Evaluation of Nonbreaking Wave-Induced Mixing Parameterization Schemes Based on a One-Dimensional Ocean Model

Surface waves have a considerable effect on vertical mixing in the upper ocean.In the past two decades,the vertical mixing induced through nonbreaking surface waves has been used in ocean and climate models to improve the simulation of the upper ocean.Thus far,several nonbreaking wave-induced mixing parameterization schemes have been proposed;however,no quantitative comparison has been performed among them.In this paper,a one-dimensional ocean model was used to compare the performances of five schemes,including those of Qiao et al.(Q),Hu and Wang(HW),Huang and Qiao(HQ),Pleskachevsky et al.(P),and Ghantous and Babanin(GB).Similar to previous studies,all of these schemes can decrease the simulated sea surface temperature(SST),increase the subsurface temperature,and deepen the mixed layer,thereby alleviating the common thermal deviation problem of the ocean model for upper ocean simulation.Among these schemes,the HQ scheme exhibited the weakest wave-induced mixing effect,and the HW scheme exhibited the strongest effect;the other three schemes exhibited roughly the same effect.In particular,the Q and P schemes exhibited nearly the same effect.In the simulation based on observations from the Ocean Weather Station Papa,the HQ scheme exhibited the best performance,followed by the Q scheme.In the experiment with the HQ scheme,the root-mean-square deviation of the simulated SST from the observations was 0.43℃,and the mixed layer depth(MLD)was 2.0 m.As a contrast,the deviations of the SST and MLD reached 1.25℃ and 8.4 m,respectively,in the experiment without wave-induced mixing.

Constrained re-calibration of two-equation Reynolds-averaged Navier–Stokes models

Machine-learned augmentations to turbulence models can be advantageous for flows within the training dataset but can often cause harm outside.This lack of generalizability arises because the constants(as well as the functions)in a Reynolds-averaged Navier–Stokes(RANS)model are coupled,and un-constrained re-calibration of these constants(and functions)can disrupt the calibrations of the baseline model,the preservation of which is critical to the model's generalizability.To safeguard the behaviors of the baseline model beyond the training dataset,machine learning must be constrained such that basic calibrations like the law of the wall are kept intact.This letter aims to identify such constraints in two-equation RANS models so that future machine learning work can be performed without violating these constraints.We demonstrate that the identified constraints are not limiting.Furthermore,they help preserve the generalizability of the baseline model.

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..

Multi-layer analytic solution for k-ωmodel equations via a symmetry approach

Despite being one of the oldest and most widely-used turbulence models in engineering computational fluid dynamics(CFD),the k-ωmodel has not been fully understood theoretically because of its high nonlinearity and complex model parameter setting.Here,a multi-layer analytic expression is postulated for two lengths(stress and kinetic energy lengths),yielding an analytic solution for the k-ωmodel equations in pipe flow.Approximate local balance equations are analyzed to determine the key parameters in the solution,which are shown to be rather close to the empirically-measured values from the numerical solution of the Wilcox k-ωmodel,and hence the analytic construction is fully validated.The results provide clear evidence that the k-ωmodel sets in it a multilayer structure,which is similar to but different,in some insignificant details,from the Navier-Stokes(N-S)turbulence.This finding explains why the k-ωmodel is so popular,especially in computing the near-wall flow.Finally,the analysis is extended to a newlyrefined k-ωmodel called the structural ensemble dynamics(SED)k-ωmodel,showing that the SED k-ωmodel has improved the multi-layer structure in the outer flow but preserved the setting of the k-ωmodel in the inner region.

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.

Effect of Time Step Size and Turbulence Model on the Open Water Hydrodynamic Performance Prediction of Contra-Rotating Propellers

A growing interest has been devoted to the contra-rotating propellers （CRPs） due to their high propulsive efficiency, torque balance, low fuel consumption, low cavitations, low noise performance and low hull vibration. Compared with the single-screw system, it is more difficult for the open water performance prediction because forward and aft propellers interact with each other and generate a more complicated flow field around the CRPs system. The current work focuses on the open water performance prediction of contra-rotating propellers by RANS and sliding mesh method considering the effect of computational time step size and turbulence model. The validation study has been performed on two sets of contra-rotating propellers developed by David W Taylor Naval Ship R ＆ D center. Compared with the experimental data, it shows that RANS with sliding mesh method and SST k-ω turbulence model has a good precision in the open water performance prediction of contra-rotating propellers, and small time step size can improve the level of accuracy for CRPs with the same blade number of forward and aft propellers, while a relatively large time step size is a better choice for CRPs with different blade numbers.

Numerical simulation and experimental study of the hydrodynamics of a modeled reef located within a current

The hydrodynamic forces and flow field of artificial reef models in steady flow were numerically investigated using the RNG κ-ε turbulent model. The numerical simulation results are consistent with results observed by experimental means. A comparative study indicates that the corresponding errors of forces between calculated values and values observed in the experiment vary in the range of2.3%-11.2% and that the corresponding errors of velocities vary in the range of 1.3%-15.8%. The flow field numerical results show that upstream and vortices exist when the current passes over and through the surface of the reef model. This study suggests that the numerical simulation method can be applied to predict the forces and flow field associated with artificial reefs.

Modeling of turbulent,isothermal and cryogenic cavitation under attached conditions

Cavitation is often triggered when the fluid pres- sure is lower than the vapor pressure at a local thermo- dynamic state. The present article reviews recent progress made toward developing modeling and computational strat- egies for cavitation predictions under both isothermal and cryogenic conditions, with an emphasis on the attached cav- ity. The review considers alternative cavitation models along Reynolds-averaged Navier-Stokes and very lager eddy simu- lation turbulence approaches to ensure that the computational tools can handle flows of engineering interests. Observing the substantial uncertainties associated with both modeling and experimental information, surrogate modeling strategies are reviewed to assess the implications and relative impor- tance of the various modeling and materials parameters. The exchange between static and dynamic pressures under the influence of the viscous effects can have a noticeable impact on the effective shape of a solid object, which can impact the cavitation structure. The thermal effect with respect to evaporation and condensation dynamics is examined to shed light on the fluid physics associated with cryogenic cav- itation. The surrogate modeling techniques are highlighted in the context of modeling sensitivity assessment. Keywords

Calculation Model of Mass Action Concentration for Mg-Al,Sr-Al and Ba-Al Melts and Determination of Their Thermodynamic Parameters

A steady three-dimensional fluid flow and solidification model was built based on CFD software by high-Reynolds-number and Lam-Bremhorst low-Reynolds-number k-ε model. During the simulation, the fixed-grid enthalpy-porosity technique was used to represent the solidification, and Darcy law was adopted to simulate the flow in mushy region. The prediction for steel flow and solidification was evaluated by the comparison of two turbulence models. It is found that both Lam-Bremhorst low-Reynolds-number and high-Reynolds-number k-ε models predict the same trend of the steel flow and temperature distribution. However, due to the effect of turbulent flow on heat transfer, the low-Reynolds-number turbulence model predicts longer penetration depth of molten steel in sub-mold region, less shell growth and higher shell surface temperature at the narrow face compared with standard k-ε model.

Numerical simulation of the flow within and over an intersection model with Reynolds-averaged Navier-Stokes method

In this study, the Reynolds-averaged Navier-Stokes （RANS） method is employed to simulate the flow within and over an intersection model with three kinds of k-ε turbulence closure schemes, namely, standard model, renormalization group （RNG） model and realizable k-ε model. The comparison between the simulated and observed flow fields shows that the RANS simulation with all the three turbulence models cannot completely and accurately reproduce the observed flow field in all details. A detailed comparison between the predicted profiles of wind velocities and the measured data shows that the realizble k-ε model is the best one among the three turbulence closure models in general. However, the extent to which the improvement is achieved by the realizable k-ε model is still not enough to completely and accurately describe the turbulent flow in a relatively complex environment.

Mechanism of local scour around submarine pipelines based on numerical simulation of turbulence model

The mechanism of local scour around submarine pipelines is studied numerically based on a renormalized group （RNG） turbulence model. To validate the numerical model, the equilibrium profiles of local scour for two cases are simulated and compared with the experimental data. It shows that the RNG turbulence model can give an appropriate prediction for the configuration of equilibrium scour hole, and it is applicable to this situation. The local scour mechanism around submarine pipelines including the flow structure, shear stress distribution and pressure field is then analyzed and compared with experiments. For further comparison and validation, especially for the flow structure, a numerical calculation employing the large eddy simulation （LES） is also conducted. The numerical results of RNG demonstrate that the critical factor governing the equilibrium profile is the seabed shear stress distribution in the case of bed load sediment transport, and the two-equation RNG turbulence model coupled with the law of wall is capable of giving a satisfying estimation for the bed shear stress. Moreover, the piping phenomena due to the great difference of pressure between the upstream and downstream parts of pipelines and the vortex structure around submarine pipelines are also simulated successfully, which are believed to be the important factor that lead to the onset of local scour.

Calculation grid and turbulence model for numerical simulating pressure fluctuations in high-speed train tunnel

Calculation grid and turbulence model for numerical simulating pressure fluctuations in a high-speed train tunnel are studied through the comparison analysis of numerical simulation and moving model test.Compared the waveforms and peak-peak values of pressure fluctuations between numerical simulation and moving model test,the structured grid and the SST k-ωturbulence model are selected for numerical simulating the process of high-speed train passing through the tunnel.The largest value of pressure wave amplitudes of numerical simulation and moving model test meet each other.And the locations of the largest value of the initial compression and expansion wave amplitude of numerical simulation are in agreement with that of moving model test.The calculated pressure at the measurement point fully conforms to the propagation law of compression and expansion waves in the tunnel.

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.

Basic Pattern in Atmospheric Turbulence Model

From the controlling equations of atmosphere motion, Prandtl's mixing length theory is used to derive the atmospheric turbulence models, such as Burgers equation model and Burgers-KdV equation model. And then the projective Riccati equations are applied to solve these atmospheric turbulence models, where much more patterns are obtained, including solitary wave pattern, singular pattern, and so on.

An iterative data-driven turbulence modeling framework based on Reynolds stress representation

Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled,but several essential issues remain that strongly affect the performance.Two problems are studied in the current research:(1)the processing of the Reynolds stress tensor and(2)the coupling method between the machine learning model and flow solver.For the Reynolds stress processing issue,we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress.Then,the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis.An adaptive regularization term is employed to enhance the representation performance.For the coupling issue,an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow.The results have high consistency with the direct numerical simulation true values,which proves the validity of the current approach.

Numerical Evaluation of Two k-εTurbulence Model for Predicting Flow and Solidification in Continuous Casting Slab

A steady three-dimensional fluid flow and solidification model was built based on CFD software by high-Reynolds-number and Lam-Bremhorst low-Reynolds-number k-ε model.During the simulation,the fixed-grid enthalpy-porosity technique was used to represent the solidification,and Darcy law was adopted to simulate the flow in mushy region.The prediction for steel flow and solidification was evaluated by the comparison of two turbulence models.It is found that both Lam-Bremhorst low-Reynolds-number and high-Reynolds-number k-ε models predict the same trend of the steel flow and temperature distribution.However,due to the effect of turbulent flow on heat transfer,the low-Reynolds-number turbulence model predicts longer penetration depth of molten steel in sub-mold region,less shell growth and higher shell surface temperature at the narrow face compared with standard k-ε model.

Turbulence and cavitation models for time-dependent turbulent cavitating flows

Cavitation typically occurs when the fluid pressure is lower than the vapor pressure at a local thermodynamic state, and the flow is frequently unsteady and turbulent. To assess the state-of-the-art of computational capabilities for unsteady cavitating flows, different cavitation and turbulence model combinations are conducted. The selected cavitation models include several widely-used models including one based on phenomenological argument and the other utilizing interface dynamics. The k-e turbulence model with additional implementation of the filter function and density correction function are considered to reduce the eddy viscosity according to the computed turbulence length scale and local fluid density respectively. We have also blended these alternative cavitation and lustrate that the eddy viscosity turbulence treatments, to ilnear the closure region can significantly influence the capture of detached cavity. From the experimental validations regarding the force analysis, frequency, and the cavity visualization, no single model combination performs best in all aspects. Furthermore, the implications of parameters contained in different cavitation models are investigated. The phase change process is more pronounced around the detached cavity, which is better illustrated by the interfacial dynamics model. Our study provides insight to aid further modeling development.

Numerical simulation of flow around square cylinder using different low-Reynolds number turbulence models

ABE-KONDOH-NAGANO,ABID,YANG-SHIH and LAUNDER-SHARMA low-Reynolds number turbulence models were applied to simulating unsteady turbulence flow around a square cylinder in different phases flow field and time-averaged unsteady flow field.Meanwhile,drag and lift coefficients of the four different low-Reynolds number turbulence models were analyzed.The simulated results of YANG-SHIH model are close to the large eddy simulation results and experimental results,and they are significantly better than those of ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMR models.The modification of the generation of turbulence kinetic energy is the key factor to a successful simulation for YANG-SHIH model,while the correction of the turbulence near the wall has minor influence on the simulation results.For ABE-KONDOH-NAGANO,ABID and LAUNDER-SHARMA models satisfactory simulation results cannot be obtained due to lack of the modification of the generation of turbulence kinetic energy.With the joint force of wall function and the turbulence models with the adoption of corrected swirl stream,flow around a square cylinder can be fully simulated with less grids by the near-wall.

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.

End-to-end differentiable learning of turbulence models from indirect observations

The emerging push of the differentiable programming paradigm in scientific computing is conducive to training deep learning turbulence models using indirect observations.This paper demonstrates the viability of this approach and presents an end-to-end differentiable framework for training deep neural networks to learn eddy viscosity models from indirect observations derived from the velocity and pressure fields.The framework consists of a Reynolds-averaged Navier–Stokes(RANS)solver and a neuralnetwork-represented turbulence model,each accompanied by its derivative computations.For computing the sensitivities of the indirect observations to the Reynolds stress field,we use the continuous adjoint equations for the RANS equations,while the gradient of the neural network is obtained via its built-in automatic differentiation capability.We demonstrate the ability of this approach to learn the true underlying turbulence closure when one exists by training models using synthetic velocity data from linear and nonlinear closures.We also train a linear eddy viscosity model using synthetic velocity measurements from direct numerical simulations of the Navier–Stokes equations for which no true underlying linear closure exists.The trained deep-neural-network turbulence model showed predictive capability on similar flows.