Search

The reattached boundary layer in the interaction of an oblique shock wave with a flat-plate turbulent boundary layer at Mach number 2.25 is studied by means of Direct Numerical Simulation (DNS). The numerical results are carefully compared with available experimental and DNS data in terms of turbulence statistics, wall pressure and skin friction. The coherent vortex structures are significantly enhanced due to the shock interaction, and the reattached boundary layer is characterized by large-scale structures in the outer region. The space-time correlation of fluctuating wall shear stress and streamwise velocity fluctuation reveals that the structural inclination angle exhibits a gradual decrease during the recovery process. The scale interactions are analyzed by using a two-point amplitude modulation correlation. A possible mechanism is proposed to account for the strong amplitude modulation in the downstream region. Moreover, the mean skin-friction is decomposed to understand the physically informed contributions. Unlike the upstream Turbulent Boundary Layer (TBL), the contribution associated with the Turbulence Kinetic Energy (TKE) production is greatly amplified, while the spatial growth contribution induced by the pressure gradient largely inhibits skin-friction generation. Based on bidimensional empirical mode decomposition, the turbulence kinetic energy production contribution is further split into different terms with specific spanwise length scales.

In this paper, we introduce techniques for animating explosions and their effects. The primary effect of an explosion is a disturbance that causes a shock wave to propagate through the surrounding medium. This disturbance determines the behavior of nearly all other secondary effects seen in explosions. We simulate the propagation of an explosion through the surrounding air using a computational fluid dynamics model based on the equations for compressible, viscous flow. To model the numerically stable formulation of shocks along blast wave fronts, we employ an integration method that can handle steep gradients without introducing inappropriate damping. The system includes two-way coupling between solid objects and surrounding fluid. Using this technique, we can generate a variety of effects including shaped explosive charges, a projectile propelled from a chamber by an explosion, and objects damaged by a blast. With appropriate rendering techniques, our explosion model can be used to create such visual effects such as fireballs, dust clouds, and the refraction of light caused by a blast wave., 7 pages, 12 figures, anc videos, 22 citations. Alternative online location: http://graphics.berkeley.edu/papers/Yngve-AEX-2000-07

Accepted: 2021-08-31, 資料番号: PA2220003000

The formation mechanism of an EFP(explosively formed projectile) using a double curvature liner under the overpressure effect generated by a regular oblique reflection was investigated in this paper. Based on the detonation wave propagation theory, the change of the incident angle of the detonation wave collision at different positions and the distribution area of the overpressure on the surface of the liner were calculated. Three-dimensional numerical simulations of the formation process of the EFP with tail as well as the ability to penetrate 45# steel were performed using LS-DYNA software, and the EFP velocity, the penetration ability, and the forming were assessed via experiments and x-ray photographs. The experimental results coincides with those of the simulations. Results indicate that the collision of the detonation wave was controlled to be a regular oblique reflection acting on the liner by setting the dimensions of the unit charge and maintaining the pressure at the collision point region at more than 2.4 times the CJ detonation when the incident angle approached the critical angle. The distance from the liner midline to the boundary of the area within which the pressure ratio of the regular oblique reflection pressure to the CJ detonation pressure was greater than 2.5, 2, and 1.5was approximately 0.66 mm, 1.32 mm, and 3.3 mm, respectively. It is noted that pressure gradient caused the liner to turn inside out in the middle to form the head of the EFP and close the two tails of the EFP at approximately 120μs. The penetration depth of the EFP into a 45# steel target exceeded 30 mm, and there was radial expansion between the head and tail of the EFP, increasing the penetration resistance of the EFP. Therefore, the structural size of the unit charge and the liner can be further optimized to reduce resistance to increase the penetration ability of the EFP.

The development of the interface tracking between two immiscible liquids is one of the most challenging problems in fluid dynamics. The simulation of the lubrication process, oil extraction, and the physicochemical mechanism that govern the behaviour of the uncertain conduct of interface is a key element in “gas-oil” or “oil–water” natural gas-oil reservoirs systems and should be tracked for optimal recovery. Motivated by the interface evolution process, in this article, an unsteady flow of two immiscible Eringen micropolar and Dusty (fluid-particle suspension) fluids is considered through a horizontal channel and the functioning of the interface is analysed. Although the channel wall is hyper-stick and no-slip, it is believed that the fluid–fluid interface is unsteady and can also be deformed from one location to another; thus, the single momentum equation is coupled for monitoring the interface profiles using the VOF (Volume of fluid) technique. The modelled coupled- partial differential equations are numerically solved by the modified B-spline differential quadrature method. The interface profile under the influence of different parameters, i.e., Froude, Capillary, wave and Reynolds number, amplitude, the ratio of viscosities, and time is analysed. Three applied pressure gradients namely constant Ge = 10, periodic Ge = 10Sin(t), and decaying Ge = e-t are considered with various constant values of other hydrodynamic parameters. It's been noted that the topology develops with time as the pulsing pattern repeats quicker for a longer period before becoming stable. The flow's qualitative characteristics remain preserved, the interface begins to move vertically as the amplitude is elevated. A higher interfacial drift is seen in the applied periodic pressure gradient case as compared to the constant and decaying pressure gradient scenario. The tracking does take high time to be stable in the presence of the micropolar parameter with all three applied pressure gradient cases.

Thermal devices with porous structures, intended for the combustion chambers of gas turbine units, as well as for cutting and boring of the turbine housings of electric power plants have been developed and studied. Photographs of combustion chambers and nozzles, studied in terms of their geometry and thickening of the nozzle walls, excess oxidant (0.3÷0.8) and the operating conditions until the limit state of the metal is reached (1×106 W/m²) have been presented. The optimal geometry of the chambers and nozzles, as well as the type of porous structure have been determined. Coolant consumption has been reduced dozens of times, which has environmental significance. The appraisal of the structures studied showed the advantages to the flow cooling system. An analytical model of the heat exchange crisis is proposed. The system of differential equations for one-dimensional flow of one-phase liquid is solved. A physical picture of the heat exchange process is presented. In the equation of motion, the coefficient which determines the viscosity in the general pressure gradient is introduced. The actual velocity of the fluid is accounted for by the coefficient of moisture content in the porous structure.

A numerical study of heat transfer and friction in the heat exchanger channels in the presence of a variable pressure gradient is performed. The research was carried out in software complexes (Code_Saturne, Salome). The results of the validation of the research method are presented and they showed that the deviation of the numerical simulation results from the calculation data according to the known criterion equations is within the error of generalization of the experimental data by the criterion equations. According to the results of studies at Red=3000, Red=4177, Red=6000, it was found that the average value of the heat transfer coeffi cient of the channel of variable cross-section is up to 20 % higher than for the channel at dp/dx 0. At the same time, the thermal-hydraulic effi ciency of the alternating channel (L=117 mm, l=58.5 mm, n=2) in the initial section at x =0...0.08 is lower than in the channel with dp/dx>0 by 26.7 %, and at x =0.08...1 it is higher by 5 ... 15 %, at dp/dx

An isothermal and incompressible flow of a magnetohydrodynamici (MHD) viscoplastic fluid has been examined while passing through the area among two co-rotating rolls. Applying lubrication approximation theory (LAT), the basic flow equations of mass and momentum are derived and subsequently non-dimensionalized. Exact solutions of velocity and pressure gradient distributions are evaluated. To evaluate the complex integrals, Trapezoidal rule for numerical integration is used. The significant engineering parameters like, the roll separation force, maximum pressure and the power transferred to the fluid by the rolls, are also numerically computed. The results demonstrate that the velocity field and pressure gradient are significantly affected due to the presence of the viscoplastic parameter. Magnetic field is found to be the controlling parameter for power input, separating force, and distance among attachment and detachment points, being extremely beneficial for the roll coating process. It has been learnt through this study that MHD can be an effective tool in the coating industry to regulate the engineering quantities in which coating thickness is the most important.

Velocity fields in flow in permeable media are of great importance to many subsurface processes such as geologic storage of CO2 , oil and gas extraction, and geothermal systems. Steady-state flow is characterized by velocity fields that do not change significantly over time. The flow field transitions to a new steady state once it experiences a disturbance such as a change in flow rate or in pressure gradient. This transition is often assumed to be instantaneous, which justifies the expression of constitutive relations as functions of instantaneous phase saturations. This work examines the evolution of velocity fields in a surrogate quasi-2D permeable medium using a microfluidic device, a microscopy system, and a high-speed camera. Tracer particles are injected into the medium along with Deionized water. The evolution of the velocity field is examined by tracing these particles in the captured images using the standard high-density particle image velocimetry algorithm founded on cross-correlation. The results suggest that the transition between steady states for an incompressible fluid takes a finite and non-negligible amount of time that is independent of the magnitude of the change in pressure gradient. The existence of transient states and the nature of the response during these states are readily interpreted by the principle of least action where flow gradually establishes an optimal configuration such that energy dissipation is minimized. The findings provide evidence against the applicability of the assumption that flowing phases relax instantaneously to their steady states and, hence, against the accuracy of the classical multiphase extension of Darcy’s law. Cited as: Sun, J., Li, Z., Furtado, F., Aryana, S. A. A microfluidic study of transient flow states in permeable media using fluorescent particle image velocimetry. Capillarity, 2021, 4(4): 76-86, doi: 10.46690/capi.2021.04.03

One of the big challenges in transporting heavy oils through the pipelines is the high pressure drop due to the effect of viscosity and shear-thinning fluid behaviour of oil. Core annular technique has been applied in industry for transporting heavy oil via pipelines to considerably reduce pressure drop. Several studies have been conducted related to oil-water core annular flow (CAF) within pipelines. However, limited works are found in cases of CAF in widely used T and Y-shaped junction pipes which have important roles for dividing or combining the flow. In this study, a computational fluid dynamic (CFD) approach was applied to simulate the high viscous oil-water CAF through T and Y-shaped junction pipe configurations. The 2k factorial statistical experimental design was applied to investigate the effect of pipe diameter and junction angle on the flow performance through T and Y-shaped junction pipes. Eight cases were run with different junction pipe configuration combinations. By applying the factorial designs method, all possible combinations of factors were able to be investigated with lowest numbers of simulation run. The selected response variables of the flow system were the average values of oil hold up and pressure gradient as well as the standard deviation of pressure from inlet to outlets of pipes. It was observed that the stability of CAF was not achieved at the downstream region. The flow transformed into stratified and slug flow. The most attractive design was measured by the small average of pressure gradient and standard deviation of pressure but with a high value of oil holdup. The T-shaped pipe with smaller inlet diameter combined with larger outlet diameter showed the most considerable effect for a better flow performance.

The dynamics of the interaction between immiscible fluids is relevant to numerous complex flows in nature and industry, including lubrication and coating processes, oil extraction, physicochemical separation techniques, etc. One of the most essential components of immiscible flow is the fluid interface, which must be consistently monitored. In this article, the unsteady flow of two immiscible fluids i.e., an Eringen micropolar and Newtonian liquid is considered in a horizontal channel. Despite the no-slip and hyper-stick shear stress condition at the channel edge, it is accepted that the liquid interface is dynamic, migrating from one position to the next and possibly get absolute change; as a result, The CS (continuum surface) model is integrated with the single moment equation based on the VOF (volume of fluid) approach to trace the interface. The immiscible fluids are considered to flow under three applied pressure gradients (constant, decaying, and periodic) and flow is analyzed under seamless shear stress over the entire interface. The modified cubic b-spline differential quadrature method (MCB-DQM) is used to solve the modeled coupled partial differential equations for the fluid interface evolution. The advection and tracking of the interface with time, wave number, and amplitude are illustrated through graphs. It is observed that the presence of micropolar parameters affects the interface with time. The novelty of the current study is that previous studies (which considered the smooth and unstable movement of the micropolar fluid, the steady stream of two immiscible fluids, and interface monitoring through different modes) are extended and generalized to consider the time-dependent flow of two immiscible fluids namely Eringen micropolar and Newtonian with a moving interface in a horizontal channel. For the decaying pressure gradient case, which requires more time to achieve the steady-state, the peak of the waves resembles those for the constant pressure gradient case. The interface becomes steady for a more extensive time when a constant pressure gradient is applied. The interface becomes stable quickly with time as the micropolar parameter is decreased for the constant pressure gradient case i.e., weaker micropolar fluids encourage faster stabilization of the interface. With periodic pressure gradient, the interface takes more time to stabilize, and the crest of the waves is significantly higher in amplitude compared to the constant and decaying pressure cases. The simulations demonstrate the excellent ability of MCB-DQM to analyze complex interfacial immiscible flows.

In this paper, a mathematical model of the blade coating of the viscoelastic Carreau fluid which passes through the gap between the fixed blade and the moving substrate is constructed. The governing equations in the light of LAT (Lubrication Approximation Theory) are nondimensionalized and the solutions for the velocity, volumetric flow rate and the pressure gradient are calculated using Adomian decomposition method and numerical method. Numerical results for the velocity distribution using shooting method have also been studied by taking the full lubrication equation without taking the binomial expansion. Some important quantities from the industrial point of view like pressure, shear stress, Nusselt number and skin friction coefficient are also calculated. The important results are graphically shown at the end. With exponential blade coater, we have calculated velocity profiles, pressure, coating thickness and blade loading. Some of these results are shown graphically while other are presented in the tabulated form.

The present paper theoretically accords a biomechanical model with a brief biological and mathematical description of the growing embryo transport in the human fallopian tube. This model incorporates transport mechanisms that involve the pressure gradient at the ampullar region entrance, peristaltic contractions of smooth muscle cells and swaying motions of ciliary cells. Shear rate dependent viscoelastic fluid characterizes the nature of growing embryo and secreted fluid. The pressure gradient at the ampullar region entrance ξ , metachronal wave parameter ∊ , amplitude ratio ϕ , the ratio of shear viscosity at infinity shear rate to shear viscosity at zero shear rate μ ∞ / 0 and Weissenberg number We emerged as flow control parameters. The assessment showed that the fluid model parameters ( μ ∞ / 0 and We) have opposite effects on appropriate residue time, boluses size and local flow behaviour. Progesterone ( P 4 ) and estradiol ( E 2 ), prostaglandin E 2 ( PGE 2 ) and prostaglandin F 2 α ( PGF 2 α ) constraint the fluid motion by controlling the ξ , secretion of the fluid through the goblet cells and amplitudes of both the sinusoidal and the metachronal waves. Furthermore, a comparison between the current results and available literature is made. The relevance of the obtained results with the growing embryo transport in the human fallopian tube is also explored.

In the current state-of-the-art, high-loss flow in the endwall significantly influences compressor performance. Therefore, the control of endwall corner separation in compressor blade rows is important to consider. Based on the previous research of the Blended Blade and EndWall (BBEW) technique, which can significantly reduce corner separation, in combination with a non-axisymmetric endwall, the full-BBEW technique is proposed in this study to further reduce the separation in endwall region. The principle of the unchanged axial passage area is considered to derive the geometric method for this technique. Three models are further classified based on different geometric characteristics of this technique: the BBEW model, Inclining-Only EndWall (IOEW) model, and full-BBEW model. The most effective design of each model is then found by performing several optimizations at the design point and related numerical investigations over the entire operational conditions. Compared with the prototype, the total pressure loss coefficient decreases by 7%–9% in the optimized full-BBEW at the design point. Moreover, the aerodynamic blockage coefficient over the entire operational range decreases more than the other models, which shows its positive effect for diffusion. This approach has a larger decrease at negative incidence angles where the intersection of the boundary layer plays an important role in corner separation. The analysis shows that the blended blade profile enlarges the dihedral angle and creates a span-wise pressure gradient to move low momentum fluid towards the mainstream. Furthermore, the inclining hub geometry accelerates the accumulated flow in the corner downstream by increasing the pressure gradient. Overall, though losses in the mainstream grow, especially for large incidences, the full-BBEW technique effectively reduces the separation in corners.

A 2D numerical investigation is performed to better understand the transient thermo-fluid processes in a vortex tube for a cold mass fraction equal to 0.44 . The results along the Ranque-Hilsch vortex tube reveal a close agreement with past numerical and experimental data. The distribution of axial, radial, and tangential velocities as well as the stagnation pressure and temperature are examined at different positions for different time steps. The results indicate that the tangential velocity is the most significant velocity component and dominates the heat transfer and energy conversion processes. In addition, it is evident that the core of the cold end experiences the highest pressure gradient along with almost zero tangential and radial velocities. The maximum axial velocity appears close to the inlet and its value increases with higher cold mass fractions due to higher pressure gradient which may lead to the enlargement of the inner vortex. The impact of different cold mass fractions in the range of 0.22 − 0.82 at tube length ratios x/L equal to 0.05, 0.5, and 0.9 for different time steps are examined. The results indicate that there is relatively no vortex decomposition near the cold outlet.

The paper deals with the cavitation at tongue of a pump-turbine in pump mode, including the typical patterns, unsteady behaviors, and the influence on pump performance and fluid-borne noise. Visualization experiments were conducted under different flow rates and rotational speeds for variation cavity regimes. The results show the patterns can be divided into three regimes with cavitation development: bubble cavitation, cloud cavitation, and lock cavitation for the gas-lock phenomenon and performance plummet. The rotor-stator interaction and jet-wake flow could affect the cavitation generation. The blade passing effect is the leading cause of bubble clusters periodic collapsing or shedding at the early stages of cavitation, while playing a small role as cavities become thick and evaporation rate rises. The combined action of the attached vortex (re-entrant jet) and the depression by pressure gradient outside cavity surface account for the shedding at the developed cloud cavitation stage. Based on the noise measurement by hydrophone at the outlet, the broadband sound in the range of 1000 HZ-2000 Hz can be used for cavitation detection since it can be rarely influenced by operating conditions under non-cavitation.

To study ellipsoidal and spherical particle flow, clogging behavior and unclogging dynamics, a series of numerical simulations were carried out using our validated 3-D coupled computational fluid dynamics–discrete element method (CFD–DEM) model. For the first time, the strength of clogging arches is assessed in terms of fluid pressure gradient, which can effectively break up the clog. The main findings are as follows. In a clogged assembly, only when the flushing fluid reaches the unclogging pressure gradient, the ellipsoidal and spherical particles can flow in a continuous state. For the ellipsoids and spheres with the same equivalent volume, the unclogging pressure gradient of an ellipsoidal assembly is 11.8 times higher than that of a spherical assembly. Clogging arches at the outlet show the highest strength when the longitudinal orientations of the ellipsoids are perpendicular to the outlet plane. In contrast, the formed arch has the lowest stability when the longitudinal orientations of the ellipsoids are in the same direction as the long side of the outlet, as shown in the graphical abstract. The unclogging pressure gradient of the former case is 1.9 times greater than that of the latter case. The granular arches observed in our 3-D model are categorized as complex 3-D backbone arches. In the flowing region, particles rotate nearly perpendicular to the outlet plane, especially those approaching the outlet. Moreover, triangular stagnant zones are formed on both sides of the bottom of the rectangular box. The model presented here offers a great promise for future investigation of various granular systems at the particle scale.

The suction force on high-sphericity seeds is important to the design of air-suction seed-metering devices. However, little systematic research has been conducted on the suction force. A self-designed suction force measurement device and idealised model were used to conduct CFD simulation, single factor experiments, and orthogonal experiments to improve the model of the suction force on seeds with sphericity over 90.34% and equivalent diameter 6.63–7.16 mm under the following conditions: suction hole diameter 4–6 mm, suction hole vacuum 3–5 kPa, seed-filling angle ±π/8, and horizontal distance from the seed centre to the suction hole 3.5–5.5 mm. The verification experiment conducted using the seeds of soybean, pea, and Panax notoginseng showed that the accuracy was higher for the improved suction force model. Simulation of flow behaviours under different factors revealed that the changes in the air velocity gradient and pressure gradient are the main causes of the change in the suction force. The relationship between the drag force model and the suction force model was studied by comparing the predicted value of the drag force and the measured value of the suction force under the same conditions.

Foam sclerotherapy is a simple and easy minimally invasive treatment for varicose veins, but foam stability is a bottleneck in the treatment. The foam-coalescence pattern can reveal the process of foam decay, whereas the effects of fluid parameters can characterize the decay patterns under various conditions. This study is instructive for clinical and research purposes. Four liquid parameters were considered by the addition of surfactant P-188 to change the liquid properties. A simplified four-foam basic unit model was developed. Two-phase flow calculations were performed in ANSYSA Fluent with grid-independence verification, and post-processing was performed using Tecplot 360. As the concentration of P-188 increased from 0 to 12%, the foam-coalescence time gradually increased from 0.28 to 0.35 ms at a growth rate of approximately 25%. The coalescence of the unit foam group of the four foams finally approached a spherical shape. The first consolidation consumed 0.03 ~ 0.05 ms, and the velocity increased sharply to 1.0 ~ 1.2 m/s in the second consolidation. The greater the concentration of P-188, the later the peak appeared. A simplified spatially stereoscopic coalescence model was developed, and the foam-coalescence time was found to increase linearly with increase in the surfactant concentration. It was revealed that foam coalescences under different conditions mainly included the coalescence proximity effect of the pressure gradient field and the repulsion effect of the vortex on the bubble surface. This paper serves as a basis for the design of more macroscopic foam-stability experiments and paves the way for ideas achieving the stability of sclerosing foam.

Shale gas plays an increasingly important role in the current energy industry. Modeling of gas flow in shale media has become a crucial and useful tool to estimate shale gas production accurately. The second law of thermodynamics provides a theoretical criterion to justify any promising model, but it has been never fully considered in the existing models of shale gas. In this paper, a new mathematical model of gas flow in shale formations is proposed, which uses gas density instead of pressure as the primary variable. A distinctive feature of the model is to employ chemical potential gradient rather than pressure gradient as the primary driving force. This allows to prove that the proposed model obeys an energy dissipation law, and thus, the second law of thermodynamics is satisfied. Moreover, on the basis of energy factorization approach for the Helmholtz free energy density, an efficient, linear, energy stable semi-implicit numerical scheme is proposed for the proposed model. Numerical experiments are also performed to validate the model and numerical method.

In the present research, a novel mathematical model for the motion of cilia using non-linear rheological fluid in a symmetric channel is developed. The strength of analytical perturbation technique is employed for the solution of proposed physical process using mectachoronal rhythm based on Cilia induced flow for pseudo plastic nano fluid model by considering the low Reynolds number and long wave length approximation phenomena. The role of ciliary motion for the fluid transport in various animals is explained. Analytical expressions are gathered for stream function, concentration, temperature profiles, axial velocity, and pressure gradient. Whereas, transverse velocity, pressure rise per wave length, and frictional force on the wall of the tubule are investigated with aid of numerical computations and their outcomes are demonstrated graphically. A comprehensive analysis for comparison of Perturb and numerical solution is done. This analysis validates the analytical solution.

This paper is devoted to the development of a mathematical model and its computational analysis targeted at investigating the effects of dual-phase lag on the heating protocol of tumor tissue by the method of electromagnetic hyperthermia. The model comprises two layers, one of them being the vessel layer in which blood flows under the action of a pressure gradient and an external magnetic field, while the other is a tissue layer containing a small rectangular tumor. The tumor tissue is heated by the periodic nature of metabolic and external heat sources. Two phase lags due to the presence of temperature gradient and heat flux are treated to observe the effect of faster heating phenomena. The wave equation representing bioheat transfer in the tissue layer is considered. The problem has been solved directly by employing a suitable finite difference numerical tool. The study shows that the phase lag caused by heat flux is more effective for heating the tumor than the phase lag due to the temperature gradient, and further that transversely applied magnetic field to the blood flow has a limited impact on enhancing the tumor temperature.

Based on the ideas of the mechanism of turbulent flows as forming a source of turbulent vortices at the turbulent flow boundaries developed and described previously for turbulent jets [2] and turbulent flows in channels [3], we have calculated the flow parameters for a turbulent boundary layer (TBL) combining the features of flows in jets and channels. The mechanism of the influence of external turbulence on the TBL flow parameters is described. A generalization of the theory for flows with an external flow pressure gradient is proposed.

Many landslides in nature may be classified as deformable landslides. The landslide volume is usually modeled as a rheological material when SPH methods are used for landslide simulation, since these methods allow for the use of particles with different fluid properties. To increase the accuracy, the Carreau-Yasuda model is chosen in this study to predict the behavior of the rheological material. This rheological model overcomes the weakness of the power-law model in predicting the viscosity at zero and infinite shear strain rates. Also, a fully explicit three-step algorithm is proposed to solve the governing equations. In the first step, the momentum equation is solved in the presence of the body forces while neglecting all other forces. In this step intermediate velocity values are computed. In the second step, the calculated intermediate velocities are employed to compute divergence of the stress tensor, and velocity components of each particle are updated to find their intermediate positions. These two steps are called predictor steps. In the third, corrector step, the pressure gradient in the momentum equation is merged with the continuity equation, and lastly the final particle velocity is calculated at the end of the time step. The fully explicit three-step algorithm is used in combination with Carreau-Yasuda model to simulate the submarine non-rigid landslide from the physical model. The comparison with the experimental data indicates good agreement between the calculated and observed water surface elevations with very low L2 relative error norm (L2) and RMSE values that are up to 70% lower than those from previous studies when Cross and Bingham rheological models were used with ISPH and WCSPH models, respectively. Moreover, the shape and the advancement of the non-rigid body made of sand are captured equally good. Ovo je recenzirana verzija rada pre konačnog slaganja teksta za časopis.

The one-equation turbulence models by Spalart and Allmaras (SA) and Sekundov et al. (Nut-92) are tested against two compressible two-dimensional flows, namely, the turbulent flat-plate boundary layer at zero pressure gradient and the mixing layer. The boundary layer (BL) approximation is applied to the system of Reynolds equations (RANS). The BL results obtained are compared with the available RANS results and the results of direct numerical simulation (DNS). The modified Nut-92m model proposed predicts the characteristics of the turbulent flat-plate boundary layer at zero pressure gradient more accurately than the Nut-92 and SA models.

Electroosmotic flows (EOF) in microfluidic devices can be greatly enhanced over superhydrophobic surfaces because the high shear rates within the electrical double layer can drive large slip velocities at the interface. Using the power law fluid model, we derive a novel formulation for the Helmholtz–Smoluchowski (HS) velocity and use it to examine the effect of slip on the hydrodynamics of a coupled pressure driven and EOF. Semi analytical relations for the velocity gradient are obtained for cases of a favourable pressure gradient but exact solutions of the velocity can be found only for certain power law indices. Cases of adverse pressure gradient and fractional power law indices are investigated using numerically using the Galerkin Finite Element Method. The validity of the semi analytical relations verified by comparison with the numerical method. The presence of velocity slip at the wall leads to an enhancement of the HS velocity that is most pronounced in shear thinning fluids. Adverse pressure gradients are observed to generate an inflection in the velocity profile and even a two-way flow for certain flow parameters. The strength of the adverse pressure gradient needed to setup a reverse flow at the channel centre reduces as the slip length is increased. The location of the point of inflection is found to depend on the channel height, pressure gradient, electric field, slip length, Debye length and non-Newtonian behaviour.

Over the years, a number of researchers have explored the possibilities of capturing the fantastic Taylor column phenomena numerically. However, comprehensive satisfactory numerical results have not been obtained in spite of the presence of well established experimental and theoretical data. One important blockade in the process is that the existing lower-order schemes cannot capture the phenomena appropriately owing to the complexity of the flow which arises due to the effect of several parameters and nonlinearities. Hence we propose to use the Higher Order Compact Scheme (HOCS) to capture the Taylor column phenomena along with all its essential features. The results obtained using HOCS are found to be in line with available experimental results in the literature. The physical analysis of streamlines, swirl velocity, surface pressure, and pressure gradient show that there arises a reverse flow near the front and a cyclonic vortex near the rear stagnation point along with a geostrophic region under certain conditions depending on the balance between the Coriolis force and the pressure gradient.

The pressure gradient term plays a vital role in convective heat transfer in the boundary layer flow of a Maxwell fluid over a stretching sheet. The importance of the effects of the term can be monitored by developing Maxwell’s equation of momentum and energy with the pressure gradient term. To achieve this goal, an approximation technique, i.e. Homotopy Perturbation Method (HPM) is employed with an application of algorithms of Adams Method (AM) and Gear Method (GM). With this approximation method we can study the effects of the pressure gradient (m), Deborah number (β), the ratio of the free stream velocity parameter to the stretching sheet parameter (ɛ) and Prandtl number (Pr) on both the momentum and thermal boundary layer thicknesses. The results have been compared in the absence and presence of the pressure gradient term m . It has an impact of thinning of the momentum and boundary layer thickness for non-zero values of the pressure gradient. The convergence of the system has been taken into account for the stretching sheet parameter ɛ. The result of the system indicates the significant thinning of the momentum and thermal boundary layer thickness in velocity and temperature profiles. On the other hand, some results show negative values of f '(η) and θ (η) which indicates the case of fluid cooling.

Couette–Poiseuille (C–P) flow, which is driven by drag from a moving wall and a pressure gradient, can exist in different states depending on the relative strengths of the two above-mentioned factors. Of particular interest is the onset of flow reversal, which is characterized kinematically by a zero shear rate on the stationary wall. This study presents two different methods for obtaining the critical conditions for the onset of flow reversal in C–P flows. In the first method, exact values of the critical flow rate and pressure gradient are computed by solving a pair of algebraic equations derived from the Weissenberg–Rabinowitsch relation. Using this method, the difficulty in solving the nonlinear differential equation is avoided. In the second method, estimates of the critical conditions are obtained analytically by locally approximating the given fluid as a power-law fluid. To evaluate the prediction accuracy, the methods are applied to the C–P flows of Carreau–Yasuda and Bingham–Carreau–Yasuda fluids. It is demonstrated that the relative errors remained reasonably low in most system parameter ranges, except in cases where the flow curve in the log–log scale is highly nonlinear.

In this article, a theoretical analysis on flow in a curvilinear horizontal coaxial cylinder with permeable walls has been proposed. Specifically, the transient impact of an oscillating pressure gradient has been taken into account. The non-linear time-dependent partial differential equation accountable for the flow has been transformed using the classical Laplace transform technique. Exact solution of the momentum equation has been obtained in Laplace domain. Due to the intricacy of the Laplace domain solutions, a numerical inversing technique which is established upon the Riemann-sum approximation (RSA) has been utilized to transform the Laplace domain solutions to time domain. Findings reveal that the outcome of suction on the porous walls and boosting the frequency of oscillation renders skin frictions on both walls of the cylinder less effective. The instability of the Dean vortices in the annular gap can be suppressed by amplifying the frequency of oscillating pressure gradient while time is maintained.

In this paper, the unsteady flow of two immiscible fluids with heat transfer is studied numerically\ud with a modified cubic B-spine Differential Quadrature Method. Generalized Couette flow of two\ud immiscible dusty (fluid-particle suspension) and pure (Newtonian) fluids are considered through\ud rigid horizontal channels for three separate scenarios: first for non-porous plates with heat\ud transfer, second for porous plates with uniform suction and injection and heat transfer, and third\ud for non-porous plates with interface evolution. The stable liquid-liquid interface is considered for\ud the two immiscible fluids in the first two cases. In the third case, it is assumed that the interface\ud travels from one position to another and may undergo serious deformation; hence the single\ud momentum equation based on the (volume of fluid) VOF method is combined with the continuum\ud surface approach model, and an interface tracking is proposed. The flow cases are considered to\ud be subjected to three different pressure gradients, of relevance to energy systems- namely, applied\ud constant, decaying, and periodic pressure gradients. For each case, the coupled partial differential\ud equations are formulated and solved numerically using MCB-DQM to compute the fluids\ud velocities, fluid temperatures, interface evolution. The effects of emerging thermo-fluid\ud parameters, i. e. Eckert (dissipation), Reynolds, Prandtl, and Froude numbers, particle\ud concentration parameter, volume fraction parameter, pressure gradient, time, and the ratio of viscosities, densities, thermal conductivities, and specific heats on velocity and temperature\ud characteristics are illustrated through graphs.

In the numerous low-permeability reservoirs, knowing the real productivity of the reservoir became one of the most important steps in its exploitation. However, the value of permeability interpreted by a conventional well-test method is far lower than logging, which further leads to an inaccurate skin factor. This skin factor cannot match the real production situation and will mislead engineer to do an inappropriate development strategy of the oilfield. In order to solve this problem, key parameters affecting the skin factor need to be found. Based on the real core experiment and digital core experiment results, stress sensitivity and threshold pressure gradient are verified to be the most influential factors in the production of low-permeability reservoirs. On that basis, instead of a constant skin factor, a well-test interpretation mathematical model is established by defining and using a time-varying skin factor. The time-varying skin factor changes with the change of stress sensitivity and threshold pressure gradient. In this model, the Laplace transform is used to solve the Laplace space solution, and the Stehfest numerical inversion is used to calculate the real space solution. Then, the double logarithmic chart of dimensionless borehole wall pressure and pressure derivative changing with dimensionless time is drawn. The influences of parameters in expressions including stress sensitivity, threshold pressure, and variable skin factor on pressure and pressure derivative and productivity are analyzed, respectively. At last, the method is applied to the well-test interpretation of low-permeability oil fields in the eastern South China Sea. The interpretation results turn out to be reasonable and can truly reflect the situation of low-permeability reservoirs, which can give guidance to the rational development of low-permeability reservoirs.

The heat transfer phenomenon plays an imperative role in several biological and industrial processes, like the oil production industries, catalytic reactors, energy losses in several thermal systems, energy storage, papers manufacture and heat exchanger systems. Therefore, the present analysis investigates the heat transfer phenomena on peristaltic transportation of the hydromagnetic flow of non-Newtonian fourth-grade fluid in a tapered asymmetric channel filled with porous media. Moreover, the impacts of heat source/sink and thermal radiation in modeling are retained. The tapered asymmetry in the channel is generated by undertaking the peristaltic wave train inflicted on the non-uniform walls to have altered phases and amplitudes. The analysis is originated by adopting suppositions of long wavelength $$\left( {\delta < < 1} \right)$$ , small Deborah number $$\left( {\Gamma \to 0} \right)$$ and low Reynolds number $$\left( {\text{R} \to 0} \right)$$ . A regular perturbation technique is utilized to acquire the series outcomes for the axial velocity, pressure gradient and streamlines distribution, while an analytical outcome has been acquired for the thermal profile. The pressure rise at each wavelength on the channel walls has been numerically computed. Impacts of arising parameters in the analysis are surveyed graphically. Outcomes divulge that magnitude of the axial velocity raises with a rise of Darcy number. In contrast, it diminishes with a raise of the magnetic parameter near the center of the channel. Furthermore, the calculated outcomes are found in admirable agreement with the outcomes acquired by the finite element technique and previously published results.

A mathematical model of two-phase Gas-Liquid or Liquid-Liquid flow hydrodynamics for non-Newtonian (shear thickening or shear thinning) continuous liquid in microchannels was build up. Governing equations are: Navier-Stokes and continuity equations in the axisymmetric problem statement, the empirical correlation for liquid film thickness. An analytical solution was obtained for velocity profiles within the liquid slug and in the liquid film, and in the plug (bubble/droplet) of dispersed phase. Following to Abiev (CES, 2017) it was assumed that pressure gradients in the liquid slug and in the liquid film, and in the plug (bubble/droplet) are not the same in general. The proposed model allows calculating shear stresses and velocity profiles, as well as mean velocities and pressure gradients in the liquid slug, in the liquid film, and in the plug. The model could be applied for non-Newtonian continuous liquids, e.g. for some solutions of high-molecular compounds and for precipitation of micro- and nanosized particles, which accumulate in the continuous phase.

This theoretical analysis considers a biomechanical model in which the Carreau fluid model characterizes the viscoelastic nature of growing human embryo and secreted fluid. This model incorporates transport mechanisms that involve the swaying motions of ciliary cells, peristaltic contractions of smooth muscle cells and pressure gradient at the ampullar region entrance. Series form solutions of the resulting partial differential equations are obtained using the regular perturbation method. A theoretical estimate of effects of the condition of pressure gradient, geometric parameters and fluid model parameters on the flow variables that have relevance to the problem of growing embryo transport in the human fallopian tube is presented through the discussion of graphs. Furthermore, an analogy between the linearly viscous fluid, and the shear thinning and shear thickening characteristics of the Carreau fluid model is also presented. The pertinence of the obtained results with growing embryo transport in the human fallopian tube revealed that when shear thickening characteristics of the Carreau fluid model are considered then complete mitotic divisions take place properly with an estimated appropriate residue time about 3–4 days. Smaller size trapped boluses of the secreted fluid make the smooth forwarding of the growing embryo in the human fallopian tube when shear thinning characteristics of the Carreau fluid model are taken into account. Key modulators: progesterone ( $$P_{4})$$ and estradiol ( $$E_{2}$$ ), prostaglandin $$E_{2}$$ ( $$PGE_{2}$$ ) and prostaglandin $$F_{2\alpha }$$ ( $$PGF_{2\alpha }$$ ) constraint the growing embryo transport.

The problem of the free streamline solutions of the Falkner–Skan equation is revisited in this paper. Until now, such solutions were found for negative values of the pressure gradient parameter β only. All of them are associated with slip velocities − 1 f ′ 0 ∞ and emerge from the trivial solution f = η of the problem. The present paper shows, however, that in the positive range 1 β ∞ , just below the interval − 1 f ′ 0 ∞ , a further branch of free streamline solutions of slip velocities − 2 ≤ f ′ 0 − 1 exists. These new solutions emerge from an exact solution of the Falkner–Skan equation which describes the flow in a converging channel with moving boundaries at the saddle–node bifurcation point f ′ 0 = − 2 , f ′ ′ 0 = 0 . For the large- β asymptotics of this solution branch a new algorithm is presented. The occurrence of further free streamline solutions in the range β 0 , as well as the existence of free streamlines of vanishing slip velocities, f ′ ′ 0 = f ′ 0 = 0 , both for positive and negative values of β is also addressed in the paper. The flow inside a cone is also considered shortly and the occurrence of free streamline solutions is pointed out also in this case.

Turbulent kinetic energy (TKE) equation based on the Reynolds averaging hypothesis was approximated in the near wall region of turbulent channel flows and an analytical solution for TKE was proposed by Absi for $$y^{ + } < 20$$ (R. Absi, Analytical solutions for the modeled k equation, Trans. ASME: J. Appl. Mech. 75 (2008) 044,501). While, comparisons with DNS data show very good agreement, some of the model approximations employed previously require revision which is the main motivation of this work. We here present an alternate formulation for the smooth near wall TKE budget and propose an improved method of solution. Results are compared against wide range of friction Reynolds numbers, Reτ DNS datasets and found to be in good agreement. Interestingly the proposed improved method reveals that beyond Reτ, = 5200 TKE profiles collapse meaning that the TKE remains independent of Reτ that is consistent with high Reynolds number turbulent characteristics reported in the DNS (Hultmark et. al., Turbulent pipe flow at extreme Reynolds numbers, Phys. Rev. Lett., 108 (2012) 094,501). Although there exist two parameters in the paresent work to be determined empirically from DNS data it is reported that these parameters become empirically free at high turbulent Reynolds numbers, Reτ → ∞.The other interesting aspect of this work is that one of these parameters may be sensitized to other additional effects viz., wall roughness, pressure gradient, magnetic field, etc. One of the potential advantages of these near wall smooth turbulent channel flow analytical solutions is to obviate the need for solving the TKE equation near the smooth wall in the RANS, hybrid RANS/LES closures thus resulting in quicker and accurate engineering computations.

Unlike the power-law model, the Ellis model describes the apparent viscosity of a shear-thinning fluid with no singularity in the limit of a vanishingly small shear stress. In particular, this model matches the Newtonian behaviour when the shear stresses are very small. The emergence of the Rayleigh-B\'enard instability is studied when a horizontal pressure gradient, yielding a basic throughflow, is prescribed in a horizontal porous layer. The threshold conditions for the linear instability of this system are obtained both analytically and numerically. In the case of a negligible flow rate, the onset of the instability occurs for the same parametric conditions reported in the literature for a Newtonian fluid saturating a porous medium. On the other hand, when high flow rates are considered, a negligibly small temperature difference imposed across the horizontal boundaries is sufficient to trigger the convective instability., Comment: 13 pages, 5 figures, 2 tables

The heavy-oil flow in porous media is characterized by non-Darcy law with variable threshold pressure gradient (TPG) due to the large fluid viscosity. However, available analytical and numerical models hardly consider this effect, which can lead to erroneous results. This paper is aimed at presenting an innovative approach and establishing a numerical simulator to analyze the heavy-oil flow behavior with waterflooding. The apparent viscosity of the oil phase and flow correction coefficient characterized by the TPG were applied to describe the viscosity anomaly of heavy oil. Considering the formation heterogeneity, the TPG was processed into a variable related to mobility and the directionality. The discretization and linearization of the mathematical model were conducted to establish a fully implicit numerical model; the TPG value on each grid node was obtained through oil phase mobility interpolation, and then, the Jacobi matrix was reassembled and calculated to solve pressure and saturation equations. The corresponding simulator was thus developed. The pre-/postprocessing module of the simulator is connected to ECLIPSE; then, an efficient algorithm is introduced to realize a fast solution. Results show that considering the TPG will not only reduce the waterflooding area but also reduce the oil displacement efficiency because of aggravating the nonpiston phenomenon and interlayer conflict. The numerical simulation study on the TPG of heavy oil provides theoretical and technical support for the rational development and adjustment of water-driven heavy oil.

One of the purposes of this investigation is to throw some additional light on the question of how to correlate between the experimental data from different sources and the theoretical approaches for the study of incompressible turbulent boundary layers development on rough surface. Moreover, the study developed included the presence of adverse pressure gradient; as well as a discussion about the effect of surface roughness on the boundary layer parameters which control the flow behaviour. On the basis of Zancow experimental work with rough surface and the velocity law of Rotta, this study has been developed. In order to obtain the numerical results for the mathematical solution outlined in this work, a computer program is constructed to perform all the necessary calculations. These results are represented in charts and can be utilised for the geometric shape of roughness.

The objective of this paper is to propose a new intermittency transport equation that is naturally capable of capturing the effects of free-stream turbulence and pressure gradient on bypass and nat...

Channel flow has been proposed as a mechanism to explain the formation of the Greater Himalayan Sequence that is bounded by normal sense ductile shear along the Himalayan orogen. The key requirements for channel flow are: (i) extruding middle-to-lower crust of low viscosity, and (ii) excess gravitational potential due to topography. We present scaled two-layer physical models where the effect of the gravitational potential with respect to the plate convergence rate is investigated. Viscous middle crust starts moving towards the surface where the strain rate imposed by the convergence is 30% of that arising from the lateral pressure gradient. How efficiently the low-viscosity crust extrudes is directly linked to the imposed pressure gradient. A simple correlation between the extruding rock’s viscosity, the convergence rate, and the topography imposing the pressure gradient is established. The upward motion of viscous material is expected already for a mid-crustal viscosity of 1021 Pa s. This is significantly higher than previously expected, suggesting that one of the fundamental requirements for channel flow might not be necessary.

The electro-osmotically driven flow of Casson fluid across a cylindrical geometry with systematically contracting and relaxing sinusoidal walls is mathematically interpreted. The phenomenon of heat transfer also has its worth in the present investigation. The Joule heating and viscous effects are also studied in detail. The mathematically formulated equations that govern the flow of Casson fluid are simplified in their dimensionless form by using lubrication approximation, i.e. ( λ → ∞ ) . Finally, exact mathematical solutions are flourished for these dimensionless equations. The graphical results are presented to further explain the exact solutions of velocity, temperature, pressure rise, pressure gradient, and streamlines pattern. The major outcomes show that electro-osmosis is very helpful in controlling both flow and heat transfer.

Crossflow instability (CFI) is crucial for triggering boundary-layer flow transition over a transonic natural laminar flow (NLF) wing, whose leading edge is swept for reducing wave drag. This paper...

In this paper, premixed syngas-air flame propagating from the open end to the closed end were experimentally investigated. The effects of equivalence ratios, 0.8 ≤ Ф ≤ 1.2, and hydrogen volume fractions, 10% ≤ α(H2) ≤ 90%, on flame deformation and oscillation had been discussed in detail. The tulip-like flame was observed because of the large pressure gradient. Results indicate that the pressure wave plays an important role in the flame deformation and oscillation. The flame oscillates as hydrogen volume fraction varies. There are two oscillation modes. When the flame oscillates as mode Ⅰ, the flame first oscillates smoothly, then the oscillation is gradually enhanced, and finally the oscillation decays. The interaction of flame and pressure waves continuously stimulates the flame deformation and oscillation, finally the violent flame folding emerges in the later stage. When the flame oscillates as mode Ⅱ, the flame just oscillates violently in the early stage.

The effect of pressure gradient on a separated boundary layer past the leading edge of an airfoil model is studied experimentally using electronically scanned pressure (ESP) and particle image velocimetry (PIV) for a Reynolds number ( Re) of 25,000, based on leading-edge diameter ( D). The features of the boundary layer in the region of separation and its development past the reattachment location are examined for three cases of β (−30°, 0°, and +30°). The bubble parameters such as the onset of separation and transition and the reattachment location are identified from the averaged data obtained from pressure and velocity measurements. Surface pressure measurements obtained from ESP show a surge in wall static pressure for β = −30° (flap deflected up), while it goes down for β = +30° (flap deflected down) compared to the fundamental case, β = 0°. Particle image velocimetry results show that the roll up of the shear layer past the onset of separation is early for β = +30°, owing to higher amplification of background disturbances compared to β = 0° and −30°. Downstream to transition location, the instantaneous field measurements reveal a stretched, disoriented, and at instances bigger vortices for β = +30°, whereas a regular, periodically shed vortices, keeping their identity past the reattachment location, is observed for β = 0° and −30°. Above all, this study presents a new insight on the features of a separation bubble receiving a disturbance from the downstream end of the model, and these results may serve as a bench mark for future studies over an airfoil under similar environment.

The vortex rope usually occurs in the draft tube of the Francis turbine operated under part-load conditions, to induce strong low-frequency pressure vibrations, and therefore, is very harmful to the safety of the hydropower unit. In the present work, three kinds of strategies are extensively investigated, i.e., the installations of the ventilation and the fin, as well as the hybrid strategy of the air admission through a fin, so as to effectively suppress the vortex rope oscillation and the pressure vibration in the draft tube of a Francis turbine, whose specific speed is 125 m-kW. For the unsteady flow simulation, the Reynolds averaged Navier-Stokes (RANS) method is applied coupled with the k-ω SST turbulence model and a homogeneous cavitation model. The flow analysis confirms that the low-frequency pressure vibrations are originated from the periodical oscillation of the vortex rope, and the cavitation usually enhances the vortex rope oscillation in the draft tube. Under the part-load condition, the dominant component of the pressure vibration in the draft tube has a frequency, for example, f1, lower than the runner rotating frequency fn. It is shown that all three strategies can be adopted to alleviate the vortex rope oscillation and the pressure vibrations in the draft tube, but their suppression mechanisms are quite different. The ventilation of an adequate amount from the turbine runner cone can change the vortex rope geometry from the spiral type to the cylindrical type, suppress the vortex rope oscillation, and consequently create the homogeneous distributions of the pressure and the pressure gradient in the draft tube. On the other hand, a fin installed at the draft tube wall can induce a small extra rope, and the interaction between the main vortex rope and the extra rope changes the flow field and alleviates the pressure vibration in the draft tube. It should be noted that a fin is much more effective to suppress the pressure vibration in the draft tube under the cavitation condition than under the non-cavitation condition. A better effect of suppressing the vortex rope oscillation can be achieved by the air admission through a fin, which is studied numerically in this paper. The result indicates that the air admission can further improve the effect of a fin for suppressing the pressure vibration in the inlet cone of the draft tube. This improvement is due to the stronger interaction between the main vortex rope and the extra air rope. However, the air admission through a fin should be carefully treated because the strong interaction may induce a larger pressure vibration in the elbow of the draft tube. Finally, it is clear that any strategy for suppressing the pressure vibration hardly changes the dominant component frequency f1, which is in the range of 0.22 fn-0.23 fn due to the main vortex rope oscillation in this study. The current results may be used in various engineering applications, where the active control of the vortex oscillation and the pressure vibrations with or without the cavitation is necessary.

The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. The solution of the governing equations is found using integral transformations (Laplace and finite Hankel transforms). For the semianalytical solution, the inverse Laplace transform is found by means of Stehfest’s and Tzou’s algorithms. The numerical calculations were performed by using Mathcad software. The flow is significantly affected by Hartmann number, inclination angle, fractional parameter, permeability parameter, and pulsatile pressure gradient frequency, according to the findings. It is deduced that there exists a significant difference in the velocity of the flow at higher time when the magnitude of Reynolds number is small and large.