Variation Of Flow Properties Research Articles

Estimating permeability from quasi-static deformation: Temporal variations and arrival-time inversion

Transient pressure variations within a reservoir can be treated as a propagating front and analyzed using an asymptotic formulation. From this perspective, one can define a pressure “arrival time” and formulate solutions along trajectories, in the manner of ray theory. We combine this methodology and a technique for mapping overburden deformation into reservoir volume change as a means to estimate reservoir flow properties, such as permeability. Given the entire “travel time” or phase field obtained from the deformation data, we can construct the trajectories directly, thereby linearizing the inverse problem. A numerical study indicates that, using this approach, we can infer large-scale variations in flow properties. In an application to Interferometric Synthetic Aperture Radar (InSAR) observations associated with a [Formula: see text] injection at the Krechba field, Algeria, we image pressure propagation to the northwest. An inversion for flow properties indicates a linear trend of high permeability. The high permeability correlates with a northwest trending fault on the flank of the anticline that defines the field.

Cavitation Analogy to Gasdynamic Shocks: Model Conservativeness Effects on the Simulation of Transient Flows in High-Pressure Pipelines

A comparison between conservative and nonconservative models has been carried out for evaluating the influence of conservativeness on the prediction of transient flows in high-pressure pipelines. For the numerical tests, a pump-line-nozzle Diesel injection system was considered because the pipe flow presented interesting cases of cavitation. The validity of a conservative model in the simulation of cavitating transient flows was substantiated by the comparison between computed pressure time histories and experimental results at two pipeline locations in the injection system. Although nonconservative models can assure satisfactory accuracy in the evaluation of the wave propagation phenomena, they introduce fictitious source terms in the discretized equations. Such terms are usually negligible, but can play a significant role in the presence of acoustic cavitation, i.e., pressure-wave-induced cavitation, producing errors in the pressure-wave speed prediction. A theoretical analysis based on unsteady characteristic lines was carried out, showing that the cavitation desinence is a shock gas-dynamic-like event, whereas cavitation inception is a supersonic expansion. The Rankine–Hugoniot jump conditions were applied to evaluate the shock wave speed in the presence of cavitation. Analytical relations to calculate the flow property variations across the cavitation-induced discontinuities were also derived. A previously published analytical expression of the sound speed in a homogeneous two-phase flow model was also derived from the eigenvalues of the Euler flow equations for the two distinct phases and a comparison was made with Wallis’ formula, which is commonly applied to cavitating flow simulation in transmission lines. Finally, a novel algorithm for calculating the shock speed, as is predicted by nonconservative models, was presented and applied to Burgers’ equation, pointing out the contribution of internal fictitious fluxes in the shock-speed wrong estimation.

Modeling of frictional gas flow effects in a piezoelectrically actuated low leak-rate microvalve under high-pressure conditions

One-dimensional modeling of steady frictional radial flow of a perfect gas through a high-pressure piezoelectrically actuated microvalve under low leak-rate conditions is studied. Focusing on the micro-scale gap between the boss and seat plates, a model was developed for axisymmetric flow between two thermally insulated, parallel disks flowing radially toward an outlet hole at the center of the bottom disk. The fourth-order Runge–Kutta algorithm was utilized to integrate a system of nonlinear ordinary differential equations that govern the variations of flow properties. The most notable observation is that of a drastic increase in density and static pressure in contrast to a rather small increase in the Mach number (or velocity). The total pressure drop was also shown to be significant across the seat rings. A 2D Stokes flow model was also derived for incompressible, axisymmetric, radial flow between two concentric parallel disks in order to verify the trends of the flow property variations from the compressible radial flow model. The Stokes flow model trends for both static and total pressure concurred with the predictions of the radial compressible flow model. In addition, a comparison of Stokes flow values for both the static pressure rise and the total pressure drop to that of the numerical results demonstrates the necessity of accounting for compressibility effects.

Effect of wall distance on the prediction of variable property flow with two-equation turbulence models

This paper investigates the effect of wall distance coordinate on predicting variable property flows with two-equation turbulence models. Three of five different definitions of wall distance coordinate are employed: the wall-property definition, the integral-property definition and the local-property definition. Three different two-equation turbulence models that involve the wall distance coordinate are tested against the varying property flow: Superheated gas flow. The definition of wall distance coordinate affects the size of the viscous region. The wall-property based unit makes the wall distance to be the smallest and contributes to widen the viscous damping region, so that the skin friction factor and the Nusselt number is lowered. All the predictions with three different wall distance coordinates lie within less than 20% in the calculated Nusselt number.

The development of membrane fouling in full-scale RO processes

A predictive model was developed in this study for simulating the development of membrane fouling with time in full-scale RO processes. The increase in resistance was used as an indicator of membrane fouling and it enabled one to better describe membrane fouling taking place in a long membrane channel. In this model, fouling potential of a feed water was defined as the increment in membrane resistance due to a unit volume of permeate passing through the membrane, which was directly measurable with a simple filtration experiment. By employing the concept of fouling potential, fouling property of a feed water could be directly related to fouling rate on a RO membrane. The local variations in flow properties and parameters were explicitly taken into consideration in the model in order to provide a more realistic description of a full-scale RO process. The results of the simulation studies demonstrated that a full-scale RO system could maintain a constant average permeate flux for a period of time even though fouling development had occurred right from the start of operation. The effects of water fouling potential, channel length, and membrane resistance on fouling development in full-scale RO processes were investigated.

Composition of joint fluid in patients undergoing total knee replacement and revision arthroplasty: correlation with flow properties

The protein, phospholipid and hyaluronic acid (HA) contents of joint fluid samples were determined in specimens obtained from patients undergoing total knee arthroplasty (TKA) and revision TKA. It was hypothesized that these components would vary widely among patients undergoing TKA, and that the composition of joint fluid in patients undergoing revision would differ from that in patients undergoing revision. It was further hypothesized that HA concentration and molecular weight would principally determine the flow properties previously reported. Biochemical assays were used to assess protein and phospholipid content, and size exclusion chromatography was used to determine HA concentration and molecular weight. Sixty samples were included in the study. HA, protein, and phospholipid concentrations all varied widely in patients undergoing index TKA and revision TKA. HA concentration was lower in patients undergoing revision arthroplasty due to wear-related failure compared to patients undergoing the index procedure (0.9±0.4 mg/ml versus 1.3±0.5 mg/ml, mean±standard deviation, p=0.04). Other components were not different between the groups. Flow properties at high shear rates were correlated with HA concentration and, to a lesser extent, HA molecular weight, but neither protein nor phospholipid concentration. The composition of joint fluid is highly variable in the context of arthroplasty. Much of the variation in flow properties, especially at high shear rate, is explained by large variation in HA concentration and small variation in HA molecular weight. The variation in composition and lower HA concentration in joints necessitating revision may relate to variation in arthroplasty lubrication leading to highly variable wear rates and clinical outcomes.

The influence of a lateral basin-slope on the depositional patterns of natural and experimental turbidity currents

Abstract Understanding topographic effects upon the depositional processes of turbidity currents and the resulting deposit characteristics is key to producing reliable depositional models for turbidity currents. In this study, the effect on depositional patterns of a lateral slope whose strike is parallel to the principal direction of flow is explored using field and experimental results. This type of basin topography is commonly found in confined turbidite systems. Field data from the Peïra Cava turbidite system of the Tertiary Alpine Foreland Basin (SE France) and experimental data show that a characteristic depositional pattern is produced by surge-type waning flows that interact with a lateral slope. This pattern comprises beds that thin (and fine in the field study) not only downstream but also markedly away from the lateral slope (Type I beds). In the Peïra Cava system, this pattern is also observed in average values of sandstone bed thickness, sandstone percentage and grain-size, derived from measured sections, demonstrating that the processes responsible for this pattern also control gross properties within this sheet system. The characteristic thinning-away-from-slope deposit geometry is interpreted as an effect of the lateral slope via its influence on spatial variations in flow properties and on the suspended load fallout rate (SLFR) from currents. Flow velocity non-uniformity cannot explain thinning into the basin because flow has a higher deceleration along streamlines away from the slope that should cause higher SLFR and thicker deposits away from the slope instead of close to the slope. A concentration non-uniformity mechanism is invoked that has the effect of maintaining relatively high flow concentrations and hence SLFR in medial and distal locations close to the slope. Experiments suggest that this may arise due to different rates of flow expansion on the obstructed and unobstructed sides of the current in proximal regions. Velocity non-uniformity can, however, explain the geometry of deposits that thicken away from slope. Beds of this type do occur occasionally in the Peïra Cava system (Type II beds). Flow velocity non-uniformity patterns have been used previously to successfully explain the spatial distributions of depositional facies of turbidity currents that have interacted with topography. The analysis in this study demonstrates that velocity non-uniformity, by itself, cannot explain depositional patterns in all basin settings. Future depositional models need to incorporate the effects of spatial changes in other flow properties, such as flow concentration, upon deposition to be able to predict turbidite facies in many different types of basin setting.

Accounting for temperature-dependent properties in viscoelastic duct flows

A numerical and theoretical study is conducted to evaluate the effect of temperature-dependent properties on the hydrodynamic and thermal characteristics of viscoelastic fluid flow. The rheological constitutive equation of the fluid under consideration follows a common form of the PTT model, which embodies both influences of elasticity and shear-thinning in viscosity. A large number of simulations were carried out for a developing channel flow with an imposed constant wall temperature by varying the parameters controlling elasticity (Weissenberg number) and viscous dissipation (Brinkman number). The resulting Nusselt number and friction factor were determined from the numerical results, for both conditions of constant and temperature-dependent properties. The properties that were allowed to vary with temperature were the viscosity, thermal conductivity, specific heat and relaxation time of the PTT model. From the results it was possible to determine how the usual correlations for Nu and C f have to be modified, following the property-correction method, in order to represent variable-property flow of this viscoelastic fluid. An alternative method to account for variable properties, based on the definition of an equivalent temperature to be used with the constant property Nu and C f expressions, is also proposed and shown to be less sensitive to the influence of viscous dissipation. The corrections are highly non-linear and strongly depend on ε We 2 and Br especially when viscous dissipation is weak.

What happens to pressure when a flow enters a side branch?

The behaviour of incompressible side-branching flows is examined theoretically at high Reynolds numbers and compared with direct numerical simulation at moderate Reynolds numbers. The theoretical model assumes the branching (daughter) tube is small compared to the main (mother) tube and that the branching angle is small. The theory is applicable to steady and unsteady flows in two or three dimensions, and to a broad range of flow splits between mother and daughter vessels. The first main result of the work is that, in the vicinity of the branch, the flow adjusts to the imposed downstream pressure in the daughter tube through a jump (a rapid change over a short length scale) in flow properties across the daughter entrance. It is shown that, for large pressure drops in the daughter tube, fluid is sucked in at high velocities from the mother and thereby provides a favourable upstream feedback. This counteracts the tendency of the flow to separate from what would otherwise be an adversely shaped upstream wall. Increased divergence of mother and daughter tubes can thus be achieved at high daughter flow rates without separation. The second main result of the work is that the direct numerical simulations confirm the very rapid variation in flow properties and show reasonable agreement with the theory at moderate Reynolds numbers.

Flow and Stress Induced Cavitation in a Journal Bearing With Axial Throughput

The problem of predicting flow between rotating eccentric cylinders with axial throughput is studied. The system models a device used to test the stability of emulsions against changes in drop size distribution. The analysis looks for the major variation in flow properties which could put an emulsion at risk due to coalescence or breakage and finds the most likely candidate in the pressure gradient defined as the ratio of the difference between the maximum and minimum pressure to the arc length between the difference. The axial throughput is modeled by flow driven by a constant pressure gradient. The flow is calculated from the Navier-Stokes equation using the code SIMPLER (Patankar 1980). The effects of inertia at values typical for the device are studied. Several eccentricities and different rotational speeds are computed to sample the changes in flow and stress parameters in the idealized device for typical conditions. The numerical analysis is validated against the lubrication approximation in the low Reynolds number case. Conditions for stress induced cavitation are evaluated. The flow is completely determined by a Reynolds number, an eccentricity ratio and a dimensionless pressure gradient and all computed results are either presented or can be easily expressed in terms of these dimensionless parameters. The effect of inertia is to shift the eddy or re-circulation zone which develops in the more open region of the gap toward the region of low relative pressure; the zero of the relative pressure migrates away from the center and the distribution breaks the skew symmetry of the Stokes flow solution. The state of stress in the journal bearing is analyzed and a cavitation criterion based on the maximum tensile stress is compared with the traditional criterion based on pressure.

Reynolds-averaged equations for free-surface flows with application to high-Froude-number jet spreading

The goals of this study were to develop a set of Reynolds-averaged governing equations for turbulent free-surface flow, and to use the resulting equations to determine the origin of the surface current in high-Froude-number jet flows. To develop the Reynolds-averaged equations, free-surface turbulent flow is treated as a two-fluid flow separated by an interface. It is shown that the general Navier–Stokes equations written for variable property flow embody the field equations applicable to each fluid, as well as the boundary conditions for the interface and, therefore, can be applied across the entire fluid domain, including the interface. With this as a starting point, a formulation of the Reynolds-averaged governing equations for turbulent free-surface flows can be developed rigorously. The resulting Reynolds-averaged equations are written in terms of density-weighted averages, their derivatives, and the probability density function for the free-surface position. These equations are similar to the conventional Reynolds-averaged equations, but include additional terms which represent the average effect of the forces acting instantaneously on the free surface, forces normally associated with the boundary conditions. These averaged equations are applied to the interaction of a turbulent jet with the free surface in order to establish, for arbitrary-Froude-number flows, the origin of the surface current, the large outward velocity which occurs in a thin layer adjacent to the surface. It is shown via an order-of-magnitude analysis that the outward acceleration associated with the surface current results from a combination of the Reynolds-stress anisotropy and the free-surface fluctuations. For low Froude number, the surface current is mainly driven by the Reynolds stress anisotropy, consistent with the results of Walker (1997); when the Froude number is large, the Reynolds-stress anisotropy is smaller and the free-surface fluctuations make a significant contribution.

Gas–particle two-phase turbulent flow in horizontal and inclined ducts

Gas–particle two-phase turbulent flows at various loadings in horizontal and inclined ducts are studied. The upgraded thermodynamically consistent two-phase flow model which includes a low Reynolds number fluid-phase turbulence closure is used in the analysis. The governing equations are discretized with the aid of a semi-implicit numerical algorithm. The case of low-concentration gas–particle turbulent flow in a horizontal channel is first analyzed, and the predicted mean velocity and solid volume fraction profiles are favorably compared with the available experimental data. Additional flow properties such as the phasic fluctuation energy and fluctuation energy production and dissipation, as well as the phasic and total normal and shear stress profiles are also presented and discussed. The case of gas–particle flow in a duct with an inclination is then analyzed. Sample model predictions for both dilute and nondilute two-phase turbulent flows under various conditions are presented. The effect of particle diameter on variation of flow properties is also studied.

Asymptotic solutions for solute transport: A formalism for tracer tomography

An asymptotic approach to the solution of the transport equation, in the limit of rapid spatial and temporal variation, produces an extremely efficient formalism for the inversion of tracer data. The technique provides tracer concentration sensitivities to porosity, permeability, and pressure gradient variations in just a single simulation run. The calculated sensitivities compare well with those derived using a numerical perturbation method, at a fraction of the computational requirements. An application to a conservative tracer test at Hill Air Force Base in Utah indicates the efficiency and utility of the approach for characterizing three‐dimensional variations in flow properties. On the basis of tracer concentration histories at 12 multilevel samplers and three extraction wells, some 44 tracer curves in all, significant small‐scale variability in permeability is inferred. In general, the permeability is found to decrease as the lower boundary of the aquifer is approached. The permeability trends we find are consistent with tracer swept volume calculations based upon a moment analysis.

Mass Flow and Thrust Performance of Nozzles With Mixed and Unmixed Nonuniform Flow

The calculated thrust and mass flow rate of a nozzle depend on the uniformity of the entering flow. The one-dimensional flow equations are extended to arrive at analytic expressions for the predicted performance of a nozzle processing two streams whose properties are determined ahead of the throat. The analysis approach forms the basis for the understanding of flows which have more complex distributions of total pressure and temperature. The uncertainty associated with mixing is examined by the consideration of the two limiting cases: compound flow with no mixing and completely mixed flow. Nozzle discharge and velocity coefficients accounting for non-uniformity are derived. The methodology can be extended to experimentally measured variations of flow properties so that proper geometric design variables may be obtained.

Pumping tests in nonuniform aquifers: The radially asymmetric case

An analytical solution for the case of transient, pumping‐induced drawdown in a nonuniform aquifer is presented. The nonuniform aquifer is conceptualized as a uniform matrix into which a disk of anomalous properties has been placed. The disk can be arbitrarily located with respect to the pumping well. This solution can be used to develop considerable insight concerning the nature of drawdown in nonuniform systems. Changes in drawdown are sensitive to the hydraulic properties of a discrete portion of an aquifer for a time of limited duration. After that time, it is virtually impossible to gain further information about those properties. The volume of the aquifer controlling a given increment of drawdown at an observation well increases greatly as the distance between the pumping and observation well increases. At observation wells located at moderate to large distances from the pumping well, this volume is so large that the effect of spatial variations in flow properties may be negligible. In general, drawdown data from wells located at a distance from the pumping well should nicely fit the ideal models of the well hydraulics literature. When combined with previous work, these results demonstrate that constant rate pumping tests are not an effective tool for characterizing lateral variations in flow properties.

Indentation load relaxation experiments with indentation depth in the submicron range

Indentation load relaxation (ILR) experiments with indentation depths in the submicron range are described. Under appropriate conditions, the ILR data are found to yield flow curves of the same shape as those based on conventional load relaxation data. Variations in flow properties as a function of depth in submicron metal films deposited on a hard substrate are detected by the experiments described.

A study of traveling wave instabilities in a horizontal channel flow with applications to chemical vapor deposition

The flow and heat transfer of helium in a horizontal channel of height H and length L with a heated bottom surface and a cooled top surface are studied. Numerical solutions of the transient, two-dimensional Navier-Stokes and energy equations reveal that for conditions of interest in chemical vapor deposition (CVD), a thermal instability in the fluid (the Rayleigh-Benard instability), produced by the temperature difference between the horizontal surfaces of the channel, can result in traveling, transverse waves. The results show the effects of these waves on the flow and the heat transfer over a range of Reynolds numbers, Re = u ̄ H v o (10 −1 < Re < 10 2) , Grashof numbers, Gr = gϵH 3 v o 2 (2.5 × 10 3 <Gr < 6.0 × 10 5) , aspect ratios, L H (4 < L H < 50) , for two temperature ratios, ϵ = (T s− T o) T o , 0.0333 and 2.333, corresponding to constant and variable property flow, respectively. The existence of transverse, traveling waves is shown to enhance the heat transfer from 50 to more than 300% over the condition without traveling waves. The important effect of the aspect ratio on the results is also emphasized.

Application of a General Technique for Prediction of Riser Vortex-Induced Response in Waves and Current

Abstract This paper describes applications of an extension to a recently developed calculation method for vortex-induced response of risers and tethers. The vortex-induced vibration response for the excited modes is generated using a semi-empirical formulation which is applied within a time domain calculation. This makes it possible to take account of the variation of flow properties along the riser length, as well as in time. The calculation method has been verified by comparison with model test data for vortex-induced response to surface vessel motions in still water. This paper presents applications of the technique for vortex shedding due to the combined action of current, surface vessel motions and waves. The mathematics of the extended prediction technique is described and results are illustrated by presenting typical vortex-induced responses for single-tube risers. The results of the prediction method are used to highlight the relative magnitudes and nature of vortex-induced response excited by currents, surface vessel motions and waves.

Numerical simulation of buoyant, turbulent flow—I. Free convection along a heated, vertical, flat plate

Two models have been developed for predicting free convection low Reynolds number turbulent flows. The models also apply to mixed convection flows. The first, a k-ε model, is based on the notion of eddy diffusivities for momentum and heat. The second, an algebraic stress model, is based on approximations derived for the anisotropic turbulent fluxes by a suitable truncation of their conservation equations. Both formulations apply to variable property flows with high overheat ratios, ΔT T ∞ , and have not required the definition of new model constants. No attempt has been made to modify previously established values of the constants in order to improve agreement between measurements and predictions of the flow investigated. Such an optimization must await the availability of more detailed and reliable experimental measurements of turbulence-related quantities. Fully elliptic forms of the differential transport equations, subject to appropriately specified boundary conditions, have been solved numerically for two flow configurations. Both are two-dimensional. The first corresponds to free convection along a heated vertical flat plate and is the subject of Part I of this study. The second corresponds to free and mixed convection from a heated cavity of arbitrary rectangular cross-section and variable orientation, and is the subject of Part II. For the case of the vertical plate, a comparison between measurements and predictions shows that both models yield fairly accurate results for the mean flow and heat transfer. Near-wall velocity and temperature distributions predicted by both models reveal the 1 3 power-law dependence derived by George and Capp [ Int. J. Heat Mass Transfer 22, 813–826 (1979)] and confirmed for temperature by Siebers et al [ J. Heat Transfer 107, 124–132 (1985)]. Values of the constants in the power-law relations for velocity and temperature have been obtained here numerically for high and low ΔT T ∞ . Predictions of the anisotropic Reynolds stress and turbulent heat flux distributions are in good qualitative agreement with the measurements of Miyamoto et al. [ Proc. 7th Int. Heat Transfer Conference, Vol. 2, pp. 323–328 (1982)]. In particular, regions of negative buoyant and shear production of turbulent kinetic energy observed experimentally are clearly revealed by the calculations.

Adiabatic Film Cooling Effectiveness From Heat Transfer Measurements in Compressible, Variable-Property Flow

A variable property correction is given for turbulent boundary layers that are film-cooled using staggered rows of injection holes inclined at 35 deg. With the correction, a relation is provided between the adiabatic film cooling effectiveness for constant property flow and heat transfer coefficients for variable property flow, which are based on the difference between the freestream recovery temperature and wall temperature. The variable property correction was determined from heat transfer measurements for a range of injection parameters at different values of the nondimensional coolant temperature and from results in the literature. Because the flow is compressible, the importance of the injection mass flux ratio, momentum flux ratio, and velocity ratio are considered in the determination of effectiveness.