Steady-state Flow Regime Research Articles

Optimum experimental design of a monitoring network for parameter identification at riverbank well fields

• Hydraulic properties of riverbed are an important indicators of clogging. • A quasi-steady state criterion under riverbank filtration was proposed. • A model-oriented approach to designing monitoring network was applied. A steady-state flow regime in riverbank well fields is often violated by fluctuations in river stages and variations in groundwater extraction. In this study, a criterion of quasi-steady flow during filtration processes at riverbank well fields was introduced. Under the assumption of steady-state flow, an analytical approach for determining the key hydraulic parameters (aquifer transmissivity and riverbed filtration resistance) between a stream and a hydraulically connected aquifer during riverbank filtration was presented. An optimal regular observation network (consisting of the locations of monitoring wells and the observation regime), which is based on the model-oriented approach using an example of a riverbank well field near the Kuybyshev Reservoir, Russia, was designed to minimise the uncertainty in the estimates of hydraulic parameters. The analyses showed that the initial recession in the surface water levels for the simplest constant groundwater withdrawal patterns can be used to determine the key hydraulic parameters; the error in these estimated parameters was less than 7% or 12%, depending on the designed monitoring network. When comparing the two typical monitoring networks, observation line A–A that passes midway through the water supply wells performed better than observation line B–B that passes through the water supply wells when estimating the hydraulic parameters. The results of this study can be used as a reference for designing and optimising a monitoring network that aims to determine the key hydraulic parameters at riverbank well fields.

Numerical investigation of incompressible fluid flow and heat transfer across a bluff body in a channel flow

The Lattice Boltzmann Method is applied to computationally investigate the laminar flow and heat transfer of an incompressible fluid with constant material properties in a two-dimensional channel with a built-in bluff body. In this study, a triangular prism is taken as the bluff body. Not only the momentum transport, but also the energy transport is modeled by the Lattice Boltzmann Method. A uniform lattice structure with a single time relaxation rule is used. For obtaining a higher flexibility on the computational grid, interpolation methods are applied, where the information is transferred from the lattice structure to the computational grid by Lagrange interpolation. The flow is investigated for different Reynolds numbers, while keeping the Prandtl number at the constant value of 0.7. The results show how the presence of a triangular prism effects the flow and heat transfer patterns for the steady-state and unsteady-periodic flow regimes. As an assessment of the accuracy of the developed Lattice Boltzmann code, the results are compared with those obtained by a commercial Computational Fluid Dynamics code. It is observed that the present Lattice Boltzmann code delivers results that are of similar accuracy to the well-established Computational Fluid Dynamics code, with much smaller computational time for the prediction of the unsteady phenomena.

Magnetohydrodynamic flow excited by rotating permanent magnets in an orthogonal container

Liquid metal magnetohydrodynamic flow driven by a system of rotating permanent magnets in a container of orthogonal cross-section has been studied. The main objective of the work is to research the impact of magnetic forcing parameters (magnetic field value, magnets arrangement, and angular velocity of their rotation) on the generated hydrodynamic structures and flow modes. On this basis, we contemplate realizing required flow features by setting certain parameters of the driving magnetic system. A numerical study of the problem in the induction-free approximation without taking into account the effect of the variable component of electromagnetic force is presented. The parameters of spin-up modes and steady-state flow regimes have been calculated by three-dimensional direct numerical simulation based on COMSOL Multiphysics 4.3a software and experimentally verified on a specially designed setup using noninvasive Doppler ultrasound technique.

Physical thermo-mechanical simulation of magnesium: An in-situ diffraction study

Time-resolved, two-dimensional synchrotron high-energy X-ray diffraction has been utilized for the in-situ investigation of the microstructural evolution of magnesium, during heating and during plastic deformation at various temperatures. Throughout static heating of the as-extruded material, first recovery, then recrystallization and finally grain growth occurred with increasing temperature. Grain rotation was observed during grain growth of the static heated samples. Subsequent plastic deformation, through compression, at lower temperatures revealed the activated deformation systems. At room temperature, extension-twinning flips the crystallite orientations abruptly from the extrusion to the compression fiber texture. In contrast, at elevated temperatures, twinning is negligible and the texture reorientation progresses in a gradual steady-state flow regime, ending in a tilted basal texture with a tilt angle depending on the degree of deformation. The methodology described herein offers parametric studies related to microstructural and deformation processes in an unprecedented way.

Pressure Data Analysis in Two Phase Naturally Fractured Reservoirs With a Pseudo Steady State Flow Regime Using the TDS Technique

The matrix-to-fracture interporosity parameter (λ), and fracture storativity (ω) are subject to changes during the life of an oil field. This depends entirely on the nature of saturation condition both in fractures and matrix blocks. Failure to consider two-phase flow parameters will result in inaccurate estimation of reservoir parameters. Because of the high amount of this type of behavior in many reservoirs worldwide, developing appropriate method is very important. A new procedure is presented for analyzing transient test in naturally fractured reservoirs with pseudo steady state two-phase (oil and water) flow using direct synthesis technique (TDS) to determining reservoir parameters. TDS is a modern technique that utilizes the characteristic lines and points found on the pressure and pressure derivative log-log plot. These points and lines are then used with appropriate equations to solve directly for desired reservoir parameters. The proposed methodology is successfully verified by its application to field simulated pressure data and a step-by-step procedure for calculating these parameters is included.

Pressure transient analysis for a reservoir with a finite- conductivity fault

The signature of the pressure derivative curve for reservoirs with finite-conductivity faults is investigated to understand their behavior and facilitate the interpretation of pressure data. Once a fault is reached by the disturbance, the pressure derivative displays a negative unit-slope indicating that the system is connected to an aquifer, meaning dominance of steady-state flow regime. Afterwards, a half-slope straight- line is displayed on the pressure derivative plot when the flow is linear to the fault. Besides, if simultaneously a linear flow occurs inside the fault plane, then a bilinear flow regime takes place which is recognized by a 1/4 slope line on the pressure derivative line. This paper presents the most complete analytical well pressure analysis methodology for finite-conductivity faulted systems using some characteristics features and points found on the pressure and pressure derivative log-log plot. Therefore, such plot is not only used as diagnosis criterion but also as a computational tool. The straight-line conventional analysis is also complemented for characterization of finite- and infinite-conductivity faults. Hence, new equations are introduced to estimate the distance to fault, the fault conductivity and the fault skin factor for such systems. The proposed expressions and methodology were successfully tested with field and synthetic cases.

Unified Fracturing Design for Water Injection Well under Steady State Flow Regime

Unified Fracture Design for fracturing optimization is a simple and reliable way to push the limit of the injection ability, reported frequently in recent years. However, most studies focus on fracture design under pseudo-steady state flow regime. The analysis of the different pressure systems between water injection well and oil production well tells us that the steady flow regime in the formation takes up most life span of water injection wells, associated with the field experience. To maximize injection capability for fractured vertical water wells under this regime, a physical optimization method is developed based on the concept of proppant number. Meanwhile, two new type curves without consideration of formation damage are obtained for quantifying the correlation between dimensionless injectivity and dimensionless conductivity. Then, calibrated design procedures accounting for gel damage and non-darcy effect, are also proposed. Finally, sensitivity studies are addressed to clarify the effect of several variables on the optimum fracture geometry.

Hemodynamics of the aortic valve and root: implications for surgery.

Hemodynamics of the aortic valve and root: implications for surgery.

Spin Drift Velocity, Polarization, and Current-Driven Domain-Wall Motion in (Ga,Mn)(As,P)

Current-driven domain-wall motion is studied in (Ga,Mn)(As,P) ferromagnetic semiconducting tracks with perpendicular anisotropy. A linear steady state flow regime is observed over a large temperature range of the ferromagnetic phase (0.1T(c)<T<T(c)). Close to 0 K, the domain-wall velocity is found to coincide with the spin drift velocity. This result is obtained below the intrinsic threshold for domain-wall motion which implies a nonadiabatic contribution to the spin transfer torque. The current spin polarization is deduced close to 0 K and to T(c). It suggests that the temperature dependence of the spin polarization can be inferred from the domain-wall dynamics.

A probabilistic determination of the limit pressure of an oil pipeline with longitudinal cracks

An algorithm is developed for the probabilistic determination of the internal limiting pressure at a tested section of an oil pipeline with a longitudinal axial crack, in a steady-state oil flow regime, given the required standard level of reliability.

On mechanism of flow softening in Ti–5Al–5Mo–5V–3Cr

The flow behaviour of Ti–5Al–5Mo–5V–3Cr with an initial microstructure containing acicular α platelets has been characterised during isothermal subtransus forging. Flow softening was observed, following yielding and limited hardening, for all investigated temperatures and strain rates, before a steady state flow regime being reached at a strain of ∼0·5. The acicular α plates were found to have been fragmented by the forging process, which is concurrent with previous findings. The flow behaviour of the fully retained β phase below the β transus temperature has been established and found to be similar to that of the steady state flow of platelet α in a β matrix. Forging the acicular α microstructure to low strains resulted in higher dislocation concentrations in the β matrix than could be observed in the α precipitates, supporting the hypothesis of hardening through dislocation impedance. Evidence of fragmentation via a pinch-off mechanism was found where slip was observed to have been transmitted across an α plate. Thus following yield the flow behaviour is dominated by the pile-up of dislocations at the α/β interface before the transmission of slip leads to plate fragmentation resulting in flow softening to a steady state regime governed entirely by the β matrix.

Specific interfacial area: The missing state variable in two‐phase flow equations?

Classical Darcy's equation for multiphase flow assumes that gravity and the gradient in fluid pressure are the only driving forces and resistance to the flow is parameterized by (relative) permeability as a function of saturation. It is conceivable that, in multiphase flow, other driving forces may also exist. This would mean that such nonequilibrium effects are lumped into a permeability coefficient. Indeed, many studies have shown that the relative permeability coefficient generally depends not only on saturation but also on dynamics of the system. Through the application of rational thermodynamics, a theory of two‐phase flow had been developed in which interfacial areas were introduced as separate thermodynamic entities and their macroscale effects were explicitly included. This theory includes new driving forces whose significance needs still to be established. To study new terms in the theory, we employ a dynamic pore network model called DYPOSIT. A long pore network (several representative elementary volumes connected in series) is generated, which represents as a one‐dimensional porous medium column. This model provides pore scale distribution of local phase pressures, capillary pressure, interfacial area, saturation, and flow rate, which are averaged to obtain the macroscale distributions of these variables. Our analysis shows that there are discrepancies between the simulation results and the classical equations to describe the transient behavior, especially for the nonwetting phase transient permeability. The coefficients in the extended equations are quantified and parameterized. Although under the applied Dirichlet boundary conditions, flow varies significantly, there is a clear trend illustrating dependency of coefficients on saturation, independent of dynamic conditions. Furthermore, using the new coefficients, it is possible to explain either transient or steady state flow regimes, which is a new achievement.

Geophysical flows with anisotropic turbulence and dispersive waves: flows with a β-effect

Geostrophic turbulence is a key paradigm in the current understanding of the large-scale planetary circulations. It implies that a flow is turbulent, rotating, stably stratified, and in near-geostrophic balance. When a small-scale forcing is present, geostrophic turbulence features an inverse energy cascade. When the meridional variation of the Coriolis parameter (or a β-effect) is included, the horizontal flow symmetry breaks down giving rise to the emergence of jet flows. The presence of a large-scale drag ensures that the flow attains a steady state. Dependent on the governing parameters, four steady-state flow regimes are possible, two of which are considered in this study. In one of these regimes, a flow is dominated by the drag while in the other one, the recently discovered regime of zonostrophic turbulence, a flow becomes strongly anisotropic and features slowly evolving systems of alternating zonal jets. Zonostrophic turbulence is distinguished by anisotropic inverse energy cascade and emergence of a new class of nonlinear waves known as zonons. In addition, meridional scalar diffusion is strongly modified in this regime. This paper provides an overview of various regimes of turbulence with a β-effect, elaborates main characteristics of friction-dominated and zonostrophic turbulence, elucidates the physical nature of the zonons, discusses the meridional diffusion processes in different regimes, and relates these results to oceanic observations.

Microflow hydrodynamics in slits: Effects of the walls relative roughness and spacer inter-filaments distance

A slit designed with very tight dimension tolerances was manufactured to perform pressure drop measurements in fully developed laminar flows, viewing the isolation of the effects of the walls roughness from those of the entrance developing flow and from uncertainties in the channel height. For that, five different values of the slit height, 0.7, 1.0, 1.2, 1.5 and 2.0 mm, were used together with five differently finished surfaces for the channel bottom wall, possessing average roughness values of 31.4, 11.4, 4.1, 1.3 and below 1 μm, which is the sensor detection limit of the contact profilometer used for the measurements. The slit allows also for flow visualization and can accommodate cylindrical-type spacers, positioned transversally to the flow and in direct contact with the bottom wall, with diverse inter-filament distances to study the critical Reynolds numbers marking the departure from the steady-state laminar flow regime. Results with deionised water and 5.4–13.9% of uncertainty for the pressure drop in the open channel showed that surface phenomena due to roughness, irrelevant at macroscale flows, are present in flows like those studied herein. Flow visualization for the same fluid and pressure drop measurements in the channel filled with ladder-type spacers showed that its height is crucial in the set up of the flow instabilities marking the departure from steady laminar flow.

Evaluation of Chlorine Decay in Drinking Water Systems for Different Flow Conditions: From Theory to Practice

An intensive study was developed to assess the influence of different flow conditions in the chlorine decay of drinking water systems based on a series of experiments tested on a loop pipe linked to the Lisbon water distribution system. Water samples and chlorine measurements were taken under three distinct flow conditions: (1) steady-state regimes; (2) combined flow situations—an initial steady-state period, followed by successive transient events and a new steady-state period; (3) isolated flow tests—steady-state flow regimes and transient flow regimes performed independently. All the tests were replicated for a typical range of Reynolds numbers in real water distribution systems. More specifically, pressure and velocity variations associated with hydraulic transients or water hammer conditions may degrade water quality. The series of results obtained in steady-state flow conditions confirmed the rate of chlorine decay increases with the Reynolds number and provided evidence that hydraulic transients have a slowing-down effect on chlorine decay rates.

On the statistical steady state gas-solid flow in a riser as predicted through a two-fluid simulation

This work is concerned with the extremely high computational costs of the two-fluid simulations of gas-solid flows in risers. In a previous article [1] a procedure was proposed to speed up the simulations towards the desired statistical steady state flow regime. In this continuing article the concern is turned to the time extent that a simulation must advance inside the statistical steady state regime so that suitable time averaged predictions can be made. An analysis is carried out using the results of a transient two-fluid simulation of a riser flow performed inside the statistical steady state regime. Time averaged results were produced considering different time averaging intervals of 5, 10, 15 and 20 seconds. Both the transient behavior of the predictions and the time averaged results are discussed. For the present case, it was found that 10 seconds of fluidization taken inside the statistical steady state regime are enough for a reasonable qualitative description of the average flow.

The role of capillary water in the stability of tailing dams

Tailings storage facilities are complex geotechnical structures. The present paper focuses on the study of a case-history, a tailing dam from the nickel industry located in Cuba, with the objective of gaining knowledge about the geotechnical behaviour of such structures. The dam behaviour was modelled by means of a coupled hydro-mechanical finite element formulation. Due to the low permeability of tailings, the phreatic surface in the deposit remains high during and after its construction. Steady-state flow regime would be reached only several decades after closure. Moreover, capillary rise causes the saturation degree to stay high in the whole storage. Under the action of rain storms, phreatic levels rise quickly due to the presence of capillary water. Following the end of the storm, phreatic levels fall slowly because of the low hydraulic conductivity. The results of the analysis show that the stability of the dam strongly depends on capillary phenomena. In the light of this conclusion it seems reasonable to propose including the measurement of capillary water in the standard monitoring schedule of tailing dams.

SCDAP/RELAP5 application to CANDU6 fuel channel analysis under postulated LLOCA/LOECC conditions

Using SCDAP/RELAP5 (RELAP/SCDAPSIM Mod 3.4), a model with postulated boundary conditions has been developed to simulate the evolution of the fuel channel in a CANada Deuterium Uranium reactor type (CANDU6) during a large loss of coolant accident (LLOCA) with a coincidence of a loss of emergency cooling (LOECC). The accident simulation is initiated from the steady-state flow regime and different steam mass flow rates are imposed in order to run sensitivity calculations of the heatup phase. Results are compared to referenced CHAN II code results for the same accident boundary conditions, concerning the fuel and pressure tube temperatures, power components (generated and exchanged to the moderator) and hydrogen production. The input model is applied both to the intact and to the disassembled bundle with 37 fuel elements. The paper includes a brief discussion of the capabilities of the present SCDAP component models, dedicated to PWR–BWR reactor components, to treat the degradation phenomena in the fuel channel during severe accidents in CANDU reactors, and also of the developments needed to enhance the quality of the code predictions.

Scales of free convection around a vertical cylinder

The natural scales of the laminar steady-state free convection flow regime surrounding an isothermal vertical cylinder are established. It is shown that nondimensionalizing the momentum and energy equations in terms of the Rayleigh or Boussinesq numbers allows the use of the Prandtl number as a criterion to establish whether the motive buoyancy force is mainly balanced by inertia or by friction. Instead, in the conventional formulation based on the Grashof number, this distinction is not possible.

Powder Flow Testing with 2D and 3D Biaxial and Triaxial Simulations

AbstractThe mechanical response of frictional powders under quasi‐static loading is studied by means of two‐ and three‐dimensional discrete element methods, compared directly with each other. The response of the system is characterized by elastic behavior for very small deformations, softening, plastic yield and critical state flow at large strain. The maximal yield stress is reached for some finite deformation of a few percent, but the decay to the critical steady state flow regime is much slower in the 3D situation than in the 2D systems examined here. The critical state regime is thus reached much later and at considerably higher dilation level in 3D. Possible reasons for this qualitative difference are discussed but more studies are needed to identify them properly.