Wavelet spectrum analysis on energy transfer of multi-scale structures in wall turbulence

The streamwise velocity components at different vertical heights in wall turbulence were measured. Wavelet transform was used to study the turbulent energy spectra, indicating that the global spectrum results from the weighted average of Fourier spectrum based on wavelet scales. W＇avelet transform with more vanishing moments can express the declining of turbulent spectrum. The local wavelet spectrum shows that the physical phenomena such as deformation position in the boundary layer, and the or breakup of eddies are related to the vertical energy-containing eddies exist in a multi-scale form. Moreover, the size of these eddies increases with the measured points moving out of the wall. In the buffer region, the small scale energy-containing eddies with higher frequency are excited. In the outer region, the maximal energy is concentrated in the low-frequency large-scale eddies, and the frequency domain of energy-containing eddies becomes narrower.

BURST EVENT DETECTION IN WALL TURBULENCE BY WVITA METHOD

Wavelet Variable Interval Time Average (WVITA) is introduced as a method incorporating burst event detection in wall turbulence. Wavelet transform is performed to unfold the longitudinal fluctuating velocity time series measured in the near wall region of a turbulent boundary layer using hot-film anemometer. This unfolding is both in time and in space simultaneously. The splitted kinetic of the longitudinal fluctuating velocity time series among different scales is obtained by integrating the square of wavelet coefficient modulus over temporal space. The time scale that related to burst events in wall turbulence passing through the fixed probe is ascertained by maximum criterion of the kinetic energy evolution across scales. Wavelet transformed localized variance of the fluctuating velocity time series at the maximum kinetic scale is put forward instead of localized short time average variance in Variable Interval Time Average (VITA) scheme. The burst event detection result shows that WVITA scheme can avoid erroneous judgement and solve the grouping problem more effectively which is caused by VITA scheme itself and can not be avoided by adjusting the threshold level or changing the short time average interval.

EXPERIMENTAL STUDY OF MEASUREMENT FOR DISSIPATION RATE SCALING EXPONENT IN HEATED WALL TURBULENCE

Experimental investigations have been devoted to the study of scaling law of coarse-grained dissipation rate structure function for velocity and temperature fluctuation of non-isotropic and inhomogeneous turbulent flows at moderate Reynolds number. Much attention has been paid to the case of turbulent boundary layer, which is typically the non-istropic and inhomogeneous trubulence because of the dynamically important existence of organized coherent structure burst process in the near wall region . Longitudinal velocity and temperature have been measured at different vertical positions in turbulent boundary layer over a heated and unheated flat plate in a wind tunnel using hot wire anemometer. The influence of non-isotropy and inhomogeneity and heating the wall on the scaling law of the dissipation rate structure function is studied because of the existence of organized coherent structure burst process in the near wall region . The scaling law of coarse-grained dissipation rate structure function is foun

New perspective in statistical modeling of wall-bounded turbulence

Despite dedicated effort for many decades,statistical description of highly technologically important wall turbulence remains a great challenge.Current models are unfortunately incomplete,or empirical,or qualitative.After a review of the existing theories of wall turbulence,we present a new framework,called the structure ensemble dynamics （SED）,which aims at integrating the turbulence dynamics into a quantitative description of the mean flow.The SED theory naturally evolves from a statistical physics understanding of non-equilibrium open systems,such as fluid turbulence, for which mean quantities are intimately coupled with the fluctuation dynamics.Starting from the ensemble-averaged Navier-Stokes（EANS） equations,the theory postulates the existence of a finite number of statistical states yielding a multi-layer picture for wall turbulence.Then,it uses order functions（ratios of terms in the mean momentum as well as energy equations） to characterize the states and transitions between states.Application of the SED analysis to an incompressible channel flow and a compressible turbulent boundary layer shows that the order functions successfully reveal the multi-layer structure for wall-bounded turbulence, which arises as a quantitative extension of the traditional view in terms of sub-layer,buffer layer,log layer and wake. Furthermore,an idea of using a set of hyperbolic functions for modeling transitions between layers is proposed for a quantitative model of order functions across the entire flow domain.We conclude that the SED provides a theoretical framework for expressing the yet-unknown effects of fluctuation structures on the mean quantities,and offers new methods to analyze experimental and simulation data.Combined with asymptotic analysis,it also offers a way to evaluate convergence of simulations.The SED approach successfully describes the dynamics at both momentum and energy levels, in contrast with all prevalent approaches describing the mean velocity profile only.Moreover,the SED theoretical framework is general,independent of the flow system to study, while the actual functional form of the order functions may vary from flow to flow.We assert that as the knowledge of order functions is accumulated and as more flows are analyzed, new principles（such as hierarchy,symmetry,group invariance,etc.） governing the role of turbulent structures in the mean flow properties will be clarified and a viable theory of turbulence might emerge.

Study on local topology model of low/high streak structures in wall-bounded turbulence by tomographic time-resolved particle image velocimetry

The relationship between the in the logarithmic law （log-law） region of bursting event and the low/high-speed streak a turbulent boundary layer is investigated. A tomographic time-resolved particle image velocimetry （TRPIV） system is used to measure the instantaneous three-dimensional-three-component （3D-3C） velocity field. The momentum thickness based Reynolds number is about 2 460. The topological information in the log-law region is obtained experimentally. It is found that the existence of the quadrupole topological structure implies a three-pair hairpin-like vortex packet, which is in connection with the low/high-speed streak. An idealized 3D topological model is then proposed to characterize the observed hairpin vortex packet and low/high-speed streak.

Zonal Embedded Grids for LES of Self-Sustaining Structures of Wall Turbulence

In this study,a zonal grid refinement method based on the solution of weakly compressible flow equations with large eddy simulation in the finite volume method（FVM） and dynamic subgrid-scale model framework was used to simulate the turbulence structures of a plane-wall flow with Reynolds number Re=U0δ /ν =10 000.Comparison and analysis were conducted on the distributions of time-averaged velocity and velocity fluctuations,as well as on the actual near-wall structures,to verify the accuracy of the turbulence features that were simulated using the zonal grid refinement method.The results show that the zonal embedded grid is a very efficient way to illustrate the turbulence structures of the near-wall region.The present method is easy to implement and extend to small Mach number flow modeling on a collocated irregular FVM mesh system.

Wall-resolved large-eddy simulation of turbulent channel flows with rough walls

Turbulent flows over rough surfaces widely exist in nature and industry.Investigating its mechanism is of theoretical and practical significance.In this work we simulate the turbulent channel flow with rough walls using large-eddy simulation with rough elements resolved using the curvilinear immersed boundary method and compare the results obtained in this work with those in the paper by Yuan and Piomelli(J.Fluid Mech.,vol.760,pp.R1,2014),where the volume of fluid method was employed for modeling rough elements.The mean streamwise velocity profiles predicted by the two methods agree well with each other.Differences in Reynolds stresses and dispersive stresses are observed,which are attributed to the different approaches in dealing with the complex geometry of the rough surface.

Modeling of drag reduction in turbulent channel flow with hydrophobic walls by FVM method and weakly-compressible flow equations

In this paper the effects of hydrophobic wall on skin-friction drag in the channel flow are investigated through large eddy simulation on the basis of weaklycompressible flow equations with the MacCormack’s scheme on collocated mesh in the FVM framework. The slip length model is adopted to describe the behavior of the slip velocities in the streamwise and spanwise directions at the interface between the hydrophobic wall and turbulent channel flow. Simulation results are presented by analyzing flow behaviors over hydrophobic wall with the Smagorinky subgrid-scale model and a dynamic model on computational meshes of different resolutions. Comparison and analysis are made on the distributions of timeaveraged velocity, velocity fluctuations, Reynolds stress as well as the skin-friction drag. Excellent agreement between the present study and previous results demonstrates the accuracy of the simple classical second-order scheme in representing turbulent vertox near hydrophobic wall. In addition, the relation of drag reduction efficiency versus time-averaged slip velocity is established. It is also foundthat the decrease of velocity gradient in the close wall region is responsible for the drag reduction. Considering its advantages of high calculation precision and efficiency, the present method has good prospect in its application to practical projects.

On properties of the deterministic turbulence and reproducibility of its instantaneous and statistical characteristics

As known from previous studies, is a post-transitional flow that is turbulent the deterministic turbulence （DeTu） according to the generally accepted statistical characteristics but possesses, meanwhile, a significant degree of determinism, i.e., reproducibility of its instantaneous structure. It is found that the DeTu can occur in those cases when transition is caused by convective instabilities; in boundary layers, in particular. The present paper is devoted to a brief description of history of discovering the DeTu phenomenon, as well as to some recent advance in investigation of instantaneous and statistical properties of such turbulent boundary layer flows.

Study on the Shear Effect on Dye Patches Diffused in Wall-Bounded Shear Flow

This paper focuses on the high intensity filaments (dye patches) embedded in dye plumes in a wall-bounded shear flow, to investigate the shear effect on the dye patch distribution. Motivated by the widely concerned inverse estimation of the source location, we try extracting useful information to know the source location from down-stream dye patches. Accordingly, we changed the dye injection location at different distances from the wall and made observations at different downstream (diffusion) distances from the source. The orientation angle and roundness of dye patches were concerned to examine the shear effect and dye patch characteristics. To capture the dye plume images, a planar laser induced fluorescence (PLIF) technique was used. The orientation and roundness of each dye patch were calculated by least-square fitting. The statistics of both the orientation angle and the roundness were compared with those in homogeneous turbulent cases to reveal the shear effect. Different from uniformly-orientated dye patches in the homogeneous flow, larger occurrence probabilities with positive orientation angles of dye patches are observed in wall-bounded shear flow, in particular, when the injection location is near the wall. As with information extraction for the inverse estimation of source location, it is found that the orientation distribution of dye patches is independent of the diffusion distance, but related with the injection location from the wall. While for the homogeneous flow cases, a strong dependence on the diffusion distance is observed in the orientation distribution profiles. As for the roundness, similar aspects are found regarding the dependencies on the injection location in shear flow and on diffusion distance in homogeneous flow.

Constraine d large-e ddy simulation of turbulent flow over inhomogeneous rough surfaces

In this work we extend the method of the constrained large-eddy simulation(CLES)to simulate the tur-bulent flow over inhomogeneous rough walls.In the original concept of CLES,the subgrid-scale(SGS)stress is constrained so that the mean part and the fluctuation part of the SGS stress can be modelled separately to improve the accuracy of the simulation result.Here in the simulation of the rough-wall flows,we propose to interpret the extra stress terms in the CLES formulation as the roughness-induced stress so that the roughness inhomogeneity can be incorporated by modifying the formulation of the constrained SGS stress.This is examined with the simulations of the channel flow with the spanwise alternating high/low roughness strips.Then the CLES method is employed to investigate the temporal response of the turbulence to the change of the wall condition from rough to smooth.We demonstrate that the temporal development of the internal boundary layer is just similar to that in a spatial rough-to-smooth transition process,and the spanwise roughness inhomogeneity has little impact on the transition process.

Amplitude modulation and extreme events in turbulent channel flow

Amplitude modulation of near-wall turbulence by large-scale structures in the outer layer is investigated by direct numerical simulation of turbulent channel flows at Reynolds number Re= 540, 1000, 2000. The effect of modulation is obvious in the two-point cross-section correlation map, and the correlation coefficients increase significantly with the Reynolds number. The influence of modulation is reflected in the tail of the probability density function of the near-wall flow signals, which expands as the Reynolds number increases. The flatness factor provides a quantitative description of the high fluctuation events due to modulation. Vortical structures associated with modulation are revealed by conditionally averaging the flow field of the near-wall extreme events, providing a depiction of how the influence of the large-scale structures penetrate towards the near-wall region.

A study of inner-outer interactions in turbulent channel flows by interactive POD

The amplitude and frequency modulation of near-wall flow structures by the large-scale motions in outer regions is studied in turbulent channel flows. The proper orthogonal decomposition(POD) method is applied to investigate the interactions between the near-wall motions and the large-scale flow modes of the outer regions based on two datasets from direct numerical simulation of turbulent channel flows at Reynolds numbers of 550–10 0 0. The fluctuations in the fields u+, v+, w+ and Reynolds shear stress-(uv)+ are studied to understand the mechanism of amplitude and frequency modulation of the nearwall structures by the outer large-scale motions. The amplitude modulation coefficient of the Reynolds shear stress is larger than that of the velocity components. The frequency modulation effect has an opposite influence in the spanwise direction compared to the streamwise direction. The streamwise characteristic frequency increases with increasing large-scale velocity. However, the spanwise characteristic frequency exhibits a decreasing trend with increasing large-scale velocity in the near-wall region.

THE RESPONSE OF TURBULENT FLOW TO THE DISTURBANCE OF A VIBRATING RIBBON

By use of the LDV, experimental investigation was carried out for a turbulent boundary layer which was disturbed with an electric-magnetic vibrating ribbon. It is found that, in the how, the response of the disturbance contains harmonic components besides the fundamental frequency of the ribbon vibration. The fundamental and harmonic disturbances can also enhance the energy of of the frequency components around them. In the experiments, the regular disturbance was introduced in the outer region of the boundary layer. Under the given flow conditions, they can significantly influence the downstream coherent structures in the wall region by suppressing the bursts and increasing their period. The effect on the burst period depends on the disturbing frequency.

Local receptivity in non-parallel boundary layer

The research on boundary-layer receptivity is the key issue for the laminarturbulent transition prediction in fluid mechanics. Many of the previous studies for local receptivity are on the basis of the parallel flow assumption which cannot accurately reflect the real physics. To overcome this disadvantage, local receptivity in the non-parallel boundary layer is studied in this paper by the direct numerical simulation （DNS）. The difference between the non-parallel and parallel boundary layers on local receptivity is investigated. In addition, the effects of the disturbance frequency, the roughness location, and the multiple roughness elements on receptivity are also determined. Besides, the relations of receptivity with the amplitude of free-stream turbulence （FST）, with the roughness height, and with the roughness length are ascertained as well. The Tollmien- Schlichting （T-S） wave packets are excited in the non-parallel boundary layer under the interaction of the FST and the localized wall roughness. A group of T-S waves are separated by the fast Fourier transform. The obtained results are in accordance with Dietz＇s measurements, Wu＇s theoretical calculations, and the linear stability theory （LST）.

EFFECTS OF WALL ROUGHNESS ON COHERENT STRUCTURE IN TURBULENT SHEAR FLOWS

There are many examples that fluid flows on rough wall, such as channel flow in nature, pipe flow, etc. In order to know the flow structure of real fluids, it is important to study the effects of wall roughness on coherent structure in turbulent shear flows. The experiments were carried out in a square glass channel, which is 600cm long, with the cross section of 30×25cm^2. The flow velocity was varied from 2 to 40 cm/s. Uniform sands whose diameters were 0.0012cm, 0.2gcm, 0.385cm, 0.594cm and 0.896cm respectively were glued to the floor of the channel. The rough Reynolds number Re_Δ= U_*Δ/ν=0.04～73, where U_*is the shear velocity, Δ is the diame- ter of uniform sand, v is the kinematic viscosity coefficient. Hydrogen bubble technique for flow visualization and HWL-II hot-film anemometer for velocity mea- surement were used in the experiments.

SCOUR OF FINE SEDIMENT BY A TURBULENT WALL JET

A total of 66 experiments were conducted to investigate the scour of fine finesediment by a turbulent wall jet. The independent variables studied were the flow velocity, the jet size, the grain sine, and the water temperature.Three Closely sized grades of bed material were used, and their median diameters were 0. 273mm, 0. 050mm, and 0. 030mm. The jet velocities varied from 0. 30m/s to 1. 10m/s for the coarse sediment (D =0. 273mm), and from 0. 30m/s to 0. 70m/s for the fine grades (D = 0. 050mm , and D= 0. 030mm). The jet size was set to 3. 18mm, 6, 35mm, and 9. 53mm for each grade size, and the water temperature varied from about 60 degrees Fahrenheit to about 85 degrees Fahrenheit.The independent variables were analyzed using dimensional analysis. Three dimentsionless Parameters, namely U(=pu2/ΔpgD), B(b/D), and G(=ΔpgD3/pv2), were obtained. These parameters enabled a close correlation of all experimental results. Other studies were also found to correlate well with these parameters.

Optimal contract wall for desired orientation of fibers and its effect on flow behavior

The orientation of suspended fibers in the turbulent contraction is strongly related to the contraction ratio,which in some cases may be detrimental to the actual production.Here for a certain contraction ratio,the contraction geometry shape is optimized to obtain the desired fiber orientation.In view of the nonlinearity and the complexity of the turbulent flow equations,the parameterized shape curve,the dynamic mesh and a quasi-static assumption are used to model the contraction with the variable boundary and to search the optimal solution.Furthermore the Reynolds stress model and the fiber orientation distribution function are solved for various wall shapes.The fiber orientation alignment at the outlet is taken as the optimization objective.Finally the effect of the wall shape on the flow mechanism is discussed in detail.

AN ESTIMATE OF THE EFFECTS OF LARGE SCALE STRUCTURES ON THE TURBULENT TRANSPORT PROCESSES NEAR WALL

Based on the three-term decomposition model for turbulent flows, the fundamental equations for quasi-periodic motions are obtained, and the approximate analytical solutions of these second-order nonlinear partial differential equations are derived by using the match method. The effects on the mo- mentum, heat and mass transport processes in the wall turbulent flows can be estimated approximately.

Transient growth in turbulent particle-laden channel flow

Linear transient growth of optimal perturbations in particle-laden turbulent channel flow is investigated in this work.The problem is formulated in the framework of a Eulerian-Eulerian approach,employing two-way coupling between fine particles and fluid flow.The model is first validated in laminar cases,after which the transient growth of coherent perturbations in turbulent channel flow is investigated,where the mean particle concentration distribution is obtained by direct numerical simulation.It is shown that the optimal small-scale structures for particles are streamwise streaks just below the optimal streamwise velocity streaks,as was previously found in numerical simulations of particle-laden channel flow.This indicates that the optimal growth of perturbations is a dominant mechanism for the distribution of particles in the near-wall region.The current study also considers the transient growth of small-and large-scale perturbations at relatively high Reynolds numbers,which reveals that the optimal large-scale structures for particles are in the near-wall region while the optimal large-scale structures for fluid enter the outer region.