Three-Dimensional Attached Viscous Flow

Hirschel, Ernst Heinrich; Cousteix, J.; Kordulla, W.

doi:10.1007/978-3-642-41378-0

Cited by 36 publications

(33 citation statements)

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“…The effect of the average surface-tangential momentum-the strength of the boundary layer-is explained best with the separation disposition of the primary boundary layer in two-dimensional flow. This boundary layer can negotiate an adverse pressure gradient the better, the more surface-tangential momentum it carries [5]. The classical example is that a laminar boundary layer will separate earlier with a given adverse pressure gradient than a turbulent one.…”

Section: Relevant Boundary-layer Propertiesmentioning

confidence: 99%

“…The recently evolved hybrid RANS/LES methods are two-domain models, too. Strong interaction models are three-domain approaches, see, e.g., [4,5].Considering the two-domain model "boundary layer flow and inviscid flow" leads to the topic of interaction. In this chapter we discuss the most important types of interaction between boundary-layer flow and inviscid flow.…”

mentioning

confidence: 99%

“…The recently evolved hybrid RANS/LES methods are two-domain models, too. Strong interaction models are three-domain approaches, see, e.g., [4,5].…”

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confidence: 99%

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Separation: Some Relevant Boundary-Layer Properties, Interaction Issues, and Drag

Hirschel¹,

Rizzi

Breitsamter

et al. 2020

Separated and Vortical Flow in Aircraft Wing Aerodynamics

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This chapter is devoted to an introduction to some of the concepts used when dealing with separated and vortical flow.We note first that the flow problems we are dealing with in general are Galilean invariant [1]. Therefore we can consider a flight vehicle in our mathematical models and in ground simulation (computational simulation, ground-facility simulation) in a fixed frame with the air-stream flowing past it. In the reality the vehicle moves through the-quasi-steady and quasi-uniform-atmosphere.In passing we also note that usually the Eulerian description of the flow is employed, which in contrast to the Lagrangian description considers the flow at every fixed point in space as steady or unsteady flow. For the different possible formulations of the governing equations see, e.g., [2,3].The flow field in our perceived reality (Model 1 in Sect. 1.5) is a one-domain entity. In aerodynamics and fluid mechanics, however, that entity is differentiated into several domains: the uniform far field, the inviscid flow field past the vehicle, the boundary layer flow at the vehicle's surface, the separated flow, the wake.The classical one-domain models to describe inviscid flow fields are the modeled potential flow (Model 4) and the discrete modeled Euler flow (Model 8). General one-domain approaches to describe viscous flow fields are the Navier-Stokes (NS) methods (Model 9), the Reynolds-Averaged Navier-Stokes (RANS) methods (Model 10), and the scale-resolving methods (Model 11).Applying a boundary-layer method (modeled viscous flow, Model 2) means working with a two-domain model, because always an inviscid flow model-first-has to be employed. The recently evolved hybrid RANS/LES methods are two-domain models, too. Strong interaction models are three-domain approaches, see, e.g., [4,5].Considering the two-domain model "boundary layer flow and inviscid flow" leads to the topic of interaction. In this chapter we discuss the most important types of interaction between boundary-layer flow and inviscid flow.

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Section: Relevant Boundary-layer Propertiesmentioning

confidence: 99%

mentioning

confidence: 99%

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Separation: Some Relevant Boundary-Layer Properties, Interaction Issues, and Drag

Hirschel¹,

Rizzi

Breitsamter

et al. 2020

Separated and Vortical Flow in Aircraft Wing Aerodynamics

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“…Three-dimensional flows can be found in swept wing turbine balls, flying ball, etc. In addition, comprehensive advantages and difficulties of three-dimensional over two-dimensional can be found in Hirschel et al [7]. Previously, Davey [8] and Davey and Schofield [9] have considered self similar solutions for the three-dimensional boundary-layer flow where outer mainstream irrotational flows are assumed in linear forms U ¼ U 1 x and V ¼ V 1 y, where U 1 and V 1 are strain rates and x and y are distances from leading edge, and the solutions exist in the range À1 c 0.…”

Section: Introductionmentioning

confidence: 99%

Computational and asymptotic methods for three-dimensional boundary-layer flow and heat transfer over a wedge

Kudenatti

Jyothi

2019

Engineering with Computers

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This paper is devoted to mathematical analysis of three-dimensional boundary-layer flow and heat transfer over a wedge. The boundary layer is formed due to the flow of a viscous and incompressible fluid and grows downstream along the walls of the wedge. This is appropriately approximated by a power of distances along both lateral directions. This analysis introduces a shear-to-strain-rate parameter c in the study which plays an essential role in three-dimensional boundary-layer study. A set of boundary-layer equations along with the conservation of energy has been transformed into a coupled nonlinear ordinary differential equations. Two methods are employed. The fluid-wedge interaction problem is solved in the circumstances where the equations are linearized and obtained the solutions in terms of confluent hypergeometric functions, and otherwise, the full-nonlinear problem numerically using the Keller-box method. In the former case, the results of eigenfunction analysis that is based on asymptotic study of the problem qualitatively support the latter numerical results. In either methods, the existence of solutions and range of parameter domain depending on various physical quantities is successfully analyzed. The two different approaches give good agreement with each other in predicting the velocity and temperature profiles in three-dimensional boundary layer. However, both approaches show that a solution to the problem exist only À 1\c\1. Since the Reynolds number is asymptotically large, the flow clearly divides into two regions showing the effects of viscosity and thermal conductivity. The velocity and thermal profiles are found to be benign. Flow always attached to the wedge surfaces and, thus, related thicknesses are becoming thinner. Extensive comparisons of the various results are made and a possible explanation on the results is discussed in some detail.

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“…Most of the books on elementary differential equations [9,10,11,12] would reveal that a boundary value problem (BVP) in a bounded domain contains two separate set of equations, one valid at the interior requiring it to be analytic or regular, and the other set of equations being prescribed at the boundaries. Equation (1) or for that matter the equations under scrutiny in [1,15,19,20,21,22,23] are no different from them.…”

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confidence: 99%

Finiteness of corner vortices

Kalita

Biswas

Panda

2018

Z. Angew. Math. Phys.

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The notion of infiniteness as pointed out in [1,2] comes from the solution of the biharmonic equation(1)The above is a simplified version of the Navier-Stokes equations for creeping flow. The author of [2] V. Shtern contends that although the solution of (1) leads to a sequence of infinite number of eddies, in physical reality, the sequence of eddies is finite. This is a clear admission that (1) does not accurately model the physical reality. In a self-contradictory defence, the author ([2]) comments that " "the sequence of corner eddies is finite", which is valid from the physical point of view, is incorrect for the mathematical solution."It is highly probable that tweaked statements such as "incorrect for mathematical solution" and "valid from physical point of view" could divert the scientific community further from the ground reality, which, on the contrary is not very difficult to fathom in the current context! If a partial differential equation modelling a physical system produces a mathematically correct solution having no physical relevance, it is a clear indication that the equation has failed to model the physical system correctly. Viscous effects on the wall, which is a pre-requisite for flow separation leading to the formation of vortex is completely absent in equation (1). We have also reiterated in our original work [1] that one of the sources of this non-physical result is the discontinuity of the boundary conditions at r = 0, ie., at the corner and failure of equation (1) in adhering to the continuum hypothesis on which the foundation of Navier-Stokes equation is built upon. R. L. Panton, in his highly acclaimed book Incompressible flows [4] concurs with our views: citing a specific case of Stokes flow in corners, he states that the remedy of removing this discontinuity lies in solving another problem that allows for a small gap at the corner (the junction of the walls). If the gap is actu-

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Three-Dimensional Attached Viscous Flow

Cited by 36 publications

References 0 publications

Separation: Some Relevant Boundary-Layer Properties, Interaction Issues, and Drag

Separation: Some Relevant Boundary-Layer Properties, Interaction Issues, and Drag

Computational and asymptotic methods for three-dimensional boundary-layer flow and heat transfer over a wedge

Finiteness of corner vortices

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