Stability Of Laminar Boundary Layer Research Articles

The influence of temperature dependent viscosity on laminar boundary-layer stability

The title problem is analyzed for small variations in viscosity by using a perturbation procedure. Consideration is restricted to incompressible, flat plate flow. The results show that appreciable stabilization may occur in water or other liquids, while air is slightly destabilized. Reasonable agreement with previous experimental results in air is obtained.

Effects of freestream disturbances on boundary-layer transition.

T effects of freestream disturbances on boundary-layer transition in flows with zero pressure gradient have been studied by several investigators. Some of the notable results have been published by Dryden, Hall and Hislop, and Schubauer and Skramstad. A study similar to that of Schubauer and Skramstad was performed and reported by Wells. In the two latter studies the transition Reynolds number was found to increase systematically with decreasing freestream disturbance intensity until a maximum was reached which was not affected by further reductions in disturbance intensity. The maximum transition Reynolds number found by Wells was 80% greater than that reported by Schubauer and Skramstad, being 5.0 X 10 and 2.8 X 10, respectively, for disturbance intensities less than 0.1% of the freestream velocity Examination of the energy spectra of the freestream disturbances indicated that most of the energy in Wells' experiments occurred at frequencies below 150 cps with acoustic content less than 10% of the total energy. The tests of Schubauer and Skramstad involved significant energy levels out to 400 cps, and in addition the spectrum exhibited large acoustic energy peaks at 60 and 95 cps which accounted for approximately 90% of the total disturbance energy that was measured for intensities less than about 0.05%. These results suggest an influence of both the spectral energy distribution and the nature of the disturbances in determining the transition Reynolds number. The effects of acoustical noise are particularly interesting in the light of recent studies by Pfenninger, Bacon, and Carlson and Jackson and Heckl concerning the stability of laminar boundary layers in the presence of intense acoustical fields. This report describes a recent series of experiments designed to extend the study reported in Ref. 4. In particular, the effects of acoustic noise fields of discrete frequencies and the broad-band turbulence created by coarse-mesh grids placed in the freestream have been investigated. These experiments are meant to be only illustrative of the problem and do not attempt to explain completely the relation between transition and free-stream disturbance energy. The results do emphasize the importance of the frequency spectra and nature of the disturbance, as well as the rms intensity of disturbance energy in predicting transition.

Stability of Laminar Boundary Layers at Separation

The stability of laminar boundary layers at separation is considered. The velocity distribution is represented by (1) a Pohlhausen fourth-degree polynomial P4, and (2) by a Falkner—Skan similarity profile at separation, Hartree β = − 0. 1988. The Orr—Sommerfeld equation is integrated using Runge—Kutta with Gram—Schmidt orthonormalization. Using single precision arithmetic, the method leads to satisfactory answers at Reynolds numbers R1 = 100 000 and larger. In either case the minimum critical Reynolds number is found to be of the order of 100. It is found that the neutral curves for the P4 profile obtained by solving the Orr—Sommerfeld equation, whether exactly (numerically) or within the framework of the asymptotic approximations, approach along the upper branch the same asymptotic value, namely α1 = 0.8028 (in the case of the β = − 0. 1988 profile, however, the corresponding values is α1 = 1.240). It is also found that the asymptotes to the lower branch in both cases vary with α1 according to R11/3∼α1 −7/9 (in the case of the β = − 0. 1988 profile however, the corresponding variation is R11/3 ∼ α1 - 0. 477).

Stability of laminar boundary layer on an elastic surface in an incompressible fluid

Interest in the present problem arose after the publication of the results of the experiments of Kramer [1–3]. In addition to the studies indicated in [4], the articles [5–8] are devoted to the question of the interaction of a flexible elastic surface with the boundary layer. In the present paper the problem of the interaction of an elastic surface with disturbances arising in the boundary layer is posed as in [4]. The approximate nature of the methods of solving the problem of the hydrodynamic stability of the laminar boundary layer leads to a difference in the final computational formulas even in the case when authors use the same Heisenberg-Tollmien-Schlichting-Lin scheme. Therefore, in what follows we present a comparison of the data on the stability of the boundary layer on a solid wall obtained by several authors with the calculations using the formulas, which are then generalized to the case of the elastic surface.

The stability of laminar boundary layers at separation

The effect of an adverse pressure gradient on the stability of a laminar boundary layer is considered in the limiting case when the skin friction at the wall vanishes, i.e. when U′(0) = 0. Such flows are not absolutely unstable as might have been expected but have a minimum critical Reynolds number of the order of 25. General results are given for the asymptotic behaviour of both the upper and lower branches of the neutral curve and a complete neutral curve is obtained for Pohlhausen's simple fourth-degree polynomial profile at separation.

Review of the effect of distributed surface roughness on boundary-layer transition : Albert L. Braslow (NASA). AGARD Report 254. April 1960. 13 pp. (Presented at AGARD Fluid Dynamics Panel, Boundary Layer Research Meeting, London, April 25–29, 1960.)

Abstract : A discussion is presented on the transition phenomena associated with distributed roughness, a correlation of three-dimensional roughness effects at both subsonic and supersonic speeds, and the effect of laminar boundary-layer stability as influenced by heat transfer, pressure gradients, and boundary-layer control on the sensitivity of laminar flow to distributed roughness. Results indicate that the transition-triggering mechanism of three-dimensional type surface roughness appears to be the same at supersonic and subsonic speeds. In either case, a Reynolds number based on the height of the roughness and the local flow conditions at the top of the roughness can be used to predict with reasonable accuracy the height of three-dimensional roughness required to cause premature transition. Neither the three-dimensional roughness Reynolds number nor the lateral spread of turbulence behind the roughness is changed to any important extent by increasing the laminar boundary-layer stability to theoretically small disturbances. Therefore, for a given stream Mach number and Reynolds number, surface cooling, boundary-layer suction, or a favorable pressure gradient will, in the presence of three-dimensional roughness, promote rather than delay transition.

The Interaction of Two Similarly Facing Shock Waves

2 Bloom, M., Further Comments on Effect of Surface Cooling on Laminar Boundary-Layer Stability, Readers' Forum, Journal of the Aeronautical Sciences, Vol. 19, No. 5, p. 359, May, 1952. 3 Lees, L., The Stability of the Laminar Boundary Layer in a Compressible Fluid, NACA Report No. 876,1947. 4 Van Driest, E. R., Calculation of the Stability of the Laminar Boundary Layer in a Compressible Fluid on a Flat Plate with Heat Transfer, Journal of the Aeronautical Sciences, Vol. 19, No. 12, pp. 801-812, 829, December, 1952. 5 Bloom, M., Calculation of Stability of Constant-Pressure Boundary Layers on Isothermal Surfaces with an Integral-Method Mean-Flow Solution, Polytechnic Institute of Brooklyn, PIBAL No. 179 (revised September 25, 1953). (To appear as a NACA TN, Contract No. NAw-5809.) 6 Chapman, D. R., and Rubesin, M. W., Temperature and Velocity Profiles in the Compressible Laminar Boundary Layer with Arbitrary Distribution of Surface Temperature, Journal of the Aeronautical Sciences, Vol. 16, No. 9, p. 547, September, 1949. 7 Lin, C. C , On the Stability of the Boundary Layer with Respect to Disturbances of Large Wave Velocity, Readers' Forum, Journal of the Aeronautical Sciences, Vol. 19, No. 2, p. 138, February, 1952. 8 Cheng, S.-I., On the Stability of Laminar Boundary Layer Flow, Quarterly of Applied Mathematics, Vol. XI , No. 3, p. 346, October, 1953.

Further Comments on "The Effect of Surface Cooling on Laminar Boundary-Layer Stability"

Further Comments on "The Effect of Surface Cooling on Laminar Boundary-Layer Stability"