Showing papers on "Velocity gradient published in 1990"

A diffusion model for velocity gradients in turbulence

Abstract: In this paper a stochastic model for velocity gradients following fluid particles in incompressible, homogeneous, and isotropic turbulence is presented and demonstrated. The model is constructed so that the velocity gradients satisfy the incompressibility and isotropy requirements exactly. It is further constrained to yield the first few moments of the velocity gradient distribution similar to those computed from full turbulence simulations (FTS) data. The performance of the model is then compared with other computations from FTS data. The model gives good agreement of one‐time statistics. While the two‐time statistics of strain rate are well replicated, the two‐time vorticity statistics are not as good, reflecting perhaps a certain lack of embodiment of physics in the model. The performance of the model when used to compute material element deformation is qualitatively good, with the material line‐element growth rate being correct to within 5% and that of surface element correct to within 20% for the lowest Reynolds number considered. The performance of the model is uniformly good for all the Reynolds numbers considered. So it is conjectured that the model can be used even in inhomogeneous, high‐Reynolds‐number flows, for the study of evolution of surfaces, a problem that is of interest particularly to combustion researchers.

Mechanical Properties of Tissue

Abstract: This chapter reviews the mechanical properties of tissues, including their densities, moduli of elasticity, and ultimate strengths. The density of tissue may be measured by comparing the mass of a sample in air with the apparent mass measured in water. The density is calculated from the ratio of the apparent masses and knowledge of the density of water at the measurement temperature. Density varies as a function of temperature. The factors affecting elasticity in a tissue can be humidity, tissue composition—either collagen or elastin—and the viscoelasticity of the tissue. Thereafter, the ultimate tensile strength of soft tissue is more amenable to simple numeric evaluation than is the general nonlinear stress–strain relationship. A number of factors may affect this soft tissue property such as age of the tissue, humidity, and the shear and bursting strength of the tissue. The viscosity of a fluid may be measured either by observing its flow along a capillary tube or by the use of a rotational viscometer. The viscometer applies an almost uniform shear rate across the fluid and can be used to investigate the variation of viscosity with velocity gradient. Subsequently, it has been noticed that blood viscosity increases with hematocrit and decreases with temperature.

Debris-flow surges : experimental simulation

Abstract: A laboratory moving-bed flume was used to study the development, behaviour and characteristics of high-concentration grain-in-fluid waves. These waves behaved similarly to reported debris-flow pulses. Observation of velocity and concentration profiles within the waves suggests that wave behaviour is mainly controlled by larger grains provided the background slurry of fine grains in water is sufficiently dense; that the front of a pulse is highly erosive while the tail is probably less erosive or depositional; and that the maximum height of a pulse is controlled by the velocity gradient within the flow

A study of the topology of dissipating motions in direct numerical simulations of time-developing compressible and incompressible mixing layers

Abstract: A preliminary investigation of the geometry of flow patterns in numerically simulated compressible and incompressible mixing layers was carried out using 3-D critical point methodology Motions characterized by high rates of kinetic energy dissipation and/or high enstrophy were of particular interest In the approach the partial derivatives of the velocity field are determined at every point in the flow These are used to construct the invariants of the velocity gradient tensor and the rate-of-strain tensor (P, Q, R, and P(sub s), Q(sub s), R(sub s) respectively) For incompressible flow the first invariant is zero For the conditions of the compressible simulation, the first invariant is found to be everywhere small, relative to the second and third invariants, and so in both cases the local topology at a point is mainly determined by the second and third invariants The data at every grid point is used to construct scatter plots of Q versus R and Q(sub s) versus R(sub s) Most points map to a cluster near the origin in Q-R space However, fine scale motions, that is motions which are characterized by velocity derivatives which scale with the square root of R(sub delta), tend to map to regions which lie far from the origin Definite trends are observed for motions characterized by high enstrophy and/or high dissipation The observed trends suggest that, for these motions, the second and third invariants of the velocity gradient and rate-of-strain tensors are strongly correlated The second and third invariants of the rate-of-strain tensor are related by K(-Q(sub s))(exp 3/2), which is consistent with the above scaling of velocity derivatives The quantity K appears to depend on Reynolds number with an upper limit K = 2(the square root of 3)/9 corresponding to locally axisymmetric flow For both the compressible and incompressible mixing layer, regions corresponding to high rates of dissipation are found to be characterized by comparable magnitudes of R(sub ij)R(sub ij) and S(sub ij)S(sub ij) For the incompressible mixing layer, regions characterized by the highest values of enstrophy are found to have relatively low strain rates

Analysis of Dispersion of Small Spherical Particles in a Random Velocity Field

Abstract: The equation of motion of a small spherical rigid particle in a turbulent flow field, including the Stokes drag, the Basset force, and the virtual mass effects, is considered. For an isotropic field, the lift force and the velocity gradient effects are neglected. Using the spectral method, responses of the resulting constant coefficient stochastic integro-differential equation are studied

Reynolds stress and the physics of turbulent momentum transport

Abstract: The nature of the momentum transport processes responsible for the Reynolds shear stress is investigated using several ensembles of fluid particle paths obtained from a direct numerical simulation of turbulent channel flow. It is found that the Reynolds stress can be viewed as arising from two fundamentally different mechanisms. The more significant entails transport in the manner described by Prandtl in which momentum is carried unchanged from one point to another by the random displacement of fluid particles. One-point models, such as the gradient law are found to be inherently unsuitable for representing this process. However, a potentially useful non-local approximation to displacement transport, depending on the global distribution of the mean velocity gradient, may be developed as a natural consequence of its definition. A second important transport mechanism involves fluid particles experiencing systematic accelerations and decelerations. Close to the wall this results in a reduction in Reynolds stress due to the slowing of sweep-type motions. Further away Reynolds stress is produced in spiralling motions, where particles accelerate or decelerate while changing direction. Both transport mechanisms appear to be closely associated with the dynamics of vortical structures in the wall region.

A Small Flume for Studying the Influence of Hydrodynamic Factors on Benthic Invertebrate Behaviour

Abstract: A compact, versatile flume for studying the influence of hydrodynamic factors on the behaviour of benthic invertebrates is described. A range of lotic micro-environments can be simulated under controlled and replicable conditions by tailoring the velocity profile at the entrance of the test section. A specially designed diffuser composed of an array of adjustable horizontal rods allows tailored flow (e.g., zone of high shear stress, adjustable velocity gradient and turbulence level) to which organisms can be exposed. Water velocities of up to a maximum of 81.5 ± 0.6 cm/s, with a turbulence intensity of 0.8% can be achieved. Simultaneous observations of flow and organism behaviours can be done by means of standard flow visualization techniques. Compact (72 cm long × 22 cm high × 10 cm wide; volume 10 L) and easily transportable, this flume is an inexpensive "desk-top" version of larger, more bulky systems, without sacrifice of performance and versatility.

Flow effects on micellar size distribution

Abstract: The authors consider for the first time the consequence of flow fields on the size of micellar aggregates. In the case of extensional flow, we incorporate directly an effective potential into the conditions for self-assembly equilibrium. While the perpendicular component of the viscous forces serves mainly to align the rodlike micelles, the parallel contribution results in a deformation energy. This latter term imposes on the size distribution an upper cutoff which is a strongly decreasing function of velocity gradient.

Enhancement of fine-scale turbulence for improving fuel-rich plume combustion

Abstract: A passive method to enhance fine-scale mixing was developed and studied in cold flows. Its effect on the combustion intensity and flame stability was then studied in reacting flows. Hot-wire anemometry was used to map the mean and turbulent flowfields of the nonreacting flows. Reacting flows were studied in a free flame and ducted gas-generator fuel-rich plume using planar laser-induced fluorescence imaging, a rake of thermocouples , and high-speed photography. A modified circular nozzle having several downstream-facing steps upstream of its exit was used to introduce numerous inflection points in the initial mean velocity profiles, thus producing multiple corresponding sources of fine-scale turbulence generators and reducing the strain rates in the initial region. Cold flow tests showed turbulence increases of up to six times the initial turbulence level relative to a circular nozzle and a substantial decrease of the mean velocity gradient. The flame of this nozzle was more intense with a homogeneous heat release in the free-flame experiments and ducted-plume combustion experiments, even when the gas-generator exhaust velocity was supersonic. Secondary plume ignition was obtained under conditions that prevented sustained afterburning using the circular nozzle.

Flow birefringence studies in transient flows of a two roll mill for the test-fluid M1

Abstract: We have studied the test-fluid M1 in flows generated by a two-roll mill. These flows are linear, and two-dimensional, and the magnitudes of the strain-rates are greater than the vorticity. The polymeric solution is shown to degrade significantly, even for small values of the velocity gradient, as measured by the changes in the macroscopic relaxation time-scales. Consequently, the determination of macroscopic properties such as elongational viscosity based upon the overall pressure difference, or the total force as measured in a spin-line rheometer, may not be representative of the properties of the fresh, undegraded fluid. In this work, the degradation of the test-fluid has been studied as a function of the strength of the velocity gradient for different values of the ratio of the strain-rate to vorticity of the flow. Furthermore, the observed relaxation time-scales have been evaluated based on data for steady state flows, and several transient flow histories such as start-up and cessation of flows, and double-step flows. These flow histories provide us with some insight into the relaxation dynamics of the polymeric structure for different initial conformation states.

A new shear apparatus for small angle neutron scattering (SANS) measurements

Abstract: A new shear apparatus for small angle neutron scattering experiments was developed. Compared to other instruments two new experimental degrees of freedom are characteristic for this apparatus: (i) there is only one shear cell and not two as in other shear apparatus, and (ii) the angle α between the incident beam of neutrons and the vector of the velocity gradient of the sheared solution can be changed between 0° and 50°. This gives the possibility to test the anisotropic distribution of nonspherical particles, like micelles, in much more detail than with the other shear apparatuses. For example the symmetry of the scattering pattern of rodlike micelles is reduced from point group 2 mm for α=0 to point group 2 for α≠0, which is shown in an experiment performed with rodlike micelles of Cetylpyridiniumsalicylate.

Flow characteristics and circular pipe flow of pulp-suspension

Abstract: An experimental investigation of a laminar plug flow of pulp-suspension in a circular pipe was made. The pressure loss was measured by pressure transducers, and the velocity gradient at pipe wall and the local velocity were measured by an electrochemical technique.From experimental relations between the pressure loss and the flow rate, and between the shear stress and the velocity gradient at pipe wall, the pulp-suspensions should be regarded as Newtonian liquids, though the values of viscosity determined from those relations were undoubtedly different from each other. On the other hand, both the measured velocity profile and the experimental relation between the velocity gradient at pipe wall and the flow rate were not those for a Newtonian liquid.This inconsistency could be explained by the consideration that the pulp-suspension had a particular average viscosity to the pulp fiber concentration prepared and behaved as a Newtonian liquid at every radial position with different viscosity which was distributed in the radial direction in a circular pipe. Furthermore, an appropriate formula for the radial distribution of viscosity was presented. The calculated velocity profiles based on the formula coincided well with the measured ones.

Concave-Wall Laminar Heat Transfer and Görtler Vortex Structure: Effects of Pre-Curvature Boundary Layer and Favourable Pressure Gradients

Abstract: The mean velocity field in the boundary layer and the streamwise and spanwise distributions of heat transfer coefficient have been measured on a concave wall in the presence of naturally-generated Gortler vortices, with and without a preceding flat wall. In near-zero pressure gradient, enhancement of the streamwise-averaged heat transfer above flat surface levels was associated with the attainment of a Gortler number of around ten, as found in previous experiments in a different flow facility with higher wall curvature, but occurred before the onset of severe distortion in the velocity profiles. Velocity gradient parameters K of 0·20 × 10−6 and 0·75 × 10−6 resulted in a more regular vortex structure, with spanwise averaged heat transfer reaching two to three times predicted levels. At K = 1·8 × 10−6, vortex amplification was suppressed to such an extent that no significant heat transfer enhancement took place. Comparison of measured Stanton numbers with those derived from skin friction factors (obtained from velocity profiles) suggested that the heat transfer enhancement is not simply a result of fuller velocity profiles in vortex downwash regions.Copyright © 1990 by ASME

Comment on Slip Velocity at a Fluid-Solid Boundary

Abstract: The assumption that fluid velocity near a solid boundary is equal to boundary velocity, i.e., the no-slip assumption, is argued to be physically untenable. The assumption is critically examined firstly for dilute gases and we show that the no-slip assumption is incompatible with even the most elementary kinetic theoretical considerations. The effective viscosity coefficient relating shear stress exerted by the solid on the gas to the velocity gradient in the gas differs from the viscosity coefficient applicable to the bulk of the gas. Qualitative arguments are used for liquids and similar conclusions are reached. A macroscopic model, applicable to both gases and liquids, consistent with the physical requirement of nonzero slip, is then proposed. The shear stress at the boundary is then interpreted as a frictional force proportional to the slip velocity and viscosity is assumed to have the same constant value everywhere.

Effects of velocity profile of to-and-fro pulsatile flow on magnetic resonance signal intensity.

Abstract: The effects of to-and-fro pulsatile flow, i.e., an oscillatory fluid motion with no net flow, on signal intensity in gated spin-echo magnetic resonance imaging are considered both theoretically and experimentally. On the basis of hydrodynamic principles, to-and-fro pulsatile flow at large Womersley numbers consists of uniform inner flow and boundary-layer-type flow adjacent to a tube wall. Therefore, the velocity profile is “trapezoidal” rather than parabolic at all times during the pulsation period. Contrary to the absence of phase dispersion and loss of signal within the inner flow where no velocity gradient exists, large velocity differences cause phase dispersion and, hence, loss of signal within the boundary layer, whose thickness is inversely proportional to the Womersley number. An understanding of these features of to-and-fro pulsatile flow provides the theoretical basis of cerebrospinal fluid flow phenomena in magnetic resonance imaging, since this type of flow exists in cerebrospinal fluid pathways. © 1990 Academic Press, Inc.

Application of holography to the measurement of velocity gradients in fluid flows sensitized with photochromic dyes

Abstract: A novel joint application of holography and photochromic materials to the experimental measurement of velocity gradients in a fluid flow is presented. A short study of some photochromic materials of interest is presented from the point of view of their applicability to experimental fluid mechanics. This includes a spatiotemporal model for the photoinduced conversion reaction which allows for optimization of the experimental conditions. The forced Rayleigh scattering method for measuring velocity gradients using photochromic materials is then briefly described and applied to the measurement of the velocity gradient in a boundary layer. Spatial resolution of 100 μm and gradient resolution of 3 sec−1 are obtained using these techniques.

An alternative derivation of Sobolev's large velocity gradient limit.

Abstract: Our concern is with the net radiative bracket for a constant source function ϱcsf(r) and with the formula ϱ csf ( r ) = γ {1 - exp[ - ( 1 γ )} derived by Sobolev for a differentially moving medium with constant velocity gradient in the large velocity gradient (LVG) limit. The usual derivation of this formula is based on the ab initio assumption γT → ∞, which thus becomes a sufficient (though not a necessary) condition for the formula to be valid. We present an alternative derivation, for a constant velocity gradient, which shows that the necessary (and sufficient) condition for ϱcsf(r) to attain the LVG limit in the case of strong absorption is γT ≳ 1 for a Doppler profile and γT → ∞ for a Lorentzian profile, and in the case of velocity-induced, near optical transparency is γT → ∞ irrespective of the shape of the absorption profile.

Response of (Poly)Atomic Fluids to Various Flows with Homogeneous Velocity Gradients

Abstract: In this paper a transient non-equilibrium method based on the so called Sllod equations of motions is developed to study polyatomic fluids in flows with a homogeneous velocity gradient in space. Various flows like pure deformational, pure rotational or elongational flows can be imposed and accommodated with periodic boundary conditions in order to avoid surface effects. The method is illustrated on an atomic fluid, on liquid butane and on liquid chlorine subject respectively to a planar Couette flow, a purely deformational flow and a pure rotational flow.

Diffusion in polyelectrolyte solutions

Abstract: Molecular migration in nonhomogeneous flows of a polyelectrolyte solution is considered. The solution is modelled as a binary mixture whose electrically-charged constituents are regarded as compressible fluids. Upon deriving a set of thermodynamic restrictions for the mixture, non-equilibrium quantities are examined in detail. As a result, two schemes are elaborated for the description of cross streamline migration, induced by the second gradient of the velocity, where also occur coupling effects. In the first scheme the migration effect is described through a stress term which involves a coupling with the conformation of the macromolecule; in the second scheme it is described through a term in the diffusion velocity where coupling occurs with the velocity gradient. In both cases the thermodynamic approach leads to a systematic framework with a minimal number of constitutive coefficients, which is an essential aspect for any comparison with experimental data.

Tensorial volume of turbulence revisited

Abstract: A corrected tensorial turbulent volume transport equation, which is exact for uniform density flows, is derived from the Navier–Stokes equations. For homogeneous turbulence, the new terms appearing in the correct equation account for the effect of the pressure velocity correlation and of the mean velocity gradient. The correct tensorial volume equation is closed only for the case of isotropic homogeneous turbulence. To solve the equation for the anisotropic case a model for the velocity spectrum is required. When applied to the cases of isotropic expansion, incompressible axisymmetric contraction, and shearing of initially isotropic turbulence, the correct equation predicts the same time evolution for the tensorial volume that rapid distortion theory does.

Concerning an equality between the net radiative bracket and escape probability in a moving medium

Abstract: With reference to line photons within an isolated source, conditions which are known to be sufficient for an equality between the escape probability and the net radiative bracket for a constant source function have been summarized and one further condition has been identified, namely, a velocity field with constant velocity gradient irrespective of the shape of the absorption profile. This latter condition applies irrespective of the magnitude of the velocity gradient (and not just in the large velocity gradient limit).

Numerical modeling of water waves recorded by a subbottom seismometer in the southwest Pacific

Abstract: The amplitudes of water waves generated by shallow explosive sources and recorded by a subbottom seismometer provide constraints on velocity and attenuation parameters of oceanic sediments and upper oceanic crust. Analysis of data collected during the 1983 Ngendei Seismic Experiment in the southwest Pacific Ocean illustrates this method. The data were recorded by a triaxial geophone emplaced 54 m into the basaltic basement. Synthetic seismograms are computed using wave number integration for several crustal models to determine the sensitivity of water wave amplitudes to specific parameters of the sediments and oceanic crust. The synthetic seismograms fit the recorded data to better than a factor of 2 for frequencies as high as 15 Hz and ranges out to 30 km. The amplitude of the direct water wave beyond critical incidence (“direct wave root”) indicates that the sediment P wave velocity is near 1.8 km/s. Modeling of the attenuation of shear wave reverberations in the sediments indicates that sediment Qβ is between 30 and 50. Modulations in water wave amplitude as a function of receiver offset are related to the velocity of the upper oceanic crust. The distances at which amplitude maxima occur indicate that the shear wave velocity of the upper crust at the Ngendei site is 2.4±0.1 km/s. This is an important result since reliable estimates of the shear wave velocity of upper oceanic crust are rare. The distances at which amplitude minima occur are used to constrain the compressional wave velocity of the uppermost crust. However, the modulations do not resolve the compressional wave velocity of the crust as well as the shear wave velocity. The relative amplitudes of successive water waves indicate that the reflection coefficient at the sediment-basement interface is 0.66. This further constrains the compressional wave velocity of the upper crust. Using estimates of the sediment properties and crustal shear wave velocity, the compressional wave velocity of the upper crust at the Ngendei site is estimated from this reflection coefficient to be 4.3–4.4 km/s. A method for estimating the velocity gradient in the upper kilometer of the crust from the interference of water waves with upgoing crustal refractions is presented. Application of the method to these data indicate that the shear wave velocity gradient is about 1.0 s−1, which is indistinguishable from the previous determination by Shearer and Orcutt (1986) using a quite different methodology. The velocity of the upper crust at the Ngendei site is consistent with velocities reported for other regions of similar crustal age (>100 m.y.) and is much greater than velocities typically found for young oceanic crust (<5 m.y.). This lends support to current theories regarding the evolution of the uppermost oceanic crust that attribute higher velocities in older crust to the closing of cracks and pores.

Aplicacion de la aproximacion circular en la estimacion de estructuras sismicas bidimensionales

Abstract: The computational procedure reported here estimates seismic wave velocities for two-dimensional heterogeneous media from observations of body-wave travel times. The solution of the forward problem is based on the circular approximation. The structure is discretized in a grid of triangular cells and the velocity gradient is held constant within each triangle. In order to estimate the velocity field, a linearized sheme is applied using a Taylor series expansion around an initial solution. The partial derivatives of the travel times with respect to the model parameters are computed from closed form expressions. The initial model does not necessarily has to be laterally heterogeneous. A double stabilization of the least-squares solution of the inverse problem follows from the application of both, the singular-value decomposition and a simple regularization scheme. The results of several numerical experiments validate the computational procedure. In these experiments, we have modeled a real situation where travel time observations are used from 15 explosions and 12 sensors located at the perimeter of a square (with sides 30 m long) to detect low-velocity regions at maximum depths of 10 to 20 m. The solutions are illustrated with maps of velocity isolines and are evaluated taking into account the smoothness of the solution, the behaviour of the residuals and the resolution matrix, as well as our prior information about the physics of the problem. The procedure is more efficient than those using rectangular homogeneous cells.

Velocity gradient measurement from time migration analysis

Abstract: Time migration velocity analysis is discussed for velocity gradients of sufficient magnitude to require nonhyperbolic diffraction time surface definition. Since multiparameter semblance analysis is costly and can be ambiguous, we developed a method of common-offset time migration that uses linear gradient theory to control the expansion coefficients defining the diffraction surface. Synthetic and field data are used to demonstrate our approach to migration parameter analysis and time imaging.

On the Correlation of Recent Numerical Computations of Laboratory-Scale Opposed-Flow Flame Spread Rates by Oseen Flow Theory and Velocity-Gradient Theory

Abstract: In this short note the predictions of two theories of opposed-flow flame spread is compared with some recent numerically-computed results. The theories in question are those of deRis and Wichman

Theoretical profiles of balmer lines in the spectra of stars with moving envelopes with allowance for spectral dependence of the hydrogen absorption coefficient

Abstract: A method for constructing theoretical profiles of emission lines in the spectra of stars with moving envelopes with allowance for a fre- quency dependence of the atomic absorption coefficient is described. The results of calculations for Voigt, Doppler, and rectangular pro- files of the absorption coefficient are compared. The example of the construction of the profile of H a for a disk envelope having differ- ent orientations relative to the observer is given. distribution of the radiating matter with respect to the radial velocities. The profiles were constructed using a rectangular profile of the hydrogen absorption coefficient in the lines. A series of models of envelopes with different sets of basic parameters describing the structure and kinematics, and also the main properties of the star, was considered. Comparison of the theoretical profiles of the lines H~_7 with the observed profiles showed that in a number of cases perfectly satisfactory agreement can be obtained. However, there are conditions under which the method becomes invalid or at least only partly valid. Three cases can be distinguished: i. The most general case is when a) an envelope is opaque in the continuum at the frequencies of the investigated lines, or b) the velocity gradient in an envelope is not sufficiently high for the two conditions described above, the basis of the calculations, to hold. Then the problem requires simultaneous solution of the stationarity equations for the energy levels and the equation of radiative transfer in the lines over the complete envelope. The problem is rather complicated and requires a special treatment that goes beyond the scope of the present paper. 2. The velocity gradient is not yet sufficiently large for one to be able to use Sobolev's method to calculate the level populations but is already too small for the real profile of the hydrogen absorption coefficient to have no influence on the form of the line profiles.