Showing papers on "Velocity gradient published in 1998"

Equation of change for ellipsoidal drops in viscous flow

Abstract: A simple phenomenological model for the deformation of a droplet immersed in a fluid subjected to a flow field with a uniform, but otherwise arbitrary, velocity gradient is presented. The model is capable of describing the transient evolution of the drop. The steady state predictions for simple shear and elongational flows are analytical. The model degenerates into Taylor theory in the limit of slow flows as well as for high viscosity ratios. It also recovers the affine deformation under the appropriate limiting conditions. The predictions are compared with some representative experimental and numerical results available in the literature.

An experimental study of a two-dimensional plane turbulent wall jet

Abstract: Laser-Doppler measurements were conducted in a plane turbulent wall jet at a Reynolds number based on inlet velocity, Re 0, of 9600. The initial development as well as the fully developed flow was studied. Special attention was given to the near-wall region, including the use of small measuring volumes and the application of specific near-wall data corrections, so that wall shear stresses were determined directly from the mean velocity gradient at the wall using only data below y +=4. It was possible to resolve the inner peak in the streamwise turbulence intensity as well as the inner (negative) peak in the shear stress. Limiting values of (u′)+ and uv + were determined. Turbulence data from the outer region of the flow were compared to earlier hot wire measurements and large differences in the normal turbulence intensity and the shear stress were found. These differences can be attributed to high turbulence intensity effects on the hot-wires.

Three-dimensional shape of a drop under simple shear flow

Abstract: The three-dimensional deformation of an isolated drop in an immiscible liquid phase undergoing simple shear flow was investigated by using a parallel-plate apparatus. The drop was observed by video-enhanced contrast optical microscopy, either along the vorticity direction or along the velocity gradient direction of the shear flow. An experimental methodology based on image analysis was especially developed to study in a quantitative way the three-dimensional shape of the deformed drop, both under steady-state flow and during transients. Up to moderate deformations, the steady-state drop shape was well described within experimental error by an ellipsoid having three different axes. The deviation of drop shape from an ellipsoid at higher deformations was also characterized in a quantitative way. Good agreement was found between the experimental results of this work and numerical simulations reported in the literature.

Binary collision of drops in simple shear flow by computer-assisted video optical microscopy

Abstract: The collision of two equi-sized drops immersed in an immiscible liquid phase undergoing a shear flow in a parallel plate apparatus has been investigated over a range of capillary numbers. The drops were observed along the vorticity direction of shear flow by video enhanced contrast optical microscopy. Images of the colliding drops were processed by image analysis techniques. The distance Δy between the drop centres along the velocity gradient direction was measured as a function of time during approach, collision and separation of the two drops. It was found that Δy increases irreversibly after collision, thus providing a mechanism for drop dispersion in a concentrated system. Drop shape evolution during collision was characterized by measuring a deformation parameter and the angle made by the drop major axis with respect to the velocity gradient direction. The extent of the near-contact region when the drops are sliding on each other was also estimated. Coalescence was a rare event and was observed in the extensional quadrant of the shear flow. The experimental results show good agreement with numerical simulations recently reported in the literature.

Turbulent coagulation of colloidal particles

Abstract: Theoretical predictions for the coagulation rate induced by turbulent shear have often been based on the hypothesis that the turbulent velocity gradient is persistent (Saffman & Turner 1956) and that hydrodynamic and interparticle interactions (van der Waals attraction and electrostatic double-layer repulsion) between colloidal particles can be neglected. In the present work we consider the effects of interparticle forces on the turbulent coagulation rate, and we explore the response of the coagulation rate to changes in the Lagrangian velocity gradient correlation time (i.e. the characteristic evolution time for the velocity gradient in a reference frame following the fluid motion). Stokes equations of motion apply to the relative motion of the particles whose radii are much smaller than the lengthscales of turbulence (i.e. small particle Reynolds numbers). We express the fluid motion in the vicinity of a pair of particles as a locally linear flow with a temporally varying velocity gradient. The fluctuating velocity gradient is assumed to be isotropic and Gaussian with statistics taken from published direct numerical simulations of turbulence (DNS). Numerical calculations of particle trajectories are used to determine the rate of turbulent coagulation in the presence and absence of particle interactions. Results from the numerical simulations correctly reproduce calculated coagulation rates for the asymptotic limits of small and large total strain where total strain is a term used to describe the product of the characteristic strain rate and its correlation time. Recent DNS indicate that the correlation times for the fluctuating strain and rotation rate are of the same order as the Kolmogorov time (Pope 1990), suggesting theories that assume either small or large total strain may poorly approximate the turbulent coagulation rate. Indeed, simulations for isotropic random flows with intermediate total strain indicate that the coagulation rate in turbulence is significantly different from the analytical limits for large and small total strain. The turbulent coagulation rate constant for non-interacting monodisperse particles scaled with the Kolmogorov time and the particle radius is 8.62±0.02, whereas the commonly used model of Saffman & Turner (1956) predicts a value of 10.35 for non-rotational flows in the limit of persistent turbulent velocity gradients. Additional simulations incorporating hydrodynamic interactions and van der Waals attraction were used to estimate the actual rate of particle coagulation. For typical values of these parameters, particle interactions reduced the coagulation rate constant by at least 50%. In general, the collision efficiency (the ratio of coagulation with particle interactions to that without) decreased with increasing particle size and Kolmogorov shear rate.

Joint probability density analysis of the structure and dynamics of the vorticity field of a turbulent boundary layer

Abstract: An experimental study of a turbulent boundary layer at Rθ≈1070 and Rτ≈543 was conducted. Detailed measurements of the velocity vector and the velocity gradient tensor within the near-wall region were performed at various distances from the wall, ranging from approximately y+=14 to y+=89. The measured mean statistical properties of the fluctuating velocity and vorticity components agree well with previous experimental and numerically simulated data. These boundary layer measurements were used in a joint probability density analysis of the various component vorticity and vorticity–velocity gradient products that appear in the instantaneous vorticity and enstrophy transport equations. The vorticity filaments that contribute most to the vorticity covariance Ω[bar]xΩ [bar]y in this region were found to be oriented downstream with angles of inclination to the wall, when projected on the streamwise (x, y)-plane, that decrease with distance moving from the buffer to the logarithmic layer. When projected on the planview (x, z)- and cross-stream (y, z)-planes, the vorticity filaments that most contribute to the vorticity covariances Ω [bar]xΩ [bar]z and Ω [bar]yΩ [bar]z have angles of inclination to the z-ordinate axis that increase with distance from it. All the elements of the ΩiΩj ∂Ui/∂xj term in the enstrophy transport equation, i.e. the term that describes the rate of increase or decrease of the enstrophy by vorticity filament stretching or compression by the strain-rate field, have been examined. On balance, the average stretching of the vorticity filaments is greater than compression at all y+ locations examined here. However, some individual velocity gradient components compress the vorticity filaments, on average, more than they stretch them.

Dynamics of velocity gradient invariants in turbulence: Restricted Euler and linear diffusion models

Abstract: A complete system of dynamical equations for the invariants of the velocity gradient, the strain rate, and the rate-of-rotation tensors is deduced for an incompressible flow. The equations for the velocity gradient invariants R and Q were first deduced by Cantwell [Phys. Fluids A 4, 782 (1992)] in terms of Hij, the tensor containing the anisotropic part of the pressure Hessian and the viscous diffusion term in the velocity gradient equation. These equations are extended here for the strain rate tensor invariants, RS and QS, and for the rate-of-rotation tensor invariant, QW, using HijS and HijW, the symmetric and the skew-symmetric parts of Hij, respectively. In order to obtain a complete system, an equation for the square of the vortex stretching vector, Vi≡Sijωj, is required. The resulting dynamical system of invariants is closed using a simple model for the velocity gradient evolution: an isotropic approximation for the pressure term and a linear model for the viscous diffusion term. The local topology ...

Two-dimensional direct numerical simulation of opposed-jet hydrogen-air diffusion flame

Abstract: Opposed-jet diffusion flame experiments are routinely analyzed with one-dimensional models obtained by assuming a specific form for the velocity field. In this study, two-dimensional simulations of the hydrogen-air laminar opposed-jet counterflow diffusion flame using detailed chemical kinetics and realistic transport were performed for parabolic and uniform inflow velocity profiles at the exits of the nozzles. Two-dimensional simulations allow for the detailed examination of the hydrodynamics and the assessment of the validity of the assumptions made in the traditional one-dimensional simulations. Using typical nozzle size and separation distance employed in experiments, we analyzed the effects of nozzle outflow boundary conditions, finite size, and finite separation distance on the structure of the strained laminar diffusion flame. We also analyzed the variations of the divergence of the velocity field (compressibility due to chemical reaction) and that of the hydrodynamic pressure. The two-dimensional simulation results show that the cost-effective one-dimensional model provides an accurate description of the flame structure even for low-strain hydrogen-air flame provided that the velocity profiles at the nozzle exits are uniform. Although in the one-dimensional model, the nozzle size to separation ratio is assumed to be large, our two-dimensional results show that a ratio of 1 is adequate. Finally, we observed that the velocity gradient (the axial derivative of the axial velocity component along the axis of symmetry) measured in experiments at a point just before the flame region is inadequate in describing the characteristic strain rate “seen” by the flame.

Burgers Turbulence with Large-scale Forcing

Abstract: Burgers turbulence supported by white-in-time random forcing at low wavenumbers is studied analytically and by computer simulation. It is concluded that the probability density Q of velocity gradient displays four asymptotic regimes at very large Reynolds number: (A) a region of large positive gradient where Q decays rapidly (reduction of gradient by stretching); (B) an intermediate region of negative gradient where Q falls off as the inverse third power of gradient (transient inviscid steepening of negative gradient); (C) an outer power-law region of negative gradient where Q falls off as the reciprocal of gradient (shoulders of mature shocks); (D) a final region of large gradient where Q decays very rapidly (interior of mature shocks). The probability density of velocity difference across an interval r, divided by r, lies on Q throughout regions A and B and into the middle of C, for small enough inertial-range r.

MHD flow and heat transfer at a general three-dimensional stagnation point

Abstract: The flow characteristics of an incompressible viscous electrically conducting fluid at a three-dimensional stagnation point with arbitary velocity gradients a and b (with a > 0 and ¦b¦ ⩽ a) in two orthogonal directions are determined. A similarity solution of the boundary layer equations for this flow over a surface permeated by a uniform transverse magnetic field is obtained when the surface is subjected to injection. Two types of stagnation point flows are distinguished: (i) nodal point flow when 0 < α ⩽ 1 with α = ba and (ii) saddle point flow with − 1 < α < 0. It is found that for nodal point flow the velocity component v in the boundary layer in the direction of the free stream with velocity gradient b approaches the free stream velocity more slowly than the corresponding velocity component u along the free stream with velocity gradient a. Further velocity at a point in the boundary layer increases with increase in the magnetic parameter M. It is found that at a saddle point for M = 0, a back flow in the v-profile occurs at α = − 0.43. A novel result of the analysis is that with increase in M, the magnitude of α for which the back flow in the v-profile first occurs also increases and for M = 1.258, no back flow occurs at all. Skin-friction components near nodal or saddle points corresponding to the u and v profiles are computed for various values of injection and magnetic parameters. Finally it is shown that increase in blowing results in decrease in the surface heat transfer thus illustrating the salutary effect of blowing in cooling the surface.

Centerline velocity decay of a circular jet in a counterflowing stream

Abstract: We use an advection hypothesis to analyze the decay of centerline velocity of a circular jet issuing into a counterflowing stream. Working in the Lagrangian frame, we follow the locations and velocity gradients of jet fluid particles along the jet central axis while the particles are being advected backwards by the counterflow. The spatial velocity gradient along the jet centerline is thus obtained and subsequently integrated to describe the spatial decay of axial velocities. Laser-doppler velocity measurements are performed in the laboratory and the data are well predicted by our analytical expression of centerline velocity decay. Looking from another view, our treatment supports that the effect of an external axial flow stream on the jet flow field can be represented by a certain degree of stretching or contracting of the jet in the axial direction.

Fluid inertia in large amplitude oscillatory shear

Abstract: Homogeneous shearing is required in sliding plate flow experiments with one plate fixed and the other oscillating. However, when fluid inertia becomes significant, the velocity gradient and the stress will not be uniform. MacDonald et al. (1969) and Schrag (1977) investigated this effect for a linear viscoelastic fluid. However, linear viscoelasticity does not describe the behavior of melts in large amplitude oscillatory shear (LAOS). Jeyaseelan et al. (1993) have shown that the Berkeley kinetic network model does accurately describe the LAOS behavior of polymer melts. In this work, the Berkeley model is solved for LAOS in sliding plate flow with fluid inertia, by numerical integration of spatially discretized forms of the governing equations. Nonlinear viscoelasticity is predicted to aggravate the effects of fluid inertia in LAOS and experiments confirm this. Specifically, fluid inertia amplifies the first harmonic and produces no even harmonics. Operating limits are presented graphically for minimizing inertial effects in LAOS experiments.

Numerical simulation of the flow in the carotid bifurcation

Abstract: Pulsatile flow through the three-dimensional carotid artery bifurcation has been studied using the artificial-compressibility method. The part of the flow with large inertia bifurcates and creates a very steep velocity gradient on the divider walls. The flow near the nondivider walls slows down because of dilation of the cross section and strong adverse pressure gradient. The secondary flow in the bifurcation region, which is similar to the Dean vortex in a curved pipe, is strong and very complex. The region of separation is not closed for the cases of steady and pulsatile flow. The extent of this region is small and the streamlines are smooth except in the decelerating phase of systole. The change of common-internal bifurcation angle (25°± 15°) for fixed internal–external bifurcation angle of 50° has more effect on the shear on the bifurcation-internal carotid wall and less effect on the shear on the common-internal carotid wall. The mean wall shears are not sensitive to the input flow-rate waveform for constant mean flow, but the maximum wall shears are.

The effect of roughness configuration on velocity profiles in an artificial channel

Abstract: In order to determine the effect of bed roughness on velocity distribution, we used seven different configurations of bed roughness, with 16 test runs of varying discharge and slope for each configuration. For each run, one-dimensional velocity profiles were measured at 1 cm vertical increments over the crest of the roughness element, and at intervals of 4·25 cm downstream. Results indicate that velocity profile shape remains fairly constant for a given slope and roughness configuration as discharge increases. As slope increases, the profiles become less linear, with a much larger near-bed velocity gradient and a more pronounced velocity peak close to 0·6 flow depth at the measurement point immediately downstream from the roughness element. The zone of large near-bed velocity gradients increases in both length and depth as roughness concentration decreases, up to a length/height ratio of about 9, at which point maximum flow resistance occurs. Longitudinal roughness elements do not create nearly as much flow resistance as do transverse elements. Rates of velocity increase suggest that roughness elements spaced at a length/height ratio of about 9 are most effective at creating flow resistance over a range of discharges in channels with steeper slopes. © 1998 John Wiley & Sons, Ltd.

Excitation wave breaking in excitable media with linear shear flow

Abstract: If an excitable medium is moving with relative shear, the waves of excitation may be broken by the motion. We consider such breaks for the case of a constant linear shear flow. The mechanisms and conditions for the breaking of solitary waves and wave trains are essentially different: the solitary waves require the velocity gradient to exceed a certain threshold, while the breaking of repetitive wave trains happens for arbitrarily small velocity gradients.

Probability Density Functions of Large-Scale Turbulence in the Ocean

Abstract: Probability density functions (pdfs) of surface velocity and surface velocity gradients in the ocean are calculated using altimetric data from the Topex / Poseidon satellite. These provide information about turbulence in a high-Reynolds-number geophysical flow. Both velocity pdfs and velocity gradient pdfs calculated over small regions are Gaussian but have more exponential shapes as the size of the region increases. We develop a simple explanation for the non-Gaussianity of velocity pdfs based on the inhomogeneity of eddy kinetic energy in the ocean. (S0031-9007(98)07902-2) Two-dimensional turbulence is a natural paradigm for the high-Reynolds-number fluid flows that dominate ocean variability on scales of 50- 80 km, the "mesoscale." Satel- lite altimeters offer a new means to study two-dimensional turbulent motions of the ocean. In this paper, we use altimeter data to calculate probability density functions (pdfs) for the ocean: pdfs are Gaussian locally but expo- nential over the global ocean. Numerical and theoretical studies have shown that two-dimensional turbulence is characterized by coherent vortices separated by irrotational regions of straining motion (1). This phenomenology provides a good con- ceptual model of the mesoscale and larger-scale oceanic circulation, which is dominated by two-dimensional motions associated with the constraints of strong stratifi- cation and the earth's rotation (2). We therefore expect two-dimensional turbulence theory to illuminate processes such as eddy-induced transports of heat, chemical tracers, and biota, which are important to the earth's climate system (3). In addition, observations can show us how notions of two-dimensional turbulence fail to describe the oceans and atmospheres. We therefore consider pdfs as measurable quantities that can be used to compare real-world turbulence with better understood physical analogs.

Pulsed-wire anemometry near walls

Abstract: This experimental investigation compares two configurations of pulsed-wire probe for measurements in the very near wall region, as introduced by Castro and Dianat (1990) and Devenport et al. (1990). Diffusion of the thermal wake causes significant errors in regions where the velocity is low and the velocity gradient high. These errors, which are about the same for either configuration, are large in the viscous sub-layer. An analysis of diffusional effects is made, and a method of correction is given that applies equally in laminar and turbulent flow. It is necessary to calibrate a probe for the effects of shear in a known flow.

Design of around-the-end hydraulic flocculators

Abstract: Hydraulic flocculators, despite their superior plug-flow properties, negligible energy requirements and robust simplicity, are commonly perceived as being inflexible. Once built, it is argued, they do not provide the operational flexibility to compensate for flow fluctuations or changing raw water characteristics. The design procedure developed in this paper demonstrates the contrary, namely that hydraulic flocculators can be designed to satisfactorily cope with tapered velocity gradients, flow variations and water quality variations. The procedure is based on a two-step approach; the horizontal layout is first determined with average values for velocity gradient and water depth; then only the floor slope and exact water depths are determined to enable satisfactory flocculation for all design scenarios.

Seismic structure of the mantle ; from subduction zone to craton

Abstract: Seismological techniques have provided much of the currently available information on the internal structure of the Earth, and in particular on the mantle. Early studies revealed the need for an increase in seismic velocity with depth in the Earth, and by 1915 Gutenberg was able to make a good estimate of the radius of the core. Knowledge of the Earth's internal structure was refined by iterative improvement of earthquake locations and the travel times for seismic phases through the Earth, so that in 1940 Jeffreys and Bullen were able to publish an extensive set of travel-time tables based on a model of both P-wave and S-wave velocities in the mantle. Their velocity profile was intentionally as smooth as possible, but it was not possible to avoid introducing a sharp change in velocity gradient near a depth of 400 km to account for the distinct change in the slope of travel-time curves at a distance of approximately 20' from the source, for both P and S waves. Subsequent studies have refined our conception of mantle structure to reveal the presence of discontinuities in velocity and zones of strong velocity gradients, which have been correlated with mineralogical phase changes.

The Stellar and Gaseous Kinematics in NGC 253

Abstract: This paper presents observations made at intermediate spectral and spatial resolutions along the major and minor axes of the starburst galaxy NGC 253. The spectral ranges analyzed are in the region of the stellar Mg I b (~5175 A) line, in the near-IR Ca II triplet (~8550 A) absorption features, and in the region of the Hα emission line. We compare the shape of the stellar features with those of reference stars and determine the line-of-sight velocity distribution of the stellar component by using a two-dimensional Gaussian decomposition algorithm, and we show for the first time the rotation curve of the stellar component in NGC 253. Comparing the recession velocity curves of the gas and stars, we show that the stellar component has a decoupled kinematics with respect to the gas, displaying a shallower velocity gradient and larger velocity dispersion than the gas in the inner regions. The minor-axis kinematics, together with the kinematics across the central 40'' along the major axis, suggest the presence of a rotating body with a kinematically misaligned axis with respect to the main disk of the galaxy. The asymmetries in the LOS velocity distribution along the minor axis, together with the steep velocity gradient of the gaseous component, suggest a merger scenario as the source of these kinematic signatures. The enclosed mass in the central regions is computed to be (2.4 ± 0.5) × 107 M☉ for a radius of r = 07 (10 pc). A double gaseous component in the central 6'' is detected from the [S III] λ9069 A data along the minor axis; this seems to be the signature of a superbubble, due to a supernova rate of 0.05 yr-1.

A mechanism of bifurcation to strongly sheared toroidal rotation in the radiatively improved mode in TEXTOR-94

Abstract: A mechanism, based on the dependence of the anomalous plasma viscosity on the velocity gradient, is proposed to explain a strong shearing of the ion toroidal velocity in the radiatively improved (RI) mode in TEXTOR-94 with unbalanced neutral injection The conditions of the bifurcation into this plasma state with a barrier in the ion momentum and heat transport are analysed, and it is demonstrated that the density peaking caused by puffing of impurities is of principal importance to achieve them The time evolution of the ion toroidal velocity and temperature by the transition into the RI mode is modelled

Transient states during spin-up of a Rayleigh–Bénard cell

Abstract: The influence of impulsive spin-up on Rayleigh–Benard convection in a cylindrical cell with radius-to-height ratio Γ=0.5 is investigated. Velocity and temperature fields in the thin layer adjacent to the top of the cell are measured by means of particle image velocimetry and thermochromic liquid crystal visualization. The cell, initially in steady nonrotating convection, is rapidly accelerated to steady rotation about its vertical axis with dimensionless rotation rates 4×103⩽Ω⩽8×104. Rayleigh numbers Ra vary from 5×107 to 5×108. In a large part of this domain of the parameter space, axisymmetric structures appear near the top of the cell. In most cases, a single ring forms with a radius close to 3/4 of the radius of the cell. The same experiment without heating produces typical Ekman spin-up devoid of ring structures. The ring is characterized by a local decrease in temperature and azimuthal velocity. As the flow evolves, an azimuthal velocity gradient forming across the ring causes shear instability and ...

Modelling and Simulation of Turbulent Gas-Solid Flows applied to Fluidization

Abstract: Modelling of gas-solid suspensions has been studied with emphasis on suitable closure laws. A study of characteristic time scales and energy dissipation mechanisms is made for the case of a simple shear flow. Applications of the modelling are presented in the form of simulation and validation of experiments in fluidized beds. The Eulerian formulation applied to isothermal gas-solid flows is given in the form of continuity and momentum equations of both phases. Closure laws are discussed for the stress tensors in both phases and for the interfacial momentum transfer. A summary and a critical assessment of published work on simulations of fluid dynamics in circulating and non-circulating fluidized beds are presented. A study of the equation of motion of a single sphere in a fluid shows that drag, gravity and transverse forces are the important mechanisms in gas-solid flows. Transverse forces are discussed in detail. Results from the Lagrangian formulation are used to derive an expression for the interfacial momentum transfer. Closure laws for the drift velocity, the fluid-particle velocity correlation tensor and the second order velocity moments in both phases are studied, and it is shown under which assumptions the models can be derived. The second order velocity moment in the discrete phase is modelled with the kinetic theory of granular flow. Models for the drift velocity and for the fluid-particle velocity correlation tensor are presented, first based on algebraic models and secondly, based on transport equations with a fluid-particle joint probability density function. Two-way coupling is discussed, and a two-equation model is introduced for modelling the gas phase turbulence. Boundary conditions are formulated. A discussion on the usefulness of the models is given as well as an application to fluidization and especially to circulating fluidized bed combustors. A mesh refinement study and a validation of two-fluid model closures has been carried out for a stationary bubbling fluidized bed application. To handle the long simulation times required to obtain acceptable statistical values, a parallel version of the two-fluid model solver, GEMINI-2D, was developed, based on a domain decomposition method for distributed memory computers. A number of problems related to the parallelization are investigated. The Eulerian two-phase solver GEMINI-2D is presented in its original version and the extension to turbulent gas-solid flows is also given. Estimates of the characteristic time scales (particle relaxation time, eddy-particle interaction time, inter-particle collision time), and of the energy dissipation mechanisms are performed together with a turbulent kinetic energy budget, for a simple equilibrium shear flow. The influence of several parameters (integral length scale, density ratio, mean velocity gradient, particle diameter and mean volume fraction) is investigated for Geldart group A and B particles. A three-dimensional simulation of a circulating fluidized bed is presented and numerical results are compared to local time-averaged measurements (vertical pressure profile and vertical and horizontal concentration profiles).

An Eulerian-based approach to elastic-plastic decomposition

Abstract: A theory for elastic-plastic metals is presented which is based on a multiplicative decomposition of the deformation gradient. When consistent definitions for the elastic and plastic velocity gradients are introduced, the corresponding Eulerian strain rate tensors become directly additive on a transformed configuration. The transformation is derived both on the principal axes of elastic strain and in tensorial form. Thermodynamical consequences of the proposed decomposition are explored.

A Study of Local Hydrodynamics in a 90° Branched Vessel with Extreme Pulsatile Flows

Abstract: To validate the pathologoical flow condition as the etiology of site-specific athero sclerosis, computer simulation and analysis are presented. Two extreme pulsatile flows, as have been measured in human femoral arteries, are used to numerically simulate in-vivo blood flow. The pulse with a steep temporal velocity gradient is assigned as “steep” pulse whereas the one with a lesser slope is called “less-steep” pulse. The effect of the extreme two pulses on the injury of endothelial cells in a 90° femoral artery of human is investigated by calculating flow parameters including instantaneous wall shear stresses. At the proximal and the distal branch apex, the oscillating wall shear stresses calculated from the ‘steep’ pulse cycle are found to be substantially greater than those from the ‘less-steep’ one. In contrast, for a straight artery, insignificant changes in flow parameters are observed for the extreme two pulses. It is evident from the calculated local wall shear stress that pathological changes can o...

Near-wall flow in a three-dimensional boundary layer on the endwall of a 30¡ bend

Abstract: Turbulence measurements are reported on the three-dimensional turbulent boundary layer along the centerline of the flat endwall in a 30° bend. Profiles of mean velocities and Reynolds stresses were obtained down to y+≈2 for the mean flow and y+≈8 for the turbulent stresses. Mean velocity data collapsed well on a simple law-of-the-wall based on the magnitude of the resultant velocity. The turbulence intensity and turbulent shear stress magnitude both increased with increased three-dimensionality. The ratio of these two quantities, the a1 structure parameter, decreased in the central regions of the boundary layer and showed profile similarity for y+<50. The shear stress vector angle lagged behind the velocity gradient vector angle in the outer region of the boundary layer, however there was an indication that the shear stress vector tends to lead the velocity gradient vector close to the wall.

Combustion rate of graphite in a high stagnation flowfield and its expression as a function of the transfer number

Abstract: An experiment has been conducted to measure combustion rate of graphite rods in a stagnation airflow with high velocity gradient, up to 40000 s −1 . At high velocity gradients, it is observed that the combustion rate increases monotonically and reaches the diffusion-limited value with increasing surface temperature, whereas when the velocity gradient is low, a discontinuous change in the combustion rate exists due to the establishment of a CO flame, with increasing surface temperature. Based on the experimental results, as well as the previous theoretical accomplishments in the literature, an attempt has been made to obtain an explicit analytical expression for the carbon combustion rate in a stagnation flowfield. It is shown that the combustion rate is approximately expressed by the transfer number in terms of a natural logarithmic term, just like that for droplet combustion. Explicit forms of the transfer numbers for three limiting conditions ( frozen, flame-detached and flame-attached modes) have also been obtained, as functions of the surface Damkohler numbers, surface and free-stream temperatures, and oxidizer concentrations. In addition, a relation between the theoretical combustion rate and the conventional, rather qualitative, combustion rate with the surface reaction rate and the mass transfer coefficient has been made clear. Although these expressions are those for limiting conditions, good agreement with experiment is demonstrated if we appropriately separate the temperature ranges by the ignition surface temperature at which a CO flame is established over the burning carbon surface. Because of the simplicity and the reasonable accuracy in these expressions, an enhancement of theoretical understanding is expected from not only a qualitative but also a quantitative viewpoint, in addition to their contribution for practical utility.