Bulk flow parameters in turbulent wall boundary layers near separation

Experiments were conducted in a turbulent boundary layer near separation along a flat plate. The pressure gradient in flow direction was varied such that three significant boundary layer configurations could be maintained. The flow in the test section thus had simultaneously a region of favourable pressure gradient, a region of strong adverse pressure gradient with boundary layer separation and a region of reattached boundary layer. Specially designed fine probes facilitated the measurements of skin friction and velocity distribution very close to the wall. Bulk flow parameters such as skin friction coefficient C _f, Reynold's number Re_δ2 and shape factors H and G, which are significant characteristics of wall boundary layers were evaluated. The dependence of these parameters on the Reynolds number and along the test section was explored and the values were compared with other empirical and analytical formulae known in the literature.     

Three-dimensional numerical study of jet-in-crossflow characteristics at low Reynolds number

A numerical study of a square jet in a cross flow is carried out at a Reynolds number of 100. The flow field and heat transfer characteristic downstream of the jet have been explored by solving three-dimensional unsteady Navier–Stokes equations and energy equation using higher order spatial and temporal discretization. The projection of vortical structure on a plane is seen to give the component of vortex normal to the plane. Four combinations of velocity profile namely (1) uniform crossflow and uniform jet, (2) laminar boundary layer crossflow and uniform jet, (3) uniform crossflow and parabolic jet profile, and (4) laminar boundary layer crossflow and parabolic jet are compared at same phase to see their effect on the flow field and heat transfer characteristic. All the four cases are seen to exhibit unsteadiness but the jet with parabolic profile is seen to show stronger unsteadiness. The instantaneous vortical structures of all the cases at the same phase show that the structures are more complex for the jet with parabolic velocity profile. The temperature field is seen to be correlated with the vortical structures. Comparison of the time averaged flow field reveals that the jet penetration is the highest for the jet having parabolic profile and boundary layer crossflow. The adiabatic effectiveness is observed to be more for the jet with uniform velocity profile and uniform crossflow and was least for the jet with parabolic velocity profile and boundary layer crossflow.     

Effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics of a sphere

Experiments were conducted in water and wind tunnels on spheres in the Reynolds number range 6 × 10³ to 6.5 × 10⁵ to study the effect of natural ventilation on the boundary layer separation and near-wake vortex shedding characteristics. In the subcritical range of Re (<2 × 10⁵), ventilation caused a marginal downstream shift in the location of laminar boundary layer separation; there was only a small change in the vortex shedding frequency. In the supercritical range (Re > 4 × 10⁵), ventilation caused a downstream shift in the mean locations of boundary layer separation and reattachment; these lines showed significant axisymmetry in the presence of venting. No distinct vortex shedding frequency was found. Instead, a dramatic reduction occurred in the wake unsteadiness at all frequencies. The reduction of wake unsteadiness is consistent with the reduction in total drag already reported. Based on the present results and those reported earlier, the effects of natural ventilation on the flow past a sphere can be categorized in two broad regimes, viz., weak and strong interaction regimes. In the weak interaction regime (subcritical Re), the broad features of the basic sphere are largely unaltered despite the large addition of mass in the near wake. Strong interaction is promoted by the closer proximity of the inner and outer shear layers at supercritical Re. This results in a modified and steady near-wake flow, characterized by reduced unsteadiness and small drag. Received: 8 September 1998 / Accepted: 1 January 2000     

Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil

A laminar separation bubble occurs on the suction side of the SD7003 airfoil at an angle of attack α =  4–8° and a low Reynolds number less than 100,000, which brings about a significant adverse aerodynamic effect. The spatial and temporal structure of the laminar separation bubble was studied using the scanning PIV method at α =  4° and Re = 60,000 and 20,000. Of particular interest are the dynamic vortex behavior in transition process and the subsequent vortex evolution in the turbulent boundary layer. The flow was continuously sampled in a stack of parallel illuminated planes from two orthogonal views with a frequency of hundreds Hz, and PIV cross-correlation was performed to obtain the 2D velocity field in each plane. Results of both the single-sliced and the volumetric presentations of the laminar separation bubble reveal vortex shedding in transition near the reattachment region at Re = 60,000. In a relatively long distance vortices characterized by paired wall-normal vorticity packets retain their identities in the reattached turbulent boundary layer, though vortices interact through tearing, stretching and tilting. Compared with the restricted LSB at Re = 60,000, the flow at Re = 20,000 presents an earlier separation and a significantly increased reversed flow region followed by “huge” vortical structures.     

Microscopic particle image velocimetry measurements of transition to turbulence in microscale capillaries

The character of transitional capillary flow is investigated using pressure-drop measurements and instantaneous velocity fields acquired by microscopic PIV in the streamwise–wall-normal plane of a 536 μm capillary over the Reynolds-number range 1,800 ≤ Re ≤ 3,400 in increments of 100. The pressure-drop measurements reveal a deviation from laminar behavior at Re = 1,900 with the differences between the measured and the predicted laminar-flow pressure drop increasing with increasing Re. These observations are consistent with the characteristics of the mean velocity profiles which begin to deviate from the parabolic laminar profile at Re = 1,900, interpreted as the onset of transition, by becoming increasingly flatter and fuller with increasing Re. A fully-turbulent state is attained at Re ≅ 3,400 where the mean velocity profile collapses onto the mean profile of fully-developed turbulent pipe flow from an existing direct numerical simulation at Re = 5,300. Examination of the instantaneous velocity fields acquired by micro-PIV in the range 1,900 ≤ Re < 3,400 reveal that transitional flows at the microscale are composed of a subset of velocity fields illustrating a purely laminar behavior and a subset of fields that capture significant departure from laminar behavior. The fraction of velocity fields displaying non-laminar behavior increases with increasing Re, consistent with past observations of a growing number of intermittent turbulent spots bounded by nominally laminar flow in macroscale pipe flow with increasing Re. Instantaneous velocity fields that are non-laminar in character consistently contain multiple spanwise vortices that appear to streamwise-align to form larger-scale interfaces that incline slightly away from the wall. The characteristics of these “trains” of vortices are reminiscent of the spatial features of hairpin-like vortices and hairpin vortex packets often observed in fully-turbulent wall-bounded flow at both the macro- and micro-scales. Finally, single-point statistics computed from the non-laminar subsets at each transitional Re, including root-mean-square velocities and the Reynolds shear stress, reveal a gradual and smooth maturation of the patches of disordered motion toward a fully-turbulent state with increasing Re.     

A bypass wake induced laminar/turbulent transition

The process of laminar to turbulent transition induced by a von Karman vortex street wake, was studied for the case of a flat plate boundary layer. The boundary layer developed under zero pressure gradient conditions. The vortex street was generated by a cylinder positioned in the free stream. An X-type hot-wire probe located in the boundary layer, measured the streamwise and normal to the wall velocity components. The measurements covered two areas; the region of transition onset and development and the region where the wake and the boundary layer merged producing a turbulent flow. The evolution of Reynolds stresses and rms-values of velocity fluctuations along the transition region are presented and discussed. From the profiles of the Reynolds stress and the mean velocity profile, a ‘negative' energy production region along the transition region, was identified. A quadrant splitting analysis was applied to the instantaneous Reynolds stress signals. The contributions of the elementary coherent structures to the total Reynolds stress were evaluated, for several x-positions of the near wall region. Distinct regions in the streamwise and normal to the wall directions were identified during the transition.     

Influence of the surface roughness on the third-order moments of velocity fluctuations

Roughness wall effects in a zero pressure gradient turbulent boundary layers were investigated using hot-wire anemometry. The skewness and diffusion factors of u and v, the longitudinal and normal velocity fluctuations, were measured and represented using wall variables. The results indicate that the wall roughness removes the crossover point between sweep and ejection events to the outer region of the layer for a single Reynolds number Re _θ  > 3,000. This behaviour exhibits that the roughness surface favours the maintaining of sweep events obtained by a quadrant analysis. These results show that communication between the wall region and outer region of a turbulent boundary layer exists and the wall similarity hypothesis for a rough wall is questionable. The effect of the wall roughness on the position of the point crossover from sweep to ejection motions with respect to the wall seems to be the same as that obtained when the Reynolds number is higher. Received: 8 March 2000/Accepted: 15 May 2000     

Assessment of dual plane PIV measurements in wall turbulence using DNS data

Experimental dual plane particle image velocimetry (PIV) data are assessed using direct numerical simulation (DNS) data of a similar flow with the aim of studying the effect of averaging within the interrogation window. The primary reason for the use of dual plane PIV is that the entire velocity gradient tensor and hence the full vorticity vector can be obtained. One limitation of PIV is the limit on dynamic range, while DNS is typically limited by the Reynolds number of the flow. In this study, the DNS data are resolved more finely than the PIV data, and an averaging scheme is implemented on the DNS data of similar Reynolds number to compare the effects of averaging inherent to the present PIV technique. The effects of averaging on the RMS values of the velocity and vorticity are analyzed in order to estimate the percentage of turbulence intensity and enstrophy captured for a given PIV resolution in turbulent boundary layers. The focus is also to identify vortex core angle distributions, for which the two-dimensional and three-dimensional swirl strengths are used. The studies are performed in the logarithmic region of a turbulent boundary layer at z ⁺ = 110 from the wall. The dual plane PIV data are measured in a zero pressure gradient flow over a flat plate at Re _τ = 1,160, while the DNS data are extracted from a channel flow at Re _τ = 934. Representative plots at various wall-normal locations for the RMS values of velocity and vorticity indicate the attenuation of the variance with increasing filter size. Further, the effect of averaging on the vortex core angle statistics is negligible when compared with the raw DNS data. These results indicate that the present PIV technique is an accurate and reliable method for the purposes of statistical analysis and identification of vortex structures.     

Characteristic Regimes of Transitional Separation Bubbles in Unsteady Flow

This experimental investigation deals with transition phenomena of a separated boundary layer under unsteady inlet flow conditions. The main purpose of this investigation is to understand the influence of the rotor-stator interaction in turbomachinery on the subsequent, highly loaded boundary layer. The research project is divided into two phases. In the first phase, which has been completed recently, only the variation of mean velocity caused by upstream blades was simulated in the experiments while the free-stream turbulence intensity was retained at a constant low level. The experiments are carried out in an Eifel-type wind tunnel to investigate the laminar separated boundary layer of a flat plate under oscillating inlet conditions. The adverse pressure gradient, similar to that of turbomachines, is generated by the contoured upper wall. The unsteadiness is produced by a rotating flap located downstream of the test section. The reduced frequency, the amplitude and the mean Reynolds number are varied to simulate the conditions prevailing in turbomachines. In addition to the Kelvin–Helmholtz instability of the separated shear layer, a lower frequency instability was observed. This is frequently referred to as `free shear layer flapping' and results in two distinctly different ways of re-attachment, depending primarily on the Reynolds number. For low momentum thickness Reynolds numbers at the separation point, large-scale vortices locked to the frequency of the unsteady main flow are identified. They originate nearly at the top of the separation bubble and are ejected downstream. A fully turbulent boundary layer develops after these vortices mix out. For higher Reynolds numbers, transition is completed within a short length of the free shear layer and there-attachment region. The characteristic momentum thickness Reynolds number separating these two regimes in unsteady flow is about 125. The Strouhal number (reduced frequency) does not appear to have any significant effect. Based on the experimental results, this behaviour is discussed in some detail. This revised version was published online in July 2006 with corrections to the Cover Date.     

An experimental study into the effects of streamwise and spanwise acceleration in a turbulent boundary layer

We compare two turbulent boundary layers produced in a low-speed water channel experiment. Both are subjected to an identical streamwise pressure gradient generated via a lateral contraction of the channel, and an additional spanwise pressure gradient is imposed on one of the layers by curving the contraction walls. Despite a relatively high streamwise acceleration, hot-film probe measurements of the mean-velocity distributions show that the Reynolds number increases whilst the coefficient of friction decreases downstream. Visualization of the viscous layers using hydrogen bubbles reveal an increase in the non-dimensional streak spacing in response to the acceleration. Changes in statistical moments of the streamwise velocity near the wall suggest an increased dominance of high-velocity fluctuations. The near-wall streaks and velocity statistics have little sensitivity to the boundary layer three-dimensionality induced by the spanwise pressure gradient, with the boundary-layer crossflow velocity reaching 11 % that of the local freestream velocity.     

Stochastic estimation of flow near the trailing edge of a NACA0012 airfoil

A stochastic estimation technique has been applied to simultaneously acquired data of velocity and surface pressure as a tool to identify the sources of wall-pressure fluctuations. The measurements have been done on a NACA0012 airfoil at a Reynolds number of Re _c  = 2 × 10⁵, based on the chord of the airfoil, where a separated laminar boundary layer was present. By performing simultaneous measurements of the surface pressure fluctuations and of the velocity field in the boundary layer and wake of the airfoil, the wall-pressure sources near the trailing edge (TE) have been studied. The mechanisms and flow structures associated with the generation of the surface pressure have been investigated. The “quasi-instantaneous” velocity field resulting from the application of the technique has led to a picture of the evolution in time of the convecting surface pressure generating flow structures and revealed information about the sources of the wall-pressure fluctuations, their nature and variability. These sources are closely related to those of the radiated noise from the TE of an airfoil and to the vibration issues encountered in ship hulls for example. The NACA0012 airfoil had a 30 cm chord and aspect ratio of 1.     

Transient growth in the asymptotic suction boundary layer

In the present experimental setup, the transient disturbance growth in a spatially invariant boundary layer flow, i.e., the asymptotic suction boundary layer (ASBL), has been investigated. The choice of the ASBL brings along several advantages compared with an ordinary spatially growing boundary layer. A unique feature of the ASBL is that the Reynolds number (Re) can be varied without changing the boundary layer thickness, which in turn allows for parameter variations not possible to carry out in traditional boundary layer flows. A spanwise array of discrete surface roughness elements was mounted on the surface to trigger modes with different spanwise wavenumbers (β). It is concluded that for each mode there exists a threshold roughness Reynolds number (Re _k ), below which no significant transient growth is present. The experimental data suggests that this threshold Re _k is both a function of β and Re. An interesting result is that the energy growth curves respond differently to a change in Re _k when caused by a change in roughness height k, implying that Re remains constant, compared with a change in the free-stream velocity U_￥U_\infty, which also affects the Re. The scaling of the energy growth curves both in level and the downstream direction is treated and appropriate scalings are found. The result shows a complex non-linear receptivity mechanism. Optimal perturbation theory, which has failed to predict the energy evolution in growing boundary layers, is tested for the ASBL and shows that it may satisfactorily predict the evolution of all transiently growing modes that are triggered by the roughness elements.     

Three-dimensional Turbulent Boundary Layer in a Shrouded Rotating System

A thre-dimensional direct numerical simulation is combined with a laboratory study to describe the turbulent flow in an enclosed annular rotor-stator cavity characterized by a large aspect ratio G = (b − a)/h = 18.32 and a small radius ratio a/b = 0.152, where a and b are the inner and outer radii of the rotating disk and h is the interdisk spacing. The rotation rate Ω considered is equivalent to the rotational Reynolds number Re = Ωb ²/ν= 9 .5 × 10⁴ (ν the kinematic viscosity of water). This corresponds to a value at which experiment has revealed that the stator boundary layer is turbulent, whereas the rotor boundary layer is still laminar. Comparisons of the computed solution with velocity measurements have given good agreement for the mean and turbulent fields. The results enhance evidence of weak turbulence by comparing the turbulence properties with available data in the literature (Lygren and Andersson, J Fluid Mech 426:297–326, 2001). An approximately self-similar boundary layer behavior is observed along the stator. The wall-normal variations of the structural parameter and of characteristic angles confirm that this boundary layer is three-dimensional. A quadrant analysis (Kang et al., Phys Fluids 10:2315–2322, 1998) of conditionally averaged velocities shows that the asymmetries obtained are dominated by Reynolds stress-producing events in the stator boundary layer. Moreover, Case 1 vortices (with a positive wall induced velocity) are found to be the major source of generation of special strong events, in agreement with the conclusions of Lygren and Andersson (J Fluid Mech 426:297–326, 2001).     

Effect of transverse stream velocity in an incompressible boundary layer on the stability of the laminar flow regime

The stability of the laminar flow regime in the boundary layer developed on a wall is increased considerably by the relatively slight extraction of fluid from the wall [1–4]. In the theoretical study of this phenomenon, all the investigators known to the present authors have taken into account only the increase in the fullness of the velocity profile in the boundary layer with suction. Computations of the stability characteristics have been made on the assumption that there are no transverse velocities in the laminar boundary layer.We present below an analysis of the stability of the laminar boundary layer in the presence of a constant transverse velocity in the near-wall region (suction). The calculations made show the existence for a given velocity profile in the boundary layer of a relative suction velocity v=v such that with suction velocities greater than v the flow remains stable at all Reynolds numbers, while the method used in the cited references gives a definite finite critical Reynolds number, equal in our notation to the Reynolds number at v=0, for each relative suction velocity.It was found that with suction of fluid from the boundary layer the region of instability has finite dimensions, i.e., there exist lower and upper critical Reynolds numbers. The flow is stable if its Reynolds number is less than the lower, or greater than the upper values of the critical Reynolds number.The instability region diminishes with increase in the relative suction velocity, and at a value of this velocity which is specific for each value of the velocity profile the instability region degenerates into a point-the flow becomes absolutely stable. Thus, with distributed suction it is advisable to increase the relative suction velocity only to a definite magnitude corresponding to disappearance of the instability region. The computational results presented make it possible to estimate this velocity for velocity profiles ranging from a Blasius profile to an asymptotic profile. Specific calculations were made for a family of Wuest profiles, since under actual conditions with suction there always exists a starting segment of the boundary layer [1, 2].     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001     

Formation of a 2D vortex pair and its 3D breakup: an experimental study

 Vortex pairs are studied using a dye tracing visualisation technique and a particle tracking velocimetry system. The vortex pairs are produced by gravity induced inlets of water issued through a uniform gap. The inlet Reynolds number is Re=Ud/ν≈875 in all tests (d being the gap width and U the cross sectional mean velocity), i.e. the flow is in the laminar regime. Initially, the dipolar vortex structure is two-dimensional, but after travelling a distance of a few times its own width, the flow structure becomes unstable, breaks up and changes into a three-dimensional flow structure. The breakup appears to be caused by an axial flow in the core centres of each vortex of the dipolar structure. These axial flows are induced by boundary effects related to the von Karman viscous pump. After the breakup, it is believed that a vortex ring is formed through reconnection of rudiments from the dipolar structure mediated by the wall induced vorticity. Received: 20 November 1995/Accepted: 14 November 1996     

UV-mediated coalescence and mixing of inkjet printed drops

In the present study, the characteristics of supersonic rectangular microjets are investigated experimentally using molecular tagging velocimetry. The jets are discharged from a convergent–divergent rectangular nozzle whose exit height is 500 μm. The jet Mach number is set to 2.0 for all tested jets, and the Reynolds number Re is altered from 154 to 5,560 by changing the stagnation pressure. The experimental results reveal that jet velocity decays principally due to abrupt jet spreading caused by jet instability for relatively high Reynolds numbers (Re > ~450). The results also reveal that the jet rapidly decelerates to a subsonic speed near the nozzle exit for a low Reynolds number (Re = 154), although the jet does not spread abruptly; i.e., a transition in velocity decay processes occurs as the Reynolds number decreases. A supersonic core length is estimated from the streamwise distribution of the centerline velocity, and the length is then normalized by the nozzle exit height and plotted against the Reynolds number. As a result, it is found that the normalized supersonic core length attains a maximum value at a certain Reynolds number near which the transition in the velocity decay process occurs.     

Flow past a cylinder: shear layer instability and drag crisis

Flow past a circular cylinder for Re=100 to 10⁷ is studied numerically by solving the unsteady incompressible two‐dimensional Navier–Stokes equations via a stabilized finite element formulation. It is well known that beyond Re ～ 200 the flow develops significant three‐dimensional features. Therefore, two‐dimensional computations are expected to fall well short of predicting the flow accurately at high Re. It is fairly well accepted that the shear layer instability is primarily a two‐dimensional phenomenon. The frequency of the shear layer vortices, from the present computations, agree quite well with the Re^0.67 variation observed by other researchers from experimental measurements. The main objective of this paper is to investigate a possible relationship between the drag crisis (sudden loss of drag at Re ～ 2 × 10⁵) and the instability of the separated shear layer. As Re is increased the transition point of shear layer, beyond which it is unstable, moves upstream. At the critical Reynolds number the transition point is located very close to the point of flow separation. As a result, the shear layer eddies cause mixing of the flow in the boundary layer. This energizes the boundary layer and leads to its reattachment. The delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients. The spatial and temporal power spectra for the kinetic energy of the Re=10⁶ flow are computed. As in two‐dimensional isotropic turbulence, E(k) varies as k^?5/3 for wavenumbers higher than energy injection scale and as k^?3 for lower wavenumbers. The present computations suggest that the shear layer vortices play a major role in the transition of boundary layer from laminar to turbulent state. Copyright © 2004 John Wiley & Sons, Ltd.     

Non-unique turbulent boundary layer flows having a moderately large velocity defect: a rational extension of the classical asymptotic theory

The classical analysis of turbulent boundary layers in the limit of large Reynolds number Re is characterised by an asymptotically small velocity defect with respect to the external irrotational flow. As an extension of the classical theory, it is shown in the present work that the defect may become moderately large and, in the most general case, independent of Re but still remain small compared to the external streamwise velocity for non-zero pressure gradient boundary layers. That wake-type flow turns out to be characterised by large values of the Rotta–Clauser parameter, serving as an appropriate measure for the defect and hence as a second perturbation parameter besides Re. Most important, it is demonstrated that also this case can be addressed by rigorous asymptotic analysis, which is essentially independent of the choice of a specific Reynolds stress closure. As a salient result of this procedure, transition from the classical small defect to a pronounced wake flow is found to be accompanied by quasi-equilibrium flow, described by a distinguished limit that involves the wall shear stress. This situation is associated with double-valued solutions of the boundary layer equations and an unconventional weak Re-dependence of the external bulk flow—a phenomenon seen to agree well with previous semi-empirical studies and early experimental observations. Numerical computations of the boundary layer flow for various values of Re reproduce these analytical findings with satisfactory agreement.     

Predicting crossflow induced transition with laminar kinetic energy transition model

The hypersonic laminar kinetic energy transition model is developed to be appropriate for crossflow induced boundary layer transition prediction. A crossflow timescale is constructed and incorporated in the k_T-k_L-ω transition model to reflect crossflow effect during three-dimensional boundary layer transition. The stream-wise vorticity is selected as the indicator of crossflow strength. Regarding the inviscid unstable characteristic of crossflow instability, the crossflow timescale is constructed by reference to the second mode timescale. To eliminate inappropriate development of the crossflow timescale where the effective length scale is large enough while the crossflow strength remains at a quite low level, a crossflow velocity limit function is proposed. The revised k_T-k_L-ω transition model has been applied to HIFiRE-5 and blunt cone with 1°angle of attack test cases. Results show good correspondence with the experimental data and DNS data, which demonstrates that the constructed crossflow timescale makes the revised transition model capable of reproducing crossflow induced transition behavior with a reasonable degree of accuracy.