Using digital holographic microscopy for simultaneous measurements of 3D near wall velocity and wall shear stress in a turbulent boundary layer

A digital holographic microscope is used to simultaneously measure the instantaneous 3D flow structure in the inner part of a turbulent boundary layer over a smooth wall, and the spatial distribution of wall shear stresses. The measurements are performed in a fully developed turbulent channel flow within square duct, at a moderately high Reynolds number. The sample volume size is 90 × 145 × 90 wall units, and the spatial resolution of the measurements is 3–8 wall units in streamwise and spanwise directions and one wall unit in the wall-normal direction. The paper describes the data acquisition and analysis procedures, including the particle tracking method and associated method for matching of particle pairs. The uncertainty in velocity is estimated to be better than 1 mm/s, less than 0.05% of the free stream velocity, by comparing the statistics of the normalized velocity divergence to divergence obtained by randomly adding an error of 1 mm/s to the data. Spatial distributions of wall shear stresses are approximated with the least square fit of velocity measurements in the viscous sublayer. Mean flow profiles and statistics of velocity fluctuations agree very well with expectations. Joint probability density distributions of instantaneous spanwise and streamwise wall shear stresses demonstrate the significance of near-wall coherent structures. The near wall 3D flow structures are classified into three groups, the first containing a pair of counter-rotating, quasi streamwise vortices and high streak-like shear stresses; the second group is characterized by multiple streamwise vortices and little variations in wall stress; and the third group has no buffer layer structures.     

Effects of wall permeability on turbulence

In order to understand the effects of the wall permeability on turbulence near a porous wall, flow field measurements are carried out for turbulent flows in a channel with a porous bottom wall by a two-component particle image velocimetry (PIV) system. The porous media used are three kinds of foamed ceramics which have almost the same porosity (0.8) but different permeability. It is confirmed that the flow becomes more turbulent over the porous wall and tends to be turbulent even at the bulk Reynolds number of Re_b=1300 in the most permeable wall case tested. Corresponding to laminar to turbulent transition, the magnitude of the slip velocity on the porous wall is found to increase drastically in a narrow range of the Reynolds number. To discuss the effects of the wall roughness and the wall permeability, detailed discussions are made of zero-plane displacement and equivalent wall roughness for porous media. The results clearly indicate that the turbulence is induced by not only the wall roughness but the wall permeability. The measurements have also revealed that as Re_b or the wall permeability increases, the wall normal fluctuating velocity near the porous wall is enhanced due to the effects of the wall permeability. This leads to the increase of the turbulent shear stress resulting in higher friction factors of turbulence over porous walls.     

Three-component,time-resolved velocity statistics in the wall region of a turbulent pipe flow

Three-component, coincident, time-resolved velocity measurements were obtained in the near wall region, y ⁺ < 100, of a fully developed turbulent pipe flow. The measurements were conducted in the ARL/PSU glycerin tunnel at a Reynolds number (Re _h), based on pipe radius and centerline velocity, of 6436 and an Re of approximately 730. The reported data include velocity statistics up to fourth order, Reynolds stresses and three component, coincident turbulent velocity spectral estimates. The current data are generally in quite good agreement with the fully developed channel flow direct numerical simulation (DNS) results of Antonia et al. (1992) at Re 700 - 700. The accuracy of the current experimental data and the very good agreement with the DNS results provides evidence for the accuracy of the DNS solutions and thus Antonia's conclusions of very near wall, y ⁺ < 20, Re dependence on turbulent velocity statistics. The very good agreement between the low Re rectangular channel flow DNS results and the low Re flat plate turbulent boundary layer statistics of Karlsson and Johansson (1988) suggests that for y ⁺ < 30 statistics of similar flows of differing geometry may be compared on the basis of equal Re . The current data are available on disk or by anonymous ftp by the first author.     

Velocity characteristics of the flow around a square cross section cylinder placed near a channel wall

Laser-Doppler measurements are reported of the flow around a square cross section cylinder placed at various heights (Y ₀) above a plane channel wall for a Reynolds number Re _H = 1.36 × 10⁴.The thickness of the turbulent boundary layer on the channel wall at the obstacle position, but with it removed from the water tunnel, was equal to 0.8 H, being H the square obstacle height and the free stream turbulence intensity was 6%. The periodic character of the flow in the near wake was characterized by measurements of turbulence spectra in the range 0 Y ₀/H 3.3 and the results revealed that regular vortex shedding was suppressed for a gap height less than 0.35 H. Detailed results of time averaged mean flow properties, turbulence intensities and Reynolds stresses revealed the structural differences of the near wakes with and without vortex shedding for Y _O = 0.5 and Y _O = 0.25 respectively.List of symbols R _e Reynolds number Re = U ₀ H/v - H Square obstacle height - Y Normal coordinate - Y ₀ Gap distance between the plane wall and obstacle face - C _f Skin friction coefficient - k Turbulent kinetic energy - u Friction velocity - Turbulent boundary layer thickness - y ⁺ Non-dimensional log law coordinate - X _r Separated flow length behind the obstacle - U Mean axial velocity - V Mean radial velocity - u² Axial turbulent stress - ² Normal turbulent stress - u Turbulent shear stress - U ₀ Mean bulk velocity - E Power spectrum energy - f Predominant frequency - h Distance between inner shear layers behind the obstacle - s Distance from the wall to the shear layer behind the obstacle - C _D Drag coefficient     

Reynolds stress and vorticity in turbulent wall flows

Experimental measurements in a boundary layer and a large-eddy simulation of plane channel flow have been used to study the dynamics of vorticity and mass transport in the nearwall region. It was found that Reynolds stress generation occurs in the vicinity of quasi-streamwise vortices, and that smoke particles tend to be ejected from the wall near these vortical structures.     

Double row vortical structures in the near field region of a plane wall jet

The qualitative and quantitative behaviour of double row vortical structures in the near field region of a plane wall jet are studied experimentally by flow visualization and hot-wire measurements. Ensemble averaging is employed to investigate the interaction of vortices with the wall. In the flow visualization study, a double row vortical structure, which includes a primary vortex formed in the outer layer region and a secondary vortex induced in the inner layer region, and the vortex lift-off phenomenon are clearly observed during the development of the wall jet. The phase averaged results of the velocity measurements show that the instability leading to induction of the secondary vortex is stimulated by the primary vortex. In the early stage of wall jet transition, the inflection point of the inner layer velocity profile moves transversely from the wall surface to the inner layer region due to passage of the well-organized primary vortex in the outer layer region. The inner layer instability is thus induced and the instability wave rolls up to form the secondary vortex. Furthermore, the secondary vortex will convect downstream faster than the primary vortex, and this difference in convective speed will lead to the subsequent phenomenon of vortex lift-off from the wall surface.List of symbols A1, A2, . . . primary vortex - B1,B2, . . . secondary vortex - fe forcing frequency - f fundamental frequency - H nozzle exit height - Re Reynolds number,U _j H/ - T period of the referred signal (=13.5 ms) - t, t time scale - U streamwise mean velocity - U _c convection speed - U _j jet exit velocity - U _m local maximum velocity - ut' streamwise turbulence intensity - uv turbulent shear stress - V transverse mean velocity - v transverse turbulence intensity - X streamwise coordinate - Y transverse coordinate - X _Ai streamwise location of vortexAi - X _Bi streamwise location of vortexBi - X _ave averaged streamwise location of the vortex - Y _m wall jet inner layer width, the distance from wall to whereU=U _m - Y _1/2 wall jet half-width, the distance from wall to whereU=1/2U _m in outer layer region - t time interval (=0.267 s) - phase averaged value     

Mathematical model of the entry length in the flow of suspensions of solid particles in a gas

A mathematical model consisting of equations of mass and momentum and for the velocity field has been used for computing the entry length of the flow of non-Newtonian fluids in laminar, transition and turbulent regions. Experimental data measured in a vertical flow of a suspension of solid particles in air have been used for verifying the predictions. n flow index for laminar flow - Re Reynolds number defined for the flow of the carrier medium - q exponent for turbulent flow - ratio of core radius with a flat velocity profile to pipe radius - _c ratio of the axial component of local velocity in the core to mean velocity - w mean flow velocity - ratio of axial distance from the pipe entrance to the pipe radius - ratio of the entrance length to the pipe radius - relative mass fraction of particles - ratio of the distance from the pipe wall to the pipe radius - coefficient of pressure loss due to friction     

Influence of localised wall suction on the anisotropy of the Reynolds stress tensor in a turbulent boundary layer

Hot-wire measurements have been carried out in a turbulent boundary layer subjected to concentrated suction applied through a short porous wall strip with a view to examine the effect suction can have on the anisotropy of the Reynolds stress tensor. The departure of the Reynolds stress ratios from their corresponding values in the undisturbed flow is increased as the normalised suction rate increases. It is argued that the alteration to the Reynolds stress containing motion reflects a cigar to pancake change in the shape of the structures near the wall.     

The structure of Reynolds stress in the near-wall region of a fully developed turbulent pipe flow

The structure of the Reynolds stress in the near-wall region of a fully developed turbulent pipe flow, at a pipe Reynolds number of 8,923, was investigated. Because the closed circuit tunnel used glycerine as a working fluid, measurements could be readily made inside the viscous sublayer. Two laser Doppler velocimeter (LDV) systems were combined to measure the two point spatial correlation, R ₁₂, between the stream wise and radial velocities in a radial plane of the pipe. The correlation measurements extended over the region from y ⁺ of 2 to 64 in the direction normal to the pipe wall and covered more than 800 wall units in the streamwise direction. Two-dimensional maps of the correlation coefficient were established for six different distances of the streamwise velocity probe from the wall. The use of LDV systems allowed the measurements to be made for small spatial separations of the probes without fear of probe interference effects. A characteristic feature of the correlation contour maps, that maxium correlation arises for small non-zero separation of the probes, may not have been observed had invasive techniques been employed.     

Modelling the time dependent flow over riblets in the viscous wall region

The flow over riblets is examined computationally using a time dependent model of the viscous wall region. This 2 1/2 D model, developed by Hatziavramidis and Hanratty (1979) and modified by Nikolaides (1984) and Chapman and Kuhn (1981, 1986) assumes homogeneity in the streamwise direction so that the flow is solved only in the cross-sectional plane. The flow at the upper boundary of the computational domain (y ⁺ 40) is described using a streamwise eddy model consisting of two scales, one of the streak spacing (⁺ 100), which dominates vertical momentum transport, and a larger scale that accounts for the influence of large outer flow eddies.The protrusion height concept (Bechert and Bartenwerfer, 1989) is used to define ay ⁺=0 location for surfaces with riblets. A control volume finite element method utilizing triangular meshes is used to exactly fit the riblet cross-sectional geometry. Results obtained using fairly large riblets compare well with the limited experimental evidence available. Observations of the transient flow suggest that the riblets interact with the near-wall streamwise vortices, weakening them by the generation of intermittent secondary vortices within the riblet valleys. The riblets also appear to limit the lateral spread of inrushes towards the wall and retain low momentum fluid in the riblet valleys effectively isolating much of the wall from such inrushes.     

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     

The Relaminarization Mechanisms of Turbulent Channel Flow at Low Reynolds Numbers

The mechanisms of laminarization in wall-bounded flows have been investigated by performing direct numerical simulations (DNS) of turbulent channel flows. By decreasing Reynolds numbers systematically, the effects of the low Reynolds number are studied in connection with the near-wall turbulent structure and turbulent statistics. At approximately the critical Reynolds number, the turbulent skin friction is reduced, and the turbulent structure changes qualitatively in the very near-wall region. Instantaneous turbulent structures reveal that streamwise vortices, the cores of which are at y+ 10, disappear, although low speed streaks and Reynolds shear stress are still produced by larger streamwise vortices located in the buffer region y+ > 10. Sweep motions induced by these vortical structures are shifted toward the center of a channel and also significantly deterred, which may heighten the effects of the viscous sublayer over most of the channel section and suppress the regeneration mechanisms of new streamwise vortices in the very near-wall region. To investigate the details of how large-scale coherent vortices affect the viscous sublayer and the relevant small-scale streamwise vortices, a body force is virtually imposed in the wall-normal direction to enhance the large streamwise vortices. As a result, it is found that when they are sufficiently enhanced, the small-scale vortices reappear, and the sweep events are again dominant in the viscous sublayer.     

Temporal development of turbulent boundary layers with embedded streamwise vortices

The interaction of streamwise vortices with turbulent boundary layer has been investigated using large-eddy simulation. The initial conditions are a pair of counterrotating Oseen vortices with flow between them directed toward the wall (common-flow-down), superimposed on various instantaneous realizations of a turbulent boundary layer. The time development of the vortices and their interaction with the boundary layer are studied by integrating the filtered Navier-Stokes equations in time. The most important effects of the vortices on the boundary layer are the thinning of the boundary layer between vortices (downwash region) and the thickening of the boundary layer in the upwash region. The vortices first move toward the wall as a result of the self-induced velocity, and then apart from each other because of the image vortices due to the solid wall. The Reynolds stress profiles highlight the highly three-dimensional structure of the turbulent boundary layer modified by the vortices. The presence of significant turbulent activity near the vortex center and in the upwash region suggests that localized instability mechanisms in addition to the convection of turbulent energy by the secondary flow are responsible for this effect. High levels of turbulent kinetic energy and secondary stresses in the vicinity of the vortex center are also observed. The numerical results show good agreement with experimental results.This work was supported by the Office of Naval Research under Grant N00014-89-J-1638. Computer time was supplied by the San Diego Supercomputing Center.     

Direct numerical simulation of turbulent flows through concentric annulus with circumferential oscillation of inner wall

Periodic wall oscillations in the spanwise or circumferential direction can greatly reduce the friction drag in turbulent channel and pipe flows. In a concentric annulus, the constant rotation of the inner cylinder can intensify turbulence fluctuations and enhance skin friction due to centrifugal instabilities. In the present study, the effects of the periodic oscillation of the inner wall on turbulent flows through concentric annulus are investigated by the direct numerical simulation (DNS). The radius ratio of the inner to the outer cylinders is 0.1, and the Reynolds number is 2 225 based on the bulk mean velocity U_m and the half annulus gap H. The influence of oscillation period is considered. It is found that for short-period oscillations, the Stokes layer formed by the circumferential wall movement can effectively inhibit the near-wall coherent motions and lead to skin friction reduction, while for long-period oscillations, the centrifugal instability has enough time to develop and generate new vortices, resulting in the enhancement of turbulence intensity and skin friction.     

Turbulence modulation in a particle-laden flow over a hemisphere-roughened wall

Turbulence modulation by the inertia particles in a spatially developing turbulent boundary layer flow over a hemisphere-roughened wall was investigated using the direct numerical simulation method. The Eulerian and Lagrangian approaches were used for the gas- and particle-phases, respectively. An immersed boundary method was employed to resolve the hemispherical roughness element. The hemispheres were staggered in the downstream direction and arranged periodically in the streamwise and spanwise directions with spacing of p_x/d= 4 and p_z/d= 2 (where p_x and p_z are the streamwise and spanwise spacing of the hemispheres, and d is the diameter). The effects of particles on the turbulent coherent structures, turbulent statistics and quadrant events were analyzed. The results show that the addition of particles significantly damps the vortices structures and increases the length scales of streak structures. Compared with the particle-laden flow over the smooth wall, the existence of the wall roughness decreases the mean streamwise velocity in the near wall region, and makes the peaks of Reynolds stresses profiles shift up. In addition, the existence of particles also increases the percentage contributions to Reynolds shear stress from the Q4 events, however, decreases the percentage contributions from other quadrant events.     

Turbulence in a three‐dimensional wall‐bounded shear flow

A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ₂‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

Turbulence measurements in a merged jet from two opposing curved wall jets

A two-dimensional flow generated by the interaction of two opposing, symmetric curved wall jets is investigated experimentally. The overall flow field can be divided into the curved wall jet region, the interaction region, and the merged jet region; thus, the results of the measurement are discussed to characterize these three distinct regions. For the curved wall jet region, the Reynolds stress distribution, the correlation coefficient, , and the ratio of normal stresses, , are presented and the effects of curvature and adverse pressure gradient on these distributions are discussed. The Reynolds stress distributions in the interaction region are analyzed in detail to illuminate the negative production of the turbulent kinetic energy. The developing jet in this region is found to accelerate owing to the very high pressure arising from the collision of the two wall jets. A counter-gradient shear flow situation is also observed in this interacting region. Measured data in the merged jet region are often compared to those of plane jets and the development of the merged jet is discussed in that respect. The spreading rate of the present merged jet is found to be much larger than that of the plane jets. To account for the larger spreading rate, the intermittency distribution is also investigated.List of symbols b position of y where U = U _c/2 - f turbulent/non-turbulent interface crossing rate - f _max maximum interface crossing rate - h slot height of the wall jet, 10 mm - L _u integral length scale - P, P _a static and atmospheric pressure, respectively - P _u ² production rate of longitudinal normal stress - P _v ² production rate of lateral normal stress - r radial distance from the cylinder surface - R radius of curvature of the cylinder, 100 mm - r _1/2 position of r where U=U _m/2 - U streamwise velocity - U _c centerline velocity of the merged jet - U _m maximum velocity of the curved wall jet - U ₀ exit velocity - \] Reynolds stresses - V lateral velocity in the merged jet - x distance along the centerline of the merged jet - y lateral distance from the centerline of the merged jet - intermittency factor     

Near-wall turbulence closure modeling without “damping functions”

An elliptic relaxation model is proposed for the strongly inhomogeneous region near the wall in wall-bounded turbulent shear flow. This model enables the correct kinematic boundary condition to be imposed on the normal component of turbulent intensity. Hence, wall blocking is represented. Means for enforcing the correct boundary conditions on the other components of intensity and on the k — equations are discussed. The present model agrees quite well with direct numerical simulation (DNS) data. The virtue of the present approach is that arbitrary damping functions are not required.     

Multiple distortion of a supersonic turbulent boundary layer

Two experiments were performed to study the response of a supersonic turbulent boundary layer to successive distortions. In the first experiment (Case 1), the flow passed over a forward-facing ramp formed by 20° compression corner followed by a 20° expansion corner located about 4_o downstream, where _o is the incoming boundary layer thickness. In the second experiment (Case 2), the forward-facing ramp was constructed of curved compression and expansion surfaces with the same turning angles and total step height as in Case 1. The radii of curvature for the compression and expansion surfaces were equal to 12_o. In both experiments, the flow relaxation was observed over a distance equal to 12_o. In this relaxation region, the mean and turbulent flow behavior of the boundary layer was measured. The mean velocity profile was found to be altered by the distortion. Recovery of the profile began near the wall and occurred rapidly, but in the outer part of the boundary layer, recovery proceeded slowly. Turbulence measurements revealed a dramatic reduction in the turbulence shear stress and a progressively decaying streamwise Reynolds stress profile.