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.

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.

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 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.

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.

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.

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.

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.

通过多转子防护装置提高潮汐水轮机性能的策略（英文）

Constructive interference between tidal stream turbines in multi-rotor fence configurations arrayed normally to the flow has been shown analytically, computationally, and experimentally to enhance turbine performance. The increased resistance to bypass flow due to the presence of neighbouring turbines allows a static pressure difference to develop in the channel and entrains a greater flow rate through the rotor swept area. Exploiting the potential improvement in turbine performance requires that turbines either be operated at higher tip speed ratios or that turbines are redesigned in order to increase thrust. Recent studies have demonstrated that multi-scale flow dynamics, in which a distinction is made between device-scale and fence-scale flow events, have an important role in the physics of flow past tidal turbine fences partially spanning larger channels. Although the reduction in flow rate through the fence as the turbine thrust level increases has been previously demonstrated, the within-fence variation in turbine performance, and the consequences for overall farm performance, is less well understood. The impact of turbine design and operating conditions, on the performance of a multi-rotor tidal fence is investigated using Reynolds-Averaged Navier-Stokes embedded blade element actuator disk simulations. Fences consisting of four, six, and eight turbines are simulated, and it is demonstrated that the combination of device-and fence-scale flow effects gives rise to cross-fence thrust and power variation. These cross-fence variations are also a function of turbine thrust, and hence design conditions,although it is shown simple turbine control strategies can be adopted in order to reduce the cross-fence variations and improve overall fence performance. As the number of turbines in the fence, and hence fence length, increases, it is shown that the turbines may be designed or operated to achieve higher thrust levels than if the turbines were not deployed in a fence configuration.

Numerical Simulation of Solitary Wave Forces on A Vertical Cylinder on A Slope Beach

Wave forces acting on a vertical cylinder at different locations on a slope beach in the near-shore region are investigated considering solitary waves as incoming waves.Based on the Reynolds-averaged Navier-Stokes equations and the k-ε turbulence model,wave forces due to the interaction between the solitary wave and cylinder are simulated and analyzed with different incident wave heights and cylinder locations.The numerical results are first compared with previous theoretical and experimental results to validate the model accuracy.Then,the wave forces and characteristics around the cylinder are studied,including the velocity field,wave surface elevation and pressure.The effects of relative wave height,Keulegan-Carpenter(KC)number and cylinder locations on the wave forces are also discussed.The results show that the wave forces exerted on a cylinder exponentially increase with the increasing incident wave height and KC number.Before the wave force peaks,the growth rate of the wave force shows an increasing trend as the cylinder moves onshore.The cylinder location has a notable effect on the wave force on the cylinder in the near-shore region.As the cylinder moves onshore,the wave force on the cylinder initially increases and then decreases.For the cases considered here,the maximum wave force appears when the cylinder is located one cylinder diameter below the still-water shoreline.Furthermore,the fluid velocity peaks when the maximum wave force appears at the same location.

Analysis on Aerodynamic Performance of Finite Swept Wing with Glaze Ice Accretions

A computational investigation was performed to predict the effects of aerodynamic performance degradation on aircraft swept taper wing with and without 10 minutes and 22.5 minutes glaze ice accretions. In this study, the three-dimensional simulated glaze ice shapes were defined from a series of two-dimensional ice sections. The aerodynamic performances of glaze iced swept wings with C-H structure multi-block grid were analyzed and evaluated. The steady Reynolds- Averaged Navier-Stokes （RANS） equations are employed to compute solutions with implementation of two equation Shear-Stress Transport （SST） turbulence model and second-order upwind differencing for entire iced wing flow field. Computed results were compared with available experimental data. The CFD computation can also accurately predict the aerodynamic performance degradation of lift, drag and pressure coefficients of finite swept wing with glaze ice accretions which have two big upper and lower horn.

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.

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.

Investigation of flow characteristics in a rotor-stator cavity under crossflow using wall-modelled large-eddy simulation

Rotor-stator cavities are frequently encountered in engineering applications such as gas turbine engines.They are usually subject to an external hot mainstream crossflow which in general is highly swirled under the effect of the nozzle guide vanes.To avoid hot mainstream gas ingress,the cavity is usually purged by a stream of sealing flow.The interactions between the external crossflow,cavity flow,and sealing flow are complicated and involve all scales of turbulent unsteadiness and flow instability which are beyond the resolution of the Reynolds-average approach.To cope with such a complex issue,a wall-modeled large-eddy simulation(WMLES)approach is adopted in this study.In the simulation,a 20°sector model is used and subjected to a uniform pre-swirled external crossflow and a stream of radial sealing flow.It is triggered by a convergent Reynoldsaveraged Navier-Stokes(RANS)result in which the shear stress transport(SST)turbulent model is used.In the WMLES simulation,the Smagoringsky sub-grid scale(SGS)model is applied.A scalar transportation equation is solved to simulate the blending and transportation process in the cavity.The overall flow field characteristics and deviation between RANS and WMLES results are discussed first.Both RANS and WMLES results show a Batchelor flow mode,while distinct deviation is also observed.Deviations in the small-radius region are caused by the insufficiency of the RANS approach in capturing the small-scale vortex structures in the boundary layer while deviations in the large-radius region are caused by the insufficiency of the RANS approach in predicting the external crossflow ingestion.The boundary layer vortex and external ingestion are then discussed in detail,highlighting the related flow instabilities.Finally,the large-flow structures induced by external flow ingress are analyzed using unsteady pressure oscillation signals.

一种改进的类DES湍流模拟方法

构造了一种基于一方程S-A(Spalart-Allmaras)模型和一方程Yoshizawa亚格子模型的混合RANS/LES(Reynolds-averaged Navier-Stokes/large eddy simulation)湍流模拟方法.在涡黏假设的基础上,将Yoshizawa亚格子湍动能方程转化为等效的亚格子湍流涡黏性输运方程,并采用混合函数将其与S-A模型方程进行混合,从而改进了DES(detached eddy simulation)模型的亚格子行为,同时克服了其依靠网格控制模型转换的缺点.模拟了超声速的带斜坡凹腔流动,并与相同网格下的LES及DES结果进行了比较,结果表明该混合RANS/LES方法在远离壁面的自由剪切流区域与LES行为一致,而在附着边界层区域表现优于LES和DES方法.

LARGE-EDDY AND DETACHED-EDDY SIMULATIONS OF THE SEPARATED FLOW AROUND A CIRCULAR CYLINDER

The separated turbulent flow around a circular cylinder is investigated using Large-Eddy Simulation （LES）, Detached-Eddy Simulation （DES, or hybrid RANS/LES methods）, and Unsteady Reynolds-Averaged Navier-Stokes （URANS）. The purpose of this study is to examine some typical simulation approaches for the prediction of complex separated turbulent flow and to clarify the capability of applying these approaches to a typical case of the separated turbulent flow around a circular cylinder. Several turbulence models, i.e. dynamic Sub-grid Scale （SGS） model in LES, the DES-based Spalart-Allmaras （S-A） and κ-ω Shear-Stress- Transport （SST） models in DES, and the S-A and SST models in URANS, are used in the calculations. Some typical results, e.g., the mean pressure and drag coefficients, velocity profiles, Strouhal number, and Reynolds stresses, are obtained and compared with previous computational and experimental data. Based on our extensive calculations, we assess the capability and performance of these simulation approaches coupled with the relevant turbulence models to predict the separated turbulent flow.

NUMERICAL INVESTIGATION OF CAVITATION PERFORMANCE OF SHIP PROPELLERS

The cavitation performance of propellers is studied based on viscous multiphase flow theories. With a hybrid grid based on Navier-Stokes （N-S） and bubble dynamics equations, some recent validation results are presented in this paper in the predictions of the thrust, the torque and the vapor volume fraction on the back side of propeller blade for a uniform inflow. The numerical predictions of the hydrodynamic performance and the sheet cavitation under several operating conditions for two propellers agree with the corresponding measured data in general. The thrust and the torque are plotted with respect to the advance rate and the cavitation number. The cavitation performance breakdown is closely related to the strong sheet cavitation around propellers. The models with parameters modified are shown to predict the propeller cavitation well.

Numerical investigation of flow separation behavior in an over-expanded annular conical aerospike nozzle

A three-part numerical investigation has been conducted in order to identify the flow separation behavior––the progression of the shock structure, the flow separation pattern with an increase in the nozzle pressure ratio（NPR）, the prediction of the separation data on the nozzle wall,and the influence of the gas density effect on the flow separation behavior are included.The computational results reveal that the annular conical aerospike nozzle is dominated by shock/shock and shock/boundary layer interactions at all calculated NPRs, and the shock physics and associated flow separation behavior are quite complex.An abnormal flow separation behavior as well as a transition process from no flow separation at highly over-expanded conditions to a restricted shock separation and finally to a free shock separation even at the deign condition can be observed.The complex shock physics has further influence on the separation data on both the spike and cowl walls, and separation criteria suggested by literatures developed from separation data in conical or bell-type rocket nozzles fail at the prediction of flow separation behavior in the present asymmetric supersonic nozzle.Correlation of flow separation with the gas density is distinct for highly overexpanded conditions.Decreasing the gas density or reducing mass flow results in a smaller adverse pressure gradient across the separation shock or a weaker shock system, and this is strongly coupled with the flow separation behavior.The computational results agree well with the experimental data in both shock physics and static wall pressure distribution at the specific NPRs, indicating that the computational methodology here is advisable to accurately predict the flow physics.