Finite-volume scheme for the solution of integral boundary layer equations

Lokatt, Mikaela; Eller, David

doi:10.1016/j.compfluid.2016.04.002

Cited by 4 publications

(6 citation statements)

References 10 publications

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“…Moreover, for convenience, we define an alternative variable G as G ≡ ln q q e = ln c τ 1/2 (13) and transform the lag equation ( 9) into the following equivalent form,…”

Section: Turbulent Closurementioning

confidence: 99%

“…As for traditional 3D boundary layer solvers, the dependence on curvilinear coordinates limits their applicability to complex geometries. This issue was later sidestepped by non-parametric IBL formulations [1,[10][11][12][13][14]. For example, continuing from Drela's 3D IBL formulation [12], Zhang et al [1,14] proposed a discontinuous Galerkin (DG) finite element method (FEM) for discretizing the IBL equations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Strongly-coupled Non-parametric Integral Boundary Layer Method for Aerodynamic Analysis with Free Transition

Zhang

Drela

Allmaras

et al. 2019

AIAA Scitech 2019 Forum

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“…Moreover, for convenience, we define an alternative variable G as G ≡ ln q q e = ln c τ 1/2 (13) and transform the lag equation ( 9) into the following equivalent form,…”

Section: Turbulent Closurementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Strongly-coupled Non-parametric Integral Boundary Layer Method for Aerodynamic Analysis with Free Transition

Zhang

Drela

Allmaras

et al. 2019

AIAA Scitech 2019 Forum

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“…Finally, it can be noticed that Lokatt and Eller recently developed a Finite-Volume scheme for unstructured grids which they applied to the 3D IBL equations. 10 The same kind of method will be used here in order to ensure conservation on arbitrarily curved surfaces, as explained in section III.…”

Section: Derivation Of the Model Iia Brief State-of-the-art Of 3dmentioning

confidence: 99%

“…In the present study, the conservative character of the equations is preserved by employing a set of rotations, similarly to what is proposed by Lokatt and Eller. 10 A schematic depicting the involved variables is provided in figure 1. Therefore, we introduce the rotation matrixQ ij which is used to express tensorial quantities from the plane associated to cell Ω i in the plane associated to cell Ω j .…”

Section: Conservationmentioning

confidence: 99%

A 3D Finite-Volume Integral Boundary Layer method for icing applications

Bempedelis¹,

Bayeux²,

Blanchard³

et al. 2017

9th AIAA Atmospheric and Space Environments Conference

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A three-dimensional integral boundary layer code was developed to allow fast computations of boundary layer flows for the purpose of ice accretion modelling. The model is derived in this paper. It is based on a surface Finite-Volume approach. The unsteady equations of momentum deficit and kinetic energy deficit are solved until convergence is reached, preventing from specifying explicitly the stagnation point or separation line. A validation of the code is also presented in the present article. First, the 3D solver is cross-checked against a 2D solver on test cases of self-similar flows and on a NACA0012 configuration. The modelling of the effects of three-dimensionality is also assessed on a self-similar flow test-case. Moreover, the use of unstructured grids is also validated. Finally, an example of the use of the code for the computation of ice accretion is presented.

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“…In particular, since integral boundary layer methods have already been developed to study wind turbines [18], and these can also be thermally protected against icing [19], the method presented here can also be applied in this area. Integral boundary layer methods may also be used for aerodynamic design in the aeronautical industry [20] or for the modeling of wall mass transfers [21] (and more generally for the rapid design and optimization of any system involving heat and mass transfer induced by forced convection). Nevertheless, in the present work, the method will be tested in representative cases of icing applications only.…”

Section: Introductionmentioning

confidence: 99%

A Galerkin Method for the Simulation of Laminar Boundary Layers on Heated Walls

2022

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This paper presents a new solution method for the calculation of laminar thermal boundary layers. The method consists of a coupling between a modal method (Galerkin method) in the direction normal to the wall and a finite volume method in the direction(s) tangential to the wall. It is similar to an integral method in the sense that only a surface mesh is required and that the unknowns are integral quantities (corresponding to the moments up to a fixed order of the temperature profile in the direction normal to the wall). A specificity of the Galerkin method used is that the domain over which the integrals are computed has a variable size that is also an unknown of the problem. Using a series of numerical tests (representative of situations that can be encountered in aeronautics in the case of a wing equipped with a thermal ice protection system), we show that the new method allows us to predict the quantities of interest with a maximum error of a few percent, while a usual integral method (with only one unknown per mesh cell) is unable to treat the case of boundary layers on heated walls with a strong longitudinal temperature gradient, as shown in the literature.

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Finite-volume scheme for the solution of integral boundary layer equations

Cited by 4 publications

References 10 publications

A Strongly-coupled Non-parametric Integral Boundary Layer Method for Aerodynamic Analysis with Free Transition

A Strongly-coupled Non-parametric Integral Boundary Layer Method for Aerodynamic Analysis with Free Transition

A 3D Finite-Volume Integral Boundary Layer method for icing applications

A Galerkin Method for the Simulation of Laminar Boundary Layers on Heated Walls

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