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.

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.

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.

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.

Characteristics of turbulent flow distribution in branch piping system

Flow distribution in branch piping system is affected by flow characteristics and different geometric variations. Most of the flow distribution studies are performed with one-dimensional analysis to yield overall information only. However, detailed analysis is required to find effects of design parameters on the flow distribution. For this aspect, three-dimensional turbulent flow analysis was performed to assess turbulence model performance and effects of upstream pressure and branch pipe geometry. Three different turbulence models of standard k-e model, realizable k-e model and standard k-co yield similar results, indicating small effects of turbulence models on flow characteristics analysis. Geometric variations include area ratio of main and branch pipes, branch pipe diameter, and connection shape of main and branch pipes. Among these parameters, area ratio and branch diameter and shape show strong effect on flow distribution due to high friction and minor loss. Uniform flow distribution is one of common requirements in the branch piping system and this can be achieved with rather high total loss design.

Effect of Downward Seepage on Turbulent Flow Characteristics and Bed Morphology around Bridge Piers

In this work, experimental investigations have been pursued to analyse the influence of downward seepage on the turbulent characteristics of flow and corresponding changes in vortex structure around circular bridge pier in alluvial channel. Experiments were conducted in sand bed channel with circular piers of different sizes for no seepage, 10% seepage and 20% seepage cases. The measurement of turbulent flow statistics such as velocity and Reynolds stresses is found to be negative within the scour hole at upstream of the pier whereas application of downward seepage retards the reversal of the flow causing a decrement in the velocity and Reynolds stresses. Higher Reynolds shear stress prevails at the downstream side because of the production of wake vortices. Contribution of all bursting events to the total Reynolds shear stress production has been observed to increase with downward seepage. The analysis of integral scale suggest that size of eddies increases with seepage, which is responsible for increase in particle mobility. Initially rate of scouring is more which abatements gradually with expanding time as well as with the increased of downward seepage. Presence of downward seepage reduces the depth and length of vortex and shifts towards downstream side of the pier.

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...

Assessment of k–ε models using tetrahedral grids to describe the turbulent flow field of a PBT impeller and validation through the PIV technique

In turbulence modeling, the RNG and Realizable models have important improvements in the turbulent production and dissipation terms in comparison to the Standard. The selection of the appropriate turbulence model has an impact on the convergence and solution in STRs, and they are used in mixing, multiphase modeling or as starting solution of transient models as DES and LES. Although there are several studies with the pitched blade turbine(PBT) impeller, most of them used the Standard model as representative of all k–ε models, using structured hexahedral grids composed of low number of cells, and in some cases under axial symmetry assumptions.Accordingly, in this work the assessment of the Standard, RNG and Realizable models to describe the turbulent flow field of this impeller, using the Multiple Reference Frame(MRF) and Sliding Mesh(SM) approaches with tetrahedral domains in dense grids, is presented. This kind of cell elements is especially suitable to reproduce complex geometries. Flow velocities and turbulent parameters were verified experimentally by PIV and torque measurements. The three models were capable of predicting fairly the pumping number, the power number based on torque, and velocities. Although the RNG improved the predictions of the turbulent kinetic energy and dissipation rate, the Realizable model presented better performance for both approaches. All models failed in the prediction of the total dissipation rate, and a dependence of its value on the number of cells for the MRF was found.

Numerical Simulation of Turbulent Flow of Hydraulic Oil through 90° Circular-sectional Bend

Oil flow through pipe bends is found in many engineering applications. However, up to now, the studies of oil flow field in the pipe bend appear to be relatively sparse, although the oil flow field and the associated losses of pipe bend are very important in practice. In this paper, the relationships between the turbulent flow of hydraulic oil in a bend and the Reynolds number Re and the curvature ratio δare studied by using computational fluid dynamics （CFD）. A particular emphasis is put on hydraulic oil, which differs from air or water, flowing through 90° circular-sectional bend, with the purpose of determining the turbulent flow characteristics as well as losses. Three turbulence models, namely, RNG κ-ε model, realizable k-ε model, and Reynolds stress model （RSM）, are used respectively. The simulation results in the form of contour and vector plots for all the three turbulence models for pipe bends having curvature ratio of δ=0.5, and the detailed pressure fields and total pressure losses for different Re and δ for RSM are presented. The RSM can predict the stronger secondary flow in the bend better than other models. As Re increases, the pressure gradient changes rapidly, and the pressure magnitude increases at inner and outer wall of the bend. When δ decreases, two transition points or transition zones of pressure gradient arise at inner wall, meanwhile, the transition point moves towards the inlet at outer wall of the bend. Owing to secondary flow, the total pressure loss factor k increases as the bend tightens, on the contrary, as Re increases, factor k decreases due to higher velocity heads, and the rapid change of pressure gradient on the surface of the bend leads to increasing of friction and separation effects, and magnified swirl intensity of secondary flow. A new mathematical model is proposed for predicting pressure loss in terms of Re and δ in order to provide support to the one-dimensional simulation software. The proposed research provides reference for the analysis of oil flow with higher Re in the large bends.

NUMERICAL SIMULATION FOR INCOMPRESSIBLE TURBULENT FLOW IN THE IMPELLER OF SEWAGE PUMP

The 3-D turbulent flow in the impeller of sewage pump is simulated. Thetime-averaged N-S equations and the kappa-epsilon turbulent model is modified. The calculation iscarried out in body-fitted coordinated grid by applying SIMPLE-C algorithm. The calculated velocity,pressure distributions of the turbulent flow in the sewage pump are obtained for the first time,which will be helpful for the optimal design and performance prediction of sewage pumps on the basisof flow field simulation.

Simultaneous determination of 15 pesticide residues in Chinese cabbage and cucumber by liquid chromatography-tandem mass spectrometry utilizing online turbulent flow chromatography

In this experiment,a liquid chromatography tandem mass spectrometry method was built to determine 15 pesticide residues in Chinese cabbage and cucumber samples based on online turbulent flow chromatography purification.After modified quick,easy,cheap,effective,rugged,and safe(QuEChERS)extraction,extracts were directly injected to the TLX(TurboFlow Liquid Xcalibur)system and brought to TurboFlow™columns for on-line purification and then transferred to analytical column for further separation and analysis.TurboFlow™columns types,transfer flow rate,and transfer time were optimized.Limits of detection and limits of quantification of the method obtained for 15 pesticide residues were ranged between 0.2–1.0μg/kg and 0.5–2.0μg/kg in Chinese cabbage and cucumber samples.Recoveries of pesticide residues were in range of 75.3%–103.7%.Matrix effects for 15 pesticides were in range of 5.6%–106.6%.The developed method has been successfully used for the determination of 15 pesticide residues in real samples.

Numerical simulation on turbulent flow field in convergentdiveroent nozzle

Because of the complication of turbulence＇s mechanism and law as well as the jet pressure in nozzle is difficult to test by experiment, five turbulent models were applied to numerically simulate the turbulent flow field in convergent-divergent nozzle. Theory analysis and experiment results of mass flow rates conclude that the RNG k-ε model is the most suitable model. The pressure distribution in the convergent-divergent nozzle was revealed by computational fluid dynamic （CFD） simulating on the turbulent flow field under different pressure conditions. The growing conditions of cavitation bubbles were shown; meanwhile, the phenomena in the experiment could be explained. The differential pres- sure between the upstream and downstream in nozzle throat section can improve the cavitating effect of cavitation water jet.

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.

Computational Simulation of Turbulent Flow Around Tractor-Trailers

A method to evaluate the properties of turbulent flow in proximity to the vehicle and close to the ground surface has been elaborated.Numerical simulations have been performed on the basis of the Unsteady Reynolds-averaged Navier-Stokes equations(URANS)written with respect to an arbitrary curvilinear coordinate system.These equations have been solved using the Spalart-Allmaras differential one-parametric turbulence model.The method of artificial compressibility has been used to improve the coupling of pressure and velocity in the framework of a finite volume approach.Time-averaged distributions of pressure fields,velocity components,streamlines in the entire area and near the tractor-trailer,as well as integral and distributed characteristic parameters(such as coefficients of pressure,friction and drag force)are presented.According to our results,the turbulent flow accelerates in the area of the tractor cabin and in the gap between surfaces.Above the driver’s cabin,a pressure drop occurs due to a sharp acceleration of flow in this area.Downstream,pressure is restored and becomes almost constant in proximity to the edge of the trailer.The dimensions of the separation area exceed the length of the transport system several times.Though agreement with experimental results is relatively limited due to the two-dimensional nature of the numerical simulations,the present approach succeeds in identifying the main physical effects involved in the considered dynamics.It might be used in future studies for initial approximate assessments of the influence of the vehicle shape on its aerodynamic characteristics.

Investigation of scale efect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers （criteria） based on turbulent kinetic and dissipation rates associ- ated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged NavierStokes equations （RANS）. The RNG k-s models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to l07 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥ 3 × 10^6. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.

Improvement of Prandtl mixing length theory and application in modeling of turbulent flow in circular tubes

In order to correctly predict tube cross section time-smoothed velocity distribution, friction factor and mass transfer behavior, two models for turbulent flow in circular tubes based on classical Prandtl mixing length theory and a modified mixing length were established. The results show that the modified mixing length includes the introduction of a damping function for the viscous sublayer and the second-order derivative to approximate eddy velocity. The calculated dimensionless time-smoothed velocity from the model based on Prandtl mixing length is much better than the result from the concept of eddy viscosity. The calculated eddy viscosity from the model based on modified mixing length is much better than the result from the model based on the classical Prandtl mixing length theory. And the friction factor calculated from the model based on the modified mixing length agrees well with the reported empirical relationships.

Numerical Simulation of the Effect of Air Distribution on Turbulent Flow and Combustion in a Tubular Heating Furnace

A three-dimension full-size numerical simulation of the effect of air distribution on turbulent flow and combustion in a tubular heating furnace was carried out. A standard k –ε turbulent model, a simplified PDF combustion model and a discrete ordinate transfer radiation model were used. The hybrid grid combining a structured and a non-structured grid was generated without any simplification of the complicated geometric configuration around the burner. It was found that the multistage combustion could reduce and control the peak value of temperature. At the same time, it was concluded that the amount of primary air had little effect on the global distribution of velocity and temperature in the furnace, but a great effect on that around the burner. It is recommended that 45% - 65% of the total amount of air be taken in in primary air inlets in the furnace. All the results are important to optimize the combustion progress.

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.

NUMERICAL STUDY OF AN OSCILLATORY TURBULENT FLOW OVER A FLAT PLATE

Oscillatory turbulent flow over a flat plate was studied by using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model was employed in LES and Saffman's turbulence model was used in RANS. The flow behaviors were discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime were also investigated for different Reynolds numbers. (Edited author abstract) 11 Refs.

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.