# Baldwin-Lomax model

(Difference between revisions)
 Revision as of 12:40, 8 September 2005 (view source)Jola (Talk | contribs)← Older edit Revision as of 13:08, 8 September 2005 (view source)Jola (Talk | contribs) Newer edit → Line 1: Line 1: == Introduction == == Introduction == - The Baldwin-Lomax model is a two-layer algebraic model which gives the eddy-viscosity, $\mu_t$, as a function of the local boundary layer velocity profile.The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace and turbomachinery applications. The model is also commonly used in this type of application, especially for quick design iterations where the robustness is more important than getting capturing all details of the flow physics. + The Baldwin-Lomax model is a two-layer algebraic 0-equation model which gives the eddy-viscosity, $\mu_t$, as a function of the local boundary layer velocity profile.The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace and turbomachinery applications. The model is also commonly used in this type of application, especially for quick design iterations where robustness is more important than capturing all details of the flow physics. == Equations == == Equations == Line 110: Line 110: - == Performance and applicability of the model == + == Model variants == - (1). Yes, I think, the state of the art of the turbulence modeling is still not capable of predicting the separated flow accurately. (2). In David Wilcox's book, Section 3.6 Separated Flows, he stated "Menter(1992b) applied the Baldwin-Lomax model to an axisymmetric flow with a strong adverse pressure gradient. The experiment was conducted by Driver(1991). Inspection of the skin friction shows that the Baldwin-Lomax model yields a separation bubble nearly twice as long as the experimentally observed bubble. The corresponding rise in pressure over the separation region is 15% to 20% higher than measured. As pointed out by Menter, the Cebeci-Smith model yields similar results." (3). The question I have is: if an application engineer run the code with Baldwin-Lomax model and obtain the reault with flow separation, then based on the Menter's study, it is not possible for the application engineer to know whether the real flow is separated or not. Menter was very lucky because he is using the experimental data performed by Driver, so he was able to spot the poor performance of the Baldwin-Lomax model. But for the application engineer using the model, I don't think he will ever conduct the experiment to see whether his case is actually separated or not. The experiment to verify the flow separation in turbomachinery is very difficult to perform. (4). At the research level, this is just another opportunity to do research. But for the application engineer, what is going to happen to the results with flow separation? and also the subsequent designs in the real product? (I guess, it's his problem, if he is not reading this forum.) + '''Add info here about about Granville and Turner-Jennions modifications ''' - You are quite right with your comments, as the original Baldwin-Lomax model indeed tends to overpredict separation bubbles. However, there are ad-hoc modifications which reduce this effect. For instance, the predictions of separation are quite sensitive to the Cwk coefficient and higher values than the original ones are known to restrict the early separation. Also, the Granville corrections take partly into account adverse pressure gradient effects, which attenuate the original weaknesses. This to mention that the model can be made to work in an efficient and adequate way for practical applications, without forgetting that, like all algebraic models, it contains less physics than two equation models, which in turn contain less physics than full Reynolds stress models. But particularly for separation predictions, much research is still needed to obtain reliable predictions with any turbulence model. + == Performance, applicability and limitations == + + The Baldwin-Lomax model is suitable for high-speed flows with thin attached boundary layers. Typical applications are aerospace and turbomachinery applications. It is a low-Re model and as such it requires a fairly well-resolved grid near the walls, with the first cell located at $y+ \approx 1$. + + The model is popular in quick design-iterations due to its robustness and reliability. It seldom leads to any convergence problems and it seldom gives completely unphysical results. + + The Baldwin-Lomax model should be used with great care in cases with large separations. It has been shown by several researcher that the Baldwin-Lomax model tends to overpredict separated regions (see for example the comments made by David Wilcox in his book Turbulence Modeling for CFD). However, there are ad-hoc modifications which reduce this problem. For instance, prediction of separation is sensitive to the value of the $C_{WK}$ coefficient and higher values than the original value have been shown to reduce the problems with too early separation. Also, the Granville corrections take partly into account adverse pressure gradient effects, which attenuate the original weaknesses.

## Introduction

The Baldwin-Lomax model is a two-layer algebraic 0-equation model which gives the eddy-viscosity, $\mu_t$, as a function of the local boundary layer velocity profile.The model is suitable for high-speed flows with thin attached boundary-layers, typically present in aerospace and turbomachinery applications. The model is also commonly used in this type of application, especially for quick design iterations where robustness is more important than capturing all details of the flow physics.

## Equations $\mu_t = \begin{cases} {\mu_t}_{inner} & \mbox{if } y \le y_{crossover} \\ {\mu_t}_{outer} & \mbox{if} y > y_{crossover} \end{cases}$ (1)

Where $y_{crossover}$ is the smallest distance from the surface where ${\mu_t}_{inner}$ is equal to ${\mu_t}_{outer}$: $y_{crossover} = MIN(y) \ : \ {\mu_t}_{inner} = {\mu_t}_{outer}$ (2)

The inner region is given by the Prandtl - Van Driest formula: ${\mu_t}_{inner} = \rho l^2 \left| \Omega \right|$ (3)

Where $l = k y \left( 1 - e^{\frac{-y^+}{A^+}} \right)$ (4) $\left| \Omega \right| = \sqrt{2 \Omega_{ij} \Omega_{ij}}$ (5) $\Omega_{ij} = \frac{1}{2} \left( \frac{\partial u_i}{\partial x_j} - \frac{\partial u_j}{\partial x_i} \right)$ (6)

The outer region is given by: ${\mu_t}_{outer} = \rho \, K \, C_{CP} \, F_{WAKE} \, F_{KLEB}(y)$ (7)

Where $F_{WAKE} = MIN \left( y_{MAX} \, F_{MAX} \,\,;\,\, C_{WK} \, y_{MAX} \, \frac{u^2_{DIF}}{F_{MAX}} \right)$ (8) $y_{MAX}$ and $F_{MAX}$ are determined from the maximum of the function: $F(y) = y \left| \Omega \right| \left(1-e^{\frac{-y^+}{A^+}} \right)$ (9) $F_{KLEB}$ is the intermittency factor given by: $F_{KLEB}(y) = \left[1 + 5.5 \left( \frac{y \, C_{KLEB}}{y_{MAX}} \right)^6 \right]^{-1}$ (10) $u_{DIF}$ is the difference between maximum and minimum speed in the profile. For boundary layers the minimum is always set to zero. $u_{DIF} = MAX(\sqrt{u_i u_i}) - MIN(\sqrt{u_i u_i})$ (11)

## Model constants

The table below gives the model constants present in the formulas above. Note that $k$ is a constant, and not the turbulence energy, as in other sections. It should also be pointed out that when using the Baldwin-Lomax model the turbulence energy, $k$, present in the governing equations, is set to zero. $A^+$ $C_{CP}$ $C_{KLEB}$ $C_{WK}$ $k$ $K$ 26 1.6 0.3 0.25 0.4 0.0168

## Performance, applicability and limitations

The Baldwin-Lomax model is suitable for high-speed flows with thin attached boundary layers. Typical applications are aerospace and turbomachinery applications. It is a low-Re model and as such it requires a fairly well-resolved grid near the walls, with the first cell located at $y+ \approx 1$.

The model is popular in quick design-iterations due to its robustness and reliability. It seldom leads to any convergence problems and it seldom gives completely unphysical results.

The Baldwin-Lomax model should be used with great care in cases with large separations. It has been shown by several researcher that the Baldwin-Lomax model tends to overpredict separated regions (see for example the comments made by David Wilcox in his book Turbulence Modeling for CFD). However, there are ad-hoc modifications which reduce this problem. For instance, prediction of separation is sensitive to the value of the $C_{WK}$ coefficient and higher values than the original value have been shown to reduce the problems with too early separation. Also, the Granville corrections take partly into account adverse pressure gradient effects, which attenuate the original weaknesses.