Spalart-Allmaras Turbulence Model Research Articles

Numerical investigation of compressibility effect on dynamic stall

A rotorcraft main-rotor blade experiences a broad range of the Mach number in high-speed forward flights or rapid maneuvers. Near the boundary of the flight envelope, the rotor blade often encounters severe dynamic stall which limits the overall aerodynamic performance. The effects of the flow compressibility on dynamic stall due to the variation of the freestream Mach number are studied here. A rotor airfoil, VR-12, is computationally investigated for both static and dynamic stall conditions in the relevant range of the Mach number, 0.2 to 0.4. For the small enough Mach number such as 0.2, both static and dynamic stalls are significantly influenced by flow separation due to adverse pressure gradient with little compressibility effect. For the highest Mach number 0.4, compressibility near the leading edge is no longer negligible, forming a local supersonic pocket there. The shock-induced separation occurs near the leading edge, which dominates both the static and dynamic stall at the high Mach number. At the intermediate Mach number 0.3, it is observed that both adverse pressure gradient and weak shock affect the stall. Unsteady compressible Reynolds-averaged Navier-Stokes equations are numerically solved with the Spalart-Allmaras turbulence model in the current study. Numerical results are compared to relevant wind-tunnel test data.

A discrete-forcing immersed boundary method for turbulent-flow simulations

For numerical simulations of ship hydrodynamics in high Reynolds number, near-wall grids with high quality are essential to accurately predict the flow field and shear stress. This article proposes a discrete-forcing immersed boundary method to simulate moving solid boundaries in turbulent flows. The technique will efficiently remove the requirement of high-quality body-conforming grids and also preserve the grid quality throughout the simulation when body motions are considered. The one-equation Spalart–Allmaras turbulence model is coupled with the immersed boundary method for turbulence closure. A key aspect of this method is to use a wall function to alleviate the near-wall cell-size requirement in high-Reynolds-number flows. In this method, the boundary conditions on the immersed surfaces are enforced without the need of spreading functions, which is favorable for high-Reynolds-number flows. The performance of the method is carefully verified and validated through various problems, including both laminar and turbulent flows for fixed and moving solid surfaces. Subsequently, this method is further examined by predicting the turbulent flows around a model-scaled double-body KVLCC2 tanker. The total resistance and the local wake field are compared with experimental data.

Aerodynamic performance enhancement for flapping airfoils by co-flow jet

Introducing active flow control into the design of flapping wing is an effective way to enhance its aerodynamic performance. In this paper, a novel active flow control technology called Co-Flow Jet (CFJ) is applied to flapping airfoils. The effect of CFJ on aerodynamic performance of flapping airfoils at low Reynolds number is numerically investigated using Unsteady Reynolds Averaged Navier-Stokes (URANS) simulation with Spalart-Allmaras (SA) turbulence model. Numerical methods are validated by a NACA6415-based CFJ airfoil case and a S809 pitching airfoil case. Then NACA6415 baseline airfoil and NACA6415-based CFJ airfoil with jet-off and jet-on are simulated in flapping motion, with Reynolds number 70,000 and reduced frequency 0.2. As a result, CFJ airfoils with jet-on generally have better lift and thrust characteristics than baseline airfoils and jet-off airfoil when Cμ is greater than 0.04, which results from the CFJ effect of reducing flow separation by injecting high-energy fluid into boundary layer. Besides, typical kinematic and geometric parameters, including the reduced frequency and the positions of the suction and injection slot, are systematically studied to figure out their influence on aerodynamic performance of the CFJ airfoil. And a variable Cμ jet control strategy is proposed to further improve effective propulsive efficiency. Compared with using constant Cμ, an increase of effective propulsive efficiency by 22.6% has been achieved by using prescribed variable Cμ for NACA6415-based CFJ airfoil at frequency 0.2. This study may provide some guidance to performance enhancement for Flapping wing Micro Air Vehicles (FMAV).

Aerodynamic Shape Optimization of a Missile Using a Multiobjective Genetic Algorithm

The aim of this paper is to demonstrate the effects of the shape optimization on the missile performance at supersonic speeds. The N1G missile model shape variation, which decreased its aerodynamic drag and increased its aerodynamic lift at supersonic flow under determined constraints, was numerically investigated. Missile geometry was selected from a literature study for optimization in terms of aerodynamics. Missile aerodynamic coefficient prediction was performed to verify and compare with existing experimental results at supersonic Mach numbers using SST k-omega, realizable k-epsilon, and Spalart-Allmaras turbulence models. In the optimization process, the missile body and fin design parameters need to be estimated to design optimum missile geometry. Lift and drag coefficients were considered objective function. Input and output parameters were collected to obtain design points. Multiobjective Genetic Algorithm (MOGA) was used to optimize missile geometry. The front part of the body, the main body, and tailfins were improved to find an optimum missile model at supersonic speeds. The optimization results showed that a lift-to-drag coefficient ratio, which determines the performance of a missile, was improved about 11-17 percent at supersonic Mach numbers.

Computational Fluid Dynamics Simulations of Aerodynamic Performance of Low-Pressure Axial Fans With Small Hub-to-Tip Diameter Ratio

Abstract Rotor-only ducted axial fans with small hub-to-tip diameter ratio are widely used in many branches of industry, especially for cooling and ventilation purposes. For such fans, extensive regions of backflow are present downstream of the fan near the hub. Only few computational fluid dynamics (CFD) studies for such fans have been reported in the scientific literature. In order to develop guidelines for obtaining accurate CFD predictions for such fans, validation simulations of a fan with small hub-to-tip diameter ratio have been performed by comparing experimental and computed aerodynamic performance characteristics. These guidelines pay special attention to the trailing edge shape, presence of nonaerodynamically shaped blade sections, tip gap, and employed turbulence model. The results for the fan studied here show that the actual (rounded) trailing edge is necessary; the main blade (without nonaerodynamically shaped blade sections) well represents the aerodynamic performance of the whole fan blade; it is recommended not to take the tip gap into consideration due to the existence of significant flow separation; the use of the Spalart–Allmaras turbulence model is advised for giving better agreement with measurements.

Adaptive sampling-based quadrature rules for efficient Bayesian prediction

A novel method is proposed to infer Bayesian predictions of computationally expensive models. The method is based on the construction of quadrature rules, which are well-suited for approximating the weighted integrals occurring in Bayesian prediction. The novel idea is to construct a sequence of nested quadrature rules with positive weights that converge to a quadrature rule that is weighted with respect to the posterior. The quadrature rules are constructed using a proposal distribution that is determined by means of nearest neighbor interpolation of all available evaluations of the posterior. It is demonstrated both theoretically and numerically that this approach yields accurate estimates of the integrals involved in Bayesian prediction. The applicability of the approach for a fluid dynamics test case is demonstrated by inferring accurate predictions of the transonic flow over the RAE2822 airfoil with a small number of model evaluations. Here, the closure coefficients of the Spalart–Allmaras turbulence model are considered to be uncertain and are calibrated using wind tunnel measurements.

Uncertainty Quantification of Spalart–Allmaras Turbulence Model Coefficients for Simplified Compressor Flow Features

Abstract Turbulence model in Reynolds-averaged Navier–Stokes (RANS) simulations has a crucial effect on predicting the compressor flows. In this paper, the parametric uncertainty of the Spalart–Allmaras (SA) turbulence model is studied in simplified two-dimensional (2D) flows, which includes some of the compressor tip flow features. The uncertainty is quantified by a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within intervals, and the quantities of interest include the velocity profile, the Reynolds stress profile, the shock front, and the separation size. An artificial neural network (ANN) is applied as the metamodel, which is tuned, trained, and tested using databases from the flow solver. The uncertainty of quantities of interest is determined by the range of the metamodel and the database samples from the flow solver. The sensitivity of the model coefficients is quantified by calculating the gradient of quantities of interest from the metamodel. Results show that the high-fidelity data of the quantities of interest cannot be fully enveloped by the uncertainty band in regions with separation and shock. Crucial model coefficients on the quantities of interest are identified. However, recalibration of these coefficients results in contradictory prediction of different quantities of interest across flow regimes, which indicates the need for a modified Spalart–Allmaras turbulence model form to improve the accuracy in predicting complex flow features.

On the verification of CFD solvers of all orders of accuracy on curved wall-bounded domains and for realistic RANS flows

This paper aims at extending a recent high-order code verification methodology to curved wall-bounded domains as well as to realistic turbulent flows such as the flat plate boundary layer modelled by the Reynolds-averaged Navier-Stokes (RANS) equations. Two new manufactured solutions (MSs) are introduced with demonstrated ability to verify the treatment of slip and no-slip boundary conditions in high-order frameworks on curved domains. These MSs serve as well to discuss the impact of the method of computation of boundary normals on the order of accuracy (OOA) of the solution at the wall. Furthermore, two turbulent boundary layer MSs from literature, devised to mimic the genuine features of RANS-modelled flows in the vicinity of wall, are compared in terms of their suitability to achieving high-order accuracy. A number of useful concepts in verification are explored through these cases such as the limit values of the Spalart-Allmaras (SA) turbulence model source terms at the wall, the verification of the modified vorticity term of the negative SA model, the grid sensitivity of wall-bounded turbulent flows, the inadequacy of substituting solution verification to code verification and the effect of non-dimensionalization of the solution on the minimization of iterative errors via residual convergence. In all cases, demonstrations are carried for orders of accuracy up to the sixth.

Comparison of turbulent Prandtl number correction models for the Stanton evaluation over rough surfaces

ABSTRACT In-flight ice accretion code predictions depend on heat loss over rough surfaces. The equivalent sand grain roughness models the friction coefficient, but an additional model is needed for heat transfer predictions. In this paper, a two parameters model based on a turbulent Prandtl number correction is derived from the sublayer Stanton-based model. For flow over rough surfaces, the new model predictions will be compared to a three parameters model from the literature. First, the models are coupled with the Spalart–Allmaras turbulence model to predict heat transfers over rough surfaces. Thereafter, the two models are implemented in the open-source software, SU2, and then verified and validated for flow over rough flat plates. Lastly, the predictions of the two models are shown to be similar for ice accretion roughness on flat plates, aerofoils and a wing. Model discrepancies are always within the experimental 15% error margin.

Correction to the Spalart–Allmaras Turbulence Model, Providing More Accurate Skin Friction

The target is boundary layers at relatively low Reynolds numbers. The correction is simple and only alters the constant, so that the calibration of the original model in free shear flows and in high-Reynolds-number boundary layers is preserved. Its effect vanishes for momentum-thickness Reynolds number larger than about 5000, in the flat-plate boundary layer. Below 5000, the agreement with experiment for skin friction is strongly improved, and the differences, which reach 15% for the original Spalart–Allmaras model, are now of the order of the experimental uncertainty. The alteration of the logarithmic law is negligible. Ultimately at very high Reynolds number, the new model shifts the curve of versus the streamwise Reynolds number to the left by units of . On the other hand, the effect on channel flow is to introduce an excess of skin friction of a few percent.

Numerical prediction of aerodynamic performance for open geometry centrifugal compressor

Numerical prediction of aerodynamic performance of compressors has been widely performed by the RANS model, but there is the tendency to overestimate the work and efficiency of the impeller of a centrifugal compressor. In the RANS, we cannot analyze unsteady phenomena such as tip leakage flow. On the other hand, the LES models universal region of turbulence by performing spatial filtering operations. Since it does not include the concept of time averaging, it can be applied to unsteady calculations. In this paper we perform numerical prediction of aerodynamic performance by the RANS with the Spalart-Allmaras turbulence model and the LES with the Smagorinsky model, and reveal the unsteady phenomena, which cannot be analyzed by the RANS, by comparing each result. The CFD solver that we use is “UPACS”, which JAXA (Japan Aerospace Exploration Agency) has developed. We clarify its prediction accuracy and problem points of UPACS. The geometry data of the centrifugal compressor that we analyze is published in the papers written by Krain. The compressor is equipped with impeller with 24 full blades and vaneless diffuser. Comparing computed characteristic curves of mass-averaged total pressure, using the LES improves the overestimation of the total pressure ratio by the RANS by 10%. It seems that the LES can analyze the unsteady phenomena which the RANS cannot.

Numerical Study of Airfoil Selection and Analysis of 3D Flow Phenomenon past Finite-Span Wings for Small UAVs

Small unmanned aerial vehicle (SUAV) is an unmanned aircraft vehicle (UAV) that flies at an altitude of lower than 1,100 m from the ground, has a maximum gross takeoff weight of 10 kg, and a flight speed of less than 50 m/s. One of the design factors for the small UAV design with a fixed-wing propeller is the airfoil selection. The selection of an airfoil profile using aerodynamic concepts leads to a performance coefficient that determines the selected airfoil’s sustainability and efficiency. The coefficients used are CL, CD, and CM. Numerical studies were carried out using Computational Fluid Dynamics using XFLR5 and ANSYS Fluent 19.1 software to evaluate airfoils in 2D and evaluate the phenomenon of induced drag on the wings in 3D. Airfoil selection was made on five types of airfoils: AH 83-150 Q, E399, E431, E715, and E662. The coefficients of CL, CD, and CM were obtained by varying α. 3D analysis of selected airfoil geometry with finite span. Simulation of steady conditions using Reynolds-Averaged-Navier-Stokes (RANS) in the Spalart-Allmaras turbulent model with variations of α = 0 ◦ , 8◦ , 12◦ , and 16◦ . The post-processor visualized the flow around the wing with pressure contours, velocity pathlines, and tip vortices. The analysis was carried out on the aerodynamic coefficients of CL, CD, CM, and CMr with α variation on the finite span wing. Based on the research, the results showed that the selected airfoil was E431, the aerodynamic performance of the CL, CD, CL/CD, CM, and CMr wings. In addition, information was also obtained regarding a decrease in the pressure difference between the upper surface and lower surface of the wing with an increasing span, 3D streamline, the extent of the contour of the vorticity magnitude, and a streamline on the wingtip on the upper surface and lower surface of the wing.

Reynolds shear stress modeling in turbulent boundary layers subject to very strong favorable pressure gradient

Recent numerical predictions of turbulent boundary layers subject to very strong Favorable Pressure Gradient (FPG) with high spatial/temporal resolution, i.e. Direct Numerical Simulation (DNS), have shown a meaningful weakening of the Reynolds shear stresses with a lengthy logarithmic behavior [1,2]. In the present study, assessment of the Shear Stress Transport and Spalart-Allmaras turbulence models (henceforth SST and SA, respectively) in Reynolds-averaged Navier-Stokes (RANS) simulations is performed. The main objective is to evaluate the ability of popular turbulence models in capturing the characteristic features present during the quasi-laminarization phenomenon in highly accelerating turbulent boundary layers. A favorable pressure gradient is prescribed by a top converging surface (sink flow) with an approximately constant acceleration parameter of K=4.0×10−6. Validation of RANS results is carried out by means of a large DNS dataset [1]. Generally speaking, the SA turbulence model has demonstrated the best compromise between accuracy and quick adaptation to the turbulent inflow conditions. Turbulence models properly captured the increasing trend of the freestream and friction velocity in highly accelerated flows; however, they fail to reproduce the decreasing behavior of the skin friction coefficient, which is typical in early stages of the quasi-laminarization process. Both models have shown deficient predictions of the decreasing and logarithmic behavior of Reynolds shear stresses as well as significantly overpredicted the production of Turbulent Kinetic Energy (TKE) in turbulent boundary layers subject to very strong FPG.

A Novel Vortex Identification Technique Applied to the 3D Flow Field of a High-Pressure Turbine

Abstract The efficiency of modern axial turbomachinery is strongly driven by the secondary flows within the vane or blade passages. The secondary flows are characterized by a complex pattern of vortical structures that origin, interact, and dissipate along the turbine gas path. The endwall flows are responsible for the generation of a significant part of the overall turbine loss because of the dissipation of secondary kinetic energy and mixing out of nonuniform momentum flows. The understanding and analysis of secondary flows requires a reliable vortex identification technique to predict and analyze the impact of specific turbine designs on the turbine performance. However, the literature shows a remarkable lack of general methods to detect vortices and to determine the location of their cores and to quantify their strength. This paper presents a novel technique for the identification of vortical structures in a general 3D flow field. The method operates on the local flow field, and it is based on a triple decomposition of motion proposed by Kolář. In contrast to a decomposition of velocity gradient into the strain and vorticity tensors, this method considers a third, pure shear component. The subtraction of the pure shear tensor from the velocity gradient remedies the inherent flaw of vorticity-based techniques, which cannot distinguish between rigid rotation and shear. The triple decomposition of motion serves to obtain a 3D field of residual vorticity whose magnitude is used to define vortex regions. The present method allows to locate automatically the core of each vortex, to quantify its strength, and to determine the vortex bounding surface. The output may be used to visualize the turbine vortical structures for the purpose of interpreting the complex three-dimensional viscous flow field and to highlight any case-to-case variations by quantifying the vortex strength and location. The vortex identification method is applied to a high-pressure turbine with three optimized blade tip geometries. The 3D flow field is obtained by computational fluid dynamics (CFD) computations performed with Numeca FINE/Open. The computational model uses steady-state Reynolds-averaged Navier–Stokes (RANS) equations closed by the Spalart-Allmaras turbulence model. Although developed for turbomachinery applications, the vortex identification method proposed in this work is of general applicability to any three-dimensional flow field.

Numerical Study of Super-cooled droplet impingement on Aeroengine

In this work, a large bypass ratio engine was taken as the research object. The impingement property of droplets with various diameters including SLD (Super-cooled Large Droplet) was obtained by Euler method based on Mundo model. The grid models of nose cone, fan, guild vanes in bypass duct and core duct were established in segments firstly. The mixed boundary was used to realize the data exchange between different flow fields. Then the Spalart-Allmaras turbulence model was applied to calculate the three dimensional engine flow field. Based on the flow field result, the droplet trajectory was calculated by Euler multiphase flow method. The LWC (Liquid Water Content), droplet collection efficiency and the effect of droplet diameter on impingement law were obtained. The method used in this paper and results could provide some references for subsequent engine icing calculation and anti-icing system design.

A Novel Viscous Throughflow Model for Compressor Analysis and Its Application

Throughflow calculations are still an inevitable step in the aerodynamic design of compressors. The viscous throughflow model derived from Navier-Stokes equations can be more capable in predicting choked flow and capturing shock waves compared to the traditional methods. In this paper, authors further developed the inviscid model for a previously developed throughflow analysis method. To obtain the governing equations, three-dimensional Navier-Stokes equations combined with the Spalart-Allmaras turbulence model were circumferentially averaged with the assumption that the flow was circumferentially uniform. A viscous blade force and an inviscid blade force had been calculated. The Miller's correlations of deviation angle and loss were incorporated to model these forces. The governing equations are discretized by an explicit four-step Runge-Kutta scheme and solved by a time-marching finite volume method. Current model was verified through predicting the performances of a 1.5 stage fan. The agreements between the experiments and calculations are reasonably good. This throughflow model can predict quite similar flow patterns and radial profiles of some parameters compared to a CFD software, which shows the potential of this model. There are still some notable deviations between the results from throughflow analysis and that from CFD calculation. Future work is to improve the prediction of deviation angle and loss near the endwall regions.

Mathematical Simulation of a Twisted Inlet Jet at Variable Mode with Using Various Turbulence Models

The article is devoted to the solution of actual task – the efficiency increasing of the air distribution using twisted and wall air jets to provide normative air parameters in premises . The purpose of the paper is to determin e the characteristics of air flow that is formed by twisted and flat wall jet s at alternating air flow and to obtain analytic equations for determining of needed dynamic parameters of the air jets, and also to design the mathematical model of incoming air flow at the alternating air flow . The mathematical model of air supply with twisted and wall air jets is improved. It is shown that for reaching the maximal efficiency of air distribution it is necessary to supply air by jets that intensively decay before entering into a working zone . Simulation of air flow was carried out using the computational fluid dynamic software Ansys FLUENT. Simulation of the flow are carried out by one-parameter Spalart-Allmaras turbulence model and two-parameter k –e turbulence model. Good coincidence between the results of simulation using both tur b ulence models is obtained. The graphical and the analytical dependences on the basis of the conducted experimental research, which can be used in subsequent engineering calculations, are shown. Dynamic parameters of air flow that is formed by t he twisted and wall air jets at alternating air flow has been determined. New 4D method of researches is proposed for researching of jets with alternating parameters of the air. Results of experimental investigations of air supply into the room by air distribution device which creates twisted air jets for obtaining more intensive turbulization of air flow in the room are presented. Obtained results of these investigations give possibility to realize engineer ing calculations of air distribution with twisted and wall air jets.

Anisotropic boundary layer mesh generation for reliable 3D unsteady RANS simulations

This paper proposes a Computational Fluid Dynamics (CFD) framework with the aim of combining consistency and efficiency for the numerical simulation of high Reynolds number flows encountered in engineering applications for aerodynamics. The novelty of the framework is the combination of a Reynolds-Averaged Navier–Stokes (RANS) model with an anisotropic mesh adaptation strategy handling arbitrary immersed geometries by building the corresponding boundary layer meshes. The numerical algorithm consists of robust and accurate solution of the unsteady incompressible Navier–Stokes equations supplemented with a Spalart–Allmaras turbulence model and boundary layer remeshing relying on a specifically designed metric. The flow solver is formulated as a Variational Multiscale (VMS) finite element method for the momentum balance and the incompressibility constraint, and as an upwind Petrov–Galerkin method for the nonlinear turbulent equation. The boundary layer remeshing strategy is flexible as it allows the adaptation of arbitrary coarse meshes by modifying the size and the orientation of elements along the immersed boundary to ensure a smooth gradation along the curvature of the body's geometry. The solver is capable of handling highly stretched anisotropic elements and is shown to successfully predict both mean and fluctuating drag/lift coefficients. Laminar and turbulent test cases in 2D and 3D are presented to assess the performance of this framework against experimental results relevant to external aerodynamics, including an airship and a flying drone.

ОБТЕКАНИЕ ЦИЛИНДРА И АЭРОДИНАМИЧЕСКОГО ПРОФИЛЯ С УЧЕТОМ ЛАМИНАРНО-ТУРБУЛЕНТНОГО ПЕРЕХОДА

A simulation of the flow around a cylinder and a NACA 4412 airfoil was carried out using the γγ-Reθ laminar-turbulent transition model and without it. Numerical simulation was performed on the basis of the Reynolds-averaged Navier-Stokes equations (URANS), using the Spalart-Allmaras differential one-parameter turbulence model. The system of initial equations was written with respect to an arbitrary curvilinear coordinate system. The coordination of the pressure and velocity fields was carried out using the method of artificial compressibility modified to calculate non-stationary problems. The integration of the system of initial equations was carried out numerically using the control volume method. For convective flows, a countercurrent Rogers-Kwak approximation was used based on the third-order Roe scheme. In turbulence models, the TVD scheme with a third-order ISNAS flow limiter was used to approximate convective terms. Comparison of the calculation results for a flow past a cylinder is carried out using the laminar-turbulent transition model and without it. It is shown that at low Reynolds numbers, when the flow around a cylinder is laminar, and the track isturbulent use of the Spalart-Allmaras turbulence model leads to the development of a turbulent boundary layer on the cylinder and, consequently, to a change in the position of the separation point. The incorrect position of the separation point affects the pressure distribution in the bottom of the cylinder and, as a result, the integral aerodynamic characteristics. The use of the transition model allows one to adequately reconstruct the laminar separation near the leading edge of the airfoil with its subsequent reattachment. The use of the Spalart-Allmaras model alone leads to excessive generation of turbulent viscosity. It is shown that the use of the γ-Reθ laminar-turbulent transition model the qualitatively and quantitatively improves the results of numerical simulation. The results of numerical simulation of the flow around a circular cylinder and the NACA 4412 aerodynamic airfoil agree well with experimental data in a wide range of Reynolds numbers.

Effects of trailing-edge movable flap on aerodynamic performance and noise characteristics of VAWT

Efficiency enhancement and noise reduction are the two critical factors in the wind turbine design. In this paper, the effects of trailing-edge flap on the aerodynamic performance and noise characteristics of NACA0018 airfoil and vertical axis wind turbine (VAWT) were investigated, and the geometric parameters including flap angle, flap position and flap length were considered. The aerodynamic performance was simulated with the Detached-Eddy Simulation (DES) based on Spalart-Allmaras turbulence model and noise characteristics is calculated by CFD combined with Ffowcs-Williams and Hawkings (FW-H) acoustic analogy method. The research results indicate that the trailing-edge flap could effectively suppress flow separation and reduce the airfoil noise at high angle of attack (AOA). The optimum flap parameters obtained by orthogonal experimental design (OED) method were applied in VAWT, and it was observed that the trailing-edge flap could significantly improve the power coefficient at high tip-speed ratio (TSR) and reduce the VAWT noise. The research in this paper provided a comprehensive reference for improving the dynamic stall characteristics and reducing the noise of VAWT in practical engineering applications.