Spanwise Velocity Fluctuations Research Articles

Transient response of Reynolds stress transport to spanwise wall oscillation in a turbulent channel flow

Turbulent channel flow at low Reynolds number subjected to spanwise wall oscillation is studied by direct numerical simulation. The Reynolds stress budgets under the influence of the oscillating wall are analyzed in the first two oscillation periods. It is found that the spanwise velocity fluctuations are enhanced at the very beginning of the wall oscillation, and the subsequent global turbulence suppression is caused by the sustained attenuation of the pressure-strain terms. The hindrance of intercomponent transfer of turbulent kinetic energy by the oscillating wall is a mechanism of the skin-friction reduction.

Turbulent Plane Couette Flow and Scalar Transport at Low Reynolds Number

Abstract The turbulence structure and passive scalar (heat) transport in plane Couette flow at Reynolds number equal to 3000 (based on the relative speed and distance between the walls) are studied using direct numerical simulation (DNS). The numerical model is a three-dimensional trilinear Galerkin finite element code. It is found that the structures of the mean velocity and temperature in plane Couette flow are similar to those in forced channel flow, but the empirical coefficients are different. The total (turbulent and viscous) shear stress and total (turbulent and conductive) heat flux are constant throughout the channel. The locations of maximum root-mean-square streamwise velocity and temperature fluctuations are close to the walls, while the location of maximum root-mean-square spanwise and vertical velocity fluctuations are at the channel center. The correlation coefficients between velocities and temperature are fairly constant in the center core of the channel. In particular, the streamwise velocity is highly correlated with temperature (correlation coefficient ≈−0.9). At the channel center, the turbulence production is unable to counterbalance the dissipation, in which the diffusion terms (both turbulent and viscous) bring turbulent kinetic energy from the near-wall regions toward the channel center. The snapshots of the DNS database help explain the nature of the correlation coefficients. The elongated wall streaks for both streamwise velocity and temperature in the viscous sublayer are well simulated. Moreover, the current DNS shows organized large-scale eddies (secondary rotations) perpendicular to the direction of mean flow at the channel center.

Direct numerical simulation of turbulent channel flow with wall velocity disturbances

This paper considers the effect of applying nonzero velocity fluctuations along a flat smooth wall, mainly with the aim of understanding how conditions at the wall interact with the outer turbulent flow. Such a study is expected to be of use in formulating effective strategies for wall turbulence control. Three direct numerical simulations of a turbulent plane channel flow are carried out, starting with a flow field with no-slip conditions. Each simulation evolves by imposing (on one wall) only one nonzero velocity component. When a nonzero longitudinal velocity fluctuation u1 is applied, drag reduction occurs. With a nonzero spanwise velocity fluctuation u3, the flow is very similar to that in an unperturbed channel. However, the use of a nonzero wall-normal velocity fluctuation u2 results in structural changes similar to those observed in a direct numerical simulation of a turbulent flow over a rough surface. From the present simplified simulations, the inference is that the salient characteristics of rough wall flows reflect mainly the presence of a nonzero wall-normal normal velocity distribution at the interface between the roughness cavities and the external flow.

An experimental study of a spanwise structure around a reattachment region of a two-dimensional backward-facing step

The flow field downstream of a two-dimensional backward-facing step is usually assumed to be independent of the direction along the span of the step. This assumption is made even though it is well known that the flow exhibits a three-dimensional vortex structure. This state of affairs is no doubt due to the lack of detailed information concerning the characteristics of the vortex structure. In this paper, we report our investigations of the flow structure around a reattachment region using an ultrasound velocity profiler to measure the spanwise velocity component as a function of the spanwise coordinate and time. The flow field is found to be very complex both in space and time. The low-frequency component of the spanwise velocity fluctuation becomes dominant in the near-wall region, with peaks in the power spectrum at frequencies fh/Uc=0.05 and fh/Uc=0.012. Using multiple ultrasound transducers, we also find that a streamwise vortex exists in the flow.

Retrieval of Flow Structures in a Convective Boundary Layer Using an Adjoint Model: Identical Twin Experiments

The applicability of a four-dimensional variational data assimilation (4DVAR) technique to retrieval of microscale turbulent structures in a convective boundary layer is assessed. Two new features are implemented into the existing 4DVAR model: a height-dependent eddy viscosity and a surface flux model. The identical twin experiments approach is adopted to utilize the model itself to generate 13 instantaneous three-dimensional radial velocity datasets uniformly spanning 5 min. An ideal experiment, using these datasets as the observations, is first tested. After 400 iterations, the resulting correlation coefficients between retrieved and exact data are 0.99 for velocity and 0.97 for temperature fields. To emulate the lidar scanning feature, the 13 three-dimensional datasets are used to construct two volume scan datasets with each horizontal data slice taken from different instantaneous datasets. Using these data as the input, the correlation coefficients for horizontal, spanwise, and vertical velocity fluctuations and temperature can still reach 0.97, 0.97, 0.94, and 0.72 after 400 iterations. Addition of a surface flux model improves retrieval quality. Allowing height-dependent eddy viscosity and diffusivity does not improve retrieval quality, whereas doubling the value of eddy diffusivity improves retrieval quality. Implementation of temporal and spatial smoothness penalty functions significantly improves retrieval quality in the presence of various sources of error.

Active Control of Wall Turbulence with Wall Deformation

The performance of an active feedback control with wall deformation was tested by direct numerical simulation of a fully developed turbulent channel flow. The local wall movement is determined based on the flow condition detected by virtual sensors distributed in the vicinity of the wall, i.e., the wall velocity is made opposite to the wall-normal velocity at y/δ=0.1. The turbulent friction drag is reduced by 10% on average. The gain in the pumping power reaches about 28 times the energy consumption for actuating the wall. The primary mode of the resultant wall velocity distribution, which should be most effective in the present drag reduction scheme, is found to have wavelengths of about 300 and 50 viscous wall units in the streamwise and spanwise directions, respectively, while the time period is of the order of the time scale of the quasi-coherent vortical structure of near-wall turbulence. The effects of active wall deformation on quasi-coherent structures are investigated by a conditional averaging technique. In the present control scheme, the Q2 vortex is displaced away from the wall and the wall-normal and spanwise velocity fluctuations associated with the Q2 event are decreased. On the other hand, the location of the Q4 vortex from the wall remains unchanged while the vorticity of the Q4 vortex is substantially decreased. In the region downstream of the Q2 event, the wall is deformed in the shape of a shallow groove, which stabilizes the near-wall streaky structures along the groove.

STUDY ON GENERATION MECHANISM OF SECONDARY CURRENTS IN OPEN-CHANNEL FLOW BY DIRECT NUMERICAL SIMULATION

Fully developed three-dimensional turbulent flow over sand ribbons in an open-channel is computed to clarify the generation mechanism of secondary currents of the second kind by direct numerical simulation (DNS) using a regular grid under a generalized curvilinear coordinate system. Stable secondary currents and turbulent characteristics are reasonably reproduced. Detailed evaluation of each term in a mean vorticity transport equation revealed that the secondary currents of the second kind is generated principally by cross-planar turbulent shear stress (-v+w+), and that the anisotropy of the cross-planar turbulent normal stresses (v+2-w+2) restrains the generation of the secondary currents, where v+and w+represent vertical and spanwise velocity fluctuations normalized by friction velocity uτ, respectively and overbar denotes the time average.

Active Control of Wall Turbulence with Wall Deformation.

The performance of an active feedback control with wall deformation was tested by direct numerical simulation of a fully developed turbulent channel flow. The local wall movement is determined based on the flow condition detected by virtual sensors distributed in the vicinity of the wall;i.e., the wall velocity is made opposite to the wall-normal velocity at y/δ=0.1. The turbulent friction drag is reduced by 10% on average. The gain in the pumping power reaches about 28 times of the energy consumption for actuating the wall. The primary mode of the resultant wall velocity distribution, which should be most effective in the present drag reduction scheme, is found to have wavelengths of about 300 and 50 viscous wall units in the streamwise and spanwise directions, respectively, while the time period is on the order of the time scale of the quasi-coherent vortical structure of near-wall turbulence. Effects of active wall deformation on quasi-coherent structures are investigated by a conditional averaging technique. With the present control scheme, the Q2 vortex is displaced away from the wall and the wall-normal and spanwise velocity fluctuations associated with the Q2 event are decreased. On the other hand, the location of Q4 vortex from the wall remains unchanged while the vorticity of Q4 vortex are substatially decreased. In the region downstream of the Q2 cvent, the wall is deformed as a shallow groove, which stabilizes the near-wall streaky structures along it.

The influence of temperature on the measurements of Reynolds stresses in shear free turbulence near a wall

Temperature changes have a significant influence on the measurements of Reynolds stresses in turbulent boundary layers. As compared to the spanwise velocity fluctuations the streamwise turbulence intensity is especially sensitive to temperature deviations. Although this is a general statement its importance is clearly elucidated in a shear-free turbulence near a solid wall, since the mixing due to turbulence production is minimized in this flow. A consequence of temperature influence on hot-wire measurements is that frictional heating from the wall has produced contradictory results in different experiments on shear-free turbulence. In the current paper, measurements of streamwise and spanwise turbulence intensities have been conducted at different wall temperatures, thereby simulating the contradictory results mentioned above. A simple model has been developed showing that the turbulence intensities are affected by both the rms. value of the temperature fluctuations and the correlation between fluctuating temperature and velocity. These correlations are measured and the developed model is used to explain deviations in earlier measurements on shear-free turbulence. Moreover, the individual magnitudes of the two correlations in the temperature correction are estimated and their individual importance is discussed.

Turbulence control with wall-adjacent thin layer damping spanwise velocity fluctuations

Direct numerical simulations (DNSs) have been carried out for fully developed turbulent channel flow and heat transfer with an assumption of a thin layer adjacent to the wall, in which a virtual body force acts to damp the spanwise velocity fluctuations. Fourth-order finite difference computations were made over a relatively small computational volume to repeat simulations under various damping force conditions. It is found that both turbulent friction and heat transfer coefficients are substantially reduced in such manipulated flows. Compared with the pumping power saved, the extra dissipation due to the damping is sufficiently small as long as the damping layer exists close to the wall. In addition, the present control method is most efficient if the damping is imposed on the layer in contact with the wall rather than away from the wall. It is observed that the streamwise elongated streaky structures meander less in the spanwise direction and the coherent vortical structures are attenuated in scale and intensity. Thus, the vortex regeneration as well as the primary turbulence mechanisms, such as the production redistribution of Reynolds stresses played by the vortical structures, should be considerably suppressed by the selective damping of the near-wall spanwise velocity fluctuations.

Effects of Mean Shear on Homogeneous Turbulence. Turbulence Statistics and Turbulence Models.

The effects of mean shear enforced on decaying isotropic turbulence have been investigated by numerical experiments with the direct numerical simulation (DNS) of Navier-Stokes equations. In flows rapidly distorted from isotropy, it is important to elucidate the behavior of turbulent quantities, in particular, the pressure-strain correlations contributing to the origin of the anisotropic state. The pressure-strain term in the Reynolds stress equations becomes positive only in the spanwise velocity fluctuations, and hence turbulence energy is extracted from components in both streamwise and shear directions. The redistribution process as well as the anisotropic behavior of turbulence statistics are accurately evaluated with a linear analysis based on the rapid distortion theory. Furthermore, from the assessment of turbulence models for pressure-strain correlations using the present DNS data, it is found that none of the existing models represent the energy sink from the shear direction except for a model using the Langevin equation, and the destruction of the Reynolds shear stress is described rather well using a classical linear model.

Length scales and the energy balance for turbulence near a free surface

The structure of turbulence near a free surface is examined by using results obtained from a direct simulation of flow between a no-slip wall and a shear free boundary, which serves as a model of a waveless free surface. An energy balance analysis shows that the pressure-strain term is the dominant producing term for the spanwise component of the turbulent kinetic energy. In addition, the dissipation rates for the horizontal components of the turbulence are reduced near the free surface, whereas the dissipation rate for the vertical component remains approximately constant. Two-point correlations, energy spectra, and length scales reveal important free surface induced effects. The length scales near the free surface are compared with the scales near the centerline of normal turbulent channel flow. This comparison reveals an increase by a factor of three in the streamwise length scales associated with the spanwise velocity fluctuations and an increase by a factor of two in the spanwise length scales for the streamwise velocity fluctuations. The length scales normal to the free surface are decreased for all velocity components. This indicates a more pancake-like eddy structure near the free surface compared with the structure near the centerline of a normal channel. The energy spectra show qualitative agreement with the Hunt-Graham model, though higher resolution calculations will be required to make more quantitative comparisons. The streaky structure in free surface bounded turbulent channel flow is noticeably more persistent than in normal turbulent channel flow. This is principally due to the attachment of streamwise oriented wall eddies to the free surface.

Streaky Structures in a Turbulent Square-Duct Flow. Identification of Streaky Structures by Combined Flow Visualization-Velocity Measurement Techniques.

Streaky structures have been studied in a fully developed turbulent square-duct flow by using combined dye flow visualization-LDV velocity measurement techniques. Transverse distributions of low-speed streaks and mean streak spacing are shown in the near-wall region, i.e., yuτ/v < 25. At z/H < 0.16, the transverse distribution of the low-speed streaks is homogeneous and their spacing is about 90v/uτ, which suggests that the streaky structures near the wall bisector may be similar to those in turbulent boundary layers. In addition, the transverse distance between the visually identified low-speed streak and the velocity-measurement point was measured for each set of visual data. Conditioning the velocity fluctuations on this transverse distance, conditional probability density distributions of the axial, wall-normal and spanwise velocity fluctuations are shown. These distributions suggest the existence of quasi-streamwise vortical motions associated with the visualized streaky structures, their wall-normal dimension and the intermittency of their appearance.

Direct Numerical Simulation of Mixing Layer (Effect of Spanwise Disturbance).

The objective of this paper is to clarify the effect of the spanwise wavelength of an initial disturbance on the secondary instability of mixing layers. To achieve this purpose, we have performed a direct numerical simulation of a three-dimensional mixing layer using a spectral method. The results are reported for the case of an initial hyperbolic tangent velocity profile with periodic excitation. From these results, we have obtained the following conclusions : 1) streamwise and transverse velocity fluctuations are slightly affected by the initial spanwise wavelength ; 2) spanwise velocity fluctuation and streamwise vorticity reflect the effect of the initial spanwise wavelength ; and 3) the spanwise perturbation that has the wavelength equal to one-third of the streamwise wavelength has the maximum growth rate.

三次元画像処理流速計によるステップ後方剥離再付着乱流の計測

The 3-D particle tracking velocimeter was applied to the detailed turbulence measurement in a flow downstream of the one-side expansion of a two-dimensional channel. The mean velocities as well as the second-order statistics of three turbulence components, which will be useful in evaluating various turbulence models, have been calculated from about 2x106 measured instantaneous velocity vectors. Based upon the analysis of the forward-flow fraction, the mean reattachment length is determined as (7.0±0.5) times the step height. The anisotropy measures of turbulence components show that the spanwise velocity fluctuation is the largest near the wall in the reattaching region unlike the equilibrium wall-layer turbulence. This fact must be properly taken into account in numerical predictions of turbulent separated and reattaching flows.

Three-dimensional Turbulent Shear Flow Structure over Sand Ribbons

Experimental study was conducted to clarify three-dimensional structure of turbulent shear flow and secondary currents. A fixed wavy bed was used to reproduce the flow pattern over sand ribbons. Cross-sectional distributions of main flow velocity, Reynolds stress and coefficients of eddy viscosity were examined with taking account of the influence of secondary currents. Generation mechanism of secondary currents was investigated on the basis of streamwise mean vorticity equation. From the result, it was confirmed that Reynolds stress (-v′w′) is the driving force for secondary currents and turbulent intensity difference (v′2-w′2) is the resisting force for them, where v′ and w′ are vertical and spanwise velocity fluctuations respectively, and overbar denotes the time average.

A digital technique for the simultaneous measurement of streamwise and lateral velocities in turbulent flows

A novel, digital, hot-wire anemometer technique for the simultaneous measurement of the instantaneous streamwise and lateral velocity fields in high-intensity turbulent flows is discussed. It involves the use of a three-wire probe comprising two 45° slanted hot wires and a normal hot wire. A comprehensive and systematic examination of several factors that can affect the fidelity of the streamwise and lateral velocity waveforms is developed to assess the performance of the new technique as well as hot-wire systems generally. These factors are: (i) rectification, which stems from the inherent insensitivity of hot wires to the direction of the instantaneous (total) velocity vector in a turbulent flow; (ii) spanwise velocity fluctuations; (iii) axial cooling of hot wires; (iv) unpredictable variations in one of four hot-wire calibration parameters; (v) random hot-wire calibration errors; (vi) spanwise separation of the hot wires. Relevant hot-wire anemometer-response equations relating instantaneous anemometer output voltages to instantaneous flow velocities were established on the basis of extensive voltage-velocity calibration data pertaining to hot wires orientated with respect to the calibration flow velocity at various yaw and pitch angles ranging from 0° to 90°. Simulated Gaussian (streamwise, lateral and spanwise) velocity fields appropriate to flows with turbulence intensity levels varying between 5 and 80% and Reynolds shear-stress coefficients varying between 0.1 and 0.5 were generated by means of a digital computer, and the associated anemometer-voltage signals computed in accordance with the response equations subject to different combinations of the first four of the aforementioned factors. In order to take into account the effects of the last two factors, viz calibration errors and spanwise wire separation, uncorrelated Gaussian ‘noise’ fluctuations were superimposed on the above voltage signals. Estimates of the known (simulated) streamwise and lateral velocity signals were then determined by simultaneous solution of (a) the actual instantaneous response equations, (b) approximate versions of them, and (c) linearized versions of them. The results indicate that reasonably accurate estimates of velocity signals from a turbulent flow can be obtained by means of conventional hot-wire anemometer techniques – which assume that anemometer voltage fluctuations are linear functions of corresponding velocity fluctuations – only if the turbulent intensity level of the flow does not exceed about 20%. In marked contrast, the 3-wire anemometer technique introduced here can be used to measure streamwise and lateral velocity signals simultaneously with a high degree of accuracy for turbulence-intensity levels of up to 40%. In addition, this technique is capable of yielding high-fidelity streamwise velocity waveforms for levels in excess of 70%.