Reynolds-Averaged Navier-Stokes Equations Describing Turbulent Flow and Heat Transfer Behavior for Supercritical Fluid

Supercritical fluid has been widely applied in many industrial applications.The traditional Reynolds-averaged Navier-Stokes(RANS)equations are directly applied for turbulent flow and heat transfer of the supercritical fluid,ignoring turbulent effect of the thermal physical properties due to the intense nonlinearity.This paper deduces a set of Reynolds-averaged Navier-Stokes equations for supercritical fluid(SCF-RANS equations)to depict turbulent flow and heat transfer of the supercritical fluid taking all the physical parameters as variables.The SCF-RANS equations include many new correlation terms due to fluctuation of the thermal physical properties.Model methods for the new correlation term have been discussed for closing the SCF-RANS equations.Some of them have relatively mature models,while others are completely new and need profound physical theoretical analysis for proposing reasonable models.This paper provides referable information for these new correlations as far as authors know.The SCF-RANS equations not only provide the formulation special for flow and heat transfer of the supercritical fluid,but also represent the most sophisticate form of the RANS equations,for every involved physical property has been considered as variable without any simplification.

The Calculations of Propeller Induced Velocity by RANS and Momentum Theory

为了提供指令因为推进器的计算用身体在壳推进器相互作用的学习导致了速度，强迫途径，三个方法被用来计算推进器导致的速度：1 ) 自我推进测试的平均 Reynolds 的海军司烧(RANS ) 模拟， 2 ) 推进器的 RANS 模拟开的水测试，并且 3 ) 推进器的动量理论。从开始的二个方法的结果对试验性的数据被验证估计计算流动领域的精确性。戳身份方法被采用获得进展速度，它然后被用来导出推进器来自全部的速度地的导致的速度。开始的二条途径计算的结果是靠近的，当那些显著地从动量理论被过高估计时。介绍结果能证明为用身体力量途径的自我推进的另外的计算有用。

Numerical analysis of the performance of a three-bladed vertical-axis turbine with active pitch control using a coupled unsteady Reynolds-averaged Navier-Stokes and actuator line model

In this paper,we present a numerical model of a vertical-axis turbine(VAT)with active-pitch torque control.The model is based upon the Wind and Tidal Turbine Embedded Simulator(WATTES)and WATTES-V turbine realisations in conjunction with the actuator line method(ALM),and uses OpenFOAM to solve the unsteady Reynolds-averaged Navier-Stokes(URANS)equations with two-equation k-εturbulence closure.Our novel pitch-controlled system is based on an even pressure drop across the entire rotor to mitigate against dynamic stall at low tip speed ratio.The numerical model is validated against experimental measurements and alternative numerical predictions of the hydrodynamic performance of a 1:6 scale UNH-RM2 hydrokinetic turbine.Simulations deploying the variable pitch mechanism exhibit improved turbine performance compared to measured data and fixed zero-pitch model predictions.Near-wake characteristics are investigated by examining the vorticity distribution near the turbine.The pitch-controlled system is demonstrated to theoretically decrease turbulence generated by turbine rotations,mitigate the intensity of vortex shedding and size of detached vortices,and significantly enhance the performance of a vertical-axis hydrokinetic turbine for rated tip-speed ratios.

Study of Tunnel Thruster Performance and Flow by Quasi-Steady Reynolds-Averaged Navier-Stokes Simulation

A numerical approach based on the solution of the Reynolds-averaged Navier-Stokes(RANS) equations using the shear-stress transport(SST) turbulence model has been employed to investigate the hydrodynamic performance and flow of tunnel thrusters.The flow passages between adjacent blades are discretized with prismatic cells so that the boundary layer flow is resolved down to the viscous sub-layer.The hydrodynamic performances predicted by the quasi-steady approach agree well with the experimental data for three impellers covering a range of blade area and pitch.Through analysis of the flow field,the reason why the hub of impeller also contributes to thrust which can amount to 40%—60% of the impeller thrust,and the mechanism of the impeller inducing an axial force on the hull are elucidated.

Assessment of advanced RANS turbulence models for prediction of complex flows in compressors

Reynolds-Averaged Navier-Stokes(RANS) Computational Fluid Dynamics(CFD) has been widely used in compressor design and analysis. However, reasonable prediction of compressor flow and its impact on compressor performance remains challenging. In this study, Menter’s Shear Stress Transport(SST) model and its variants, as well as the ω-based Reynolds stress model(Stress-BSL) are assessed. For a single rotor(Rotor 67), under the peak efficiency operating condition, all studied turbulence models predict its performance with reasonable accuracy;under the off-design conditions, SST with Helicity correction(SST-Helicity) shows superiority in predicting the effect of flow on the spanwise distribution of aerodynamic parameters. For Darmstadt’s 1.5-stage transonic axial compressor, SST-Helicity outperforms SST, SST with the Quadratic Constitutive Relation(SST-QCR) and Stress-BSL in predicting the performance as well as the spanwise distribution of aerodynamic parameters. At the design rotating speed, the stall margin given by SST-Helicity(20.90%) is the closest to the experimental measurement(24.81%), which is more than twice that by SST(8.71%) and 1.5 times that by SST-QCR(14.14%). This paper demonstrates that SSTHelicity model, together with a good quality and sufficiently refined grid, can capture the compressor flow features with reasonable accuracy, which results in a credible prediction of compressor performance and stage matching.

6种典型飞行器的RANS计算及大分离区域的DES分析

提出了一种将RANS(Reynolds averaged Navier-Stokes)与DES(detached eddy simulation)相结合计算流场的工程新算法,并用于第一代载人飞船Mercury、第二代载人飞船Gemini、人类第一枚成功到达火星上空的Fire-Ⅱ探测器、具有丰富风洞实验数据(来流Mach数从0.50变到2.86)的巡航导弹、高升阻比的Waverider(乘波体)以及具有大容积效率与高升阻比的CAV(common aero vehicle)等6种国际上著名飞行器的绕流计算.在流场计算中,采用分区技术,即首先对全流场采用RANS计算,然后对分离较大或者分离较严重的那些区域采用DES分析技术.文中所完成的6个典型算例总共63个工况的数值计算表明:仅在分离较大的区域采用DES分析技术,虽然从严格意义上讲这样的处理并非真正意义上的DES,但这样近似处理后所得到的流场数值结果(其中包括气动力和气动热)与相关实验数据较为贴近,并且流场的计算效率较全场进行DES计算时要高得多.

基于两种螺旋桨建模方法的全附体船模斜拖试验数值模拟

应用计算流体动力学(CFD)方法数值模拟约束模试验以获取船舶操纵水动力导数,是建立船舶操纵运动数学模型的有效方法.在数值模拟全附体约束模试验中,选定合适的螺旋桨建模方法,是既快速又准确地计算船体水动力的关键.应用CFD方法求解雷诺平均Navier-Stokes(RANS)方程,分别采用体积力法和基于实桨的滑移网格法对螺旋桨进行处理,数值模拟了全附体KCS船模的斜拖试验;通过水动力数值计算结果与基准试验数据的比较,验证了所采用的数值方法的可靠性.对两种螺旋桨建模方法的结果进行比较可以发现,综合考虑计算成本和计算精度,体积力法可以代替实桨方法进行全附体约束模斜拖试验数值模拟.

使用非定常粘性和无粘求解器研究双螺旋桨在不同船舶尾流场中的性能

In this study,the performance of a twin-screw propeller under the influence of the wake field of a fully appended ship was investigated using a coupled Reynolds-averaged Navier–Stokes(RANS)/boundary element method(BEM)code.The unsteady BEM is an efficient approach to predicting propeller performance.By applying the time-stepping method in the BEM solver,the trailing vortex sheet pattern of the propeller can be accurately captured at each time step.This is the main innovation of the coupled strategy.Furthermore,to ascertain the effect of the wake field of the ship with acceptable accuracy,a RANS solver was developed.A finite volume method was used to discretize the Navier–Stokes equations on fully unstructured grids.To simulate ship motions,the volume of the fluid method was applied to the RANS solver.The validation of each solver(BEM/RANS)was separately performed,and the results were compared with experimental data.Ultimately,the BEM and RANS solvers were coupled to estimate the performance of a twin-screw propeller,which was affected by the wake field of the fully appended hull.The proposed model was applied to a twin-screw oceanography research vessel.The results demonstrated that the presented model can estimate the thrust coefficient of a propeller with good accuracy as compared to an experimental self-propulsion test.The wake sheet pattern of the propeller in open water(uniform flow)was also compared with the propeller in a real wake field.

Flow Dynamics of a Spiral-groove Dry-gas Seal

The dry-gas seal has been widely used in different industries. With increased spin speed of the rotator shaft, turbulence occurs in the gas film between the stator and rotor seal faces. For the micro-scale flow in the gas film and grooves, turbulence can change the pressure distribution of the gas film. Hence, the seal performance is influenced. However, turbulence effects and methods for their evaluation are not considered in the existing industrial designs of dry-gas seal. The present paper numerically obtains the turbulent flow fields of a spiral-groove dry-gas seal to analyze turbulence effects on seal performance. The direct numerical simulation （DNS） and Reynolds-averaged Navier-Stokes （RANS） methods are utilized to predict the velocity field properties in the grooves and gas film. The key performance parameter, open force, is obtained by integrating the pressure distribution, and the obtained result is in good agreement with the experimental data of other researchers. Very large velocity gradients are found in the sealing gas film because of the geometrical effects of the grooves. Considering turbulence effects, the calculation results show that both the gas film pressure and open force decrease. The RANS method underestimates the performance, compared with the DNS. The solution of the conventional Reynolds lubrication equation without turbulence effects suffers from significant calculation errors and a small application scope. The present study helps elucidate the physical mechanism of the hydrodynamic effects of grooves for improving and optimizing the industrial design or seal face pattern of a dry-gas seal.

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.

URANS COMPUTATION OF CAVITATING FLOWS AROUND SKEWED PROPELLERS

Cavitating flows around skewed propellers are investigated numerically by means of the unsteady Reynolds Averaged Navier-Stokes （RANS） Equation method. The standard k - c turbulence and the modified Z-G-B cavitation models are employed. A measured nominal wake is used for the inlet velocity boundary condition. Predicted cavitating evolution processes and tip cavity patterns are compared with experimental observations. In addition, the influence of the skew angles on the cavitation and unsteadiness performances of propellers operating in a non-uniform wake is also studied. Results show that the modified Z-G-B cavitation model performs better to simulate the cavitating flow cases studied in this paper. Comparisons demonstrate that the skewed propeller with a skew angle of 20~ is the best choice for a given stern wake with a assigned thrust and the minimum force fluctuations.

Numerical Wave Flume Study on Wave Motion Around Submerged Plates

Nonlinear interaction between surface waves and a submerged horizontal plate is investigated in the absorbed numerical wave flume developed based on the volume of fluid (VOF) method. The governing equations of the numerical model are the continuity equation and the Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ε turbulence equations. Incident waves are generated by an absorbing wave-maker that eliminates the waves reflected from structures. Results are obtained for a range of parameters, with consideration of the condition under which the reflection coefficient becomes maximal and the transmission coefficient minimal. Wave breaking over the plate, vortex shedding downwave, and pulsating flow below the plate are observed. Time-averaged hydrodynamic force reveals a negative drift force. All these characteristics provide a reference for construction of submerged plate breakwaters.

AERODYNAMIC OPTIMIZATION FOR TURBINE BLADE BASED ON HIERARCHICAL FAIR COMPETITION GENETIC ALGORITHMS WITH DYNAMIC NICHE

A global optimization approach to turbine blade design based on hierarchical fair competition genetic algorithms with dynamic niche （HFCDN-GAs） coupled with Reynolds-averaged Navier-Stokes （RANS） equation is presented. In order to meet the search theory of GAs and the aerodynamic performances of turbine, Bezier curve is adopted to parameterize the turbine blade profile, and a fitness function pertaining to optimization is designed. The design variables are the control points＇ ordinates of characteristic polygon of Bezier curve representing the turbine blade profile. The object function is the maximum lift-drag ratio of the turbine blade. The constraint conditions take into account the leading and trailing edge metal angle, and the strength and aerodynamic performances of turbine blade. And the treatment method of the constraint conditions is the flexible penalty function. The convergence history of test function indicates that HFCDN-GAs can locate the global optimum within a few search steps and have high robustness. The lift-drag ratio of the optimized blade is 8.3% higher than that of the original one. The results show that the proposed global optimization approach is effective for turbine blade.

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.

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.

An Efficient Hydrodynamic Model for Surface Waves

In the present study, a semi-implicit finite difference model for non-hydrostatic, free-surface flows is analyzed and discussed. The governing equations are the three-dimensional free-surface Reynolds-averaged Navier-Stokes equations defined on a general, irregular domain of arbitrary scale. At outflow, a combination of a sponge layer technique and a radiation boundary condition is applied to minimize wave reflection. The equations are solved with the fractional step method where the hydrostatic pressure component is determined first, while the non-hydrostatic component of the pressure is computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The advection and horizontal viscosity terms are discretized by use of a semi-Lagrangian approach. The resulting model is computationally efficient and unrestricted to the CFL condition. The developed model is verified against analytical solutions and experimental data, with excellent agreement.

URANS simulations of ship motion responses in long-crest irregular waves

In this paper, numerical prediction of ship motion responses in long-crest irregular waves by the URANS-VOF method is presented. A white noise spectrum is applied to generate the incoming waves to evaluate the motion responses. The procedure can replace a decade of simulations in regular wave with one single run to obtain a complete curve of linear motion response, considerably reducing computation time. A correction procedure is employed to adjust the wave generation signal based on the wave spectrum and achieves fairly better results in the wave tank. Three ship models with five wave conditions are introduced to validate the method. The computations in this paper are completed by using the solver naoe-FOAM-SJTU, a solver developed for ship and ocean engineering based on the open source code OpenFOAM. The computational motion responses by the irregular wave procedure are compared with the results by regular wave, experiments and strip theory. Transfer functions by irregular wave closely agree with the data obtained in the regular waves, showing negligible difference. The comparison between computational results and experiments also show good agreements. The results better predicted by CFD method than strip theories indicate that this method can compensate for the inaccuracy of the strip theories. The results confirm that the irregular wave procedure is a promising method for the accurate prediction of motion responses with less accuracy loss and higher efficiency compared with the regular wave procedure.

Characteristics of transonic moist air flows around butterfly valves with spontaneous condensation

Effects of spontaneous condensation of moist air on the shock wave dynamics around butterfly valves in transonic flows are investigated by experimental and numerical simulations.Two symmetric valve disk shapes namely-a flat rectangular plate and a mid-plane cross-section of a prototype butterfly valve have been studied in the present research.Results showed that in case with spontaneous condensation,the root mean square of pressure oscillation(induced by shock dynamics)is reduced significantly with those without condensation for both shapes of the valves.Moreover,local aerodynamic moments were reduced in case with condensation which is considered to be beneficial in torque requirement in case of on/off applications of valves as flow control devices.However,total pressure loss was increased with spontaneous condensation in both the valves.Furthermore,the disk shape of a prototype butterfly valve showed better aerodynamic performances compared to flat rectangular plate profile in respect of total pressure loss and vortex shedding frequency in the wake region.

拖体机翼水动力数值仿真

采用具有k～ε两方程涡粘模型的Reynolds平均方法(RANS)求解Navier-Stokes方程,得到了水下拖体机翼周围的流场,与机翼敞水试验结果对比验证了k～ε模型数值解法是可行的。同时给出了机翼在流场中时水流流过机翼的流动细节,指出由于展长有限而在机翼两端出现涡脱落现象,从而在机翼尾部形成旋涡。