Experimental investigation of the effect of Reynolds number on flow structures in the wake of a circular parachute canopy

In the present study, an experimental study was conducted to characterize the effect of Reynolds number on flow structures in the turbulent wake of a circular parachute canopy by utilizing stereoscopic particle image velocime- try （Stereo-PIV） technique. The parachute model tested in the present study was attached by 28 nylon suspension lines and placed horizontally at the test section center of the wind tunnel. The obtained results showed that with the in- crease of Reynolds number, the intensities of the vortices near the downstream region of the canopy skirt were found to increase accordingly. However, the increase of Reynolds number did not result in a significant change in ensemble- averaged normalized x-component of the velocity, ensembleaveraged normalized vorticity, normalized Reynolds stress, and normalized turbulent kinetic energy distributions in the turbulent wake of the circular parachute canopy. The obtained results are very useful to further our understanding about the unsteady aerodynamics in the wake of flexible circular parachute canopies and to constitute a reference for CFD computation.     

Towards multi-fidelity simulation of flows around an underwater vehicle with appendages and propeller

Flow around a real-life underwater vehicle often happens at a high Reynolds number with flow structures at different scales from the boundary layer around a blade to that around the hull. This poses a great challenge for large-eddy simulation of an underwater vehicle aiming at resolving all relevant flow scales. In this work, we propose to model the hull with appendages using the immersed boundary method, and model the propeller using the actuator disk model without resolving the geometry of the blade. The proposed method is then applied to simulate the flow around Defense Advanced Research Projects Agency(DARPA) suboff. An overall acceptable agreement is obtained for the pressure and friction coefficients. Complex flow features are observed in the near wake of suboff. In the far wake, the core region is featured by a jet because of the actuator disk, surrounded by an annular region with velocity deficit due to the body of suboff.     

A NON-ISOTROPIC MULTIPLE-SCALE TURBULENCE MODEL

This paper describes a newly developed non-isotropic multiple-scale turbulence model(MS/ASM)for complex flow calculations.This model focuses on the direct modeling of Reynolds stresses and utilizes split-spectrum concepts to model multiple-scale effects in turbulence.Validation studies on free shear flows,rotating flows and recirculating flows show that the current model performs significantly better than the single-scale k-εmodel.The present model is relatively inexpensive in terms of CPU time which makes in suitable for broad engineering flow applications.     

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples:turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder (GL) model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.     

Investigation of scale effect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale effect of turbulent flow around a circular cylinder, two similarity numbers （criteria） based on turbulent kinetic and dissipation rates associ- ated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged NavierStokes equations （RANS）. The RNG k-s models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102 to l07 is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re ≥ 3 × 10^6. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.     

Investigation of scale efect for the computation of turbulent flow around a circular cylinder

In order to investigate the scale efect of turbulent flow around a circular cylinder, two similarity numbers(criteria) based on turbulent kinetic and dissipation rates associated with the fluctuation characteristics of turbulence wake are deduced by analyzing the Reynolds averaged Navier–Stokes equations(RANS). The RNG k–ε models and finite volume method are used to solve the governing equations and the second-order implicit time and upwind space discretization algorithms are used to discrete the governing equations. A numerical computation of flow parameters around a two-dimensional circular cylinder with Reynolds numbers ranging from 102to 107is accomplished and the result indicates that the fluctuation of turbulence flow along the center line in the wake of circular cylinder can never be changed with increasing Reynolds numbers when Re3 × 106. This conclusion is useful for controlling the scale of numerical calculations and for applying model test data to engineering practice.     

Analytical investigation on 3D non-Boussinesq mountain wave drag for wind profiles with vertical variations

A new analytical model was developed to predict the gravity wave drag (GWD) induced by an isolated 3-dimensional mountain, over which a stratified, non-rotating non-Boussinesq sheared flow is impinged. The model is confined to small amplitude motion and assumes the ambient velocity varying slowly with height. The modified Taylor-Goldstein equation with variable coefficients is solved with a Wentzel-Kramers-Brillouin (WKB) approximation, formally valid at high Richardson numbers. With this WKB solution, generic formulae of second order accuracy, for the GWD and surface pressure perturbation (both for hydrostatic and non-hydrostatic flow) are presented, enabling a rigorous treatment on the effects by vertical variations in wind profiles. In an ideal test to the circular bell-shaped mountain, it was found that when the wind is linearly sheared, that the GWD decreases as the Richardson number decreases. However, the GWD for a forward sheared wind (wind increases with height) decreases always faster than that for the backward sheared wind (wind deceases with height). This difference is evident whenever the model is hydrostatic or not.     

Multiphase fluid dynamics and transport processes of low capillary number cavitating flows

To better understand the multiphase fluid dynamics and associated transport processes of cavitating flows at the capillary number of 0.74 and 0.54, and to validate the numerical results, a combined computational and experimental investigation of flows around a hydrofoil is studied based on flow visualizations and time-resolved interface movement. The computational model is based on a modified RNG k-ε model as turbulence closure, along with a vapor-liquid mass transfer model for treating the cavitation process. Overall, favorable agreement between the numerical and experimental results is observed. It is shown that the cavi- tation structure depends on the interaction of the water-vapor mixture and the vapor among the whole cavitation stage, the interface between the vapor and the two-phase mixture exhibits substantial unsteadiness. And, the adverse motion of the interface relates to pressure and velocity fluctuations inside the cavity. In particular, the velocity in the vapor region is lower than that in the two-phase region.     

Lift force on rotating sphere at low Reynolds numbers and high rotational speeds

The lift force on an isolated rotating sphere in a uniform flow was investigated by means of a three-dimensional numerical simulation for low Reynolds numbers (based on the sphere diameter) (Re<68.4) and high dimensionless rotational speeds (Г5). The Navier-Stokes equations in Cartesian coordinate system were solved using a finite volume formulation based on SIMPLE procedure. The accuracy of the numerical simulation was tested through a comparison with available theoretical, numerical and experimental results at low Reynolds numbers, and it was found that they were in close agreement under the above mentioned ranges of the Reynolds number and rotational speed. From a detailed computation of the flow field around a rotational sphere in extended ranges of the Reynolds number and rotational speed, the results show that, with increasing the rotational speed or decreasing the Reynolds number, the lift coefficient increases. An empirical equation more accurate than those obtained by previous studies was obtained to describe both effects of the rotational speed and Reynolds number on the lift force on a sphere. It was found in calcttlations that the drag coefficient is not significantly affected by the rotation of the sphere. The ratio of the lift force to the drag force, both of which act on a sphere in a uniform flow at the same time, was investigated. For a small spherical particle such as one of about 100μm in diameter, even if the rotational speed reaches about 10^6 revolutions per minute, the lift force can be neglected as compared with the drag force.     

Particle image velocimetry （PIV） measurements of tip vortex wake structure of wind turbine

Large-view flow field measurements using the particle image velocimetry (PIV) technique with high resolution CCD cameras on a rotating 1/8 scale blade model of the NREL UAE phase VI wind turbine are conducted in the engineering-oriented Φ3.2 m wind tunnel.The motivation is to establish the database of the initiation and development of the tip vortex to study the flow structure and mechanism of the wind turbine.The results show that the tip vortex first moves inward for a very short period and then moves out...     

Recent progress on the study of asymmetric vortex flow over slender bodies

The investigations of forebody vortex flow and its flow control have great importance in both academic field and engineering application areas. A large number of papers and many review papers have been published. However in this research field of forebody asymmetric vortices, three problems such as tip perturbation effect, Reynolds number effect and flow instability are less studied and thus not understood completely. So many researches are still working on the issues in recent years. The present paper attempts to provide a review of recent research progress on first two problems. The first problem is mainly concerned with how the vortex flow evolves after tip perturbation; how to solve the problem of repeatability and reproducibility of wind tunnel testing data; how to develop a conception of active flow control technique with tip perturbation based on the study of vortex flow response to tip perturbation. For the second problem one is mainly concerned that how the asymmetric vortices are developed with the increase of Reynolds number; how to classify the vortex flow patterns in different Reynolds number regimes; how to develop an appropriate boundary layer transition technique to simulate flows at high Reynolds number in the convention wind tunnels. Finally, some important ques- tions that deserve answers are proposed in the concluding remarks.     

Numerical simulation of Gurney flap on SFYT15thick airfoil

A two-dimensional steady Reynolds-averaged Navier–Stokes(RANS) equation was solved to investigate the effects of a Gurney flap on SFYT15 thick airfoil aerodynamic performance. This airfoil was designed for flight vehicle operating at 20 km altitude with freestream velocity of 25 m/s. The chord length(C) is5 m and the Reynolds number based on chord length is Re = 7.76 × 105. Gurney flaps with the heights ranging from 0.25%C to 3%C were investigated. The shear stress transport(SST) k-ω turbulence model was used to simulate the flow structure around the airfoil. It is showed that Gurney flap can enhance not only the prestall lift but also lift-to-drag ratio in a certain range of angles of attack. Specially, at cruise angle of attack(α = 3°), Gurney flap with 0.5%C height can increase lift-to-drag ratio by 2.7%, and lift coefficient by 12.9%, respectively. Furthermore, the surface pressure distribution, streamlines and trailing-edge flow structure around the airfoil are illustrated, which are helpful to understand the mechanisms of Gurney flap on airfoil aerodynamic performance. Moreover, it is found that the increase of airfoil drag with Gurney flap can be attributed to the increase of pressure drag between the windward and the leeward sides of Gurney flap itself.     

Nonlinear turbulence models for predicting strong curvature effects

Prediction of the characteristics of turbulent flows with strong streamline curvature, such as flows in turbomachines, curved channel flows, flows around airfoils and buildings, is of great importance in engineering applications and poses a very practical challenge for turbulence modeling. In this paper, we analyze qualitatively the curvature effects on the structure of turbulence and conduct numerical simulations of a turbulent Uduct flow with a number of turbulence models in order to assess their overall performance. The models evaluated in this work are some typical linear eddy viscosity turbulence models, nonlinear eddy viscosity turbulence models （NLEVM） （quadratic and cubic）, a quadratic explicit algebraic stress model （EASM） and a Reynolds stress model （RSM） developed based on the second-moment closure. Our numerical results show that a cubic NLEVM that performs considerably well in other benchmark turbulent flows, such as the Craft, Launder and Suga model and the Huang and Ma model, is able to capture the major features of the highly curved turbulent U-duct flow, including the damping of turbulence near the convex wall, the enhancement of turbulence near the concave wall, and the subsequent turbulent flow separation. The predictions of the cubic models are quite close to that of the RSM, in relatively good agreement with the experimental data, which suggests that these models may be employed to simulate the turbulent curved flows in engineering applications.     

Extended intrinsic mean spin tensor for turbulence modelling in non-inertial frame of reference

We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.     

Effects of shear-thinning/thickening nature on the stability of Couette-like flow with uniform crossflow

The linear stability of wall-injected pressure- driven Couette-like flow in power-law fluids is studied. Previous study on this kind of flow for Newtonian fluids by Nicoud and Angilella [Phys. Rev. E 56, 3000 （1997）] was extended to power-law fluids to understand the effects of shear-thinning/thickening nature on the flow stability. A related expression between the critical crossflow Reynolds number for Newtonian fluids and that for power-law fluids is obtained as the streamwise Reynolds number is large enough based on numerical computations, and verified theoretically in the case of a limiting condition with the power-law index.     

A NEW TURBULENCE MODEL WITH THE SEPARATE CONSIDERATION OF LARGE AND SMALL VORTEXES

Recently the k-ε model has been widely used,but it is a kind of gradient model.Because the life-time of turbulence vortexes is very long,in common flow problems theinfluence of up-stream vortexes must be important,and the vortexes are not in quasi-equilibrium.So the usefulness of the k-εmodel and other gradient models is limited.Inthis paper,according to actual cases of the turbulence,the velocity fluctuations areseparated into large and small vortexes,and the laree vortexes consist of two parts.onecomes from up-stream and around,the other is locally generated.Thus we get a turbulencemodel,which consists of three parts.     

Aeroelastic modeling of wind loading on a cable-net supported glass wall

Wind loading study on a cable-net supported glass wall is conducted by means of wind tunnel tests. An equiva- lent aeroelastic model is designed and constructed. Response of displacements of the wall is measured and analyzed. In order to design a glass wall under wind loading, the ＂wind- vibration factor＂ is estimated and discussed. In fact, the mech- anism of wind acting on the wall is commonly known not only as positive pressure, but also as negative pressure caused by the flow separation on the corners of the building. Due to the diffidence in the mechanism of wind acting, two typi- cal response cases are classified. The results show that the dynamic response of the structure caused by the negative pressure is stronger than that of the positive pressure case. To determine the aerodynamic wind loading on a flexible part of structure on a building, wind tunnel study may be useful and play an important role.     

Studies on gas turbulence and particle fluctuation in dense gas-particle flows

Particle fluctuation and gas turbulence in dense gas-particle flows are less studied due to complexity of the phenomena. In the present study, simulations of gas turbulent flows passing over a single particle are carried out first by using RANS modeling with a Reynolds stress equation turbulence model and sufficiently fine grids, and then by using LES. The turbulence enhancement by the particle wake effect is studied under various particle sizes and relative gas velocities, and the turbulence enhancement is found proportional to the particle diameter and the square of velocity. Based on the above results, a turbulence enhancement model for the particle-wake effect is proposed and is incorporated as a sub-model into a comprehensive two-phase flow model, which is then used to simulate dilute gas-particle flows in a horizontal channel. The simulation results show that the predicted gas turbulence by using the present model accounting for the particle wake effect is obviously in better agreement with the experimental results than the prediction given by the model not accounting for the wake effect. Finally, the proposed model is incorporated into another two-phase flow model to simulate dense gasparticle flows in a downer. The results show that the particle wake effect not only enhances the gas turbulence, but also amplifies the particle fluctuation.     

Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls

The cases of large Reynolds number and small expansion ratio for the asym- metric laminar flow through a two-dimensional porous expanding channel are considered. The Navier-Stokes equations are reduced to a nonlinear fourth-order ordinary differential equation by introducing a time and space similar transformation. A singular perturbation method is used for the large suction Reynolds case to obtain an asymptotic solution by matching outer and inner solutions. For the case of small expansion ratios, we are able to obtain asymptotic solutions by double parameter expansion in either a small Reynolds number or a small asymmetric parameter. The asymptotic solutions indicate that the Reynolds number and expansion ratio play an important role in the flow behavior. Nu- merical methods are also designed to confirm the correctness of the present asymptotic solutions.     

Comparisons and applications of numerical simulation methods for predicting aerodynamic heating around complex configurations

Numerical simulation methods of aerodynamic heating were compared by considering the inuence of numerical schemes and turbulence models,and attempting to investigate the applicability of numerical simulation methods on predicting heat flux in engineering applications. For some typical cases provided with detailed experimental data,four spatial schemes and four turbulence models were adopted to calculate surface heat flux. By analyzing and comparing,some inuencing regularities of numerical schemes and turbulence models on calculating heat flux had been acquired. It is clear that AUSM+-up scheme with rapid compressibilitymodified high Reynolds number k-ω model should be appropriate for calculating heat flux. The numerical methods selected as preference above were applied to calculate the heat flux of a 3-D complex geometry in high speed turbulent flows. The results indicated that numerical simulation can capture the complex flow phenomena and reveal the mechanism of aerodynamic heating. Especially,the numerical result of the heat flux at the stagnation point of the wedge was well in agreement with the prediction of Kemp-Riddel formula,and the surface heat flux distribution was consistent with experiment results,which implied that numerical simulation can be introduced to predict heat flux in engineering applications.