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Nomenclature

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   <td><math>k</math></td>
   <td><math>k</math></td>
   <td>Turbulent kinetic energy</td>
   <td>Turbulent kinetic energy</td>
-
   <td><math>J/kg</math></td>
+
   <td><math>J/kg = m^2/s^2</math></td>
</tr>
</tr>
<tr>
<tr>
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   <td>[[Ratio of specific heats | Specific heat ratio]] = <math>C_p/C_v</math></td>
   <td>[[Ratio of specific heats | Specific heat ratio]] = <math>C_p/C_v</math></td>
   <td></td>
   <td></td>
 +
</tr>
 +
<tr>
 +
  <td><math>\epsilon</math></td>
 +
  <td>Turbulence dissipation</td>
 +
  <td><math>J / kg s = m^2 / s^3</math></td>
</tr>
</tr>
<tr>
<tr>
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   <td><math>m^2/s</math></td>
   <td><math>m^2/s</math></td>
</tr>
</tr>
-
<tr>
 
<tr>
<tr>
   <td><math>\rho</math></td>
   <td><math>\rho</math></td>
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   <td><math>s^{-1}</math></td>
   <td><math>s^{-1}</math></td>
</tr>
</tr>
 +
 +
<tr>
 +
  <td><math>Y_k</math></td>
 +
  <td> [[Mass Fraction]] of species k</td>
 +
</tr>
 +
 +
<tr>
 +
  <td><math>X_k</math></td>
 +
  <td> [[Molar Fraction]] of species k</td> 
 +
</tr>
 +
 +
<tr>
 +
  <td><math>[X_k]</math></td>
 +
  <td>Molar Concentration of species k</td>
 +
  <td><math>mol/m^3</math></td>
 +
</tr>
 +
 +
<tr>
 +
  <td><math>W_k</math></td>
 +
  <td>Molecular weight of species k</td>
 +
  <td><math>kg/mol</math></td>
 +
</tr>
 +
 +
<tr>
 +
  <td><math>  \overline{W} </math></td>
 +
  <td>Mean molecular weight of a mixture</td>
 +
  <td><math>kg/mol</math></td>
 +
</tr>
 +
 +
<tr>
 +
  <td><math> \dot \omega_k  </math></td>
 +
  <td>k-species reaction rate </td>
 +
  <td><math>kg/m^3 s</math></td>
 +
</tr>
 +
 +
</table>
</table>
-
== Dimensionless Parameters: ==
+
== Dimensionless parameters: ==
<table cellspacing="10">
<table cellspacing="10">
 +
<tr>
 +
<th align="left">Parameter</th>
 +
<th align="left">Description</th>
 +
<th align="left">Definition</th>
 +
</tr>
<tr>
<tr>
   <td><math>Nu</math></td>
   <td><math>Nu</math></td>
-
   <td>Nusselt number</td>
+
   <td>[[Nusselt number]]</td>
-
   <td><math>q_w</math><math>L/k\Delta</math>T</td>
+
   <td><math>\frac{h L}{k}</math></td>
</tr>
</tr>
<tr>
<tr>
   <td><math>Pr</math></td>
   <td><math>Pr</math></td>
-
   <td>Prandtl number</td>
+
   <td>[[Prandtl number]]</td>
-
   <td><math>\mu</math><math>C_p/k</math></td>
+
   <td><math>\frac{\mu C_p}{k}</math></td>
</tr>
</tr>
<tr>
<tr>
   <td><math>Re</math></td>
   <td><math>Re</math></td>
-
   <td>Reynolds number</td>
+
   <td>[[Reynolds number]]</td>
-
   <td><math>\rho</math><math>VL/\mu</math></td>
+
   <td><math>\frac{\rho VL}{\mu}</math></td>
</tr>
</tr>
<tr>
<tr>
   <td><math>St</math></td>
   <td><math>St</math></td>
-
   <td>Strouhal number</td>
+
   <td>[[Strouhal number]]</td>
-
   <td><math>fL/V</math></td>
+
   <td><math>\frac{fL}{V}</math></td>
 +
</tr>
 +
<tr>
 +
  <td><math>Ma</math></td>
 +
  <td>[[Mach number]]</td>
 +
  <td><math>\frac{v}{C}</math></td>
</tr>
</tr>
</table>
</table>

Latest revision as of 20:23, 11 June 2011

Acronym Description Unit
C_p Specific heat at constant pressure J/kgK
C_v Specific heat at constant volume J/kgK
e Internal energy J/kg
e_0 Total energy J/kg
h Enthalpy J/kg
k Turbulent kinetic energy J/kg = m^2/s^2
p Static pressure Pa
R Specific gas constant J/kgK
S_{ij}^* Trace-less viscous strain-rate tensor s^{-1}
t Time s
T Static temperature K
u^* Friction velocity m/s
u_i Velocity m/s
\gamma Specific heat ratio = C_p/C_v
\epsilon Turbulence dissipation J / kg s = m^2 / s^3
\delta_{ij} Kronecker's delta function
\mu Dynamic viscosity Ns/m^2
\nu Kinematic viscosity m^2/s
\rho Density kg/m^3
\tau_{ij} Shear stress tensor N/m^2
\omega Specific dissipation s^{-1}
Y_k Mass Fraction of species k
X_k Molar Fraction of species k
[X_k] Molar Concentration of species k mol/m^3
W_k Molecular weight of species k kg/mol
\overline{W} Mean molecular weight of a mixture kg/mol
\dot \omega_k k-species reaction rate kg/m^3 s

Dimensionless parameters:

Parameter Description Definition
Nu Nusselt number \frac{h L}{k}
Pr Prandtl number \frac{\mu C_p}{k}
Re Reynolds number \frac{\rho VL}{\mu}
St Strouhal number \frac{fL}{V}
Ma Mach number \frac{v}{C}

Subscript:

tTurbulent property
0Stagnation / total property

Superscript:

convConvective part
diffDiffusive part
lamLaminar part
totLaminar + turbulent part
turbTurbulent part
'Reynolds fluctuating part
''Favre fluctuating part
\widetilde{\cdot}Density weighted (Favre) average
\overline{\cdot}Normal average (time or space)
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