = -p\delta_{ij} + P_{ij}.

1) From the conservation of energy I can derive the energy equation (EE), which is used in OF v 2.1.0 but I can not reach the EE which is implemented in version 1.6-ext. Why is the difference between EE? The left hand sides of the energy equations are the same in both versions and similarly the enthalpy definitions.

Steady-state case without volume forces and viscous term (same EE implemented in OF 2.1.0):
\rho  u_{i}\frac{\partial h}{\partial  x_{i}} + \frac{\partial q_{i}}{\partial  x_{i}} = -\rho  u_{i}\frac{\partial }{\partial  x_{i}}\left[\frac{u_{i}u_{i}}{2}\right],

In OF 1.6-ext the EE:
\rho   u_{i}\frac{\partial h}{\partial x_{i}} + \frac{\partial  q_{i}}{\partial  x_{i}} = fvc::div[\frac{\phi}{fvc::interpolate \rho},   \frac{\rho}{\psi}] -   \frac{\rho}{\psi}*fvc::div[\frac{\phi}{fvc::interpolate \rho}].


2) I solved some simple case (diffuser), which can be "easy" described analytically. The OF 2.1.0 solver gives the best results.. BUT.. When I applied both version of OF solvers for same turbomachinery case, the version 2.1.0 gave unrealistic temperature field (convergent solution in both version, 6000it). If EE should be the same in both versions, why I have obtained so much different result for identically same case (velocity filed, temperature, pressure, thermoModel, turbulence, ...)?

Your answers would be very helpful for me.
Thank you.

Michal

Last edited by majkl; June 20, 2012 at 10:30.
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Old   February 1, 2013, 02:51
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prasant
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Hello Michal,

I am solving one Impeller case. For me also, Temperature values are not coming properly at outlet. Did you recieve any information from people? If so, Could you please share that information?

Regards
Prasant.
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Old   February 1, 2013, 04:02
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Michal
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Quote:
Originally Posted by prasant View Post
Hello Michal,

I am solving one Impeller case. For me also, Temperature values are not coming properly at outlet. Did you recieve any information from people? If so, Could you please share that information?

Regards
Prasant.
Hi,

no answer today.

M
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Old   February 1, 2013, 06:31
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hi dear michal.i have had doubt about energy equation ever.but i didn't understand what you have done.did diffuser problems were solved properly at both versions but another problem didn't?both versions gave incorrect results in second experiment or just one did so?
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