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June 20, 2012, 09:40
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Energy equation for compressible flow
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#1 |
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New Member
Michal
Join Date: Apr 2012
Location: Czech Republic
Posts: 27
Rep Power: 14  |
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,](/Forums/vbLatex/img/aa73f642a71cf54b48a7e9905ffe7cc7-1.gif "\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  is the stress tensor: 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],](/Forums/vbLatex/img/bb17ce54bcef51608d90d155714b6133-1.gif "\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}].](/Forums/vbLatex/img/ad4384588a9ffc0be99af644821ae49e-1.gif "\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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