A simple interaction law for viscous–inviscid interaction

The viscous–inviscid interaction (VII) philosophy for modelling aerodynamic boundary layers is discussed. ‘Traditionally’ the shear-layer equations are solved with pressure prescribed by the inviscid flow, but then the solution breaks down in a singularity related to flow separation. In the quasi-simultaneous coupling approach this singularity is overcome by making use of an interaction law. A novel mathematical analysis is presented of the essential properties of such interaction laws, which is based on classical theory for non-negative matrices. The performance of a highly simplified interaction law is demonstrated for separated airfoil flow beyond maximum lift.

[1]  S. F. Shen,et al.  The spontaneous generation of the singularity in a separating laminar boundary layer , 1980 .

[2]  Arthur Veldman,et al.  A numerical method for the calculation of laminar, incompressible boundary layers with strong viscous - inviscid interaction , 1979 .

[3]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[4]  H. Schlichting.  Boundary Layer Theory , 1955 .

[5]  R. Houwink,et al.  Steady and unsteady seperated flow computations for transonic airfoils , 1984 .

[6]  Arthur Veldman,et al.  A new, quasi-simultaneous method to calculate interacting boundary layers , 1980 .

[7]  D. Catherall,et al.  The integration of the two-dimensional laminar boundary-layer equations past the point of vanishing skin friction , 1966, Journal of Fluid Mechanics.

[8]  J. Van der Vooren,et al.  A fast robust viscous-inviscid interaction solver for transonic flowabout wing/body configurations on the basis of full potential theory , 1993 .

[9]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[10]  A. Veldman.  A calculation method for incompressible boundary layers with strong viscous-inviscid interaction , 1980 .

[11]  J. W. Elliott,et al.  Dynamic stall due to unsteady marginal separation , 1987, Journal of Fluid Mechanics.

[12]  W. C. Reynolds,et al.  Calculation of Turbulent Flows , 1975 .

[13]  I. H. Abbott,et al.  Theory of Wing Sections , 1959 .

[14]  P. Lagerstrom,et al.  Solutions of the Navier-Stokes equation at large Reynolds number , 1975 .

[15]  John W. Edwards,et al.  Calculated Viscous and Scale Effects on Transonic Aeroelasticity , 2008 .

[16]  Tuncer Cebeci,et al.  An Engineering Approach to the Calculation of Aerodynamic Flows , 1999 .

[17]  Walter F. O'Brien,et al.  Simultaneous Solution of the Boundary Layer and Freestream with Separated Flow , 1978 .

[18]  F. Smith.  Steady and Unsteady Boundary-Layer Separation , 1986 .

[19]  A. Messiter.  Boundary-Layer Flow Near the Trailing Edge of a Flat Plate , 1970 .

[20]  Arthur Veldman,et al.  Quasi-Simultaneous Viscous-Inviscid Interaction for Transonic Airfoil Flow , 2005 .

[21]  Klaus Gersten,et al.  Boundary-Layer Theory - 8th Revised and Enlarged Edition , 2000 .

[22]  M. Lighthill,et al.  On boundary layers and upstream influence. I. A comparison between subsonic and supersonic flows , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  Francis J. Smith,et al.  Steady and unsteady 3D interactive boundary layers , 1991 .

[24]  Terry L. Holst,et al.  Viscous transonic airfoil workshop compendium of results , 1988 .

[25]  J. Périaux,et al.  Domain Decomposition Methods in Science and Engineering , 1994 .

[26]  M. Lighthill.  On displacement thickness , 1958, Journal of Fluid Mechanics.

[27]  A. Veldman,et al.  On the breakdown of the steady and unsteady interacting boundary-layer description , 1987, Journal of Fluid Mechanics.

[28]  S. Goldstein,et al.  ON LAMINAR BOUNDARY-LAYER FLOW NEAR A POSITION OF SEPARATION , 1948 .

[29]  K. Stewartson,et al.  On the flow near the trailing edge of a flat plate II , 1969 .

[30]  E. de Boer,et al.  VISTRAFS: A Simulation Method for Strongly Interacting Viscous Transonic Flow , 1990 .

[31]  Arthur Veldman.  A numerical view on strong viscous-inviscid interaction , 1983 .

[32]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[33]  J. E. Carter,et al.  Solutions for incompressible separated boundary layers including viscous-inviscid interaction , 1975 .

[34]  T. Cebeci,et al.  Modeling and Computation of Boundary-Layer Flows: Laminar, Turbulent and Transitional Boundary Layers in Incompressible Flows , 1998 .

[35]  K. Stewartson.  Multistructured Boundary Layers on Flat Plates and Related Bodies , 1974 .

[36]  E. Carter,et al.  VISCOUS-INVISCID INTERACTION ANALYSIS OF TRANSONIC TURBULENT SEPARATED FLOW , 1981 .

[37]  Ronald F. Probstein,et al.  Hypersonic Flow Theory , 1959 .

[38]  Neil D. Sandham,et al.  Transitional separation bubbles and unsteady aspects of aerofoil stall , 2008, The Aeronautical Journal (1968).

[39]  J Cousteix,et al.  Three-Dimensional and Unsteady Boundary- Layer Computations , 1986 .

[40]  M. Giles,et al.  ISES - A two-dimensional viscous aerodynamic design and analysis code , 1987 .

[41]  B. R. Williams,et al.  Viscous-inviscid interactions in external aerodynamics , 1987 .

[42]  M. Lighthill,et al.  On boundary layers and upstream influence II. Supersonic flows without separation , 1953, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[43]  Arthur Veldman,et al.  Matched asymptotic expansions and the numerical treatment of viscous-inviscid interaction , 2001 .