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.

Fluctuation Velocity Correlation Closure Model for Dense Gas-Particle Turbulent Flow

Turbulence model of kg-εg-kp-εp-kpg-θ is proposed.In the model,the two-phase velocity correlation turbulent kinetic energy k pg is modeled by transport equation.To close this turbulence model,algebraic expressions of two-phase Reynolds stresses and two-phase velocity correlation variable are established by considering both gas-particle interaction and anisotropy.This turbulence model is used to simulate dense gas-particle flow in a riser and in a downer.The predicted results show the core-annulus flow structure observed in the riser and the skin effect of particle concentration in the downer.The present model gives simulation results in much better agreement with the experimental results than those obtained by kg-εg-kp-εp-θmodel which is simply closed using a semi-empirical dimensional analysis.

Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows

Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

Turbine Passage Secondary Flow Dynamics and Endwall Heat Transfer Under Different Inflow Turbulence

This study presents endwall hydrodynamics and heat transfer in a linear turbine cascade at Re 5×105 at low and high intensities of turbulence.Results are numerically predicted using the standard SST model and Reθ-γtransition model as well as using the high-resolution LES separately.The major secondary flow components,comprising the horseshoe,corner,and passage vortices are recognized and the impact on heat or mass transfer is investigated.The complicated behavior of turbine passage secondary flow generation and establishment are impacted by the perspective of boundary layer attributes and inflow turbulence.The passage vortex concerning the latest big leading-edge vane is generated by the enlargement of the circulation developed at the first instance adjacent to the pressure side becomes powerful and mixes with other vortex systems during its migration towards the suction side.The study conclusions reveal that substantial enhancements are attained on the endwall surface,for the entire spanwise blade extension on the pressure surface,and in the highly 3-D region close to the endwall on the suction surface.The forecasted suction surface thermal exchange depicts great conformity with the measurement values and precisely reproduces the enhanced thermal exchange owing to the development and lateral distribution of the secondary flows along the midspan of the blade passage downstream.The impacts of the different secondary flow structures on the endwall thermal exchange are described in depth.

Analysis of particle dispersion in a turbulent flow considering particle rotation

Non-spherical particles exist widely in natural and industrial fluid systems and the motions of nonspherical particles are significantly different from that of spherical particles.In this paper,a simplified model of non-spherical particles considering particle drag correction,lift,and rotation was established.Based on the Eulerian-Lagrangian simulation,the dispersion characteristics of spherical and nonspherical particles with different Stokes numbers in a high-speed turbulent jet were analyzed and compared considering the effect of particle rotation.The results show that,the differences in particle dispersion and radial velocity fluctuation between non-spherical particles and spherical particles in the jet are significant,especially when Stokes number is large.Moreover,the effects of different type of forces on the dispersion of non-spherical particles and spherical particles were compared in detail,which revealed that the change of the Magnus force caused by the increase in the angular velocity of non-spherical particles plays a dominant role in the differences of particle dispersion.

Observed characteristics of flow,water mass,and turbulent mixing in the Preparis Channel

Preparis Channel is the very important exchange path of energy and materials between the northern Bay of Bengal and Andaman Sea(AS).A set of hydrographic measurements,a microstructure profiler,and a deep mooring were used to determine the characteristics of water masses,turbulent mixing,and flows in the Preparis Channel.The unprecedented short-term mooring data reveal that a deep current in the deep narrow passage(below 400 m)of the Preparis Channel flows toward the Bay of Bengal(BoB)with a mean along-stream velocity of 25.26 cm/s at depth of 540 m;above the deep current,there are a relatively weak current flows toward the AS with a mean along-stream velocity of 15.46 cm/s between 500 m and 520 m,and another weak current flows toward the BoB between 430 m and 500 m.Thus,a sandwiched vertical structure of deep currents(below 400 m)is present in the Preparis Channel.The volume transport below 400 m is 0.06 Sv(1 Sv=106 m^(3)/s)from the AS to the BoB.In the upper layer(shallower than 300 m),the sea water of the AS is relatively warmer and fresher than that in the BoB,indicating a strong exchange through the channel.Microstructure profiler observations reveal that the turbulent diffusivity in the upper layer of the Preparis Channel reaches O(10−4 m^(2)/s),one order larger than that in the interior of the BoB and over the continental slope of the northern AS.We speculate that energetic high-mode internal tides in the Preparis Channel contribute to elevated turbulent mixing.In addition,a local“hotspot”of turbidity is identified at the deep mooring site,at depth of about 100 m,which corresponds to the location of elevated turbulent mixing in the Preparis Channel.

Artificial neural network-based subgrid-scale models for LES of compressible turbulent channel flow

Fully connected neural networks(FCNNs)have been developed for the closure of subgrid-scale(SGS)stress and SGS heat flux in large-eddy simulations of compressible turbulent channel flow.The FCNNbased SGS model trained using data with Mach number Ma=3.0 and Reynolds number Re=3000 was applied to situations with different Mach numbers and Reynolds numbers.The input variables of the neural network model were the filtered velocity gradients and temperature gradients at a single spatial grid point.The a priori test showed that the FCNN model had a correlation coefficient larger than 0.91 and a relative error smaller than 0.43,with much better reconstructions of SGS unclosed terms than the dynamic Smagorinsky model(DSM).In a posteriori test,the behavior of the FCNN model was marginally better than that of the DSM in predicting the mean velocity profiles,mean temperature profiles,turbulent intensities,total Reynolds stress,total Reynolds heat flux,and mean SGS flux of kinetic energy,and outperformed the Smagorinsky model.

Simulation Analysis of New Energy Vehicle Engine Cooling System Based on K-E Turbulent Flow Mathematical Model

New energy vehicles have better clean and environmental protection characteristics than traditional fuel vehicles.The new energy engine cooling technology is critical in the design of new energy vehicles.This paper used oneand three-way joint simulation methods to simulate the refrigeration system of new energy vehicles.Firstly,a k-εturbulent flow model for the cooling pump flow field is established based on the principle of computational fluid dynamics.Then,the CFD commercial fluid analysis software FLUENT is used to simulate the flow field of the cooling pump under different inlet flow conditions.This paper proposes an optimization scheme for new energy vehicle engines’“boiling”phenomenon under high temperatures and long-time climbing conditions.The simulation results show that changing the radiator’s structure and adjusting the thermostat’s parameters can solve the problem of a“boiling pot.”The optimized new energy vehicle engine can maintain a better operating temperature range.The algorithm model can reference each cryogenic system component hardware selection and control strategy in the new energy vehicle’s engine.

A USM-Θ two-phase turbulence model for simulating dense gas-particle flows

A second-order moment two-phase turbulence model for simulating dense gas-particle flows （USM-Θ model）, combining the unified second-order moment twophase turbulence model for dilute gas-particle flows with the kinetic theory of particle collision, is proposed. The interaction between gas and particle turbulence is simulated using the transport equation of two-phase velocity correlation with a two-time-scale dissipation closure. The proposed model is applied to simulate dense gas-particle flows in a horizontal channel and a downer. Simulation results and their comparison with experimental results show that the model accounting for both anisotropic particle turbulence and particle-particle collision is obviously better than models accounting for only particle turbulence or only particle-particle collision. The USM-Θ model is also better than the k-ε-kp-Θ model and the k-ε-kp-εp-Θ model in that the first model can simulate the redistribution of anisotropic particle Reynolds stress components due to inter-particle collision, whereas the second and third models cannot.

Large Eddy Simulation of Particle Wake Effect and RANS Simulation of Turbulence Modulation in Gas-Particle Flows

The turbulence enhancement by particle wake effect is studied by large eddy simulation （LES） of turbulent gas flows passing a single particle. The predicted time-averaged and root-mean-square fluctuation velocities behind the particle are in agreement with the Reynolds-averaged Navier-Stokes modeling results and experimental results. A semi-empirical turbulence enhancement model is proposed by the present-authors based on the LES resuits. This model is incorporated into the second-order moment two-phase turbulence model for simulating vertical gas-particle pipe flows and horizontal gas-particle channel flows. The simulation results show that compared with the model not accounting for the particle wake effect, the present model gives simulation results for the gas turbulence modulation in much better agreement with the experimental results.

Studies on gas turbulence and particle fluctuation in dense gas-particle flows

Particle fluctuation and gas turbulence in dense gas-particle flows are less studied due to complexity of the phenomena. In the present study, simulations of gas turbulent flows passing over a single particle are carried out first by using RANS modeling with a Reynolds stress equation turbulence model and sufficiently fine grids, and then by using LES. The turbulence enhancement by the particle wake effect is studied under various particle sizes and relative gas velocities, and the turbulence enhancement is found proportional to the particle diameter and the square of velocity. Based on the above results, a turbulence enhancement model for the particle-wake effect is proposed and is incorporated as a sub-model into a comprehensive two-phase flow model, which is then used to simulate dilute gas-particle flows in a horizontal channel. The simulation results show that the predicted gas turbulence by using the present model accounting for the particle wake effect is obviously in better agreement with the experimental results than the prediction given by the model not accounting for the wake effect. Finally, the proposed model is incorporated into another two-phase flow model to simulate dense gasparticle flows in a downer. The results show that the particle wake effect not only enhances the gas turbulence, but also amplifies the particle fluctuation.

A two-scale second-order moment two-phase turbulence model for simulating dense gas-particle flows

A two-scale second-order moment two-phase turbulence model accounting for inter-particle collision is developed, based on the concepts of particle large-scale fluctuation due to turbulence and particle small-scale fluctuation due to collision and through a unified treatment of these two kinds of fluctuations. The proposed model is used to simulate gas-particle flows in a channel and in a downer. Simulation results are in agreement with the experimental results reported in references and are near the results obtained using the sin- gle-scale second-order moment two-phase turbulence model superposed with a particle collision model （USM-θ model） in most regions.

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.

Numerical simulation of gas–liquid flow in the bubble column using Wray–Agarwal turbulence model coupled with population balance model

In this paper,an improved computational fluid dynamic(CFD)model for gas-liquid flow in bubble column was developed using the one-equation Wary-Agarwal(WA)turbulence model coupled with the population balance model(PBM).Through 18 orthogonal test cases,the optimal combination of interfacial force models,including drag force,lift force,turbulent dispersion force.The modified wall lubrication force model was proposed to improve the predictive ability for hydrodynamic behavior near the wall of the bubble column.The values simulated by optimized CFD model were in agreement with experimental data,and the errors were within±20%.In addition,the axial velocity,turbulent kinetic energy,bubble size distribution,and the dynamic characteristic of bubble plume were analyzed at different superficial gas velocities.This research work could provide a theoretical basis for the extension of the CFD-PBM coupled model to other multiphase reactors..

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.

ON BASIC EQUATIONS OF TURBULENT SWIRLING GAS-SOLID FLOWS AND THEIR APPLICATION IN CYCLONES

The basic equations of turbulent gas-solid flows are derived by using the pseudo-fluid model of particle phase with a refined two-phase turbulence model.These equations are then applied to swirling gas-particle flows for analyzing the collection efficiency in cyclone separators.