rotationVelocity in rotatingTotalPressure and SRF

deepblue17 · July 18, 2009, 06:20

Hello,

I think the computation of the rotationVelocity in rotatingTotalPressure and SRF could be simplified. The piece of code is:

Code:

vector axisHat = omega_/mag(omega_);
vectorField rotationVelocity =
omega_ ^ (patch().Cf() - axisHat*(axisHat & patch().Cf()));

In mathematical formulation this yields to:

$\vec{axis} = \frac{\vec{\omega} }{ |\vec{\omega}|}$
$\vec{V} = \vec{\omega} \times ( \vec{r} - \vec{axis} \bullet (\vec{axis} \bullet \vec{r} ) ) = \vec{\omega} \times \vec{r} - \vec{\omega} \times \vec{axis} \bullet (\vec{axis} \bullet \vec{r} )$

Reformulation of the right term:
$\vec{\omega} \times \vec{axis} \bullet (\vec{axis} \bullet \vec{r} ) = ( \vec{\omega} \times \frac{ \vec{\omega} }{ |\vec{\omega}|} ) \bullet (\vec{axis} \bullet \vec{r} ) = ( \vec{\omega} \times \vec{\omega} ) \bullet \frac{ (\vec{axis} \bullet \vec{r} )}{ |\vec{\omega}|} = \vec{0}$

This reduces the computation of the rotationVelocity to:

$\vec{V} = \vec{\omega} \times \vec{r}$

or in C++

Code:

vectorField rotationVelocity = omega_ ^ patch().Cf();

immortality · December 7, 2012, 08:11

can we use rotatingTotalPressure in a 2-D case?

July 18, 2009, 06:20	rotationVelocity in rotatingTotalPressure and SRF	#1
deepblue17 Member Oliver Borm Join Date: Mar 2009 Posts: 59 Rep Power: 6	Hello, I think the computation of the rotationVelocity in rotatingTotalPressure and SRF could be simplified. The piece of code is: Code: vector axisHat = omega_/mag(omega_); vectorField rotationVelocity = omega_ ^ (patch().Cf() - axisHat*(axisHat & patch().Cf())); In mathematical formulation this yields to: $\vec{axis} = \frac{\vec{\omega} }{ \|\vec{\omega}\|}$ $\vec{V} = \vec{\omega} \times ( \vec{r} - \vec{axis} \bullet (\vec{axis} \bullet \vec{r} ) ) = \vec{\omega} \times \vec{r} - \vec{\omega} \times \vec{axis} \bullet (\vec{axis} \bullet \vec{r} )$ Reformulation of the right term: $\vec{\omega} \times \vec{axis} \bullet (\vec{axis} \bullet \vec{r} ) = ( \vec{\omega} \times \frac{ \vec{\omega} }{ \|\vec{\omega}\|} ) \bullet (\vec{axis} \bullet \vec{r} ) = ( \vec{\omega} \times \vec{\omega} ) \bullet \frac{ (\vec{axis} \bullet \vec{r} )}{ \|\vec{\omega}\|} = \vec{0}$ This reduces the computation of the rotationVelocity to: $\vec{V} = \vec{\omega} \times \vec{r}$ or in C++ Code: vectorField rotationVelocity = omega_ ^ patch().Cf();

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December 7, 2012, 08:11		#2
immortality Banned ehsan Join Date: Oct 2012 Location: Iran Posts: 1,106 Rep Power: 0	can we use rotatingTotalPressure in a 2-D case?