Numerical investigation of unsteady laminar incompressible boundary layer flows with cylindrical symmetry.
Unsteady laminar incompressible time dependent boundary layer flows with cylindrical symmetry, transverse boundaries and no swirl
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Unsteady laminar incompressible time dependent boundary layer flows with cylindrical symmetry, transverse boundaries and no swirl
Linear stability theory is used to study the effect of crossflow on Goertler instability in incompressible boundary layers. The results cover a wide range of sweep angle, pressure gradient, and wall curvature parameters. It is shown that the crossflow stabilizes Goertler disturbances by reducing the maximum growth rate and shrinking the unstable band of spanwise wave numbers. On the other hand, the effect of concave wall curvature on crossflow instability is destabilizing. Calculations show that the changeover from Goertler to crossflow instabilities is a function of Goertler number, pressure gradient, and sweep angle. The results demonstrate that Goertler instability may still be relevant in the transition process on swept wings even at large angles of sweep if the pressure gradient is sufficiently small. The influence of pressure gradient and sweep can be combined by defining a crossflow Reynolds number. Thus, the changeover from Goertler to crossflow instability takes place at some critical crossflow Reynolds number whose value increases with Goertler number.
Superposition techniques are used to calculate the rate of heat transfer from a flat plate to a turbulent incompressible boundary layer for several cases of variable surface temperature. The predictions of a number of these calculations are compared with experimental heat-transfer rates, and good agreement is obtained. A simple computing procedure for determining the heat-transfer rates from surfaces with arbitrary wall-temperature distributions is presented and illustrated by two examples. The inverse problem of determining the temperature distribution from an arbitrarily prescribed heat flux is also treated, both experimentally and analytically.
Superposition techniques are used to calculate the rate of heat transfer from a flat plate to a turbulent incompressible boundary layer for several cases of variable surface temperature. The predictions of a number of these calculations are compared with experimental heat- transfer rates, and good agreement is obtained. A simple computing procedure for determining the heat-transfer rates from surfaces with arbitrary wall-temperature distributions is presented and illustrated by two examples. The inverse problem of determining the temperature distribution from an arbitrarily prescribed heat flux is also treated, both experimentally and analytically.
The effect of the location of transition on the heat transfer to the turbulent incompressible boundary layer is analyzed. The analysis indicates that considerably higher heat-transfer rates may occur for some distance downstream if the transition is very late. The results of a limited experimental investigation are in substantial agreement with the results of the analysis. If the extent of the transition region is known, the analysis also allows adequate prediction of heat-transfer coefficients within the transition region. The nature of this analysis is such that it should predict local shear coefficients in the transition region equally well.
Heat-transfer rates, velocity profiles, and temperature profiles for the turbulent incompressible flow of air over a flat plate with a constant surface temperature have been measured at Reynolds numbers up to 3.5 x lO(exp 6). The turbulent heat-transfer measurements agree well with the von Karman analogy, and the velocity profiles agree with the data of previous investigators. The temperature profiles are similar to the velocity profiles, both being adequately described by power formulas.
Heat-transfer rates and temperature profiles for the turbulent incompressible flow of air over a flat plate with a stepwise temperature distribution (unheated starting length) were measured for a variety of step positions at Reynolds numbers up to 3.5 x 10(exp 6). Comparison of the data with existing heat-transfer analyses indicates that an improved analysis is needed. An integral analysis is made that agrees very well with the data and allows a simple correction for the unheated starting length. In addition, a differential analysis is made that allows prediction of the temperature profiles from the velocity profiles, and good agreement with experimental profiles is obtained.
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This report documents the full details of the condensed journal article by Ashpis & Reshotko (JFM, 1990) entitled "The Vibrating Ribbon Problem Revisited." A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (JFM, 1965) is modified by application of the Briggs method and a careful treatment of the complex double Fourier transform inversions. Expressions are obtained in a natural way for the discrete spectrum as well as for the four branches of the continuous spectra. These correspond to discrete and branch-cut singularities in the complex wave-number plane. The solutions from the continuous spectra decay both upstream and downstream of the ribbon, with the decay in the upstream direction being much more rapid than that in the downstream direction. Comments and clarification of related prior work are made.
We have developed a code where the nonlinear terms are treated implicitly. The equations are discretized using the two-point fourth order compact scheme in the y-direction and the backward Euler method in the x-direction. We investigated the transition process in a Blasius boundary layer due to fundamental type breakdown. With 8 modes in the w and 3 planes, we could compute the evolution of disturbances up to Re(x)=910, which is well into the strongly nonlinear region. The transition onset point is located around Re(x)=850. The comparison with the measurements and with the DNS computations are very good up to Re(x)=880.
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