Difference between revisions of "User talk:Ferrandm"
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The hypotheses to simplify the Navier-Stokes equations are : | The hypotheses to simplify the Navier-Stokes equations are : | ||
* The total energy balance according to Poinsot-Veynante is descreibed below, if <math> E=e_{s}+\dfrac{1}{2}u_{i}^{2} </math> : | * The total energy balance according to Poinsot-Veynante is descreibed below, if <math> E=e_{s}+\dfrac{1}{2}u_{i}^{2} </math> : | ||
| − | <math>{\rho}\dfrac{DE}{Dt}=\dfrac{\partial{{\rho}E}}{\partial{t}}+\dfrac{\partial{{\rho}u_{i}E}}{\partial{x_{i}}} | + | <math>{\rho}\dfrac{DE}{Dt}=\dfrac{\partial{{\rho}E}}{\partial{t}}+\dfrac{\partial{{\rho}u_{i}E}}{\partial{x_{i}}}=\dot{\omega_{T}}+\dfrac{\partial}{\partial{x_{i}}}({\lambda}\dfrac{\partial{T}}{\partial{x_{i}}})-\dfrac{\partial}{\partial{x_{i}}}({\rho}{\sum}_{k=1}^{N}h_{s,k}Y_{k}V_{k,i})+\dfrac{\partial{\sigma_{ij}}u_{i}}{\partial{x_{j}}}+\dot{Q}+{\rho}{\sum}_{k-1}^{N}Y_{k}f_{k,i}(u_{i}+V_{k,i}) </math> |
| − | =\dot{\omega_{T}}+\dfrac{\partial}{\partial{x_{i}}}({\lambda}\dfrac{\partial{T}}{\partial{x_{i}}}) | + | |
| − | -\dfrac{\partial}{\partial{x_{i}}}({\rho}{\sum}_{k=1}^{N}h_{s,k}Y_{k}V_{k,i}) | + | |
| − | +\dfrac{\partial{\sigma_{ij}}u_{i}}{\partial{x_{j}}} | + | |
| − | +\dot{Q}+{\rho}{\sum}_{k-1}^{N}Y_{k}f_{k,i}(u_{i}+V_{k,i}) </math> | + | |
The term <math>\dfrac{\partial}{\partial{x_{i}}}({\rho}{\sum}_{k=1}^{N}h_{s,k}Y_{k}V_{k,i})</math> can be ignored with regard to <math>\dot{\omega_{T}}</math>, which is the heat release due to combustion. | The term <math>\dfrac{\partial}{\partial{x_{i}}}({\rho}{\sum}_{k=1}^{N}h_{s,k}Y_{k}V_{k,i})</math> can be ignored with regard to <math>\dot{\omega_{T}}</math>, which is the heat release due to combustion. | ||
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<math>\dot{\omega_{T}}=-\sum_{k=1}^{N}\Delta h_{f,k}^{0}\dot{\omega_{k}} | <math>\dot{\omega_{T}}=-\sum_{k=1}^{N}\Delta h_{f,k}^{0}\dot{\omega_{k}} | ||
=\nu_{F}M_{F}\dot{\omega}Q_{m}</math> | =\nu_{F}M_{F}\dot{\omega}Q_{m}</math> | ||
| + | |||
| + | <math>{\rho}{\sum}_{k=1}^{N}h_{s,k}Y_{k}V_{k,i}</math> is the power produced by volume forces <math>f_{k}</math> on species k. | ||
Revision as of 16:38, 6 June 2012
Hypotheses
The hypotheses to simplify the Navier-Stokes equations are :
- The total energy balance according to Poinsot-Veynante is descreibed below, if :
The term can be ignored with regard to , which is the heat release due to combustion.
This release can be defined by this equations :
is the power produced by volume forces on species k.
