From 79d27708ac8017fa58a334bcda716a509435095d Mon Sep 17 00:00:00 2001 From: dmontgomeryNREL Date: Mon, 21 Oct 2024 13:06:04 -0600 Subject: [PATCH] Minor fix in Docs --- Docs/sphinx/manual/Model.rst | 19 +++++++++---------- 1 file changed, 9 insertions(+), 10 deletions(-) diff --git a/Docs/sphinx/manual/Model.rst b/Docs/sphinx/manual/Model.rst index 0893ecf5..f8372c2b 100644 --- a/Docs/sphinx/manual/Model.rst +++ b/Docs/sphinx/manual/Model.rst @@ -115,34 +115,33 @@ For the standard ideal gas EOS, .. math:: - \frac{DT}{Dt} &= \frac{1}{\rho}\left[ - \nabla \cdot \boldsymbol{Q} + S_{\text{ext},\rho h} - h S_{\text{ext},\rho}\right] - \sum_m \frac{h_m}{ c_p} \frac{DY_m}{Dt}, \\ - \frac{DY_m}{Dt} &= \frac{1}{\rho}\left[ - \nabla \cdot \boldsymbol{\mathcal{F_m}} + \rho \dot \omega_m + S_{\text{ext},\rho Y_m} - Y_m S_{\text{ext},\rho}\right]. + \frac{DT}{Dt} &= \frac{1}{\rho}\Big[ - \nabla \cdot \boldsymbol{Q} + S_{\text{ext},\rho h} - h S_{\text{ext},\rho}\Big] - \sum_m \frac{h_m}{ c_p} \frac{DY_m}{Dt}, \\ + \frac{DY_m}{Dt} &= \frac{1}{\rho}\Big[ - \nabla \cdot \boldsymbol{\mathcal{F_m}} + \rho \dot \omega_m + S_{\text{ext},\rho Y_m} - Y_m S_{\text{ext},\rho}\Big]. Therefore, the divergence constraint on velocity becomes: .. math:: - \nabla \cdot \boldsymbol{u} &= \frac{1}{\rho c_p T} \left(-\nabla \cdot \boldsymbol{Q} + S_{\text{ext},\rho h} - h S_{\text{ext},\rho} \right) - - \sum_m \frac{h_m}{\rho c_p T} \left( - \nabla \cdot \boldsymbol{\mathcal{F}}_m + \rho \dot \omega_m + S_{\text{ext},Y_m} - Y_m S_{\text{ext},\rho}\right) \\ - &\;\;\;+ \frac{1}{\rho} \sum_m \frac{W}{W_m} \left( - \nabla \cdot \boldsymbol{\mathcal{F}}_m + \rho \dot \omega_m + S_{\text{ext},Y_m} - Y_m S_{\text{ext},\rho}\right) + \frac{1}{\rho}S_{\text{ext},\rho}\equiv S . + \nabla \cdot \boldsymbol{u} &= \frac{1}{\rho c_p T} \Big(-\nabla \cdot \boldsymbol{Q} + S_{\text{ext},\rho h} - h S_{\text{ext},\rho}\Big) \\ + &\;\;\;\; + \sum_m \bigg( \frac{W}{\rho W_m} - \frac{h_m}{\rho c_p T}\bigg)\bigg( - \nabla \cdot \boldsymbol{\mathcal{F}}_m + \rho \dot \omega_m + S_{\text{ext},\rho Y_m} - Y_m S_{\text{ext},\rho}\bigg) + \frac{1}{\rho} S_{\text{ext},\rho}\equiv S . However, it can be shown that .. math:: - \sum_m h_m Y_m S_{\text{ext},\rho} = h S_{\text{ext},\rho} + + \sum_m \frac{W}{\rho W_m} Y_m S_{\text{ext},\rho} = \frac{1}{\rho}S_{\text{ext},\rho} and .. math:: + \sum_m h_m Y_m S_{\text{ext},\rho} = h S_{\text{ext},\rho}. - \sum_m \frac{W}{\rho W_m} Y_m S_{\text{ext},\rho} = \frac{1}{\rho}S_{\text{ext},\rho}. - -Thus, the terms containing :math:`S_{\text{ext},\rho}` cancel and the divergence constraint for the standard ideal gas EOS simplifies to +Thus, the terms containing :math:`S_{\text{ext},\rho}` cancel and the divergence constraint for the standard ideal gas EOS simplifies to: .. math:: \nabla \cdot \boldsymbol{u} = \frac{1}{\rho c_p T} \Big(-\nabla \cdot \boldsymbol{Q} + S_{\text{ext},\rho h} \Big) - + \sum_m \bigg( \frac{W}{\rho W_m} - \frac{h_m}{\rho c_p T}\bigg)\bigg( - \nabla \cdot \boldsymbol{\mathcal{F}}_m + \rho \dot \omega_m + S_{\text{ext},Y_m} \bigg) \equiv S . + + \sum_m \bigg( \frac{W}{\rho W_m} - \frac{h_m}{\rho c_p T}\bigg)\bigg( - \nabla \cdot \boldsymbol{\mathcal{F}}_m + \rho \dot \omega_m + S_{\text{ext},\rho Y_m} \bigg) \equiv S . Confined domain ambient pressure ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^