Energy equation for compressible flow

majkl · June 20, 2012, 10:40

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

prasant · February 1, 2013, 02:51

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.

majkl · February 1, 2013, 04:02

Quote:

Originally Posted by prasant

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

immortality · February 1, 2013, 06:31

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?

anthony761 · February 10, 2021, 13:13

Hello foamers,

Did you succeed to perform any compressible flow simulation for turbomachinery application? What is you feedback? I have also encoutered some problems you were talking about. This is my case:

OpenFOAM-v2006
Geometry: Centrifugal compressor, only one blade passage with cyclic/cyclicAMI (with diffuser vanedless and without volute)
BCs: flowRateInletVelocity with fixedValue temperature inlet and fixedValue pressure outlet
MRF model
Turbulence: kOmegaSST
Thermophysical: hePsiThermo, pureMixture, transport const, hConst, perfectGas, sensibleInternalEnergy

Tried Solvers: rhoSimpleFoam, rhoCentralFoam, sonicFoam

Results are strange, the pressure increased as expected at the exit but not the temperature which seems remain almost constant. Do you have any idea of the problem?

HPE · February 10, 2021, 16:17

I kindly suggest you to review the understanding of yours for the problem at hand: I don't see any application that you can subsequently test {rhoSimpleFoam, rhoCentralFoam, sonicFoam} for modelling of the same physical phenomena. Yet note that compressible flow simulations in general are far more sensitive to the numerical settings than its incompressible counterparts.

If the concern of yours is the numerical stability: I suggest you to test these fvOptions: limitTemperature, (if the case is unsteady) limitVelocity, (if the case is steady) velocityDampingConstraint.

June 20, 2012, 10:40	Energy equation for compressible flow	#1
majkl 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: $\rho \frac{D}{Dt} \left[\frac{u_{i}u_{i}}{2} + e\right] - \rho k_{i}u_{i} - \frac{\partial}{\partial x_{j}}[\tau_{ji}u_{i}] + \frac{\partial q_{i}}{\partial x_{i}} = 0,$ 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 11:30.*

February 10, 2021, 16:17		#6
HPE Senior Member Herpes Free Engineer Join Date: Sep 2019 Location: The Home Under The Ground with the Lost Boys Posts: 931 Rep Power: 13	I kindly suggest you to review the understanding of yours for the problem at hand: I don't see any application that you can subsequently test {rhoSimpleFoam, rhoCentralFoam, sonicFoam} for modelling of the same physical phenomena. Yet note that compressible flow simulations in general are far more sensitive to the numerical settings than its incompressible counterparts. If the concern of yours is the numerical stability: I suggest you to test these fvOptions: limitTemperature, (if the case is unsteady) limitVelocity, (if the case is steady) velocityDampingConstraint. __________________ The OpenFOAM community is the biggest contributor to OpenFOAM: User guide/Wiki-1/Wiki-2/Code guide/Code Wiki/Journal Nilsson/Guerrero/Holzinger/Holzmann/Nagy/Santos/Nozaki/Jasak/Primer Governance Bugs/Features: OpenFOAM (ESI-OpenCFD-Trademark) Bugs/Features: FOAM-Extend (Wikki-FSB) Bugs: OpenFOAM.org How to create a MWE New: Forkable OpenFOAM mirror

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February 1, 2013, 02:51		#2
prasant Member prasant Join Date: Jan 2013 Posts: 33 Rep Power: 13	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.

February 1, 2013, 06:31		#4
immortality Senior Member Ehsan Join Date: Oct 2012 Location: Iran Posts: 2,208 Rep Power: 27	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?

February 10, 2021, 13:13		#5
anthony761 New Member Join Date: Oct 2019 Posts: 13 Rep Power: 7	Hello foamers, Did you succeed to perform any compressible flow simulation for turbomachinery application? What is you feedback? I have also encoutered some problems you were talking about. This is my case: OpenFOAM-v2006 Geometry: Centrifugal compressor, only one blade passage with cyclic/cyclicAMI (with diffuser vanedless and without volute) BCs: flowRateInletVelocity with fixedValue temperature inlet and fixedValue pressure outlet MRF model Turbulence: kOmegaSST Thermophysical: hePsiThermo, pureMixture, transport const, hConst, perfectGas, sensibleInternalEnergy Tried Solvers: rhoSimpleFoam, rhoCentralFoam, sonicFoam Results are strange, the pressure increased as expected at the exit but not the temperature which seems remain almost constant. Do you have any idea of the problem?