Analytical approximation of two-dimensional separated turbulent boundary-layer velocity profiles

Swafford, T. W.

doi:10.2514/3.8177

Cited by 47 publications

(17 citation statements)

References 8 publications

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“…see references 27,28,29 ). It is interesting to note that in a recent study, Seubers 30 showed the derivation of the integral boundary layer equations with a streamline based control volume approach including terms for non-classical (separating) boundary layers.…”

Section: Iia Integral Boundary Layer Methodsmentioning

confidence: 99%

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Unsteady Interacting Boundary Layer Method

Özdemir

Garrel

Ravishankara

et al. 2017

35th Wind Energy Symposium

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Within this study an unsteady, two-dimensional interacting boundary layer method is presented for the incompressible flow around wind turbine rotor blade sections. The main approach is to divide the flow field in to two regions; the one in the vicinity of the surface where the viscosity is effective (so called boundary layer) and the one away from the surface where the flow can be assumed as inviscid. The solutions obtained from these two regions are matched with a quasi-simultaneous viscous-inviscid interaction scheme. For the viscous flow, unsteady integral boundary layer equations together with laminar and turbulent closure sets are solved employing a high-order quadrature-free discontinuous Galerkin method. Laminar to turbulent transition is modeled with the e N method. The potential flow is solved by using the linear-strength vortex panel method. It is shown that introducing the interaction scheme leads to non-conservative mechanisms in the system. The discontinuous Galerkin method is extended to handle these non-conservative flux terms. Furthermore it is shown that this numerical method achieves the designed order of accuracy for smooth problems. Results are presented for the individual numerical solution methods which are verified on various test cases and subsequently for the coupled system which is applied on a chosen test case. Evaluation of a laminar flow over an airfoil section is shown and the results (converged to a steady state solution) are compared with other numerical solutions as well as with the experimental data where available. It is shown that the results of the developed numerical solution method are in good agreement with the experimental data and other computational methods.

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Section: Iia Integral Boundary Layer Methodsmentioning

confidence: 99%

“…11 Integral boundary layer equations have been commonly discretized with Finite-Difference schemes. 24,10 More recently also Finite-Element and Finite-Volume discretizations are employed.…”

Section: Unsteady Interacting Boundary Layer Methodsmentioning

confidence: 99%

Unsteady Interacting Boundary Layer Method

Özdemir

Garrel

Ravishankara

et al. 2017

35th Wind Energy Symposium

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“…The turbulent reattachment point is generally obtained using the skin-friction and velocity profile formulas of Swafford [7].…”

Section: Introductionmentioning

confidence: 99%

A thermographic method to evaluate laminar bubble phenomena on airfoil operating at low Reynolds number

Cesini¹,

Ricci²,

Montelpare³

et al. 2002

Proceedings of the 2002 International Conference on Quantitative InfraRed Thermography

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The aim of this research is the study of the laminar boundary layer separation phenomena on aerodynamic bodies by infrared thermography. The presence and the size of laminar bubble are mainly observed. A thermographic method is adjusted to detect the presence and the longitudinal dimension of the laminar bubble. In this region the convective heat transfer coefficient is lower than in the surroundings, because of the recirculating flow. Heating the airfoil surface, the laminar bubble will appear warmer than the other zones and so it is possible to know its presence and position.

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“…Near the minimum, high values of the derivative increases the error in the second basic differential equation (24). The singular point can be avoided by solving in an inverse manner, in which is specific and du iw /ds is unknown.…”

Section: Inverting Viscous Calculationsmentioning

confidence: 99%

“…The skin-friction coefficient is taken from the work of Swafford,24 which gives C f < 0 when the flow is separated.…”

Section: Closure Conditionsmentioning

confidence: 99%

Viscous-Inviscid Method for Airfoil Analysis and Design for Aviation and Windmills

Peltonen

2006

Journal of Aircraft

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This study examines an advanced viscous-inviscid interactive method developed for the analysis and design of airfoils in two-dimensional subsonic compressible flow (Ma ∞ < 0.4). Inviscid flow is solved with a panel method. The laminar boundary layer is calculated by Thwaites' method. Transition is determined by Michel's relation or the e n method. An integral solution for a turbulent boundary layer is derived from an entrainment equation. Closure conditions are obtained with empirical relations. Singularities near the separation are avoided by inverting the boundary-layer method. Inviscid and viscous flows are coupled with transpiration. The analysis method is used as a "black box" in the design tasks. The geometry of the starting airfoil is perturbed iteratively by transpiration until the pressure distribution converges to a predefined target. This study proposes the necessary degrees of freedom in the target velocity distribution to obtain a closed airfoil. Design cases are included, which support the general applicability and accuracy of the numerical design method.

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Analytical approximation of two-dimensional separated turbulent boundary-layer velocity profiles

Cited by 47 publications

References 8 publications

Unsteady Interacting Boundary Layer Method

Unsteady Interacting Boundary Layer Method

A thermographic method to evaluate laminar bubble phenomena on airfoil operating at low Reynolds number

Viscous-Inviscid Method for Airfoil Analysis and Design for Aviation and Windmills

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