Three-dimensional Steady Flow Research Articles

THREE-DIMENSIONAL STAGNATION-POINT FLOW OVER A PERMEABLE STRETCHING/SHRINKING SHEET WITH A SECOND ORDER SLIP FLOW

The problem of steady laminar three-dimensional stagnation-point flow on a permeable stretching/shrinking sheet with second order slip flow model is studied numerically. Similarity transformation has been used to reduce the governing system of nonlinear partial differential equations into the system of ordinary (similarity) differential equations. The transformed equations are then solved numerically using the \texttt{bvp4c} function in MATLAB. Multiple solutions are found for a certain range of the governing parameters. The effects of the governing parameters on the skin friction coefficients and the velocity profiles are presented and discussed. It is found that the second order slip flow model is necessary to predict the flow characteristics accurately.

Thin Film Flow of Tangent Hyperbolic Fluid with Nonlinear Mixed Convection Flow and Entropy Generation

This paper examined the three-dimensional steady thin film flow of tangent hyperbolic fluid with nonlinear mixed convection flow and entropy generation past a stretching surface under the influence of magnetic field. For the flow problem, the Cattaneo–Christov heat and mass diffusion model was employed to examine heat and mass transfer characteristics and impacts of the normally directed magnetic field. To transform nonlinear PDEs into ODEs, the variable transformation technique was used. The bvp4c algorithm was implemented to solve these ODEs. The behavior of every leading parameter on the velocities, temperature, concentration profile, entropy generation, and Bejan number was reported with tabular and figurative form. The results show that as the values of Br increase, the entropy generation enhances, but the Bejan number decreases. Moreover, as the values of B increase, the opposite characteristics are observed in entropy generation and Bejan number graphs. Furthermore, the skin friction coefficient number, local Nusselt number, and Sherwood number are graphically discussed for the active involved parameters. The best agreement is recorded when we compare this paper with the previous literature for various values of M .

Analysis of entropy generation in a power-law nanofluid flow over a stretchable rotatory porous disk

A theoretical entropy generation analysis is conducted by applying the MHD and nonlinear thermal radiation effects contained in porous material for a steady three-dimensional power-law nanofluid flow near the stagnation point region. With the assistance of a thermally radiated non-uniform heat source /sink subject to convective boundary conditions, the heat transformation phenomenon is explored within the boundary layer over the stretchable rotatory disk. Multi-wall carbon nanotubes (MWCNTs) are incorporated in the ethylene glycol (C2H6O2) as a base fluid. The proposed problem of fluid flow is mathematically modeled. The governing nonlinear partial differential equations (PDEs) are lessened to highly mixed nonlinear ordinary differential equations (ODEs) after the utilization of appropriate transformations. The effects of several classes of relevant parameters upon total entropy generation and Bejan number profiles are investigated by numerically addressing the ODEs with the purpose of a well-known Keller Box method. Furthermore, the skin friction coefficients and local Nusselt number are calculated for shear-thinning and shear-thickening behaviors of the power-law fluid. Also, the total entropy generation increases for the Brinkman number and the permeability parameter but decreases for the material parameter, whereas the Bejan number has different behavior from entropy generation.

Computational study of three-dimensional flow and heat transfer of 25 nm Cu–H2O nanoliquid with convective thermal condition and radiative heat flux using modified Buongiorno model

The three-dimensional steady flow of an incompressible 25 nm water-based copper nanoliquid over a bi-directional elongated surface with convective thermal boundary condition is studied. This work may meet various thermal engineering applications for instance thermal energy exchangers, solar energy collectors, geophysical transports, radiators, electronic cooling devices, and nuclear reactors. Corcione's model for effective thermal conductivity and dynamic viscosity is used in conjunction with correlations based on effective medium theory for density, specific heat, and electrical conductivity. The effects of radiative heat and convective thermal energy conditions are also taken into account. Modified Buongiorno inhomogeneous model-based governing equations transmuted to nonlinear ordinary boundary value problem. The subsequent system has been deciphered using computer algebraic system software. The method used is validated against the available data and found an exceptional agreement. Two dimensional charts are designed to analyze the impact of the key parameters involved in the model. Three dimensional surface plots are plotted for the study of the Nusselt number, friction coefficients, and Sherwood number values are tabulated for several key parameters. A regression analysis is also performed for the local Nusselt number.

Stability Analysis of Thermocapillary Convection of B<sub>2</sub>O<sub>3</sub>/Sapphire Melt in an Annular Pool

Aiming at the thermocapillary convection stability of sapphire crystal grown by liquid-encapsulated Czochralski method, by non-linear numerical simulation, obtained the flow function and temperature distribution of R-Z cross section, as well as the velocity and temperature distribution at liquid-liquid interface and monitoring point of B2O3/sapphire melt in annular two liquid system, covered with solid upper wall and in microgravity. By means of linear stability analysis, obtained the neutral stability curve and critical stability parameters of the system, and revealed the temperature fluctuation of the liquid-liquid interface. The calculated results of B2O3/sapphire melt were compared with 5cSt silicone oil/HT-70. The results show that under the same geometrical conditions, the flow of B2O3/sapphire melt system is more unstable than 5cSt silicone oil/HT-70, there are two unstable flow patterns, radial three-dimensional steady flow cell and hydrothermal waves near the hot wall. The larger the ratio of Pr number of upper and lower fluid layers is, the better the effect of restraining the flow of lower fluid layers is.

Numerical validation and physical explanation of the universal force theory of three-dimensional steady viscous and compressible flow

In a recent paper, Liu et al. [“Lift and drag in three-dimensional steady viscous and compressible flow”, Phys. Fluids 29, 116105 (2017)] obtained a universal theory for the aerodynamic force on a body in three-dimensional steady flow, effective from incompressible all the way to supersonic regimes. In this theory, the total aerodynamic force can be determined solely with the vorticity distribution on a single wake plane locating in the steady linear far field. Despite the vital importance of this result, its validity and performance in practice has not been investigated yet. In this paper, we performed Reynolds-averaged Navier–Stokes simulations of subsonic, transonic, and supersonic flows over a three-dimensional wing. The aerodynamic forces obtained from the universal force theory are compared with those from the standard wall-stress integrals. The agreement between these two formulas confirms for the first time the validity of the theory in three-dimensional steady viscous and compressible flow. The good performance of the universal formula is mainly due to the fact that the turbulent viscosity in the wake is much larger than the molecular viscosity therein, which can reduce significantly the distance of the steady linear far field from the body. To further confirm the correctness of the theory, comparisons are made for the flow structures on the wake plane obtained from the analytical results and numerical simulations. The underlying physics relevant to the universality of the theory is explained by identifying different sources of vorticity in the wake.

Stability analysis and modeling for the three-dimensional Darcy-Forchheimer stagnation point nanofluid flow towards a moving surface

In this research, the three-dimensional (3D) steady and incompressible laminar Homann stagnation point nanofluid flow over a porous moving surface is addressed. The disturbance in the porous medium has been characterized by the Darcy-Forchheimer relation. The slip for viscous fluid is considered. The energy equation is organized in view of radiative heat flux which plays an important role in the heat transfer rate. The governing flow expressions are first altered into first-order ordinary ones and then solved numerically by the shooting method. Dual solutions are obtained for the velocity, skin friction coefficient, temperature, and Nusselt number subject to sundry flow parameters, magnetic parameter, Darcy-Forchheimer number, thermal radiation parameter, suction parameter, and dimensionless slip parameter. In this research, the main consideration is given to the engineering interest like skin friction coefficient (velocity gradient or surface drag force) and Nusselt number (temperature gradient or heat transfer rate) and discussed numerically through tables. In conclusion, it is noticed from the stability results that the upper branch solution (UBS) is more reliable and physically stable than the lower branch solution (LBS).

Stability of Conical Shocks in the Three-Dimensional Steady Supersonic Isothermal Flows Past Lipschitz Perturbed Cones

We are concerned with the structural stability of conical shocks in the three-dimensional steady supersonic flows past Lipschitz perturbed cones whose vertex angles are less than the critical angle. The flows under consideration are governed by the steady isothermal Euler equations for potential flow with axisymmetry so that the equations contain a singular geometric source term. We first formulate the shock stability problem as an initial-boundary value problem with the leading conical shock-front as a free boundary, and then establish the existence and asymptotic behavior of global entropy solutions of bounded variation (BV) of the problem. To achieve this, we first develop a modified Glimm scheme to construct approximate solutions via self-similar solutions as building blocks in order to incorporate with the geometric source term. Then we introduce the Glimm-type functional, based on the local interaction estimates between weak waves, the strong leading conical shock, and self-similar solutions, as well as the estimates of the center changes of the self-similar solutions. To make sure the decreasing of the Glimm-type functional, we choose appropriate weights by careful asymptotic analysis of the reflection coefficients in the interaction estimates, when the Mach number of the incoming flow is sufficiently large. Finally, we establish the existence of global entropy solutions involving a strong leading conical shock-front, besides weak waves, under the conditions that the Mach number of the incoming flow is sufficiently large and the weighted total variation of the slopes of the generating curve of the Lipschitz perturbed cone is sufficiently small. Furthermore, the entropy solution is shown to approach asymptotically the self-similar solution that is determined by the incoming flow and the asymptotic tangent of the cone boundary at infinity.

Mathematical analysis of heat and mass transfer in a Maxwell fluid with double stratification

The objective of the present research is to study the effects of variable thermal conductivity on the three-dimensional steady flow of Maxwell nanofluid in the presence of heat generation/absorption and double stratification. The theory of Cattaneo-Christov is used instead of the law of Fourier because the law of Fourier has parabolic equations and move at infinite speed in space. By using adequate transformation, the nonlinear partial differential equations (PDEs) are transformed into a set of ordinary equations (ODEs). The set of equations are solved numerically by adopting the bvp4c Matlab technique. The effects of different evolving parameters on axial velocity, temperature, and concentration are described in graphs. It is perceived that thermal and concentration stratification parameters result in the reduction of temperature and concentration distribution. Further, the heat generation parameter enhances the temperature distribution.

Steady three-dimensional ideal flows with nonvanishing vorticity in domains with edges

We prove an existence result for solutions to the stationary Euler equations in a domain with nonsmooth boundary. This is an extension of a previous existence result in smooth domains by Alber (1992) [1]. The domains we consider have a boundary consisting of three parts, one where fluid flows into the domain, one where the fluid flows out, and one which no fluid passes through. These three parts meet at right angles. An example of this would be a right cylinder with fluid flowing in at one end and out at the other, with no fluid going through the mantle. A large part of the proof is dedicated to studying the Poisson equation and the related compatibility conditions required for solvability in this kind of domain.

Size-dependent particle migration and trapping in three-dimensional microbubble streaming flows

Acoustically actuated sessile bubbles can be used as a tool to manipulate microparticles, vesicles and cells. In this work, using acoustically actuated sessile semi-cylindrical microbubbles, we demonstrate experimentally that finite-sized microparticles undergo size-sensitive migration and trapping towards specific spatial positions in three dimensions with high reproducibility. The particle trajectories are successfully reproduced by passive advection of the particles in a steady three-dimensional streaming flow field augmented with volume exclusion from the confining boundaries. For different particle sizes, this volume exclusion mechanism leads to three regimes of qualitatively different migratory behavior, suggesting applications for separating, trapping, and sorting of particles in three dimensions.

A theoretical analysis of steady three-dimensional flow and heat transfer of Power-Law nanofluid over a stretchable rotating disk filled with gyrotactic microorganisms

The current research study investigates the steady three-dimensional flow and heat transfer of a power-law nanofluid in the presence of the uniformly applied magnetic field and nonlinear thermal radiation over the stretchable rotating disk filled with gyrotactic microorganisms. The physically modeled partial differential equations (PDEs) are lessened to combined nonlinear ordinary differential equations (ODEs) with appropriate transformation. The influence of several types of pertinent parameters upon the dimensionless distributions of velocity, temperature, the concentration of nanoparticles, and microorganisms are analyzed graphically by solving the ODEs with a well-known shooting method. The tabular comparison is provided for the verification between the present results with those in the literature. Also, the physical quantities of interest are calculated, and the effects are scrutinized. Furthermore, it is noticed that the emerging parameters have produced a significant influence upon the velocity components, temperature, concentration of nanoparticles, and motile density of microorganisms.

Stress-driven spin-down of a viscous fluid within a spherical shell

Abstract

Simulation of heat transfer characteristics of phase change material dispersed with Titanium oxide nanoparticles in horizontal channel

Phase Changing Materials (PCM) is proving to be one of the major breakthroughs in industries as it has various applications in sustainable and renewable energy. The present study investigates the melting and solidification of phase change material (ice) in the presence of titanium oxide nanoparticles in a horizontal channel with internal heat source. The parametric study is carried out by varying the inlet velocity, heat source strength and nanoparticle volume fractions. The problem is modeled as three-dimensional laminar steady flow considering the effects of melting and solidification using Ansys Fluent. The heat sources mounted at the lower wall of the channel are specified with constant wall temperature boundary condition and the remaining walls are considered as adiabatic. The forced velocity inlet boundary condition is specified for the longitudinal velocity at the inlet and pressure outlet boundary condition is considered at the outlet of the channel. The results are analyzed by plotting the pathlines, longitudinal velocity contours, pressure and temperature contours. The results indicate that the longitudinal inlet velocity significantly affects the flow and heat transfer characteristics inside the horizontal channel. The increase in inlet velocity strengthens the melting rate and increases the heat transfer rate inside the channel. It is also found that the melting rate increases linearly with increase in the heat source intensity and nanoparticle volume fraction.

Lagrangian chaos in steady three-dimensional lid-driven cavity flow.

Steady three-dimensional flows in lid-driven cavities are investigated numerically using a high-order spectral-element solver for the incompressible Navier-Stokes equations. The focus is placed on critical points in the flow field, critical limit cycles, their heteroclinic connections, and on the existence, shape, and dependence on the Reynolds number of Kolmogorov-Arnold-Moser (KAM) tori. In finite-length cuboidal cavities at small Reynolds numbers, a thin layer of chaotic streamlines covers all walls. As the Reynolds number is increased, the chaotic layer widens and the complementary KAM tori shrink, eventually undergoing resonances, until they vanish. Accurate data for the location of closed streamlines and of KAM tori are provided, both of which reach very close to the moving lid. For steady periodic Taylor-Görtler vortices in spanwise infinitely extended cavities with a square cross section, chaotic streamlines occupy a large part of the flow domain immediately after the onset of Taylor-Görtler vortices. As the Reynolds number increases, the remaining KAM tori vanish from the Taylor-Görtler vortices, while KAM tori grow in the central region further away from the solid walls.

Numerical and experimental studies of gas-liquid flow and pressure drop in multiphase pump valves.

A numerical and experimental study was carried out to investigate the two-phase flow fields of the typical three valves used in the multiphase pumps. Under the gas volume fraction conditions in the range of 0%-100%, the three-dimensional steady and dynamic two-phase flow characteristics, pressure drops, and their multipliers of the ball valve, cone valve, and disk valve were studied, respectively, using Eulerian-Eulerian approach and dynamic grid technique in ANSYS FLUENT. In addition, a valve test system was built to verify the simulated results by the particle image velocimetry and pressure test. The flow coefficient CQ (about 0.989) of the disk valve is greater than those of the other valves (about 0.864) under the steady flow with a high Reynolds number. The two-phase pressure drops of the three valves fluctuate in different forms with the vibration of the cores during the dynamic opening. The two-phase multipliers of the fully opened ball valve are consistent with the predicted values of the Morris model, while those of the cone valve and disk valve had the smallest differences with the predicted values of the Chisholm model. Through the comprehensive analysis of the flow performance, pressure drop, and dynamic stability of the three pump valves, the disk valve is found to be more suitable for the multiphase pumps due to its smaller axial space, resistance loss, and better flow capacity.

Numerical simulation of variable thermal conductivity on 3D flow of nanofluid over a stretching sheet

AbstractThe present investigation deals with the steady three-dimensional flow and heat transfer of nanofluids due to stretching sheet in the presence of magnetic field and heat source. Three types of water based nanoparticles namely, copper (Cu), aluminium oxide (Al2O3), and titanium dioxide (TiO2) are considered in this study. The temperature dependent variable thermal conductivity and thermal radiation has been introduced in the energy equation. Using suitable similarity transformations the dimensional non-linear expressions are converted into dimensionless system and are then solved numerically by Runge-Kutta-Fehlberg scheme along with well-known shooting technique. The impact of various flow parameters on axial and transverse velocities, temperature, surface frictional coefficients and rate of heat transfer coefficients are visualized both in qualitative and quantitative manners in the vicinity of stretching sheet. The results reviled that the temperature and velocity of the fluid rise with increasing values of variable thermal conductivity parameter. Also, the temperature and normal velocity of the fluid in case of Cu-water nanoparticles is more than that of Al2O3- water nanofluid. On the other hand, the axial velocity of the fluid in case of Al2O3- water nanofluid is more than that of TiO2nanoparticles. In addition, the current outcomes are matched with the previously published consequences and initiate to be a good contract as a limiting sense.

Multistage Turbomachinery Design Using the Discrete Adjoint Method Within the Open-Source Software SU2

This paper documents a fully turbulent discrete adjoint method for three-dimensional multistage turbomachinery design. The method is based on a duality preserving algorithm and is implemented in the open-source computational fluid dynamics tool SU2. The SU2 Reynolds-averaged Navier–Stokes solver is first extended to treat three-dimensional steady turbomachinery flow using a conservative formulation of the mixing-plane coupled to nonreflective boundary conditions. The numerical features of the flow solver are automatically inherited by the discrete adjoint solver, ensuring the same convergence rate of the primal solver. The flow solver is then validated against experimental data available for three turbine configurations, namely, a one-and-half axial turbine stage, a transonic radial turbine coupled to a downstream diffuser, and a supersonic mini–organic Rankine cycle radial turbine operating with a fluid made by a heavy molecule. Finally the adjoint-based optimization framework is applied to the concurrent shape optimization of three rows of the axial turbine, demonstrating the advantages deriving from adopting multirow automated design methods in the context of turbomachinery design.

Mixed Oscillation Flow of Binary Fluid with Minus One Capillary Ratio in the Czochralski Crystal Growth Model

This work presented a series of three-dimensional unsteady numerical simulations on the characteristics of the mixed oscillation flows of binary mixture in a Czochralski crystal growth model. The silicon-germanium melt is investigated and the capillary ratio is minus one. The simulation results showed that, for the special capillary ratio, the thermal and solutocapillary forces are imposed in opposite directions and counteract each other. With the effect of buoyancy, the balance between the capillary forces is disturbed. Mixed with the forced convection driven by rotation, the capillary-buoyancy convection is complex. The basic mixed flow streamlines are presented as various rolling cells. The directions of the rolls are dependent on the combinations of surface and body forces. With the increase of temperature gradient, the basic flow stability is broken, and the oscillations occur. The crucible rotation has an effective influence on the stability enhancement. However, affected by the crystal rotation, the critical condition experiences an increase to a turning point, and then undergoes a sharp reduction to zero. Once the instability is incubated, the surface oscillations are analyzed. For the three-dimensional steady flow, only spatial oscillations are observed circumferentially, and the surface patterns of spokes, rosebud, and pulsating ring are obtained. For the unsteady oscillation flow, the spiral hydrosoultal waves, rotating waves, and superimposition of spirals and spokes are observed, and the oscillation behaviors are also discussed.

Regular path-constrained time-optimal control problems in three-dimensional flow fields

This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved by virtue of an indirect method based on the maximum principle in Gamkrelidze’s form. The proposed computational method essentially uses a certain regularity condition imposed on the data of the problem. A regularity assumption guarantees the continuity of the measure multiplier associated with the state constraint and ensures the appropriate behavior of the corresponding numerical procedure which, in general, consists of computing the entire field of extremals for the problem in question. Several examples of vector fields are considered to illustrate the computational approach.