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The Method of Integral Relations is extended to apply to the calculation of Unsteady Flow in a Laminar Boundary Layer. The effectiveness of the method is demonstrated in an application to uniform flow past a circular cylinder, resulting from an impulsive start. Both first and second approximations are worked out, the latter showing good agreement with results of previous calculations.
The calculation of the phenomena within the boundary layer of bodies immersed in a flow underwent a decisive development on the basis of L. Prandtl's trains of thought, stated more than forth years ago, and by numerous later treatises again and again touching upon them. The requirements of the steadily improving aerodynamics of airplanes have greatly increased with the passing of time and recently research became particularly interested in such phenomena in the boundary layer as are caused by small external disturbances. Experimental results suggest that, for instance, slight fluctuations in the free stream velocities as they occur in wind tunnels or slight wavelike deviations of outer wing contours from the prescribed smooth course as they originate due to construction inaccuracies may exert strong effects on the extent of the laminar boundary layer on the body and thus on the drag. The development of turbulence in the last part of the laminar portion of the boundary layer is, therefore, the main problem, the solution of which explains the behavior of the transition point of the boundary layer. A number of reports in literature deal with this problem,for instance, those of Tollmien, Schlichting, Dryden, and Pretsch. The following discussion of the behavior of the laminar boundary layer for periodically oscillating pressure variation also purports to make a contribution to that subject.
Disclosed is a method of visualizing laminar to turbulent boundary layer transition, shock location, and laminar separation bubbles around a test surface. A liquid crystal coating is formulated using an unencapsulated liquid crystal operable in a temperature bandwidth compatible with the temperature environment around the test surface. The liquid crystal coating is applied to the test surface, which is preferably pretreated by painting with a flat, black paint to achieve a deep matte coating, after which the surface is subjected to a liquid or gas flow. Color change in the liquid crystal coating is produced in response to differences in relative shear stress within the boundary layer around the test surface. The novelty of this invention resides in the use of liquid crystals which are sensitive to shear stress to show aerodynamic phenomena such as a boundary layer transition, shock location, and laminar separation bubbles around a test surface.
Low density, leading edge bluntness, and ablation effects on wedge induced laminar boundary layer separation at moderate enthalpies in hypersonic flow
The effect of a small amplitude progressive wave on the laminar boundary layer on a semi-infinite flat plate, due to a uniform supersonic freestream flow, is considered. The perturbation to the flow divides into two streamwise zones. In the first, relatively close to the leading edge of the plate, on a transverse scale comparable to the boundary layer thickness, the perturbation flow is described by a form of the unsteady linearized compressible boundary layer equations. In the freestream, this component of flow is governed by the wave equation, the solution of which provides the outer velocity conditions for the boundary layer. This system is solved numerically, and also the asymptotic structure in the far downstream limit is studied. This reveals a breakdown and a subsequent second streamwise zone, where the flow disturbance is predominantly inviscid. The two zones are shown to match in a proper asymptotic sense.
This is an account of an investigation in which oscillations were discovered in the laminar boundary layer along a flat plate. These oscillations were found during the course of an experiment in which transition from laminar to turbulent flow was being studied on the plate as the turbulence in the wind stream was being reduced to unusually low values by means of damping screens. The first part of the paper deals with experimental methods and apparatus, measurements of turbulence and sound, and studies of transition. A description is then given of the manner in which oscillations were discovered and how they were found to be related to transition, and then how controlled oscillations were produced and studied in detail.
It was previously observed that an incident acoustic field on a wing with laminar flow can cause transition to turbulent flow if the fluctuating acoustic velocities are of sufficient amplitude and in the critical frequency range for an unstable laminar boundary layer. A section of a wing was modified with a natural laminar flow (NLF) glove to allow direct measurement of the effect of varying engine noise on the extent of laminar flow. The flight test program was completed in June, 1985. At each flight condition, the engine power was varied from about 2600 r/min (idle) to about 4500 r/min (maximum continuous power). The spectral data provides considerable insight into the influences of the various sound sources that contribute to the overall noise levels. Additional analysis will be required to assess the impact of these sources on boundary layer transition. These results demonstrate that substantial laminar flow on the wing of a transport configuration with wing-mounted engines can be obtained.
Results of experimental study of regularities of a natural transition of a laminar boundary layer to a turbulent layer at low subsonic air flow velocities are presented, analyzed and compared with theory and model experiments.
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Approximation analysis for laminar two dimensional boundary layer behind plane shock wave moving over infinite flat plate
Numerical solutions of the laminar, incompressible boundary-layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified, and the pressure is deduced from the solution. A stream function/vorticity formulation of the boundary-layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite-difference equations, in which the flow direction is taken into account, are obtained by a successive column iteration scheme. Results are compared with Klineberg and Steger's (1974) separated boundary-layer calculations, and with Briley's (1971) solution of the Navier-Stokes equations for a separated region.
Three problems concerning laminar-turbulent transition are addressed by solving a series of initial value problems. The first problem is the calculation of resonance within the continuous spectrum of the Blasius boundary layer. The second is calculation of the growth of Tollmien-Schlichting waves that are a direct result of disturbances that only lie outside of the boundary layer. And, the third problem is the calculation of non-parallel effects. Together, these problems represent a unified approach to the study of freestream disturbance effects that could lead to transition. Solutions to the temporal, initial-value problem with an inhomogeneous forcing term imposed upon the flow is sought. By solving a series of problems, it is shown that: A transient disturbance lying completely outside of the boundary layer can lead to the growth of an unstable Tollmien-Schlichting wave. A resonance with the continuous spectrum leads to strong amplification that may provide a mechanism for bypass transition once nonlinear effects are considered. A disturbance with a very weak unstable Tollmien-Schlichting wave can lead to a much stronger Tollmien-Schlichting wave downstream, if the original disturbance has a significant portion of its energy in the continuum modes.
An approximation which reduces the computation of three dimensional, laminar, compressible, boundary layer equations to the problem of solving two dimensional type boundary layer equations is presented. A comparison of this method with a fully three dimensional boundary layer calculation is provided.
The laminar boundary-layer flow about a circular cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry by a method applicable in general to the flow about conical bodies. At the bottom of the cone, velocity profiles were obtained showing the expected tendency of the boundary layer to become thinner on the under side of the cone as the angle of attack is increased. At the top of the cone, the analysis failed to yield unique solutions except for small angles of attack. Beyond a certain critical angle of attack, boundary-layer flow does not exist in the plane of symmetry, thus indicating separation. This critical angle is presented as a function of Mach number and cone vertex angle.
A flight test program was performed using the Boeing 757 flight research airplane to investigate the effect of noise from wing mounted engines on laminar boundary layer transition. An NLF glove was installed on the right wing panel just outboard of the engine. The extent of laminar flow on the glove was measured as a function of engine power setting for a range of flight conditions. A combination of surface and probe microphones was distributed over the upper and lower wing surfaces to measure sound spectra. The flight test program was completed in June 1985 and the results of preliminary analysis indicate that a maximum of about 29 percent of chord laminar flow was obtained on the upper surface and about 28 percent on the lower surface (at a high sideslip condition). The engine speed was varied from about 2600 (idle) to about 4500 (maximum continuous power) r/min. This produced changes in sound pressure level up to 20 dB on the lower surface. On the upper surface, the noise levels were independent of engine power but sensitive to airplane Mach number. No effect of engine power setting on upper surface transition location was observed, and only a small forward movement of the transition location on the lower surface was observed at the high power settings. Volume 1 of this report contains the program description and data analysis. Volume 2 is a compilation of all of the flight test data.
The finite difference computation method was investigated for solving problems of interaction between a shock wave and a laminar boundary layer, through solution of the complete Navier-Stokes equations. This method provided excellent solutions, was simple to perform and needed a relatively short solution time. A large number of runs for various flow conditions could be carried out from which the interaction characteristics and principal factors that influence interaction could be studied.
Drag measurements were obtained for circular cylinders attached perpendicularly to a flat-plate surface. Measurements were obtained for a single cylinder and for rows of cylinders. The cylinders were alined at various sweep angles relative to the free-stream velocity vector and at spacings appropriate for roughness elements used as boundary layer trips. The drag measurements were obtained for Mach numbers of 3.95 and 4.60, ratios of cylinder height to an undisturbed laminar boundary layer displacement thickness of approximately 1.0 to 3.0, a cylinder height-to-diameter ratio of approximately 2, and sweep angles up to 60. A complete presentation of the experimental results is given. A discussion of the more significant findings, including the most appropriate parameters for correlating the experimental results, is presented.
A computer program called STAYLAM is presented for the computation of the compressible laminar boundary-layer flow over a yawed infinite wing including distributed suction. This program is restricted to the transonic speed range or less due to the approximate treatment of the compressibility effects. The prescribed suction distribution is permitted to change discontinuously along the chord measured perpendicular to the wing leading edge. Estimates of transition are made by considering leading edge contamination, cross flow instability, and instability of the Tollmien-Schlichting type. A program listing is given in addition to user instructions and a sample case.