Nature of the surface heart transfer fluctuation in a hypersonic separated turbulent flow

This paper presents the results of an experimental study of the unsteady nature of a hypersonic separated turbulent flow. The nomimal test conditions were a freestream Mach number of 7.8 and a unit Reynolds number of 3.5×10⁷/m. The separated flow was generated using finite span forward facing steps. An array of flush mounted high spatial resolution and fast response platinum film resistance thermometers was used to make multi-channel measurements of the fluctuating surface heat trtansfer within the separated flow. Conditional sampling analysis of the signals shows that the root of separation shock wave consists of a series of compression wave extending over a streamwise length about one half of the incoming boundary layer thickness. The compression waves converge into a single leading shock beyond the boundary layer. The shock structure is unsteady and undergoes large-scale motion in the streamwise direction. The length scale of the motion is about 22 percent of the upstream influence length of the separation shock wave. There exists a wide band of frequency of oscillations of the shock system. Most of the frequencies are in the range of 1–3 kHz. The heat transfer fluctuates intermittently between the undisturbed level and the disturbed level within the range of motion of the separation shock wave. This intermittent phenomenon is considered as the consequence of the large-scale shock system oscillations. Downstream of the range of shock wave motion there is a separated region where the flow experiences continuous compression and no intermittency phenomenon is observed. The project supported by National Natural Science Foundation of China     

Experiment and prediction of a cavity type separated flow

A detail study involving flow visualization, Laser Doppler Velocimeter (LDV) measurements and numerical prediction is presented. The visualization experiments revealed striking results of a pulsatile motion in the separated flow region associated with the formation and passage of large eddy structures. Measurements of mean velocities and turbulence intensity profiles across the separated flow field, provided information about the separated shear layer development and the recirculating flow pattern. The numerical predictions, obtained with a two-layer turbulence model in conjunction with the SIMPLE algorithm, failed to reproduce the coherent eddies and the pulsatile motion, but the mean velocities are reasonably reproduced.     

To formulating a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil

A general formulation of a nonlinear initial-boundary problem of an unsteady separated flow around an airfoil by an ideal incompressible fluid is considered. The problem is formulated for a complex velocity. Conditions of shedding of vortex wakes from the airfoil are analyzed in detail. The proposed system of functional relations allows constructing algorithms for solving a wide class of problems of the wing theory. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 48–56, March–April, 2007.     

Turbulent flow past a transverse cavity with inclined side walls. 1. Flow structure

The process of vortex formation in a cavity with inclined walls, which has a moderate aspect ratio, is experimentally studied, and the distribution of pressure coefficients is measured. The angle of inclination of the side walls ϕ is varied from 30 to 90°. It is found that the flow in the cavity becomes unstable in the range of inclination angles ϕ = 60–70°. Flow reconstruction occurs, which substantially alters the surface-temperature and static-pressure distributions. Large changes in these characteristics and their nonuniform distributions for these angles are observed across the cavity on its frontal wall and on the bottom. For small angles (ϕ = 30 and 45°), the pressure on the rear wall drastically increases, which leads to a small increase in pressure averaged over the entire cavity surface. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 68–76, September–October, 2006.     

Temperature factor effect on the structure of the separated flow within a supersonic gas stream

The effect of the temperature factor, that is, the ratio of the body temperature to the freestream stagnation temperature, on the structure of the separated flow formed in the presence of a concave corner in a supersonic stream is studied. The strong influence of the temperature factor on the separation zone length and the flow-generated aerodynamic characteristics is established. It is shown that for fairly large deflection angles this flow cannot be described by free interaction, or triple deck, theory.     

Turbulent flow past a transverse cavity with inclined side walls. 2. Heat transfer

Convective heat transfer in a transverse cavity with a small aspect ratio, angle of wall inclination ϕ = 30–90°, and heated bottom, frontal, and rear walls of the cavity is studied experimentally. Temperature distributions are measured in longitudinal and transverse sections on three walls; temperature fields are measured over the entire heated surface. Local and mean heat-transfer coefficients are calculated. The highest intensification of heat transfer is found to occur on the rear wall for low values of ϕ Reconstruction of the one-cell structure to the two-cell structure of the primary vortex in the cavity leads to a drastic decrease in heat transfer over the cavity span from the end faces toward the center in the case with ϕ = 60 and 70°. A certain increase in the mean heat-transfer coefficient averaged over the entire heated surface is noted for ϕ = 60°. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 23–29, July–August, 2007.     

Wall shear stress characterization of a 3D bluff-body separated flow

Efficient flow control strategies aimed at reducing the aerodynamic drag of road vehicles require a detailed knowledge of the reference flow. In this work, the flow around the rear slanted window of a generic car model was experimentally studied through wall shear stress measurements using an electrochemical method. The mean and fluctuating wall shear stress within the wall impact regions of the recirculation bubble and the main longitudinal vortex structures which develop above the rear window are presented. Correlations allow a more detailed characterization of the recirculation phenomenon within the separation bubble. In the model symmetry plane the recirculation structure compares well with simpler 2D configurations; specific lengths, flapping motion and shedding of large-scale vortices are observed, these similarities diminish when leaving the middle plane due to the strong three-dimensionality of the flow. A specific attention is paid to the convection processes occurring within the recirculation: a downstream convection velocity is observed, in accordance with 2D recirculations from the literature, and an upstream convection is highlighted along the entire bubble length which has not been underlined in some previous canonical configurations.     

Numerical study of turbulent flow over two‐dimensional surface‐mounted ribs in a channel

This study accurately predicts the cases of turbulent flow around a surface‐mounted two‐dimensional rib with varying lengths. The numerical method employs a differencing scheme for integrating the elliptic Reynolds‐averaged Navier–Stokes equations and the continuity equation. A two‐equation k–ε turbulence model is employed to simulate the turbulent transport quantities and close the solving problem. The near‐wall regions of the separated sides of the rib are resolved by a near‐wall model of a two‐layer approach instead of the wall function approximation. Computations for flow over a surface‐mounted rectangular rib are conducted for the variations in the rib lengths. Results indicate that upstream of the obstacle, the length of the recirculating region remains unchanged with varying rib lengths; while the downstream length of the recirculating region is a strong function of rib length and changes nearly linearly for the varying lengths of B/H=0.1 to B/H=4.0. Reattachment on top of the rib, owing to its increasing length, affects the downstream boundary layer development. Copyright © 1999 John Wiley & Sons, Ltd.     

Self-consistency and the use of correlated stochastic separated flow models for prediction of particle-laden flows

Computational fluid dynamics (CFD) is being used increasingly in the design and analysis of particle-laden flows. A significant challenge of this work is in correctly predicting the interaction of the fluid turbulence with the particulate phase. Typically, Lagrangian tracking is used to calculate the particle trajectories with stochastic treatments used to provide an instantaneous turbulent flow field. The stochastic calculations are based on the mean velocities and turbulence quantities calculated by the CFD solver. The current work examines the correlated stochastic separated flow (SSF) model used to synthesize the instantaneous fluid velocity field. Two functional forms of the Eulerian spatial correlation are considered: exponential, and Frenkiel with loop parameter m equal to unity. It is well known that the use of a Frenkiel function is incorrect due to the Markovian nature of the model. Nonetheless, a literature review indicates that the Frenkiel function is still being used in the CFD community. In order to illustrate the implications of this, numerical predictions are compared to Taylor's analytical result for fluid particle dispersion in homogeneous isotropic turbulence. Excellent predictions are obtained with the exponential correlation and recommendations on timestep requirements are made. In contrast, predictions from the Frenkiel model are in poor agreement with Taylor's solution. This poor agreement results from an inconsistency between the effective correlation of fluid velocities arising from the model and the original intended correlation.     

Effect of collision and velocity model of lattice Boltzmann model on three-dimensional turbulent flow simulation

Various collision and velocity models of the lattice Boltzmann model (LBM) were compared to determine their effects on the efficiency of a three-dimensional homogeneous isotropic decaying turbulent flow simulation. We determined that a decrease in the number of velocities, in particular, 13-velocities, which can be used in the quasi-equilibrium lattice Boltzmann and in the multiple-relaxation time models (MRT), could considerably decrease the computational effort. However, decreasing the number of velocities deteriorates the stability and the accuracy of the results. By comparing the collision models, we also determined that the stability of the entropic lattice Boltzmann model (ELBM), and 19- and 27- velocity MRT is much higher than in other models. However, the numerical viscosity introduced by the ELBM underestimates the enstrophy, and the computational effort increases because of the calculation overhead required to solve the additional equations if special care is not given to the calculation.     

平板大攻角绕流升力和阻力系数的计算

二维平板或二维对称薄翼型大攻角绕流升力和阻力系数与攻角之间存在的函数关系一般用数据表格的形式给出。本文根据垂直平板绕流阻力实验数据和对称薄翼型全攻角绕流实验数据,分析得到了平板大攻角绕流总压力及其升力分量和阻力分量系数的近似计算公式。结果表明：平板总压力系数约等于攻角正弦值的2倍;总压力的阻力分量系数约等于攻角正弦值平方的2倍;升力分量系数约为攻角2倍的正弦值。计算结果与两组试验数据具有较好的一致性。     

Some Features of a Turbulent Separated Flow and Heat Transfer Behind a Step and a Rib. 2. Heat Transfer in a Separated Flow

Results of an experimental study of heat transfer in a separated flow behind a step and a rib are presented. The influence of the obstacle height (H = 6–30 mm) on heat and mass transfer and the structure of the thermal boundary layer is studied. The features of heat transfer in recirculation and relaxation zones of the separated flow are analyzed, and the effect of separation on intensification and suppression of turbulent heat transfer is determined.     

Numerical study of an oscillatory turbulent flow over a flat plate

Oscillatory turbulent flow over a flat plate is studied using large eddy simulation (LES) and Reynolds-average Navier-Stokes (RANS) methods. A dynamic subgrid-scale model is employed in LES and Saffman's turbulence model is used in RANS. The flow behaviors are discussed for the accelerating and decelerating phases during the oscillating cycle. The friction force on the wall and its phase shift from laminar to turbulent regime are also investigated for different Reynolds numbers. The project supported by the Youngster Funding of Academia Sinica and by the National Natural Science Foundation of China     

Numerical analysis of turbulent flow separation in a rectangular duct with a sharp 180‐degree turn by algebraic Reynolds stress model

Turbulent flow in a rectangular duct with a sharp 180‐degree turn is difficult to predict numerically because the flow behavior is influenced by several types of forces, including centrifugal force, pressure‐driven force, and shear stress generated by anisotropic turbulence. In particular, this type of flow is characterized by a large‐scale separated flow, and it is difficult to predict the reattachment point of a separated flow. Numerical analysis has been performed for a turbulent flow in a rectangular duct with a sharp 180‐degree turn using the algebraic Reynolds stress model. A boundary‐fitted coordinate system is introduced as a method for coordinate transformation to set the boundary conditions next to complicated shapes. The calculated results are compared with the experimental data, as measured by a laser‐Doppler anemometer, in order to examine the validity of the proposed numerical method and turbulent model. In addition, the possibility of improving the wall function method in the separated flow region is examined by replacing the log‐law velocity profile for a smooth wall with that for a rough wall. The analysis results indicated that the proposed algebraic Reynolds stress model can be used to reasonably predict the turbulent flow in a rectangular duct with a sharp 180‐degree turn. In particular, the calculated reattachment point of a separated flow, which is difficult to predict in a turbulent flow, agrees well with the experimental results. In addition, the calculation results suggest that the wall function method using the log‐law velocity profile for a rough wall over a separated flow region has some potential for improving the prediction accuracy. Copyright © 2007 John Wiley & Sons, Ltd.     

The flow structure of dilute gas-particle suspensions behind a shock wave moving along a flat surface

The asymptotic and numerical investigations of shock-induced boundary layers in gas-particle mixtures are presented.The Saffman lift force acting on a particle in a shear flow istaken into account.It is shown that particle migration across the boundary layer leads tointersections of particle trajectories.The corresponding modification of dusty gas model isproposed in this paper.The equations of two-phase sidewall boundary layer behind a shock wave moving at aconstant speed are obtained by using the method of matched asymptotic expansions.Themethod of the calculation of particle phase parameters in Lagrangian coordinates isdescribed in detail.Some numerical results for the case of small particle concentration aregiven.     

Control of the separated flow downstream of a two-dimensional fence by low-frequency forcing

Streamwise distributions of wall shear-stress, reverse-flow-factor and static pressure were measured in the turbulent separation regions upstream and downstream of a two-dimensional fence. In front of the fence, boundary layer profiles were measured with a pulsed-wire probe traversing out of the wall. The flow was then manipulated by a periodic disturbance which was located upstream of the forward separation region. Two different disturbances were tested: an oscillating spoiler and a two-dimensional oscillating jet with zero mean mass flow, driven by a loudspeaker. Both manipulators were orientated parallel to the fence. With appropriate tuning of the parameters, the reattachment length behind the fence could be reduced by 50%.     

Three-dimensional particle-tracking velocimetry measurement of turbulence statistics and energy budget in a backward-facing step flow

Using a three-dimensional (3-D) particle-tracking velocimeter, detailed turbulent flow measurements were made in a plane channel with a one-sided 50% abrupt expansion, which acted as a backward-facing step. The turbulent channel flow reached a fully developed state well upstream of the step. The Reynolds number based on the upstream centerline velocity and the step height H was 5540. With the mean reattachment point located at 6.51H downstream of the step, the measurement region ranged from −2H upstream to 12H downstream of the step. Various turbulent statistics and the energy budget were calculated from numerous instantaneous vector distributions. As in previous experimental investigations, the Reynolds normal and shear stresses had maximum values upstream of the reattachment. The stress anisotropy tensor revealed a peculiar phenomenon near the reattachment wall, wherein the spanwise normal stress was the largest among the three normal stresses. The triple velocity correlations indicated large values in the separating shear layer, and hence the turbulent diffusion was a major term in the energy budget. Comparison was made between the present results and those of the direct numerical simulation (DNS) of Le et al. (1993), and it was found that the mean and fluctuating velocities, the Reynolds shear stress, and the turbulent energy budget were in excellent agreement, although there was a considerable difference in the inflow conditions.     

Simulations of the unsteady separated flow past a normal flat plate

Well-resolved two-dimensional numerical simulations of the unsteady separated flow past a normal flat plate at low Reynolds numbers have been performed using a fractional step procedure with high-order spatial discretization. A fifth-order upwind-biased scheme is used for the convective terms and the diffusive terms are represented by a fourth-order central difference scheme. The pressure Poisson equation is solved using a direct method based on eigenvalue decomposition of the coefficient matrix. A systematic study of the flow has been conducted with high temporal and spatial resolutions for a series of Reynolds numbers. The interactions of the vortices shed form the shear layers in the near-and far-wake regions are studied. For Reynolds numbers less than 250 the vortices are observed to convect parallel to the freestream. However, at higher Reynolds numbers (500 and 1000), complex interactions including vortex pairing, tearing and deformations are seen to occur in the far-wake region. Values of the drag coefficient and the wake closure length are presented and compared with previous experimental and numerical studies.     

Aerodynamic characteristics of a thin airfoil cascade in an ideal incompressible flow with separation from the leading edges

A new method of solving the problem of separation flow past a cascade of thin airfoils is proposed. The method is based on the model of separated flow past a single airfoil in which vortex wakes shed from the airfoil edges are modeled by vortex layers with time-averaged intensities. Under the assumption of a small deviation of the freestream angle α from the “impactless entry” angle α ₀ the singular integral equation governing the flow kinematics is closed by a dynamic equation. It is shown that the separation effect on the time-averaged aerodynamic characteristics of the cascade is associated with the total pressure loss due to the flow energy expenditure on the vortex wake formation. The aerodynamic characteristics of the cascade calculated with and without account for flow separation differ by the second-order quantity ? = α ? α ₀.     

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.