Three-dimensional Unsteady Flow Research Articles

Unsteady three-dimensional MHD flow and heat transfer in porous medium suspended with both microorganisms and nanoparticles due to rotating disks

In the present study, the silent characteristics of magnetized mixed convection flow in porous medium suspended with both microorganisms and nanoparticles induced by two expanded or contracted disks are investigated. The Buongiorno’s model, in which the Brownian diffusion and thermophoresis are taken as dominant factors, is introduced to describe behaviors of the nanofluid. Multiple slip boundary conditions are also included into this problem. The nonlinear system is converted into five fully coupled nonlinear ordinary differential equations via suitable scaling transformations. The homotopy-based algorithm BVPh2.0 is employed to give their solutions. Physical interpretation is made through analyzing the graphs of different constraints for profiles of velocity, temperature, nanoparticle volume concentration and density of motile organism. Furthermore, we extend this model to seek the physical behaviors of heat transfer and the wall motile microorganism fluxes. Significant findings are presented, including that the wall expansion ratio and the magnetic parameter impose contrary effects on microorganism profiles, the Prandtl number and the radiation parameter play opposite roles on heat transfer rate, and the Brownian motion and the thermophoresis exhibit totally different influence on microorganism flux rate. It is expected that this study is helpful to understand heat transfer mechanism in multiple physical fields.

Rotating detonation waves in annular gap with variable stagnation pressure

We consider a three-dimensional unsteady flow with one, two, or four rotating detonation waves arising in an annular gap of an axially symmetric device between two parallel planes perpendicular to its symmetry axis. The corresponding problem is formulated and studied. It is assumed that there is a reservoir with quiescent homogeneous propane–air combustible mixture with given stagnation parameters; the mixture flows from the reservoir into the annular gap through its external cylindrical surface toward the symmetry axis, and the parameters of the mixture are determined by the pressure in the reservoir and the static pressure in the gap. The detonation products flow out from the gap into a space bounded on one side by an impermeable wall that is an extension of a side of the gap. Through a hole on the other side of the gap and through a conical output section with a half-opening angle of $$45^{\circ }$$ , the gas flows out from the engine into the external space. We formulate a model of detonation initiation by energy supply in which the direction of rotation of the detonation wave is defined by the position of the energy-release zone of the initiator with respect to the solid wall situated in a plane passing through the symmetry axis. After a while, this solid wall disappears (burns out). We obtain and analyze unsteady shock-wave structures that arise during the formation of a steady rotating detonation. We measure and compare thrust characteristics for different numbers of detonation waves. It was shown that the thrust weakly depends on the number of waves while the specific impulse increases with increasing number of waves. The study of rotating detonation at various values of the stagnation pressure was conducted. The calculation results show that at a stagnation pressure less than the critical value, the realization of rotating detonation is impossible. It is established that, depending on the stagnation pressure, qualitatively different shock-wave structures can be observed. The analysis is carried out within single-stage combustion kinetics by the numerical method based on the Godunov scheme with the use of an original software system developed for multi-parameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.

Flow over rectangular cylinder: Effects of cylinder aspect ratio and Reynolds number

Numerical simulations of two- and three-dimensional unconfined flows over rectangular cylinders are conducted at Reynolds number Re = 30 – 200. The cylinder cross-sectional aspect ratio AR (length-to-width) is varied as 0.25, 0.5, 1.0, 2.0, 3.0 and 4.0. The focus is given on how AR and Re influence the flow structure and associated aerodynamic parameters. The first critical Reynolds number (Recr1) associated with the transition from the steady flow to the two-dimensional unsteady flow is determined for each AR and found to linearly increase with increasing AR. The same observation is made for the second critical Reynolds number (Recr2) where the two-dimensional unsteady flow metamorphoses into the three-dimensional unsteady flow. A larger Re is required for a larger AR to have the onset of vortex shedding or the transition from two-dimensional flow to the three-dimensional. Three distinct scenarios of the flow separation and reattachment are identified in the ranges of Re and AR examined. The physical insight into the flow dependence on AR and Re is provided. Both AR and Re play a role in the formation of separation bubbles on the cylinder side surfaces. Two distinct mechanisms of the separation bubble formation are imparted. The detailed flow structures are linked to the mean and fluctuating forces and Strouhal numbers. The vortex strength beefs up with increasing Re but diminishes with AR, as do the normal and shear stresses and fluctuating forces.

Comparative Study on CFD Turbulence Models for the Flow Field in Air Cooled Radiator

This paper compares the performances of three Computational Fluid Dynamics (CFD) turbulence models, Reynolds Average Navier-Stokes (RANS), Detached Eddy Simulation (DES), and Large Eddy Simulation (LES), for simulating the flow field of a wheel loader engine compartment. The distributions of pressure fields, velocity fields, and vortex structures in a hybrid-grided engine compartment model are analyzed. The result reveals that the LES and DES can capture the detachment and breakage of the trailing edge more abundantly and meticulously than RANS. Additionally, by comparing the relevant calculation time, the feasibility of the DES model is proved to simulate the three-dimensional unsteady flow of engine compartment efficiently and accurately. This paper aims to provide a guiding idea for simulating the transient flow field in the engine compartment, which could serve as a theoretical basis for optimizing and improving the layout of the components of the engine compartment.

Calculation of the speed characteristics of an upward swirling gas flow under conditions of side wind

The paper presents the results of numerical modeling of lateral wind effects on three-dimensional unsteady air flows in an upward swirling stream of an artificially created tornado in a stationary mode of operation. The mathematical model is the complete system of Navier-Stokes equations taking into account the viscosity and thermal conductivity of a moving gas, as well as the action of gravity and Coriolis. Using an explicit difference scheme and an appropriate choice of initial and boundary conditions, solutions are obtained numerically for the complete system of Navier-Stokes equations in the computational domain in the form of a rectangular parallelepiped. All components of the gas flow velocity were calculated at fixed time instants and
 instantaneous streamlines were constructed with constant horizontal wind direction taken into account. The calculations showed that the result of the wind effect on the upward swirling flow is an asymmetric change in peripheral speed, its uneven
 deformation in opposite sections, and the total displacement of the vortex in the direction of the wind. In addition, the displacement and curvature of the vertical part of the vortex in the direction of the wind was established, a “detachment” of some instantaneous streamlines from the vertical rotating part and the appearance in the center of the vortex of an area that is free of streamlines increasing in diameter were recorded. In the studied time variation range, the stability of the air vortex to wind action and the stable operation of the used computational scheme are observed.

Analysis of the 3D flow of an impinging jet on a slotted plate using TR-Tomo PIV and Proper Orthogonal Decomposition

Impinging jets on plates with specific geometries, found in habitable enclosures, require a fundamental knowledge of the flow topology in order to reduce any acoustic or aeraulic discomfort. However, the flow in this type of jets is three-dimensional, time-dependent and turbulent. Thus, a high-speed volumetric velocity measurement technique is required to investigate the complete topology of the three-dimensional unsteady coherent flow structures. The research in the present paper has as aim the analysis of the flow from a volumetric point of view by using Time Resolved-Tomographic Particle Image Velocimetry (TR-TPIV) measurements. For this reason, an impinging jet on a slotted plate experimental set up has been developed and implemented. The kinematic fields of the studied volume are measured by TPIV acquisitions. Afterwards, the flow’s most energetic features were understood by the use of the snapshot Proper Orthogonal Decomposition (POD) technique which was applied on the kinematic fields. The results have shown that the first two modes were the most energetic and reflected the convective motion through the volume.

On unsteady flows of pore pressure-activated granular materials

We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid matrix behaves as an ideal plastic material before the activation takes place and then it starts to flow as a Newtonian or a generalized Newtonian fluid. The plastic yield stress is non-constant and depends on the difference between the given lithostatic pressure and the pressure of the fluid in a pore space. We study unsteady three-dimensional flows in an impermeable container, subject to stick-slip boundary conditions. Under realistic assumptions on the data, we establish long-time and large-data existence theory.

Some new characteristics of the confined flow over circular cylinders at low reynolds numbers

This study summarises some new characteristics of the fluid flow over a confined circular cylinder at low Reynolds numbers. Results from both two- and three-dimensional direct numerical simulations are presented at blockage ratio between 0.1 and 0.9 and Reynolds number between 120 and 500. Floquet stability analysis of selected cases will also be presented. From the two-dimensional simulations, it is found that the fluctuating lift forces decreases with blockage ratio and becomes zero (where the flow is steady) at blockage ratio of approximately 0.7–0.8. Upon further increasing the blockage ratio to 0.9, the simulations show a dramatic increase in the fluctuating lift forces, nearly an order of magnitude greater than previously reported for an unconfined cylinder flow. It is also found that for blockage ratio of 0.5, there is a long term two-dimensional instability that becomes more prominent with increasing Reynolds number. This instability has a time scale of approximately 105 time units (D/Umax) at Reynolds number of 500. In addition, the transition between two- and three-dimensional flow at blockage ratios up to 0.5 is investigated. It is shown that the transition Reynolds number decreases with increasing blockage ratio. At high blockage ratio of 0.5, as we increase the Reynolds number, the transition to three-dimensional flow is shown to go from unsteady two-dimensional to steady three-dimensional before transitioning to unsteady three-dimensional flow.

Effect of nonlinear radiation on 3D unsteady MHD stagnancy flow of Fe3O4/graphene–water hybrid nanofluid

ABSTRACT Three-dimensional unsteady magnetohydrodynamic stagnancy flow of hybrid nanoliquid, with nonlinear radiation and uneven heat rise/sag, is studied hypothetically. We considered Fe3O4/graphene nanoparticles embedded in water. The physical problem is modelled mathematically and resolved using Runge–Kutta Fourth order with a shooting procedure. Influences of pertinent parameters on the flow and energy transport are noted numerically and graphically. Moreover, the wall friction and the local Nusselt number are computed and a comparative analysis of nano/hybrid nanofluids is performed with the help of streamlines and isotherms. It is found that the drive and energy transport of nano/hybrid nanofluid is highly influenced by the variation in the particle volume fraction as well as unsteadiness factor. Also, the average temperature of nanofluid in the saddle stagnation region is higher than that of hybrid nanofluid.

Calculation of the thermodynamic characteristics of an upward swirling gas flow under conditions of side wind

The paper presents the results of numerical modeling of lateral wind effects on three-dimensional unsteady air flows in an upward swirling stream of an artificially created tornado after entering a stationary mode. Under the corresponding initial and boundary conditions, the solutions of the complete system of Navier-Stokes equations in the computational domain in the form of a rectangular parallelepiped are numerically obtained using the explicit difference scheme. At fixed points in time, the gas-dynamic characteristics of air flows are calculated under the action of gravity and Coriolis, as well as taking into account the constant horizontal directional wind speed. Numerical calculations showed that the resulting density, temperature, and pressure gradients lead to significant and asymmetric changes in air flows at different points in time and at different points in the computational domain. The total displacement of the vortex in the direction of the wind, the deformation and increase in the diameter of the vortex, which begin in the bottom part and pass into its vertical part, are established. In the considered range of time changes, the stability of the air vortex under study against wind action and the stable operation of the computational scheme used are noted.

Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion

Abstract We prove that there exists a weak solution to a system governing an unsteady flow of a viscoelastic fluid in three dimensions, for arbitrarily large time interval and data. The fluid is described by the incompressible Navier-Stokes equations for the velocity v , coupled with a diffusive variant of a combination of the Oldroyd-B and the Giesekus models for a tensor 𝔹. By a proper choice of the constitutive relations for the Helmholtz free energy (which, however, is non-standard in the current literature, despite the fact that this choice is well motivated from the point of view of physics) and for the energy dissipation, we are able to prove that 𝔹 enjoys the same regularity as v in the classical three-dimensional Navier-Stokes equations. This enables us to handle any kind of objective derivative of 𝔹, thus obtaining existence results for the class of diffusive Johnson-Segalman models as well. Moreover, using a suitable approximation scheme, we are able to show that 𝔹 remains positive definite if the initial datum was a positive definite matrix (in a pointwise sense). We also show how the model we are considering can be derived from basic balance equations and thermodynamical principles in a natural way.

Numerical simulation of gas-liquid mixed top blowing to enhance momentum diffusion

The presence of magnetic iron in slag increases the viscosity of the matte-slag mixture, impeding the precipitation and separation of matte from the slag. Magnetic iron can be reduced by injecting diesel oil into the molten bath and the resulting reaction enhanced by adding nitrogen to the spray lance. This study establishes a three-dimensional mathematical unsteady flow model of a y-shaped pipe containing a gas-liquid mixture, which is top-blown to enhance momentum agitation. By changing the inlet velocity of the y-pipe branch while maintaining a constant oil inlet speed, eight working conditions with different oil-gas ratios were established. These were used to investigate the effect of changing the two-phase flow pattern in the vertical tube with the inlet gas-liquid ratio. The simulation results agree well with published water model results. Experimental and simulation results show that when the ratio of oil to gas is 1:2, due to tangential disturbance of the branch gas relative to the main oil phase,rotational flow forms during the mixed descent process. After entering the molten bath, the circumferential gas-liquid mixing disturbance forms the optimum effect of swirling flow diffusion in the molten bath. The complex flow pattern formed by the nonlinear momentum diffusion of diesel mixed with bubbles can effectively improve the reduction rate of magnetic iron in the molten bath, thus reducing copper content in the slag.

Vortex force maps for three-dimensional unsteady flows with application to a delta wing

Abstract

Simulations of Unsteady Three-Dimensional Hypersonic Double-Wedge Flow Experiments

Hypersonic flow over a three-dimensional 30–55 deg double wedge is investigated for three different conditions of varying enthalpy and Reynolds number with nitrogen as the test gas. Streamwise and spanwise wall heat flux are compared to the experimental data that were obtained at the University of Illinois at Urbana–Champaign and the California Institute of Technology. In previous studies, there were concerns that portions of the flowfield were rarefied; however, after an in-depth analysis, we find the flowfield to be firmly in the continuum regime. Comparisons of heat flux at an instant of time in the simulations show good agreement with the experiments. However, averaged heat flux over a long period of time relative to the experimental test time are underpredicted and develop low-frequency periodic motion. To better understand the unsteadiness and three-dimensionality of the flowfield, we analyze the mass flux through a spanwise plane, and we perform sparsity-promoting dynamic mode decomposition for the wall heat flux and midplane pressure. Finally, we analyze the effect of vibrational nonequilibrium on the flowfield. It is found that the flowfield dynamics vary with increasing enthalpy and Reynolds number. Furthermore, the flowfield is found to be three dimensional, unsteady, and asymmetric for all cases.

Analysis of Unsteady Pressure Fluctuation in a Semi-Open Cutting Pump

In order to understand the pressure fluctuation characteristics of a semi-open cutting pump, the three-dimensional unsteady flow fields were calculated. External and internal flow characteristics of four schemes with different relative angles between the rotary cutter and the impeller were studied. The pressure fluctuations in the lower plate, the upper plate, the clearance between the rotary cutter and the fixed cutter, the first section in volute and nearby parts of the tongue were all analyzed, which are all the places that pressure distributions are greatly affected by the static and dynamic interaction, and at the same time, the force on the impeller was also analyzed. The results show that the fluctuations at different positions change periodically; the main frequency is blade frequency. The amplitude of pressure fluctuation decreases from near the rotating part to far away, from near the tongue to far from the tongue. Due to the influence of both impeller and rotary cutter, the pressure fluctuation on the lower plate is the largest. The pressure fluctuation is affected by flow rate, the larger the flow rate, the greater the pressure fluctuation. The radial and axial forces of the impeller change periodically with time, and the number of wave peaks and wave valleys is the same as the number of blades.

Numerical investigation and characteristic analysis of the swirl meter with different swirlers

The swirl meter is one of the gas flow meters used in the industry. Its advantages are as follows: a strong signal level, easy maintenance, and stable performance. Hence, it has become widely accepted for natural gas metering. In this study, the numerical computation of the three-dimensional unsteady flow in a swirl meter was conducted using the renormalization group k–ε turbulence model and SIMPLE algorithm. The internal flow fields were analyzed in detail, wherein the velocity and pressure distributions were discussed under six flow rates (6, 15, 25, 40, 70, and 100 m3/h) and three swirl cone angles (11°, 20°, and 30°). The obtained results are reported and discussed as follows: the stable performance of the swirl meter was due to its capacity to maintain its internal characteristics over a large flow range. Also, it was detected that though the pressure decrease was gradual on the wall, an opposite tendency was shown at the center. On the other hand, the swirler structure was crucial to the metering capacity of the swirl meter, and the swirler cone angle influenced the pressure and velocity.

Research on Calculation of Thermal Resistance of Water-Cooling Radiator of Cooling Tower of Thermal Power Plant Based on Fluid Software Fluent

This paper introduces the method of calculating the thermal resistance and thermal resistance of high-power water-cooled radiators in cooling towers of thermal power plants using computational fluid software (CDF) Fluent. By solving the three-dimensional unsteady flow field and thermal field, the thermal resistance and thermal resistance value of the water cooling radiator of the cooling tower of the thermal power plant under different flow rates are calculated, which provides the temperature calculation for the steady state and dynamic process of the high-power inverter in accordance with.

Unsteady Three-Dimensional Free Convection Flow Near the Stagnation Point Over a General Curved Isothermal Surface in a Nanofluid

This study deals with an unsteady three-dimensional free convection flow near the stagnation point region over a general curved isothermal surface placed in a nanofluid. Nanofluids are great scientific interest because these new thermal transport phenomena surpass the fundamental limits of conventional macroscopic theories of suspensions. Since the heat and mass transfer are very extensive in the industry, the unsteady three-dimensional body near stagnation point can give a significant impact on the heat transfer process. The main objective of the present study is to investigate the effects of some governing parameters on the skin friction coefficients, local Nusselt and local sheerwood numbers as well as related profiles of unsteady free convection in a nanofluid. The momentum equations in x-and y-directions, energy balance equation, and nanoparticle concentration equation are reduced to a set of four fully-coupled nonlinear differential equations under appropriate similarity transformations. The well-known technique Keller-box method is used numerically for different values of governing parameters entering these equations. Further, the present results have been compared with the previous published results for a particular case and the comparisons are found to be in good agreement. The skin friction, local Nusselt number and Sherwood number is increases with an increase in curvature parameter. Rising values of the Lewis number and Brownian motion parameter has enhanced the flow while rising values of the buoyancy and thermophoresis parameter will decelerate the flow. The temperature profile is increases when Brownian motion, buoyancy and thermophoresis parameter increases and concentration profile increase with an increases in buoyancy and thermophoresis parameter.

Analysis of the influence of aerodynamic qualities of the components of mixtures on separation in power-saving vortex vehicles

The object of research is gas-dynamic vortex processes in heterogeneous polydisperse flows. One of the most problematic issues is the determination of the aerodynamic characteristics of the components of a heterogeneous polydisperse medium, which are necessary to create a mathematical model of the separation process. The study used methods of mathematical modeling based on the theory of similarity. A technique has been developed for assessing the aerodynamic parameters of mixture components, on the basis of which a number of aerodynamic similarities have been compiled. The coefficients of lift, aerodynamic drag, lateral force, longitudinal, transverse and rotational moments of the components of the grain mixture are obtained. This is necessary for theoretical studies of gas-dynamic processes in vortex separators in unsteady three-dimensional flow with variable flow density, concentration and flow rate of the separated mixture components and the carried fractions. The Reynolds vibration criterion is obtained, based on which the trajectories and energy of the vortex motion of individual components and the separation degree of heterogeneous mixtures are determined. This allows to improve the mathematical model of the distribution process of heterogeneous polydisperse mixtures in the proposed energy-saving vortex separators. The obtained results provide the basis for improving the general theory of heterogeneous vortex flows by introducing an external disturbance criterion that takes into account the drag of the vortex force field and the amplitude-frequency energy level. Thanks to this, it is possible to evaluate the influence of any argument in the desired function. The research results make it possible to automate the analysis of process characteristics and compare them by parameters with experimental data. And also to evaluate the correspondence of dynamic, kinematic and gas-dynamic functions calculated from the given geometric parameters of the vortex devices with the functions obtained from the averaged values. These data makes it possible to work out a range of variations in the parameters of the geometric design of vortex apparatuses by zones, parameters at the inlet, outlet, and degrees of separation, minimize the number of manufactured laboratory and semi-industrial vortex apparatuses, and unify a number of units. Compared with similar known separators, vortex apparatuses are proposed that reduce the cost of preparing raw materials in the grain mill area by a factor of tens due to the elimination of moving working parts, assemblies and screens.

Physical topology of three-dimensional unsteady flows with spheroidal invariant surfaces.

Scope is the response of Lagrangian flow topologies of three-dimensional time-periodic flows consisting of spheroidal invariant surfaces to perturbation. Such invariant surfaces generically accommodate nonintegrable Hamiltonian dynamics and, in consequence, intrasurface topologies composed of islands and chaotic seas. Computational studies predict a response to arbitrary perturbation that is dramatically different from the classical case of toroidal invariant surfaces: said islands and chaotic seas evolve into tubes and shells, respectively, that merge into "tube-and-shell" structures consisting of two shells connected via (a) tube(s) by a mechanism termed "resonance-induced merger" (RIM). This paper provides conclusive experimental proof of RIM and advances the corresponding structures as the physical topology of realistic flows with spheroidal invariant surfaces; the underlying unperturbed state is a singular limit that exists only for ideal conditions and cannot be achieved in a physical experiment. This paper furthermore expands existing theory on certain instances of RIM to a comprehensive theory (supported by experiments) that explains all observed instances of this phenomenon. This theory reveals that RIM ensues from perturbed periodic lines via three possible scenarios: truncation of tubes by (i) manifolds of isolated periodic points emerging near elliptic lines or by either (ii) local or (iii) global segmentation of periodic lines into elliptic and hyperbolic parts. The RIM scenario for local segmentation includes a perturbation-induced change from elliptic to hyperbolic dynamics near degenerate points on entirely elliptic lines (denoted "virtual local segmentation"). This theory furthermore demonstrates that RIM indeed accomplishes tube-shell merger by exposing the existence of invariant surfaces that smoothly extend from the tubes into the chaotic shells. These phenomena set the response to perturbation-and physical topology-of flows with spheroidal invariant surfaces fundamentally apart from flows with toroidal invariant surfaces. Its entirely kinematic nature and reliance solely on continuity and solenoidality of the velocity field render the comprehensive theory and its findings universal and generically applicable for (arbitrary perturbation of) basically any incompressible flow-in fact any smooth solenoidal vector field-accommodating spheroidal invariant surfaces.