Validating the URANS shear stress transport γ −Reθ model for low‐Reynolds‐number external aerodynamics

A numerical investigation on low‐Reynolds‐number external aerodynamics was conducted using the transitional unsteady Reynolds‐averaged Navier–Stokes shear stress transport γ ?Re_θ model and the ANSYS‐CFX computational fluid dynamics suite. The NACA 0012 airfoil was exposed to chord‐based Reynolds numbers of 5.0 ×10⁴, 1.0 ×10⁵ and 2.5 ×10⁵ at 0°, 4°and 8°angles of attack. Time‐averaged and instantaneous flow features were extracted and compared with fully turbulent shear stress transport results, XFLR5 panel e ^N method results, and published higher order numerical and experimental studies. The current model was shown to reproduce the complex flow phenomena, including the laminar separation bubble dynamics and aerodynamic performance, with a very good degree of accuracy. The sensitivity of the model to domain size, grid resolution and quality, timestepping scheme, and free‐stream turbulence intensity was also presented. In view of the results obtained, the proposed model is deemed appropriate for modelling low‐Reynolds‐number external aerodynamics and provides a framework for future studies for the better understanding of this complex flow regime. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of differential quadrature method to simulate natural convection in a concentric annulus

In this paper, the Fourier expansion‐based differential quadrature (FDQ) and the polynomial‐based differential quadrature (PDQ) methods are applied to simulate the natural convection in a concentric annulus with a horizontal axis. The comparison and grid independence of PDQ and FDQ results are studied in detail. It was found that both PDQ and FDQ can obtain accurate numerical solutions using just a few grid points and requiring very small computational resources. It was demonstrated in the paper that the FDQ method can be applied to a periodic problem or a non‐periodic problem. When FDQ is applied to a non‐periodic problem (half of annulus), it can achieve the same order of accuracy as the PDQ method. And when FDQ is applied to the periodic problem (whole annulus), it is very efficient for low Rayleigh numbers. However, its efficiency is greatly reduced for the high Rayleigh numbers. The benchmark solution for Ra=10², 10³, 3×10³, 6×10³, 10⁴, 5×10⁴ are also presented in the paper. Copyright © 1999 John Wiley & Sons, Ltd.     

Temperature and velocity field characteristics of turbulent natural convection in a vertical parallel-plate channel with asymmetric heating

Turbulent natural convection in an asymmetrically heated vertical parallel-plate channel has been studied experimentally and numerically using LDA and CFD. Simultaneous velocity and temperature measurements across the channel at different elevations have been carried out. Three different Ra(b/h) values of 1.91 × 10⁷, 2.74 × 10⁷ and 3.19 × 10⁷ are considered with the channel aspect ratio of b/h = 1/20. Experimental and numerical data are presented in the form of streamwise direction heated wall surface temperature, mean velocity, mean temperature, Reynolds shear stress and turbulent kinetic energy profiles along the channel for one case. These profiles exhibit the flow field development along the channel emphatically. The numerical technique used predicts temperature field fairly well, considerably over-estimating velocity field in the core region.     

Analysis of Natural Convection During Solidification of a Pure Metal

A numerical study of solidification of gallium in a closed cavity is presented and the influence of natural convection on phase change is investigated.

The mathematical formulation is based on the enthalpy-porosity method, while the equations are discretized on a fixed grid by means of a finite volume technique. Advancing in time is obtained using the SIMPLE algorithm, while the solution of the elliptic equation for pressure correction is obtained by means of a preconditioned BI-CGStab method.

As a test case a square cavity with Ra ranging from 4.68 × 10³ to 9.36 × 10⁵ is adopted. Results will be presented in terms of streamlines, isotherms, solid-liquid interface position and Nu and compared, when possible with available data.     

Laminar near wake of a sharp wedge in hypersonic perfect-gas flow

The laminar near wake behind a sharp wedge with the semi-vertex angle of 10° and a flat base section placed at zero incidence in a Mach 6 uniform perfect-gas flow with the specific heat ratio 1.4 at Reynolds numbers ranging from 3 × 10² to 10⁵ is considered. The study is carried out on the basis of the numerical solution of the Navier-Stokes equations. The results on the base pressure and the pressure and local stagnation temperature distributions along the plane of symmetry and in several cross-sections in the near wake are compared in detail with the data [1].     

Fluctuating lift on a circular cylinder: review and new measurements

Apart from providing some new experimental data the paper reviews previous investigations concerning fluctuating lift acting on a stationary circular cylinder in cross-flow. In particular, effects of Reynolds number in the nominal case of an infinitely long and nonconfined cylinder in a smooth oncoming flow are discussed. The Reynolds number range covered is from about Re=47 to 2×10⁵, i.e., from the onset of vortex shedding up to the end of the subcritical regime. At the beginning of the subcritical regime (Re≃0.3×10³) a spanwise correlation length of about 30 cylinder diameters is indicated, the correlation function being based on near-cylinder velocity fluctuations in outer parts of the separated shear layer. In between Reynolds numbers 1.6×10³ and 20×10³, an approximate 10-fold increase in the sectional r.m.s. lift coefficient is indicated. This range contains a fundamental change-over from one flow state to another, starting off at Re≃5×10³ and seemingly fully developed at Re≃8×10³.     

Comparison of experimental data with results of some drying models for regularly shaped products

This paper presents an experimental and theoretical investigation of drying of moist slab, cylinder and spherical products to study dimensionless moisture content distributions and their comparisons. Experimental study includes the measurement of the moisture content distributions of slab and cylindrical carrot, slab and cylindrical pumpkin and spherical blueberry during drying at various temperatures (e.g., 30, 40, 50 and 60°C) at specific constant velocity (U = 1 m/s) and the relative humidity φ = 30%. In theoretical analysis, two moisture transfer models are used to determine drying process parameters (e.g., drying coefficient and lag factor) and moisture transfer parameters (e.g., moisture diffusivity and moisture transfer coefficient), and to calculate the dimensionless moisture content distributions. The calculated results are then compared with the experimental moisture data. A considerably high agreement is obtained between the calculations and experimental measurements for the cases considered. The effective diffusivity values were evaluated between 0.741 × 10⁻⁵ and 5.981 × 10⁻⁵ m²/h for slab products, 0.818 × 10⁻⁵ and 6.287 × 10⁻⁵ m²/h for cylindrical products and 1.213 × 10⁻⁷ and 7.589 × 10⁻⁷ m²/h spherical products using the Model-I and 0.316 × 10⁻⁵–5.072 × 10⁻⁵ m²/h for slab products, 0.580 × 10⁻⁵–9.587 × 10⁻⁵ m²/h for cylindrical products and 1.408 × 10⁻⁷–13.913 × 10⁻⁷ m²/h spherical products using the Model-II.     

LES and RANS for Turbulent Flow over Arrays of Wall-Mounted Obstacles

Large-eddy simulation (LES) has been applied to calculate the turbulent flow over staggered wall-mounted cubes and staggered random arrays of obstacles with area density 25%, at Reynolds numbers between 5 × 10³ and 5 10⁶, based on the free stream velocity and the obstacle height. Re = 5 × 10³ data were intensively validated against direct numerical simulation (DNS) results at the same Re and experimental data obtained in a boundary layer developing over an identical roughness and at a rather higher Re. The results collectively confirm that Reynolds number dependency is very weak, principally because the surface drag is predominantly form drag and the turbulence production process is at scales comparable to the roughness element sizes. LES is thus able to simulate turbulent flow over the urban-like obstacles at high Re with grids that would be far too coarse for adequate computation of corresponding smooth-wall flows. Comparison between LES and steady Reynolds-averaged Navier-Stokes (RANS) results are included, emphasising that the latter are inadequate, especially within the canopy region.     

Three-dimensional simulations of natural convection in a sidewall-heated cube

A high-resolution, finite difference numerical study is reported on three-dimensional natural convection of air in a differentially heated cubical enclosure over an extensive range of Rayleigh number from 10³ to 10¹⁰. The maximum number of grid points is 122 × 62 × 62. Solutions to the primitive variable formulation of the incompressible Navier-Stokes and energy equations are acquired by a control-volume-based procedure together with a higher-order upwind-differencing technique. The field characteristics at large-time limits are examined in detail by state-of-the-art numerical visualizations of the three-dimensional results. The emergence of the well-defined boundary layers and the interior core at high Rayleigh numbers is captured by elaborate numerical visualizations. Both the similarities and discrepancies between the three- and two-dimensional computations are pointed out. These emphasize the need for three-dimensional calculations to accurately determine the flow characteristics and heat transfer properties in realistic, high-Rayleigh-number situations.     

Concurrent calorimetric and interferometric studies of steady-state natural convection from miniaturized horizontal single plate-fin systems and plate-fin arrays

Concurrent calorimetric and interferometric studies have been conducted to investigate the effect that reduction of the base-plate dimensions has on the steady-state performance of the rate of natural convection heat transfer from miniaturized horizontal single plate-fin systems and plate-fin arrays. The effect was studied through comparison of the present results with those of earlier relevant calorimetric, interferometric, or numerical studies. Results shown that a reduction of the base-plate area by 74% increased natural convection coefficient by 1.5 times to 26.0 W m^?2 K^?1 for single fin systems and by 1.8 times to 18 W m^?2 K^?1 for fin arrays in the range of the base-plate temperature excess of 20–50°C. A simple correlation for the Nusselt number of miniaturized horizontal plate-fin arrays is proposed in the range of Rayleigh number divided by the number of fins to the 2.7 power from 2 × 10 to 5 × 10⁵.     

Heat transfer characteristics of staggered wing-shaped tubes bundle at different angles of attack

An experimental and numerical study has been conducted to clarify heat transfer characteristics and effectiveness of a cross-flow heat exchanger employing staggered wing-shaped tubes at different angels of attack. The water-side Re_w and the air-side Re_a were at 5 × 10² and at from 1.8 × 10³ to 9.7 × 10³, respectively. The tubes arrangements were employed with various angles of attack θ_1,2,3 from 0° to 330° at the considered Re_a range. Correlation of Nu, St, as well as the heat transfer per unit pumping power (ε) in terms of Re_a and design parameters for the studied bundle were presented. The temperature fields around the staggered wing-shaped tubes bundle were predicted by using commercial CFD FLUENT 6.3.26 software package. Results indicated that the heat transfer increased with the angle of attack in the range from 0° to 45°, while the opposite was true for angles of attack from 135° to 180°. The best thermal performance and hence the efficiency η of studied bundle occurred at the lowest Re_a and/or zero angle of attack. Comparisons between the experimental and numerical results of the present study and those, previously, obtained for similar available studies showed good agreements.     

Natural convection with surface radiation from a planar heat generating element mounted freely in a vertical channel

Experiments and numerical simulations have been conducted to study the conjugate heat transfer by natural convection and surface radiation from a planar heat generating element placed centrally between two adiabatic vertical plates. The relevant problem dependent parameters considered in this study are modified Rayleigh number, channel aspect ratio, stream-wise location of the heat generating element, and surface emissivities of the heat generating element and the adiabatic side plates. Experiments are conducted for different values of modified Rayleigh number ranging from 3.2 × 10⁵ to 1.6 × 10⁷ and surface emissivities 0.05, 0.55, 0.75 and 0.85. The interdependence between the heat transfer mechanism and the flow field under the influence of surface radiation on natural convection is explored and discussed. Experimental correlations for total and convective Nusselt number, and dimensionless temperature in terms of relevant parameters have been developed. The mathematical model governing the problem has been numerically solved using a commercial computational fluid dynamics package FLUENT 6.3 and the numerical predictions substantiate the experimental observations.     

Transient mixed convection in an enclosure driven by a sliding lid

Transient convection of an incompressible viscous fluid in a square cavity is investigated. The temperature at the top lid is higher than that at the bottom wall, producing a stably stratified overall configuration. The vertical sidewalls are insulated. Flow is initiated by an impulsive start of the sliding motion of the top lid. The transient features of the mixed convection are delineated by procuring numerical solutions in a wide range of parameters, i.e., 400≤Re≤4,000, 1.6×10⁵≤Gr≤1.6×10⁷. Flows and heat transfer characteristics are described both in the interior core and boundary-layer regions. In the large-time limit, the steady state features are depicted. Parallel experimental efforts are made by employing the particle image velocimetry (PIV) to visualize the steady state flow and thermal fields, together with thermocouple measurements.     

Time-dependent natural convection in a square cavity: Application of a new finite volume method

A new finite volume (FV) approach with adaptive upwind convection is used to predict the two-dimensional unsteady flow in a square cavity. The fluid is air and natural convection is induced by differentially heated vertical walls. The formulation is made in terms of the vorticity and the integral velocity (induction) law. Biquadratic interpolation formulae are used to approximate the temperature and vorticity fields over the finite volumes, to which the conservation laws are applied in integral form. Image vorticity is used to enforce the zero-penetration condition at the cavity walls. Unsteady predictions are carried sufficiently forward in time to reach a steady state. Results are presented for a Prandtl number (Pr) of 0-71 and Rayleigh numbers equal to 10³, 10⁴ and 10⁵. Both 11 × 11 and 21 × 21 meshes are used. The steady state predictions are compared with published results obtained using a finite difference (FD) scheme for the same values of Pr and Ra and the same meshes, as well as a numerical bench-mark solution. For the most part the FV predictions are closer to the bench-mark solution than are the FD predictions.     

Nonlinear dynamics between two differentially heated vertical plates in the presence of stratification

We consider the numerical simulation of the flow between infinite, differentially heated vertical plates with positive stratification. We use a two-dimensional Boussinesq approximation, with periodic boundary conditions in the vertical direction. The relative stratification parameter ${\gamma=(\frac{1}{4}Ra S)^{1/4}}$ , where Ra is the Rayleigh number and S the adimensional stratification, is kept constant and equal to 8. The Prandtl number is 0.71. We derive a complex Ginzburg-Landau equation from the equations of motion. Coefficients are computed analytically, but we find that the domain of validity of these coefficients is small and rely on the numerical simulation to adjust the coefficients over a wider range of Rayleigh numbers. We show that the Ginzburg-Landau equation is able to accurately predict the characteristics of the periodic solution at moderate Rayleigh numbers. Above the primary bifurcation at Ra = 1.63 × 10⁵, the Ginzburg-Landau model is found to be Benjamin-Feir unstable and to be characterized by modulated traveling waves and phase-defect chaos, which is supported by evidence from the DNS. As the Rayleigh number is increased beyond Ra = 2.7 × 10⁵, nonlinearities become strong and the flow is characterized by cnoidal waves.     

Numerical simulation of time-dependent buoyant flows in an enclosed vertical channel

A time-accurate Finite Volume method is used to investigate the two-dimensional buoyant flow in a closed cabinet containing two vertical heating plates. These are parallel, and form a channel at the centre of the cabinet enclosure. The cases of isothermal plates, and of uniform heat generation within them, are both considered for two values, 1×10⁵ and 1×10⁷, of the leading non-dimensional parameter, the Grashof number. Air (Pr = 0.71) is considered as the working fluid. Transient and long term thermal and flow behaviours are investigated. Steady-state solutions are asymptotically found at the lower Gr-value. However, time-dependent long-term solutions are predicted at Gr = 1×10⁷. Received on 20 May 1998     

Simulation of the flow past a circular cylinder in the supercritical regime by blending RANS and variational-multiscale LES models

A strategy which blends a variational multiscale large eddy simulation (VMS-LES) model and a RANS model in a hybrid approach is investigated. A smooth blending function, which is based on the value of a blending parameter, is used for switching from VMS-LES to RANS. Different definitions of the blending parameter are investigated. The capabilities of the novel hybrid approach are appraised in the simulation of the flow around a circular cylinder at a Reynolds number 1.4×10⁵, based on the freestream velocity and on the cylinder diameter, in the presence of turbulent boundary-layer due to turbulent inflow conditions. A second study at Reynolds numbers from Re=6.7×10⁵ to 1.25×10⁶ is also presented. The effect of using the VMS-LES approach in the hybrid model is evaluated. Results are compared to those of other RANS, LES and hybrid simulations in the literature and with experimental data     

Leray-α Regularization of the Smagorinsky-Closed Filtered Equations for Turbulent Jets at High Reynolds Numbers

The article reports on blending of the Leray-α regularization with the conventional Smagorinsky subgrid-scale closure as an option for large-eddy-simulation of turbulent flows at very high Reynolds number on coarse meshes. The model has been tested in the self-similar far-field region of a jet at a range of Reynolds numbers spanning over two decades (4×10³, 4×10⁴ and 4×10⁵) on two very coarse meshes of 2×10⁵ and 3×10⁴ mesh cells. The results are compared with the well-resolved DNS for $Re_D=4\times 10^3$ on 15 million cells and experimental data for higher Re numbers. While the pure Leray-α can fail badly at high Re numbers on very coarse meshes, a blending of the two strategies by adding a small amount of extra-dissipation performs well even at a huge jet Reynolds number of $Re_D=4\times 10^5$ on a very coarse mesh (2×10⁵ cells), despite the ratio of the typical mesh spacing to the Kolmogorov length exceeding 300. It is found that the main prerequisite for successful LES, both for the classic Smagorinsky and the blended Leray-α/Smagorinsky model, is to resolve the shear-length $L_s=\sqrt{\varepsilon/{\cal S}^3}$ (where ${\cal S}$ is the shear-rate modulus), defined by the constraint Δ/L _s ?<?1, where Δ is the typical mesh-cell size. For the mixed Leray-α/Smagorinsky model the regularization parameter should also be related to the shear-length rather than the local mesh size or Reynolds number, for which we propose a guide criterion α?=?0.15÷0.3 L _s .     

Numerical simulation and hydrodynamic visualization of transient viscous flow around an oscillating aerofoil

Unsteady viscous flow around a large-amplitude and high-frequency oscillating aerofoil is examined in this paper by numerical simulation and experimental visualization. The numerical method is based on the combination of a fourth-order Hermitian finite difference scheme for the stream function equation and a classical second-order scheme to solve the vorticity transport equation. Experiments are carried out by a traditional visualization method using solid tracers suspended in water. The comparison between numerical and experimental results is found to be satisfactory. Time evolutions of the flow structure are presented for Reynolds numbers of 3 × 10³ and 10⁴. The influence of the amplitude and frequency of the oscillating motion on the dynamic stall is analysed.     

Time-averaged topological flow patterns and their influence on vortex shedding of a square cylinder in crossflow at incidence

Flow characteristics around the square cylinder and their influence on the wake properties are studied. Time-averaged flow patterns on the surfaces of square cylinder in a cross-stream at incidence are experimentally probed by surface-oil flow technique and analyzed by flow topology for Reynolds numbers between 3.9×10⁴ and 9.4×10⁴ as the incidence angle changes from 0° to 45°. Vortex shedding characteristics are measured by a single-wire hot-wire anemometer for Reynolds numbers between 5×10³ and 1.2×10⁵. The effects of topological flow patterns on the wake properties then are revealed and discussed. Flows around the square cylinder are identified as three categories: the subcritical, supercritical, and wedge flows according to the prominently different features of the topological flow patterns. The Strouhal number of vortex shedding, turbulence in the wake, and wake width present drastically different behaviors in different characteristic flow regimes. A critical incidence angle of 15° separates the subcritical and supercritical regimes. At the critical incidence angle the wake width and shear-layer turbulence present minimum values. The minimum wake width appearing at the critical incidence angle, which leads to the maximum Strouhal number, is due to the reattachment of one of the separated boundary layer to the lateral face of the square cylinder. If the Strouhal numbers are calculated based on the wake width instead of the cross-stream projection width of cylinder, the data in the subcritical and supercritical regimes are well correlated into two groups, which would approach constants at high Reynolds numbers.