Turbulence modelling of the flow past a pitching NACA0012 airfoil at and Reynolds numbers

This paper provides a study of the NACA0012 dynamic stall at Reynolds numbers 10⁵ and 10⁶ by means of two- and three-dimensional numerical simulations. The turbulence effect on the dynamic stall is studied by statistical modelling. The results are compared with experiments concerning each test case. Standard URANS turbulence modelling have shown a quite dissipative character that attenuates the instabilities and the vortex structures related to the dynamic stall. The URANS approach Organised Eddy Simulation (OES) has shown an improved behaviour at the high Reynolds number range. Emphasis is given to the physical analysis of the three-dimensional dynamic stall structure, for which there exist few numerical results in the literature, as far as the Reynolds number range is concerned. This study has shown that the downstroke phases of the pitching motion are subjected to strong three-dimensional turbulence effects along the span, whereas the flow is practically two-dimensional during the upstroke motion.     

Some new characteristics of the confined flow over circular cylinders at low reynolds numbers

This study summarises some new characteristics of the fluid flow over a confined circular cylinder at low Reynolds numbers. Results from both two- and three-dimensional direct numerical simulations are presented at blockage ratio between 0.1 and 0.9 and Reynolds number between 120 and 500. Floquet stability analysis of selected cases will also be presented. From the two-dimensional simulations, it is found that the fluctuating lift forces decreases with blockage ratio and becomes zero (where the flow is steady) at blockage ratio of approximately 0.7–0.8. Upon further increasing the blockage ratio to 0.9, the simulations show a dramatic increase in the fluctuating lift forces, nearly an order of magnitude greater than previously reported for an unconfined cylinder flow. It is also found that for blockage ratio of 0.5, there is a long term two-dimensional instability that becomes more prominent with increasing Reynolds number. This instability has a time scale of approximately 105 time units ($D/U_{\mathit{max}}$) at Reynolds number of 500. In addition, the transition between two- and three-dimensional flow at blockage ratios up to 0.5 is investigated. It is shown that the transition Reynolds number decreases with increasing blockage ratio. At high blockage ratio of 0.5, as we increase the Reynolds number, the transition to three-dimensional flow is shown to go from unsteady two-dimensional to steady three-dimensional before transitioning to unsteady three-dimensional flow.     

Double-diffusive convection in a cubical lid-driven cavity with opposing temperature and concentration gradients

A numerical study of three-dimensional incompressible viscous flow inside a cubical lid-driven cavity is presented. The flow is governed by two mechanisms: (1) the sliding of the upper surface of the cavity at a constant velocity and (2) the creation of an external gradient for temperature and solutal fields. Extensive numerical results of the three-dimensional flow field governed by the Navier-Stokes equations are obtained over a wide range of physical parameters, namely Reynolds number, Grashof number and the ratio of buoyancy forces. The preceding numerical results obtained have a good agreement with the available numerical results and the experimental observations. The deviation of the flow characteristics from its two-dimensional form is emphasized. The changes in main characteristics of the flow due to variation of Reynolds number are elaborated. The effective difference between the two-dimensional and three-dimensional results for average Nusselt number and Sherwood number at high Reynolds numbers along the heated wall is analyzed. It has been observed that the substantial transverse velocity that occurs at a higher range of Reynolds number disturbs the two-dimensional nature of the flow.     

Experimental and numerical investigation on steady blowing flow control within a compact inlet duct

A combined experimental and numerical investigation of flow control actuation in a short, rectangular, diffusing S-shape inlet duct using a two-dimensional tangential control jet was conducted. Experimental and numerical techniques were used in conjunction as complementary techniques, which are utilized to better understand the complex flow field. The compact inlet had a length-to-hydraulic diameter ratio of 1.5 and was investigated at a free-stream Mach number of 0.44. In contrast to the baseline flow, where the flow field was fully separated, the two-dimensional control jet was able to eliminate flow separation at the mid-span portion of the duct and changed considerably the three-dimensional flow field, and ultimately, the inlet performance. A comparison between the baseline (no actuation) and forced flow fields showed that secondary flow structures dominated both flow fields, which is inevitably associated with total pressure loss. Contrary to the baseline case, the secondary flow structures in the forced case were established from the core flow stagnating on the lower surface of the duct close to the aerodynamic interface plane. High fidelity spectral analysis of the experimental results at the inlet’s exit plane showed that the baseline flow field was dominated by pressure fluctuations corresponding to a Strouhal number based on hydraulic diameter of 0.26. Not only did the two-dimensional tangential control jet improve the time-averaged pressure recovery at the inlet exit plane (13.3% at the lower half of the aerodynamic interface plane), it essentially eliminated the energy content of the distinct unsteady fluctuations which characterized the baseline flow field. This result has several implications for the design of a realistic engine inlet; furthermore, it depicts that a single non-intrusive static pressure measurement at the surface of the duct can detect flow separation.     

An experimental and three-dimensional numerical study on the convective heat transfer inside a trapezoidal duct under constant wall temperature

In this study, steady-state forced convection heat transfer and pressure drop characteristics for hydrodynamically fully developed thermally developing three-dimensional turbulent flow in a horizontal smooth trapezoidal duct with corner angle of 75° and hydraulic diameter of 0.043 m were both experimentally and numerically investigated in the Reynolds number range from 2.6 × 10³ to 67 × 10³ for isothermal conditions. Results have shown that there is a good agreement between the present experimental and numerical results.     

Unsteady PTV velocity field past an airfoil solved with DNS: Part 1. Algorithm of hybrid simulation and hybrid velocity field at <Emphasis Type="Italic">Re</Emphasis> ≈ 10<Superscript>3</Superscript>

We develop a hybrid unsteady-flow simulation technique combining direct numerical simulation (DNS) and particle tracking velocimetry (PTV) and demonstrate its capabilities by investigating flows past an airfoil. We rectify instantaneous PTV velocity fields in a least-squares sense so that they satisfy the equation of continuity, and feed them to the DNS by equating the computational time step with the frame rate of the time-resolved PTV system. As a result, we can reconstruct unsteady velocity fields that satisfy the governing equations based on experimental data, with the resolution comparable to numerical simulation. In addition, unsteady pressure distribution can be solved simultaneously. In this study, particle velocities are acquired on a laser-light sheet in a water tunnel, and unsteady flow fields are reconstructed with the hybrid algorithm solving the incompressible Navier–Stokes equations in two dimensions. By performing the hybrid simulation, we investigate nominally two-dimensional flows past the NACA0012 airfoil at low Reynolds numbers. In part 1, we introduce the algorithm of the proposed technique and discuss the characteristics of hybrid velocity fields. In particular, we focus on a vortex shedding phenomenon under a deep stall condition (α = 15°) at Reynolds numbers of Re = 1000 and 1300, and compare the hybrid velocity fields with those computed with two-dimensional DNS. In part 2, the extension to higher Reynolds numbers is considered. The accuracy of the hybrid simulation is evaluated by comparing with independent experimental results at various angles of attack and Reynolds numbers up to Re = 10⁴. The capabilities of the hybrid simulation are also compared with two-dimensional unsteady Reynolds-Averaged Navier–Stokes (URANS) solutions in part 2. In the first part of these twin papers, we demonstrate that the hybrid velocity field approaches the PTV velocity field over time. We find that intensive alternate vortex shedding past the airfoil, which is predicted by the two-dimensional DNS, is substantially suppressed in the hybrid simulation and the resultant flow field is similar to the PTV velocity field, which is projection of the three-dimensional velocity field on the streamwise plane. We attempt to identify the motion that originates three-dimensional flow patterns by highlighting the deviation of the PTV velocity field from the two-dimensional governing equations at each snapshot. The results indicate that the intensive spots of the deviation appear in the regions in which three-dimensional instabilities are induced in the shear layer separated from the pressure side.     

Numerical simulations of laminar flow over a 3D backward-facing step

A numerical investigation of laminar flow over a three-dimensional backward-facing step is presented with comparisons with detailed experimental data, available in the literature, serving to validate the numerical results. The continuity constraint method, implemented via a finite element weak statement, was employed to solve the unsteady three-dimensional Navier–Stokes equations for incompressible laminar isothermal flow. Two-dimensional numerical simulations of this step geometry underestimate the experimentally determined extent of the primary separation region for Reynolds numbers Re greater than 400. It has been postulated that this disagreement between physical and computational experiments is due to the onset of three-dimensional flow near Re ≈ 400. This paper presents a full three-dimensional simulation of the step geometry for 100⩽ Re⩽ 800 and correctly predicts the primary reattachment lengths, thus confirming the influence of three-dimensionality. Previous numerical studies have discussed possible instability modes which could induce a sudden onset of three-dimensional flow at certain critical Reynolds numbers. The current study explores the influence of the sidewall on the development of three-dimensional flow for Re greater than 400. Of particular interest is the characterization of three-dimensional vortices in the primary separation region immediately downstream of the step. The complex interaction of a wall jet, located at the step plane near the sidewall, with the mainstream flow reveals a mechanism for the increasing penetration (with increasing Reynolds number) of three-dimensional flow structures into a region of essentially two-dimensional flow near the midplane of the channel. The character and extent of the sidewall-induced flow are investigated for 100⩽Re⩽ 800. © 1997 John Wiley & Sons, Ltd.     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

Experimental investigation of flow and heat transfer in rectangular cross-sectioned duct with baffles mounted on the bottom surface with different inclination angles

In this study, steady-state forced convection heat transfer and pressure drop characteristics in a horizontal rectangular cross-sectioned duct, baffles mounted on the bottom surface with different inclination angles were investigated experimentally in the Reynolds number range from 1 × 10³ to 1 × 10⁴. The study was performed under turbulent flow conditions. Effects of different baffle inclination angles on flow and heat transfer were studied. Results are also presented in terms of thermal enhancement factor. It is observed that increasing in baffle inclination angle enhances the heat transfer and causes an increase in pressure drop in the duct.     

Numerical and experimental investigation of turbulent flow in a rectangular duct

Details of the turbulent flow in a 1:8 aspect ratio rectangular duct at a Reynolds number of approximately 5800 were investigated both numerically and experimentally. The three-dimensional mean velocity field and the normal stresses were measured at a position 50 hydraulic diameters downstream from the inlet using laser doppler velocimetry (LDV). Numerical simulations were carried out for the same flow case assuming fully developed conditions by imposing cyclic boundary conditions in the main flow direction. The numerical approach was based on the finite volume technique with a non-staggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with a linear and a non-linear (Speziale) k–ε model, combined with the Lam–Bremhorst damping functions for low Reynolds numbers. The secondary flow patterns, as well as the magnitude of the main flow and overall parameters predicted by the non-linear k–ε model, show good agreement with the experimental results. However, the simulations provide less anisotropy in the normal stresses than the measurements. Also, the magnitudes of the secondary velocities close to the duct corners are underestimated. © 1998 John Wiley & Sons, Ltd.     

Some Reynolds number effects on two- and three-dimensional turbulent boundary layers

Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re _θ =23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds number effects are examined using fine spatial resolution (Δy ⁺=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations for Re _θ =23,200 and previously reported data for a much thinner boundary layer at Re _θ =5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due to deceleration, acceleration, and skewing, profiles of the parameter correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re _θ case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement stations. Received: 9 June 2000/Accepted: 26 January 2001     

Local Nusselt number and temperature field in turbulent flow through a heated square-sectioned U-bend

Local heat transfer coefficients and temperature distributions within the fluid for air flow around a 180° square-sectioned bend have been measured. The ratio of bend radius to hydraulic diameter of the duct is 3.35:1 and the flow entering the bend is sensibly fully developed. Measurements of air and wall temperatures span a range of Reynolds numbers from 9.9 × 10³ to 9.2 × 10⁴ with the principal emphasis given to the case of Re ? 5.6 × 10⁴. This Reynolds number and geometric configuration coincide with that of a companion LDA study carried out by Chang et al¹ which provides detailed maps of the mean and turbulent velocity fields. The data show that by 45° into the bend the heat transfer coefficients on the inner convex wall of the bend drop markedly while those on the other walls increase. By 90° the ratio of the heat transfer coefficients at the mid positions of the concave and convex walls is more than 2:1. Nevertheless this ratio is less than would be anticipated from considering two-dimensional flow on weakly curved surfaces. There is a general consistency between the velocity and the temperatyre field data in the heated fluid     

Flow-induced vibration of a circular cylinder subjected to wake interference at low Reynolds number

Two- and three-dimensional numerical simulations of the flow around two circular cylinders in tandem arrangements are performed. The upstream cylinder is fixed and the downstream cylinder is free to oscillate in the transverse direction, in response to the fluid loads. The Reynolds number is kept constant at 150 for the two-dimensional simulations and at 300 for the three-dimensional simulations, and the reduced velocity is varied by changing the structural stiffness. The in-line centre-to-centre distance is varied from 1.5 to 8.0 diameters, and the results are compared to that of a single isolated flexible cylinder with the same structural characteristics, m^?=2.0 and ζ=0.007. The calculations show that significant changes occur in the dynamic behaviour of the cylinders, when comparing the flow around the tandem arrangements to that around an isolated cylinder: for the tandem arrangements, the lock-in boundaries are wider, the maximum displacement amplitudes are greater and the amplitudes of vibration for high reduced velocities, outside the lock-in, are very significant. The main responsible for these changes appears to be the oscillatory flow in the gap between the cylinders.     

Three-dimensional flow in a lid-driven cavity with width-to-height ratio of 1.6

The flow in a lid-driven cavity with width-to-height ratio of 1.6 is investigated numerically and experimentally. Experimental investigation use an apparatus with a spanwise length-to-height ratio of $\Uplambda = 10.85.$ Λ = 10.85 . Increasing the Reynolds number, we experimentally find a gradual change from the quasi-two-dimensional basic flow to a three-dimensional flow pattern. The three-dimensional flow has a significant amplitude at considerably low Reynolds numbers. Streak-line photographs and PIV vector maps are presented to illustrate the structure of the finite-amplitude flow pattern. The smooth transition is in contrast to the linear instability predicted by a linear-stability analysis for a cavity with infinite span. LDV measurements confirm the absence of a distinct threshold Reynolds number and indicate an imperfect bifurcation. The deviations between experimental observations and numerical critical Reynolds number for infinite span are explained by conducting three-dimensional simulations for a finite-span geometry. A good agreement between experimental and numerical simulation is obtained. The numerical and experimental data lead to the conjecture of a premature onset of the three-dimensional flow caused by strong secondary flows which are induced by the cavity end walls. Nevertheless, the flow structure in the finite-span cavity carries the same characteristic signatures as the nonlinear flow in the corresponding infinite-length cavity. We conclude that the observed flow can be identified as the continuation of the normal mode C _e ⁴ earlier identified in a linear-stability analysis.     

Finite element analysis of two- and three-dimensional flows around square columns in tandem arrangement

Two- (2D) and three-dimensional (3D) finite element analyses for flow around two square columns in tandem arrangement were performed with various column spacings and Reynolds numbers. The computed values were compared with the wind-tunnel results in terms of the aerodynamic characteristics of the leeward column. In most 2D computations, strong vortices were formed behind the windward column, irrespective of widely changed Reynolds numbers. This was different from the experimental phenomena of equivalent spacing, so that the computed time-averaged pressure coefficients were not identical to the experimental values except when the distance between the two columns was adequately wide or narrow. On the other hand, in 3D computation, distinct differences in flow structures behind the column were observed between Reynolds numbers of 10³ and 10⁴ and the pressure coefficient in the 3D analysis with Re=10⁴ agreed well with the experimental value. Thus, the effectiveness of 3D computations and Reynolds number effects on the flow around two square columns have been confirmed. © 1998 John Wiley & Sons, Ltd.     

The structure of parallel layers in steady two-dimensional magnetohydrodynamic flows in sudden duct expansions and contractions

The structure of non-linear, steady, two-dimensional parallel layers at high values of the Hartmann number, Ha, the Reynolds number, Re, and the interaction parameter, N, for duct expansions and contractions has been investigated. The magnetic field is transverse to the flow. For the flow regime, in which the electromagnetic force balances the inertial force in the layer, a viscous sublayer at the solid wall parallel to the magnetic field has been obtained, in which the flow is driven by the pressure gradient induced in the outer, inviscid layer.     

Numerical prediction of vortex shedding behind a square cylinder

It is common knowledge that flow around bluff bodies exhibits oscillatory behaviour. The aim of the present study is to compute the steady two-dimensional flow around a square cylinder at different Reynolds numbers and to determine the onset of unsteadiness through a linear stability analysis of the steady flow. Stability of the steady flow to small two-dimensional perturbations is analysed by computing the evolution of these perturbations. An analysis of various time-stepping techniques is carried out to select the most appropriate technique for predicting the growth of the perturbations and hence the stability of the flow. The critical Reynolds number is determined from the growth rate of the perturbations. Computations are then made for periodic unsteady flow at a Reynolds number above the critical value. The predicted Strouhal number agrees well with experimental data. Heat transfer from the cylinder is also studied for the unsteady laminar flow.     

Vortex shedding and three-dimensional behaviour of flow past a cylinder confined in a channel

A numerical investigation of the flow past a circular cylinder centred in a two-dimensional channel of varying width is presented. For low Reynolds numbers, the flow is steady. For higher Reynolds numbers, vortices begin to shed periodically from the cylinder. In general, the Strouhal frequency of the shedding vortices increases with blockage ratio. In addition, a two-dimensional instability of the periodic vortex shedding is found, both empirically and by means of a Floquet stability analysis. The instability leads to a beating behaviour in the lift and drag coefficients of the cylinder, which occurs at a Reynolds number higher than the critical Reynolds number for the three-dimensional mode A-type instability, but lower than a Reynolds number for any mode B-type instability.     

A LES study of the flow interference between tandem square cylinder pairs

The results of an investigation on the interference effects of the tandem square cylinders exposed to a uniform flow are presented in this paper. Time-dependent and three-dimensional flow simulations are carried out using large eddy simulation with a one-equation subgrid model. An incompressible three-dimensional finite volume code with a collocated grid arrangement is used for solving filtered Navier–Stokes equations. These equations are solved with an implicit fractional two-step method. Simulations are conducted with different Reynolds numbers between 10³ and 10⁵. The longitudinal spacing between the cylinders is selected 4D for the chosen Reynolds numbers, where D is the side of the cylinders. Also the effect of the spacing between cylinders, ranging from 1D to 12D, is studied for the selected Reynolds numbers. The instantaneous flow field is studied by analyzing the vortices, pressure, streamlines and Q-criterion to assist understanding of the various flow patterns, vortical structures and Kelvin–Helmholtz vortices in the separating shear layers. The hysteresis is observed in a certain range of the gap spacing, which this range depends on the selected Reynolds number. The global results are also computed and compared with available experimental results. The results indicate that there is a satisfactory agreement between the predictions and available experimental data considering the fine grid adopted.     

Use of zero-net-mass-flow for separation control in diffusing S-duct

Flow control using zero-net-mass-flow jets in an S-shaped diffusing duct was investigated. Experiments were conducted in a channel flow facility at a Reynolds number, Re = 4.1 × 10⁴ with particle image velocimetry measurements in the symmetry plane of the duct. In the natural configuration, separation of the boundary layer occurs in a region of the duct with an high degree of curvature. A stability analysis of the wall normal base flow at the location of the applied control is presented and estimates the most effective frequency of the actuator. Time-averaged velocity fields show total reattachment of the boundary layer using active flow control.