Streamwise Velocity Perturbation Research Articles

Wall turbulence at high friction Reynolds numbers

An instantaneous streamwise velocity perturbation of a new simulation of a turbulent channel flow at an unprecedented friction Reynolds number of 10000 is conducted. One point statistics and turbulent budgets are discussed, solving some questions and raising new ones.

Stability of obliquely driven cavity flow

The linear stability of the incompressible flow in an infinitely extended cavity with rectangular cross-section is investigated numerically. The basic flow is driven by a lid which moves tangentially, but at yaw with respect to the edges of the cavity. As a result, the basic flow is a superposition of the classical recirculating two-dimensional lid-driven cavity flow orthogonal to a wall-bounded Couette flow. Critical Reynolds numbers computed by linear stability analysis are found to be significantly smaller than data previously reported in the literature. This finding is confirmed by independent nonlinear three-dimensional simulations. The critical Reynolds number as a function of the yaw angle is discussed for representative aspect ratios. Different instability modes are found. Independent of the yaw angle, the dominant instability mechanism is based on the local lift-up process, i.e. by the amplification of streamwise perturbations by advection of basic flow momentum perpendicular to the sheared basic flow. For small yaw angles, the instability is centrifugal, similar as for the classical lid-driven cavity. As the spanwise component of the lid velocity becomes dominant, the vortex structures of the critical mode become elongated in the direction of the bounded Couette flow with the lift-up process becoming even more important. In this case the instability is made possible by the residual recirculating part of the basic flow providing a feedback mechanism between the streamwise vortices and the streamwise velocity perturbations (streaks) they promote. In the limit when the basic flow approaches bounded Couette flow the critical Reynolds number increases very strongly.

Receptivity of inviscid modes in supersonic boundary layers to wall perturbations

The present paper investigates the receptivity of inviscid first and second modes in a supersonic boundary layer to time-periodic wall disturbances in the form of local blowing/suction, streamwise velocity perturbation and temperature perturbation, all introduced via a small forcing slot on the flat plate. The receptivity is studied using direct numerical simulations (DNS), finite- and high-Reynolds-number approaches, which complement each other. The finite-Reynolds-number formulation predicts the receptivity as accurately as DNS, but does not give much insight to the detailed excitation process, nor can it explain the significantly weaker receptivity efficiency of the streamwise velocity and temperature perturbations relative to the blowing/suction. In order to shed light on these issues, an asymptotic analysis was performed in the limit of large Reynolds number. It shows that the receptivity to all three forms of wall perturbations is reduced to the same mathematical form: the Rayleigh equation subject to an equivalent suction/blowing velocity, which can be expressed explicitly in terms of the physical wall perturbations. Estimates of the magnitude of the excited eigenmode can be made a priori for each case. Furthermore, the receptivity efficiencies for the streamwise velocity and temperature perturbations are quantitatively related to that for the blowing/suction by simple ratios, which are of O(R^{-1/2}) and have simple expressions, where R is the Reynolds number based on the boundary-layer thickness at the centre of the forcing slot. The simple leading-order asymptotic theory predicts the instability and receptivity characteristics accurately for sufficiently large Reynolds numbers (about 10^4), but appreciable error exists for moderate Reynolds numbers. An improved asymptotic theory is developed by using the appropriate impedance condition that accounts for the O(R^{-1/2}) transverse velocity induced by the viscous motion in the Stokes layer adjacent to the wall. The improved theory predicts both the instability and receptivity at moderate Reynolds numbers (R=O(10^3)) with satisfactory accuracy. In particular, it captures well the finite-Reynolds-number effects, including the Reynolds-number dependence of the receptivity and the strong excitation occurring near the so-called synchronisation point.

Growth mechanisms of second-mode instability in hypersonic boundary layers

Abstract

Reattachment streaks in hypersonic compression ramp flow: an input–output analysis

We employ global input–output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock–boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat-flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favourably with observations from two different hypersonic compression ramp experiments. Furthermore, our analysis of inviscid transport equations demonstrates that base-flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Finally, the appearance of the temperature streaks near reattachment is triggered by the growth of streamwise velocity and streamwise vorticity perturbations as well as by the amplification of upstream temperature perturbations by the reattachment shock.

Turbulence in intermittent transitional boundary layers and in turbulence spots

Direct numerical simulation data of bypass transition in flat-plate boundary layers are analysed to examine the characteristics of turbulence in the transitional regime. When intermittency is 50 % or less, the flow features a juxtaposition of turbulence spots surrounded by streaky laminar regions. Conditionally averaged turbulence statistics are evaluated within the spots, and are compared to standard time averaging in both the transition region and in fully turbulent boundary layers. The turbulent-conditioned root-mean-square levels of the streamwise velocity perturbations are notably elevated in the early transitional boundary layer, while the wall-normal and spanwise components are closer to the levels typical for fully turbulent flow. The analysis is also extended to include ensemble averaging of the spots. When the patches of turbulence are sufficiently large, they develop a core region with similar statistics to fully turbulent boundary layers. Within the tip and the wings of the spots, however, the Reynolds stresses and terms in the turbulence kinetic energy budget are elevated. The enhanced turbulence production in the transition zone, which exceeds the levels from fully turbulent boundary layers, contributes to the higher skin-friction coefficient in that region. Qualitatively, the same observations hold for different spot sizes and levels of free-stream turbulence, except for young spots which do not yet have a core region of developed turbulence.

Linear and nonlinear evolution of a localized disturbance in polymeric channel flow

AbstractThe evolution of an initially localized disturbance in polymeric channel flow is investigated, with the FENE-P model used to characterize the viscoelastic behaviour of the flow. In the linear growth regime, the flow response is stabilized by viscoelasticity, and the maximum attainable disturbance-energy amplification is reduced with increasing polymer concentration. The reduction in the energy growth rate is attributed to the polymer work, which plays a dual role. First, a spanwise polymer-work term develops, and is explained by the tilting action of the wall-normal vorticity on the mean streamwise conformation tensor. This resistive term weakens the spanwise velocity perturbation thus reducing the energy of the localized disturbance. The second action of the polymer is analogous, with a wall-normal polymer work term that weakens the vertical velocity perturbation. Its indirect effect on energy growth is substantial since it reduces the production of Reynolds shear stress and in turn of the streamwise velocity perturbation, or streaks. During the early stages of nonlinear growth, the dominant effect of the polymer is to suppress the large-scale streaky structures which are strongly amplified in Newtonian flows. As a result, the process of transition to turbulence is prolonged and, after transition, a drag-reduced turbulent state is attained.

The lift-up effect: The linear mechanism behind transition and turbulence in shear flows

The formation and amplification of streamwise velocity perturbations induced by cross-stream disturbances is ubiquitous in shear flows. This disturbance growth mechanism, so neatly identified by Ellingsen and Palm in 1975, is a key process in transition to turbulence and self-sustained turbulence. In this review, we first present the original derivation and early studies and then discuss the non-modal growth of streaks, the result of the lift-up process, in transitional and turbulent shear flows. In the second part, the effects on the lift-up process of additives in the fluid and of a second phase are discussed and new results presented with emphasis on particle-laden shear flows. For all cases considered, we see the lift-up process to be a very robust process, always present as a first step in subcritical transition.

Turbulent spots in a channel: large-scale flow and self-sustainability

AbstractUsing a large-time-resolved particle image velocimetry field of view, a developing turbulent spot is followed in space and time in a rectangular channel flow for more than 100 advective time units. We show that the flow can be decomposed into a large-scale motion consisting of an asymmetric quadrupole centred on the spot and a small-scale part consisting of streamwise streaks. From the temporal evolution of the energy of the streamwise and spanwise velocity perturbations, it is suggested that a self-sustaining process can occur in a turbulent spot above a given Reynolds number.

A Large-Eddy Simulation Study of Thermal Effects on Turbulence Coherent Structures in and above a Building Array

AbstractThermal effects on turbulent flow in and above a cubical building array are numerically investigated using the parallelized large-eddy simulation model (PALM). Two cases (no heating and bottom heating) are simulated and are compared with each other, focusing on thermal effects on turbulence coherent structures. In the no-heating case, the streaky or streamwise-elongated structures of low-speed regions appear above the building array and ejections in the low-speed regions play an important role in transporting momentum downward. In the bottom-heating case, plume-shaped structures appear with streamwise-elongated structures and the magnitude of vertical turbulent momentum flux averaged over the low-speed regions increases. Elliptical structures of negative streamwise velocity perturbation and vortical structures similar to hairpin vortices appear above the building array in the conditionally averaged fields in both cases, and the coherent structures expand more vertically when the bottom is heated. At or just above the rooftop height, high-speed streaks are distinct and sweeps induced by the streaks or shear instability are important for momentum transport in both cases. In the bottom-heating case, the magnitude of vertical turbulent momentum flux at the tops of cavity spaces increases, partly owing to the strengthened ejections. Below the rooftop height, the high-speed streaks occasionally enter intersection spaces and induce spanwise diverging flow there in both cases. When the bottom is heated, intensified updrafts induce more organized secondary circular flow and the spanwise flow in the building array is strengthened by the secondary flow.

Algebraic/transcendental disturbance growth behind a row of roughness elements

This paper is a continuation of the work begun in Goldstein et al. (J. Fluid Mech., vol. 644, 2010, p. 123), who constructed an asymptotic high-Reynolds-number solution for the flow over a spanwise periodic array of relatively small roughness elements with (spanwise) separation and plan form dimensions of the order of the local boundary-layer thickness. While that paper concentrated on the linear problem, here the focus is on the case where the flow is nonlinear in the immediate vicinity of the roughness with emphasis on the intermediate wake region corresponding to streamwise distances that are large in comparison with the roughness dimension, but small in comparison with the distance between the roughness array and the leading edge. An analytical O(h2) asymptotic solution is obtained for the limiting case of a small roughness height parameter h. These weakly nonlinear results show that the spanwise variable component of the wall-pressure perturbation decays as x−5/3 ln x when x → ∞ (where x denotes the streamwise distance scaled on the roughness dimension), but the corresponding component of the streamwise velocity perturbation (i.e. the wake velocity) exhibits an O(x1/3 ln x) algebraic/transcendental growth in the main boundary layer. Numerical solutions for h = O(1) demonstrate that the wake velocity perturbation for the fully nonlinear case grows in the same manner as the weakly nonlinear prediction – which is considerably different from the strictly linear result obtained in Goldstein et al. (2010).

Effect of Thermal Bump in Supersonic Flow Control

A three-dimensional numerical study is performed to explore the effect of a pulsed rectangular heating element (also denoted as thermal bump) in a Mach 1.5 laminar flat plate boundary layer. The thermal bump is modeled as a time-dependent step surface temperature rise. The thermal bump generates a series of counter-rotating streamwise vortices formed at the four edges of the element. When the bump is pulsed, vortex shedding is observed. These vortices interact with each other, generating a complicated vortical field, and grow in the spanwise direction with the downstream distance. Results show that the vertical perturbation velocity plays a key role in generating a lifting effect to sustain the horizontal disturbances. The streamwise velocity perturbation produces a low-speed region downstream of the centerline and a high-speed region on each side of the bump. The disturbance energy shows that the streamwise kinetic disturbance energy dominates over other components.

Direct numerical simulation of vortex synchronization due to small perturbations

Direct numerical simulation (DNS) is performed to investigate the vortex synchronization phenomena in the wake behind a circular cylinder at the Reynolds numbers, Re = 220 (mode-A regime) and 360 (mode-B regime). To generate vortex synchronization, a sinusoidal streamwise velocity perturbation, the frequency of which is about twice the natural shedding frequency, is superimposed on the free stream velocity. At Re = 360, vortex synchronization occurs when the perturbation frequency is exactly twice the natural shedding frequency. However, at Re = 220, it does not occur when the same perturbation frequency condition is imposed. Instead, it occurs when the perturbation frequency is near twice the hypothetical two-dimensional laminar vortex shedding frequency as if there were no wake transition at Re = 220. It is elucidated that, as a result of vortex synchronization, the trajectory of the Karman vortices and the vortex structure are changed. The Karman vortices are formed along the mean separating streamline slightly inside the mean wake bubble at Re = 220, but slightly outside at Re = 360. Thus, the Reynolds shear stress force has different contribution to the streamwise force balance of the mean wake bubble depending on the Reynolds numbers: its magnitude is negligible at Re = 220, compared to other force components, while it reverses its sign at Re = 360. More importantly, at Re = 220, the mode-A instability is suppressed into two-dimensional laminar flow with strong Karman vortices. At Re = 360, the dominant instability mode changes from mode B to mode A.

Effect of wall perturbations on the receptivity of a hypersonic boundary layer

The receptivity of a Mach 5.92 flat plate boundary layer to periodic two-dimensional wall perturbations is studied by numerical simulations and linear stability theory (LST). Free stream flow conditions are the same as the leading edge receptivity experiment of Maslov et al., J. Fluid Mech. 426, 73 (2001). Steady base flow is simulated by solving compressible Navier–Stokes equations with a combination of a fifth-order shock-fitting method and a second-order total variation diminishing scheme. The accuracy of the steady base flow is validated by comparisons with the experimental measurements of Maslov et al. and self-similar boundary-layer solution. In receptivity simulations, streamwise velocity perturbation, blowing suction, and temperature perturbation are introduced to the steady base flow with a forcing slot on flat plate. A model of wall perturbation is proposed based on physical properties of the electric pulse generator used in the experiment of Maslov et al. Stability characteristics of boundary-layer waves are identified and evaluated by comparing the results of LST and numerical simulation. Numerical simulation results show that all three types of wall perturbations eventually result in the same type of instability wave (mode S) in the boundary layer, which indicates that receptivity mechanism of the hypersonic boundary layer to wall perturbation is independent of specific perturbation type. On the other hand, the hypersonic boundary layer is found to be most sensitive to blowing-suction and least sensitive to temperature perturbation.

Re=360에서 교란유동장에 놓인 원형실린더 후류의 유동공진 현상에 대한 직접수치해석

Lock-on phenomenon in the wake of a circular cylinder is investigated at the Reynolds number of 360 using direct numerical simulation (DNS). To induce lock-on, a streamwise velocity perturbation with a frequency of twice the natural shedding frequency is superimposed on the free stream velocity. The Reynolds stress distributions are investigated to analyze the streamwise force balance acting on the recirculation region and the results are compared with the previous experimental result. When the lock-on occurs, the pressure force on the recirculation region is shown to increase mainly due to the reversal of the Reynolds shear stress distribution, which is consistent with our previous results using PIV measurement. It is also shown that, with the lock-on, the strength of the primary vortices increases whereas that of the secondary vortices decreases significantly. Further, under the lock-on condition the wavelength of the secondary vortices increases by as much as 2.5 times.

Experimental characterization of initial conditions and spatio-temporal evolution of a small-Atwood-number Rayleigh–Taylor mixing layer

(Received 17 October 2005 and in revised form 11 April 2006) The initial multi-mode interfacial velocity and density perturbations present at the onset of a small-Atwood-number, incompressible, miscible Rayleigh–Taylor instabilitydriven mixing layer have been quantified using a combination of experimental techniques. The streamwise interfacial and spanwise interfacial perturbations were measured using high-resolution thermocouples and planar laser-induced fluorescence (PLIF), respectively. The initial multi-mode streamwise velocity perturbations at the twofluid density interface were measured using particle-image velocimetry (PIV). It was found that the measured initial conditions describe an initially anisotropic state, in which the perturbations in the streamwise and spanwise directions are independent of one another. The evolution of various fluctuating velocity and density statistics, together with velocity and density variance spectra, were measured using PIV and high-resolution thermocouple data. The evolution of the velocity and density statistics is used to investigate the early-time evolution and the onset of strongly nonlinear, transitional dynamics within the mixing layer. The early-time evolution of the density and vertical velocity variance spectra indicate that velocity fluctuations are the dominant mechanism driving the instability development. The implications of the present experimental measurements on the initialization of Reynolds-averaged turbulent transport and mixing models and of direct and large-eddy simulations of Rayleigh–Taylor instability-induced turbulence are discussed.

Development of low-frequency streaks in Blasius boundary layer

A response of flat plate boundary layer to a single free-stream axial vortex of limited spanwise extent with periodically modulated strength is investigated. The response is dominated by a streamwise velocity perturbation (streak), whose characteristics are in agreement with data of previous experiments performed with natural streaks developed under the effect of free-stream turbulence. This confirms that the experimental approach used is suitable for an accurate modeling of the low-frequency natural streaks in controlled conditions. A quantitative comparison of the observed streak characteristics with available theoretical approaches is performed.

Receptivity of a flat plate boundary layer to a free stream axial vortex

A single free stream axial vortex of controlled strength and position was used to investigate a vortical receptivity of Blasius boundary layer. Excited boundary-layer disturbances were dominated by streamwise velocity perturbations, that grew downstream essentially linearly with the streamwise coordinate. It was shown that the disturbance characteristics are in agreement with data of previous experiments performed under natural and control conditions concerning the ‘by-pass’ transition initiated at high free stream disturbance levels. It was proved that the role of the leading edge in the receptivity process and disturbance growth under consideration is not dominant.

Development of Piezoelectric Actuators for Active Flow Control

The development of piezoelectric actuators for active e ow control is discussed. The type of actuators considered consists of a single sheet of piezoceramic material bonded to the underside of a shim: a “ unimorph” e ap design. Existing theoretical beam models are extended to incorporate a linear strain distribution in the composite unimorph beam structure. This model is combined with an optimization scheme to design a e ap that maximizes the tip dee ection per unit voltage for a given bandwidth. The optimization model is then used to design a piezoelectric actuator. The model predictions compare favorably to measurements of the actuator frequency response function. A sample application to control of separated e ow from a backward-facing step is also described, in which the actuator is installed at the origin of the free shear layer. Detailed hot-wire measurements, together with dimensional analysis, reveal the physical mechanism responsible for the e uid-structure coupling. A quasi-static model based on the solid-body displacement of the incoming shear layer accurately describes the peak streamwise velocity perturbations produced by the actuator. This model leads to a proportional relationship between the e ap tip displacement, the incoming boundary-layer proe le parameters, and the streamwise velocity e uctuations produced by the actuator.

On the Environmental Realizability of Algebraically Growing Disturbances and Their Relation to Klebanoff Modes

A theoretical explanation of some experimentally observed phenomena associated with the so-called Klebanoff modes is obtained by analyzing the flow over a finite thickness flat plate resulting from a small-amplitude distortion imposed on the upstream mean flow. The analysis shows (among other things) how the stretching of the vortex lines around the plate leads to streamwise vorticity at the plate surface, which then produces a streamwise velocity perturbation within the boundary layer that can be related to the experimentally observed Klebanoff mode. The complete evolution of this flow must be found by solving the boundary-region equations of Kemp (1951) and Davis and Rubin (1980), but a limiting analytical solution can also be obtained. Since the initial growth of the boundary-layer disturbance is nearly algebraic, our results demonstrate how the algebraically growing disturbances promoted by Landahl and others can be generated by a realistic external-disturbance environment. The relationship between these results and various bypass transition mechanisms is discussed.