Экспериментально-теоретическое исследование обтекания сферы с учетом вдува газа с ее поверхности

New methods for studying the effect of gas injection from the surface of a solid spherical particle on its drag coefficient in the transient and self-similar regimes of flow around the particle have been presented. An advantage of the proposed methods is the ability to isolate in a pure form the effect of the mass flux from the particle surface (without the effect of other factors, for example, particle acceleration) on the drag coefficient. New results of an experimental study of the effect of air flow blowing on the drag coefficient of a solid perforated sphere in the Reynolds number range Re = 133÷9900 have been presented. It has been shown that the drag coefficient decreases when air is blown from the particle surface. As the Reynolds number Re increases, the drag coefficient CD upon gas injection in the transient flow regime decreases to a certain critical value corresponding to the onset of the self-similar regime. At the onset of the selfsimilar regime (reaching the critical value of CD), the drag coefficient increases with an increase in the Reynolds number and asymptotically tends to a constant value CD = 0.44. However, the opposite effect has been found for a small diameter of the particle (D = 1 cm) at a blowing velocity ue ≥ 1.3 m/s: an increase in the drag coefficient of the particle CD at air efflux from the particle surface in comparison with the drag coefficient value in the absence of gas flow injection (ue = 0 m/s). This is apparently associated with a change in the characteristics of the boundary layer of the particle due to the rearrangement of the flow profile near the spherical particle surface caused by a decrease in its size. An empirical dependence of the drag coefficient of a solid sphere on the ratio of the velocity of injection from the surface of the particle to the velocity of blowing CD = 0.15 + (0.44 - 0.15)/ (1 + 9ū/53.8) (with the coefficient of determination R2 = 0.89) has been obtained for a self-similar particle regime flow. Contribution of the authors: the authors contributed equally to this article. The authors declare no conflicts of interests.

The slow unsteady settling of a fluid sphere toward a flat fluid interface

In this paper, the effect of free-stream turbulence (FST) on the flow over a sphere is experimentally investigated at the Reynolds numbers of 0.5×105–2.8×105. Three levels of FST are generated in a wind tunnel by installing three different types of grids upstream of the sphere. It is found that FST triggers the boundary layer instability above the sphere surface and delays the separation. Once laminar separation occurs, the disturbances both from the boundary-layer instability and FST trigger the shear-layer instability. Then, high momentum is entrained toward the sphere surface and the separated flow is reattached, forming a separation bubble on the sphere surface. Due to high momentum near the surface, the main separation is delayed and the drag is reduced. The critical Reynolds number, at which the drag coefficient decreases rapidly, decreases as the FST intensity increases. With increasing Reynolds number, the first separation point moves downstream, but the reattachment and main separation points are nearly fixed, resulting in a constant drag coefficient. As the Reynolds number further increases, the separation bubble finally disappears but the main separation point is still nearly unchanged, resulting in a constant drag coefficient within the Reynolds number range considered. Therefore, the formation, regression, and disappearance of a separation bubble on the sphere surface are the key mechanisms of the drag change by FST.

It is shown that in flow past a system of spheres of radius a situated at the nodes of a cubic lattice with the period b in the direction of one of the principal translations of the lattice under the condition (a/b) · · P1/3≪1 (P is the Peclet number, P≫1), the concentration of dissolved material absorbed by the sphere surfaces diminishes logarithmically at distances large compared with b, but small compared with L=Pb2/4πa. At distances considerably larger than L, the decrease is described by an exponential law which coincides with the law of concentration decrease at distances much larger than b in the case of a spatially homogeneous distribution of the spheres. We consider the flow of an incompressible fluid with the velocity U past a system of spheres of radius a. We assume that the Reynolds number R=Ua/ν (where ν, the kinematic viscosity coefficient, is much larger than unity). Dissolved in the fluid is a material of concentration c which is absorbed by the sphere surfaces. The diffusion coefficient D is assumed to be sufficiently small for the Peclet number P=Ua/D to be much larger than unity. The spheres are situated at the nodes of a cubic lattice with the period b. As will be shown below, it is necessary that P(a/b)3≪1. Under these assumptions the concentration varies in a thin (of the order aP−1/3) diffusion layer near the surface of each sphere. A diffusion wake is formed behind each sphere. The transverse dimensions of this wake for a sufficiently widely spaced lattice (aP1/3≪ ≪b) exceed the effective thickness of the diffusion boundary layer, which enables us to reduce the problem of concentration absorption on the surface of the system of spheres to the problem considered by Levich [1] concerning the convective diffusion of a material of constant constant concentration flowing past a single sphere. Hasimoto [2] considers the solution of the Stokes equation describing the motion of a viscous fluid past an array of spheres situated at the nodes of a cubic lattice. However, he does not give an expression for the velocity field applicable near the surface of some single sphere which is necessary to the solution of the diffusion problem. In the method of Lamb [3] (§336) and Burgers [4], in dealing with the flow of a viscous stream past a single sphere, one considers the equation of motion in space, including the interior of the sphere, and not just the solution of the equation in the space outside the sphere with boundary conditions at the sphere surface. At the center of the sphere one places a concentrated force and a system of multipoles whose magnitude is chosen in such a way as to ensure fulfillment of the required boundary conditions. This idea of introducing an effective potential is used in [2] to find the velocity field of a fluid flowing past an array of spheres. We propose a treatment of the effective potential method somewhat different from that of [2].

Near-miscible gas injection represents a number of processes of great importance to reservoir engineers including hydrocarbon gas injection and CO2 flood. Very little experimental data is available in the literature on displacements involving very low-IFT (interfacial tension). In this paper, we present the results of a series of two-phase and three-phase gas injection (drainage) and oil injection (imbibition) core flood experiments for an gas/oil system at near-miscible (IFT= 0.04 mN.m‒1) conditions. Two different cores; a high-permeability (1000 mD) and a lower permeability (65 mD) core were used in the experiments and both water-wet and mixed-wet conditions were examined. The results show that despite a very low gas-oil IFT, there is significant hysteresis between the imbibition and drainage oil and gas relative permeabilities (kr) curves in the 65mD core. Hysteresis was less for 1000mD core (compared to the 65 mD core) but it still could not be ignored. Near-miscible kr hysteresis was significant for both water-wet and mixed-wet systems. Presence of immobile water in the water-wet cores improved oil relative permeabilities but reduced gas relative permeabilities in both imbibition and drainage directions. As a result, oil recovery for gas injection experiments improved when the rock contained immobile water. Both oil and gas relative permeabilities reduced when the rock wettability was altered to mixed wet from water wet and as a result, oil recovery by gas injection in the mixed-wet rock was less than that obtained under water-wet conditions. We offer explanations for these observations based on our understanding of the pore-scale interactions and mechanisms, the distribution of fluid phases and their spreading bahaviour. The results help us better understand the impact of some of the important parameters pertinent to kr and its hysteresis especially in very low IFT gas-oil systems and mixed-wet rocks. Understanding these effects and behavior is important for improved prediction of the performance of gas injection and water-alternating gas (WAG) injection in oil reservoirs.

Numerical simulation of flow around a triangular cylinder placed both in left and right position at Reynolds number Re = 80–200 is presented in this study. The single relaxation time lattice Boltzmann method is used. The results are obtained in terms of vorticity contour visualization, drag and lift coefficients, and force statistics. Regular vortex shedding is observed for both cases, but the vortices generated for a triangular cylinder placed in the right position move toward the top downstream position as the range of Reynolds number increases due to effect of pressure (effect of thrust). The drag coefficient is constant, and lift coefficient is containing negative values from Re = 80–150 for that case, but negative Cdmean values are not observed for a triangular cylinder placed in the left position. In that case, it is due to the reason that the effect of thrust diminishes. The maximum value of Cdmean is obtained at Re = 200, that is, 1.5006 for the left triangular cylinder, but the value of the mean drag coefficient for the right triangular cylinder is zero throughout the cases for Re = 80–200. No fluid forces are produced for right triangular case. The Strouhal number (St) values increased by increasing the Reynolds number, i.e., Re = 80–200, for the right triangular cylinder, and it has a mixed trend for the left triangular cylinder. In literature, a lot of work has been found on rectangular and square cylinders, but triangular cylinder has not been studied much.

Water alternating gas (WAG) injection is widely practiced for improved light oil recoveries. In this experimental study, we compare the WAG process against the continuous gas injection (CGI) process by conducting tertiary mode miscible and immiscible corefloods. Inferences resulting from performance evaluations using ‘conventional’ tertiary recovery plots were found inappropriate. Therefore, a new parameter ‘Tertiary Recovery Factor’ (the oil recovery per unit volume of gas injected) was defined, and used in conjunction with the CO2 utilization factor, for the evaluation of tertiary coreflood recoveries. The definition of TRF not only helped to demonstrate experimentally that miscibility development has a positive effect on oil recovery, but also showed that the WAG mode of injection is better than Continuous Gas Injection (CGI) when overall performances are considered. The WAG floods demonstrated continual increase in the TRF throughout the life of the flood, however, for CGI miscible flood, TRF crested at about 0.6 PV injection and later declined with increasing gas injection. These plots demonstrate that the WAG process has better CO2 utilization efficiency compared to CGI. These results indicate that optimum performance could be obtained by a combination of CGI and WAG modes of gas injection. This paper provides conceptual analysis and experimental demonstration of WAG, CGI and their combination at reservoir conditions.

Predicting aerodynamic forces on bluff bodies remains to be a challenging task due to the unpredictable flow behavior, specifically at higher Reynolds numbers. Experimental approaches to determine aerodynamic coefficients could be costly and time consuming. In the meantime, use of numerical techniques could also require a considerable computational cost and time depending on complexity of the flow behavior. The research focusses on developing an effective deep learning technique to predict aerodynamic force coefficients acting on elliptical bluff bodies for a given aspect ratio and given flow condition. Collecting data for drag and lift coefficients of several aspect ratios for flow conditions starting from onset of vortex shredding to verge of subcritical region is conducted by an accurate full order model. The specified region will provide a transient flow behavior and thus lift coefficient will be represented in terms of root mean square value and drag coefficient in terms of a mean value. With variations in flow behavior and vortex shredding frequencies, it requires to select an appropriate turbulence model, optimum discretization of fluid domain and time step to obtain an accurate result. Flow simulations are conducted primarily using Unsteady Reynolds Averaged Navier-Stokes Equations (URANS) model and Detached Eddy Simulations (DES) model. Effectiveness in using different turbulence models for specified flow regimes are also explored in comparison to available experimental results. At lower Reynolds numbers, aerodynamic force coefficients for a specified body will only depend on Reynolds number. But after a certain specific Reynolds number, aerodynamic forces are dependent on the Mach number in addition to Reynolds number. Therefore, for higher Reynolds numbers, aerodynamic force coefficients are recorded for multiple Mach numbers with same Reynolds number and will be fed to the neural network. With the development of the machine learning and neural network modelling, many of the fields have nourished and created effective and efficient technologies to ease complex functions and activities. Our goal is to ease the complexity in the computational fluid dynamic field with a deep neural network tool created to predict drag and lift coefficient of elliptical bluff bodies for a given aspect ratio with an acceptable accuracy level. Researchers have developed deep neural network tools to predict various flow conditions and have succeeded with sufficient accuracy and a satisfying reduction of computational cost. In our proposed deep learning neural network, we have chosen to model the network with inputs as the geometry setup and the flow conditions with validated drag and lift coefficients. The model will extract the necessary flow features into filters with the convolution operation performed on the inputs. Our main directive is to create a deep learned neural network tool to predict the target values within an acceptable range of accuracy while minimizing the computation cost.

In this paper, ferrofluid flow at lower stagnation point on solid sphere is investigated theoretically by considering mixed convection boundary layer flow. The sphere surface is exposed to the magnetic field and thermal radiation by taking into account constant wall temperature boundary conditions. The discovery of the existing magnetic field near the surface while the ferrofluid flowing leads to the development of phenomenology called magnetohydrodynamic. The magnetite (Fe3O4) acts as nanoparticles dispersant and suspended in the water contained in ferrofluid are assumed as Newtonian fluid and behave as single-phase fluid flow is studied. These assumptions give physical insight into the behaviour of ferrofluid flow to be analysed and discussed. The Keller-box method is applied to solve the transformed partial differential equations numerically. The numerical results found the viscosity measured from magnetite (Fe3O4) volume fraction is the main element provided to the trend of the ferrofluid velocity flow. Besides, the ferrofluid temperature at lower stagnation point on sphere is proven influence the ferrofluid viscosity and change the velocity of ferrofluid flow.

Direct numerical simulation of compressible turbulent channel flows using the discontinuous Galerkin method

Summary The objective of this study is the experimental and theoretical investigation of the fall mechanics of continuous flow plungers. Fall velocity of the two-piece plungers with different sleeve and ball combinations and bypass plungers are examined in both static and dynamic conditions to develop a drag coefficient relationship. The dimensionless analysis conducted included the wall effect, inclination, and the liquid holdup correction of the fall stage. A fall model is developed to estimate fall velocities of the ball, sleeve, and bypass plungers. Sensitivity analysis is performed to reveal influential parameters to the fall velocity of continuous flow plungers. In a static facility, four sleeves with different height, weight, and outer diameter (OD); three balls made with different materials; and a bypass plunger are tested in four different mediums. The wall effect on the settling velocity is defined, and it is used to validate the ball drag coefficient results obtained from the experimental setup. Two-phase flow experiments were conducted by injecting gas into the static liquid column, and the liquid holdup effect on the drag coefficient is observed. Experiments in a dynamic facility are used for liquid holdup and deviation corrections. The fall model is developed to estimate fall velocities of the continuous flow plungers against the flow. Dimensionless parameters obtained in the experiments are combined with multiphase flow simulation to estimate the fall velocity of plungers in the field scale. Reference drag coefficient values of plungers are obtained for respective Reynolds number values. Experimental wall effect, liquid holdup, and inclination corrections are provided. The fall model results for separation time, fall velocity, total fall duration, and maximum flow rate to fall against are estimated for different cases. Sensitivity analysis showed that the drag coefficient, the weight of plungers, pressure, and gas flow rate are the most influential parameters for the fall velocity of the plungers. Furthermore, the fall model revealed that plungers fall slowest at the wellhead conditions for the range of gas flow rates experienced in field conditions. Lower pressure at the wellhead had two opposing effects; namely, reduced gas density, thereby reducing the drag and gas expansion that increased the gas velocity, which in turn increased the drag. Estimating fall velocity of continuous flow plungers is crucial to optimize ball and sleeve separation time, plunger selection, and the gas injection rate for plunger-assisted gas lift (PAGL). The fall model provides maximum flow rate to fall against, which is defined as the upper operational boundary for continuous flow plungers. This study presents a new methodology to predict fall velocity using the drag coefficient vs. Reynolds number relationship, wall effect, liquid holdup, deviation corrections, and incorporating multiphase flow simulation.

A new adaptive-passive control device is introduced to optimally reduce the drag on a sphere over a wide range of Reynolds numbers, Re = 0.4 × 105–4.4 × 105. The device, called an adaptive moving ring (AMR), is designed to change its size (i.e., protrusion height) adaptively depending on the wind speed (i.e., the Reynolds number) without energy input. An empirical model is formulated to accurately predict the drag coefficient as a function of the size of AMR and the Reynolds number. Based on the model, we estimate how the optimal size of AMR should vary with the Reynolds number to maximize the drag reduction. Following the estimation of the optimal size, the optimally tuned AMR reduces its protrusion height with increasing Reynolds number, and the drag decreases monotonically by up to 74% compared to that of a smooth sphere. The drag reduction by AMR is attributed to different mechanisms depending on the Reynolds number. For low Reynolds numbers, the locally separated flow at large AMR is energized by the disturbance induced by AMR and reattaches to the sphere surface, forming a large recirculation region. Then, the main separation is delayed downstream due to the increased near-wall momentum. On the other hand, at high Reynolds numbers, no recirculation zone is formed at AMR due to its low protrusion height, but a secondary separation bubble is generated on the rear sphere surface. Therefore, the boundary-layer flow becomes turbulent, and the main separation is significantly delayed, resulting in more drag reduction than for low Reynolds numbers.

Flow-structure interaction of separated shear flow from the sphere and a flat plate was investigated by using dye visualization and the particle image velocimetry technique. Later, a passive control method was applied with 2mm o- ring located on the sphere surface at 55 o from front stagnation point. The experiments were carried out in open water channel for Reynolds number value of Re=5000. Flow characteristics have been examined in terms of the 2-D instantaneous and time-averaged velocity vectors, patterns of vorticity, streamlines, rms of velocity fluctuations and Reynolds stress variations and discussed from the point of flow physics, vortex formation, lengths of large-scale Karman Vortex Streets and Kelvin-Helmholtz vortices depending on the sphere locations over the flat plate. It is demonstrated that the gap flow occurring between the sphere bottom point and the flat plate surface has very high scouring effect until h/d=0.25 and then unsymmetrical flow structure of the wake region keeps up to h/D=1.0 for smooth sphere. For the sphere with o-ring, the wake flow structure becomes symmetrical at smaller gap ratios and reattachment point on the flat plate surface occurs earlier. Moreover, o-ring on the sphere diminishes peak magnitudes of the flow characteristics and thus it is expected that the flow-induced forces will be lessened both on the sphere and flat plate surface. Vortex formation lengths and maximum value occurring points become closer locations to the rear surface of the sphere with o-ring.

The numerical simulation of a flow through a duct requires an externally specified forcing that makes the fluid flow against viscous friction. To this end, it is customary to enforce a constant value for either the flow rate (CFR) or the pressure gradient (CPG). When comparing a laminar duct flow before and after a geometrical modification that induces a change of the viscous drag, both approaches lead to a change of the power input across the comparison. Similarly, when carrying out direct numerical simulation or large-eddy simulation of unsteady turbulent flows, the power input is not constant over time. Carrying out a simulation at constant power input (CPI) is thus a further physically sound option, that becomes particularly appealing in the context of flow control, where a comparison between control-on and control-off conditions has to be made. We describe how to carry out a CPI simulation, and start with defining a new power-related Reynolds number, whose velocity scale is the bulk flow that can be attained with a given pumping power in the laminar regime. Under the CPI condition, we derive a relation that is equivalent to the Fukagata–Iwamoto–Kasagi relation valid for CFR (and to its extension valid for CPG), that presents the additional advantage of naturally including the required control power. The implementation of the CPI approach is then exemplified in the standard case of a plane turbulent channel flow, and then further applied to a flow control case, where a spanwise-oscillating wall is used for skin-friction drag reduction. For this low-Reynolds-number flow, using 90 % of the available power for the pumping system and the remaining 10 % for the control system is found to be the optimum share that yields the largest increase of the flow rate above the reference case where 100 % of the power goes to the pump.

Film boiling collapse in solid spheres immersed in a sub-cooled liquid