Planar velocity measurements of a two-dimensional compressible wake

The present study describes the application of particle image velocimetry (PIV) to investigate the compressible flow in the wake of a two-dimensional blunt base at a freestream Mach number M_X=2. The first part of the study addresses specific issues related to the application of PIV to supersonic wind tunnel flows, such as the seeding particle flow-tracing fidelity and the measurement spatial resolution. The seeding particle response is assessed through a planar oblique shock wave experiment. The measurement spatial resolution is enhanced by means of an advanced image-interrogation algorithm. In the second part, the experimental results are presented. The PIV measurements yield the spatial distribution of mean velocity and turbulence. The mean velocity distribution clearly reveals the main flow features such as expansion fans, separated shear layers, flow recirculation, reattachment, recompression and wake development. The turbulence distribution shows the growth of turbulent fluctuations in the separated shear layers up to the reattachment location. Increased velocity fluctuations are also present downstream of reattachment outside of the wake due to unsteady flow reattachment and recompression. The instantaneous velocity field is analyzed seeking coherent flow structures in the redeveloping wake. The instantaneous planar velocity and vorticity measurements return evidence of large-scale turbulent structures detected as spatially coherent vorticity fluctuations. The velocity pattern consistently shows large masses of fluid in vortical motion. The overall instantaneous wake flow is organized as a double row of counter-rotating structures. The single structures show vorticity contours of roughly elliptical shape in agreement with previous studies based on spatial correlation of planar light scattering. Peak vorticity is found to be five times higher than the mean vorticity value, suggesting that wake turbulence is dominated by the activity of large-scale structures. The unsteady behavior of the reattachment phenomenon is studied. Based on the instantaneous flow topology, the reattachment is observed to fluctuate mostly in the streamwise direction suggesting that the unsteady separation is dominated by a pumping-like motion.     

Sensitivity analysis of freestream turbulence parameters on stagnation region heat transfer using a neural network

A neural network has been used to predict stagnation region heat transfer in the presence of freestream turbulence. The neural network was trained using data from an experimental study to investigate the influence of freestream turbulence on stagnation region heat transfer. The integral length scale, Reynolds number, all three components of velocity fluctuations and the vorticity field were used to characterize the freestream turbulence. The neural network is able to predict 50% of the test data within ±1%, while the maximum error of any data point is under 3%. A sensitivity analysis of the freestream turbulence parameters on stagnation region heat transfer was performed using the trained neural network. The integral length scale is found to have the least influence on the stagnation line heat transfer, while the normal and spanwise turbulence intensities have the highest influence.     

Estimation of velocity eigenfunction and vorticity distributions from the timeline visualization technique

For the case of quasi-periodic flow, it is demonstrated that use of the hydrogen bubble timeline method leads to reasonable estimates of the eigenfunction of the streamwise velocity fluctuation. Both amplitude and phase distributions across an unstable wake flow are well-approximated. It is shown that the vorticity extrema, as well as the degree of concentration of vorticity, are in good agreement with those calculated from linear stability theory. A critical assessment is given of the possible uncertainties associated with this technique: the existence of a finite, but unknown cross-stream velocity component; bubble rise due to buoyancy effects; wake defect created downstream of the bubble wire; and resolution of the digitized image. Furthermore, the uncertainty in the streamwise velocity, arising from existence of a finite cross-stream velocity component, is actually less than that corresponding to a single-element hot film probe over certain regimes of operation.     

PIV analysis of near-wake behind a sphere at a subcritical Reynolds number

The vortical structure of near-wake behind a sphere is investigated using a PIV technique in a circulating water channel at Re = 11,000. The measured velocity fields show a detailed vortical structure in the recirculation region such as recirculation vortices, reversed velocity zone, and out-of-plane vorticity distribution. The vorticity distribution of the sphere wake shows waviness in cross-sectional planes. The time-averaged turbulent structures are consistent with the visualized flow showing the onset of shear layer instability. The spatial distributions of turbulent intensities provide turbulent statistics for validating numerical predictions.     

均匀、振荡及组合流绕平板流动的尾迹研究

本文利用离散涡模型及改进的新生涡产生机制对三种不同来流绕平板的近尾迹进行数值研究。计算讨论了定常流中平板绕流流动的总体特性和近尾迹流场;对于简谐振荡来流,相应于K_c=2.0、4.0 和10.0 分别得到两种不同的尾迹形态。给出了小 K_c 数平板尾迹涡配对、运动的新模式而相应的阻力、惯性力系数计算比以前涡模拟结果更接近于 U 型管实验结果。对于流向组合来流本文模拟了涡锁定及其动力特性并于实验相符,给出了流向扰动对平板绕流流动的影响。     

Coherent vortical and straining structures in the finite wall-mounted square cylinder wake

Topological aspects of the turbulent wake of a finite, surface-mounted, square-cross-section cylinder of h/d = 4 are addressed by decomposing the velocity field into a quasi-periodic coherent part and the unresolved incoherent fluctuations. The three-dimensional large scale structure is educed through a reconstruction of planar phase-averaged PIV measurements using the simultaneously sampled surface pressure difference on opposing sides of the obstacle as a phase reference. A topological model for the vortex structure is educed and mean streamwise wake vorticity is explained in terms of the connections between initially vertical structures shed alternately from either side of the obstacle, rather than previously proposed ‘tip’ vortex structures generated at the obstacle free-end. The coherent structure educed accounts for a significant portion of the fluctuating energy in the wake. The turbulent field is further analyzed by finding Lagrangian straining structures that form by induction of the coherent vorticity field, and these structures are related to the energy transfer from the base phase-averaged flow since they act to stretch incoherent vorticity fluctuations in their neighbourhood.     

Solution of the Navier–Stokes equations in velocity–vorticity form using a Eulerian–Lagrangian boundary element method

This paper describes the Eulerian–Lagrangian boundary element model for the solution of incompressible viscous flow problems using velocity–vorticity variables. A Eulerian–Lagrangian boundary element method (ELBEM) is proposed by the combination of the Eulerian–Lagrangian method and the boundary element method (BEM). ELBEM overcomes the limitation of the traditional BEM, which is incapable of dealing with the arbitrary velocity field in advection‐dominated flow problems. The present ELBEM model involves the solution of the vorticity transport equation for vorticity whose solenoidal vorticity components are obtained iteratively by solving velocity Poisson equations involving the velocity and vorticity components. The velocity Poisson equations are solved using a boundary integral scheme and the vorticity transport equation is solved using the ELBEM. Here the results of two‐dimensional Navier–Stokes problems with low–medium Reynolds numbers in a typical cavity flow are presented and compared with a series solution and other numerical models. The ELBEM model has been found to be feasible and satisfactory. Copyright © 2000 John Wiley & Sons, Ltd.     

Orthogonal wavelet analysis of turbulent wakes behind various bluff bodies

The multi-scale structures of turbulent wakes generated by three kinds of bluff body, i.e. circular cylinder, square cylinder and compound of cylinder and square (CS) cylinders, have been experimentally investigated in this paper. Firstly, the instantaneous velocity fields and vorticity were measured by the high-speed PIV technique in a circulating water channel. The instantaneous streamlines and corresponding normalized vorticity contours are obtained at a Reynolds number of 5600. Then one- and two-dimensional wavelet multi-resolution technique was used to analyze the instantaneous velocities and vorticity measured by the high-speed PIV. The turbulence structures were separated into a number of subsets based on their central frequencies, which are linked with the turbulence scales. The instantaneous vorticity and Reynolds shear stresses of various scales were examined and compared between the three generators. It is found that the large-scale turbulent structure makes the largest contribution to the vorticity and Reynolds shear stresses for the three wake generators and exhibits a strong dependence upon the initial conditions or the wake generators. The large-scale vorticity and the sizes of vortex in the circular and square cylinders are larger than those in the CS cylinder wake. The contributions to the Reynolds shear stresses from the large-scale turbulent structures account for 90-96% to the measured maximum Reynolds shear stresses for the three wakes. However, the small-scale structures make less contribution to the vorticity and Reynolds shear stresses.     

Effect of velocity ratio on the streamwise vortex structures in the wake of a stack

The time-averaged velocity and streamwise vorticity fields within the wake of a stack were investigated in a low-speed wind tunnel using a seven-hole pressure probe. The experiments were conducted at a Reynolds number, based on the stack external diameter, of Re_D=2.3×10⁴. The stack, of aspect ratio AR=9, was mounted normal to a ground plane and was partially immersed in a flat-plate turbulent boundary layer, where the ratio of the boundary layer thickness to the stack height was δ/H≈0.5. The jet-to-cross-flow velocity ratio was varied from R=0 to 3, which covered the downwash, crosswind-dominated and jet-dominated flow regimes. In the downwash and crosswind-dominated flow regimes, two pairs of counter-rotating streamwise vortex structures were identified within the stack wake. The tip vortex pair located close to the free end of the stack, and the base vortex pair located close to the ground plane within the flat-plate boundary layer, were similar to those found in the wake of a finite circular cylinder, and were associated with the upwash and downwash flow fields within the stack wake, respectively. In the jet-dominated flow regime, a third pair of streamwise vortex structures was observed, referred to as the jet-wake vortex pair, which occurred within the jet-wake region above the free end of the stack. The jet-wake vortex pair had the same orientation as the base vortex pair and was associated with the jet rise. The peak vorticity and strength of the streamwise vortex structures were functions of the jet-to-cross-flow velocity ratio. For the tip vortex structures, their peak vorticity and strength reduced as the jet-to-cross-flow velocity ratio increased.     

Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).     

Solid/free-surface juncture boundary layer and wake

 The Reynolds-averaged flow for a solid/free-surface juncture boundary layer and wake is documented. The three mean-velocity components and five of the Reynolds stresses are measured for a surface-piercing flat plate in a towing tank using a laser-Doppler velocimeter system for both boundary-layer and wake planes in regions close to the free surface. The experimental method is described, including the foil-plate model, laser-Doppler velocimeter system, conditions, and uncertainty analysis. The underlying flow data is in excellent agreement with benchmark data. Inner (near the plate and wake centerplane and below the free surface) and outer (near the free surface) regions of high streamwise vorticity of opposite sign are observed, which transport, respectively, high mean velocity and low turbulence from the outer to the inner and low mean velocity and high turbulence from the inner to the outer portions of the boundary layer and wake. For the wake, the inner region of vorticity is relatively weak. The physical mechanism for the streamwise vorticity is analyzed with regard to the Reynolds-averaged streamwise vorticity equation. The anisotropy of the crossplane normal Reynolds stresses closely correlates with the vorticity and, additionally, indicates similarity, i.e., its nature is such that it only depends on the proximity to the plate and free surface boundaries or wake centerplane symmetry plane. Free-surface effects on the Reynolds stresses are analyzed with regard to the behavior close to the free surface of the turbulent kinetic energy and the normal components of the anisotropy tensor and the anisotropy invariants. Close to the free surface, the turbulent kinetic energy is nearly constant and increases for the inner and outer portions, respectively, of the boundary layer and wake and the normal components of the anisotropy tensor and the anisotropy invariants roughly correspond to the limiting values for two-component turbulence. The similarities and differences between the present results and analysis with those from related studies are discussed. The data and analysis should have practical application with regard to the development of turbulence models for computational fluid dynamics methods for the Reynolds-averaged Navier–Stokes equations. Received: 27 May 1997/Accepted: 1 August 1997     

Fast Flow Field Estimation for Various Applications with A Universally Applicable Machine Learning Concept

This paper presents an approach for the prediction of incompressible laminar steady flow fields over various geometry types. In conventional approaches of computational fluid dynamics (CFD), flow fields are obtained by solving model equations on computational grids, which is in general computationally expensive. Based on the ability of neural networks to intuitively identify and approximate nonlinear physical relationships, the proposed method makes it possible to eliminate the explicit implementation of model equations such as the Navier–Stokes equations. Moreover, it operates without iteration or spatial discretization of the flow problem. The method is based on the combination of a minimalistic multilayer perceptron (MLP) architecture and a radial-logarithmic filter mask (RLF). The RLF acts as a preprocessing step and its purpose is the spatial encoding of the flow guiding geometry into a compressed form, that can be effectively interpreted by the MLP. The concept is applied on internal flows as well as on external flows (e.g. airfoils and car shapes). In the first step, datasets of flow fields are generated using a CFD-code. Subsequently the neural networks are trained on defined portions of these datasets. Finally, the trained neural networks are applied on the remaining unknown geometries and the prediction accuracy is evaluated. Dataset generation, neural network implementation and evaluation are carried out in MATLAB. To ensure reproducibility of the results presented here, the trained neural networks and sample applications are made available for free download and testing.

     

Unsteady flow structure and vorticity convection over the airfoil oscillating at high reduced frequency

Unsteady vortex structures and vorticity convection over the airfoil (NACA 0012), oscillating in the uniform inflow, are studied by flow visualization and velocity measurements. The airfoil, pivoting at one-third of the chord, oscillates periodically near the static stalling angle of attack (AOA) at high reduced-frequency. The phase-triggering and modified phase-averaged techniques are employed to reconstruct the pseudo instantaneous velocity field over the airfoil. During the down stroke cycle, the leading-edge separation vortex is growing and the vortex near the trailing edge begins to shed into the wake. During the upstroke cycle, the leading-edge separation vortex is matured and moves downstream, and the counter clockwise vortex is forming near the trailing edge. Convection speeds and wavelength of the unsteady vortex structure over the airfoil equal to that of the counter clockwise vortex shed into the wake. This kind of vortex structure is termed as “synchronized shedding” type. The wavelength of unsteady vortex structure over the airfoil is significantly different from that at low reduced-frequency. Consistent convection speeds of the leading-edge separation vortex are acquired from the spatial-temporal variations of local circulation and local surface vorticity generation, and equals that predicted from flow visualization. Spatial-temporal variations of the local surface vorticity generation clearly reveal the formation and passage of the leading-edge separation vortex only in the region where the flow does not separate completely from the surface. Significant amounts of the surface vorticity are generated within the leading-edge region of the airfoil during the upstroke cycle. Only negligible amount of surface vorticity is produced within the region of complete flow separation. During the down stroke cycle, the surface vorticity generation is mild along the airfoil surface, except the leading-edge region where a small scale leading-edge separation vortex is forming and growing.     

A NUMERICAL STUDY OF CYLINDERS IN WAVES AND CURRENTS

The research on combination flow of planar oscillatory flow plus an in-line steady stream is of importance to the situation of structures in waves and current. The combination flow has not been studied extensively. There is still little information about the effect of current and about combined effect of current and waves on hydrodynamic loading of the structures. The present study investigates the combination flow around a circular cylinder using a vortex-based method incorporating vortex moving particles (discrete vortices) with a finite-difference scheme for the vorticity diffusion. The main attention is paid to the effects of a small current on in-line fluid forces and vortex patterns in the wake. Morison's equation and an equation with two drag terms are examined. The results show that the presence of a small current in an oscillatory flow can reduce the drag coefficient significantly. Morison's equation gives reasonably good predictions for the in-line forces for an oscillatory flow plus a small current. The current tends to bring the whole vortex wake downstream and tries to form the stable Karman asymmetrical form in the downstream wake. The present results show certain agreement with some previous experimental results.     

Numerical solutions for impulsively started and decelerated viscous flow past a circular cylinder

A finite difference study of the unsteady two-dimensional flow past a circular cylinder has been conducted using vorticity and streamfunction as the dependent variables. The two cases considered were impulsively started and decelerated flows. The impulsively started problem was considered to validate the method and has yielded results which agree quite closely with existing results from both calculations and experiments. The decelerated flow analysis produced results which can be explained in terms of induced velocity effects from existing wake vortices for both suddenly stopped and uniformly decelerated flows.     

Flow structures and dynamics in the wakes of sliding bubbles

An experimental investigation is reported for the flow structures in the wake of an air bubble sliding under an inclined surface in quiescent water. Time-resolved particle image velocimetry (PIV) is used to study the wakes of sliding bubbles for a range of measurement planes, bubble diameters and surface inclination angles. Additionally, key aspects of the bubble’s motion are measured simultaneously using a novel method that accounts for the motion of the bubble’s interface. Thus, vortex shedding may be linked to changes in the bubble shape and path.Analysis of the measured velocity and vorticity fields reveals a wake structure consisting of a near wake that moves in close proximity to the bubble, shedding vorticity at the inversion points of the bubble path. Downstream of the bubble in the far wake, these structures evolve into asymmetrical, oppositely-oriented hairpin vortices that are generated in the near wake. These hairpin vortices bear similarities to those observed behind freely rising bubbles and near-wall bluff bodies and are found to cause significant motion of the bulk fluid. This bulk fluid motion has the potential to offer significant convective cooling of adjacent heated surfaces, such as submerged electronics components.     

DNS OF 2D TURBULENT FLOW AROUND A SQUARE CYLINDER

Two-dimensional ‘turbulent’ flow around a rectangular cylinder has been simulated at Re=10,000 using a sixth- order-accurate finite volume method for the discretization of convection and diffusion. The spatial discretization consists of a combination of a seventh- order upwind-biased method for the convective terms and an eighth-order central method for the diffusive terms, discretized on a stretched and staggered grid. To cope with the stretching of the grid, Lagrange interpolations are used. The method applied to obtain a boundary condition for the velocity in the x-direction at the outflow boundary is shown not to affect the flow in the interior of the computational domain in a way that is visible in various snapshots of the vorticity field. The variation in the velocity in the x-direction with time is itself found to be relatively small near the outflow boundary. Several turbulence statistics have been gathered from a simulation of the flow developed during 77 dimensionless time units. Snapshots of the vorticity field of the developed flow show the presence of a vortex-street- like structure. Typical 2D turbulent behaviour, such as the appearance of monopolar, dipolar and tripolar vortices due to the amalgamation of vorticity in the wake and the x^−1/2 scaling of the velocity defect in the wake, has been obtained. © 1997 John Wiley & Sons, Ltd.     

Cross-Stream Vorticity Field Induced by Streamwise Vortices in Unbounded and Wall-Bounded Shear Flows

This computational study examines the unsteady cross-stream vorticity structures that form when one or more streamwise vortices are immersed in homogeneous and boundary-layer shear flows. A quasi-two-dimensional limit is considered in which the velocity and vorticity fields, while still possessing three nonzero components, have vanishing gradient in the streamwise direction. This idealization is suitable to applications such as streamwise vortices that occur along a ship hull or airplane fuselage and it can be used as an idealized representation of the quasi-streamwise vortices in the near-wall region of a turbulent boundary layer. In this quasi-two-dimensional idealization, the streamwise velocity has no effect on the cross-stream velocity associated with the vortex. However, the vortex acts to modify the cross-stream vorticity component, resulting in regions of the flow with strong deviations in streamwise velocity. This paper examines the complex structures that form as the cross-stream vorticity field is wrapped up by the vortex and the effect of these structures on the streamwise velocity field, first for vortices immersed in homogeneous shear flow and then for vortices immersed in a boundary layer along a flat wall. Received 2 January 2002 and accepted 13 August 2002 Published online 3 December 2002 RID="*" ID="*" This project was supported by the Office of Naval Research under Grant Number N00014-01-1-0015. Dr. Thomas Swain is the program manager. Communicated by T.B. Gatski     

Performance of a three-component vorticity probe in a turbulent far-wake

  A new four X-wire vorticity probe has been developed to measure all three components of the vorticity fluctuation vector simultaneously. The performance of this probe is tested in a turbulent far-wake. The measured Reynolds stresses agree with those obtained previously from simpler hot wire configurations. The variances of the lateral vorticity components agree within ±15% with those measured with a one-component vorticity probe. The variances of the streamwise vorticity component are also in reasonable agreement with those inferred from two X-wires. At high wavenumbers, the measured vorticity spectra agree with those obtained by direct numerical simulation (DNS) in the central region of a turbulent channel flow. The comparison of measured high-order moments of vorticity on the wake centerline with local isotropy also suggests the probe performs satisfactorily. Received: 31 December 1997/Accepted: 6 January 1999     

Comparison of flow structures in the downstream region of a cylinder and sphere

An experimental investigation of flow structures downstream of a circular cylinder and sphere immersed in a free-stream flow is performed for Re = 5000 and 10,000 using qualitative and quantitative flow visualization techniques. The obtained results are presented in terms of time-averaged velocity vectors, patterns of streamlines, vorticity, Reynolds stress correlations and turbulent kinetic energy distributions. Flow data reveal that the size of wake flow region, the location of singular and double points, the peak values of turbulence quantities, such as Reynolds stress correlations, vorticity fluctuations and turbulent kinetic energy vary as a function of models’ geometry and Reynolds Numbers. The concentration of small scale vortices is more dominant in the wake of the sphere than that of the cylinder. The maximum value of turbulent kinetic energy (TKE) occurs close to the saddle point for the cylinder case while two maximum values of TKE occur along shear layers for the sphere one because of the 3-D flow behavior.