PIV measurements of turbulent flow in planar mixing layer

A turbulent mixing layer consists of two different flow types, i.e. shear layer (shear-flow turbulence) and free stream regions (nearly homogeneous turbulence). The inherent non-uniform seeding tracer distributions observed around the interfaces between the shear layer and two free stream regions usually lead to a difficulty in particle image velocimetry (PIV) measurements. A parametric study on the application of PIV to the measurement of velocity field in a planar mixing layer is made by means of six factors, including interrogation window size, aspect ratio of interrogation window, interrogation window offset, threshold of data validation, sharpening spatial filters (Prewitt and Sobel masks), and smoothing spatial filter (median mask). The objective of this study is to obtain accurate turbulent measurements in both mean and fluctuating velocities using PIV under an appropriate parametric setting. The optimal levels, which are trade-off in between the accuracy and fine spatial resolution of velocity field measurements, are determined with the aid of the Taguchi method. It is shown that the PIV measurements made with this optimal set of parameters are in good agreement with the measurements made by a two-component hot-wire anemometer. Case independency of the proposed optimal set of parameters on the flow condition of the mixing layer is validated through the applications to two additional tests under the different experimental conditions in changing solely either velocity ratio of high-speed to low-speed free stream velocities or Reynolds number.     

Momentum transport in a turbulent mixing layer

The turbulent momentum transport phenomena in a two-dimensional mixing layer are investigated numerically by a discrete vortex method. The numerical model and calculations are verified through a comparison with existing numerical simulations and experimental measurements. The main emphasis is placed on the exploration of the detailed time-dependent instantaneous local momentum fluctuations and on the comparison of numerical results with available experimental measurements. The current simulations confirm qualitatively the various trends in the turbulent momentum flux and fluctuating components of the velocity in the mixing layer found with several experimental results. The study shows that similarity exists in turbulent momentum quantities along the axial direction of the mixing layer. The calculations also show a definite correlation between the passage of a large-scale structure and a burst in the turbulent momentum flux. The probability density functions of the fluctuating quantities are shown to be mostly Gaussian-like, with only a few exceptions.     

Reconstruction of large coherent structures from SPIV measurements in a forced turbulent mixing layer

A procedure is suggested here for reconstructing the time variation of a three-dimensional (3D) coherent velocity field, based on applying Least Square Method to a very limited number of phase-locked measurements. The measurements are performed in a spanwise plane of a forced turbulent mixing layer by employing the stereo particle image velocimetry system. The forcing is produced by oscillating two- and three-dimensional (3D) flappers placed at the edge of the splitter plate. The feasibility and validity of the procedure for velocity field reconstruction are checked by using Hot Wire Measurements. Very clear patterns are observed of two types of coherent structures: spanwise K-H billows (rolls) and streamwise vortices. These are due to primary and secondary instabilities and their time evolution is presented.     

On harmonic perturbations in a turbulent mixing layer

A theoretical model of harmonic perturbations in a turbulent mixing layer is proposed. The model is based on the triple decomposition method. It is assumed that the instantaneous velocities and pressure consist of three distinctive components: the mean (time average), the coherent (phase average), and the random (turbulent) motion. The interaction between incoherent turbulent fluctuations and large-scale coherent disturbances is incorporated by the Newtonian eddy viscosity model. A slight divergence of the flow is also taken into account, and the results are compared with experimental data. For a high amplitude of the perturbations, the nonlinear feedback to the mean flow is taken into account by means of the coherent Reynolds stresses. The results reveal the possibility of a negative spreading rate of the mixing layer. A simultaneous consideration of the mean flow divergence and nonlinear self-interaction results in Landau-like amplitude equations. It is observed that the nonlinear term in the amplitude equation is not significant at the levels of amplitude considered. The velocity disturbance profiles of the second harmonic are also presented and, at low-level amplitude, they are in good agreement with experiments.     

Large-eddy simulation of turbulent buoyancy-driven flow in a rectangular cavity

Turbulent buoyancy-driven flow in a rectangular cavity with two differentially heated opposite walls is investigated numerically by means of large-eddy simulation (LES). Different dynamic global-coefficient subgrid-scale models for weakly compressible flows are applied to simulate the natural convective flow. It is shown that transition of the boundary layer is delayed in cases where the model coefficients are fixed or changing dynamically according to the Germano identity. On the contrary, in the ‘global equilibrium’ approach, the result shows an earlier change in flow regime due to lower subgrid-scale viscosity. Further, it is also demonstrated that three-dimensional effects of the natural convective flow may be significant due to the presence of adiabatic side walls.     

Three-component LDA measurements in a turbulent boundary layer

An experimental study of a three-dimensional, pressuredriven, attached turbulent boundary-layer flow was made at Mach 0.4. Both the mean velocities and the full Reynolds stress tensor were measured simultaneously by a three-component LDA system. Value of the resultant shear stress to turbulent kinetic energy ratio varied between 0.1 and 0.2 and did not remain constant across the boundary-layer. Slopes of the streamwise and azimuthal mixing length distributions in the wall region were around 0.4 and 1.2, respectively. Skew angle of the turbulent shear stress was larger than skew angle of the velocity gradient.     

RMS spanwise vorticity measurements in a turbulent boundary layer

Turbulent boundary layer measurements of the rms spanwise vorticity t_z with a four hot-wire probe are in reasonable agreement with direct numerical simulations and other published measurements at comparable Reynolds numbers. It is shown that a reasonable accurate approximation for _z can be obtained with only two parallel hot wires.     

Eulerian-Lagranigan simulation of aerosol evolution in turbulent mixing layer

The formation and evolution of aerosol in turbulent flows are ubiquitous in both industrial processes and nature. The intricate interaction of turbulent mixing and aerosol evolution in a canonical turbulent mixing layer was investigated by a direct numerical simulation (DNS) in a recent study (Zhou, K., Attili, A., Alshaarawi, A., and Bisetti, F. Simulation of aerosol nucleation and growth in a turbulent mixing layer. Physics of Fluids, 26, 065106 (2014)). In this work, Monte Carlo (MC) simulation of aerosol evolution is carried out along Lagrangian trajectories obtained in the previous simulation, in order to quantify the error of the moment method used in the previous simulation. Moreover, the particle size distribution (PSD), not available in the previous works, is also investigated. Along a fluid parcel moving through the turbulent flow, temperature and vapor concentration exhibit complex fluctuations, triggering complicate aerosol processes and rendering complex PSD. However, the mean PSD is found to be bi-modal in most of the mixing layer except that a tri-modal distribution is found in the turbulent transition region. The simulated PSDs agree with the experiment observations available in the literature. A different explanation on the formation of such PSDs is provided.     

A turbulent boundary layer over a two-dimensional rough wall

Particle image velocimetry (PIV) measurements and planar laser induced fluorescence (PLIF) visualizations have been made in a turbulent boundary layer over a rough wall. The wall roughness consisted of square bars placed transversely to the flow at a pitch to height ratio of λ/k = 11 for the PLIF experiments and λ/k = 8 and 16 for the PIV measurements. The ratio between the boundary layer thickness and the roughness height k/δ was about 20 for the PLIF and 38 for the PIV. Both the PLIF and PIV data showed that the near-wall region of the flow was populated by unstable quasi-coherent structures which could be associated to shear layers originating at the trailing edge of the roughness elements. The streamwise mean velocity profile presented a downward shift which varied marginally between the two cases of λ/k, in agreement with previous measurements and DNS results. The data indicated that the Reynolds stresses normalized by the wall units are higher for the case λ/k = 16 than those for λ/k = 8 in the outer region of the flow, suggesting that the roughness density effects could be felt well beyond the near-wall region of the flow. As expected the roughness disturbed dramatically the sublayer which in turn altered the turbulence production mechanism. The turbulence production is maximum at a distance of about 0.5k above the roughness elements. When normalized by the wall units, the turbulence production is found to be smaller than that of a smooth wall. It is argued that the production of turbulence is correlated with the form drag.     

Mean and turbulent velocity measurements of supersonic mixing layers

The behavior of supersonic mixing layers under three conditions has been examined by schlieren photography and laser Doppler velocimetry. In the schlieren photographs, some large-scale, repetitive patterns were observed within the mixing layer; however, these structures do not appear to dominate the mixing layer character under the present flow conditions. It was found that higher levels of secondary freestream turbulence did not increase the peak turbulence intensity observed within the mixing layer, but slightly increased the growth rate. Higher levels of freestream turbulence also reduced the axial distance required for development of the mean velocity. At higher convective Mach numbers, the mixing layer growth rate was found to be smaller than that of an incompressible mixing layer at the same velocity and freestream density ratio. The increase in convective Mach number also caused a decrease in the turbulence intensity ( _u/U).List of symbols a speed of sound - b total mixing layer thickness between U ₁ – 0.1 U and U ₂ + 0.1 U - f normalized third moment of u-velocity, f u³/(U)³ - g normalized triple product of u² , g u²/(U)³ - h normalized triple product of u ², h u ²/(U)³ - l _u axial distance for similarity in the mean velocity - l _u axial distance for similarity in the turbulence intensity - M Mach number - M _c convective Mach number (for ₁ = ₂), M _c (U ₁ – U ₂)/(a ₁ + a ₂) - P static pressure - r freestream velocity ratio, r U ₂/U ₁ - Re unit Reynolds number, Re U/ - s freestream density ratio, s ₂/₁ - T _t total temperature - u instantaneous streamwise velocity - u deviation of u-velocity, uu – U - U local mean streamwise velocity - U ₁ primary freestream velocity - U ₂ secondary freestream velocity - average of freestream velocities, (U ₁ + U ₂)/2 - U freestream velocity difference, U U ₁ – U ₂ - instantaneous transverse velocity - v deviation of -velocity, – V - V local mean transverse velocity - x streamwise coordinate - y transverse coordinate - y ₀ transverse location of the mixing layer centerline - ensemble average - ratio of specific heats - boundary layer thickness (y-location at 99.5% of free-stream velocity) - similarity coordinate, (y – y ₀)/b - compressible boundary layer momentum thickness - viscosity - density - standard deviation - dimensionless velocity, (U – U ₂)/U - 1 primary stream - 2 secondary stream A version of this paper was presented at the 11th Symposium on Turbulence, October 17–19, 1988, University of Missouri-Rolla     

Two-phase measurements of saltating turbulent boundary layer flow

Mean wind and particle speed measurements as functions of heigh were made for a saltating turbulent boundary layer flow. An exponential dependence of particle flux with height above the surface was found independent of windspeed and particle size. Particle-speed distributions as functions of height above the surface were measured for experiments conducted at two ambient pressures: atmospheric pressure and approximately 1% atmospheric pressure. The wind was shown to be a more efficient mover of particles at atmospheric pressure.High-speed motion pictures of saltating ground walnut shells (of diameter 500–1500 μm and density 1.1 g/cm³) were taken in an environmental wind tunnel to simulate the planetary boundary layer. These experiments verify the existence and magnitude of particle spin rates proposed by White & Schulz (1977). There was remarkable agreement between numerical trajectory solutions, including the spin effect, and the filmed trajectories. An observation was made that not all particles spin exclusively in the vertical longitudinal plane (in the direction of flow). At low pressures (0.6 kPa) the effect of spin forces on the particle's trajectory was shown to have little influence and was verified by a theoretical force ration balance of spin to drag force.     

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re_θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.     

Instantaneous velocity and pressure measurements in turbulent mixing layers

This paper presents a comprehensive comparison of the mean velocity and turbulence measurements from a four-hole pressure probe, also known as the Cobra probe, and an X-probe in plane mixing layers. The objective is to validate the measurement accuracy of the Cobra probe in a flow where the turbulence reaches high levels, but whose properties are well known. The comparison is made for the mean velocities, Reynolds stresses, triple products, and spectra, and demonstrates that the Cobra probe has reasonable accuracy for some of these quantities, such as the mean streamwise velocity and primary shear stress, but not for others, such as the mean normal velocity. The correlation of the pressure and the streamwise velocity, measured by the Cobra probe, behaves correctly in the potential flow. However, the correlation of the pressure and the cross-stream velocity, which appears in the transport equation for the turbulent kinetic energy, and the pressure redistribution term in the corresponding equation for the streamwise normal stress, are poorly measured.     

PIV measurements in a weakly separating and reattaching turbulent boundary layer

A high Reynolds number flat plate turbulent boundary layer was studied in a wind-tunnel experiment using particle image velocimetry (PIV). The flow is subjected to an adverse pressure gradient (APG) which is designed such that the boundary layer separates and reattaches, forming a weak separation bubble. With PIV we are able to get a more complete picture of this complex flow phenomenon. The view of a separation bubble being composed of large scale coherent regions of instantaneous backflow occurring randomly in a three-dimensional manner in space and time is verified by the present PIV measurements. The PIV database was used to test the applicability of various velocity scalings around the separation bubble. We found that the mean velocity profiles in the outer part of the boundary layer, and to some extent also the Reynolds shear-stress, are self-similar when using a velocity scale based on the local pressure gradient. The same can be said for the so called Perry–Schofield scaling, which suggests that the two velocity scales are connected. This can also be interpreted as an experimental evidence of the claimed relation between the latter velocity scale and the maximum Reynolds shear-stress.     

Velocity measurements for a turbulent nonseparated flow over solid waves

The laser-Doppler velocimeter was used to obtain measurements of the streamwise velocity over solid sinusoidal waves of small enough amplitude that a nonseparated flow existed. The measurements provide a critical test for Reynolds stress closure models since they are particularly sensitive to happenings in the viscous wall region (y ⁺ < 40), for which present theories are of uncertain accuracy. The results are compared with calculations that use an eddy viscosity model that successfully describes measurements of the wall shear stress along waves of small enough amplitude that a linear response is obtained. These calculations are in approximate agreement with measurements because they exactly account for inertia and viscous effects. However, there are significant differences which point to the inadequacy of turbulence models. In particular, non-linear effects and the amplitudes of the wave-induced velocity variations are underpredicted.     

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of \(L/D=6\) are analyzed at a free-stream Mach number of \(M_\infty =0.6\) and depth-based Reynolds number of \(Re_D=502\). In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of \(\beta =0\). To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of \(W/D=1\) and 2. We find that the 2D wake mode is not present in the 3D cavity flow with \(W/D=2\), in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of \(\lambda /D=0.5{-}2.0\) to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.     

Flow field analysis of a turbulent boundary layer over a riblet surface

The near-wall flow structures of a turbulent boundary layer over a riblet surface with semi-circular grooves were investigated experimentally for the cases of drag decreasing (s ⁺=25.2) and drag increasing (s ⁺=40.6). One thousand instantaneous velocity fields over riblets were measured using the velocity field measurement technique and compared with those above a smooth flat plate. The field of view was 6.75 × 6.75 mm² in physical dimension, containing two grooves. Those instantaneous velocity fields were ensemble averaged to get turbulent statistics including turbulent intensities and turbulent kinetic energy. To see the global flow structure qualitatively, flow visualization was also carried out using the synchronized smoke-wire technique under the same experimental conditions. For the case of drag decreasing (s ⁺=25.2), most of the streamwise vortices stay above the riblets, interacting with the riblet tips frequently. The riblet tips impede the spanwise movement of the streamwise vortices and induce secondary vortices. The normalized rms velocity fluctuations and turbulent kinetic energy are small near the riblet surface, compared with those over a smooth flat plate. Inside the riblet valleys, these are sufficiently small that the increased wetted surface area of the riblets can be compensated. In addition, in the outer region (y ⁺ > 30), these values are almost equal to or slightly smaller than those for the smooth plate. For the case of drag increasing (s ⁺=40.6), however, most of the streamwise vortices stay inside the riblet valleys and contact directly with the riblet surface. The high-speed down-wash flow penetrating into the riblet valley interacts actively with the wetted riblet surface and increases the skin friction. The rms velocity fluctuations and turbulent kinetic energy have larger values compared with those over a smooth flat plate. Received: 24 March 1999/Accepted: 10 March 2000