Modification of near-wall turbulence structure in a shear-driven three-dimensional turbulent boundary layer

 Most high Reynolds number flows of engineering interest are three-dimensional in nature. Key features of three-dimensional turbulent boundary layers (3DTBLs) include: non-colateral shear stress and strain rate vectors, and decreasing ratio of the shear stresses to the turbulent kinetic energy with increasing three-dimensionality. These are indicators that the skewing has a significant effect on the structure of turbulence. In order to further investigate the flow physics and turbulence structure of these complex flows, an innovative method for generating a planar shear-driven 3DTBL was developed. A specialized facility incorporating a relatively simple geometry and allowing for varying strengths of crossflow was constructed to facilitate studies where the skewing is decoupled from the confounding effects of streamwise pressure gradient and curvature. On-line planar particle image velocimetry (PIV) measurements and flow visualization results indicate that the experimental configuration generates the desired complex flow, which exhibits typical characteristics associated with 3DTBLs. Furthermore, spanwise shear results in modification of the near-wall turbulence structure. Analysis of near-wall flow visualization photographs revealed a reduction of mean streak length with increasing spanwise shear, while streak spacing remained relatively constant. In the most strongly sheared case, where the belt velocity is twice that of the freestream velocity, the mean streak length was reduced by approximately 50%. Received: 28 October 1997/Accepted: 4 February 1998     

变高度圆柱诱导的激波边界层干扰

采用分区方法及Ｒｏｅ三阶流通量差分分裂格式求解雷诺平均Ｎ－Ｓ方程,湍流附加黏性系数用Ｂａｌｄｗｉｎ－Ｌｏｍａｘ模型计算,数值模拟了高超声速条件下变高度圆柱诱导的激波边界层层干扰,其流场的主要特性均与实验结果一致或规律相同,结果清晰地展示了流场结构以及气动载荷分布随柱高度的变化特征,产说明激波碰撞和旋涡运动都可能导致飞行器表面局部气动载荷的增加。     

Predictions of Axial and Transverse Injection into Supersonic Flow

CFD calculations are performed on a swept ramp injecting fuelaxially, and on a two-hole transverse fuel injection downstream of abackward-facing step, both into a supersonic turbulent flow. Theresulting complex flowfields are predicted using a cubick–ε turbulence closure. Comparisons with experimental data show very good agreement. A discussion of the main flow features is presented. The fast computational convergence demonstrates the readiness of the method for the design cycle. This revised version was published online in July 2006 with corrections to the Cover Date.     

Observations on the predictions of fully developed rotating pipe flow using differential and explicit algebraic Reynolds stress models

The differences between two differential Reynolds stress models (DRSM) and their corresponding explicit algebraic Reynolds stress models (EARSM) are investigated by studying fully developed axially rotating turbulent pipe flow. The mean flow and the turbulence quantities are strongly influenced by the imposed rotation, and is well captured by the differential models as well as their algebraic truncations. All the tested models give mean velocity profiles that are in good qualitative agreement with the experimental data. It is demonstrated that the predicted turbulence kinetic energy levels vary dramatically depending on the diffusion model used, and that this is closely related to the model for the evolution of the length-scale determining quantity. Furthermore, the effect of the weak equilibrium assumption, underlying the EARSMs, and the approximation imposed for 3D mean flows on the turbulence levels are investigated. In general the predictions obtained with the EARSMs rather closely follow those of the corresponding DRSMs.     

Reliable validation based on optical flow visualization for CFD simulations

A reliable validation based on the optical flow visualization for numerical simulations of complex flowfields is addressed in this paper. Several test cases, including two-dimensional, axisymmetric and three-dimensional flowfields, were presented to demonstrate the effectiveness of the validation and gain credibility of numerical solutions of complex flowfields. In the validation, images of these flowfields were constructed from numerical results based on the principle of the optical flow visualization, and compared directly with experimental interferograms. Because both experimental and numerical results are of identical physical representation, the agreement between them can be evaluated effectively by examining flow structures as well as checking discrepancies in density. The study shows that the reliable validation can be achieved by using the direct comparison between numerical and experiment results without any loss of accuracy in either of them.     

Turbulence in a three‐dimensional wall‐bounded shear flow

A new turbulent flow with distinct three‐dimensional characteristics has been designed in order to study the impact of mean‐flow skewing on the turbulent coherent vortices and Reynolds‐averaged statistics. The skewing of a unidirectional plane Couette flow was achieved by means of a spanwise pressure gradient. Direct numerical simulations of the statistically steady Couette–Poiseuille flow enabled in‐depth explorations of the turbulence field in the skewed flow. The imposition of a modest spanwise gradient turned the mean flow about 8° away from the original Couette flow direction and this turning angle remained nearly the same over the entire cross section. Nevertheless, a substantial non‐alignment between the turbulent shear stress angle and the mean velocity gradient angle was observed. The structure parameter turned out to slightly exceed that in the pure Couette flow, contrary to the observations made in some other three‐dimensional shear flows. Coherent flow structures, which are known to be associated with the Reynolds shear stress in near‐wall regions, were identified by the λ₂‐criterion. Instantaneous and ensemble‐averaged vortices resembled those found in the unidirectional Couette flow. In the skewed flow, however, the vortex structures were turned to align with the local mean‐flow direction. The conventional symmetry between Case 1 and Case 2 vortices was broken due to the mean‐flow three‐dimensionality. The turning of the coherent vortices and the accompanying symmetry‐breaking gave rise to secondary and tertiary turbulent shear stress components. By averaging the already ensemble‐averaged shear stresses associated with Case 1 and Case 2 vortices in the homogeneous directions, a direct link between the educed near‐wall structures and the Reynolds‐averaged turbulent stresses was established. These observations provide evidence in support of the hypothesis that the structural model proposed for two‐dimensional turbulent boundary layers remains valid also in flows with moderate mean three‐dimensionality. Copyright © 2009 John Wiley & Sons, Ltd.     

Turbulence in a skewed three‐dimensional wall‐bounded shear flow: effect of mean vorticity on structure modification

Mean‐flow three‐dimensionalities affect both the turbulence level and the coherent flow structures in wall‐bounded shear flows. A tailor‐made flow configuration was designed to enable a thorough investigation of moderately and severely skewed channel flows. A unidirectional shear‐driven plane Couette flow was skewed by means of an imposed spanwise pressure gradient. Three different cases with 8°, 34°and 52°skewing were simulated numerically and the results compared with data from a purely two‐dimensional plane Couette flow. The resulting three‐dimensional flow field became statistically stationary and homogeneous in the streamwise and spanwise directions while the mean velocity vector V and the mean vorticity vector Ω remained parallel with the walls. Mean flow profiles were presented together with all components of the Reynolds stress tensor. The mean shear rate in the core region gradually increased with increasing skewing whereas the velocity fluctuations were enhanced in the spanwise direction and reduced in the streamwise direction. The Reynolds shear stress is known to be closely related to the coherent flow structures in the near‐wall region. The instantaneous and ensemble‐averaged flow structures were turned by the skewed mean flow. We demonstrated for the medium‐skewed case that the coherent structures should be examined in a coordinate system aligned with V to enable a sound interpretation of 3D effects. The conventional symmetry between Case 1 and Case 2 vortices was broken and Case 1 vortices turned out to be stronger than Case 2. This observation is in conflict with the common understanding on the basis of the spanwise (secondary) mean shear rate. A refined model was proposed to interpret the structure modifications in three‐dimensional wall‐flows. What matters is the orientation of the mean vorticity vector Ω relative to the vortex vorticity vector ω _v, that is, the sign of Ω · ω _v. In the present situation, Ω · ω _v > 0 for the Case 1 vortices causing a strengthening relative to the Case 2 vortices. Copyright © 2011 John Wiley & Sons, Ltd.     

Rotation effects on a fully-developed turbulent pipe flow

A fully-developed turbulent pipe flow is allowed to pass through a rotating pipe section, whose axis of rotation coincides with the pipe axis. At the exit end of the rotating section, the flow passes into a stationary pipe. As a result of the relaxation of surface rotation, the turbulent flow near the pipe wall is affected by extra turbulence production created by the large circumferential shear strain set up by the rapid decrease of the rotational velocity to zero at the wall. However, the flow in the most part of the pipe is absent of this extra turbulence production because the circumferential strain is zero as a result of the solid-body rotation imparted to the flow by the rotating pipe section. The combined effect of these two phenomena on the flow is investigated in detail using hot-wire anemometry techniques. Both mean and turbulence fields are measured, together with the wall shear and the turbulent burst behavior at the wall. A number of experiments at different rotational speeds are carried out. Therefore, the effects of rotation on the behavior of wall shear, turbulent burst at the wall, turbulence production and the near-wall flow can be documented and analysed in detail.     

Unsteady characteristics of the static stall of an airfoil subjected to freestream turbulence level up to 16%

Fluctuation of the separation point on an airfoil under high turbulence level is investigated using pressure measurements and flow visualisations. The characteristics of the unsteady loads induced by Karman vortex shedding are studied. This is related with a local approach based on the study of the oscillation zone. A method based on the pressure standard deviation is proposed to obtain the length of this zone, which is found to be independent of the turbulence level. This result is in agreement with that obtained by spectral analysis which shows no effect of the turbulence level on the Karman vortex shedding frequency.     

Effects of inlet guide-vane number on flowfields in a side-dump combustor

The flowfields of a side-dump combustor with various number of side-inlet guide-vane are measured using laser-Doppler velocimetry (LDV). The Reynolds number based on the bulk mean velocity and combustor diameter was 2.6×10⁴. Quantities such as mean velocity, turbulence intensity, turbulent kinetic energy, vorticity, friction factor, and wall static pressure oscillation are used to characterize the fluid flow. In the dome region of the inlet-jet plane, there is one pair of counter-rotating vortices for the no-vane, one-vane, and two-vane cases and two pairs of counter-rotating vortices for the three-vane case, respectively. This trend is reversed in the impinging plane. The combustor flowfield downstream of the X_c^*=2.5 station is found to be insensitive to the variation of inlet guide-vane number. In addition, the guide-vane number which provides the least pressure loss and the lowest pressure oscillation is identified for the first time. Based on the presented data, a better guide-vane number for practical reference is suggested.     

Variation of fiber orientation in turbulent flow inside a planar contraction with different shapes

In this study, we have investigated the influence of shape of planar contractions on the orientation distribution of stiff fibers suspended in turbulent flow. To do this, we have employed a model for the orientational diffusion coefficient based on the data obtained by high-speed imaging of suspension flow at the centerline of a contraction with flat walls. This orientational diffusion coefficient depends only on the contraction ratio and turbulence intensity. Our measurements show that the turbulence intensity decays exponentially independent of the contraction angle. This implies that the turbulence variation in the contraction is independent of the shape, consistent with the results by the rapid distortion theory and the experimental results of axisymmetric contractions. In order to determine the orientation anisotropy, we have solved a Fokker–Planck type equation governing the orientation distribution of fibers in turbulent flow. Although the turbulence variation and the orientational diffusion are independent of the contraction shape, the results show that the variation of the orientation anisotropy is dependent on shape. This can be explained by the variation of the rotational Péclet number, Pe_r, inside the contractions. This quantity is a measure of the importance of the mean rate of the strain relative to the orientational diffusion. We have shown that when Pe_r < 10 turbulence can significantly influence the evolution of the orientation anisotropy. Since in contractions with identical inlet conditions the streamwise position where Pe_r = 10 depends on the shape, the orientation anisotropy is dependent on the variation of rate of strain in a given contraction. We demonstrate the shape effect by considering contraction with flat walls as well as three contractions with different mean rate of strain variation.     

Numerical investigation of the effect of winglets on the evolution of an aircraft vortex wake

The effect of winglets on the aerodynamic characteristics of a heavy aircraft and the parameters of the vortex wake behind it is investigated for the landing regime. The solution of the complete problem is obtained by breaking up the wake into three regions, namely, the near, intermediate, and far flowfields, in which the corresponding subproblems are successively solved. The wake flowfields are obtained at different distances from the aircraft, together with the distributions of the mean azimuthal velocity over the vortex radius, and the lifetime of the vortex system is estimated for several one-and two-element wingtip versions. All the results are compared with those for the baseline layout with no winglets.     

Compressibility effects due to turbulent fluctuations

This paper deals with intrinsic effects of compressibility, i.e. with dilatation fluctuations in response to pressure fluctuations. Three different types of turbulent flows are considered in more detail: homogeneous turbulent shear flow, wall-bounded turbulent shear flow and shock/turbulence interaction. A survey of the present knowledge in this field, mainly based on DNS data, is given. Using the linear inviscid perturbation equations a direct link between fluctuations of dilatation and of velocity in the direction of mean shear is presented for homogeneous shear flow. This relation might form the basis for a more universal pressure-dilatation model. It is conjectured that the insignificance of intrinsic compressibility effects in wall-bounded supersonic shear flow is mainly due to the impermeability constraint of the wall. To this end, a linear stability analysis of supersonic channel flow along cooled, but permeable walls has been performed based on Coleman et al.'s [5] mean flow data. It shows an increase in the moduli of eigenfunctions related to compressibility, like pressure, and in moduli of quantities derived from eigenfunctions such as ‘pressure dilatation’ and squared dilatation. Although these results do not prove our hypothesis they provide hints in this direction. Shock/turbulence interaction is viewed as a source of compressibility. Former DNS data of Hannappel and Friedrich [10] for shock/isotropic turbulence interaction showing the effect of compressibility on the amplification of fluctuations are interpreted based on linear perturbation equations.     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Free-stream turbulence effects on vortex-induced vibration of two side-by-side elastic cylinders

The effect of free-stream turbulence on vortex-induced vibration of two side-by-side elastic cylinders in a cross-flow was investigated experimentally. A turbulence generation grid was used to generate turbulent incoming flow with turbulence intensity around 10%. Cylinder displacements in the transverse direction at cylinder mid-span were measured in the reduced velocity range 1.45<U_r0<12.08, corresponding to a range of Reynolds number (Re), based on the mean free-stream velocity and the diameter of the cylinder, between Re=5000–41 000. The focus of the study is on the regime of biased gap flow, where two cylinders with pitch ratio (T/D) varying from 1.17 to 1.90 are considered. Results show that the free-stream turbulence effect is to enhance the vortex-induced force, thus to restore the large-amplitude vibration associated with the lock-in resonance. However, the enhancement is significant at a different Strouhal number (St) for different pitch ratios. When the spacing between two cylinders is relatively small (1.17<T/D<1.50), the enhancement is significant at St≈0.1. When the spacing is increased, the Strouhal number at which the enhancement is significant shifts to St≈0.16. This enlarges the range of reduced velocity to be concerned. An energy analysis showed that free-stream turbulence feeds energy to the cylinder at multiple frequencies of vortex shedding. Therefore, the lock-in region is still of main concern when the approach flow is turbulent.     

基于声涡转化对穿孔板切向流效应的研究

建立了一种有关切向流对小孔声阻抗影响的小扰动势流模型,其要点是使用法向质点速度连续而非广为采用的质点位移连续边界条件来匹配小孔剪切层两侧的声场,并在小孔前缘施加 Kutta条件以反映切向流效应的机理——锐缘处的声涡转化;模型中还考虑了实际应用中经常遇到的小孔形状和穿孔板厚度两个重要因素.理论预测的声阻和声抗与实验结果吻合良好.     

Turbulence energy balance in reacting turbulent flows

The turbulence accompanying combustion and the propagation of detonation waves in gases has been studied theoretically and experimentally in many papers [1–8]. The attention of researchers has been concentrated on essential questions like how the turbulent flow field interacts with the kinetics of the chemical reaction and to what extent the process of chemical change is intensified, and how the turbulence itself is deformed by the heat released and the accompanying expansion of the gases. The various mechanisms proposed for these phenomena are based on various hypotheses concerning the structure of the combusion zone and the determinative stage of the interaction of the turbulence with the chemical-reaction kinetics. The mechanism of turbulence generation by combustion proposed in a number of papers [3–6] is based on the observation in turbulent flow of a weakly curved flickering laminar flame. This gives rise to a nonuniform flow field of the gas, part of the energy of which goes over into the energy of turbulent fluctuations. Other authors [7, 8] considered the turbulence field to interact with the chemical-reaction kinetics via a volume mechanism and suggested a criterion of turbulence intensification based on certain physical considerations, e.g., the condition for the intensification of thermogaskinetic oscillations proposed by Rayleigh [9]. In the present paper the problem is analyzed by introducing Kolmogorov's general equation for the turbulence energy balance in reacting turbulent flows [10]. In accordance with, this equation the turbulence energy can vary due to energy exchange between the turbulent motion and the mean gas flow as a result of the work on turbulent mass transport in the acceleration field of the mean flow, and due to the effect of pressure fluctuations on the rate of thermal expansion from the chemical reaction. Each of these effects is considered and analyzed.     

Statistical structure of the velocity field in cavitating flow around a 2D hydrofoil

Transformation of flow turbulence structure with cavitation occurrence, determination of the flow conditions favorable for nucleation of cavitation bubbles, influence of the statistical structure of turbulence on this process and the inverse effect of cavitation on the flow dynamics are challenging problems in modern fluid mechanics. The paper reports on the results of statistical processing of the velocity fields measured by a PIV technique in cavitating flow over a 2D symmetric hydrofoil for four flow conditions, starting from a cavitation-free regime and finishing by unsteady cloud cavitation. We analyze basic information on the statistical structure of velocity fluctuations in the form of histograms and Q-Q diagrams along with profiles of the mean velocity and turbulent kinetic energy. The research reveals that the flow turbulence pattern and distributions of turbulent fluctuations change significantly with the cavitation development. Under unsteady cloud cavitation conditions, the probability density function of the fluctuating velocity has a two-mode distribution, which indicates switching of two alternating flow conditions in a region above the hydrofoil aft part due to periodic passing of cavitation clouds. Behaviors of the mean and most probable velocities unexpectedly appear to be different with a monotonous increase of the incoming flow velocity. This finding must be caused by modification of the skewness coefficient of the fluctuating velocity.     

Some Results Based on Near-wall Turbulence

In this paper some results based on the near-wall mean characteristics of a bounded turbulent flow are presented. In the study empirical polynomials and experimental data for an attached wall-bounded flow are used with the objective of studying the time-scales similarities in the very-near-wall region. As a result of this analysis a new parameter to characterize the high to low-Reynolds turbulence transition in the context of turbulence models is proposed. A relation for the Reynolds stress in the buffer region is also proposed, which allows a mean velocity profile through the buffer region to be obtained. This mean velocity profile joins the logarithmic ones at the beginning of the inertial sub-layer and fits appropriately to experimental data. Another result derived from the previous analysis is an expression for the eddy viscosity through the very-near-wall region. Comparison of this expression with those relations used by four known low-Reynolds models reveals that it has a very good performance.     

ON THE INFLUENCE OF THE CHOICE OF TRANSPORT AND CHEMICAL MODELS FOR NON-EQUILIBRIUM HYPERSONIC FLOW SIMULATIONS

SUMMARY

The influence of the choice of transport and chemical models on the numerical simulation of hypersonic flows in chemical non-equilibrium is investigated. A coupled Euler/boundary layer method is employed, which facilitates the incorporation of different models and simplifies the calculation of the resulting flowfields. By considering hypersonic flows with different freestream conditions, it is shown that for flows dominated by chemical reactions, the computed flowfields can be sensitive to the choice of model. This sensitivity must be taken into account when defining test cases for the validation of numerical simulations of hypersonic re-entry flows.