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en>Niceguyedc: WPCleaner v1.33 - Repaired 1 link to disambiguation page - (You can help) - Distributive

2014-10-02T05:28:43Z

WPCleaner v1.33 - Repaired 1 link to disambiguation page - (You can help) - Distributive

← Older revision		Revision as of 07:28, 2 October 2014
Line 1:		Line 1:
	~~{{Multiple issues\|~~		Hello buddy. Let me introduce myself. I am Luther Aubrey. What she loves doing is taking part in croquet and she is attempting to make it a profession. He currently life in Idaho and his parents reside close by. My occupation is a messenger.<br><br>Feel free to visit my web site; [http://Vollrausch-gaming.de/index.php?mod=users&action=view&id=2209 Vollrausch-gaming.de]
	~~{{context\|date=May 2011}}~~
	~~{{technical\|date=May 2011}}~~
	}}

	~~The '''Spalart–Allmaras model''' is a one equation model for [[turbulent]] [[viscosity]]~~. ~~It solves a [[transport equation]] for a viscosity-like variable <math>\tilde{\nu}</math>~~. ~~This may be referred to as the Spalart–Allmaras variable~~.

	~~== Original model ==~~
	~~The turbulent [[Viscosity\|eddy viscosity]]~~ is ~~given by~~

	~~:<math>~~
	~~\nu_t = \tilde{\nu} f_{v1}, \quad f_{v1} = \frac{\chi^3}{\chi^3 + C^3_{v1}}, \quad \chi := \frac{\tilde{\nu}}{\nu}~~
	~~</math>~~

	~~:<math>~~
	\frac{\partial \tilde{\nu}}{\partial t} + u_j \frac{\partial \tilde{\nu}}{\partial x_j} = C_{b1} [1 - f_{t2}] \tilde{S} \tilde{\nu} + \frac{1}{\sigma} \{ \nabla \cdot [(\nu + \tilde{\nu}) \nabla \tilde{\nu}] + C_{b2} \| \nabla \nu \|^2 \} - \left[C_{w1} f_w - \frac{C_{b1}}{\kappa^2} f_{t2}\right] \left( \frac{\tilde{\nu}}{d} \right)^2 + f_{t1} \Delta U^2
	~~</math>~~

	~~:<math>~~
	~~\tilde{S} \equiv S + \frac{ \tilde{\nu} }{ \kappa^2 d^2 } f_{v2}, \quad f_{v2} = 1 - \frac{\chi}{1 + \chi f_{v1}}~~
	~~</math>~~

	~~:<math>~~
	~~f_w = g \left[ \frac{ 1 + C_{w3}^6 }{ g^6 + C_{w3}^6 } \right]^{1/6}, \quad g = r + C_{w2}(r^6 - r), \quad r \equiv \frac{\tilde{\nu} }{ \tilde{S} \kappa^2 d^2 }~~
	~~</math>~~

	~~:<math>~~
	~~f_{t1} = C_{t1} g_t \exp\left( -C_{t2} \frac{\omega_t^2}{\Delta U^2} [ d^2 + g^2_t d^2_t] \right)~~
	~~</math>~~

	~~:<math>~~
	~~f_{t2} = C_{t3} \exp\left(-C_{t4} \chi^2 \right)~~
	~~</math>~~

	~~:<math>~~
	~~S = \sqrt{2 \Omega_{ij} \Omega_{ij}}~~
	~~</math>~~

	~~The [[rotation]] [[tensor]] is given by~~
	~~:<math>~~
	~~\Omega_{ij} = \frac{1}{2} ( \partial u_i / \partial x_j - \partial u_j / \partial x_i )~~
	~~</math>~~
	and d is ~~the distance from the closest surface.~~

	~~The [[Constant (mathematics)\|constants]] are~~

	~~:<math>~~
	~~\begin{matrix}~~
	~~\sigma &=& 2/3\\~~
	~~C_{b1} &=& 0.1355\\~~
	~~C_{b2} &=& 0.622\\~~
	~~\kappa &=& 0.41\\~~
	~~C_{w1} &=& C_{b1}/\kappa^2 + (1 + C_{b2})/\sigma \\~~
	~~C_{w2} &=& 0.3 \\~~
	~~C_{w3} &=& 2 \\~~
	~~C_{v1} &=& 7.1 \\~~
	~~C_{t1} &=& 1 \\~~
	~~C_{t2} &=& 2 \\~~
	~~C_{t3} &=& 1.1 \\~~
	~~C_{t4} &=& 2~~
	~~\end{matrix}~~
	~~</math>~~

	~~== Modifications to original model ==~~
	~~According~~ to ~~Spalart~~ it ~~is safer to use the following values for the last two constants:~~
	~~:<math>~~
	~~\begin{matrix}~~
	~~C_{t3} &=& 1~~.~~2 \\~~
	~~C_{t4} &=& 0~~.5
	~~\end{matrix}~~
	~~</math>~~

	~~Other models related to the S-A model:~~

	~~DES (1999) [http://www.cfd-online.com/Wiki/Detached_eddy_simulation_%28DES%29]~~

	~~DDES (2006)~~

	~~== Model for compressible flows ==~~
	~~There are two approaches to adapting the model for [[compressible flow]]s. In the first approach, the turbulent dynamic viscosity~~ is ~~computed from~~

	~~:<math>~~
	~~\mu_t = \rho \tilde{\nu} f_{v1}~~
	~~</math>~~

	~~where <math>\rho</math> is the local density~~. ~~The [[convective]] terms in the equation for~~ <~~math~~>~~\tilde{\nu}~~<~~/math~~> ~~are modified~~ to

	~~:<math>~~
	~~\frac{\partial \tilde{\nu}}{\partial t} + \frac{\partial}{\partial x_j} (\tilde{\nu} u_j)= \mbox{RHS}~~
	~~</math>~~

	~~where the~~ [~~[Sides of an equation\|right hand side]] (RHS) is the same as in the original model.~~

	~~== Boundary conditions ==~~
	~~Walls~~: ~~<math>\tilde{\nu}=0<~~/~~math>~~

	~~Freestream:~~

	~~Ideally <math>\tilde{\nu}=0<~~/~~math>, but some solvers can have problems with a zero value, in which case <math>\tilde{\nu}<=\frac{\nu}{2}</math> can be used~~.

	~~This is if the trip term is used to "start up" the model. A convenient option is to set <math>\tilde{\nu}=5{\nu}<~~/~~math> in the [[freestream]]~~. ~~The model then provides "Fully Turbulent" behavior, i.e., it becomes turbulent in any region that contains [[shear stress\|shear]].~~

	~~Outlet: convective outlet.~~

	== ~~References~~ ==

	* ''Spalart, P. R. and Allmaras, S. R.'', 1992, '''"A One-Equation Turbulence Model for Aerodynamic Flows"''' ''AIAA Paper 92-0439''

	~~== External links ==~~

	* This article was based on the [http://www.cfd-~~online~~.~~com/Wiki/Spalart-Allmaras_model Spalart-Allmaras model] article in [http://www.cfd-online.com/Wiki CFD-Wiki]~~
	* [http://www.kxcad.net/STAR-CCM/online/138-spalartAllmarasTurbulence-02.html What Are the Spalart-Allmaras Turbulence Models?] from kxcad.net
	* [http://turbmodels.larc.nasa.gov/spalart.html The Spalart-Allmaras Turbulence Model] at NASA's Langley Research Center Turbulence Modelling Resource site

	~~{{DEFAULTSORT:Spalart-Allmaras turbulence model}}~~
	~~[[Category:Turbulence models]~~]

en>Cydebot: Robot - Speedily moving category Nonassociative algebra to :Category:Non-associative algebra per CFDS.

2013-05-23T05:26:27Z

Robot - Speedily moving category Nonassociative algebra to Category:Non-associative algebra per CFDS.

← Older revision		Revision as of 07:26, 23 May 2013
Line 1:		Line 1:
	~~Hello~~. ~~Let me introduce~~ the ~~author~~. ~~Her name~~ is ~~Emilia Shroyer but~~ it's ~~not~~ the ~~most feminine title out there. Puerto Rico~~ is ~~exactly~~ where ~~he and his spouse live~~. ~~Bookkeeping~~ is ~~what I do~~. ~~Playing baseball~~ is the ~~hobby he will never quit doing~~.<br><br>~~Also visit my blog post~~ - [http://www.~~neweracinema~~.com/~~tube~~/~~user~~/~~D69E~~ at ~~home std testing~~]		{{Multiple issues\|
			{{context\|date=May 2011}}
			{{technical\|date=May 2011}}
			}}

			The '''Spalart–Allmaras model''' is a one equation model for [[turbulent]] [[viscosity]]. It solves a [[transport equation]] for a viscosity-like variable <math>\tilde{\nu}</math>. This may be referred to as the Spalart–Allmaras variable.

			== Original model ==
			The turbulent [[Viscosity\|eddy viscosity]] is given by

			:<math>
			\nu_t = \tilde{\nu} f_{v1}, \quad f_{v1} = \frac{\chi^3}{\chi^3 + C^3_{v1}}, \quad \chi := \frac{\tilde{\nu}}{\nu}
			</math>

			:<math>
			\frac{\partial \tilde{\nu}}{\partial t} + u_j \frac{\partial \tilde{\nu}}{\partial x_j} = C_{b1} [1 - f_{t2}] \tilde{S} \tilde{\nu} + \frac{1}{\sigma} \{ \nabla \cdot [(\nu + \tilde{\nu}) \nabla \tilde{\nu}] + C_{b2} \| \nabla \nu \|^2 \} - \left[C_{w1} f_w - \frac{C_{b1}}{\kappa^2} f_{t2}\right] \left( \frac{\tilde{\nu}}{d} \right)^2 + f_{t1} \Delta U^2
			</math>

			:<math>
			\tilde{S} \equiv S + \frac{ \tilde{\nu} }{ \kappa^2 d^2 } f_{v2}, \quad f_{v2} = 1 - \frac{\chi}{1 + \chi f_{v1}}
			</math>

			:<math>
			f_w = g \left[ \frac{ 1 + C_{w3}^6 }{ g^6 + C_{w3}^6 } \right]^{1/6}, \quad g = r + C_{w2}(r^6 - r), \quad r \equiv \frac{\tilde{\nu} }{ \tilde{S} \kappa^2 d^2 }
			</math>

			:<math>
			f_{t1} = C_{t1} g_t \exp\left( -C_{t2} \frac{\omega_t^2}{\Delta U^2} [ d^2 + g^2_t d^2_t] \right)
			</math>

			:<math>
			f_{t2} = C_{t3} \exp\left(-C_{t4} \chi^2 \right)
			</math>

			:<math>
			S = \sqrt{2 \Omega_{ij} \Omega_{ij}}
			</math>

			The [[rotation]] [[tensor]] is given by
			:<math>
			\Omega_{ij} = \frac{1}{2} ( \partial u_i / \partial x_j - \partial u_j / \partial x_i )
			</math>
			and d is the distance from the closest surface.

			The [[Constant (mathematics)\|constants]] are

			:<math>
			\begin{matrix}
			\sigma &=& 2/3\\
			C_{b1} &=& 0.1355\\
			C_{b2} &=& 0.622\\
			\kappa &=& 0.41\\
			C_{w1} &=& C_{b1}/\kappa^2 + (1 + C_{b2})/\sigma \\
			C_{w2} &=& 0.3 \\
			C_{w3} &=& 2 \\
			C_{v1} &=& 7.1 \\
			C_{t1} &=& 1 \\
			C_{t2} &=& 2 \\
			C_{t3} &=& 1.1 \\
			C_{t4} &=& 2
			\end{matrix}
			</math>

			== Modifications to original model ==
			According to Spalart it is safer to use the following values for the last two constants:
			:<math>
			\begin{matrix}
			C_{t3} &=& 1.2 \\
			C_{t4} &=& 0.5
			\end{matrix}
			</math>

			Other models related to the S-A model:

			DES (1999) [http://www.cfd-online.com/Wiki/Detached_eddy_simulation_%28DES%29]

			DDES (2006)

			== Model for compressible flows ==
			There are two approaches to adapting the model for [[compressible flow]]s. In the first approach, the turbulent dynamic viscosity is computed from

			:<math>
			\mu_t = \rho \tilde{\nu} f_{v1}
			</math>

			where <math>\rho</math> is the local density. The [[convective]] terms in the equation for <math>\tilde{\nu}</math> are modified to

			:<math>
			\frac{\partial \tilde{\nu}}{\partial t} + \frac{\partial}{\partial x_j} (\tilde{\nu} u_j)= \mbox{RHS}
			</math>

			where the [[Sides of an equation\|right hand side]] (RHS) is the same as in the original model.

			== Boundary conditions ==
			Walls: <math>\tilde{\nu}=0</math>

			Freestream:

			Ideally <math>\tilde{\nu}=0</math>, but some solvers can have problems with a zero value, in which case <math>\tilde{\nu}<=\frac{\nu}{2}</math> can be used.

			This is if the trip term is used to "start up" the model. A convenient option is to set <math>\tilde{\nu}=5{\nu}</math> in the [[freestream]]. The model then provides "Fully Turbulent" behavior, i.e., it becomes turbulent in any region that contains [[shear stress\|shear]].

			Outlet: convective outlet.

			== References ==

			* ''Spalart, P. R. and Allmaras, S. R.'', 1992, '''"A One-Equation Turbulence Model for Aerodynamic Flows"''' ''AIAA Paper 92-0439''

			== External links ==

			* This article was based on the [http://www.cfd-online.com/Wiki/Spalart-Allmaras_model Spalart-Allmaras model] article in [http://www.cfd-online.com/Wiki CFD-Wiki]
			* [http://www.kxcad.net/STAR-CCM/online/138-spalartAllmarasTurbulence-02.html What Are the Spalart-Allmaras Turbulence Models?] from kxcad.net
			* [http://turbmodels.larc.nasa.gov/spalart.html The Spalart-Allmaras Turbulence Model] at NASA's Langley Research Center Turbulence Modelling Resource site

			{{DEFAULTSORT:Spalart-Allmaras turbulence model}}
			[[Category:Turbulence models]]

en>FrescoBot: Bot: fixing section wikilinks

2012-07-08T03:07:35Z

Bot: fixing section wikilinks

New page

Hello. Let me introduce the author. Her name is Emilia Shroyer but it's not the most feminine title out there. Puerto Rico is exactly where he and his spouse live. Bookkeeping is what I do. Playing baseball is the hobby he will never quit doing.<br><br>Also visit my blog post - [http://www.neweracinema.com/tube/user/D69E at home std testing]