Stochastic Analysis and Modeling of Velocity Observations in Turbulent Flows

Highly turbulent water flows,often encountered near human constructions like bridge piers,spillways,and weirs,display intricate dynamics characterized by the formation of eddies and vortices.These formations,varying in sizes and lifespans,significantly influence the distribution of fluid velocities within the flow.Subsequently,the rapid velocity fluctuations in highly turbulent flows lead to elevated shear and normal stress levels.For this reason,to meticulously study these dynamics,more often than not,physical modeling is employed for studying the impact of turbulent flows on the stability and longevity of nearby structures.Despite the effectiveness of physical modeling,various monitoring challenges arise,including flow disruption,the necessity for concurrent gauging at multiple locations,and the duration of measurements.Addressing these challenges,image velocimetry emerges as an ideal method in fluid mechanics,particularly for studying turbulent flows.To account for measurement duration,a probabilistic approach utilizing a probability density function(PDF)is suggested to mitigate uncertainty in estimated average and maximum values.However,it becomes evident that deriving the PDF is not straightforward for all turbulence-induced stresses.In response,this study proposes a novel approach by combining image velocimetry with a stochastic model to provide a generic yet accurate description of flow dynamics in such applications.This integration enables an approach based on the probability of failure,facilitating a more comprehensive analysis of turbulent flows.Such an approach is essential for estimating both short-and long-term stresses on hydraulic constructions under assessment.

NUMERICAL STUDY OF TURBULENT FLOWS OVER WAVY BOUNDARIES

The fully developed túrbulent flows over wavy boundaries are investigated by means of the k-ε model.Predicted flow characteristics over rigid wavy walls are in good agreement with the availa- ble experimental data.Moreover drag reduction has been found in a 2-dimensional channel with periodi- cal wavy walls.The energy input from turbulent wind to regular waves is also studied in the paper by the same turbulence model with carefully posed boundary conditions at wind-wave interface.Better agreement has been obtained in the prediction of the growth rates of wind waves as compared with the previous theoretical and numerical results.

THE NUMERICAL SIMULATION OF TURBULENT FLOWS OF NEWTONIAN AND A SORT OF NON-NEWTONIAN FLUID IN 180-DEGREE SQUARE SECTIONED BEND

Using k- model of turbulence and measured wall functions, turbulent flows of Newtonian (pure water) andasort of non-Newtonian fluid (dilute, drag-reduction solution of polymer) in a 180-degree curved bend were simulated numerically. The calculated results agreed well with the measured velocity profiles. On the basis of calculation and measurement, appropriateness of turbulence model to complicated flow in which the large-scale vortex exists was analyzed and discussed.

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.

Experimental investigation of turbulent flows around high-rise structure foundations and implications on scour

Many studies have been undertaken to predict local scour around offshore high-rise structure foundations(HRSFs),which have been used in constructing the Donghai Wind Farm in China.However,there have been few works on the turbulent flow that drives the scour process.In this study,the characteristics of the turbulent flow fields around an HRSF were investigated using the particle image velocimetry technique.The mean flow,vorticity,and turbulence intensity were analyzed in detail.The relationship between the flow feature and scour development around an HRSF was elaborated.The results showed that the flow velocity increased to its maximum value near the third row of the pile group.The shear layer and wake vortices could not be fully developed downstream of the last row of the piles at small Reynolds numbers.The strong flow and turbulent fluctuation near the third piles explained the existence of a longtail scour pattern starting from the HRSF shoulders and a trapezoidal deposition region directly downstream of HRSF.This laboratory experiment gains insight into the mechanism of the turbulent flow around HRSFs and provides a rare dataset for numerical model verifications.

Basic Laws in Mechanics of Turbulent Flows

Turbulent flow is a basic form of fluid motion widely observed in nature. In hydraulic engineering, especially in the study of sediment movement, turbulence is a key problem. In this paper, based on the stochastic theory of wall turbulence developed by the author and the results by other investigators, fluc-tuation and mean structures and drag coefficient for Newtonian and drag reduction flows in all states (laminar, transitional, turbulent) and in all regions (smooth, transitional, rough) are theoretically discussed in detail. General laws for laminar and turbulent flows obtained by the author are verified by the experimental results obtained by others, and there is good agreement between them.

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method （LBM） is coupled with the multiple-relaxation- time （MRT） collision model and the three-dimensional 19-discrete-velocity （D3Q19） model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high- order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investi- gated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity （ESS） method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This valida~ tion provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.

Simulation of Non-Isothermal Turbulent Flows Through Circular Rings of Steel

This article is intended to examine the fluid flow patterns and heat transfer in a rectangular channel embedded with three semi-circular cylinders comprised of steel at the boundaries.Such an organization is used to generate the heat exchangers with tube and shell because of the production of more turbulence due to zigzag path which is in favor of rapid heat transformation.Because of little maintenance,the heat exchanger of such type is extensively used.Here,we generate simulation of flow and heat transfer using nonisothermal flow interface in the Comsol multiphysics 5.4 which executes the Reynolds averaged Navier stokes equation(RANS)model of the turbulent flow together with heat equation.Simulation is tested with Prandtl number(Pr=0.7)with inlet velocity magnitude in the range from 1 to 2 m/sec which generates the Reynolds number in the range of 2.2×10^(5) to 4.4×10^(5) with turbulence kinetic energy and the dissipation rate in ranges(3.75×10^(−3) to 1.5×10^(−2))and(3.73×10^(−3)−3×10^(−2))respectively.Two correlations available in the literature are used in order to check validity.The results are displayed through streamlines,surface plots,contour plots,isothermal lines,and graphs.It is concluded that by retaining such an arrangement a quick distribution of the temperature over the domain can be seen and also the velocity magnitude is increasing from 333.15%to a maximum of 514%.The temperature at the middle shows the consistency in value but declines immediately at the end.This process becomes faster with the decrease in inlet velocity magnitude.

Cavitation Inception in Turbulent Flows Around a Hydrofoil

The phenomenon of cavitation inception around a hydrofoil is studied experimentally. The flow velocities around the foil are measured by a laser doppler velocimetry （LDV）. The inception cavitation aspects are observed by using a high-speed video camera. In the experiment, the Reynolds number is fixed at a value of 7.0 × 10^5. The boundary layer around the foil undergoes turbulent flow under the experiment condition. The LDV measurement results show that the flow in the boundary layer around the foil doesn＇t separate from the surface. It is found that the cavitation inception in non-separated turbulent flow is related to the coherent structures in the boundary layer. It is clear that the turbulent bursting and the hairpin-shaped vortex structure accompany the incipient cavitation.

Large eddy simulations of zinc ions transfer to turbulent flows from hyporheic zone

Metal contaminants from surface water pollution events often enter hyporheic zones,under certain conditions,they may be released back into streams,causing secondary pollution to the water quality.The present study investigated the effects of adsorption,permeability,and anisotropy of sediment beds on the release of zinc ions(Zn^(2+))from the hyporheic zone into overlying turbulent flows using large-eddy simulations(LES).The volume-averaged Navier-Stokes equations and advection-diffusion equation with adsorption term were used to describe the sediment in-flow,adsorption,and convective diffusion of Zn^(2+) within the sediment layer.The effects of sediment permeability on the Zn^(2+)concentration distribution and mass transfer processes were investigated by time-averaged statistics of flow and concentration fields.The results show that adsorption becomes stronger as the pH value increases,leading to a slow increase in Zn^(2+)concentration in the overlying water layer and reaching a lower steady-state concentration.Higher overall permeability of the sediment layer can enhance mass and momentum exchange near the sediment-water interface(SWI),and intensify the release of Zn^(2+)from the sediment layer into the overlying water.As the wall-normal permeability of the sediment layer increases,the normal turbulent intensity strengthens,momentum transport enhances,the wall-normal Zn^(2+)concentration flux increases,the effective diffusion coefficient increases,and the concentration in the overlying water increases.

Advances in Studies on Turbulent Dispersed Multiphase Flows

Dispersed multiphase flows,including gas-particle(gas-solid),gas-spray,liquid-particle(liquid-solid) ,liquid-bubble,and bubble-liquid-particle flows,are widely encountered in power,chemical and metallurgical,aeronautical and astronautical,transportation,hydraulic and nuclear engineering. In this paper,advances and re-search needs in fundamental studies of dispersed multiphase flows,including the particle/droplet/bubble dynamics,particle-particle,droplet-droplet and bubble-bubble interactions,gas-particle and bubble-liquid turbulence interac-tions,particle-wall interaction,numerical simulation of dispersed multiphase flows,including Reynolds-averaged modeling(RANS modeling),large-eddy simulation(LES) and direct numerical simulation(DNS) are reviewed. The research results obtained by the present author are also included in this review.

An efficient parallel algorithm for DNS of buoyancy-driven turbulent flows

In this paper,an explicit low-storage simplified M-stage Runge-Kutta(SRK)scheme for high Reynolds-number incompressible flows is presented.In the SRK scheme,the Poisson equation is solved only once in the final substage of each time step.By taking advantage of the SRK scheme and the advanced hybrid MPI+MPI model,we have developed an efficient parallel solver for buoyancy-driven turbulent flow.The spatial and temporal accuracies of the solver are validated with Taylor-Green vortex flow.Both the RK and SRK schemes are implemented for the simulation of turbulent Rayleigh-Benard convection as well as Rayleigh-Taylor flow.The results show that the SRK scheme can save approximately 20%of the computation time.

NUMERICAL SOLUTION FOR TURBULENT FLOWS ON CONCAVE SURFACES OF SPILLWAY DAMS

This paper is concerned with the numerical solution of turbulent flows on the concave surfaces of spillway dams. Orthogonal curvilinear coordinates are used to deal with the complicated computational region and the effects of streamline curvature on turbulent flows are included. The SIMPLEC procedure has been used for the transformed governing equations in the transformed domain. The comparison between computed results and experimental data shows a satisfactory agreement.

THE EXPERIMENTAL RESULTS OF 2-D FREE SHEAR TURBULENT FLOWS AND THE COMPARISON WITH THE THEORETICAL COMPUTATION

An extensive set of measurements in 2-D turbulent mixing layer, wake and jet flow by the hot-wire technique and data sampling are presented. The measured quantities, i. e. the mean velocity, the turbulence intensity, the Reynolds stress and higher-order correlations of the fluctuating velocity in the self-preserving region of the above free shear flows are compared with the computational results based on Zhou's theory for the shear turbulence of in- compressible fluid. The experimental and computational results are in good agreement.

Simulation of Turbulent Flows Using a Finite-Volume Based Lattice Boltzmann Flow Solver

In this study,the Lattice Boltzmann Method(LBM)is implemented through a finite-volume approach to perform 2-D,incompressible,and turbulent fluid flow analyses on structured grids.Even though the approach followed in this study necessitates more computational effort compared to the standard LBM(the so called stream and collide scheme),using the finite-volume method,the known limitations of the stream and collide scheme on lattice to be uniform and Courant-Friedrichs-Lewy(CFL)number to be one are removed.Moreover,the curved boundaries in the computational domain are handled more accurately with less effort.These improvements pave the way for the possibility of solving fluid flow problems with the LBM using coarser grids that are refined only where it is necessary and the boundary layers might be resolved better.

AN INVESTIGATION ON ASM TURBULENCE MODEL IN PREDICTIING NONISOTROPIC TURBULENT FLOWS

Non-isotropy is evident for flows with large streamline curvature. Algebraic stress model can fairly simulate non-isotropy of turbulence. Some flow situations were investigated with a well developed ASM model. The calcu- lated results show that the distributions of Reynolds stresses in different directions are obviously different. The non-isotropy of the flow is evident. The effect of streamline curvature on the flow feature of submerged water jet restricted by solid boundaries were studied, and its application in the design of energy dissipators of free trajectory jet type was disscused.

Staggered Calculation of Turbulent Flows Over a 3D Bluff Body Using Curvilinear Nonorthogonal Coordinates

A finite difference method is developed to predict turbulent flows over 3D bluffbodies. The K-ε turbulence model with Launder and Spalding's wall treatment isemployed. The solution alsorithm is based on a body fitted nonorthogonalcurvilinear eourdinate system and a stagsered grid arrangement. The covariantvelocity components are chosen as dependent variables. Convective fluxes aredescribed by the Power haw Scheme. The grids are generated with an ellipticgrid generator using control functions. Results obtained are compared withexporiment measurements and other calculations.

NUMERICAL SIMULATIONS OF TURBULENT FLOWS PASSED THROUGH AN ORIFICE ENERGY DISSIPATOR WITHIN A FLOOD DISCHARGE TUNNEL

When water flows through a multiple-orifice energy disspator, flow vibration and cavitation may become very important problems. A new kind of the energy dissipator has recieved much attention because of its effectiveness in energy dissipation. In this paper numerical simulations of turbulent flows in a dissipator were presented. The flow was considered to be an asymmetric two-dimensional steady flow. K-Ε turbulent model was used and solution procedure was described. The calculation was performed with different flow conditions. Calculated results of the flow field are compared with experiments. The results demonstrate that turbulent flow through dissipator can be predicted.

Subgrid-scale model based on the vorticity gradient tensor for rotating turbulent flows

A new subgrid-scale(SGS)stress model is proposed for rotating turbulent flows,and the new model is based on the traceless symmetric part of the square of the velocity gradient tensor and the symmetric part of the vorticity gradient tensor(or the so-called vorticity strain rate tensor).The new subgrid-scale stress model is taken into account the effect of the vortex motions in turbulence,which is reflected on the anti-symmetric part of the velocity gradient tensor.In addition,the eddy viscosity of the new model reproduces the proper scaling as O(y^3)near the wall.Then,the new SGS model is applied in large-eddy simulation of the spanwise rotating turbulent channel flow.Different simulating cases are selected to test the new model.The results demonstrate that the present model can well predict the mean velocity profiles,the turbulence intensities,and the rotating turbulence structures.In addition,it needs no a second filter,and is convenient to be used in the engineering rotational flows.

LES prediction of space-time correlations in turbulent shear flows

We compare the space-time correlations calculated from direct numerical simulation （DNS） and large-eddy simulation （LES） of turbulent channel flows. It is found from the comparisons that the LES with an eddy-viscosity subgrid scale （SGS） model over-predicts the space-time corre- lations than the DNS. The overpredictions are further quantified by the integral scales of directional correlations and convection velocities. A physical argument for the overpre- diction is provided that the eddy-viscosity SGS model alone does not includes the backscatter effects although it correctly represents the energy dissipations of SGS motions. This argument is confirmed by the recently developed elliptic model for space-time correlations in turbulent shear flows. It suggests that enstrophy is crucial to the LES prediction of spacetime correlations. The random forcing models and stochastic SGS models are proposed to overcome the overpredictions on space-time correlations.