Instability waves in the wall region of a turbulent boundary layer on a flat plate

Coherent structures and the bursting phenomena in the wall region of a turbulent boundary layer play a very important role in determining the characteristics of the boundary layer. Yet the nature and the origin of the coherent structures are unclear until now. In this paper, nonlinear stability calculations for the wall region of a turbulent boundary layer have been made. It was found that there do exist instability waves which may be responsible for the coherent structures. The project is supported by the National Natural Science Foundation of China.     

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.     

A mechanism for excitation of coherent structures in wall region of a turbulent boundary layer

Introduction Themechanismforthegenerationofcoherentstructuresinthewallregionofaturbulent boundarylayerhasalwaysbeeninconcernandinvestigated.AccordingtoTsujimotoand Miyake[1],thecharacteristicsofturbulenceinthewallregionweremainlydeterminedbythe generationandevolutionofcoherentstructures,notbythesmall_scaleturbulence.However, excitationsfromregionofy >60werefoundtobenecessary,otherwisethewallregionwould degeneratetolaminarflow.Therefore,theinvestigationofthemechanismthathowcoherent structuresi…     

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.     

Mechanism of turbulent boundary layer separation from a smooth wall

The mechanism of turbulent boundary layer separation under the influence of a positive pressure gradient is analyzed. The process of turbulent separation from a smooth wall in a plane diffuser channel has been experimentally investigated. It is shown that separation is determined by the nature of the flow in a certain inner part of the boundary layer, where the friction effect is unimportant. This region of the boundary layer is most exposed to the action of the positive pressure gradient and it is there that the stagnant zone primarily appears.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 69–77, November–December, 1990.     

A theoretical model of the coherent structure in the wall region of a turbulent boundary layer

In this paper,the formation of the coherent structures in the wall region of aturbulent boundary layer was studied,using the nonlinear theory of the hydrodynamicstability.The spanwise and streamwise wavelengths of the most amplified unstablewave obtained by this study were found in good agreement with the experiments,whichmakes the distinct feature of this study in the present paper,as the basis of thestability analysis,a more rational velocity profile has been used,which is different fromthat of the turbulent mean flow.And also,the new nonlinear theory was used.Theresult is useful in understanding of the quasi-periodicity of the coherent structure in theturbulent boundary layer.     

Small scale intermittency in a rough wall turbulent boundary layer

Relatively good quality isotropy is observed in the central region of a turbulent boundary layer developing over a mesh screen rough wall. Spectra of velocity and, more especially, vorticity fluctuations satisfy isotropy over a significant wavenumber range. Inertial range scaling exponents ζ _u2 (p) and ζ _u3 (p) of moments of order p(?8) of increments of the transverse velocity fluctuations u ₂ and u ₃ are significantly smaller than the exponents ζ _u1 (p) of increments of the longitudinal velocity fluctuation u ₁. Exponents inferred from the locally averaged values of squared transverse vorticity fluctuations are only slightly smaller than ζ _u1 (p). The difference between ζ _u1 (p) and ζ _u2 (p) [or ζ _u3 (p)] more likely reflects the departure from isotropy of inertial range scales. There is evidence to suggest that the difference decreases with an increase in the Reynolds number and/or a decrease in the magnitude of the mean shear.     

Scale-by-scale energy budget in a turbulent boundary layer over a rough wall

Hot-wire velocity measurements are carried out in a turbulent boundary layer over a rough wall consisting of transverse circular rods, with a ratio of 8 between the spacing (w) of two consecutive rods and the rod height (k). The pressure distribution around the roughness element is used to accurately measure the mean friction velocity ($U_{\tau }$) and the error in the origin. It is found that $U_{\tau }$ remained practically constant in the streamwise direction suggesting that the boundary layer over this surface is evolving in a self-similar manner. This is further corroborated by the similarity observed at all scales of motion, in the region $0.2⩽y/\delta ⩽0.6$, as reflected in the constancy of Reynolds number ($R_{\lambda }$) based on Taylor’s microscale and the collapse of Kolmogorov normalized velocity spectra at all wavenumbers.A scale-by-scale budget for the second-order structure function $〈{(\delta u)}^2〉$ ($\delta u=u(x+r)-u(x)$, where u is the fluctuating streamwise velocity component and r is the longitudinal separation) is carried out to investigate the energy distribution amongst different scales in the boundary layer. It is found that while the small scales are controlled by the viscosity, intermediate scales over which the transfer of energy (or $〈{(\delta u)}^3〉$) is important are affected by mechanisms induced by the large-scale inhomogeneities in the flow, such as production, advection and turbulent diffusion. For example, there are non-negligible contributions from the large-scale inhomogeneity to the budget at scales of the order of $\lambda$, the Taylor microscale, in the region of the boundary layer extending from $y/\delta =0.2$ to 0.6 ($\delta$ is the boundary layer thickness).     

Simulation of particles released near the wall in a turbulent boundary layer

A direct numerical simulation was used along with a Lagrangian particle tracking technique to study particle motion in a horizontal, spatially developing turbulent boundary layer along an upper-wall (with terminal velocity directed away from the wall). The objective of the research was to study particle diffusion, dispersion, reflection, and mean velocity in the context of two parametric studies: one investigated the effect of the drift parameter (the ratio of particle terminal velocity to fluid friction velocity) for a fixed and finite particle inertia, and the second varied the drift parameter and particle inertia by the same amount (i.e. for a constant Froude number). A range of drift parameters from 10⁻⁴ to 10⁰ were considered for both cases. The particles were injected into the simulation at a height of four wall units for several evenly distributed points across the span and a perfectly elastic wall collision was specified at one wall unit.Statistics collected along the particle trajectories demonstrated a transition in particle movement from one that is dominated by diffusion to one that is dominated by gravity. For small and intermediate sized particles (i.e. ones with outer Stokes numbers and drift parameters much less than unity) transverse diffusion away from the wall dominated particle motion. However, preferential concentration is seen near the wall for intermediate-sized particles due to inhomogeneous turbulence effects (turbophoresis), consistent with previous channel flow studies. Particle–wall collision statistics indicated that impact velocities tended to increase with increasing terminal velocity for small and moderate inertias, after which initial conditions become important. Finally, high relative velocity fluctuations (compared to terminal velocity) were found as particle inertia increased, and were well described with a quasi-one-dimensional fluctuation model.     

Direction of streamlines near the wall in a three-dimensional turbulent boundary layer

Expressions are derived that, for a large class of flows, enable one to determine the direction of the streamlines near the wall in a three-dimensional turbulent boundary layer without integrating the system of boundary-layer equations. Comparison with available experimental data reveals a completely satisfactory agreement between the calculations and the experimental data.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 19–25, March–April, 1980.     

Kinematics of a turbulent boundary layer

In the article an attempt is made, within the framework of the Navier-Stokes equations, to describe the field of the instantaneous velocities of a liquid in the region of a turbulent flow near the wall. It is assumed that the velocities of the liquid are determined by the field of the eddies arising in regions of ejections under the action of pressure pulses in the region near the wall.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 34–40, September–October, 1973.     

Error-tolerant calibration of dual sensor probes used in a turbulent wall boundary layer

A computer-aided calibration method for hot film probes is presented which tolerates statistical and some systematic errors, and which allows data evaluation in real-time. Essentially, the velocity is approximated by a power series at each yaw angle and for each sensor. A weighting function minimizes the influences of errors. At measurement time the anemometer voltages are roughly linearized. The digitized voltages are subjected to a combination of iteration and interpolation in order to compute the velocity components. RMS-values of the two velocity components parallel to the wall, u and w, and of their partial derivatives with respect to time in a turbulent wall boundary layer are shown and will be used for comparison.     

Anisotropy of the Reynolds stresses in a turbulent boundary layer on a rough wall

The measured anisotropy invariants of the Reynolds stress tensor in a self-preserving rough wall turbulent boundary layer indicate that the anisotropy is significantly smaller than in a smooth wall layer.RAA is grateful to Dr. P. Spalart for the DNS data. The support of the Australian Research Council is acknowledged.     

Effect of a moving wall on a fully developed, equilibrium turbulent boundary layer

Experiments were conducted in a wind tunnel to assess the effect of a moving wall on a fully developed, equilibrium turbulent boundary layer. Pitot-static and total head probes were used in conjunction with both single- and two-component hot-wire anemometer probes to quantify the effect of wall motion on the boundary layer velocity statistics. A variable speed, seamless belt formed the wind tunnel test section wall. When stationary, the belt was found to possess a fully developed, equilibrium turbulent boundary layer in excellent agreement with archival data. With the tunnel wall moving at the free-stream speed, and at a sufficient distance above the wall, the velocity statistics in the moving-wall boundary layer were found to collapse well when scaled as a self-preserving turbulent wake. The near-wall mean velocity profile of the moving wall was found to exhibit an extended region of linearity compared to canonical turbulent boundary layer and internal flows. This can be attributed to the reduced shear resulting from wall motion and the subsequent reduction in Reynolds stress. Received: 2 June 1999/Accepted: 8 August 2000     

Self-similar reverse flows in the region of separation of a turbulent boundary layer

The Kármán momentum equation and very simple scaling arguments relating to the profiles of the turbulent tangential stresses are used to construct a self-similar reverse flow of an incompressible fluid that, depending on the values of the empirical constants occurring in it, can be realized either behind the separation point of a turbulent boundary layer or in front of its point of reattachment. The empirical constants are determined by means of several independent experimental studies on turbulent separating flows of liquids and gases at subsonic and supersonic velocities.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. A, pp. 173–177, July–August, 1988.     

Propagation of shear-layer structures in the near-wall region of a turbulent boundary layer

Two non-intrusive techniques, namely laser Doppler anemometry (LDA) and the electrochemical method, have been used for simultaneous measurements of the instantaneous streamwise velocity (U) and longitudinal wall shear stress (S), evaluated in a zero pressure gradient turbulent boundary layer. The space-time correlation between the fluctuating velocity and shear stress suggests that the coherent flow structures are propagated (i) under a slight angle of 5° in the near-wall region and (ii) at an average angle of 15.5° for y⁺>30. It is shown that the time shift obtained from the correlation between the LDA and the electrochemical signals is due to the dynamic behaviour of the electrodiffusion probe, but also to the leaning character of the coherent structures.     

Measurements of wall shear stress of a turbulent boundary layer using a micro-shear-stress imaging chip

Measurements of wall shear-stress streaks of a turbulent boundary layer in the channel flow were carried out using a MEMS-based micro-shear-stress imaging chip, which contains about 100 sensors. The chip is designed and fabricated by surface micromachining technology. One arrray of 25 micro-shear-stress sensors in the chip that covers a length of 7.5 mm is used to measure the instantaneous spanwise distribution of the surface shear stress. The statistics of high shear-stress streaks were established. Based on the measurement, the physical quantities associated with the high shear-stress streaks, such as their length, width and peak shear-stress level, were obtained. We found out that a high correlation exists between the peak shear-stress level and front-end shear-stress slope of a high shear-stress streak. This important property is currently being applied to the deisgn of a real-time flow control logic.