Summary
Statistically two-dimensional and steady high Reynolds number boundary layers over a flat plate with a sudden change in the freestream longitudinal pressure gradient are simulated based on the Navier-Stokes equations for an incompressible fluid. Low-pass filtering of these equations via integration over the mesh volume of a cartesian equidistant staggered grid leads to a second order accurate finite difference scheme in space which conserves mass exactly. The explicit time integration scheme applied is of second order accuracy with respect to convective terms. The use of the projection method results in a Poisson equation for the pressure which is evaluated with the help of a vectorized direct Poisson solver. Three different flow situations are simulated corresponding to zero-, negative- and positive pressure gradient boundary layers. In all three cases the same inflow boundary conditions are used which are Dirichlet conditions for the velocity vector at each time step, taken from a separate large eddy simulation of a turbulent boundary layer. Thus, a direct comparison of the effects of acceleration and deceleration on the turbulence structure is possible. It is found that the statistically observed inhibition of turbulence fluctuations in an accelerated boundary layer is due to a decrease in the intensity of coherent (shear stress producing) structures whereas the characteristic enhancement of fluctuating activity results from an increase in peak fluctuations of these structures.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bradshaw, P. 1987 Coherent Structure. Proc. CTR Summer Progam. Rept CTR-S87. Stanford University.
Chorin, A.J. 1968 Numerical solution of the Navier-Stokes equations. Mathematics of Computations 22, p. 745–762.
Deissler, R.G. 1974 Int. J. Heat Mass Transfer 17, p. 1079.
Fiedler, H.E. 1987 Coherent Structures. In Advances in Turbulence (ed. G. Comte-Bellot & J. Mathieu), Proc. 1st Europ. Turbulence Conf., July 1986, p. 320–336.
Friedrich, R. & Richter, K. 1989 Effect of rapid change in pressure gradient on turbulent momentum and heat transport in flat plate boundary layers. In Notes on Numerical Fluid Mechanics, Vol. 25, p. 108–124, Vieweg Verlag, Braunschweig.
Grötzbach, G. 1986 In Encyclopedia of Fluid Mechanics (ed. N.P. Cheremisinoff), Gulf Publishing, West Orange, New Jersey.
Hussain, A.K.M.F. 1986 Coherent Structures and Turbulence. J. Fluid. Mech. 173, 303–356.
Klebanoff,P.S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA—TR-1247.
Peyret, R. & Taylor, Th.D. 1983 Computational methods for fluid flow. Springer Series in Computational Physics. Springer, New York, Heidelberg.
Piomelli,U., Ferziger,J. & Moin, P. 1989 New Approximate Boundary Conditions For Large Eddy Simulations of Wall-Bounded Flows.,to appear in Phys. Fluids.
Richter, K., Friedrich, R. & Schmitt,L. 1987 In Proc. 6th Turbulent Shear Flow Conference, Toulouse, France, Sept. 7–9.
Schmitt, L. 1988 Grobstruktursimulation turbulenter Grenzschicht-, Kanal-und Stufenstrmungen. Dissertation TU München.
Schumann, U. 1975 Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comp. Physics 18, p. 376–404.
Schumann, U. & Sweet, R.A. 1976 A direct method for the solution of Poisson’s equation with Neumann boundary conditions on a staggered grid of arbitrary size. J. Comp. Physics 20, p. 171–182.
Townsend, A.A. 1962 J. Fluid Mech. 12, p. 536.
Van Dyke, M. 1982 An Album of Fluid Motion. The Parabolic Press, p.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Friedrich, R., Unger, F. (1991). Large eddy simulation of boundary layers with a step change in pressure gradient. In: Metais, O., Lesieur, M. (eds) Turbulence and Coherent Structures. Fluid Mechanics and Its Applications, vol 2. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7904-9_10
Download citation
DOI: https://doi.org/10.1007/978-94-015-7904-9_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4063-3
Online ISBN: 978-94-015-7904-9
eBook Packages: Springer Book Archive