Effect Of Pressure Gradient Research Articles

A stationary oil inflow to the wellbore taking into account the initial pressure gradient

In the development of deposits with abnormal properties of hydrocarbons, a number of complex and specific problems arise related to the study of the physical and hydrodynamic foundations of the manifestation of the non-Newtonian nature of filtration in a porous medium. Unlike conventional oil reservoirs, in deposits with anomalous oils, some minimum shear stress is required dependent on the properties of the fluid and the collector, to initiate filtration. In this paper, it is shown that for a steady flow of hydrocarbons to a well, taking into account the static (i.e., initial) pressure gradient, in contrast to the existing formula for production rate, the value of the initial pressure depression Δp0 depends on the radius of the power contour in a nonlinear manner. A more accurate formula for the pressure distribution was obtained, and a plot of the dependence of the drainage radius on depression for different values of Δp0 was constructed, and it was found that the effect of the initial pressure gradient on the well drainage radius is more significant than was found in earlier studies.

DNS analysis of boundary layer flashback in turbulent flow with wall-normal pressure gradient

The presence of swirl in combustion systems produces a marked change in their boundary layer flashback behaviour. Two aspects of swirling flow are investigated in this study: the effect of the swirl-generated wall-normal pressure gradient, and the effect of misalignment between the mean flow direction and the direction of flame propagation. The analysis employs Direct Numerical Simulation (DNS) of fuel-lean premixed hydrogen-air flames in turbulent planar channel flow with friction Reynolds number of 180. The effect of swirl on the flashback process is investigated by imposing a wall-normal pressure gradient profile. Analysis of the DNS data shows how the resulting differences in flow field and flame topology contribute to the differences in the overall flashback speed. Misalignment of the flow and propagation directions leads to asymmetry in the flame shape statistics as streaks of high velocity fluid in the boundary layer cleave into the flame front at an angle, yielding an increase in flame surface density away from the wall. Swirl has a stabilising effect on the turbulent flame front during flashback along the centre-body of a swirling annular flow due to the density stratification across the flame front, and produces a reduction in turbulent consumption speed. However the swirl also sets up a hydrostatic pressure difference that drives the flame forward, and the net effect is that the flashback speed is increased. The dominance of hydrostatic effects motivates development of relatively simple modelling for the effect of swirl on flashback speed. A model accounting for the inviscid momentum balance and for confinement effects is presented which adequately describes the effect of swirl on flashback speed observed in previous experimental studies.

The Effect of Longitudinal Pressure Gradient on Heat Transfer in a Separated Flow Behind a Sudden Expansion of the Channel

The results of an experimental study of the influence of longitudinal positive and negative pressure gradients in a rectangular flat channel with a backward-facing step on turbulent heat transfer in the zones of separation, attachment, and relaxation of the flow are presented. The studies were carried out in a turbulent flow regime at Reynolds numbers 4 × 103–1.2 × 104. The height of the step was equal to the half height of the channel before separation, so that the degree of its expansion was 1.5. The angle of diffuser opening varied from 0° to 4°, and confuser contraction ranged from 0° to 7.5°. The pressure fields and heat transfer coefficients in the recirculation and relaxation regions of the flow behind a sudden expansion of the channel were measured as a part of the experimental study. It is shown that with a change in the longitudinal pressure gradient, the behavior of the separated flow behind the step changes significantly. It has been determined that for a convergent channel with an increase in the pressure gradient, the maximum value of the Nusselt number increases, while for the expanding channel it decreases. The maximum Nusselt number position shifts downstream with diffuser expansion and approaches a step in the confusion flow.

A numerical study over the effect of curvature and adverse pressure gradient on development of flow inside gas transmission pipelines

In order to inspect the effects of adverse pressure gradient (APG) and curvature on the corrosion in the main gas transmission pipelines, the mean velocity and turbulence boundary layer on the walls of six different geometries including a straight pipe (A), a convex pipe (B1), a concave pipe (B2), a convex diffuser (C1), a concave diffuser (C2) and a straight diffuser (D) are calculated. The values of pressure gradient and curvature parameters are chosen 0.62 and 0.023, respectively. The results indicate that the corrosion in the concave curvature is greater than that the corrosion in the convex curvature, since the turbulence intensity increases in the concave curvature while it is suppressed in the convex curvature. In addition, when the boundary layer is exposed to APG and concave curvature simultaneously, the corrosion is greater than the situation when there is only APG or concave curvature. Ultimately, it was found that for the six studied geometries, there are two flow regimes (for velocities lower than 36 m/s) that the turbulence quantities are dependent on velocity. However, for velocities more than 36 m/s, the turbulence quantities and other affected quantities in the shear region are independent.

Aerodynamic investigation of the shock train in a scramjet with the effects of backpressure and divergent angles

AbstractNumerical simulations are carried out to study the effect of divergence angle and adverse pressure gradient on the movement of a shock wave train in a scramjet isolator. The commercial software tool ANSYS Fluent 16 was used to simplify the two‐dimensional Reynolds‐averaged Navier‐Stokes equation with the compressible fluid flow by considering the density‐based solver with the standard k‐ε turbulence model. The species transport model with a single‐step volumetric reaction mechanism is employed. Initially, the simulated results are validated with experimental results available in the open literature. The obtained results show that the variation of the divergence angle and backpressure on the scramjet isolator has greater significance on the flow field. Also, with an increase in the backpressure, due to the intense turbulent combustion, the shock wave train developed should expand along the length and also move towards the leading edge of the isolator leading to a rapid rise in the pressure so that the pressure at the entrance of the isolator can match the enhanced backpressures.

Numerical Study of Three-dimensional Boundary-layer Flow over a Wedge: Magnetic Field Analysis

The magnetohydrodynamic flow of a viscous fluid over a constant wedge in three- dimensional boundary-layer has been analyzed both numerically and asymptotically. The magnetic field is applied normal to the flow. The mainstream flows aligned with wedge surface are assumed to be proportional to the power of the coordinate distances. The system is described using three-dimensional MHD boundary-layer equations which are converted to couple nonlinear ordinary differential equations using similarity transformations. The resulting equations are solved numerically using the Keller-box method which is second-order accurate and asymptotically for far-field behavior. Both numerical and asymptotic solutions give good agreement in predicting the velocity behaviors and wall shear stresses. The effects of Hartmann number, pressure gradient and shear-to- strain-rate on the velocity fields are studied. Particularly, it is shown that the solutions of three-dimensional boundary-layer for variable pressure gradient exist, its effects are important on the boundary-layer flow. Results show that there are new families of solutions for some range of shear-to-strain-rate and there exists a threshold value of it beyond which no solutions exist. For some range of parameters, there is a reverse flow at which our boundary-layer assumptions are no longer valid. Various results for the velocity profiles, wall-shear stresses and displacement thicknesses are also obtained. The physical mechanisms behind these results are discussed.

Effect of pressure gradient in the connection region on the stability of the edge pedestal

We have numerically investigated the dependence of pedestal properties such as the pedestal height and the pedestal width on the normalized pressure gradient () in the connection region, . We used an ideal MHD stability code, MISHKA, and the pedestal predictive model, EPED1, to analyze the effect of on the edge stability and predict pedestal structure. Edge stability is affected by because the unstable mode extends radially into the core. Improvement of pedestal properties can be achieved by reducing . Effect of on the edge instability is largest for the intermediate mode n. Larger gradient of Shafranov shift, , also improves the pedestal width and height by stabilizing peeling-ballooning mode (PBM). Our result has been applied to JET hybrid discharges to explain the coupling between core and edge pressure profile in H-mode plasma configuration through and . The extended correlation loop between poloidal beta and the pedestal parameters is presented.

Turbulent kinetic energy budget in a wall-mounted cylinder wake using PIV measurements

In high flow velocity areas, turbulence intensity is high and flow variations may have a major impact on tidal turbines behaviour. Previous studies show that a square wall-mounted cylinder produces a very extended and energetic wake. In this work, two-component PIV measurements are conducted in the symmetry plane of the flow in order to evaluate the Turbulent Kinetic Energy (TKE) budget. This analysis enables to show how the TKE, produced in the shear-layer region, is re-distributed and dissipated within the flow. The Large-Eddy PIV method enables to obtain full spatial maps of dissipation and to assess the validity of the constant involved in the spectral method. Results show that the production occurs when the Reynolds shear stress is the more intense, so is the dissipation. Energy is then transported through turbulent motion into the outer flow and swept to the bottom due to the pressure gradient effects. Production is directly due to the periodic vortex shedding unlike for other terms. A better description of the energy exchanges in the turbulent wake flow is obtained. This knowledge is important for the performance determination of a tidal turbine positioned in such an obstacle wake which affects the flow-induced dynamic load on turbine.

Transient transfer shape factor for fractured tight reservoirs: Effect of the dynamic threshold pressure gradient in unsteady flow

AbstractIn fractured tight reservoirs, the seepage capacity of the matrix is poor, and fluid migration mainly depends on matrix/fracture transfer. An accurate understanding of the matrix/fracture flow is the basis of well tests and numerical simulations for tight reservoirs. In this paper, the unsteady flow equation for tight reservoirs is deduced based on the boundary layer theory, which can reflect the effect of the dynamic threshold pressure gradient, and the theoretical flow equation is verified by seepage experiments. Based on the study of the flow equation, the approximate semi‐analytical solution of the matrix/fracture unsteady transfer shape factor and the transfer function for tight reservoirs are established considering the early stage of matrix/fracture transfer (pressure does not propagate to the matrix center) and the late stage of matrix/fracture transfer (pseudo‐steady state). The results show that the shape factor of the tight reservoir is mainly affected by three factors (minimum threshold pressure gradient, static boundary layer thickness, and sensitivity coefficient of the fluid boundary layer), and the theoretical curves show that the intermediate transfer enters the pseudo‐steady state when the dimensionless time reaches approximately 0.14. The higher the minimum threshold pressure gradient is, the larger the transfer shape factor. The larger the static boundary layer thickness is, the larger the transfer shape factor; additionally, the larger the sensitivity coefficient of the fluid boundary layer is, the faster the change rate of the shape factor. Finally, the transfer shape factor is applied to a well test interpretation. Examples prove that the fitting accuracy of the new curve type is improved by 34.2% compared with the curve type for the conventional well test interpretation method.

Enabling Adaptive Mesh Refinement for Spectral-Element Simulations of Turbulence Around Wing Sections

The implementation of adaptive mesh refinement (AMR) in the spectral-element method code Nek5000 is used for the first time on the well-resolved large-eddy simulation of the turbulent flow over wings. In particular, the flow over a NACA4412 profile with a 5^circ angle of attack at chord-based Reynolds number {text {Re}}_c=200{,}000 is analyzed in the present work and compared with a previous conformal simulation used as baseline. The mesh, starting from a coarse resolution, is progressively and automatically refined by means of AMR, which allows for high resolution near the wall and wake whereas significantly larger elements are used in the far-field. The resulting mesh, which remains unchanged in the production runs (i.e. AMR is used to create the final mesh, which is then fixed), is of higher resolution than those in previous conformal cases, and it allows for the use of larger computational domains, avoiding the use of precursor RANS simulations to determine the boundary conditions. This is achieved with, approximately, 2 times lower total number of grid points if the same spanwise length is used. Turbulence statistics obtained in the AMR simulation show good agreement with the ones obtained with the conformal mesh, and the pressure-coefficient distribution along the wing surface matches pressure-scan experimental data obtained in the MTL wind tunnel at KTH. The use of AMR is therefore expected to enable the simulation of high-Reynolds numbers turbulent flows over complex geometries (such as wings), thus allowing the study of pressure-gradient effects at high Reynolds numbers relevant for practical applications.

Solving the Nonlinear Boundary Layer Flow Equations with Pressure Gradient and Radiation

The physical problem under consideration is the boundary layer problem of an incompressible, laminar flow, taking place over a flat plate in the presence of a pressure gradient and radiation. For the mathematical formulation of the problem, the partial differential equations of continuity, energy, and momentum are taken into consideration with the boundary layer simplifications. Using the dimensionless Falkner–Skan transformation, a nonlinear, nonhomogeneous, coupled system of partial differential equations (PDEs) is obtained, which is solved via the homotopy analysis method. The obtained analytical solution describes radiation and pressure gradient effects on the boundary layer flow. These analytical results reveal that the adverse or favorable pressure gradient influences the dimensionless velocity and the dimensionless temperature of the boundary layer. An adverse pressure gradient causes significant changes on the dimensionless wall shear parameter and the dimensionless wall heat-transfer parameter. Thermal radiation influences the thermal boundary layer. The analytical results are in very good agreement with the corresponding numerical ones obtained using a modification of the Keller’s-box method.

Compressible plane turbulent wakes under pressure gradients evolving in a constant area section

Development of statistically two-dimensional (2-D) turbulent wakes under pressure gradients is a common feature of many industrial and aerodynamic flows. The usual set-up is to generate a wake, and study its development through a passage with a variable area; if the downstream area decreases (increases) a favourable pressure gradient or FPG (adverse pressure gradient or APG) is imposed. In applications such as in turbomachinery, however, the wakes develop in a periodic constant area passage in the stator–rotor gap and with an imposed pressure gradient. To study these flows, here, we develop a canonical set-up for this new kind of wake evolution in FPG and APG of different strengths by placing a 2-D flat plate normal to the flow in a periodic constant area passage and a fixed inflow mass flux. Employing compressible direct numerical simulations, we impose pressure gradients through a ramped body force term to the momentum and total energy equations while the wake is allowed to develop spatially in a region of fixed width. The resultant mean velocity statistics, wake width, energy budgets and entropy generation rates are scrutinised to assess the effect of the pressure gradients, and where possible, the similarities and differences to the conventional case of variable area pressure gradients are discussed. The results show that the effect of a constant area pressure gradient on flow statistics is non-trivial, resulting from significant density changes. The pressure gradients also have an effect on the different energy budgets, which produces a gain for FPG and loss for APG in the mean kinetic energy. Consequently, the entropy generation rate diminishes and augments for the FPG and APG, respectively, compared to the zero pressure gradient. Finally, the effect of different passage heights ( ) relative to the wake half-width ( ) is studied using large eddy simulations. We find that wake width and hence the spreading, depends primarily on the wake–wake interaction for small and pressure gradients for larger , and this has implications for the design of turbomachinery.

An improved prediction model for corner stall in axial compressors with dihedral effect

Corner stall predictions are important and difficult in axial compressors. However, all of the prediction models have proved to be ineffective for advanced compressor blades, which tend to use the combined sweep and dihedral. As for the prediction parameter DL, although it effectively modeled the effects of the adverse pressure gradient and secondary flow, it failed to predict the corner stall of curved blades because the model failed to consider the intersection of the boundary layer at the corner region. In this paper, the shape factor gradient Ψ of the boundary layer at the corner region was investigated by numerically studying specially shaped expansion pipes under different adverse pressure gradients. The improved prediction parameter DJ was presented based on the model of Ψ and the circumferential pressure gradient ξ. A comparison of the critical range of the prediction parameters DL and DJ was investigated using the NACA65 cascade database, which was established by a numerical method. Then, the stall criterion was validated according to the experimental results of various test facilities with different blade geometries and experimental conditions. The results show that the improved prediction parameter is able to predict the corner separation/stall flows and is in good agreement with the experimental results for axial compressors with three-dimensional designed blades.

Pore Network Modeling of the Effects of Viscosity Ratio and Pressure Gradient on Steady-State Incompressible Two-Phase Flow in Porous Media

We perform steady-state simulations with a dynamic pore network model, corresponding to a large span in viscosity ratios and capillary numbers. From these simulations, dimensionless steady-state time-averaged quantities such as relative permeabilities, residual saturations, mobility ratios and fractional flows are computed. These quantities are found to depend on three dimensionless variables, the wetting fluid saturation, the viscosity ratio and a dimensionless pressure gradient. Relative permeabilities and residual saturations show many of the same qualitative features observed in other experimental and modeling studies. The relative permeabilities do not approach straight lines at high capillary numbers for viscosity ratios different from 1. Our conclusion is that this is because the fluids are not in the highly miscible near-critical region. Instead they have a viscosity disparity and intermix rather than forming decoupled, similar flow channels. Ratios of average mobility to their high capillary number limit values are also considered. Roughly, these vary between 0 and 1, although values larger than 1 are also observed. For a given saturation, the mobilities are not always monotonically increasing with the pressure gradient. While increasing the pressure gradient mobilizes more fluid and activates more flow paths, when the mobilized fluid is more viscous, a reduction in average mobility may occur.

A 3D Gas and Water Simulator Considering Nonlinear Flow Behaviors for Abnormal High-Pressure Tight Gas Reservoirs

Fluid flow in tight gas reservoirs with abnormal high pressure presents nonlinear behaviors. A mathematical description of these behaviors is essential for establishing the flow model. In this study, a mathematical model is presented that describes the effect of threshold pressure gradient and rock deformation on gas flow parameters in a tight gas reservoir. A fully implicit 3D gas and water phase numerical model was derived using the finite difference method. Based on software engineering principles, a 3D gas and water simulator was developed, which can be used in research on nonlinear flow mechanisms and flow simulation in abnormal high-pressure gas reservoir. The simulator proved to be reliable through a comparison with a commercial simulator, and it was used successfully for prediction of gas production in the M reservoir.

Pressure gradient tailoring effects on the mechanisms of bluff-body flame extinction

The mechanisms of flame blowout under pressure gradient effects are explored for a bluff-body stabilized flame. The blowout process is induced through equivalence ratio reduction from a lean stabilized flame to complete blowout. Simultaneous high-speed particle image velocimetry (PIV) and C2*/CH* chemiluminescence imaging diagnostics are used to obtain the instantaneous flame structure, vorticity field, equivalence ratio, and local strain rate during the extinction process. The goal is to elucidate the effect of flame-generated vorticity on lean flame extinction. Three test-sections configured as a nozzle, a rectangular duct, and a diffuser, are used to alter the downstream pressure gradient yielding high, nominal, and low magnitudes of flame-generated baroclinic torque. For all three configurations, the flame brush narrows and the shear layer vorticity expands in the transverse direction resulting in flame-shear interactions and extinction. The flame-shear layer interaction increases the strain rate along the flame; however, the strong flame-generated vorticity for the nozzle case delayed the strain rate increase by keeping the flame away from the shear layer the longest. The sharp increase in the Karlovitz number above unity caused by the sudden increase in the strain rate corresponds to the time of flame brush contraction and shear layer width expansion. It is shown that the downstream pressure gradient can either augment or attenuate the time required for the Karlovitz number to reach a critical value of unity, which is associated with local extinctions along the flame. In all of the test-section configurations, the flame-generated vorticity has a weak influence on the Bénard von Kármán (BVK) instability mode and its harmonics. The Strouhal number during blow-out remained relatively constant in all of the cases showing greater sensitivity to the shear layer length than to the BVK frequency.

Bypass transition in boundary layers subject to strong pressure gradient and curvature effects

This paper aims at characterizing the bypass transition in boundary layers subject to strong pressure gradient and curvature effects. A series of highly resolved large-eddy simulations of a high-pressure turbine vane are performed, and the primary focus is on the effects of free-stream turbulence (FST) states on transition mechanisms. The turbulent fluctuations that have convected from the inlet first interact with the blunt blade leading edge, forming vortical structures wrapping around the blade. For cases with relatively low-level FST, streamwise streaks are observed in the suction-side boundary layer, and the instabilities of the streaks cause the breakdown to turbulence. Moreover, the varicose mode of streak instability is predominant in the adverse pressure gradient region, while the sinuous mode is more common in the (weak) favourable pressure gradient region. On the other hand, for cases with higher levels of FST, the leading-edge structures are more irregularly distributed and no obvious streak instability is observed. Accordingly, the transition onset occurs much earlier, through the breakdown caused by interactions between vortical structures. Comparing between different cases, it is the competing effect between the FST intensity and the stabilizing pressure gradient that decides the path to transition and also the transition onset, whereas the integral length scale of FST affects the scales of the streamwise streaks in the boundary layer. Furthermore, while the streaks in the low-level FST cases are mainly induced by leading-edge vortical structures, the corresponding fluctuations show a stage of algebraic growth despite the weak favourable pressure gradient and curvature.

Effects of favorable pressure gradient on turbulence structures and statistics of a flat-plate supersonic turbulent boundary layer

A Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a moderate favorable pressure gradient (FPG) induced by external expansion waves is investigated through direct numerical simulation and compared with a zero pressure gradient (ZPG) boundary layer. It is found that under FPG, the logarithmic region in the van Driest transformed velocity profile is lifted above the log law, while the wake region deviates below its ZPG counterpart. The near-wall streaks are elongated in the streamwise direction with wider spanwise spacing, which leads to an attenuated meandering effect compared to the ZPG case. Although small-scale motions in the outer layer are evidently suppressed, they survive mostly in the inner layer. On the other hand, large-scale motions tend to correlate further with the lifted fluid from upstream due to bulk dilatation. However, their relative locations within the boundary layer remain unchanged. Different responses of turbulence structures in the inner and the outer layer to FPG show that this two-layer feature within the boundary layer is mainly associated with the bulk dilatation rather than the wall curvatures. The profiles of turbulent kinetic energy (TKE) and turbulent Mach number also show a two-layer behavior, where the reduction in turbulence in the outer layer is more prominent than in the inner. Positive convection occurs from the buffer to the outer layer according to the TKE budget analysis, which compensates the production and resists the decrease in the turbulence level.

Elliptic Flow of Identified Particles in Pb–Pb Collisions at sNN=5.02 TeV

In this paper, by using a Tsallis-Pareto-type function and the multisource thermal model, the elliptic flow coefficients of particles π±, K±, p+p¯, Λ+Λ¯, and KS0 produced in Pb–Pb collisions at the center-of-mass energy of sNN=5.02TeV are investigated. In the process of collisional evolution, because of geometric structure, pressure gradient, and thermal diffusion effects, deformation and translation occurred in the isotropic emission source, leading to anisotropy in the azimuth distribution of the final-state particles. Based on these dynamic factors, the dependence of elliptic flow on transverse momentum is described as well.

Impact of pressure gradients on fish scales in a jet fish pump

Pressure gradients cannot be avoided in jet fish pumps due to their contracting and expanding sections. Pressure gradients are an important source of fish injuries, particularly for damage to fish scales. The distribution of pressure on the surface of a fish passing through a jet fish pump was studied experimentally and also by numerical simulation. A theoretical model of the forces on fish scales caused by pressure gradient was established. The results showed that the pressure on the surface a fish firstly decreases and then increases as fish passes through a jet pump. Surface pressures reach a minimum when the fish is in the throat. Pressure gradient is also a key factor for damaging fish scales. Axial pressure gradients were greater at the inlet and outlet of the throat than in other parts of the pump and radial pressure gradients increased with radial position. Also, the greater the flow rate the higher both axial and radial pressure gradients produced. Radial position is therefore an important factor for both pressure gradients and determining the force on fish scales. The forces caused by pressure gradients on scales increase with radial distance and with flow rate ratio. Thus, this study specifies the effects of pressure gradients on fish scales in a jet fish pump and discusses the relative influencing factors. These results could provide a basis for improved jet fish pump designs.