Parallelization of the algorithm of asymptotic partial domain decomposition in thin tube structures

The method of asymptotic partial domain decomposition for thin tube structures (finite unions of thin cylinders) is revisited. Its application to the Newtonian and non-Newtonian flows in great systems of vessels is considered. The possibility of a parallelization of its algorithm is discussed for linear and non-linear models.     

Localized disturbances in parallel shear flows

The development of localized disturbances in parallel shear flows is reviewed. The inviscid case is considered, first for a general velocity profile and then in the special case of plane Couette flow so as to bring out the key asymptotic results in an explicit form. In this context, the distinctive differences between the wave-packet associated with the asymptotic behavior of eigenmodes and the non-dispersive (inviscid) continuous spectrum is highlighted. The largest growth is found for three-dimensional disturbances and occurs in the normal vorticity component. It is due to an algebraic instability associated with the lift-up effect. Comparison is also made between the analytical results and some numerical calculations.Next the viscous case is treated, where the complete solution to the initial value problem is presented for bounded flows using eigenfunction expansions. The asymptotic, wave-packet type behaviour is analyzed using the method of steepest descent and kinematic wave theory. For short times, on the other hand, transient growth can be large, particularly for three-dimensional disturbances. This growth is associated with cancelation of non-orthogonal modes and is the viscous equivalent of the algebraic instability. The maximum transient growth possible to obtain from this mechanism is also presented, the so called optimal growth.Lastly the application of the dynamics of three dimensional disturbances in modeling of coherent structures in turbulent flows is discussed.     

Steady waves in a stratified flow over a combined obstacle

A problem of steady internal waves in subcritical flows of a stratified liquid over a finite sequence of bottom elevations is considered. An asymptotic solution of the second order of accuracy, which takes into account nonlinear effects, is constructed by the method of perturbations in terms of the small parameter of the obstacle height. Near-field interference wave structures are studied.     

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high-order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.     

Direct numerical simulation of bubble dynamics in subcooled and near-saturated convective nucleate boiling

With the long-term objective of Critical Heat Flux (CHF) prediction, bubble dynamics in convective nucleate boiling flows has been studied using a Direct Numerical Simulation (DNS). A sharp-interface phase change model which was originally developed for pool boiling flows is extended to convective boiling flows. For physical scales smaller than the smallest flow scales (smaller than the grid size), a micro-scale model was used. After a grid dependency study and a parametric study for the contact angle, four cases of simulation were carried out with different wall superheat and degree of subcooling. The flow structures around the growing bubble were investigated together with the accompanying physics. The relation between the heat flux evolution and the bubble growth was studied, along with investigations of bubble diameter and bubble base diameter evolutions across the four cases. As a validation, the evolutions of bubble diameter and bubble base diameter were compared to experimental observations. The bubble departure period and the bubble shapes show good agreement between the experiment and the simulation, although the Reynolds number of the simulation cases is relatively low.     

Effect of compressibility on the development of taylor-görtler vortices at high reynolds numbers

The development of disturbances in viscous compressible flows caused by centrifugal forces is investigated. On the basis of an asymptotic analysis of the Navier-Stokes equations at high Reynolds and Görtler numbers, mathematical models describing the development of three-dimensional unstable vortex structures are constructed. Various linear boundary-value problems are analytically solved. One type of boundary layer instability is that generated by a centrifugal force field. This kind of instability can manifest itself in the flow past concave surfaces or, in general, in flows with streamlines of positive curvature [1, 2]. Instability-driven Görtler vortices have been the subject of much research which was reviewed, for example, in [2–4].     

On the origin of drag increase in varying-phase opposition control

This study investigates the physics underlying the drag increase in a low Reynolds number turbulent channel flow due to varying-phase opposition control by means of direct numerical simulation and modal analysis. The drag increase occurs for an extended region of the parameter space and we consider a controller with a positive phase shift in Fourier domain between sensor measurement and actuator response as a representative example for this regime. Analyses of instantaneous flow fields as well as spatial power spectra show that the structure of drag-increased flows is remarkably different from that of drag-reduced and canonical flows. In particular, the near-wall region is dominated by structures of short streamwise and large spanwise extent. Isolation of a representative control scale shows that these energetic structures can be characterized as spanwise rollers, which induce strong ejection and sweep motions and lead to drag increase. The presence of rollers, and therefore drag increase, in the full nonlinear system correlates well with the presence of an amplified eigenvalue in the eigenspectrum of the linearized Navier–Stokes operator. It is further shown that the scales responsible for drag increase at positive phase shifts are inactive at negative phase shifts and do not contribute to drag reduction. These scales can therefore be excluded from a controller aimed at drag reduction, which relaxes the spatial resolution requirements on the control hardware. The eigenspectrum may be used as a computationally cheap tool to identify such detrimental scales during an early design stage.     

Higher-order and length-scale statistics of velocity and temperature fluctuations in turbulent boundary layer along a heated vertical flat plate

Time-developing direct numerical simulation (DNS) was performed to clarify the higher-order turbulent behaviors in the thermally-driven boundary layers both in air and water along a heated vertical flat plate. The predicted statistics of the heat transfer rates and the higher-order turbulent behaviors such as skewness factors, flatness factors and spatial correlation coefficients of the velocity and temperature fluctuations in the natural-convection boundary layer correspond well with those obtained from experiments for space-developing flows. The numerical results reveal that the turbulent structures of the buoyancy-driven boundary layers are mainly controlled by the fluid motions in the outer region of the boundary layer, and these large-scale structures are strongly connected with the generation of turbulence in the thermally-driven boundary layers, in accordance with the actual observations for space-developing flows. Moreover, to specify the turbulence structures of the boundary layers, the cross-correlation coefficients and the characteristic length scales are examined for the velocity and thermal fields. Consequently, it is found that with a slight increase in freestream velocity, the cross-correlation coefficient for the Reynolds shear stress and turbulent heat flux increases for opposing flow and decreases for aiding flow, and the integral scales for the velocity and temperature fields become larger for opposing flow and smaller for aiding flow compared with those for the pure natural-convection boundary layer.     

剪切湍流大尺度相干结构的模式研究

发展了一种计算剪切湍流大尺度相干结构的新模式．该模式的基础是认为大尺度相干结构为湍流场中流体脉动能量增长最快的那部分，且包含大部分的湍流脉动能量．在此基础上。通过对湍流相干能量方程的推演。建立了描述大尺度相干结构的特征控制方程，并应用Ｃｈｅｂｙｓｈｅｖ多项式方法求得湍流相干能量的最大增长率在波数空间的分布，从而获得对应的大尺度相干结构．应用该模式研究了槽流和一自然对流中的大尺度相干结构，得到的近壁区流动结构与实验现象十分接近．     

Length scales in cryogenic injection at supercritical pressure

Length scales provide some understanding of the injection of cryogenic propellants in rocket chambers on mixing efficiency, which translates to burning efficiency and performance. This project uses supercritical cryogenic nitrogen to look at high-density core flows such as those of coaxial injectors used in rocket engines. The investigation considers test conditions from 4.0 to 6.0 MPa chamber pressure at two injection velocities and temperatures. Experimental data taken by using shadowgraph images provides a means of characterizing turbulent flow structures using a two-point correlation method to determine length scales and structure shapes. The experimental results are compared to computational models.     

Compressible Turbulence and Energetic Scales: What Is Known from Experiments in Supersonic Flows?

Some properties of large-scale structures in supersonic turbulent flows are examined through experiments. The large eddies considered here include energetic scales, which contribute predominantly to, say, turbulent energy and coherent structures. Different features are presented, such as the level of energy in supersonic free shear flows, the average size of energetic structures, and their characteristic timescales. It is shown that compressibility affects the level of velocity and the size of the energetic eddies, but in many common supersonic situations, the estimation of the timescales can be made from rules valid for solenoidal turbulence. Some implications for compressible turbulence modeling are suggested. Finally, the properties of coherent structures are considered in the case of mixing layers and in a separated shock/boundary layer interaction. Some features relative to the organization of the large eddies are given and the importance of the shock motion is discussed in relation to the shock/layer interaction. This revised version was published online in August 2006 with corrections to the Cover Date.     

Effects of free‐stream turbulence on large‐scale coherent structures of separated boundary layer transition

It has been well established that large‐scale structures, usually called coherent structures, exist in many transitional and turbulent flows. The topology and range of scales of those large‐scale structures vary from flow to flow such as counter‐rotating vortices in wake flows, streaks and hairpin vortices in turbulent boundary layer. There has been relatively little study of large‐scale structures in separated and reattached transitional flows. Large‐eddy simulation (LES) is employed in the current study to investigate a separated boundary layer transition under 2% free‐stream turbulence on a flat plate with a blunt leading edge. The Reynolds number based on the inlet free stream velocity and the plate thickness is 6500. A dynamic subgrid‐scale model is employed to compute the subgrid‐scale stresses more accurately in the current transitional flow case. Flow visualization has shown that the Kelvin–Helmholtz rolls, which have been so clearly visible under no free‐stream turbulence (NFST) are not as apparent in the present study. The Lambda‐shaped vortical structures which can be clearly seen in the NFST case can hardly be identified in the free‐stream turbulence (FST) case. Generally speaking, the effects of free‐stream turbulence have led to an early breakdown of the boundary layer, and hence increased the randomization in the vortical structures, degraded the spanwise coherence of those large‐scale structures. Copyright © 2005 John Wiley & Sons, Ltd.     

Turbulent time and length scale measurements in high-velocity open channel flows

In high-velocity open channel flows, the measurements of air–water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air–water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8E+5 to 7.1E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air–water depth Y ₉₀. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95–0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.     

Asymptotics, structure, and integration of sound-proof atmospheric flow equations

Relative to the full compressible flow equations, sound-proof models filter acoustic waves while maintaining advection and internal waves. Two well-known sound-proof models, an anelastic model by Bannon and Durran’s pseudo-incompressible model, are shown here to be structurally very close to the full compressible flow equations. Essentially, the anelastic model is obtained by suppressing ? _t ρ in the mass continuity equation and slightly modifying the gravity term, whereas the pseudo-incompressible model results from dropping ? _t p from the pressure equation. For length scales small compared to the density and pressure scale heights, the anelastic model reduces to the Boussinesq approximation, while the pseudo-incompressible model approaches the zero Mach number, variable density flow equations. Thus, for small scales, both models are asymptotically consistent with the full compressible flow equations, yet the pseudo-incompressible model is more general in that it remains valid in the presence of large density variations. For the relatively small density variations found in typical atmosphere–ocean flows, both models are found to yield very similar results, with deviations between models much smaller than deviations obtained when using different numerical schemes for the same model. This in agreement with Smolarkiewicz and Dörnbrack (Int J Numer Meth Fluids 56:1513–1519, 2007). Despite these useful properties, neither model can be derived by a low-Mach number asymptotic expansion for length scales comparable to the pressure scale height, i.e., for the regime they were originally designed for. Derivations of these models via scale analysis ignore an asymptotic time scale separation between advection and internal waves. In fact, only the classical Ogura and Phillips model, which assumes weak stratification of the order of the Mach number squared, can be obtained as a leading-order model from systematic low Mach number asymptotic analysis. Issues of formal asymptotics notwithstanding, the close structural similarity of the anelastic and pseudo-incompressible models to the full compressible flow equations makes them useful limit systems in building computational models for atmospheric flows. In the second part of the paper, we propose a second-order finite-volume projection method for the anelastic and pseudo-incompressible models that observes these structural similarities. The method is applied to test problems involving free convection in a neutral atmosphere, the breaking of orographic waves at high altitudes, and the descent of a cold air bubble in the small-scale limit. The scheme is meant to serve as a starting point for the development of a robust compressible atmospheric flow solver in future work.     

Wavelet spatial scaling for educing dynamic structures in turbulent open cavity flows

In this work a methodology was developed for the selection of wavelet spatial scales to educe dynamic structures in turbulent cavity flows. The wavelet transform was applied to both the temporal signal and spatial fields to extract structures from the oscillating shear layer. The dominant frequencies were identified from the temporal transform of the shear layer oscillations, and then the corresponding wavelength was obtained using the relation U_cT=λ at each frequency. The wavelet spatial scaling was examined and a one-to-one relationship was established with respect to the wavelength. At each spatial scale, the transformed images of vorticity, velocity, and pressure fluctuations captured the vortical structures. Using this methodology, the dynamic vortical structures were extracted from the turbulent open cavity flows. Energy analysis was performed to examine the contributions of each structure.     

Secondary regimes in couette flow

We consider the asymptotic solutions of secondary steady flows in a fluid contained between cylinders rotating in the same direction for large Reynolds numbers.The existence of secondary axisymmetric steady flows in a fluid contained between cylinders rotating in the same direction was shown in [1, 2]. In the following we present the asymptotic behavior of such solutions for the case of large Reynolds numbers. The construction follows the scheme suggested in [3].     

Asymptotic Profiles for the Blasius and Sakiadis flows in a Darcy–Brinkman Isotropic Porous Medium Either with Uniform Suction or with Zero Transverse Velocity

The Blasius and Sakiadis flows with uniform suction or with zero transverse velocity, at the asymptotic state, in a Darcy–Brinkman porous medium are investigated in this note. Exact analytical solutions are derived for velocity as well as for the integral quantities. It is found that both the dimensional and non-dimensional displacement thickness, momentum thickness, energy thickness and the absolute wall shear stress are identical in both Blasius and Sakiadis flows at the asymptotic state.     

A Matched Asymptotic Expansion Analysis of Highly Unsteady Porous Media Flows

The method of matched asymptotic expansions is used to analyse a mixture of wave and diffusive behaviours governing flow in a saturated porous medium inside an elastic pipe that is suddenly subjected to a large hydraulic gradient at its entrance. At early times and near the entrance, the head is a diffusing wave that can be reduced to the linear and non-linear telegrapher equations for the laminar and partially developed turbulent flows, respectively. At later times, laminar flows are diffusive and partially developed turbulent flows follow a ‘fast diffusion’ behaviour. In the case of fully developed turbulence, flows at later times follow a fast diffusion form which is complicated by advection at extremely high gradients. A matched asymptotic expansion approach is used to match flows at early times and near the entrance, with complementary forms that are away from the entrance and which occur at later times.