ALGEBRAIC TURBUL ENCE MODEL WITH MEM ORY FOR COMPUTATION OF 3-D TURBULENT BOUNDARY LAYERS WITH VALIDATION

Additional equations were found based on experiments for an algebraic turbulence model to improve the prediction of the behavior of three dimensional turbulent boundary layers by taking account of the effects of pressure gradient and the historical variation of eddy viscosity, so the model is with memory. Numerical calculation by solving boundary layer equations was carried out for the five pressure driven three dimensional turbulent boundary layers developed on flat plates, swept wing, and prolate spheroid in symmetrical plane. Comparing the computational results with the experimental data, it is obvious that the prediction will be more accurate if the proposed closure equations are used, especially for the turbulent shear stresses.

Effect of Counter-Gradient in the Computation of Turbulent Fluxes of Heat and Moisture in a Regional Model

The counter-gradient terms in the computations of turbulent fluxes of heat and moisture have been included in the PBL parameterization of a regional model for monsoon prediction. Results show that inclusion of counter-gradient terms has a marginal impact in the prediction of large scale monsoon circulation and rainfall rates.

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.

Comparison of the Reynolds-averaged Turbulence Models on Single Phase Flow Simulation in Agitated Extraction Columns

The flow field of liquid phase (water) of agitated extraction columns is simulated with the help of computational fluid dynamics (CFD). Four kinds of Reynolds-averaged turbulence models, i.e. the standard k-ε model, the RNG (renormalization group) k-s model, the realizable k-ε model and the Reynolds stress model, are compared in detail in order to judge which is the best model in terms of the accuracy, less CPU time and memory required. The performance of the realizable k-s model is obviously improved by reducing the model constant from C2 = 1.90 to C2 = 1.61. It is concluded that the improved realizable k-e model is the optimal model.

Numerical Modelling of Proppant Transport in Hydraulic Fractures

The distribution of proppant injected in hydraulic fractures significantly affects the fracture conductivity and well performance.The proppant transport in thin fracturing fluid used during hydraulic fracturing in the unconventional reservoirs is considerably different from fracturing fluids in the conventional reservoir due to the very low viscosity and quick deposition of the proppants.This paper presents the development of a three-dimensional Computational Fluid Dynamics(CFD)modelling technique for the prediction of proppant-fluid multiphase flow in hydraulic fractures.The proposed model also simulates the fluid leak-off behaviour from the fracture wall.The Euler-Granular and CFD-Discrete Element Method(CFD-DEM)multiphase modelling approach has been applied,and the equations defining the fluid-proppant and inter-proppant interaction have been solved using the finite volume technique.The proppant transport in hydraulic fractures has been studied comprehensively,and the computational modelling results of proppant distribution and other flow properties are in good agreement with the published experimental study.The parametric study is performed to investigate the effect of variation in proppant size,fluid viscosity and fracture width on the proppant transport.Smaller proppants can be injected early,followed by larger proppants to maintain high propping efficiency.This study has enhanced the understanding of the complex flow phenomenon between proppant and fracturing fluid and can play a vital role in hydraulic fracturing design.

A turbulent mass diffusivity model for analyzing the mixing characteristics in an impinging stream-rotating packed bed

In this study,the fluid flow and mixing process in an impinging stream-rotating packed bed(IS-RPB)is simulated by using a new three-dimensional computational fluid dynamics model.Specifically,the gaseliquid flow is simulated by the Euler-Euler model,the hydrodynamics of the reactor is predicted by the RNG k-εmethod,and the high-gravity environment is simulated by the sliding mesh model.The turbulent mass transfer process is characterized by the concentration variance c^(2) and its dissipation rateεc formulations,and therefore the turbulent mass diffusivity can be directly obtained.The simulated segregation index Xs is in agreement with our previous experimental results.The simulated results reveal that the fringe effect of IS can be offset by the end effect at the inner radius of RPB,so the investigation of the coupling mechanism between IS and RPB is critical to intensify the mixing process in IS-RPB.

CFD study of non-premixed swirling burners: Effect of turbulence models

This research investigates a numerical simulation of swirling turbulent non-premixed combustion.The effects on the combustion characteristics are examined with three turbulence models:namely as the Reynolds stress model,spectral turbulence analysis and Re-Normalization Group.In addition,the P-1 and discrete ordinate(DO)models are used to simulate the radiative heat transfer in this model.The governing equations associated with the required boundary conditions are solved using the numerical model.The accuracy of this model is validated with the published experimental data and the comparison elucidates that there is a reasonable agreement between the obtained values from this model and the corresponding experimental quantities.Among different models proposed in this research,the Reynolds stress model with the Probability Density Function(PDF)approach is more accurate(nearly up to 50%)than other turbulent models for a swirling flow field.Regarding the effect of radiative heat transfer model,it is observed that the discrete ordinate model is more precise than the P-1 model in anticipating the experimental behavior.This model is able to simulate the subcritical nature of the isothermal flow as well as the size and shape of the internal recirculation induced by the swirl due to combustion.

Assessment of Turbulence Models on Bridge-Pier Scour Using Flow-3D

The main purpose of this paper is to analyze the influence of different turbulence flow models on scouring pit of bridge-pier. Flow-3D software is applied in line with the purpose. The key motivation for this study is to contribute to the Flow-3D software by means of some modification and adjustment in the sediment scour model and shallow water model. An assessment of turbulence model adopted with the parameters of the Melville experiment to estimate the maximum scour-depth was performed. In the simulation results, the alternate eddy formation and shedding were repeated while the Karman vortex street formed behind the pier for the large eddy simulation LES turbulence model is more realistic in the flow phenomenon. The results of the scour development of large eddy simulation (LES) turbulence model were found to be more satisfied than the Renormalized group (RNG) turbulence model and close to the prior experiment results. The simulated scour results were significantly different with the observed data collected from previous literature in the reason of some unsuitability of meshing method in Flow-3D software.

Three-Di mensional Computations of Multiple TandemJets in Crossflow

The mixing and merging characteristics of multiple tandem jets in crossflow are investigated by use of the Computational Fluid Dynamics （CFD） code FI,UENT. The realizable k - ε model is employed for turbulent elosure of the Reynolds-averaged Navier-Stokes equations. Numerical experiments are performed for 1-, 2- and 4-jet groups, tbr jet-tocrossflow velocity ratios of R = 4.2 ～ 16.3. The computed velocity and scalar concentration field are in good agreement with experiments using Particle Image Velocimetry （PIV） and Laser Induced Fluorescence （LIF）, as well as previous work. The results show that the leading jet behavior is similar to a single free jet in crossflow, while all the downstream rear jets have less bent-over jet trajectories - suggesting a reduced ambient velocity for the rear jets. The concentration decay of the leading jet is greater than that of the rear jets. When normalized by appropriate crossflow momentum length scales, all jet trajectories follow a universal relation regardless of the sequential order of jet position and the nund）er of jets. Supported by the velocity and trajectory measurements, the averaged maximum effective crossflow velocity ratio is computed to be in the range of 0.39 to 0.47.

Theoretical and numerical study of hydraulic characteristics of orifice energy dissipator

Different factors affecting the efficiency of the orifice energy dissipator were investigated based on a series of theoretical analyses and numerical simulations. The main factors investigated by dimension analysis were identified, including the Reynolds number （Re）, the ratio of the orifice diameter to the inner diameter of the pipe （ did ）, and the ratio of distances between orifices to the inner diameter of the pipe （ LID ）. Then, numerical simulations were conducted with a k-ε two-equation turbulence model. The calculation results show the following： Hydraulic characteristics change dramatically as flow passes through the orifice, with abruptly increasing velocity and turbulent energy, and decreasing pressure. The turbulent energy appears to be low in the middle and high near the pipe wall. For the energy dissipation setup with only one orifice, when Re is smaller than 105, the orifice energy dissipation coefficient K increases rapidly with the increase of Re. When Re is larger than l05, K gradually stabilizes. As diD increases, K and the length of the recirculation region L1 show similar variation patterns, which inversely vary with diD. The function curves can be approximated as straight lines. For the energy dissipation model with two orifices, because of different incoming flows at different orifices, the energy dissipation coefficient of the second orifice （K2） is smaller than that of the first. If LID is less than 5, the K value of the LID model, depending on the variation of/（2, increases with the spacing between two orifices L, and an orifice cannot fulfill its energy dissipation function. If LID is greater than 5, K2 tends to be steady; thus, the K value of the LID model gradually stabilizes. Then, the flow fully develops, and L has almost no impact on the value of K.

Dynamic Performance Research on Reversing Valve of Hydraulic Breaker

The structure and operational principle on a new type reversing valve of hydraulic breaker are introduced. The nonlinear mathematic model and simulation model of the new type reversing valve are built. The dynamic simulation research of the new type reversing valve is conducted. The effects of the system parameters on the working performance are researched systematically and deeply. The regular understanding on the motion of the reversing valve is obtained, which provides theoretical basis for the innovation and manufacturing of a new generation of hydraulic breaker reversing valve.

Influence of Swimming Pool Design on Hydraulic Behavior: A Numerical and Experimental Study

A swimming pool can be considered as a chemical reactor with specific hydraulic and macro-mixing characteristics. The nature of flow into the pool depends on various characteristics, such as water inlets and outlets (number and position), pool geometry, and flow rate. This study investigates how swimming pool design affects hydraulic behavior based on experimental and computational fluid dynamics studies (CFD). This paper does not describe the hydraulic behavior of all existing swimming pools, however the cases studied here are representative of pool designs widely used in Europe and the United States. The model developed, based on the principle of a stirred reactor, could be used as a first approach in describing the hydraulic behavior of regular pools. This model is suitable for the study of physical and chemical phenomena with long characteristic times. Other, more advanced, models were shown to be more suitable to the case of fast chemical processes.

Deep learning to develop zero-equation based turbulence model for CFD simulations of the built environment

This study aims to improve the accuracy and speed of predictions for thermal comfort and air quality in built environments by creating a coupled framework between computational fluid dynamics(CFD)simulations and deep learning models.The coupling approach is showcased by the development of a data-driven turbulence model.The new turbulence model is built using a deep learning neural network,whose mapping structure is based on a zero-equation turbulence model for built environment simulations,and is coupled with the CFD software OpenFOAM to create a hybrid framework.The neural network is a standard shallow multi-layer perceptron.The number of hidden layers and nodes per layer was optimized using Bayesan optimization algorithm.The framework is trained on an indoor environment case study,as well as tested on an indoor office simulation and an outdoor building array simulation.Results show that the deep learning based turbulence model is more robust and faster than traditional two-equation Reynolds average Navier-Stokes(RANS)turbulence models,while maintaining a similar level of accuracy.The model also outperforms the standard algebraic zero-equation model due to its superior ability to generalize to various flow scenarios.Despite some challenges,namely the mapping constraint,the limited training dataset size and the source of generation of training data,the hybrid framework demonstrates the viability of the coupling technique and serves as a starting point for future development of more reliable and advanced models.

New prospects for computational hydraulics by leveraging high-performance heterogeneous computing techniques

In the last two decades, computational hydraulics has undergone a rapid development following the advancement of data acquisition and computing technologies. Using a finite-volume Godunov-type hydrodynamic model, this work demonstrates the promise of modern high-performance computing technology to achieve real-time flood modeling at a regional scale. The software is implemented for high-performance heterogeneous computing using the OpenCL programming framework, and developed to support simulations across multiple GPUs using a domain decomposition technique and across multiple systems through an efficient implementation of the Message Passing Interface （MPI） standard. The software is applied for a convective storm induced flood event in Newcastle upon Tyne, demonstrating high computational performance across a GPU cluster, and good agreement against crowd- sourced observations. Issues relating to data availability, complex urban topography and differences in drainage capacity affect results for a small number of areas.

Computation method and control strategy of rotating separation flows in hydraulic machinery

Rotating separation flow(RSF)in hydraulic machinery is characterized by the large flow separations and complex vortical structures induced by the effects of strong rotation,large curvature and multiple wall surfaces,and conducting efficient engineering computation and putting forward effective control strategy for the RSF are important topics in the inner flow theory.To meet these engineering requirements,the studies on computational method and control strategy of the RSF are conducted in this paper.In terms of the computational method,the time-scale-driven(TSD)hybrid unsteady Reynolds-averaged Navier-Stokes/large eddy simulation(URANS/LES)modelling strategy is clarified,and an adaptive TSD hybrid model is established based on the RSF characteristics in hydraulic machinery,thereby avoiding the problem of non-monotonic grid convergence and improving the robustness.Besides,a novel vortex-feature-driven idea suitable for the RSF is further developed inspired by it.In terms of the control strategy,the secondary flow generation mechanism in a rotor domain is revealed,and the relationship between natural secondary flows and blade loading distributions is grasped.On the basis of it,an active control strategy with general significance is proposed,and a general alternate loading technique(GALT)is established.Both aspects can provide generalized paradigms with expandable potential,which are of benefit to the efficient computation and effective control of the RSF in hydraulic machinery.

Numerical Simulation of Blood Flow in Aorta with Dilation:A Comparison between Laminar and LES Modeling Methods

Computational modeling methods have been increasingly employed to quantify aortic hemodynamic parameters that are challenging to in vivo measurements but important for the diagnosis/treatment of aortic disease.Although the presence of turbulence-like behaviors of blood flow in normal or diseased aorta has long been confirmed,the majority of existing computational model studies adopted the laminar flow assumption(LFA)in the treatment of sub-grid flow variables.So far,it remains unclear whether LFA would significantly compromise the reliability of hemodynamic simulation.In the present study,we addressed the issue in the context of a specific aortopathy,namely aortic dilation,which is usually accompanied by disturbed flow patterns.Three patient-specific aortas with treated/untreated dilation of the ascending segment were investigated,and their geometrical models were reconstructed from computed tomography angiographic images,with the boundary conditions being prescribed based on flow velocity information measured in vivo with the phase contrast magnetic resonance imaging technique.For the modeling of blood flow,apart from the traditional LFA-based method in which sub-grid flow dynamics is ignored,the large eddy simulation(LES)method capable of incorporating the dissipative energy loss induced by turbulent eddies at the sub-grid level,was adopted and taken as a reference for examining the performance of the LFA-based method.Obtained results showed that the simulated large-scale flow patterns with the two methods had high similarity,both agreeing well with in vivo measurements,although locally large between-method discrepancies in computed hemodynamic quantities existed in regions with high intensity of flow turbulence.Quantitatively,a switch from the LES to the LFAbased modeling method led to mild(<6%)changes in computed space-averaged wall shear stress metrics(i.e.,SA-TAWSS,SA-OSI)in the ascending aortic segment where intensive vortex evolution accompanied by high statistical Reynolds stress was observed.In addition,comparisons among the three aortas revealed that the treatment status of aortic dilation or the concomitant presence of aortic valve disease,despite its remarkable influence on flow patterns in the ascending aortic segment,did not significantly affect the degrees of discrepancies between the two modeling methods in predicting SA-TAWSS and SA-OSI.These findings suggest that aortic dilation per se does not induce strong flow turbulence that substantially negates the validity of LFA-based modeling,especially in simulating macro-scale hemodynamic features.

Modeling the effects of mechanical parameters on the hydrodynamic behavior of vertical current classifiers

This study modeled the effects of structural and dimensional manipulations on hydrodynamic behavior of a bench vertical current classifier. Computational fluid dynamics （CFD） approach was used as modeling method, and turbulent intensity and fluid velocity were applied as system responses to predict the over- flow cut size variations. These investigations showed that cut size would decrease by increasing diameter and height of the separation column and cone section depth, due to the decrease of turbulent intensity and fluid velocity. As the size of discharge gate increases, the overflow cut-size would decrease due to freely fluid stream out of the column. The overflow cut-size was significantly increased in downward fed classifier compared to that fed by upward fluid stream. In addition, reforming the shape of angular overflow outlet＇s weir into the curved form prevented stream inside returning and consequently unselec- tire cut-size decreasing.

Turbulent Evolution and Energetics of Lock-Release Gravity Currents

Turbulence modeling by use of the renormalization group （RNG） κ-ε model for Reynolds-stress closure is carried out to reveal the evolution dynamics for lock release gravity currents with the so-called slumping, inviscid and viscous phases. Field evolution of the turbulent current is investigated, and time transition of global energy balance is presented between the terms of potential energy, averaged kinetic energy, turbulent kinetic energy, turbulent dissipation and viscous dissipation. It is well illustrated that turbulent dissipation and viscous force are respectively dominant in the inviscid and viscous phases, while inertia effect accounts for the slumping.

CFD modeling of a headbox with injecting dilution water in a central step diffusion tube

For engineering applications of water dilution controlling system,the fluid dynamics of a mixed flow was studied with computational fluid dynamics(CFD) simulations and self-designed experimental set-up.In order to examine the predictability of CFD model for the headbox in industrial scale,two pulp suspensions before mixing were treated as homogeneous flows separately.Standard k-ε turbulence models with the mass diffusion in turbulent flows-species transport approach were applied in the simulations.A numerical simulation of this headbox model was analyzed with semi-implicit method for pressure linked equations scheme with pressure–velocity coupling.Results show that the model can predict hydrodynamic characteristics of headbox with injecting dilution water in a central diffusion tube,and the distribution of water content at the outlet of the slice lip is ideally normal at different speeds.

About One Discrete Mathematical Model of Perfect Fluid

In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical objects: circles and spheres for two-dimensional and three-dimensional cases, respectively. The mechanism of interaction between the liquid particles on a binary level and on the level of the n-cluster is formulated. This mechanism has previously been found by the author as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived and investigated the potential interaction of pairs of liquid particles, which contained a singularity of the branch point. Exactly, this is possible to build in this article discrete stochastic-deterministic model of an ideal fluid. The results of computational experiment to simulate various kinds of flows in two-dimensional and three-dimensional ensembles of liquid particles are presented. Modeling was carried out in the areas of quadratic or cubic form. On boundary of a region satisfies the condition of elastic reflection liquid particles. The flows with spontaneous separation of particles in a region, various kinds of eddy streams, with the quite unexpected statistical properties of an ensemble of particles characteristic for the Fermi-Pasta-Ulam effect were found. We build and study the flow in which the velocity of the particles is calibrated. It was possible using the appropriate flows of liquid particles of the ensemble to demonstrate the possibility to reproduce any prescribed image by manipulating the parameters of the interaction. Calculations of the flows were performed with using MATLAB software package according to the algorithms presented in this article.