Showing papers on "Reynolds number published in 2000"

Passive mixing in a three-dimensional serpentine microchannel

Abstract: A three-dimensional serpentine microchannel design with a "C shaped" repeating unit is presented in this paper as a means of implementing chaotic advection to passively enhance fluid mixing. The device is fabricated in a silicon wafer using a double-sided KOH wet-etching technique to realize a three-dimensional channel geometry. Experiments using phenolphthalein and sodium hydroxide solutions demonstrate the ability of flow in this channel to mix faster and more uniformly than either pure molecular diffusion or flow in a "square-wave" channel for Reynolds numbers from 6 to 70. The mixing capability of the channel increases with increasing Reynolds number. At least 98% of the maximum intensity of reacted phenolphthalein is observed in the channel after five mixing segments for Reynolds numbers greater than 25. At a Reynolds number of 70, the serpentine channel produces 16 times more reacted phenolphthalein than a straight channel and 1.6 times more than the square-wave channel. Mixing rates in the serpentine channel at the higher Reynolds numbers are consistent with the occurrence of chaotic advection. Visualization of the interface formed in the channel between streams of water and ethyl alcohol indicates that the mixing is due to both diffusion and fluid stirring.

An Introduction to Fluid Dynamics

Abstract: Preface Conventions and notation 1. The physical properties of fluids 2. Kinematics of the flow field 3. Equations governing the motion of a fluid 4. Flow of a uniform incompressible viscous fluid 5. Flow at large Reynolds number: effects of viscosity 6. Irrotational flow theory and its applications 7. Flow of effectively inviscid liquid with vorticity Appendices.

Flow Control: Passive, Active, and Reactive Flow Management

Abstract: Preface Nomenclature 1. Introduction 2. Governing equations 3. Unifying principles 4. Coherent structures 5. Reynolds number effects 6. Transition control 7. Compliant coatings 8. Separation control 9. Low-Reynolds-number aerodynamics 10. Drag reduction 11. Mixing enhancement 12. Noise reduction 13. Microelectromechanical systems 14. Frontiers of flow control Epilogue Bibliography Index.

Reynolds-number scaling of the flat-plate turbulent boundary layer

Abstract: Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.

Fluid mechanics in the driven cavity

Abstract: This review pertains to the body of work dealing with internal recirculating flows generated by the motion of one or more of the containing walls. These flows are not only technologically important, they are of great scientific interest because they display almost all fluid mechanical phenomena in the simplest of geometrical settings. Thus corner eddies, longitudinal vortices, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same closed geometry. This facilitates the comparison of results from experiment, analysis, and computation over the whole range of Reynolds numbers. Considerable progress has been made in recent years in the understanding of three-dimensional flows and in the study of turbulence. The use of direct numerical simulation appears very promising.

Elastic turbulence in a polymer solution flow

Abstract: Turbulence is a ubiquitous phenomenon that is not fully understood. It is known that the flow of a simple, newtonian fluid is likely to be turbulent when the Reynolds number is large (typically when the velocity is high, the viscosity is low and the size of the tank is large). In contrast, viscoelastic fluids such as solutions of flexible long-chain polymers have nonlinear mechanical properties and therefore may be expected to behave differently. Here we observe experimentally that the flow of a sufficiently elastic polymer solution can become irregular even at low velocity, high viscosity and in a small tank. The fluid motion is excited in a broad range of spatial and temporal scales, and we observe an increase in the flow resistance by a factor of about twenty. Although the Reynolds number may be arbitrarily low, the observed flow has all the main features of developed turbulence. A comparable state of turbulent flow for a newtonian fluid in a pipe would have a Reynolds number as high as 10(5) (refs 1, 2). The low Reynolds number or 'elastic' turbulence that we observe is accompanied by significant stretching of the polymer molecules, resulting in an increase in the elastic stresses of up to two orders of magnitude.

The Motion of High-Reynolds-Number Bubbles in Inhomogeneous Flows

Abstract: ▪ Abstract Predicting the motion of bubbles in dispersed flows is a key problem in fluid mechanics that has a bearing on a wide range of applications from oceanography to chemical engineering. In this review we synthesize the recent progress made in describing bubble motion in inhomogeneous flow. A trident approach consisting of experimental, analytical, and numerical work has given a clearer description of the hydrodynamic forces experienced by isolated bubbles moving either in inviscid flows or in slightly viscous laminar flows. A significant part of the paper is devoted to a discussion of drag, added-mass force, and shear-induced lift experienced by spheroidal bubbles moving in inertially dominated, time-dependent, rotational, nonuniform flows. The important influence of surfactants and shape distortion on bubble motion in a quiescent liquid is highlighted. Examples of bubble motion in inhomogeneous flows combining several of the effects mentioned above are discussed.

Numerical studies of flow over a circular cylinder at ReD=3900

Abstract: Flow over a circular cylinder at Reynolds number 3900 is studied numerically using the technique of large eddy simulation. The computations are carried out with a high-order accurate numerical method based on B-splines and compared with previous upwind-biased and central finite-difference simulations and with the existing experimental data. In the very near wake, all three simulations are in agreement with each other. Farther downstream, the results of the B-spline computations are in better agreement with the hot-wire experiment of Ong and Wallace [Exp. Fluids 20, 441–453 (1996)] than those obtained in the finite-difference simulations. In particular, the power spectra of velocity fluctuations are in excellent agreement with the experimental data. The impact of numerical resolution on the shear layer transition is investigated.

Detached-Eddy Simulations past a circular cylinder

Abstract: The flow is calculated with laminar separation (LS) at Reynolds numbers 50,000 and 140,000, and with turbulent separation (TS) at140,000 and 3 × 106. The TS cases are effectively tripped, but compared with untripped experiments at very high Reynolds numbers. The finest grid has about 18,000 points in each of 56 grid planes spanwise; the resolution is far removed from Direct Numerical Simulations, and the turbulence model controls the separation if turbulent. The agreement is quite good for drag, shedding frequency, pressure, and skin friction. However the comparison is obscured by large modulations of the vortex shedding and drag which are very similar to those seen in experiments but also, curiously, durably different between cases especially of the LS type. The longest simulations reach only about 50 shedding cycles. Disagreement with experimental Reynolds stresses reaches about 30%, and the length of the recirculation bubble is about double that measured. The discrepancies are discussed, as are the effects of grid refinement, Reynolds number, and a turbulence-model curvature correction. The finest grid does not give the very best agreement with experiment. The results add to the validation base of the Detached-Eddy Simulation (DES) technique for smooth-surface separation. Unsteady Reynolds-averaged simulations are much less accurate than DES for LS cases, but very close for TS cases. Cases with a more intricate relationship between transition and separation are left for future study.

The mixing transition in turbulent flows

Abstract: Data on turbulent mixing and other turbulent-flow phenomena suggest that a (mixing) transition, originally documented to occur in shear layers, also occurs in jets, as well as in other flows and may be regarded as a universal phenomenon of turbulence. The resulting fully-developed turbulent flow requires an outer-scale Reynolds number of Re = U[delta]/v [greater, similar] 1–2 × 104, or a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100–140, to be sustained. A proposal based on the relative magnitude of dimensional spatial scales is offered to explain this behaviour.

Reynolds number independent instability of the boundary layer over a flat surface : optimal perturbations

Abstract: The dependence on initial conditions of the three-dimensional algebraic spatial instability of the Blasius boundary layer is examined by a recently developed method of receptivity analysis based on the upstream integration of adjoint equations. This method allows us to determine optimal perturbations, i.e. initial perturbations that maximize the energy growth, even in the wavenumber range where the problem is not amenable to a mode analysis, and thus to complement a previous paper in which the small-wavenumber regime was described.

An approach to wall modeling in large-eddy simulations

Abstract: Channel flow with friction Reynolds number Reτ as high as 80 000 is treated by large-eddy simulation at a moderate cost, using the subgrid-scale model designed for detached-eddy simulations. It includes wall modeling, and was not adjusted for this flow. The grid count scales with the logarithm of the Reynolds number. Three independent codes are in fair agreement with each other. Reynolds-number variations and grid refinement cause trades between viscous, modeled, and resolved shear stresses. The skin-friction coefficient is too low, on the order of 15%. The velocity profiles contain a “modeled” logarithmic layer near the wall and some suggest a “resolved” logarithmic layer farther up, but the two layers have a mismatch of several units in U+.

Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries

Abstract: Direct numerical simulations are performed of gravity-current fronts in the lock-exchange configuration The case of small density differences is considered, where the Boussinesq approximations can be adopted The key objective of the investigation is a detailed analysis of the flow structure at the foremost part of the front, where no previous high-resolution data were available For the simulations, high-order numerical methods are used, based on spectral and spectral-element discretizations and compact finite differences A three-dimensional simulation is conducted of a front spreading along a no-slip boundary at a Reynolds number of about 750 The simulation exhibits all features typically observed in experimental flows near the gravity-current head, including the lobe-and-cleft structure at the leading edge The results reveal that the flow topology at the head differs from what has been assumed previously, in that the foremost point is not a stagnation point in a translating system Rather, the stagnation point is located below and slightly behind the foremost point in the vicinity of the wall The relevance of this finding for the mechanism behind the lobe-and-cleft instability is discussed In order to explore the high-Reynolds-number regime, and to assess potential Reynolds-number effects, two-dimensional simulations are conducted for Reynolds numbers up to about 30 000, for both no-slip and slip (ie shear-stress free) boundaries It is shown that although quantitative Reynolds-number effects persist over the whole range examined, no qualitative changes in the flow structure at the head can be observed A comparison of the two-dimensional results with laboratory data and the three-dimensional simulation provides evidence that a two-dimensional model is able to capture essential features of the flow at the head The simulations also show that for the free-slip case the shape of the head agrees closely with the classical inviscid theory of Benjamin

Approximate Wall Boundary Conditions in the Large-Eddy Simulation of High Reynolds Number Flow

Abstract: The near-wall regions of high Reynolds numbers turbulent flows must be modelled to treat many practical engineering and aeronautical applications. In this review we examine results from simulations of both attached and separated flows on coarse grids in which the near-wall regions are not resolved and are instead represented by approximate wall boundary conditions. The simulations use the dynamic Smagorinsky subgrid-scale model and a second-order finite-difference method. Typical results are found to be mixed, with acceptable results found in many cases in the core of the flow far from the walls, provided there is adequate numerical resolution, but with poorer results generally found near the wall. Deficiencies in this approach are caused in part by both inaccuracies in subgrid-scale modelling and numerical errors in the low-order finite-difference method on coarse near-wall grids, which should be taken into account when constructing models and performing large-eddy simulation on coarse grids. A promising new method for developing wall models from optimal control theory is also discussed.

Numerical investigation of transitional and weak turbulent flow past a sphere

Abstract: This work reports results of numerical simulations of viscous incompressible flow past a sphere. The primary objective is to identify transitions that occur with increasing Reynolds number, as well as their underlying physical mechanisms. The numerical method used is a mixed spectral element/Fourier spectral method developed for applications involving both Cartesian and cylindrical coordinates. In cylindrical coordinates, a formulation, based on special Jacobi-type polynomials, is used close to the axis of symmetry for the efficient treatment of the ‘pole’ problem. Spectral convergence and accuracy of the numerical formulation are verified. Many of the computations reported here were performed on parallel computers. It was found that the first transition of the flow past a sphere is a linear one and leads to a three-dimensional steady flow field with planar symmetry, i.e. it is of the ‘exchange of stability’ type, consistent with experimental observations on falling spheres and linear stability analysis results. The second transition leads to a single-frequency periodic flow with vortex shedding, which maintains the planar symmetry observed at lower Reynolds number. As the Reynolds number increases further, the planar symmetry is lost and the flow reaches a chaotic state. Small scales are first introduced in the flow by Kelvin–Helmholtz instability of the separating cylindrical shear layer; this shear layer instability is present even after the wake is rendered turbulent.

Dynamics and low-dimensionality of a turbulent near wake

Abstract: We investigate the dynamics of the near wake in turbulent flow past a circular cylinder up to ten cylinder diameters downstream. The very near wake (up to three diameters) is dominated by the shear layer dynamics and is very sensitive to disturbances and cylinder aspect ratio. We perform systematic spectral direct (DNS) and large-eddy simulations (LES) at Reynolds number ( Re ) between 500 and 5000 with resolution ranging from 200 000 to 100 000 000 degrees of freedom. In this paper, we analyse in detail results at Re = 3900 and compare them to several sets of experiments. Two converged states emerge that correspond to a U-shape and a V-shape mean velocity profile at about one diameter behind the cylinder. This finding is consistent with the experimental data and other published LES. Farther downstream, the flow is dominated by the vortex shedding dynamics and is not as sensitive to the aforementioned factors. We also examine the development of a turbulent state and the inertial subrange of the corresponding energy spectrum in the near wake. We find that an inertial range exists that spans more than half a decade of wavenumber, in agreement with the experimental results. In contrast, very low-resolution spectral simulation as well as other dissipative LES do not describe accurately the inertial range although they predict low-order statistics relatively accurately. This finding is analysed in the context of coherent structures using a phase averaging technique and a procedure to extract the most energetic (on the average) eigenmodes of the flow. The results suggest that a dynamical model would require of the order of twenty modes to describe the vortex shedding dynamics with reasonable accuracy.

Statistical mechanical description and modelling of turbulent collision of inertial particles

Abstract: The collision rate of monodisperse solid particles in a turbulent gas is governed by a wide range of scales of motion in the flow. Recent studies have shown that large-scale energetic eddies are the dominant factor contributing to the relative velocity between two colliding particles (the turbulent transport effect), whereas small-scale dissipative eddies can enhance the collision rate significantly by inducing local non-uniform particle distribution (the accumulation effect). The turbulent transport effect is most noticeable when the particle inertial response time τp is of the order of the flow integral timescale and the accumulation effect is most pronounced when τp is comparable to the flow Kolmogorov time.We study these two contributions separately through direct numerical simulations. The two effects are quantified carefully with a numerical procedure that is independent of the computation of average collision rate. This facilitates the study of not only the statistical description of the collision kernel, but also the relative contributions and modelling of the two physical effects. Simulations at several flow Reynolds numbers were performed to suggest a model for the accumulation effect. The data show that the accumulation effect scales linearly with flow Taylor microscale Reynolds number Rλ, while the theory for fully developed turbulence indicates that the maximum level of the turbulent transport effect scales with R1/2λ. Finally, an integrated model has been developed to predict the collision rate at arbitrary flow Reynolds numbers and particle inertia.

A note on the overlap region in turbulent boundary layers

Abstract: Two independent experimental investigations of the behavior of turbulent boundary layers with increasing Reynolds number were recently completed. The experiments were performed in two facilities, the Minimum Turbulence Level (MTL) wind tunnel at Royal Institute of Technology (KTH) and the National Diagnostic Facility (NDF) wind tunnel at Illinois Institute of Technology (IIT). Both experiments utilized oil-film interferometry to obtain an independent measure of the wall-shear stress. A collaborative study by the principals of the two experiments, aimed at understanding the characteristics of the overlap region between the inner and outer parts of the boundary layer, has just been completed. The results are summarized here, utilizing the profiles of the mean velocity, for Reynolds numbers based on the momentum thickness ranging from 2500 to 27 000. Contrary to the conclusions of some earlier publications, careful analysis of the data reveals no significant Reynolds number dependence for the parameters desc...

Flow-pattern identification for two staggered circular cylinders in cross-flow

Abstract: The flow around two circular cylinders of equal diameter, arranged in a staggered configuration, was investigated using flow visualization and particle image velocimetry for centre-to-centre pitch ratio P/D = 1[ratio ]0 to 5.0 and angle of incidence. α = 0° to 90°. Experiments were conducted within the low subcritical Reynolds number regime, from Re = 850 to 1900. Nine flow patterns were identified, and processes of shear layer reattachment, induced separation, vortex pairing and synchronization, and vortex impingement, were observed. New insight was gained into previously published Strouhal number data, by considering the flow patterns involved. The study revealed that vortex shedding frequencies are more properly associated with individual shear layers than with individual cylinders; more specifically, the two shear layers from the downstream cylinder often shed vortices at different frequencies.

Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5

Abstract: A direct numerical simulation of a supersonic turbulent boundary layer has been performed. We take advantage of a technique developed by Spalart for incompressible flow. In this technique, it is assumed that the boundary layer grows so slowly in the streamwise direction that the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for by a coordinate transformation and a multiple-scale analysis. The result is a modified system of equations, in which the flow is homogeneous in both the streamwise and spanwise directions, and which represents the state of the boundary layer at a given streamwise location. The equations are solved using a mixed Fourier and B-spline Galerkin method.Results are presented for a case having an adiabatic wall, a Mach number of M = 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of Reθ′ = 849. The Reynolds number based on momentum integral thickness and free-stream viscosity is Reθ = 1577. The results indicate that the Van Driest transformed velocity satisfies the incompressible scalings and a small logarithmic region is obtained. Both turbulence intensities and the Reynolds shear stress compare well with the incompressible simulations of Spalart when scaled by mean density. Pressure fluctuations are higher than in incompressible flow. Morkovin's prediction that streamwise velocity and temperature fluctuations should be anti-correlated, which happens to be supported by compressible experiments, does not hold in the simulation. Instead, a relationship is found between the rates of turbulent heat and momentum transfer. The turbulent kinetic energy budget is computed and compared with the budgets from Spalart's incompressible simulations.

The Dynamics of Lava Flows

Abstract: Lava flows are gravity currents of partially molten rock that cool as they flow, in some cases melting the surface over which they flow but in all cases gradually solidifying until they come to rest. They present a wide range of flow regimes from turbulent channel flows at moderate Reynolds numbers to extremely viscous or plastic, creeping flows, and even brittle rheology may play a role once some solid has formed. The cooling is governed by the coupling of heat transport in the flowing lava with transfer from the lava surface into the surrounding atmosphere or water or into the underlying solid, and it leads to large changes in rheology. Insta- bilities, mostly resulting from cooling, lead to flow branching, surface folding, rifting, and fracturing, and they contribute to the distinctive styles and surface appearances of different classes of flows. Theoretical and laboratory models have complemented field studies in developing the current understanding of lava flows, motivated by the extensive roles they play in the development of planetary crusts and ore deposits and by the immediate hazards posed to people and property. However, much remains to be learned about the mechanics governing creeping, turbulent, and transitional flows in the presence of large rheology change on cooling and particularly about the advance of flow fronts, flow instabilities, and the development of flow morphology. I introduce the dynamical problems involved in the study of lava flows and review modeling approaches.

The Effect of Resistivity on the Nonlinear Stage of the Magnetorotational Instability in Accretion Disks

Abstract: We present three-dimensional magnetohydrodynamic simulations of the nonlinear evolution of the magnetorotational instability (MRI) with a nonzero ohmic resistivity. The simulations begin from a homogeneous (unstratified) density distribution and use the local shearing-box approximation. The evolution of a variety of initial field configurations and strengths is considered for several values of the constant coefficient of resistivity ?. For uniform vertical and toroidal magnetic fields, we find unstable growth consistent with the linear analyses; finite resistivity reduces growth rates and, when large enough, stabilizes the MRI. Even when unstable modes remain, resistivity has significant effects on the nonlinear state. The properties of the saturated state depend on the initial magnetic field configuration. In simulations with an initial uniform vertical field, the MRI is able to support angular momentum transport even for large resistivities through the quasi-periodic generation of axisymmetric radial channel solutions rather than through the maintenance of anisotropic turbulence. Reconnective processes rather than parasitic instabilities mediate the resurgent channel solution in this case. Simulations with zero-net flux show that the angular momentum transport and the amplitude of magnetic energy after saturation are significantly reduced by finite resistivity, even at levels where the linear modes are only slightly affected. The MRI is unable to sustain angular momentum transport and turbulent flow against diffusion for ReM 104, where the Reynolds number is defined in terms of the disk scale height and sound speed, ReM = csH/?. As this is close to the Reynolds numbers expected in low, cool states of dwarf novae, these results suggest that finite resistivity may account for the low and high angular momentum transport rates inferred for these systems.

Reconstruction of the global velocity field in the axisymmetric mixing layer utilizing the proper orthogonal decomposition

Abstract: Experimental data are presented from 138 synchronized channels of hot-wire anemometry in an investigation of the large-scale, or coherent, structures in a high Reynolds number fully developed, turbulent axisymmetric shear layer. The dynamics of the structures are obtained from instantaneous realizations of the streamwise velocity field in a single plane, x/D = 3, downstream of a round jet nozzle. The Proper Orthogonal Decomposition (POD) technique is applied to an ensemble of these realizations to determine optimal representations of the velocity field, in a mean-square sense, in terms of an orthogonal basis. The coefficients of the orthogonal functions, which describe the temporal evolution of the POD eigenfunctions, are determined by projecting instantaneous realizations of the velocity field onto the basis.Evidence is presented to show that with a partial reconstruction of the velocity field, using only the first radial POD mode, the large-scale structure is objectively educed from the turbulent field. Further, it is shown that only five azimuthal Fourier modes (0,3,4,5,6) are necessary to represent the evolution of the large-scale structure. The results of the velocity reconstruction using the POD provide evidence for azimuthally coherent structures that exist near the potential core. In addition to the azimuthal structures near the potential core, evidence is also found for the presence of counter-rotating, streamwise vortex pairs (or ribs) in the region between successive azimuthally coherent structures as well as coexisting for short periods with them. The large-scale structure cycle, which includes the appearance of the ring structure, the advection of fluid by the ribs in the braid region and their advection toward the outside of the layer by a following ring structure, repeats approximately every one integral time scale. One surprising result was that the most spatially correlated structure in the flow, the coherent ring near the potential core which ejects fluid in the streamwise direction in a volcano-like eruption, is also the one with the shortest time scale.

Mechanisms of transition and heat transfer in a separation bubble

Abstract: The laminar boundary layer on a flat surface is made to separate by way of aspiration through an opposite boundary, causing approximately a 25% deceleration. The detached shear layer transitions to turbulence, reattaches, and evolves towards a normal turbulent boundary layer. We performed the direct numerical simulation (DNS) of this flow, and believe that a precise experimental repeat is possible. The pressure distribution and the Reynolds number based on bubble length are close to those on airfoils; numerous features are in agreement with Gaster's and other experiments and correlations. At transition a large negative surge in skin friction is seen, following weak negative values and a brief contact with zero; this could be described as a turbulent re-separation. Temperature is treated as a passive scalar, first with uniform wall temperature and then with uniform wall heat flux. The transition mechanism involves the wavering of the shear layer and then Kelvin–Helmholtz vortices, which instantly become three-dimensional without pairing, but not primary Gortler vortices. The possible dependence of the DNS solution on the residual incoming disturbances, which we keep well below 0.1%, and on the presence of a ‘hard’ opposite boundary, are discussed. We argue that this flow, unlike the many transitional flows which hinge on a convective instability, is fully specified by just three parameters: the amount of aspiration, and the streamwise and the depth Reynolds numbers (heat transfer adds the Prandtl number). This makes comparisons meaningful, and relevant to separation bubbles on airfoils in low-disturbance environments. We obtained Reynolds-averaged Navier–Stokes (RANS) results with simple turbulence models and spontaneous transition. The agreement on skin friction, displacement thickness, and pressure is rather good, which we attribute to the simple nature of ‘transition by contact’ due to flow reversal. In contrast, a surge of the heat-transfer coefficient violates the Reynolds analogy, and is greatly under-predicted by the models.

Direct simulation of the turbulent boundary layer along a compression ramp at M = 3 and Reθ = 1685

Abstract: The turbulent boundary layer along a compression ramp with a deflection angle of 18° at a free-stream Mach number of M = 3 and a Reynolds number of Reθ = 1685 with respect to free-stream quantities and mean momentum thickness at inflow is studied by direct numerical simulation. The conservation equations for mass, momentum, and energy are solved in generalized coordinates using a 5th-order hybrid compact- finite-difference-ENO scheme for the spatial discretization of the convective fluxes and 6th-order central compact finite differences for the diffusive fluxes. For time advancement a 3rd-order Runge–Kutta scheme is used. The computational domain is discretized with about 15 × 106 grid points. Turbulent inflow data are provided by a separate zero-pressure-gradient boundary-layer simulation. For statistical analysis, the flow is sampled 600 times over about 385 characteristic timescales δ0/U∞, defined by the mean boundary-layer thickness at inflow and the free-stream velocity. Diagnostics show that the numerical representation of the flow field is sufficiently well resolved.Near the corner, a small area of separated flow develops. The shock motion is limited to less than about 10% of the mean boundary-layer thickness. The shock oscillates slightly around its mean location with a frequency of similar magnitude to the bursting frequency of the incoming boundary layer. Turbulent fluctuations are significantly amplified owing to the shock–boundary-layer interaction. Reynolds-stress maxima are amplified by a factor of about 4. Turbulent normal and shear stresses are amplified differently, resulting in a change of the structure parameter. Compressibility affects the turbulence structure in the interaction area around the corner and during the relaxation after reattachment downstream of the corner. Correlations involving pressure fluctuations are significantly enhanced in these regions. The strong Reynolds analogy which suggests a perfect correlation between velocity and temperature fluctuations is found to be invalid in the interaction area.

Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method

Abstract: A spherical drop, placed in a second liquid of the same density, is subjected to shearing between parallel plates. The subsequent flow is investigated numerically with a volume-of-fluid (VOF) method. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds number. Our simulations compare well with previous theoretical, numerical, and experimental results. For capillary numbers greater than the critical value, the drop deforms to a dumbbell shape and daughter drops detach via an end-pinching mechanism. The number of daughter drops increases with the capillary number. The breakup can also be initiated by increasing the Reynolds number.