Cluster-based control of a separating flow over a smoothly contoured ramp

The ability to manipulate and control fluid flows is of great importance in many scientific and engineering applications. The proposed closed-loop control framework addresses a key issue of model-based control: The actuation effect often results from slow dynamics of strongly nonlinear interactions which the flow reveals at timescales much longer than the prediction horizon of any model. Hence, we employ a probabilistic approach based on a cluster-based discretization of the Liouville equation for the evolution of the probability distribution. The proposed methodology frames high-dimensional, nonlinear dynamics into low-dimensional, probabilistic, linear dynamics which considerably simplifies the optimal control problem while preserving nonlinear actuation mechanisms. The data-driven approach builds upon a state space discretization using a clustering algorithm which groups kinematically similar flow states into a low number of clusters. The temporal evolution of the probability distribution on this set of clusters is then described by a control-dependent Markov model. This Markov model can be used as predictor for the ergodic probability distribution for a particular control law. This probability distribution approximates the long-term behavior of the original system on which basis the optimal control law is determined. We examine how the approach can be used to improve the open-loop actuation in a separating flow dominated by Kelvin–Helmholtz shedding. For this purpose, the feature space, in which the model is learned, and the admissible control inputs are tailored to strongly oscillatory flows.     

Numerical simulation of wall roughness effects in cavitating flow

Hydrodynamic cavitation has an important effect on the performance of Diesel injectors. It influences the nature of the fuel spray and the efficiency of the combustion process. In the present study, we investigate numerically the effect of wall roughness in the cavitating and turbulent flow developing inside a Diesel injector. The mixture model based on a single fluid is adopted and the commercial Fluent software is used to solve the transport equations.The discharge coefficient C_d is computed for different cavitation numbers and wall roughness heights. Profiles of density mixture, vapor volume fraction, mean velocity and turbulent kinetic energy are reported. The effects of wall roughness and injection pressure are analyzed.     

The effect of roughness on separating flow over two-dimensional hills

Two new experimental data sets for turbulent flow over a steep, rough hill are presented. These include detailed laser Doppler anemometry measurements obtained at the separation and reattachment points and, in particular, within the reverse flow region on the lee side of the hill. These results allow the development of a new parametrization for rough wall boundary layers and validate the use of Stratford’s solution for a separating rough flow. The experiments were conducted in a water channel for two different Reynolds numbers. In the first set of rough wall experiments, the flow conditions and the hill shape are similar to those presented in Loureiro et al. (Exp. Fluids, 42:441–457, 2007a) for a smooth surface, leading to a much reduced separation region. In the second set of experiments, the Reynolds number is raised ten times. The region of separated flow is then observed to increase, but still to a length shorter than that recorded by Loureiro et al. (Exp. Fluids, 42:441–457, 2007a). Detailed data on mean velocity and turbulent quantities are presented. To quantify the wall shear stress, global optimization algorithms are used. The merit function is defined in terms of a local solution that is shown to reduce to the classical law of the wall far away from a separation point and to the expression of Stratford at a separation point. The flow structure at the separation point is also discussed.     

Visualization of a locally-forced separated flow over a backward-facing step

A laboratory water channel experiment was made of the separated flow over a backward-facing step. The flow was excited by a sinusoidally oscillating jet issuing from a separation line. The slit was connected to a cavity in which water was forced through a rigid pipe by a scotch-yoke system. The Reynolds number based on the step height (H) was fixed at Re _H =1200. The forcing frequency was varied in the range 0.305?St _H ?0.955 at the forcing amplitude A ₀=0.3. Time-averaged flow measurements were made by a LDV system, especially in the recirculating region behind the backward-facing step. To characterize the large-scale vortex evolution due to the local forcing, flow visualizations were performed by a dye tracer method with fluorescent ink. The vortex amalgamation process was captured at the effective forcing frequency (St _H =0.477) for laminar separation. This vortex merging process enhances flow mixing, which leads to the shortening of the reattachment length.     

Turbulent separated flow over and downstream of a two-element airfoil

Flow characteristics in the vicinity of the flap of a single-slotted airfoil are presented and analysed. The flow remained attached over the model surfaces except in the vicinity of the flap trailing edge where a small region of boundary-layer separation extended over the aft 7% of flap chord. The airfoil configuration was tested at a Mach number of 0.09 and a chord Reynolds number of 1.8 × 10⁶ in the NASA Ames Research Center 7- by 10-Foot Wind Tunnel. The flow was complicated by the presence of a strong, initially inviscid, jet, emanating from the slot between airfoil and flap, and a gradual merging of the main airfoil wake and flap suction-side boundary layer.Research Engineer, NRC Research AssociateAerospace Engineer     

Effect of spanwise-varying local forcing on turbulent separated flow over a backward-facing step

An experimental study was made of turbulent separated flows over a backward-facing step. A local forcing was given to the separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. To produce a spanwise-varying local forcing at the separation edge, a banded thin tape covered the slit. Effects of the spanwise-varying local forcings on the separated flow were scrutinized by altering the spatially banded blocking width (w) and the open slit distance (g). An optimal value of w/g was sought, which led to the minimum reattachment length (x _R ). The effect of spanwise-varying local forcing on x _R was found to be slight compared to the case of two-dimensional forcing (w=0). The experiment was made at Re _H =33000 and A ₀=0.018 by changing the forcing frequency (0?St _H ?1.0).     

Turbulence production in flow over a wavy wall

Measurements of the spatial and time variation of two components of the velocity have been made over a sinusoidal solid wavy boundary with a height to length ratio of 2a/λ = 0.10 and with a dimensionless wave number of α⁺ = (2π/λ)(v/u ^?) = 0.02. For these conditions, both intermittent and time-mean flow reversals are observed near the troughs of the waves. Statistical quantities that are determined are the mean streamwise and normal velocities, the root-meansquare of the fluctuations of the streamwise and normal velocities, and the Reynolds shear stresses. Turbulence production is calculated from these measurements. The flow is characterized by an outer flow and by an inner flow extending to a distance of about α^?1 from the mean level of the surface. Turbulence production in the inner region is fundamentally different from flow over a flat surface in that it is mainly associated with a shear layer that separates from the back of the wave. Flow close to the surface is best described by an interaction between the shear layer and the wall, which produces a retarded zone and a boundary-layer with large wall shear stresses. Measurements of the outer flow compare favorably with measurements over a flat wall if velocities are made dimensionless by a friction velocity defined with a shear stress obtained by extrapolating measurements of the Reynolds stress to the mean levels of the surface (rather than from the drag on the wall).     

Control of turbulent separated flow over a backward-facing step by local forcing

An experimental study was made of the flow over a backward-facing step. Excitations were given to separated flow by means of a sinusoidally oscillating jet issuing from a thin slit near the separation line. The Reynolds number based on the step height (H) varied 13000 Re _H 33000. Effect of local forcing on the flow structure was scrutinized by altering the forcing amplitude (0 A ₀ 0.07) and forcing frequency (0 St _H 5.0). Small localized forcing near the separation edge enhanced the shear-layer growth rate and produced a large roll-up vortex at the separation edge. A large vortex in the shear layer gave rise to a higher rate of entrainment, which lead to a reduction in reattachment length as compared to the unforced flow. The normalized minimum reattachment length (x _r )_min/x _x0 was obtained at St 0.01. The most effective forcing frequency was found to be comparable to the shedding frequency of the separated shear layer.List of symbols a ₀ forcing amplitude=(Q _forced–Q _unforced)/U ₀ - AR aspect ratio=W/H - C _p wall-pressure coefficient=(P-P ₀)/(l/2) U ₀ ² - ER expansion ratio=(2H+H)/2H - f _f forcing frequency, Hz - f _s shedding frequency, Hz - g slit width = 1.0 ± 0.1 mm - H step height = 50 mm - P wall-static pressure, Pa - P ₀ wall-static pressure at x/H= -2.0, Pa - Q _forced total velocity measured at reference position for forced flow, m/s - Q _unforced total velocity measured at reference position for unforced flow, m/s - Re _H Reynolds number based on H and U ₀,= U ₀ H/v - St _H Reduced forcing frequency, Strouhal number = f _f H/U ₀ - St Reduced forcing frequency based on the momentum thickness = f _f /U ₀ - U, V streamwise and vertical time-mean velocity, m/s - u streamwise fluctuation velocity, m/s - U ₀ free-stream velocity, m/s - r.m.s. intensity of streamwise velocity fluctuation, m/s - x _r reattachment length, m - X _{r 0} reattachment length for A ₀ = 0, m - x, y, z distance of streamwise, vertical and spanwise respectively, m - W width of test section = 625 mm Greek symbols boundary-layer thickness, cm - ^* displacement thickness, cm - _p forward-flow time fraction - density of air for measurement, kg/m³ - v kinematic viscosity of air for measurement, m²/s - momentum thickness, cm     

Turbulent boundary layer over a smooth wall with widely separated transverse square cavities

Laser-Doppler velocimetry (LDV) measurements and flow visualizations are used to study a turbulent boundary layer over a smooth wall with transverse square cavities at two values of the momentum thickness Reynolds number (R =400 and 1300). The cavities are spaced 20 element widths apart in the streamwise direction. Flow visualizations reveal a significant communication between the cavities and the overlying shear layer, with frequent inflows and ejections of fluid to and from cavities. There is evidence to suggest that quasi-streamwise near-wall vortices are responsible for the ejections of fluid out of the cavities. The wall shear stress, which is measured accurately, increases sharply immediately downstream of the cavity. This increase is followed by a sudden decrease and a slower return to the smooth wall value. Integration of the wall shear stress in the streamwise direction indicates that there is an increase in drag of 3.4% at bothR .Nomenclature C _f skin friction coefficient - C _fsw friction coefficient for a continuous smooth wall - k height of the cavity - k ⁺ ku / - R Reynolds number based on momentum thickness (U ₁ /v) - Rx Reynolds number based on streamwise distance (U ₁ x/) - s streamwise distance between two cavities - t time - t ⁺ tu ₂ / - U ₁ freestream velocity - mean velocity inx direction - u,v,w rms turbulent intensities inx,y andz directions - u local friction velocity - u _sw friction velocity for a continuous smooth wall - w width of the cavity - x streamwise co-ordinate measured from the downstream edge of the cavity - y co-ordinate normal to the wall - z spanwise co-ordinate - y ⁺ yu / - boundary layer thickness - ₀ boundary layer thickness near the upstream edge of the cavity - _i thickness of internal layer - kinematic viscosity of water - ⁺ zu / - momentum thickness     

Three-dimensional coherent structure in a separated and reattaching flow over a backward-facing step

An experimental study was carried out to elucidate the large-scale vortical structure in a separated and reattaching flow over a backward-facing step. The Reynolds number based on the step height (H) was Re _H =33,000. The large-scale vortical structure was probed by means of three-dimensional velocity measurements performed at the recirculation zone (x/H=4.0) and the reattachment zone (x/H=7.5). A 32-channel microphone array extending in the streamwise and spanwise directions was used for sensing the wall pressure fluctuations. The relationship between the flow field and the relevant spatial mode of the pressure field was determined by examining the spatial box filtering. From the relevant spatial mode of the wall pressure fluctuations, a conditional averaging technique was employed to characterize the coherent structure. In addition, the cross-correlation between velocity and wall pressure fluctuations was calculated to identify the structure and the length scale of the large-scale vortex. The cross-correlation results revealed that the large-scale hairpin vortices have a three-dimensional structure, in agreement with previous findings. The present results clearly show the growth and downstream elongation of the hairpin vortices.List of symbols H step height, m - k turbulent kinetic energy, m²/s² - q freestream dynamic pressure, Pa - Re _H Reynolds number based on U ₀ and H,U _oH/ - U ₀ freestream velocity, m/s - U _c convection velocity, m/s - X ₀ streamwise coordinate of the measurement origin, m - x _R time mean reattachment length, m Greek symbols _p forward flow time fraction - cross-correlation coefficient - time delay, s - vorticity, m²/s     

Optimization of jet parameters to control the flow on a ramp

This study deals with the use of optimization algorithms to determine efficient parameters of flow control devices. To improve the performance of systems characterized by detached flows and vortex shedding, the use of flow control devices such as oscillatory jets are intensively studied. However, the determination of efficient control parameters is still a bottleneck for industrial problems. Therefore, we propose to couple a global optimization algorithm with an unsteady flow simulation to derive efficient flow control rules. We consider as a test case a backward-facing step with a slope of 25°, including a synthetic jet actuator. The aim is to reduce the time-averaged recirculation length behind the step by optimizing the jet blowing/suction amplitude and frequency.     

Self-similar problem of separated ideal-fluid flow over an expanding plate

The research carried out in [1–8] is developed by considering the self-similar problem of the unsteady separated flow over a plate expanding from a point with the constant velocity D of a plane-parallel stream of ideal fluid with velocity V_∞. At infinity the flow is uniform, steady and normal to the surface of the plate. A wide range of values of the parameter α=V_∞/D is investigated. On the value of α there depends, in particular, the direction of shedding of the vortex sheets (VS) which, in accordance with the Joukowsky-Chaplygin condition, occur in separated flow over a plate. A comparison is made with the results obtained when the sheets are replaced by vortex filaments (VF). In accordance with [9] the choice of the intensity of the VF ensures, like the introduction of VS, the finiteness of the flow velocity at the edges of the plate. Within the framework of the unsteady analogy and the law of plane sections the problem of the flow over a delta wing at an angle of attack reduces to the unsteady flow over an expanding plate investigated. In addition to [3, 9], this question was also examined in [10–15]. In [11–15] and in [3] the analysis is based on VS and in [9, 10] on VF. Special attention is paid to the topology of the flow, in particular, to the structure of the so-called conical streamlines and their points of convergence and divergence (this was done in [3] for a special, nonlinear law of expansion of the plate and a variable free-stream velocity). The results obtained for the models with VS and VF are compared over a broad range of values of α, not only with respect to the integral characteristics, as in [12], but also with respect to the flow patterns. Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 62–69, September–October, 1988.     

PIV measurement of separated flow over a blunt plate with different chord-to-thickness ratios

The influence of the chord-to-thickness ratio (c/t) on the spatial characteristics of the separated shear layer over a blunt plate and the leading-edge vortices embedded in the separated shear layer was studied extensively using planar particle image velocimetry (PIV). Three systems corresponding to different shedding modes were chosen for the comparative study: c/t=3, 6 and 9. The Reynolds number based on the plate's thickness (t) was Re_t=1×10³. A gigapixel CCD camera was used to acquire images with a spatial resolution of 0.06t×0.06t in the measurement range of 9.5t×4.5t. Distributions of statistical quantities, such as the streamline pattern, streamwise velocity fluctuation intensity, shear stress and reverse flow intermittency, showed that the separated shear layer in the system with c/t=3 did not reattach to the plate's surface, while the near‐wake behind the trailing edge was highly unstable because the energetic leading-edge vortices were shed into the wake. The separated shear layer of the system with c/t=6 periodically reattached to the plate's surface, which resulted in intensified fluctuations of the near wake behind the trailing edge. In the longest system (c/t=9), the separated shear layer always reattached to the plate's surface far upstream from the trailing edge, which did not induce large fluctuations of the near wake. Furthermore, the proper orthogonal decomposition (POD) was extensively employed to filter the original velocity fields spatially to identify the large-scale vortices immersed in the separated shear layer easily. The distribution of the v-v correlation coefficients of the spatially filtered flow fields reflected the organized large-scale vortices in the three systems. The number of alternations of the positive and negative correlation coefficients across the flow field were determined to be 1, 2 and 3 for the systems with c/t=3, 6 and 9, respectively; this is in agreement with the shedding mode of each system. The distribution of the swirling strength of the separated shear layer accurately determined the positions and structures of the large-scale vortices formed above the plate surface.     

Assessment of the organization of a turbulent separated and reattaching flow by measuring wall pressure fluctuations

The effect of local forcing on the organization of a turbulent separated and reattaching flow was assessed by measuring wall pressure fluctuations. Multi-arrayed microphones were installed on the surface to measure the simultaneous spatial and temporal wall pressure fluctuations. Local forcing at the separation edge was applied to the separated flow over a backward-facing step through a thin slit. The organization of the separated and reattaching flow was found to be greatest at the effective forcing frequency. The flow structure was diagnosed by analyzing several characteristics of the wall pressure fluctuations: the wall pressure fluctuation coefficients, wall pressure spectrum, wavenumber-frequency spectrum, coherence, cross-correlation, and multi-resolution autocorrelations of pressure fluctuations using the maximum overlap discrete wavelet transform and continuous wavelet transform. Features indicative of the amalgamation of vortices under the local forcing were observed; this amalgamation process accounted for the observed reduction of the reattachment length. Examination of the wall pressure fluctuations revealed that introduction of local forcing enhanced flapping motion as well as the streamwise and spanwise dispersions of vortical structures.     

A method for determining the frictional velocity in a turbulent channel flow with roughness on the bottom wall

A method is proposed for determining the frictional velocity U on both walls of a fully developed turbulent channel flow, one smooth and the other rough. This should aid experimentalists in obtaining a reliable estimate of U with knowledge of only the pressure drop and location where the Reynolds shear stress is zero. The method is general and does not depend on the roughness geometry that is used. It has been validated against direct estimates of the wall stress using DNS databases for two types of two-dimensional roughness. Results for a surface composed of staggered cubes are also in accord with the method.     

Temperature fluctuations in a separated and reattached turbulent flow over a blunt flat plate

Investigated in the present study are some statistical features of temperature fluctuations in a two-dimensional separated and reattached turbulent flow over a blunt flat plate. Clarified are statistic behaviors of temperature fluctuation intensities, its autocorrelation coefficients, integral time scales, power spectra, probability density functions, skewness and flatness factors in the separated, reattached and redeveloped flow regions. Further, the present results are compared with the existing ones for a normal turbulent boundary layer over a flat plate without separation.

---

Temperaturschwankungen in einer abgelösten und wiederanliegenden turbulenten Strömung über eine stumpfe ebene Platte

Zusammenfassung In der vorliegenden Untersuchung wurden mehrere statistische Charakteristika der Temperaturschwankungen im Bereich der abgelösten, wiederanliegenden und wiederausgebildeten zwei-dimensionalen turbulenten Luftströmung über eine ebene Platte mit stumpfer Vorderkante experimentell untersucht. Besonders wurde das statistische Verhalten der Intensität der Temperaturschwankungen, die Autokorrelationskoeffizienten, der integrale Zeitmaßstab, das Leistungsspektrum und die Wahrscheinlichkeits-Dichte-Funktion und die schiefen und ebenen Beiwerte im Bereich der abgelösten, wiederanliegenden und wiederausgebildeten Luftströmung beschrieben. Die erhaltenen Ergebnisse werden mit bereits existierenden Ergebnissen für eine turbulente Grenzschicht ohne Druckgradient über eine ebene Platte verglichen.

---

Nomenclature E(k) power spectrum - z flatness factor - f frequency - 2H plate thickness - k wave number=2f/U - l time-mean reattachment length - P() probability density function - q _w heat flux per unit area and time - R () autocorrelation coefficient - Re Reynolds number=U·H/v - S skewness factor - T integral time scale - U velocity of upstream uniform flow - U,u local streamwise mean and turbulent fluctuating velocity - u ⁺ friction velocity= - x distance from leading edge along plate surface - y distance normal to wall - y ⁺ nondimensional wall distance=u ⁺·y/v - _T nominal thermal boundary layer thickness defined as a wall distance of (-)/(gQ _W - )=0.01 - _m momentum thickness - , mean and turbulent fluctuating temperature - temperature at upstream uniform flow - _w wall temperature - v kinematic viscosity of air - fluid density - time lag - _w wall shear stress     

Near wall characterization of the flow over a two-dimensional steep smooth hill

Near-wall data for the strongly perturbed flow in a neutrally stable boundary layer encountering a steep, smooth, two-dimensional hill are presented. Observations were made on the centerplane of a water channel at thirteen stations relative to the hill by laser Doppler anemometry. The large reverse flow region that is formed on the lee of the hill was particularly scrutinized through seven measuring stations. Results are presented for the mean and turbulent properties of the flow. Wall shear stress was evaluated through fitting procedures that resorted to the near wall behavior of the velocity profile. Logarithmic fits as well as predictions through the Reynolds stress profiles are also presented.     

The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation

Numerical simulation of Poiseuille flow of liquid Argon in a rough nano-channel using the non-equilibrium molecular dynamics simulation is performed. Density and velocity profiles across the channel are investigated in which roughness is implemented only on the lower wall. The Lennard–Jones potential is used to model the interactions between all particles. The effects of surface roughness geometry, gap between roughness elements (or roughness periodicity), surface roughness height and surface attraction energy on the behavior of the flow undergoing Poiseuille flow are presented. Results show that surface shape and roughness height have a decisive role on the flow behaviors. In fact, by increasing the roughness ratio (height to base ratio), the slip velocity and the maximum velocity in the channel cross section are reduced, and the density fluctuations near the wall increases. Results also show that the maximum density near the wall for a rough surface is less than a smooth wall. Moreover, the simulation results show that the effect of triangle roughness surface on the flow behavior is more than the cylindrical ones.