Three-dimensional turbulent flow over cube-obstacles

In order to investigate the influence of surface roughness on turbulent flow and examine the wall-similarity hypothesis of Townsend, three-dimensional numerical study of turbulent channel flow over smooth and cube-rough walls with different roughness height has been carried out by using large eddy simulation（LES） coupled with immersed boundary method（IBM）. The effects of surface roughness array on mean and fluctuating velocity profiles, Reynolds shear stress, and typical coherent structures such as quasi-streamwise vortices（QSV） in turbulent channel flow are obtained. The significant influences on turbulent fluctuations and structures are observed in roughness sub-layer（five times of roughness height）.However, no dramatic modification of the log-law of the mean flow velocity and turbulence fluctuations can be found by surface cube roughness in the outer layer. Therefore, the results support the wall-similarity hypothesis. Moreover, the von Karman constant decreases with the increase of roughness height in the present simulation results. Besides, the larger size of QSV and more intense ejections are induced by the roughness elements, which is crucial for heat and mass transfer enhancement.

Optimal convergence rates for three-dimensional turbulent flow equations

In this paper, the convergence turbulent flow equations are considered. By rates of solutions to the three-dimensional combining the LP-Lq estimate for the linearized equations and an elaborate energy method, the convergence rates are obtained in various norms for the solution to the equilibrium state in the whole space when the initial perturbation of the equilibrium state is small in the H3-framework. More precisely, the optimal convergence rates of the solutions and their first-order derivatives in the L2-norm are obtained when the LP-norm of the perturbation is bounded for some p ε [1, 6）.

Energy dissipation statistics along the Lagrangian trajectories in three-dimensional turbulent flows

Energy dissipation rate is relevant in the turbulent phenomenology theory, such as the classical Kolmogorov 1941 and1962 refined similarity hypothesis. However, it is extremely difficult to retrieve experimentally or numerically. In this paper, the full energy dissipation, its proxy and the pseudo-energy dissipation rate along the Lagrangian trajectories in the three-dimensional turbulent flows are examined by using a state-of-art high resolution direct numerical simulation database with a Reynolds number Re;= 400. It is found that the energy dissipation proxy ε;is more correlated with the full energy dissipation rate ε. The corresponding correlation coefficient p between the velocity gradient and ε shows a Gaussian distribution. Furthermore, the coarse-grained dissipation rate is considered. The cross correlation p is found to be increased with the increasing of the scale τ.Finally, the hierarchical structure is extracted for the full energy dissipation rate, its proxy and the pseudo one.The results show a power-law behavior in the inertial range10≤τ/τ;≤100. The experimental scaling exponent of the full energy dissipation rate is found to be h;=0.69, agrees very well with the one found for the Eulerian velocity. The experimental values for ε;and ε;are around h;=0.78, implying a more intermittent Lagrangian turbulence. Therefore, the intermittency parameter provided by ε;and ε;will be biased.

Three-dimensional turbulent model of heat transfer and fluid flow in GTAW process

A two-equation K-ε turbulent fluid flow model is built to model the heat transfer and fluid flow in gas tungsten arc welding （GTAW） process of stainless steel S US310 and S US316. This model combines the buoyancy force, lorentz force and marangni force as the driving forces of thefluidflow in the weld pool. The material properties are functions of temperature in this model. The simulated results show that the molten metal flowing outward is mainly caused by the marangoni convection, which makes the weld pool become wider and shallower. The comparison of the weld pool shape of SUS310 and SUS316 shows that the slight differences of the value of thermal conductivity mainly attributes to the difference of the weld pool shape and the distinction of heat transport in laminar and turbulent model makes large diversity in the simulated results.

NUMERICAL INVESTIGATION OF THREE-DIMENSIONAL VISCOUS INCOMPRESSIBLE FLOWS IN DIVERGENT CURVED CHANNELS AND TURBULENT MODEL STUDY

In order to make the numerical calculation of viscous flows more convenient for the flows in channel with complicated profile governing equations expressed in the arbitrary curvilinear coordinates were derived by means of Favre density-weighted averaged method, and a turbulent model with effect of curvature modification was also derived. The numerical calculation of laminar and turbulent flown in divergent curved channels was carried out by means of parabolizeil computation method. The calculating results were used to analyze and investigate the aerodynamic performance of talor cascades in compressors preliminarily.

NUMERICAL CALCULATION OF THREE-DIMENSIONAL TURBULENT FLOW IN A DISTORTING DUCT

A Navier-Stokes procedure based on the Finite Volume Method (FVM) is developed to calculate three-dimensional duct flows with complex geometry. This method is applied to analyze the flow in a distorting duct, and the numercal results are in good a-greement with the experimental ones.

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.

THREE-DIMENSIONAL EVOLUTIION OF VORTICES AND EARLY FEATURES OF COHERENT STRUCTURE IN THE TURBULENT WAKE BEHIND A 2-D CIRCULAR CYLINDER

3-D evolution of Karman vortex filaments and vortex filaments in braid regions in the turbulent wake of a 2-D circulax cylinder is investigated numeri- cally based on inviscid vortex dynamics by analyzing the response of the initially 2-D spanwise vortex filaments to periodic spanwise disturbance of varying magnitude, wavelength and initial phase angles. Our results reveal a kind of 3-D vortex system in the wake which consists of large scale horseshoe-shaped vortices and small scale λ-shaped vortex filaments as well as vortex loops. The mechanism and the dynamic process about the generation of streamwise vortical structure and the 3-D coherent structure are reported.

Three-dimensional numerical simulation of the flow past a circular cylinder based on LES method

The hydrodynamic characteristics of a rigid, single, circular cylinder in a three dimensional, incompressible, uniform cross flow were calculated using the large-eddy simulation method of CFX5. Solutions to the three dimensional N-S equations were obtained by the finite volume method. The focus of this numerical simulation was to research the characteristics of pressure distribution （drag and litt forces） and vortex tubes at high Reynolds numbers. The results of the calculations showed that the forces at every section in the spanwise direction of the cylinder were symmetrical about the middle section and smaller than the forces calculated in two dimensional cases. Moreover, the flow around the cylinder obviously presents three dimensional characteristics.

STUDY ON TURBULENT SPOTS IN PLANE COUETTE FLOW

Turbulent spots play a key role in the formation of the turbulence and the transition. The generation and evolution of turbulent spots using the wall impulse model in the plane Couette flow are studied by direct numerical simulation of Navier-Stokes equations. A group of three-dimensional coupling compact difference schemes with high accuracy and high resolution is used in the numerical calculation. The important characteristics of turbulent spots based on the results of examples are analyzed, including the formation of random pulse, the generation of Reynolds stress, the growth of disturbance amplitude, and the continuous change of spot shape, especially the complex evolution process of the streamwise vortices. Computational results confirm that basic properties of turbulent spots in the laminar flow are similar to those in the turbulent flow.

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.

NUMERICAL SIMULATION OF 3-D DENSE SOLID-LIQUID TWO-PHASE TURBULENT FLOW IN A NON-CLOGGING MUD PUMP

A mathematical model is set to evaluate the 3-D dense solid-liquid two-phaseturbulent flow in a non-clogging mud pump, the flow feature in the impeller channel is simulatedwith the tool of IPSA. Meanwhile, resort to TECPLOT as the post-processor, the simulation results isvisualized. The results show the main flow characteristics: There exists backflow and aberrantvelocities at inlet area and a relative velocity slip between two phases; A jet-wake flow pattern isdiscerned around the shroud-suction side area; The relative velocity vector of solid phase iscloser to the pressure surface than that of liquid phase and the trend is more obvious with theincrease of diameter; The kinetic energy of turbulence k and the dissipation rate e reach theirpeaks at the corner of pressure and suction surface. The simulation results show a good agreementwith the experimental flow features in the impeller channel, which prove the turbulent model used isvalid and provide a theoretical design basis to non-clogging pumps.

Structural ensemble dynamics based closure model for wall-bounded turbulent flow

Wall-bounded turbulent flow involves the development of multi-scale turbulent eddies, as well as a sharply varying boundary layer. Its theoretical descriptions are yet phenomenological. We present here a new framework called structural ensemble dynamics （SED）, which aims at using systematically all relevant statistical properties of turbulent structures for a quantitative description of ensemble means. A new set of closure equations based on the SED approach for a turbulent channel flow is presented. SED order functions are defined, and numerically determined from data of direct numerical simulations （DNS）. Computational results show that the new closure model reproduces accurately the solution of the original Navier-Stokes simulation, including the mean velocity profile, the kinetic energy of the streamwise velocity component, and every term in the energy budget equation. It is suggested that the SED-based studies of turbulent structure builds a bridge between the studies of physical mechanisms of turbulence and the development of accurate model equations for engineering predictions.

Numerical Simulation on Gas-Solid Two-Phase Turbulent Flow in FCC Riser Reactors(Ⅰ) Turbulent Gas-Solid Flow-Reaction Model

Gas-solid two-phase turbulent flows,mass transfer,heat transfer and catalytic cracking reactions areknown to exert interrelated influences in commercial fluid catalytic cracking(FCC)riser reactors.In the presentpaper,a three-dimensional turbulent gas-solid two-phase flow-reaction model for FCC riser reactors was devel-oped.The model took into account the gas-solid two-phase turbulent flows,inter-phase heat transfer,masstransfer,catalytic cracking reactions and their interrelated influence.The k-V-k_P two-phase turbulence modelwas employed and modified for the two-phase turbulent flow patterns with relatively high particle concentration.Boundary conditions for the flow-reaction model were given.Related numerical algorithm was formed and a nu-merical code was drawn up.Numerical modeling for commercial FCC riser reactors could be carried out with thepresented model.

The investigation and optimization of drag reduction in turbulent flow of Newtonian fluid passing through horizontal pipelines using functionalized magnetic nanophotocatalysts and lecithin

The nanophotocatalysts were synthesized in four stages and evaluated by FTIR, FESEM and VSM analysis. The influence of nanofluids containing functionalized magnetic Ti O2 nanophotocatalyst and dipalmitoylphosphatidylcholine lecithin in drag reduction of turbulent flow in four horizontal pipelines was studied. The effective parameters on drag reduction(nanoparticle concentration, surfactant concentration, p H and Re number) were investigated and optimized in each pipeline using response surface method. The drag reduction in 1/2 " galvanized, 3/4" galvanized, 1/2 "five-layer and 1/2" cuprous pipelines was found 99.1%, 92.5%, 87.6% and 85.2%, respectively. The model adequacy was measured using ANOVA. Based on the high determination coefficient, more than 95% of variance of experimental data in all pipelines was described by quadratic model.

Numerical investigation of velocity distribution of turbulent flow through vertically double-layered vegetation

The velocity structures of flow through vertically double-layered vegetation(VDLV)as well as single-layered rigid vegetation(SLV)were investigated computationally with a three-dimensional(3D)Reynolds stress turbulence model,using the computational fluid dynamics(CFD)code FLUENT.The detailed velocity distribution was explored with a varying initial Froude number(Fr),with consideration of the steady subcritical flow conditions of an inland tsunami.In VDLV flows,the numerical model successfully captured the inflection point in the profiles of mean streamwise velocities in the mixing-layer region around the top of short submerged vegetation.An upward and downward movement of flow occurred at the positions located just behind the tall and short vegetation,respectively.Overall,higher streamwise velocities were observed in the upper vegetation layer due to high porosity,with Pr=98%(sparse vegetation,where Pr is the porosity),as compared to those in the lower vegetation layer,which had comparatively low porosity,with Pr=91%(dense vegetation).A rising trend of velocities was found as the flow passed through the vegetation region,followed by a clear sawtooth distribution,as compared to the regions just upstream and downstream of vegetation where the flow was almost uniform.In VDLV flows,a rising trend in the flow resistance was observed with the increase in the initial Froude number,i.e.,Fr?0.67,0.70,and 0.73.However,the flow resistance in the case of SLV was relatively very low.The numerical results also show the flow structures within the vicinity of short and tall vegetation,which are difficult to attain through experimental measurements.

Effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows

As the Reynolds number increases, the skin friction has been identified as the dominant drag in many practical applications. In the present paper, the effects of the Reynolds number on the mean skin friction decomposition in turbulent channel flows up to Reτ= 5 200 are investigated based on two different methods, i.e., the FukagataIwamoto-Kasagi(FIK) identity(FUKAGATA, K., IWAMOTO, K., and KASAGI, N.Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows.Physics of Fluids, 14(11), L73–L76(2002)) and the Renard-Deck(RD) identity(DECK,S., RENARD, N., LARAUFIE, R., and WEISS, P.′E. Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Reθ= 13 650.Journal of Fluid Mechanics, 743, 202–248(2014)). The direct numerical simulation(DNS) data provided by Lee and Moser(LEE, M. and MOSER, R. D. Direct numerical simulation of turbulent channel flow up to Reτ≈ 5 200. Journal of Fluid Mechanics,774, 395–415(2015)) are used. For these two skin friction decomposition methods, their decomposed constituents are discussed and compared for different Reynolds numbers.The integrands of the decomposed constituents are locally analyzed across the boundary layer to assess the actions associated with the inhomogeneity and multi-scale nature of turbulent motion. The scaling of the decomposed constituents and their integrands are presented. In addition, the boundary layer is divided into three sub-regions to evaluate the contributive proportion of each sub-region with an increase in the Reynolds number.

Study of Turbulent Flow of Film Cooling Holes with Lateral Expanded Exits

Hot wire measurements and flow visualization are presented for studying the turbulent flow field over a flat gas turbine film cooling blade with lateral expanded holes. Three mass flux ratios of jet to free stream, M = 0.5, 0.89, 1.5, are tested. The streamwise velocity, the turbulent intensities and the Reynolds shear stress are measured. The effect of the lateral expanded holes on the improvement of the turbulent flow field for film cooling of gas turbines can be analyzed from the measured spatial di...

Study on Quantitative Relationship between Surface Wettability and Frictional Coefficient of Liquid Flowing in a Turbulent Horizontal Pipe

This paper had investigated the effects of surface wettability on the frictional resistance of turbulent horizontal flow for tap water in five pipes made of various materials and four kinds of liquids in a polytetrafluoroethylene(PTFE) pipe,with the same inner diameter of 14 mm. Pressure drops were measured under different flow rates through an experimental flow loop. The contact angles and adhesion work of liquids in contact with pipe surfaces were determined using a contact angle meter. Based on the dimension and regression analyses, two kinds of modified relationships between the frictional coefficient and the surface wettability were established according to the measured results corresponding to tap water in five pipes and four liquids in PTFE pipe. The experimental results show that the surface wettability has some influence on frictional coefficient of the studied liquids flowing in macroscale pipes, and the frictional coefficient decreases with the increase of the contact angle at the same Reynolds number. Meanwhile the effect of wettability on the hydrophobic surface is greater than that on the hydrophilic one. The frictional coefficients predicted by the modified formulas have verified to be in good agreement with the experimental values, the relative errors of which are within ±6% and ±3% for the tap water flowing in five different pipes and four kinds of liquids flowing in PTFE pipe, respectively.

Solution of general dynamic equation for nanoparticles in turbulent flow considering fluctuating coagulation

A new averaged general dynamic equation （GDE） for nanoparticles in the turbulent flow is derived by considering the combined effect of convection, Brownian diffusion, turbulent diffusion, turbulent coagulation, and fluctuating coagulation. The equation is solved with the Taylor-series expansion moment method in a turbulent pipe flow. The experiments are performed. The numerical results of particle size distribu- tion correlate well with the experimental data. The results show that, for a turbulent nanoparticulate flow, a fluctuating coagulation term should be included in the averaged particle GDE. The larger the Schmidt number is and the lower the Reynolds number is, the smaller the value of ratio of particle diameter at the outlet to that at the inlet is. At the outlet, the particle number concentration increases from the near-wall region to the near-center region. The larger the Schmidt number is and the higher the Reynolds num- ber is, the larger the difference in particle number concentration between the near-wall region and near-center region is. Particle polydispersity increases from the near-center region to the near-wall region. The particles with a smaller Schmidt number and the flow with a higher Reynolds number show a higher polydispersity. The degree of particle polydispersity is higher considering fluctuating coagulation than that without considering fluctuating coagulation.