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Showing papers on "Reynolds number published in 1997"


Journal ArticleDOI
TL;DR: In this article, the smoothed particle hydrodynamics (SPH) method is extended to model incompressible flows of low Reynolds number, and the results show that the SPH results exhibit small pressure fluctuations near curved boundaries.

1,696 citations


Journal ArticleDOI
TL;DR: In this paper, a simulation of the Navier-Stokes equations of a backward-facing step flow was performed at a Reynolds number of 5100 based on the step height h and inlet free-stream velocity.
Abstract: Turbulent flow over a backward-facing step is studied by direct numerical solution of the Navier–Stokes equations. The simulation was conducted at a Reynolds number of 5100 based on the step height h and inlet free-stream velocity, and an expansion ratio of 1.20. Temporal behaviour of spanwise-averaged pressure fluctuation contours and reattachment length show evidence of an approximate periodic behaviour of the free shear layer with a Strouhal number of 0.06. The instantaneous velocity fields indicate that the reattachment location varies in the spanwise direction, and oscillates about a mean value of 6.28h. Statistical results show excellent agreement with experimental data by Jovic & Driver (1994). Of interest are two observations not previously reported for the backward-facing step flow: (a) at the relatively low Reynolds number considered, large negative skin friction is seen in the recirculation region; the peak |Cf| is about 2.5 times the value measured in experiments at high Reynolds numbers; (b) the velocity profiles in the recovery region fall below the universal log-law. The deviation of the velocity profile from the log-law indicates that the turbulent boundary layer is not fully recovered at 20 step heights behind the separation.The budgets of all Reynolds stress components have been computed. The turbulent kinetic energy budget in the recirculation region is similar to that of a turbulent mixing layer. The turbulent transport term makes a significant contribution to the budget and the peak dissipation is about 60% of the peak production. The velocity–pressure gradient correlation and viscous diffusion are negligible in the shear layer, but both are significant in the near-wall region. This trend is seen throughout the recirculation and reattachment region. In the recovery region, the budgets show that effects of the free shear layer are still present.

1,076 citations


Journal ArticleDOI
TL;DR: In this article, a self-sustaining process for wall-bounded shear flows is investigated, which consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls.
Abstract: A self-sustaining process conjectured to be generic for wall-bounded shear flows is investigated. The self-sustaining process consists of streamwise rolls that redistribute the mean shear to create streaks that wiggle to maintain the rolls. The process is analyzed and shown to be remarkably insensitive to whether there is no-slip or free-slip at the walls. A low-order model of the process is derived from the Navier–Stokes equations for a sinusoidal shear flow. The model has two unstable steady solutions above a critical Reynolds number, in addition to the stable laminar flow. For some parameter values, there is a second critical Reynolds number at which a homoclinic bifurcation gives rise to a stable periodic solution. This suggests a direct link between unstable steady solutions and almost periodic solutions that have been computed in plane Couette flow. It is argued that this self-sustaining process is responsible for the bifurcation of shear flows at low Reynolds numbers and perhaps also for controlling the near-wall region of turbulent shear flows at higher Reynolds numbers.

914 citations


Journal ArticleDOI
TL;DR: In this article, a new and simplified formula for predicting the settling velocity of natural sediment particles is developed, which is applicable to a wide range of Reynolds numbers from the Stokes flow to the turbulent regime.
Abstract: A new and simplified formula for predicting the settling velocity of natural sediment particles is developed. The formula proposes an explicit relationship between the particle Reynolds number and a dimensionless particle parameter. It is applicable to a wide range of Reynolds numbers from the Stokes flow to the turbulent regime. The proposed formula has the highest degree of prediction accuracy when compared with other published formulas. It also agrees well with the widely used diagrams and tables proposed by the U.S. Inter-Agency Committee in 1957.

532 citations


Journal ArticleDOI
TL;DR: In this paper, six subgrid models for the turbulent stress tensor are tested by conducting large-eddy simulations (LES) of the weakly compressible temporal mixing layer: the Smagorinsky, similarity, gradient, dynamic eddy-viscosity, dynamic mixed and dynamic Clark models.
Abstract: Six subgrid models for the turbulent stress tensor are tested by conducting large-eddy simulations (LES) of the weakly compressible temporal mixing layer: the Smagorinsky, similarity, gradient, dynamic eddy-viscosity, dynamic mixed and dynamic Clark models. The last three models are variations of the first three models using the dynamic approach. Two sets of simulations are performed in order to assess the quality of the six models. The LES results corresponding to the first set are compared with filtered results obtained from a direct numerical simulation (DNS). It appears that the dynamic models lead to more accurate results than the non-dynamic models tested. An adequate mechanism to dissipate energy from resolved to subgrid scales is essential. The dynamic models have this property, but the Smagorinsky model is too dissipative during transition, whereas the similarity and gradient models are not sufficiently dissipative for the smallest resolved scales. In this set of simulations, at moderate Reynolds number, the dynamic mixed and Clark models are found to be slightly more accurate than the dynamic eddy-viscosity model. The second set of LES concerns the mixing layer at a considerably higher Reynolds number and in a larger computational domain. An accurate DNS for this mixing layer can currently not be performed, thus in this case the LES are tested by investigating whether they resemble a self-similar turbulent flow. It is found that the dynamic models generate better results than the non-dynamic models. The closest approximation to a self-similar state was obtained using the dynamic eddy-viscosity model.

487 citations


Journal ArticleDOI
TL;DR: In this paper, the Young equation is used to describe the motion of an interface between immiscible viscous fluids along a smooth homogeneous solid surface in the case of small capillary and Reynolds numbers, and an analytical expression for the dependence of the dynamic contact angle on the contact-line speed and parameters characterizing properties of contacting media is derived.
Abstract: A general mathematical model which describes the motion of an interface between immiscible viscous fluids along a smooth homogeneous solid surface is examined in the case of small capillary and Reynolds numbers. The model stems from a conclusion that the Young equation, σ1 cos θ = σ2 − σ3, which expresses the balance of tangential projection of the forces acting on the three-phase contact line in terms of the surface tensions σi and the contact angle θ, together with the well-established experimental fact that the dynamic contact angle deviates from the static one, imply that the surface tensions of contacting interfaces in the immediate vicinity of the contact line deviate from their equilibrium values when the contact line is moving. The same conclusion also follows from the experimentally observed kinematics of the flow, which indicates that liquid particles belonging to interfaces traverse the three-phase interaction zone (i.e. the ‘contact line’) in a finite time and become elements of another interface – hence their surface properties have to relax to new equilibrium values giving rise to the surface tension gradients in the neighbourhood of the moving contact line. The kinematic picture of the flow also suggests that the contact-line motion is only a particular case of a more general phenomenon – the process of interface formation or disappearance – and the corresponding mathematical model should be derived from first principles for this general process and then applied to wetting as well as to other relevant flows. In the present paper, the simplest theory which uses this approach is formulated and applied to the moving contact-line problem. The model describes the true kinematics of the flow so that it allows for the ‘splitting’ of the free surface at the contact line, the appearance of the surface tension gradients near the contact line and their influence upon the contact angle and the flow field. An analytical expression for the dependence of the dynamic contact angle on the contact-line speed and parameters characterizing properties of contacting media is derived and examined. The role of a ‘thin’ microscopic residual film formed by adsorbed molecules of the receding fluid is considered. The flow field in the vicinity of the contact line is analysed. The results are compared with experimental data obtained for different fluid/liquid/solid systems.

402 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that the spanwise end conditions which control the primary mode of vortex shedding significantly affect the shear-layer instability and contributed to the large discrepancy in quoted values of the critical Reynolds number.
Abstract: Notwithstanding the fact that the instability of the separated shear layer in the cylinder wake has been extensively studied, there remains some uncertainty regarding not only the critical Reynolds number at which the instability manifests itself, but also the variation of its characteristic frequency with Reynolds number (Re). A large disparity exists in the literature in the precise value of the critical Reynolds number, with quoted values ranging from Re = 350 to Re = 3000. In the present paper, we demonstrate that the spanwise end conditions which control the primary mode of vortex shedding significantly affect the shear-layer instability. For parallel shedding conditions, shear-layer instability manifests itself at Re ≈ 1200, whereas for oblique shedding conditions it is inhibited until a significantly higher Re ≈ 2600, implying that even in the absence of a variation in free-stream turbulence level, the oblique angle of primary vortex shedding influences the onset of shear-layer instability, and contributes to the large disparity in quoted values of the critical Reynolds number. We confirm the existence of intermittency in shear-layer fluctuations and show that it is not related to the transverse motion of the shear layers past a fixed probe, as suggested previously. Such fluctuations are due to an intermittent streamwise movement of the transition point, or the location at which fluctuations develop rapidly in the shear layer.Following the original suggestion of Bloor (1964), it has generally been assumed in previous studies that the shear-layer frequency (normalized by the primary vortex shedding frequency) scales with Re1/2, although a careful examination of the actual data points from these studies does not support such a variation. We have reanalysed all of the actual data points from previous investigations and include our own measurements, to find that none of these studies yields a relationship which is close to Re1/2. A least-squares analysis which includes all of the previously available data produces a variation of the form Re0·67. Based on simple physical arguments that account for the variation of the characteristic velocity and length scales of the shear layer, we predict a variation for the normalized shear-layer frequency of the form Re0·7, which is in good agreement with the experimental measurements.

397 citations


Journal ArticleDOI
TL;DR: In this paper, the authors simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization.
Abstract: We have simulated flow past a circular cylinder at a Reynolds number of 3.9 X 10 3 using a solver that employs an energy-conservative second-order central difference scheme for spatial discretization. Detailed comparisons of turbulence statistics and energy spectra in the downstream wake region (7.0 < x/D < 10.0) have been made with the results of Beaudan and Moin and with experiments to assess the impact of numerical diffusion on the flowfield. Based on these comparisons, conclusions are drawn on the suitability of higher-order upwind schemes for LES in complex geometries.

397 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a direct numerical simulation of a fully turbulent channel flow of a dilute polymer solution, where the polymer chains are modeled as finitely extensible and elastic dumbbells.
Abstract: In this work, we present from first principles a direct numerical simulation (DNS) of a fully turbulent channel flow of a dilute polymer solution. The polymer chains are modeled as finitely extensible and elastic dumbbells. The simulation algorithm is based on a semi-implicit, time-splitting technique which uses spectral approximations in the spatial coordinates. The computations are carried out on a CRAY T3D parallel computer. The simulations are carried out under fully turbulent conditions albeit, due to computational constraints, not at as high Reynolds number as that usually encountered in polymer-induced drag reduction experiments. In order to compensate for the lower Reynolds number, we simulate more elastic fluids than the ones encountered in drag reduction experiments resulting in Weissenberg numbers (a dimensionless number characterizing the flow elasticity) of similar magnitude. The simulations show that the polymer induces several changes in the turbulent flow characteristics, all of them consi...

382 citations


Journal ArticleDOI
TL;DR: In this article, a simulation of the transition from two-dimensional to three-dimensional states due to secondary instability in the wake of a circular cylinder is presented. And the authors quantify the nonlinear response of the system to threedimensional perturbations near threshold for the two separate linear instabilities of the wake: mode A and mode B.
Abstract: Results are reported on direct numerical simulations of transition from two-dimensional to three-dimensional states due to secondary instability in the wake of a circular cylinder. These calculations quantify the nonlinear response of the system to three-dimensional perturbations near threshold for the two separate linear instabilities of the wake: mode A and mode B. The objectives are to classify the nonlinear form of the bifurcation to mode A and mode B and to identify the conditions under which the wake evolves to periodic, quasi-periodic, or chaotic states with respect to changes in spanwise dimension and Reynolds number. The onset of mode A is shown to occur through a subcritical bifurcation that causes a reduction in the primary oscillation frequency of the wake at saturation. In contrast, the onset of mode B occurs through a supercritical bifurcation with no frequency shift near threshold. Simulations of the three-dimensional wake for fixed Reynolds number and increasing spanwise dimension show that large systems evolve to a state of spatiotemporal chaos, and suggest that three-dimensionality in the wake leads to irregular states and fast transition to turbulence at Reynolds numbers just beyond the onset of the secondary instability. A key feature of these ‘turbulent’ states is the competition between self-excited, three-dimensional instability modes (global modes) in the mode A wavenumber band. These instability modes produce irregular spatiotemporal patterns and large-scale ‘spot-like’ disturbances in the wake during the breakdown of the regular mode A pattern. Simulations at higher Reynolds number show that long-wavelength interactions modulate fluctuating forces and cause variations in phase along the span of the cylinder that reduce the fluctuating amplitude of lift and drag. Results of both two-dimensional and three-dimensional simulations are presented for a range of Reynolds number from about 10 up to 1000.

349 citations


Journal ArticleDOI
TL;DR: In this study, blood flow through a model stenosis with Reynolds numbers ranging from 300 to 3,600 was analyzed using both experimental and numerical methods to describe the fluid dynamics mechanisms relevant to prior measurements of platelet deposition in canine blood flow.
Abstract: In this study, we analyzed blood flow through a model stenosis with Reynolds numbers ranging from 300 to 3,600 using both experimental and numerical methods. The jet produced at the throat was turbulent, leading to an axisymmetric region of slowly recirculating flow. For higher Reynolds numbers, this region became more disturbed and its length was reduced. The numerical predictions were confirmed by digital particle image velocimetry and used to describe the fluid dynamics mechanisms relevant to prior measurements of platelet deposition in canine blood flow (R.T. Schoephoersteret al., Atherosclerosis and Thrombosis 12:1806–1813, 1993). Actual deposition onto the wall was dependent on the wall shear stress distribution along the stenosis, increasing in areas of flow recirculation and reattachment. Platelet activation potential was analyzed under laminar and turbulent flow conditions in terms of the cumulative effect of the varying shear and elongational stresses, and the duration platelets are exposed to them along individual platelet paths. The cumulative product of shear rate and exposure time along a platelet path reached a value of 500, half the value needed for platelet activation under constant shear (J. M. Ramstacket al., Journal of Biomechanics 12: 113–125, 1979).

Journal ArticleDOI
TL;DR: In this paper, the effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders are investigated using a lattice Boltzmann formulation.
Abstract: The effects of fluid inertia on the pressure drop required to drive fluid flow through periodic and random arrays of aligned cylinders is investigated. Numerical simulations using a lattice-Boltzmann formulation are performed for Reynolds numbers up to about 180.The magnitude of the drag per unit length on cylinders in a square array at moderate Reynolds number is strongly dependent on the orientation of the drag (or pressure gradient) with respect to the axes of the array; this contrasts with Stokes flow through a square array, which is characterized by an isotropic permeability. Transitions to time-oscillatory and chaotically varying flows are observed at critical Reynolds numbers that depend on the orientation of the pressure gradient and the volume fraction.In the limit Re[Lt ]1, the mean drag per unit length, F, in both periodic and random arrays, is given by F/(μU) =k1+k2Re2, where μ is the fluid viscosity, U is the mean velocity in the bed, and k1 and k2 are functions of the solid volume fraction ϕ. Theoretical analyses based on point-particle and lubrication approximations are used to determine these coefficients in the limits of small and large concentration, respectively.In random arrays, the drag makes a transition from a quadratic to a linear Re-dependence at Reynolds numbers of between 2 and 5. Thus, the empirical Ergun formula, F/(μU) =c1+c2Re, is applicable for Re>5. We determine the constants c1 and c2 over a wide range of ϕ. The relative importance of inertia becomes smaller as the volume fraction approaches close packing, because the largest contribution to the dissipation in this limit comes from the viscous lubrication flow in the small gaps between the cylinders.

Journal ArticleDOI
TL;DR: In this paper, a range of Reynolds numbers from 3800 to 22,000 were investigated, and the effect of coflow velocity was examined, showing that the instantaneous flame base is anchored primarily in the low-velocity regions of the jet, with axial and radial movement of the flame to meet this criterion.

Journal ArticleDOI
TL;DR: Here, the linear relationships between forces and torques and translational and angular velocities of helical objects are examined to understand the nature of flagellar propulsion.
Abstract: [At very low Reynolds number, the regime in which fluid dynamics is governed by Stokes equations, a helix that translates along its axis under an external force but without an external torque will necessarily rotate. By the linearity of the Stokes equations, the same helix that is caused to rotate due to an external torque will necessarily translate. This is the physics that underlies the mechanism of flagellar propulsion employed by many microorganisms. Here, I examine the linear relationships between forces and torques and translational and angular velocities of helical objects to understand the nature of flagellar propulsion.]

01 Feb 1997
TL;DR: In this paper, the roll-up of a wingtip vortex, at Reynolds number based on chord of 4.6 million, was studied with an emphasis on suction side and near wake measurements.
Abstract: The roll-up of a wingtip vortex, at Reynolds number based on chord of 4.6 million was studied with an emphasis on suction side and near wake measurements. The research was conducted in a 32 in. x 48 in. low-speed wind tunnel. The half-wing model had a semi-span of 36 in. a chord of 48 in. and a rounded tip. Seven-hole pressure probe measurements of the velocity field surrounding the wingtip showed that a large axial velocity of up to 1.77 U(sub infinity) developed in the vortex core. This level of axial velocity has not been previously measured. Triple-wire probes have been used to measure all components of the Reynolds stress tensor. It was determined from correlation measurements that meandering of the vortex was small and did not appreciably contribute to the turbulence measurements. The flow was found to be turbulent in the near-field (as high as 24 percent RMS w - velocity on the edge of the core) and the turbulence decayed quickly with streamwise distance because of the nearly solid body rotation of the vortex core mean flow. A streamwise variation of the location of peak levels of turbulence, relative to the core centerline, was also found. Close to the trailing edge of the wing, the peak shear stress levels were found at the edge of the vortex core, whereas in the most downstream wake planes they occurred at a radius roughly equal to one-third of the vortex core radius. The Reynolds shear stresses were not aligned with the mean strain rate, indicating that an isotropic-eddy-viscosity based prediction method cannot accurately model the turbulence in the cortex. In cylindrical coordinates, with the origin at the vortex centerline, the radial normal stress was found to be larger than the circumferential.

Journal ArticleDOI
TL;DR: In this paper, a class of subgrid stress models for large-eddy simulation (LES) is presented based on the idea of structure-based Reynolds-stress closure, where the subgrid structure of the turbulence is assumed to consist of stretched vortices whose orientations are determined by the resolved velocity field.
Abstract: A class of subgrid stress (SGS) models for large-eddy simulation (LES) is presented based on the idea of structure-based Reynolds-stress closure. The subgrid structure of the turbulence is assumed to consist of stretched vortices whose orientations are determined by the resolved velocity field. An equation which relates the subgrid stress to the structure orientation and the subgrid kinetic energy, together with an assumed Kolmogorov energy spectrum for the subgrid vortices, gives a closed coupling of the SGS model dynamics to the filtered Navier-Stokes equations for the resolved flow quantities. The subgrid energy is calculated directly by use of a local balance between the total dissipation and the sum of the resolved-scale dissipation and production by the resolved scales. Simple one- and two-vortex models are proposed and tested in which the subgrid vortex orientations are either fixed by the local resolved velocity gradients, or rotate in response to the evolution of the gradient field. These models are not of the eddy viscosity type. LES calculations with the present models are described for 32^(3) decaying turbulence and also for forced 32^(3) box turbulence at Taylor Reynolds numbers R-lambda in the range R(lambda)similar or equal to 30 (fully resolved) to R-lambda=infinity. The models give good agreement with experiment for decaying turbulence and produce negligible SGS dissipation for forced turbulence in the limit of fully resolved flow.

Journal ArticleDOI
TL;DR: In this article, simulation results of flow-induced vibrations of an infinitely long flexible cable at Reynolds numbers Re = 100 and Re = 200, corresponding to laminar and early transitional flow states, respectively, are presented.
Abstract: We present simulation results of flow-induced vibrations of an infinitely long flexible cable at Reynolds numbers Re = 100 and Re = 200, corresponding to laminar and early transitional flow states, respectively. The question as to what cable motions and flow patterns prevail is investigated in detail. Both standing wave and travelling wave responses are realized but in general the travelling wave is the preferred response. A standing wave cable response produces an interwoven pattern of vorticity, while a travelling wave cable response produces oblique vortex shedding. A sheared inflow produces a mixed standing wave/travelling wave cable response and chevron-like patterns with vortex dislocations in the wake. The lift force on the cable as well as its motion amplitudes are larger for the standing wave response. At Re = 200, the cable and wake response are no longer periodic, and the maximum amplitude of the cable is about one cylinder diameter, in agreement with experimental results.

01 Jan 1997
TL;DR: In this paper, the linear relationship between forces and torques and translational and angular velocities of helical objects was examined to understand the nature of f lagellar propulsion.
Abstract: At very low Reynolds number, the regime in which f luid dynamics is governed by Stokes equations, a helix that translates along its axis under an external force but without an external torque will necessarily rotate. By the linearity of the Stokes equations, the same helix that is caused to rotate due to an external torque will necessarily translate. This is the physics that underlies the mechanism of f lagellar propulsion employed by many microorganisms. Here, I exam- ine the linear relationships between forces and torques and translational and angular velocities of helical objects to understand the nature of f lagellar propulsion.)

Journal ArticleDOI
TL;DR: In this article, a planform wing was tested at Reynolds numbers as low as 20 000 in a low turbulence wind tunnel and the best profile was a thin plate with a 5% circular arc camber.
Abstract: Rectangular planform wings were tested at Reynolds numbers as low as 20 000 in a low turbulence wind tunnel. The lift and drag measurements on a NACA 0012 profile were compared with those for thin flat and cambered plates. For all Reynolds numbers below 70 000 the best profile was a thin plate with a 5% circular arc camber. At all turbulence levels this profile produced the greatest lift-drag ratio, and had the highest lift coefficient at all angles of attack. The 5% camber and all of the thin plates tested were relatively insensitive to either a variation in the Reynolds number, or an increase in the wind tunnel turbulence level, whereas the NACA 0012 was very seriously affected by either, at Reynolds numbers below 50 000.

Journal ArticleDOI
TL;DR: In this paper, the effect of expanded metal mesh geometry on the heat transfer coefficient and friction factor has been investigated for fully developed turbulent flow in a rectangular duct with large aspect ratio (11: 1).

Journal ArticleDOI
TL;DR: In this paper, a stabilized finite element formulation is employed to study incompressible flows past a pair of cylinders at Reynolds numbers 100 and 1000 in tandem and staggered arrangements, and the results show that the qualitative nature of the flow depends strongly on the arrangement of cylinders and the Reynolds number.
Abstract: SUMMARY A stabilized finite element formulation is employed to study incompressible flows past a pair of cylinders at Reynolds numbers 100 and 1000 in tandem and staggered arrangements. Computations are carried out for three sets of cylinder arrangements. In the first two cases the cylinders are arranged in tandem and the distance between their centres is 25 and 55 diameters. The third case involves the two cylinders in staggered arrangement. The distance between their centres along the flow direction is 55 diameters, while it is 07 diameter in the transverse direction. The results are compared with flows past a single cylinder at corresponding Reynolds numbers and with experimental observations by other researchers. It is observed that the qualitative nature of the flow depends strongly on the arrangement of cylinders and the Reynolds number. In all cases, when the flow becomes unsteady, the downstream cylinder, which lies in the wake of the upstream one, experiences very large unsteady forces that may lead to wake-induced flutter. The Strouhal number, based on the dominant frequency in the time history of the lift coefficient, for both cylinders attains the same value. In some cases, even though the near wake of the two cylinders shows temporal periodicity, the far wake does not. # 1997 John Wiley & Sons, Ltd.

Journal ArticleDOI
TL;DR: In this paper, a numerical study of laminar incompressible flows in symmetric plane sudden expansions was carried out, and the results revealed that the flow remains symmetric up to a certain Reynolds number depending on the expansion ratio, while asymmetries appear at higher Reynolds numbers.
Abstract: A numerical study of laminar incompressible flows in symmetric plane sudden expansions was carried out. Computations were performed for various Reynolds number and expansion ratios. The results revealed that the flow remains symmetric up to a certain Reynolds number depending on the expansion ratio, while asymmetries appear at higher Reynolds numbers. The computations indicated that the critical Reynolds number of the symmetry‐breaking bifurcation reduces when increasing the expansion ratio while the flow regains symmetry downstream of an initial channel length. The flow asymmetries were verified by comparing several discretization schemes up to fourth order of accuracy as well as various iterative solvers.

Journal ArticleDOI
TL;DR: In this paper, the simulation of 3D gas-particle flow through a fibrous filter has been studied for different Stokes numbers to study the influence of hydrodynamics on particle deposition.

Journal ArticleDOI
TL;DR: In this paper, high resolution, two-dimensional LDV measurements in a turbulent pipe flow of water over the Reynolds number range 5000-25000 are presented, as well as power spectra in the near-wall region.
Abstract: We present in this paper high resolution, two-dimensional LDV measurements in a turbulent pipe flow of water over the Reynolds number range 5000–25000. Results for the turbulence statistics up to the fourth moment are presented, as well as power spectra in the near-wall region. These results clearly show that the turbulence statistics scaled on inner variables are Reynolds-number dependent in the aforementioned range of Reynolds numbers. For example, the constants in the dimensionless logarithmic mean-velocity profile are shown to vary with Reynolds number. Our conclusion that turbulence statistics depend on the Reynolds number is consistent with results found in other flow configurations, e.g., a channel flow. Our results for the pipe flow, however, lead nevertheless to quite different tendencies.

Journal ArticleDOI
TL;DR: In this paper, a 3D boundary-integral algorithm for deformable drops moving in a viscous medium at low Reynolds numbers is developed, which overcomes some familiar difficulties with boundaryintegral calculations.
Abstract: A new three-dimensional boundary-integral algorithm for deformable drops moving in a viscous medium at low Reynolds numbers is developed, which overcomes some familiar difficulties with boundary-integral calculations. The algorithm is used to simulate different modes of interaction between drops or bubbles, primarily for buoyancy-driven motion. The present iterative method for mean curvature calculation is found to be more robust and accurate than contour integration schemes. A novel iterative strategy based on combining biconjugate gradient and simple iterations overcomes the poor convergence of “successive substitutions” for drops in very close approach with extreme viscosity ratio. A substantially new variational method of global mesh stabilization solves the problem of mesh degradation with advantageous, soft stability constraints. A curvatureless boundary-integral formulation is also derived and shown to provide, in principle, a more accurate description of the drop breakup than the conventional formulation. The efficiency of these techniques is demonstrated by numerical examples for two drops in gravity-induced motion with high surface resolutions. The present code successfully simulates mutual approach of slightly deformable drops to extremely small separations, as well as their rotation when in “apparent contact,” thus bridging the gap between finite deformation calculations and a recent asymptotic theory for small capillary numbers. Also provided is a 3D simulation of the experimental phenomenon of enhanced bubble coalescence, discovered by Manga and Stone [J. Fluid Mech. 256, 647 (1993); 300, 231 (1995)]. For drops of viscosity comparable to that of the surrounding fluid, it is shown in contrast that breakup is a typical result of hydrodynamic interaction in gravity-induced motion for large and even moderate capillary numbers. The code is readily applicable to any type of an ambient flow and may be adapted to more than two drops.

Journal ArticleDOI
Abstract: Results of flow visualization, hot wire, and base pressure measurements were conducted for an investigation of the near wake of a circular cylinder at subcritical Reynolds numbers between 2700 to 46000. A base mounted splitter plate allowed for the modification of the formation region characteristics without disrupting the normal Karman shedding. The results provide an explanation for the non-linearity in the relationship between shedding frequency and splitter plate length and extend the previous investigations of Roshko (1954), Gerrard (1966) and Apelt et al. (1973). In addition to the nominal 2-D configurations, a sinuous trailing edge splitter plate, cylinder taper, and shear flow were incorporated to study the effects of mild 3-dimensionality. A strong spanwise coherence was found to exist in the formation region. A superposition principle was discovered which showed that certain 3-D geometry and flow configurations could be combined to produce a nominal 2-D wake.

Journal ArticleDOI
TL;DR: In this paper, a new high-lift airfoil design philosophy has been developed and experimentally validated through wind-tunnel tests, which makes use of a concave pressure recovery with aft loading.
Abstract: A new high-lift airfoil design philosophy has been developed and experimentally validated through wind-tunnel tests A key element of the high-lift design philosophy was to make use of a concave pressure recovery with aft loading Three codes for airfoil design and analysis (PROFOIL, the Eppler code, and ISES) were used to design the example S1223 high-lift airfoil for a Reynolds number of 2 3 10 5 In windtunnel tests, the new airfoil yielded a maximum lift coefe cient of 22 With vortex generators and a 1% chord Gurney eap (used separately), the Cl,max increased to 23 The airfoil demonstrates the rather dramatic gains in Cl,max over those airfoils previously used for high-lift low Reynolds number applications

Journal ArticleDOI
TL;DR: In this paper, the effect of insoluble surfactant on the transient deformation and asymptotic shape of a spherical drop that is subjected to a linear shear or extensional flow at vanishing Reynolds number is studied using a numerical method.
Abstract: The effect of an insoluble surfactant on the transient deformation and asymptotic shape of a spherical drop that is subjected to a linear shear or extensional flow at vanishing Reynolds number is studied using a numerical method. The viscosity of the drop is equal to that of the ambient fluid, and the interfacial tension is assumed to depend linearly on the local surfactant concentration. The drop deformation is affected by non-uniformities in the surface tension due to the surfactant molecules convection–diffusion. The numerical procedure combines the boundary-integral method for solving the equations of Stokes flow, and a finite-difference method for solving the unsteady convection–diffusion equation for the surfactant concentration over the evolving interface. The parametric investigations address the effect of the ratio of the vorticity to the rate of strain of the incident flow, the Peclet number expressing the ability of the surfactant to diffuse, the elasticity number expressing the sensitivity of the surface tension to variations in surfactant concentration, and the capillary number expressing the strength of the incident flow. At small and moderate capillary numbers, the effect of a surfactant in a non-axisymmetric flow is found to be similar to that in axisymmetric straining flow studied by previous authors. The accumulation of surfactant molecules at the tips of an elongated drop decreases the surface tension locally and promotes the deformation, whereas the dilution of the surfactant over the main body of the drop increases the surface tension and restrains the deformation. At large capillary numbers, the dilution of the surfactant and the rotational motion associated with the vorticity of the incident flow work synergistically to increase the critical capillary number beyond which the drop exhibits continuous elongation. The numerical results establish the regions of validity of the small-deformation theory developed by previous authors, and illustrate the influence of the surfactant on the flow kinematics and on the rheological properties of a dilute suspension. Surfactants have a stronger effect on the rheology of a suspension than on the deformation of the individual drops.

Journal ArticleDOI
TL;DR: In this article, the simulation of flow in a circular pipe rotating about its axis, at low Reynolds number, is performed by a finite difference scheme, second-order accurate in space and in time.
Abstract: Flow in a circular pipe rotating about its axis, at low Reynolds number, is investigated. The simulation is performed by a finite difference scheme, second-order accurate in space and in time. A non-uniform grid in the radial direction yields accurate solutions with a reasonable number of grid points. The numerical method has been tested for the non-rotating pipe in the limit ν→0 to prove the energy conservation properties. In the viscous case a grid refinement check has been performed and some conclusions about drag reduction have been reached. The mean and turbulent quantities have been compared with the numerical and experimental non-rotating pipe data of Eggels et al. (1994a, b). When the pipe rotates, a degree of drag reduction is achieved in the numerical simulations just as in the experiments. Through the visualization of the vorticity field the drag reduction has been related to the modification of the vortical structures near the wall. A comparison between the vorticity in the non-rotating and in the high rotation case has shown a spiral motion leading to the transport of streamwise vorticity far from the wall.

Journal ArticleDOI
TL;DR: In this paper, a least-squares functional for the generalized Stokes equations was developed by adding a pressure term in the continuity equation, which yields optimal discretization error estimates for finite element spaces in an H1 product norm appropriately weighted by the Reynolds number.
Abstract: Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H1 product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are naturally uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity, where we obtain the more substantive result that the estimates are uniform in the Poisson ratio.