空间发展圆管转捩的直接数值模拟

利用直接数值模拟研究圆管流动中由局部壁面引入的周期性吹吸(PSB)扰动沿流向的空间发展,流动的雷诺数Re选定为3000.在临界幅值的PSB扰动下,在较短的圆管内,圆管中的扰动沿流向快速增长,在足够长的圆管内,扰动沿流向持续增长发生转捩,流动发展到湍流阶段.     

Analysis of pipe flow transition. Part I. Direct numerical simulation

We have developed an accurate hybrid finite-difference code for the simulation of unsteady incompressible pipe flow. The numerical scheme uses compact finite differences of at least eighth-order accuracy for the axial coordinate, and Chebyshev and Fourier polynomials for the radial and azimuthal coordinates, respectively. Boundary conditions for the incompressible flow are enforced using an influence-matrix technique, and the Poisson equation for pressure is solved using a fast direct method. The code has been used to simulate and analyze the spatial transition process in developed laminar pipe flow at a Reynolds number of Re=2350. Results of the simulation are compared to experimental data given by Han, Tumin and Wygnanski [18]. PACS 47.11.+j, 47.20.Ft, 47.27.Cn     

An improved EMMS model for turbulent flow in pipe and its solution

Based on the existing energy-minimization multi-scale (EMMS) model for turbulent flow in pipe, an improved version is proposed, in which not only a new radial velocity distribution is introduced but also the quantification of total dissipation over the cross-section of pipe is improved for the dominant mechanism of fully turbulent flow in pipe. Then four dynamic equality constraints and some other constraints are constructed but there are five parameters involved, leading to one free variable left. Through the compromise in competition between dominant mechanisms for laminar and fully turbulent flow in pipe respectively, the above four constructed dynamic equality constraints can be closed. Finally, the cases for turbulent flow in pipe with low, moderate and high Reynolds number are simulated by the improved EMMS model. The numerical results show that the model can obtain reasonable results which agree well with the data computed by the direct numerical simulation and those obtained by experiment. This illustrates that the improved EMMS model for turbulent flow in pipe is reasonable and the compromise in competition between dominant mechanisms is indeed a universal governing principle hidden in complex systems. Especially, one more EMMS model for a complex system is offered, promoting the further development of mesoscience.     

On the Electric Potential Induced by a Homogeneous Magnetic Field in a Turbulent Pipe Flow

In this paper we study a turbulent pipe flow of a weakly electrical conducting fluid subjected to a homogeneous magnetic field which is applied perpendicular to the flow. This configuration forms the basis of a so-called electromagnetic induction flow meter. When the Hartmann number is small so that modification of flow by the Lorenz force can be neglected, the influence of the magnetic field results only in a spatially and temporally varying electric potential. The magnitude of the potential difference across the pipe is then proportional to the flow rate and this constitutes the principle of the flow meter. In this study the flow and electric potential are computed with help of a numerical flow simulation called Large-Eddy Simulation (LES) to which we have added an equation for the electrical potential. The results of the LES have been compared with experiments in which the electric potential is measured as a function of time at several positions on the circumference of the pipe. Both the experimental and numerical results for the mean potential at the pipe wall agree very well with an exact solution that can be obtained in this particular case of a homogeneous magnetic field. Furthermore, it is found that fluctuations in the electric potential due to the turbulence, are small compared to the velocity fluctuations. Based on the results we conclude that electrical-magnetic effects in pipe flow can be accurately computed with LES.     

Subcritical spatial transition of swept Hiemenz flow

It is known from experimental investigations that the leading-edge boundary layer of a swept wing exhibits transition to turbulence at subcritical Reynolds numbers, i.e. at Reynolds numbers which lie below the critical Reynolds number predicted by linear stability theory. In the present work, we investigate this subcritical transition process by direct numerical simulations of a swept Hiemenz flow in a spatial setting. The laminar base flow is perturbed upstream by a pair of stationary counter-rotating vortex-like disturbances. This perturbation generates high- and low-speed streaks by a non-modal growth mechanism. Further downstream, these streaky structures exhibit a strong instability to secondary perturbations which leads to a breakdown to turbulence.The observed transition mechanism has strong similarities to by-pass transition mechanisms found for two-dimensional boundary layers. It can be shown that transition strongly depends on the amplitude of the primary perturbation as well as on the frequency of the secondary perturbation.     

A microstructural investigation of the nonlinear response of electrorheological suspensions

In the preceding paper, Part 1, the transition from linear to nonlinear behavior for electrorheological (ER) suspensions under start-up of steady shear flow was found to first arise from the slight rearrangement of unstable structures. In this paper, we investigate the transition to nonlinear behavior for ER suspensions under oscillatory shear flow, focusing on the role of the rearrangement of unstable structures, and employing experimental and simulation results. Again, we find that nonlinear deformation first arises from these rearrangements, as opposed to the gross rearrangement or rupture of particulate chains. The Fourier transform of the simulated time-dependent shear stress is employed to quantify the dependence of the critical strain on the deformation frequency and electric field strength. The predicted behavior is consistent with experimental trends. Methods for verifying the predictions are discussed, as well as possible avenues for exploiting this information in improved operating strategies and improved ER fluids.     

Universal threshold of the transition to localized turbulence in shear flows

Experimental and numerical studies have shown similarities between localized turbulence in channel and pipe flows. By scaling analysis of a disturbed-flow model, this paper proposes a local Reynolds number Re_M to characterize the threshold of transition triggered by finite-amplitude disturbances. The Re_M represents the maximum contribution of the basic flow to the momentum ratio between the nonlinear convection and the viscous diffusion. The lower critical Re_M observed in experiments of plane Poiseuille flow, pipe Poiseuille flow and plane Couette flow are all close to 323, indicating the uniformity of mechanism governing the transition to localized turbulence.     

Bypass transition through interactions of localized disturbances in wall-bounded flows

A new mechanism bypass in a wall-bounded internal flow is proposed and the proposal is checked by direct numerical simulations of high temporal and spatial resolution. The mechanism is based on the interactions of the localized perturbations, rather than the effect of a single perturbation investigated so far in the classical bypass transition process. It is first shown by theoretical considerations that two pairs of quasistreamwise vortices can interact near the wall in such a manner that the compression (stretching) of the existing wall-normal vorticity induced by one of the pairs can enhance a new streamwise vorticity zone that can lead to new coherent structures and enhance considerably the transition process. Direct numerical simulations confirm this hypothesis.     

绕振荡水翼流动及其转捩特性的数值计算研究简

通过对比标准k-ω SST 湍流模型和基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型对绕振荡NACA66 水翼流动的数值计算结果与实验结果,对水翼振荡过程的水动力特性和流场结构变化进行了分析研究. 结果表明：与标准k-ω SST 湍流模型的数值计算结果相比,基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型能有效预测绕振荡翼型流场结构和水动力特性,捕捉流场边界层发生的流动分离和转捩现象;绕振荡水翼的流动过程可分为5 个特征阶段,当来流攻角较小时,在水翼前缘发生层流向湍流的转捩现象,水翼动力特征曲线出现变化拐点;随着来流攻角的增大,顺时针尾缘涡逐渐形成并向水翼前缘发展;当攻角较大时,前缘涡分离导致动力失速,水翼的动力特征曲线出现大幅波动;水翼处于顺时针向下旋转阶段,绕水翼的流动状态逐渐由湍流过渡为层流.     

Spatial direct numerical simulation of high-speed boundary-layer flows Part II: Transition on a cone in Mach 8 flow

The laminar breakdown of the boundary-layer flow of an axisymmetric sharp cone in a Mach 8 flow is simulated by a synergistic approach that combines the parabolized stability equation (PSE) method and spatial direct numerical simulation (DNS). The transitional state is triggered by a symmetric pair of oblique second-mode disturbances whose nonlinear interactions generate strong streamwise vorticity, which leads in turn to severe spanwise variations in the flow and eventual laminar breakdown. The PSE method is used to compute the weakly and moderately nonlinear initial stages of the transition process and, thereby, to derive a harmonically rich inflow condition for the DNS. The strongly nonlinear and laminar-breakdown stages of transition are then computed by well-resolved DNS, with a highly accurate algorithm that exploits spectral collocation and high-order compact-difference methods. Evolution of the flow is presented in terms of modal energies, mean quantities (e.g., skin friction), Reynolds stresses, turbulent kinetic energy, and flow visualization. The numerical test case is an approximate computational analog of one of the few stability experiments performed for hypersonic boundary-layer flows. Comparisons and contrasts are drawn between the experimental and the computational results. Rope-like waves similar to those observed in schlieren images of high-speed transitional flows are also observed in the numerical experiment and are shown to be visual manifestations of second-mode instability waves.This research was supported under NASA Contracts NAS1-19831 and NAS1-20059 for the first and second authors, respectively.     

Experimental investigation of horizontal air–water bubbly-to-plug and bubbly-to-slug transition flows in a 3.81 cm ID pipe

The present study seeks to investigate horizontal bubbly-to-plug and bubbly-to-slug transition flows. The two-phase flow structures and transition mechanisms in these transition flows are studied based on experimental database established using the local four-sensor conductivity probe in a 3.81 cm inner diameter pipe. While slug flow needs to be distinguished from plug flow due to the presence of large number of small bubbles (and thus, large interfacial area concentration), both differences and similarities are observed in the evolution of interfacial structures in bubbly-to-plug and bubbly-to-slug transitions. The bubbly-to-plug transition is studied by decreasing the liquid flow rate at a fixed gas flow rate. It is found that as the liquid flow rate is lowered, bubbles pack near the top wall of the pipe due to the diminished role of turbulent mixing. As the flow rate is lowered further, bubbles begin to coalesce and form the large bubbles characteristic of plug flow. Bubble size increases while bubble velocity decreases as liquid flow rate decreases, and the profile of the bubble velocity changes its shape due to the changing interfacial structure. The bubbly-to-slug transition is investigated by increasing the gas flow rate at a fixed liquid flow rate. In this transition, gas phase becomes more uniformly distributed throughout the cross-section due to the formation of large bubbles and the increasing bubble-induced turbulence. The size of small bubbles decreases while bubble velocity increases as gas flow rate increases. The distributions of bubble size and bubble velocity become more symmetric in this transition. While differences are observed in these two transitions, similarities are also noticed. As bubbly-to-plug or bubbly-to-slug transition occurs, the formation of large elongated bubbles is observed not in the uppermost region of bubble layer, but in a lower region. At the beginning of transitions, relative differences in phase velocities near the top of the pipe cross-section to those near the pipe center become larger for both gas and liquid phases, because more densely packed bubbles introduce more resistance to both phases.     

Nonlinear Instability in the Region of Laminar-Turbulent Transition in Supersonic Three-Dimensional Flow over a Flat Plate

Direct numerical simulation is applied to obtain laminar-turbulent transition in supersonic flow over a flat plate. It is shown that, due to the nonlinear instability, Tollmien–Schlichting waves generated in the boundary layer lead to the formation of oblique disturbances in the flow. These represent a combination of compression and expansion waves, whose intensities can be two orders higher than that of external harmonic disturbances. The patterns of the three-dimensional flow over the plate are presented and the structures of the turbulent flat-plate boundary layers are described for the freestream Mach numbers M = 2 and 4.     

含双侧分支受限空间油气爆炸火焰行为与超压特性大涡模拟

为研究含分支结构狭长受限空间油气爆炸特性规律,基于大涡模拟WALE模型和Zimont预混火焰模型,对横截面为100 mm×100 mm的含双侧分支管道受限空间油气泄压爆炸特性进行了数值模拟。通过对火焰形态、火焰传播速度和动态超压3个物理量的对比,验证了所建立模型对于含分支结构受限空间油气爆炸计算的适用性。基于数值模拟结果,对爆炸过程中的流场结构、火焰形态和超压变化规律进行了分析,指出了“浪花状”火焰的形成原因。结果表明:（1）火焰传播进入分支管道前,在主管道和分支管道交界处会产生旋转方向相反的对称涡旋结构,并随着火焰传播不断向分支管道内部发展;（2）当火焰传播进入分支管道后,分支管道内部前期已建立流场决定了火焰的形态,火焰锋面在涡旋结构作用下呈“浪花状”,此后火焰和流场相互影响,流场向湍流转捩,火焰锋面褶皱变形;（3）爆炸超压升压过程可划分为4个阶段,受到火焰锋面面积和分支管道泄压共同作用,表明爆炸流场、火焰行为和动态超压呈现出显著耦合性。     

Nonlinear evolution of Klebanoff type second mode disturbances in supersonic flat-plate boundary layer简

Studying the evolution of 3D disturbances is of crucial theoretical importance for understanding the transition process. The present study concerns the nonlinear evolution of second mode unstable disturbances in a supersonic boundary layer by the numerical simulation, and discusses the selectivity of 3D disturbances and possibility to transition. The results indicate that a Klebanoff type nonlinear interaction between 2D and 3D disturbances with the same frequency may amplify a band of 3D disturbances centered at a finite spanwise wavenumber. That is, certain 3D disturbances can be selectively and rapidly amplified by the unstable 2D disturbances, and certain small-scale 3D structures will appear.     

FLOW-INDUCED INTERNAL RESONANCES AND MODE EXCHANGE IN HORIZONTAL CANTILEVERED PIPE CONVEYING FLUID （Ⅱ）

Based on the nonlinear mathematical model of motion of a horizontally can-tilevered rigid pipe conveying fluid, the 3:1 internal resonance induced by the minimum critical velocity is studied in details. With the detuning parameters of internal and primary resonances and the amplitude of the external disturbing excitation varying, the flow in the neighborhood of the critical flow velocity yields that some nonlinearly dynamical behaviors occur in the system such as mode exchange, saddle-node, Hopf and co-dimension 2 bifurcations. Correspondingly, the periodic motion losses its stability by jumping or flutter, and more complicated motions occur in the pipe under consideration. The good agreement between the analytical analysis and the numerical simulation for several parameters ensures the validity and accuracy of the present analysis.     

界面张力梯度驱动对流向湍流转捩的研究

作为空间自然对流热质输运的基本形式,界面张力梯度驱动对流是流动和传热强耦合的复杂非线性过程,也是一个多控制参数耦合作用的过程,表现出丰富的流动时空特征.界面张力梯度驱动对流是微重力流体物理的重要研究内容和学科前沿,同时在空间燃料输运过程和空间能源或热管利用等空间流体管理问题中均有重要应用.本文综述了界面张力梯度驱动对流...     

Modeling of nonparallel effects in temporal direct numerical simulations of compressible boundary-layer transition

One important alternative to spatial direct numerical simulation (SDNS) of a growing boundary-layer transition is a temporal direct numerical simulation (TDNS), where the flow is assumed to be locally parallel and the transition develops in time. To model nonparallel effects of a growing boundary layer, the TDNS allows the boundary layer to grow in time. This approach has been shown to be effective for an incompressible boundary layer. For a compressible boundary layer, however, a simple application of this approach has been found to be insufficient. To investigate this issue, we first split the variation of the flow field in the streamwise direction into a slowly evolving part and a fast and small-scale fluctuation part. By Taylor-expanding the slowly evolving large-scale part, this study shows that the Navier-Stokes operator can be reformulated as a power series of the perturbation parameter (x–x ₀), yielding one set of equations for each power. Each set of these equations has a periodic solution in the streamwise direction, and therefore a modified TDNS method can be employed to solve these equations. Only the first set of the equations is considered in the applications presented. During the linear stage of transition, the results from this extended formulation show a significant improvement over those from the previous parallel flow formulation, especially for second modes which have short wavelengths. The results are well comparable with those from parabolized stability equations (PSE) and SDNS. A good agreement between this extended formulation and SDNS results is also demonstrated at the nonlinear stage.Part of this work was supported by the Deutsche Forschungsgemeinschaft (DFG).     

绕振荡水翼流动及其转捩特性的数值计算研究

通过对比标准k-ω SST 湍流模型和基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型对绕振荡NACA66 水翼流动的数值计算结果与实验结果,对水翼振荡过程的水动力特性和流场结构变化进行了分析研究. 结果表明:与标准k-ω SST 湍流模型的数值计算结果相比,基于标准k-ω SST 湍流模型修正的γ-Re_θ 转捩湍流模型能有效预测绕振荡翼型流场结构和水动力特性,捕捉流场边界层发生的流动分离和转捩现象;绕振荡水翼的流动过程可分为5 个特征阶段,当来流攻角较小时,在水翼前缘发生层流向湍流的转捩现象,水翼动力特征曲线出现变化拐点;随着来流攻角的增大,顺时针尾缘涡逐渐形成并向水翼前缘发展;当攻角较大时,前缘涡分离导致动力失速,水翼的动力特征曲线出现大幅波动;水翼处于顺时针向下旋转阶段,绕水翼的流动状态逐渐由湍流过渡为层流.      

HOPF BIFURCATION OF A NONLINEAR RESTRAINED CURVED PIPE CONVEYING FLUID BY DIFFERENTIAL QUADRATURE METHOD

This paper proposes a new method for investigating the Hopf bifurcation of a curved pipe conveying fluid with nonlinear spring support. The nonlinear equation of motion is derived by forces equilibrium on microelement of the system under consideration. The spatial coordinate of the system is discretized by the differential quadrature method and then the dynamic equation is solved by the Newton-Raphson method. The numerical solutions show that the inner fluid velocity of the Hopf bifurcation point of the curved pipe varies with different values of the parameter,nonlinear spring stiffness. Based on this, the cycle and divergent motions are both found to exist at specific fluid flow velocities with a given value of the nonlinear spring stiffness. The results are useful for further study of the nonlinear dynamic mechanism of the curved fluid conveying pipe.