Free-stream Disturbances Research Articles

Experimental investigation of convecting vortex/boundary-layer interactions

The interaction between propagating spanwise vortices and a turbulent boundary layer was studied experimentally. The results focus on the relationship between the passage of vortex structures and the response of the boundary layer in terms of ensemble-average unsteady mean velocity, wall shear, and turbulent stresses. Both positive and negative circulation vortices were studied at different heights above the test surface. The results indicate that the sign of the vortex has an effect on the wall shear response as well as the height of the vortex above the surface. The negative circulation vortices were found to interact more closely with and penetrate deeper into the boundary layer than the positive sense vortices. A phase lag between the freestream disturbance caused by the vortex and the wall shear stress response is demonstrated. The relationship of the measured wall-shear stress to the pressure gradient and to a scaling velocity determined from the standard log-law fit for the overlap layer are discussed. The response of the boundary-layer turbulence is examined at key phases during the interaction.

Interaction of a weak shock with freestream disturbances

A new transonic small-disturbance model to analyze the interactions of freestream disturbances with a weak shock has been developed. The model equation has an extended form of the classic small-disturbance equation for unsteady transonic aerodynamics. An alternative approach shows that the pressure field may be described by an equation that has an extended form of the classic nonlinear acoustic equation that describes the propagation of sound beams with a narrow angular spectrum. The model shows that diffraction effects, nonlinear steepening effects, focusing effects, and induced vorticity fluctuations interact simultaneously to determine the development of the shock wave in space and time and the pressure field behind it. A finite difference algorithm to solve the mixed-type elliptic/hyperbolic flows around the shock wave has also been developed. Numerical calculations of shock wave interactions with various deterministic vorticity and temperature disturbances result in complicated shock wave structures and describe peaked as well as rounded pressure signatures across the shock front, as were recorded in experiments of sonic booms running through atmospheric turbulence.

On the interaction between the shock wave attached to a wedge and freestream disturbances

We present a study of the interaction of small amplitude, unsteady, freestream disturbances with a shock wave induced by a wedge in supersonic flow. These disturbances may be acoustic waves, vorticity waves, or entropy waves (or indeed a combination of all three). Their interactions then generate behind the shock disturbances of all three classes, an aspect that is investigated in some detail. Also, the possibility of enhanced mixing owing to additional vorticity produced by the shock-body coupling is investigated. It is shown that disturbances behind the shock may either decay downstream, or alternatively experience sustained oscillations. The precise regimes under which either behaviour is found are stated.

Prediction of supersonic inlet unstart caused by freestream disturbances

The objective of this article is to report progress toward the development of an Euler analysis procedure for predicting the unstart tolerance of supersonic inlets. As an aid to understanding boundary condition issues, a one-dimensional, linear-analysis procedure was developed and used to analyze inlet unstart behavior. Using these results as a guide, an Euler analysis procedure was extended through the addition of a new bleed boundary condition, a new compressor face boundary condition, and an engine demand model for the simulation of unsteady inlet flows caused by freestream flow disturbances. Five unstart conditions were identified with the Euler analysis of the axisymmetric inlet for both 20- and 90-deg throat bleed configurations. Results show that both increases and decreases in temperature or velocity will unstart the inlet, whereas only pressure decreases will unstart the inlet. It was also found that 90-deg throat bleed improves the unstart tolerance relative to 20-deg throat bleed for freestream pressure decreases, temperature increases, and changes in velocity.

Bypass Transition in Boundary Layers Including Curvature and Favorable Pressure Gradient Effects

Recent experimental studies of two-dimensional boundary layers undergoing bypass transition have been reviewed to attempt to characterize the effects of free-stream turbulence level, acceleration, and wall curvature on bypass transition. Results from several studies were cast in terms of “local” boundary layer coordinates (momentum and enthalpy thickness Reynolds numbers) and compared. In unaccelerated flow on flat walls, skin friction coefficients were shown to match those from a laminar integral solution before transition and quickly adjusted to match those from a fully turbulent correlation after transition. Stanton number data also matched a correlation in the laminar region, but do not match correlation values so well in the turbulent region. The data showed that the relationship between skin friction coefficient and momentum thickness Reynolds number is unaffected by streamwise acceleration. Stanton numbers were strongly affected by acceleration, however, indicating a breakdown in Reynolds analogy. Concave curvature caused the formation of Go¨rtler vortices, which strongly influenced the skin friction. Convex curvature had an opposite, and lesser effect. The location and length of the transition region generally followed the expected trends as free-stream turbulence level, curvature, and acceleration were varied; the onset location and the transition length were extended by acceleration and convex curvature and reduced by concave curvature and enhanced turbulence. When individual cases were compared, some inconsistencies were observed. These inconsistencies indicate a need to characterize the flows to be compared more completely. Better spectral and length scale measurements of the free-stream disturbance would help in this regard. Within the transition region, the intermittency data from all the cases on flat walls (no curvature) were consistent with an intermittency distribution from the literature. Turbulent spot production rates were shown to be mostly dependent on free-stream turbulence, with a noted increase in spot production rate due to concave curvature and little effect of convex curvature. The acceleration effect on spot production rate was small for the cases studied.

The receptivity problem for O (1) wavelength Görtler vortices

In this paper we make an investigation of the receptivity of boundary layer flows to Görtler vortex modes. A study by Denier et al . (1991) of the generation of vortices by wall roughness elements concluded that such elements are extremely poor as mechanisms to stimulate short wavelength modes. That work also examined the equivalent problem pertaining to O (1) wavelength modes but that analysis was flawed. We re-examine this problem here and demonstrate how the form of the wall roughness is crucial in determining the vortex stability characteristics downstream of the roughness. In particular we investigate the cases of both isolated and distributed forcing functions and show that in general a distributed function is much more important in generating vortices than are either isolated roughness or free-stream disturbances.

Fluid Mechanics and Heat Transfer Measurements in Transitional Boundary Layers Conditionally Sampled on Intermittency

An experimental investigation of transition on a flat-plate boundary layer was performed. Mean and turbulence quantities, including turbulent heat flux, were sampled according to the intermittency function. Such sampling allows segregation of the signal into two types of behavior—laminarlike and turbulentlike. Results show that during transition these two types of behavior cannot be thought of as separate Blasius and fully turbulent profiles, respectively. Thus, simple transition models in which the desired quantity is assumed to be an average, weighted on intermittency, of the laminar and fully turbulent values may not be entirely successful. Deviation of the flow identified as laminarlike from theoretical laminar behavior is due to a slow recovery after the passage of a turbulent spot, while deviation of the flow identified as turbulentlike from fully turbulent characteristics is possibly due to an incomplete establishment of the fully turbulent power spectral distribution. Measurements were taken for two levels of free-stream disturbance—0.32 and 1.79 percent. Turbulent Prandtl numbers for the transitional flow, computed from measured shear stress, turbulent heat flux, and mean velocity and temperature profiles, were less than unity.

Transition of compressible high enthalpy boundary layer flow over a flat plate

AbstractThis paper presents the results of an experimental investigation into the characteristics of boundary layer transition to turbulence in hypervelocity air flows. A series of experiments was conducted using a flat plate model, equipped with static pressure and thin film heat transfer transducers, in a free piston shock tunnel. Transition was observed in the stagnation enthalpy range of 2·35 to 19·2 MJ/kg. The transition Reynolds number correlates well with the unit Reynolds number through a simple empirical relation. The influences of Mach number, pressure and wall cooling are examined. The measured heat transfer rates in laminar and turbulent regions are compared with empirical predictions. Freestream disturbances of the test flow were also measured and analysed.

Distributed excitation of Tollmien–Schlichting waves by vortical free-stream disturbances

Nonlocalized receptivity to vortical free-stream disturbances is analyzed for a Blasius boundary layer over a wavy surface. Vortical disturbances are rescaled through an interaction with steady disturbances generated by the surface waviness. The rescaled disturbances provide a distributed energy transfer to the natural eigenmodes when conditions are close to resonance; this occurs in the neighborhood of the lower branch of neutral stability. Downstream of the energy transfer, the traveling wave solution is dominated by the natural eigenmode. Forcing from the vortical disturbances is concentrated in the outer region of the boundary layer. This leads to a relatively weak receptivity as compared to the acoustic problem. Total receptivity amplitudes are approximately ten times larger than for localized vortical receptivity, but approximately fifty times smaller than for nonlocalized acoustic receptivity.

Acoustic forcing of oblique wave resonance in the far wake

In this paper, we investigate to what extent the far-wake ‘signature’ of the near-wake vortex dynamics of a nominally two-dimensional bluff body is affected by the character of the free-stream noise. We confirm the existence of an oblique wave resonance (at frequency, fK–fT), which is caused by nonlinear ‘quadratic’ interactions between primary oblique shedding waves (fK) and secondary two-dimensional waves (fT), which are amplified from free-stream disturbances. In this work, oblique wave resonance is induced by acoustic forcing of two-dimensional waves. The use of acoustic forcing reveals a set of higher-order oblique wave resonances corresponding to frequencies (fK–nfT), where n is an integer. We find from visualization that, even when the secondary two-dimensional waves have the same frequency as the oblique waves, it is the oblique waves that are preferentially amplified. Oblique wave angles up to 74° have been observed. The response of the wake to a large range of forcing frequencies shows a broad region of peak response, centred around F = (fT/fK) = 0.55, and is in reasonable agreement with predictions from linear stability analysis. A similar broad response is found for each of the higher-order oblique wave modes. Simple equations for the oblique waves yield approximate conditions for maximum wake response, with a frequency for peak response given by Fmax = 1/2n = 1/2, 1/4, 1/6,…, and an oblique wave angle given by θmax = 2θK, where θK is the angle of oblique vortex shedding. An increase in forcing amplitude has the effect of bringing the nonlinear wave interactions, leading to oblique wave resonance, further upstream. Paradoxically, the effect of an increase in amplitude (A) of the two-dimensional wave forcing is to further amplify the oblique waves in preference to the two-dimensional waves and, under some conditions, to inhibit the appearance of prominent two-dimensional waves where they would otherwise appear. With a variation in forcing amplitude, the amplitude of oblique wave response is found to be closely proportional to A½. In summary, this investigation confirms the surprising result that it is only through the existence of noise in the free stream that the far wake is ‘connected’ to the near wake.

A new mechanism for oblique wave resonance in the ‘natural’ far wake

There has been some debate recently on whether the far-wake structure downstream of a cylinder is dependent on, or ‘connected’ with, the precise details of the near-wake structure. Indeed, it has previously been suggested that the far-wake scale and frequency are unconnected with those of the near wake. In the present paper, we demonstrate that both the far-wake scale and frequency are dependent on the near wake. Surprisingly, the characteristic that actually forges a ‘connection’ between the near and far wakes is the sensitivity to free-stream disturbances. It is these disturbances that are also responsible for the regular three-dimensional patterns that may be visualized. Observations of a regular ‘honeycomb’-like three-dimensional pattern in the far wake is found to be caused by an interaction between oblique shedding waves from upstream and large-scale two-dimensional waves, amplified from the free-stream disturbances. The symmetry and spanwise wavelength of Cimbala, Nagib & Roshko's (1988) three-dimensional pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that such a three-dimensional pattern is clearly dependent on upstream oblique vortex shedding.With the deductions above as a starting point, we describe a new mechanism for the resonance of oblique waves, as follows. In the case of two-dimensional waves, corresponding to a very small spectral peak in the free stream (fT) interacting (quadratically) with the oblique shedding waves frequency (fK), it appears that the most amplified or resonant frequency in the far wake is a combination frequency fFW = (fK–fT), which corresponds physically with ‘oblique resonance waves’ at a large oblique angle. The large scatter in (fFW/fK) from previous studies is principally caused by the broad response of the far wake to a range of free-stream spectral peaks (fT). We present clear visualization of the oblique wave phenomenon, coupled with velocity measurements which demonstrate that the secondary oblique wave energy can far exceed the secondary two-dimensional wave energy by up to two orders of magnitude. Further experiments show that, in the absence of an influential free-stream spectral peak, the far wake does not resonate, but instead has a low-amplitude broad spectral response. The present phenomena are due to nonlinear instabilities in the far wake, and are not related to vortex pairing. There would appear to be distinct differences between this oblique wave resonance and the subharmonic resonances that have been previously studied in channel flow, boundary layers, mixing layers and airfoil wakes.

Interaction of disturbances with an oblique detonation wave attached to a wedge

The linear response of an oblique overdriven detonation to imposed free-stream disturbances or to periodic movements of the wedge is examined. The free-stream disturbances are assumed to be steady vorticity waves and the wedge motions are considered to be time periodic oscillations either about a fixed pivot point or along the plane of symmetry of the wedge aligned with the incoming stream. All disturbances are assumed to have wavelengths large compared to the thickness of the detonation so that the detonation is considered to be a region of infinitesimal thickness in which a finite amount of heat is released. The response to the imposed disturbances is a function of the Mach number of the incoming flow, the wedge angle, and the exothermicity of the reaction within the detonation. It is shown that, as the degree of overdrive increases, the amplitude of the response increases significantly; furthermore, a fundamental difference in the dependence of the response on the parameters of the problem is found between the response to a free-stream disturbance and to a disturbance emanating from the wedge surface.

Transition of Flat Plate Boundary Layer Caused by Turbulent Wake of Circular Cylinder in Free Stream. Flow Pattern and Appearance of Streaks.

The boundary layer transition caused by the disturbance generated by a circular cylinder placed in the free stream is experimentally investigated. The cylinder is located dwnstream of the leading edge where the Reynolds number is above the critical value, although the boundary layer is laminar to this point. The distance between the cylinder and the wall is chosen so that the cylinder wake gradually merges with the boundary layer downstream. In contrast to the case of small free-stream disturbance, the transition process in this case starts with the appearance of streaks. For large cylinder-wall distances, the streaks are followed by turbulent spots, while for the small distances, they directly generate turbulence downstream. A geometrical parameter is newly defined, with which the spanwise spacings of the streaks are correlated, and the observed flow patterns are easily classified.

On the instability of boundary layers on heated flat plates

The stability of a boundary layer on a heated flat plate is investigated in the linear regime. The flow is shown to be unstable to longitudinal vortex structures which develop in a non-parallel manner in the streamwise direction. Solutions of the non-parallel equations are obtained numerically at O(1) values of the appropriate stability parameter, i.e. the Grashof number. We investigate the particular cases in which instability is induced by localized or distributed wall roughness or non-uniform wall heating. The case when the vortices are induced by free-stream disturbances is also considered. We then investigate the high-Grashof-number limit and the fastest growing mode. The fastest growing mode is found to be governed by a quasi-parallel theory and occurs at high wavenumbers. The wavenumber and growth rate of the fastest growing mode are found in closed form. At low wavenumbers the vortex instability is shown to be closely related to Tollmein–Schlichting waves; the effect of wall heating or cooling on the latter type of instability is discussed.

Receptivity of a laminar boundary layer to the interaction of a three-dimensional roughness element with time-harmonic free-stream disturbances

Receptivity of a laminar boundary layer to the interaction of time-harmonic free-stream disturbances with a three-dimensional roughness element is studied. The three-dimensional nonlinear triple–deck equations are solved numerically to provide the basic steady-state motion. At high Reynolds numbers, the governing equations for the unsteady motion are the unsteady linearized three-dimensional triple-deck equations. These equations can only be solved numerically. In the absence of any roughness element, the free-stream disturbances, to the first order, produce the classical Stokes flow, in the thin Stokes layer near the wall (on the order of our lower deck). However, with the introduction of a small three-dimensional roughness element, the interaction between the hump and the Stokes flow introduces a spectrum of all spatial disturbances inside the boundary layer. For supercritical values of the scaled Strouhal number, S0 > 2, these Tollmien–Schlichting waves are amplified in a wedge-shaped region, 15° to 18° to the basic-flow direction, extending downstream of the hump. The amplification rate approaches a value slightly higher than that of two-dimensional Tollmien–Schlichting waves, as calculated by the linearized analysis, far downstream of the roughness element.

Boundary-layer receptivity due to a wall suction and control of Tollmien–Schlichting waves

A numerical study of the generation of Tollmien–Schlichting (TS) waves due to the interaction between a small free-stream disturbance and a small localized suction strip on an otherwise flat surface has been carried out using finite-difference methods. The nonlinear steady flow is of the viscous–inviscid interactive (i.e., triple-deck) type while the unsteady disturbed flow is assumed to be governed by the triple-deck approximation of the unsteady Navier–Stokes equations linearized about this mean flow. Numerical solutions illustrate the growth or decay of the TS waves generated by the interaction between the free-stream disturbance and the suction strip, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the Tollmien–Schlichting waves and the demonstration of the possible active control of the growth of Tollmien–Schlichting waves.

Data analysis for unsteady turbulence measurements over airfoils

Studies of unsteady flows about pitching airfoils and flows with unsteady freestream components require a consistent method of nonstationary data analysis for proper characterization of unsteady turbulent behavior. A method has been developed for data analysis of flows composed of high-frequenc y turbulence fluctuations superimposed upon a time-dependent low-frequency component or ensemble-averaged mean velocity with the goal of establishing a consistent method for the presentation of results from varying tests and flow situations. A nonstationary mean was determined by ensemble-aver aging and frequency-domain low-pass filtering. Turbulence intensities were calculated based on a local mean using frequency-domain low-pass filtering methods. A nonstationary power spectral density estimator was developed to estimate the time-varying spectral characteristics of a turbulent boundary layer subjected to an unsteady freestream disturbance. A discussion concerning the choice of cutoff frequencies and digital filters is included.

The unsteady laminar boundary layer on an axisymmetric body subject to small-amplitude fluctuations in the free-stream velocity

The effect of small-amplitude, time-periodic, free-stream disturbances on an otherwise steady axisymmetric boundary layer on a circular cylinder is considered. Numerical solutions to the problem are presented, and an asymptotic solution to the flow, valid far downstream along the axis of the cylinder is detailed. Particular emphasis is placed on the unsteady eigensolutions that occur far downstream, which turn out to be very different from the analogous planar eigensolutions. These axisymmetric eigensolutions are computed numerically and also are described by asymptotic analyses valid for low and high frequencies of oscillation.

Experiments on transitional boundary layers with wake-induced unsteadiness

Hot-wire measurements were carried out in boundary layers developing along a flat plate over which wakes passed periodically. The wakes were generated by cylinders moving on a squirrel cage in front of the plate leading edge. The flow situation studied is an idealization of that occurring on turbomachinery blades where unsteady wakes are generated by the preceding row of blades. The influence of wake-passing frequency on the boundary-layer development and in particular on the transition processes was examined. The hot-wire signals were processed to yield ensemble-average values and the fluctuations could be separated into periodic and stochastic turbulent components. Hot-wire traces are reported as well as time variations of periodic and ensemble-averaged turbulent fluctuations and of the boundary-layer integral parameters, yielding a detailed picture of the flow development. The Reynolds number was relatively low so that in the limiting case of a boundary layer undisturbed by wakes this remained laminar over the full length of the test plate. When wakes passed over the plate, the boundary layer was found to be turbulent quite early underneath the free-stream disturbances due to the wakes, while it remained initially laminar underneath the undisturbed free-stream regions in between. The turbulent boundary-layer stripes underneath the disturbed free stream travel downstream and grow together so that the embedded laminar regions disappear and the boundary layer becomes fully turbulent. The streamwise location where this happens moves upstream with increasing wake-passing frequency, and a clear correlation could be determined in the experiments. The results are also reported in a mean Lagrangian frame by following fluid parcels underneath the disturbed and undisturbed free stream, respectively, as they travel downstream.

Boundary Layer Receptivity Theory

The receptivity mechanisms by which free-stream disturbances generate instability waves in laminar boundary layers are discussed. Free-stream disturbances have wavelengths which are generally much longer than those of instability waves. Hence, the transfer of energy from the free-stream disturbance to the instability wave requires a wavelength conversion mechanism. Recent analyses using asymptotic methods have shown that the wavelength conversion takes place in regions of the boundary layer where the mean flow adjusts on a short streamwise length scale. This paper reviews recent progress in the theoretical understanding of these phenomena.