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At least 109 records · Page 6

A general approach for the prediction of localized instability generation in boundary layer flows

The present approach to the prediction of instability generation that is due to the interaction of freestream disturbances with regions of subscale variations in surface boundary conditions can account for the finite Reynolds number effects, while furnishing a framework for the study of receptivity in compressible flow and in 3D boundary layers. The approach is illustrated for the case of Tollmien-Schlichting wave generation in a Blasius boundary layer, due to the interaction of a freestream acoustic wave with a localized wall inhomogeneity. Results are presented for the generation of viscous and inviscid instabilities in adverse pressure-gradient boundary layers, supersonic boundary layer instabilities, and cross-flow vortex instabilities.

Choudhari, Meelan↗

Fully coupled resonant-triad interaction in an adverse-pressure-gradient boundary layer

The nonlinear resonant-triad interaction, proposed by Raetz (1959), Craik (1971), and others for a Blasius boundary layer, is analyzed here for an adverse-pressure-gradient boundary layer. We assume that the adverse pressure gradient is in some sense weak and, therefore, that the instability growth rate is small. This ensures that there is a well-defined critical layer located somewhere within the flow and that the nonlinear interaction is effectively confined to that layer. The initial interaction is of the parametric resonance type, even when the modal amplitudes are all of the same order. This means that the oblique instability waves exhibit faster than exponential growth and that the growth rate of the two-dimensional mode remains linear. However, the interaction and the resulting growth rates become fully coupled, once oblique-mode amplitudes become sufficiently large, but the coupling terms are now quartic, rather than quadratic as in the Craik (1971) analysis. More importantly, however, new nonlinear interactions, which were not present in the Craik-type analyses, now come into play. These interactions eventually have a dominant effect on the instability wave development.

Goldstein, M. E.↗

Horton, pipe hydraulics, and the atmospheric boundary layer (The Robert E. Horton Memorial Lecture)

The early stages of Horton's scientific career which provided the opportunity and stimulus to delve into the origins of some contemporary concepts on the atmospheric boundary layer are reviewed. The study of Saph and Schoder provided basis for the experimental verification and validation of similarity by Blasius, Staton and Pannel, and for the subsequent developments that led to the present understanding of the turbulent boundary layer. Particular attention is given to incorporation of similarity and scaling in the analysis of turbulent flow.

Brutsaert, Wilfried↗

Leading-edge effects on boundary-layer receptivity

Numerical calculations are presented for the incompressible flow over a parabolic cylinder. The computational domain extends from a region upstream of the body downstream to the region where the Blasius boundary-layer solution holds. A steady mean flow solution is computed and the results for the scaled surface vorticity, surface pressure and displacement thickness are compared to previous studies. The unsteady problem is then formulated as a perturbation solution starting with and evolving from the mean flow. The response to irrotational time harmonic pulsation of the free-stream is examined. Results for the initial development of the velocity profile and displacement thickness are presented. These calculations will be extended to later times to investigate the initiation of instability waves within the boundary-layer.

Gatski, Thomas B.↗

On the instability of flow in a streamwise corner

The linear stability of an incompressible laminar flow in the blending boundary layer between the boundary layer in a 90 deg streamwise corner and a Blasius boundary layer well away from the corner is examined using a locally parallel flow approximation. It is shown that the influence of the outer boundary conditions associated with oblique modes of disturbances which are anti-symmetric about the bisector plane have a profound effect on the stability of the flow. As a result, in good agreement with observation, the critical streamwise Reynolds number, associated with a spanwise location is significantly reduced as the corner is approached, being R(sub Cr) = 60 approximately for spanwise distance of z* = 6x*R(sup -1) from the corner compared with R(sub Cr) = 322 approximately for z* = 20x*R(sup -1), where x* measures downstream distance from the leading edges. At R = 600, the growth rate of the most amplified mode of disturbance at the former location is over six times greater than that at the latter; the corresponding wave angle at the two locations is respectively 44 deg and 5 deg, approximately.

Dhanak, Manhar R.↗

A study of eigenvalue sensitivity for hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.

Schmid, Peter J.↗

Compressible flow about symmetrical Joukowski profiles

The method of Poggi is employed for the determination of the effects of compressibility upon the flow past an obstacle. A general expression for the velocity increment due to compressibility is obtained. The general result holds whatever the shape of the obstacle; but, in order to obtain the complete solution, it is necessary to know a certain Fourier expansion of the square of the velocity of flow past the obstacle. An application is made to the case flow of a symmetrical Joukowski profile with a sharp trailing edge, fixed in a stream of an arbitrary angle of attack and with the circulation determined by the Kutta condition. The results are obtained in a closed form and are exact insofar as the second approximation to the compressible flow is concerned, the first approximation being the result for the corresponding incompressible flow. Formulas for lift and moment analogous to the Blasius formulas in incompressible flow are developed and are applied to thin symmetrical Joukowski profiles for small angles of attack.

Kaplan, Carl↗

Direct Measurements of Skin Friction

A device has been developed to measure local skin friction on a flat plate by measuring the force exerted upon a very small movable part of the surface of the flat plate. These forces, which range from about 1 milligram to about 100 milligrams, are measured by means of a reactance device. The apparatus was first applied to measurements in the low-speed range, both for laminar and turbulent boundary layers. The measured skin-friction coefficients show excellent agreement with Blasius' and Von Karman's results. The device was then applied to high-speed subsonic flow and the turbulent-skin-friction coefficients were determined up to a Mach number of about 0.8. A few measurements in supersonic flow were also made. This paper describes the design and construction of the device and the results of the measurements.

Dhawan, Satish↗

Investigation at supersonic speeds of the variation with Reynolds number and Mach number of the total, base, and skin-friction drag of seven boattail bodies of revolution designed for minimum wave drag

An investigation has been conducted in the Langley 9-inch supersonic tunnel to determine the effect of the variation with Reynolds number and Mach number of the total, base, and skin-friction drag at zero lift of seven boattail bodies of revolution designed for minimum wave drag according to NACA TN 2550. The tests covered a Reynolds number range from approximately 1.0 x 10(6) to 10.0 x 10(6) at Mach numbers of 1.62, 1.93, and 2.41, respectively. The results show that base drag and, in general, the total drag increase with increasing values of the ratio of base area to maximum area B/S(sub max), although the results reported in NACA TN 3054 showed that the wave drag decreased with increasing values of B/S(sub max). The laminar skin-friction drag is in agreement with the theoretical predictions used, and, within the Mach number range of these tests, the simple Blasius incompressible theory gives a satisfactory prediction. Except for values of B/S (sub max) near 1, the Reynolds number of transition increases with increasing Mach number and as this ratio approaches 1 this variation is seen to reverse. These variations in Reynolds number of transition with Mach number appear to be associated with the changes in pressure gradient over the rear of the bodies.

Bromm, August F , Jr↗

A simple numerical method for the calculation of the laminar boundary layer

An iteration difference method for the calculation of the incompressible laminar boundary layer is described. The method uses Prandtl's boundary layer equation and the boundary conditions directly and permits the attainment of an arbitrary accuracy. The method has been tested successfully in the continuation of the Blasius profile on the flat plate, on the circular cylinder investigated by Heimenz and on an elliptical cylinder of fineness ratio 1:4. The method makes possible the testing of previously developed methods, all of which contain important assumptions.

BOUNDARY LAYER, LAMINAR - CALCULATIONS - SCHRODER ↗

Inviscid instability of streamwise corner flow

Linear stability of the incompressible flow along a stream wise corner is studied by solving the two-dimensional eigenvalue problem governed by partial differential equations. It is found that this fully three-dimensional flow is subject to inviscid instability due to the inflectional nature of the stream wise velocity profile. The higher growth rates for the inviscid instability mode, which is symmetric about the corner bisector, as compared to the viscous Tollmien-Schlichting instability operative away from the corner is consistent with the experimental findings that the corner flow transitions to turbulence earlier than the two-dimensional Blasius flow away from the corner.

Balachandar, S.↗

Boundary layer receptivity and control

Receptivity processes initiate natural instabilities in a boundary layer. The instabilities grow and eventually break down to turbulence. Consequently, receptivity questions are a critical element of the analysis of the transition process. Success in modeling the physics of receptivity processes thus has a direct bearing on technological issues of drag reduction. The means by which transitional flows can be controlled is also a major concern: questions of control are tied inevitably to those of receptivity. Adjoint systems provide a highly effective mathematical method for approaching many of the questions associated with both receptivity and control. The long term objective is to develop adjoint methods to handle increasingly complex receptivity questions, and to find systematic procedures for deducing effective control strategies. The most elementary receptivity problem is that in which a parallel boundary layer is forced by time-harmonic sources of various types. The characteristics of the response to such forcing form the building blocks for more complex receptivity mechanisms. The first objective of this year's research effort was to investigate how a parallel Blasius boundary layer responds to general direct forcing. Acoustic disturbances in the freestream can be scattered by flow non-uniformities to produce Tollmien-Schlichting waves. For example, scattering by surface roughness is known to provide an efficient receptivity path. The present effort is directed towards finding a solution by a simple adjoint analysis, because adjoint methods can be extended to more complex problems. In practice, flows are non-parallel and often three-dimensional. Compressibility may also be significant in some cases. Recent developments in the use of Parabolized Stability Equations (PSE) offer a promising possibility. By formulating and solving a set of adjoint parabolized equations, a method for mapping the efficiency with which external forcing excites the three-dimensional motions of a non-parallel boundary layer was developed. The method makes use of the same computationally efficient formulation that makes the PSE currently so appealing. In the area of flow control, adjoint systems offer a powerful insight into the effect of control forces. One of the simplest control strategies for boundary layers involves the application of localized mean wall suction.

Hill, D. C.↗

On the nonlinear stability of viscous modes within the Rayleigh problem on an infinite flat plate

The stability has been investigated of the unsteady flow past an infinite flat plate when it is moved impulsively from rest, in its own plane. For small times the instantaneous stability of the flow depends on the linearized equations of motion which reduce in this problem to the Orr-Sommerfeld equation. It is known that the flow for certain values of Reynolds number, frequency and wave number is unstable to Tollmien-Schlichting waves, as in the case of the Blasius boundary layer flow past a flat plate. With increase in time, the unstable waves only undergo growth for a finite time interval, and this growth rate is itself a function of time. The influence of finite amplitude effects is studied by solving the full Navier-Stokes equations. It is found that the stability characteristics are markedly changed both by the consideration of the time evolution of the flow, and by the introduction of finite amplitude effects.

Webb, J. C.↗

Boundary-layer receptivity due to distributed surface imperfections of a deterministic or random nature

Acoustic receptivity of a Blasius boundary layer in the presence of distributed, 2D surface irregularities is investigated analytically. It is shown that, out of the entire spatial spectrum of the surface irregularities, only a narrow band of Fourier components can lead to an efficient conversion of the acoustic input at any given frequency to an unstable eigenmode of the boundary-layer flow. Random irregularities which are spatially homogeneous in nature, and also possess a continuous spectrum in the streamwise direction, lead to instability amplitudes that are intermediate to those caused by the periodic and isolated irregularities, respectively, being, in fact, of the same order as the geometrical mean of the amplitudes in the latter two cases. A physical explanation for these asymptotic scalings is given, in addition to providing an analytical expression for the expected value of the instability amplitude for an ensemble of statistically irregular surfaces with random phase distributions.

Choudhari, Meelan↗

Boundary layer transition studies

A small-scale wind tunnel previously used for turbulent boundary layer experiments was modified for two sets of boundary layer transition studies. The first study concerns a laminar separation/turbulent reattachment. The pressure gradient and unit Reynolds number are the same as the fully turbulent flow of Spalart and Watmuff. Without the trip wire, a laminar layer asymptotes to a Falkner & Skan similarity solution in the FPG. Application of the APG causes the layer to separate and a highly turbulent and approximately 2D mean flow reattachment occurs downstream. In an effort to gain some physical insight into the flow processes a small impulsive disturbance was introduced at the C(sub p) minimum. The facility is totally automated and phase-averaged data are measured on a point-by-point basis using unprecedently large grids. The evolution of the disturbance has been tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. At first, the amplitude decays exponentially with streamwise distance in the APG region, where the layer remains attached, i.e. the layer is viscously stable. After separation, the rate of decay slows, and a point of minimum amplitude is reached where the contours of the wave packet exhibit dispersive characteristics. From this point, exponential growth of the amplitude of the disturbance is observed in the detached shear layer, i.e. the dominant instability mechanism is inviscid. A group of large-scale 3D vortex loops emerges in the vicinity of the reattachment. Remarkably, the second loop retains its identify far downstream in the turbulent boundary layer. The results provide a level of detail usually associated with CFD. Substantial modifications were made to the facility for the second study concerning disturbances generated by Suction Holes for laminar flow Control (LFC). The test section incorporates suction through interchangeable porous test surfaces. Detailed studies have been made using isolated holes in the impervious test plate that used to establish the Blasius base flow. The suction is perturbed harmonically and data are averaged on the basis of the phase of the disturbance, for conditions corresponding to strong suction and without suction. The technique was enhanced by using up to nine multiple probes to reduce the experimental run-time. In both cases, 3D contour surfaces in the vicinity of the hole show highly 3D TS waves which fan out in the spanwise direction forming bow-shaped waves downstream. The case without suction has proved useful for evaluating calculation methods. With suction, the perturbations on the centerline are much stronger and decay less rapidly, while the TS waves in the far field are similar to the case without suction. Downstream, the contour surfaces of the TS waves develop spanwise irregularities which eventually form into clumps. The spanwise clumping is evidence of a secondary instability that could be associated with suction vortices. Designers of porous surfaces use Goldsmith's Criterion to minimize cross-stream interactions. It is shown that partial TS wave cancellation is possible, depending on the hole spacing, disturbance frequency and free-stream velocity. New high-performance Constant Temperature Hot-Wire Anemometers were designed and built, based on a linear system theory analysis that can be extended to arbitrary order. The motivation was to achieve the highest possible frequency reponse while ensuring overall system stability. The performance is equal to or superior to commercially available instruments at about 10% of the cost. Details, such as fabrication drawings and a parts list, have been published to enable the instrument to be construced by others.

Watmuff, Jonathan H.↗

A self-contained, automated methodology for optimal flow control validated for transition delay

This paper describes a self-contained, automated methodology for flow control along with a validation of the methodology for the problem of boundary layer instability suppression. The objective of control is to match the stress vector along a portion of the boundary to a given vector; instability suppression is achieved by choosing the given vector to be that of a steady base flow, e.g., Blasius boundary layer. Control is effected through the injection or suction of fluid through a single orifice on the boundary. The present approach couples the time-dependent Navier-Stokes system with an adjoint Navier-Stokes system and optimality conditions from which optimal states, i.e., unsteady flow fields, and control, e.g., actuators, may be determined. The results demonstrate that instability suppression can be achieved without any a priori knowledge of the disturbance, which is significant because other control techniques have required some knowledge of the flow unsteadiness such as frequencies, instability type, etc.

Joslin, Ronald D.↗

Further Development of a New, Flux-Conserving Newton Scheme for the Navier-Stokes Equations

This paper is one of a series of papers describing the development of a new numerical approach for solving the steady Navier-Stokes equations. The key features in the current development are (1) the discrete representation of the dependent variables by way of high order polynomial expansions, (2) the retention of all derivatives in the expansions as unknowns to be explicitly solved for, (3) the automatic balancing of fluxes at cell interfaces, and (4) the discrete simulation of both the integral and differential forms of the governing equations. The main purpose of this paper is, first, to provide a systematic and rigorous derivation of the conditions that are used to simulate the differential form of the Navier-Stokes equations, and second, to extend our previously-presented internal flow scheme to external flows and nonuniform grids. Numerical results are presented for high Reynolds number flow (Re = 100,000) around a finite flat plate, and detailed comparisons are made with the Blasius flat plate solution and Goldstein wake solution. It is shown that the error in the streamwise velocity decreases like r(sup alpha)(Delta)y(exp 2), where alpha approx. 0.25 and r = delta(y)/delta(x) is the grid aspect ratio.

Scott, James R.↗

Determination of Stability and Translation in a Boundary Layer

Reducing the infinite degrees of freedom inherent in fluid motion into a manageable number of modes to analyze fluid motion is presented. The concepts behind the center manifold technique are used. Study of the Blasius boundary layer and a precise description of stability within the flow field are discussed.

Crepeau, John↗