Inviscid flow
From CFD-Wiki
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*Continuity equation | *Continuity equation | ||
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\frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x_j}(\rho u_j)= 0 | \frac{\partial \rho}{\partial t} + \frac{\partial}{\partial x_j}(\rho u_j)= 0 | ||
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*Momentum equation | *Momentum equation | ||
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\frac{\partial}{\partial t}(\rho u_i) + \frac{\partial}{\partial x_j}(\rho u_i u_j + p \delta_{ij}) = 0 | \frac{\partial}{\partial t}(\rho u_i) + \frac{\partial}{\partial x_j}(\rho u_i u_j + p \delta_{ij}) = 0 | ||
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*Energy equation | *Energy equation | ||
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\frac{\partial}{\partial t}(\rho E) + \frac{\partial}{\partial x_j}[(\rho E + p)u_j] = 0 | \frac{\partial}{\partial t}(\rho E) + \frac{\partial}{\partial x_j}[(\rho E + p)u_j] = 0 | ||
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* <math>E</math> is the total energy per unit mass of fluid | * <math>E</math> is the total energy per unit mass of fluid | ||
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E = \frac{p}{\gamma - 1} + \frac{1}{2} \rho |u|^2 | E = \frac{p}{\gamma - 1} + \frac{1}{2} \rho |u|^2 | ||
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The above equations are closed by taking an equation of state, the simplest being the ideal gas | The above equations are closed by taking an equation of state, the simplest being the ideal gas | ||
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p = \rho R T | p = \rho R T | ||
</math> | </math> | ||
Revision as of 11:41, 12 September 2005
A flow in which viscous effects can be neglected is known as inviscid flow. At high Reynolds numbers, flow past slender bodies involve thin boundary layers. Viscous effects are important only inside the boundary layer and the flow outside it is nearly inviscid. If the boundary layer is not separated then the inviscid flow model can be used to predict the pressure distribution with reasonable accuracy.
Governing Equations
The governing equations for inviscid flow, also known as Euler equations, are obtained by discarding the viscous terms from the Navier-Stokes equations
- Continuity equation
- Momentum equation
- Energy equation
![\frac{\partial}{\partial t}(\rho E) + \frac{\partial}{\partial x_j}[(\rho E + p)u_j] = 0](/W/images/math/e/7/3/e73b09e7ac9cb3a2f73034d30bfbcb11.png)
where
-
is the density
-
is the fluid velocity
-
is the pressure
-
is the total energy per unit mass of fluid
-
is the ratio of specific heats
The above equations are closed by taking an equation of state, the simplest being the ideal gas
where
-
is the gas constant
-
is the absolute temperature
