Search

Looking for an optimal flow shape for culture growth in vortex bioreactors, an intriguing and impressive structure has been observed that mimics the strong swirling flows in the atmosphere (tornado) and ocean (waterspout). To better understand the flow nature and topology, this experimental study explores the development of vortex breakdown (VB) in a lab-scale swirling flow of two immiscible fluids filling a vertical cylindrical container. The rotating bottom disk drives the circulation of both fluids while the sidewall is stationary. The container can be either sealed with the still top disk (SC) or open (OC). As the rotation strength (Re) increases, a new circulation cell occurs in each fluid—the dual VB. In case SC, VB first emerges in the lower fluid at Re = 475 and then in the upper fluid at Re = 746. In case OC, VB first emerges in the upper fluid at Re = 524 and then in the lower fluid at Re = 538. The flow remains steady and axisymmetric with the interface and the free surface being just slightly deformed in the studied range of Re. Such two-VB swirling flows can provide efficient mixing in aerial or two-fluid bioreactors.

This paper reviews counterflows, double counterflows, and circulation cells in vortex motion and argues that all these seemingly paradoxical phenomena can be caused by a common swirl-decay mechanism (SDM). It is shown that the SDM explains (a) the counterflow of water and oil in hydrocyclones, (b) the elongated counterflow of hot and cold air in vortex tubes, (c) the double counterflow occurring in vortex combustion chambers, and (d) the back flow in tubular chimneys of vortex units. The SDM also explains the development and disappearance of circulation cells, often referred to as vortex breakdown bubbles, in sealed cylindrical containers where the flow is driven by rotation of one end disk. The SDM also works in two-fluid flows modeling vortex bioreactors. In a few words, the SDM works as follows. Because of the balance of the centrifugal force and the radial gradient of pressure in a fast-swirling flow, the pressure at the rotation axis is smaller than that at the periphery. If the swirl decays downstream, the pressure grows along the axis. This axial gradient of pressure decelerates the near-axis flow and can reverse it, thus developing a local or global counterflow.

This experimental and numerical work explains why a vortex breakdown bubble first emerges and then disappears as the fluid rotation speeds up. To this end, we explore a flow in a sealed cylindrical container with one end disk rotating and all other walls stationary. The rotation drives the meridional circulation: the fluid filling the container moves away from the rotating disk along the sidewall, converges to the axis near the stationary disk, and goes back to the rotating disk near the axis. As the rotation speed Re increases, a cell of counter circulation—a vortex breakdown bubble (VBB)—emerges, expands, contracts, and disappears. On the (h, Re) map, the boundary of the VBB region consists of two branches, which meet and terminate at a fold point as h decreases ($$\mathrm{h} =H/R$$, where $$H$$ is the height and $$R$$ is the radius of the cylinder). This study is the first to focus on the VB disappearance and explains the geometry of VBB region: why the VBB first emerges and then disappears as Re increases at a fixed h. In a few words, the mechanism is as follows. The convergence of the swirling flow to the axis reduces the pressure above the center of the stationary disk. Suction because of the reduced pressure creates a VBB and attracts it closer to the disk. This VBB shift deteriorates the flow convergence to the axis and concentrates the meridional circulation near the sidewall. The pressure grows above the still disk, the suction weakens, which kills the VBB, and the fluid stagnates near the axis. This mechanism is even more pronounced in a two-fluid flow.

The hydrodynamics of secondary flow phenomena in a disc-shaped gas vortex unit (GVU) is investigated using experimentally validated numerical simulations. The simulation using ANSYS FLUENT® v.14a reveals the development of a backflow region along the core of the central gas exhaust, and of a counterflow multivortex region in the bulk of the disc part of the unit. Under the tested conditions, the GVU flow is found to be highly spiraling in nature. Secondary flow phenomena develop as swirl becomes stronger. The backflow region develops first via the swirl-decay mechanism in the exhaust line. Near-wall jet formation in the boundary layers near the GVU end-walls eventually results in flow reversal in the bulk of the unit. When the jets grow stronger the counterflow becomes multivortex. The simulation results are validated with experimental data obtained from Stereoscopic Particle Image Velocimetry and surface oil visualization measurements.

Vortex reactors take advantage of the synergy between enhanced heat and mass transfer rates and multifunctional phenomena at different temporal and spatial scales. Proof-of-concept experiments with our novel and innovative STAtor-Rotor VOrtex Chamber (STARVOC) confirm its advantageous features for the sustainable production of chemicals and fuels. STARVOC is a high-g contactor that uses carrier flow (gas or liquid) tangential injection to drive a rotor attached to low-friction bearings. The vortex chamber inside the rotor contains a secondary phase or phases, such as a solids bed, a liquid layer, or a suspension. Carrier fluid passes through the perforated rotor wall and contacts a densely and uniformly distributed secondary phase with enhanced slip velocities. Experiments focused on pressure profiles, rotor angular velocity, and solids azimuthal velocity. With air as the carrier fluid and different solid particle beds as the secondary phase, STARVOC reached bed azimuthal velocities up to four-fold compared to those reached in Gas-Solid Vortex Units with fully static geometry. These results show its potential to improve interfacial heat and mass transfer rates and take advantage of flow energy and angular momentum. Due to its process intensification capabilities, STARVOC is a promising alternative for the state-of-the-art chemical industry.

This numerical study analyzes the stability of a steady axisymmetric air–water flow driven by a rotating top disk in a sealed semispherical container. A motivation is possible applications in aerial bioreactors. The centrifugal force pushes the air to periphery near the disk, downward near sidewall, toward the axis near the interface, and upward near the axis. This meridional circulation of air drives the water counter-circulation while the centrifugal force tends to induce the water co-circulation. Their competition results in the development of a three-eddy pattern as the rotation intensifies. The air circulation and the water co-circulation are separated by a thin layer of water counter-circulation. It is shown that the time-oscillatory helical instability emerges when the three-eddy pattern is well formed. The azimuthal wave number is m = 1 in the shallow-water case and m = 2 otherwise. The analysis of flow patterns and critical-disturbance energy distributions indicates that the instability emerges in the air domain and likely is of the shear-layer type.

A modified continuum model for the sintering of biporous materials is proposed. Along with the viscous flow of the matrix resulting from the sintering potential, the vacancy flow from small to large pores is considered. The capabilities of the modified theory to consider the above phenomena are used to predict and explain the effect of constraints on local porosity increase and instability of the sintering process. Potential ways for using the results obtained are identified.

This experimental study describes a hysteresis—a vivid manifestation of strongly nonlinear flow physics. A sealed vertical cylindrical container of radius 45 mm and height 90 mm is filled with water and sunflower oil. The rotating lid drives swirl and themeridional circulation of both fluids. As the rotation strength Re increases, the oil–water interface rises near the axis, touches the lid at Re = Re1, and moves toward the container sidewall. Then as Re decreases, the interface returns to the axis and separates fromthe lid at Re = Re2 < Re1. At each Re from the range, Re2 < Re < Re1, two different stable steady flow states are observed, which is typical of hysteresis. The hysteresis only occurs if a volume fraction of oil is small. The hysteresis disappears as the oil fraction exceeds a threshold, which is around 0.4.

An experimental study reveals the formation of a thin circulation layer (TCL) adjacent to the entire interface of a two-fluid swirling flow in a sealed, vertical cylindrical container. The TCL scenario differs from that predicted numerically.

This experimental study reveals a counterflow slip at the interface of two immiscible fluids filling a sealed vertical cylindrical container whose bottom disk rotates while other walls are stationary. An advanced particle image velocimetry helps us analyze and quantify streamline patterns and velocity profiles of the steady axisymmetric flows of both fluids. As the angular velocity of a disk increases, starting from zero, three changes occur in topology of the upper-fluid flow while topology of the lower-fluid flow remains invariant. These changes result in the counterflow slip at the entire interface, whose nature is speculatively discussed and requires further research.

As a result of mathematic modeling, construction of the multisectional thermoelements for generators working in 300 K–1200 K temperature range was designed using the developed software. Thermal linear expansion coefficients of thermoelectric materials for sections of thermoelement have been studied in the field of operating temperatures. Vertical quartz dilatometer DL-1500RH (ULVAC Sinku-Riko) and the measuring complex developed by authors have been used for this research. The design method for calculation of thermoelement thermal expansion has been developed. The accuracy of the method was determined by comparing with the data for thermoelement thermal expansion investigated in 293 K–473 K temperature range. Calculated and measured data have a good correlation and the difference between them is less than 5%. The developed method has been used for calculation of thermoelement thermal expansion at the temperatures from 293 K to 1173 K.

To clarify the three-dimensional structure of near-wall jets observed in disc-like gas vortex units, experimental and numerical studies are performed. The experimental results are obtained using Particle Image Velocimetry (PIV), Laser Doppler Anemometry (LDA), pressure probes and surface oil flow visualization techniques. The first three techniques have been used to investigate the bulk flow hydrodynamics of the vortex unit. Surface oil flow visualization is adopted to visualize streamlines near the end-walls of the vortex unit. The surface streamlines help determine the azimuthal and radial velocity components of the radial near-wall jets. Simulations of the vortex unit using FLUENT® v.14a are simultaneously performed, computationally resolving the near-wall jet regions in the axial direction. The simulation results together with the surface oil flow visualization establish the three-dimensional structure of the near-wall jets in gas vortex units for the first time in literature. It is also conjectured that the near-wall jets develop due to combined effects of bulk flow acceleration and swirl. The centrifugal force diminishes in the vicinity of the end-walls. The radially inward pressure gradient in these regions, no longer balanced by the centrifugal force, pushes gas radially inward thus developing the near-wall jets. This article is protected by copyright. All rights reserved.

The paper analyses the typical topology of swirling flows of two immiscible fluids generated in the cylindrical container by its rotating end wall. Using the flow visualization and velocity measurements by PIV for different parameters of rotation of the upper end of the cylinder, this study reveals general features of the evolution of counter flow (bubble-like vortex breakdown, VB) which is common for vortex flows with various liquids at the interface or the solid rotated end. In both fluids, the rotation generates centrifugal meridional circulations and a local circulation cell (vortex breakdown bubble, VBB). The research shows that the scenario for the VBB appearance depends weakly on the properties of the medium that restricts the circulation of the working fluid. Patterns and formation of cellular structure appear common for flows with “liquid bottom” and “liquid rotating lid”. The VBB scenario is similar to that occurring in a single-fluid flow and in the upper or lower fluids of a two-fluid flow, but the range of the Reynolds numbers can be different depending on the volume of the upper fluid and kinematic viscosity of the lower liquid. This study can serve as the first step in the “rotating liquid lid” and “liquid lid” technology for chemical and biological processes where fine, gentle, and nonintrusive mixing is favourable.

This work reveals a jump of azimuthal velocity at the interface that can be important for vortex bioreactors. The rotating lid controls the flow of two fluids in a vertical cylindrical container, the other walls of which are stationary. Near the lid, a centrifugal force pushes the upper fluid toward the sidewall, thereby developing its centrifugal meridional circulation. This motion drives the bulk counter-circulation in the lower fluid at a slow rotation. The use of sunflower oil for the upper fluid, alcohol-glycerine solutions for the lower fluid and the assembly of averaged PIV images allow measuring velocity and visualizing pattern even in a creeping motion. This advanced experimental method helps to detect velocity jumps occurring at the interface.

Two-fluid swirling flows are rich in features of fundamental and practical interest. Among them, the most intriguing phenomenon that is important for applications is the formation of local circulation cells (vortex breakdown, VB). Our experimental study explores flows of two immiscible liquids in a sealed vertical cylindrical container driven by the rotating lid. The lid rotation generates the meridional circulation of an adjacent fluid, which serves as a rotating “liquid lid” for the lower fluid. The upper fluid goes from the cylinder axis to the periphery near the lid and back near the interface. This centrifugal circulation tends to propel the circulation in the main-fluid domain – in the lower fluid. As the angular speed of lid rotation increases, vortex breakdown occurs in the lower fluid. Using visualization of the flow and measurement of velocity by PIV method, we reveal common features of the VB development in the lower fluid at different thicknesses of the upper fluid. We show that the range of Reynolds numbers, where VB occurs, might be different depending on the volume of the upper liquid and its kinematic viscosity.

This experimental and numerical study discusses the formation of double vortex breakdown in a swirling flow of two immiscible fluids where new circulation cells evolve in both fluids. The rotating lid drives the steady axisymmetric motion in a sealed vertical cylindrical container whose other walls are stationary. As the rotation intensifies, multiple topological changes occur in the flow. This study explains how two new circulation cells (vortex breakdown bubbles) almost simultaneously develop near the centers of both upper and lower fluids while the flow remains steady and axisymmetric. Such multi-cell flows can help provide fine, gentle, and nonintrusive mixing in chemical and biological reactors.

Recent theoretical and numerical studies predict the Moffatt eddies near the interface-wall intersection in a two-fluid flow. The current work provides the first experimental evidence of this phenomenon of fundamental interest. It also reveals a jump of the azimuthal velocity at the interface which can be important for vortex bioreactors. The rotating lid drives a two-fluid flow in a vertical cylindrical container whose other walls are stationary. Near the lid, the centrifugal force pushes the upper fluid to the sidewall thus developing its centrifugal meridional circulation. This motion drives the bulk counter-circulation and the Moffatt eddies in the lower fluid at a slow rotation. Using sunflower oil for the upper fluid, water-glycerin or alcohol-glycerin solutions for the lower fluid, and assemble averaging of PIV images allow for velocity measurement and flow visualization even in a creeping motion. This advanced experimental technique helps detect velocity jumps, occurring at the interface and the Moffatt outermost eddy.

This experimental study reveals a spectacular and important phenomenon—double vortex breakdown—in a swirling flow of two immiscible fluids where vortex breakdown bubbles evolve simultaneously in both fluids. The rotating lid drives the steady axisymmetric motion in a sealed vertical cylindrical container whose other walls are stationary. As the rotation intensifies, topological metamorphoses occur, resulting in a multicellular flow. Two new circulation cells (vortex breakdown bubbles) simultaneously develop near the centers of both fluids while the flow remains steady and axisymmetric. Such a pattern can help provide fine, gentle, and nonintrusive mixing in chemical and biological reactors.

This numerical study reveals and explains a mechanism of eddy emergence in the steady two-dimensional thermal convection. A thin horizontal container is filled with water. The bottom and top walls are adiabatic while the sidewalls have prescribed temperatures. Gravity and a horizontal gradient of temperature drive the water circulation from the cold end to the hot end near the bottom and back near the top. As the flow strength, characterized by the Grashof number Gr , increases, the horizontal velocity reverses and local circulation cells emerge via bifurcation near the central stagnation point. We argue that the reversals are likely caused by the entrainment effect of jets, which form near the horizontal walls. This explains the experimental observations of Kirdyashkin (1984). No instability develops for Gr ⩽ 10 7 due to the stable vertical stratification of density. The obtained results are of fundamental interest and can be relevant for the development of efficient heat exchangers.

A unique normalized radial pressure profile characterizes the bed of a gas‐solid vortex reactor over a range of particle densities and sizes, solid capacities, and gas flow rates: 950–1240 kg/m3, 1–2 mm, 2 kg to maximum solids capacity, and 0.4–0.8 Nm3/s (corresponding to gas injection velocities of 55–110 m/s), respectively. The combined momentum conservation equations of both gas and solid phases predict this pressure profile when accounting for the corresponding measured particle velocities. The pressure profiles for a given type of particles and a given solids loading but for different gas injection velocities merge into a single curve when normalizing the pressures with the pressure value downstream of the bed. The normalized—with respect to the overall pressure drop—pressure profiles for different gas injection velocities in particle‐free flow merge in a unique profile. © 2015 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 61: 4114–4125, 2015

The instability of the steady axisymmetric flow in a sealed elongated cylinder, driven by a rotating end disk, is studied with the help of numerical simulations. It is argued that this instability is of the shear-layer type, being caused by the presence of an inflection point in the radial distribution of axial velocity of the base circulatory flow. The disturbance kinetic energy is localized in both the radial and axial directions, reaching its peak near the rotating disk, where the magnitude of base-flow axial velocity is close to its maximum. The critical Reynolds number, $\mathit{Re}_{cr}$, is found to be nearly $h$-independent for $h>5$; $h$ is the cylinder length-to-radius ratio. It is shown that the sidewall co-rotation suppresses the instability. As the co-rotation increases, the centrifugal instability becomes the most dangerous, i.e. determines $\mathit{Re}_{cr}$. Physical explanations are given for the stabilizing effect of the co-rotation, which is stronger (weaker) for the shear-layer (centrifugal) instability.

Ponencia de: 6th International Conference Heat and Mass Transfer and Hydrodynamics in Swirling Flows 21–23 November 2017, Novosibirsk, Russian Federation This experimental and numerical study addresses a flow of water and sunflower oil. This flow is driven by the rotating lid in a sealed vertical cylinder. The experiments were performed in a glass container with a radius of 45 mm and a height of 45 mm with the water volume fraction of 20%. Different densities and immiscibility of liquids provide the stable and sharp interface. At the rest, the interface is flat and horizontal. As the rotation speeds up, a new water-flow cell emerges near the bottom center. This cell expands and occupies almost the entire water domain while the initial water circulation shrinks into a thin layer adjacent to the interface. The water, rising near the container axis, strongly deforms the interface (upward near the axis and downward near the sidewall). A new oil-flow cell emerges above the interface near the axis. This cell disappears as the interface approaches the lid. The water separates from the sidewall, reaches the lid, and forms a column. As the rotation is decreased, the scenario reverses, but the flow states differ from those for the increasing rotation, i.e., a hysteresis is observed. The numerical simulations agree with the experiment and help explain the flow metamorphoses. Russian Science Foundation 14-29-00093

This paper explores patterns and stability of the air water thermal gravitational convection in a thin and wide horizontal container whose top and bottom walls are adiabatic while vertical sidewalls have prescribed different temperatures A compact polynomial solution describes a slow multi cell motion and a temperature distribution away from the sidewalls The solution explicitly shows how the flow topology depends on the water fraction thermal surface tension effect characterized by the Marangoni number Ma and buoyancy strength characterized by the Grashof number Gr The performed numerical simulations agree with the analytical solution for small Gr and Ma and describe changes in the flow topology for large Gr and Ma The flow transforms into a boundary layer pattern with jets located near the interface and container walls The jet entrainment generates new cells in the bulk water flow As Ma increases the Marangoni stresses focus near the sidewalls and develop a thin thermal boundary layer near the cold wall The performed stability study reveals that the steady convection is stable for Gr and Ma values considered The stability is due to the favorable stratification of water density provided by the adiabatic walls The results can be utilized for the development of efficient heat exchangers nbsp

This paper explains a mechanism of eddy formation in a slow air–water motion, driven by the rotating top disk, in a vertical sealed cylinder. The numerical simulations reveal nine changes in the flow topology as water volume fraction $H_{w}$ varies from 0 to 1. At $H_{w}$ around 0.8, there are two large regions of the clockwise meridional circulation, one in air and one in water. These regions are separated by two small cells of the anticlockwise circulation adjacent to the interface near the sidewall in water and near the axis in air. The air cell is a thin layer and topologically is a bubble–ring for $0.745 < H_{w} < 0.785$. Alterations of this flow pattern are explored as (i) pressure increases, (ii) the bottom disk co-rotates and (iii) the top-disk rotation speeds up. This paper provides the physical reasoning behind the flow transformations; the results are of fundamental interest and can be utilized in bioreactors.

This paper reviews counterflows, double counterflows, and circulation cells in swirling flows and argues that all these seeming paradoxical phenomena can be caused by a common swirl- decay mechanism (SDM). It is shown that SDM explains (a) the counterflow of water and oil in hydrocyclones, (b) the elongated counterflow of hot and cold air in vortex tubes, and (c) the double counterflow occurring in vortex combustion chambers. SDM also explains the development and disappearance of circulation cells, often referred to as vortex breakdown bubbles, in sealed cylindrical containers where the flow is driven by rotation of one end disk. In a few words, SDM is the following. The balance of the centrifugal force and the radial gradient of pressure in a fast- swirling flow results in that pressure at the rotation axis is smaller than pressure at the periphery. If swirl decays downstream, pressure grows along the axis. This axial gradient of pressure decelerates the near-axis flow and can reverse it thus developing a local or global counterflow. It is shown that SDM also works in two-fluid flows modeling vortex bioreactors.

Ground-source heat pumps are gaining popularity in Eastern Europe, especially those which are using the horizontal ground heat exchanger (GHX). Due to the difficulty of accessing GHX after the installation, materials and the quality of the installation must satisfy the very high requirements. An inaccurate calculation of GHX can be the reason of a scarcity of heat power in a crucial moment. So far, there isn’t any appropriate mathematical description of the horizontal GHX which takes into account the mutual influence of GHX pipes on each other. To solve this problem we used the temperature wave approach. As a result, a mathematical model which describes the dependence of the heat transfer rate per unit length of the horizontal GHX pipe on the thermal properties of soil, operating time of GHX and the distance between pipes was obtained. Using this model, heat transfer rates per unit length of a horizontal GHX were plotted as functions of the distance between pipes and operating time. The modeling shows that heat transfer rates decreases rapidly with the distance between pipes lower then 2 meters. After the launch of heat pump, heat power of GHX is reduced during the first 20 - 30 days and get steady after that. The obtained results correlate with experimental data. Therefore the proposed mathematical model can be used to design a horizontal GHX with the optimal characteristics, and predict its capability during operation.

The paper describes an asymptotic flow of a viscous fluid in an infinite annular cylindrical cavity as the distance from the flow source tends to infinity. If the driving flow near the source is axisymmetric then the asymptotic pattern is cellular; otherwise it is typically not. Boundary conditions are derived to match the asymptotic axisymmetric flow with that near the source. For a narrow cavity, the asymptotic solutions for the axisymmetric and three-dimensional flows are obtained analytically. For any gap, the flow is described by a numerical solution of an eigenvalue problem. The least decaying mode corresponds to azimuthal wavenumber $m= 1$.

Computer simulation has been used to study the warm compaction of complex powder parts. Relations of the plasticity theory for porous bodies and finite-element method are employed. The effect of the velocity ratio of different pressing elements on the density distribution is analyzed. The possible nonuniformity of density distribution is due to external friction and complex shape of parts. The optimal ratio is found. All other velocity ratios of pressing elements lead to unacceptable distribution of properties in powder parts.

This paper shows that decrease of velocity magnitude downstream enhances the shear-layer instability in jetlike single- and two-fluid flows. This feature has not been recognized in stability studies, performed in the parallel and quasi-parallel flow approximations, because the deceleration effect is strongly non-parallel. It was first revealed in conical similarity flows. The similarity allows for reducing the base-flow and stability problems to ordinary differential equations exactly conserving the acceleration terms. This helps reveal the deceleration effect. The development of numerical technique for stability studies of two-dimensional flows helped understand the instability nature of swirling flows in sealed containers. It was found for an elongated cylinder with one rotating end disk and stationary other walls that the instability develops in the counterflow near the rotating disk, where the backflow decelerates and the shear-layer and deceleration effects cooperate. An interesting stabilizing effect of acceleration is observed in a model heat exchanger. The thermal convection develops in a rotating cylindrical container whose sidewall is adiabatic and the end disks have different temperatures. The centrifugal acceleration suppresses, while the temperature difference stimulates, the shear-layer instability of this flow. Next, the review discusses two-fluid flows in a sealed vertical container, driven by either bottom (whirlpool model) or lid (waterspout model) rotation. As the rotation speeds up, the shear-layer instability develops in a jet-like boundary layer in the air–water flows. The jet forms near a rotating disk, goes to the interface near the sidewall, and converges to the axis near the interface. New circulatory cells emerge in both fluids and the interface significantly bends. The instability develops after such flow pattern becomes well formed. The instability focuses near the interface where the jet-like motion approaches a new cell, decelerates, and diverges—hence the deceleration and shear-layer effects work together. In oil–water flows, the instability develops in the lower fluid, either in its depth or near the interface depending on the water volume fraction. Thus, the review shows that deceleration enhanced the shear-layer instability in a wide group of flows.

This experimental and numerical study of a two-fluid swirling flow reveals a discontinuity of the radial velocity at the interface. The motion is driven by the rotating lid in a sealed vertical cylindrical container. The upper fluid radially diverges near the lid, goes downward near the sidewall, converges to the axis near the interface, and rises near the axis. This centrifugal circulation drives a bulk counter-circulation of the lower fluid at a slow rotation. As the rotation intensifies, a new circulation cell emerges in the lower fluid. The numerical simulations, performed under the continuity condition for all velocity and stress components, predict that the new cell emerges near the bottom and expands upward. In contrast, the new cell emerges near the interface and expands downward in the experiment. A slip condition is proposed for the radial velocity at the interface. The slip occurs due to the centrifugal force and difference in the fluid densities. The numerical simulations, performed with the slip condition, agree with the experiment.

The behavior of porous materials with bimodal pore distribution under external loads and kinematic constraints is considered. Numerical methods of continuum mechanics of sintering are used. The effect of partial and complete constraining of the surface bounding the billets in sintering is studied. Corresponding distributions of small and large pores are determined. The sensitivity of the distributions to constraining/loading paths is established.

vive wild turbulent mixing in these devices. To this end, an analytical solution to the Reynoldsaveraged Navier–Stokes equations is obtained that describes the turbulent flow in a cylindrical container. The Reynolds stresses are modeled using the Prandtl mixing length approach modified here for swirling flows. A fluid enters the container through a tangential inlet and leaves through a central exhaust, both located at the same end wall. Despite the inlet and exhaust being close, there is no shortcut flow. The fluid goes from the inlet near the sidewall to the dead end, turns around, and goes back near the axis to the exhaust. This global counterflow occurs due to swirl decay caused by friction at the sidewall. The combined effects of the end wall, swirl and friction causes pressure drops from the inlet to the dead end near the sidewall and from the dead end to the exhaust near the axis. Such a pressure distribution drives the counterflow and provides its survival against turbulent mixing. A simple experiment is performed confirming the counterflow geometry.

The results are given of the investigation into the structure of powdered bodies subjected to plastic deformation by broaching. Different schemes of deforming broaching have been considered, which involve direct contact of the workpiece surface with a deforming element and broaching in a closed system. A mathematical model of the process is given and calculated patterns of the distribution of the density and accumulated deformation of powdered compacts at different moments of deforming are discussed. The structural manifestations of the application of both schemes of deforming broaching have been compared.

Analytical solutions of the viscous gas equations are applied to model velocity and temperature fields in a vortex combustor with volume-distributed oxidation. The solutions show that swirl generates high-speed meridional circulation, which occupies around 2/3 of the combustor volume and serves as a flame holder and a double mixer. It is found that particle trajectories have double-spiral geometry in both the circulation and flow-through regions. The particle residence time is larger by an order of magnitude than the mixing time. In addition to the internal circulation, the external recirculation of a share of the flue gas is analyzed. Consideration of the mass and energy balance reveals the optimal share value. A proof-of-concept experiment confirms the modeling predictions.

This numerical study analyzes the development of eddies in a slow steady axisymmetric air–water flow in a sealed semispherical container, driven by a rotating top disk. As the water height, H w , increases, new flow cells emerge in both water and air. First, an eddy emerges near the axis-bottom intersection. Then this eddy expands and reaches the interface, inducing a new cell in the air flow. This cell appears as a thin near-axis layer which then expands and occupies the entire air domain. As the disk rotation intensifies at H w = 0.8 , the new air cell shrinks to the axis and disappears. The bulk water circulation becomes separated from the interface by a thin layer of water counter-circulation. These changes in the flow topology occur due to (a) competing effects of the air meridional flow and swirl, which drive meridional motions of opposite directions in water, and (b) feedback of water flow on the air flow. In contrast to flows in cylindrical and conical containers, there is no interaction with Moffatt corner vortices here.

Computer modelling is used to study warm compaction. Relationships of irreversible porous body flow and the finite element method are used. It is established that in view of nonuniform temperature distribution within a compact there is radial flow of powder. The more heated layer of the material is more intensely compacted than the less heated layer. Nonuniform temperature distribution affects the magnitude of axial and radial pressures. Modelling of compaction of a stepped article of complex shape makes it possible to establish that nonuniform heating may increase radial powder flow that in turn promotes levelling of the density. The results of modelling may be used in order to optimize warm compaction of powder articles by choosing special billet heating schemes.

The connection of Bal'shin consolidation theory with contemporary compaction mechanics is considered. The main principles of Bal'shin and proposals for powder compaction theory formulated by him are analyzed. A connection is established between the identity principle and the hypothesis of the existence of a representative element, and one possible way of determining its dimensions is demonstrated. The main attention is devoted to the hypothesis of continuity and the results of compaction mechanics, which are obtained based on it. A connection is noted between consolidation theory and the concept of the mean-square viscous stresses of Skorokhod. Problems of Bal'shin are indicated that may easily be resolved by means of the concept of mean-square viscous stress. The relative solution of the problem of evaluating density distribution is noted. Problems are discussed for powder breaking directly during compaction in a rigid die. The contribution of scientists from Armenia, Belarus, Russia and Ukraine in setting up contemporary compaction mechanics is evaluated.

An axial gradient of temperature can either suppress or enhance vortex breakdown (VB). The underlying mechanism of such VB control is centrifugal or/and gravitational convection. An additional thermal-convection flow directed oppositely to the base flow suppresses VB while a co-flow enhances VB. Our numerical simulations of a compressible flow in a sealed cylinder induced by a rotating bottom disk clearly reveal these effects. We vary the temperature gradient (e), Mach (Ma), Froude (Fr), and Reynolds (Re) numbers, and the aspect ratio (h). As e increases (e>0 corresponding to a temperature gradient parallel to the downward near-axis flow), the VB “bubble,” which occurs at e=0, diminishes and then totally disappears. The opposite temperature gradient (e

An on-parallel analysis of time-oscillatory instability of conical jets reveals important features not found in prior studies. Flow deceleration significantly enhances the shearlayer instability for both swirl-free and swirling jets. In swirl-free jets, flow deceleration causes the axisymmetric instability (absent in the parallel approximation). The critical Reynolds number Rea fo rt his instability is an order of magnitude smaller than the critical Rea predicted before for the helical instability (where Rea = rva/ν, r is the distance from the jet source, va is the jet maximum velocity at a given r, and ν is the viscosity). Swirl, intensifying the divergence of streamlines, induces an additional, divergent instability (which occurs even in shear-free flows). For the swirl Reynolds number Res (circulation to viscosity ratio) exceeding 3, the critical Rea for the single-helix counter-rotating mode becomes smaller than those for axisymmetric and multi-helix modes. Since the critical Res is less than 10 for the near-axis jets, the boundary-layer approximation (used before) is invalid, as is Long’s Type II boundary-layer solution (whose stability has been extensively studied). Thus, the nonparallel character of jets strongly affects their stability. Our results, obtained in a far-field approximation allowing reduction of the linear stability problem to ordinary differential equations, are more valid for short wavelengths.

We present a new method for controlling vortex breakdown (VB) via addition of co- or counter-rotation near the axis. Co-rotation is adequate to totally suppress VB, whereas counter-rotation increases the number and size of VB “bubbles” and makes the flow unsteady. We study these effects in a closed cylindrical container, in which a rotating end disc drives the base flow; an independently rotating central rod (with rod radius≪disk radius) is employed to control VB. This flow, being free of ambient disturbances, is well suited for understanding both the VB mechanism and its control; the present work appears to be the first to study VB control. We develop and explain our control strategy using flow visualization and simple analytical reasoning. Our results suggest that an additional co- or counter-rotation, applied near the vortex axis, can be effective in suppressing or enhancing VB in practical flows.

This numerical study explains the eddy formation and disappearance in a slow steady axisymmetric air–water flow in a vertical truncated conical container, driven by the rotating top disk. Numerous topological metamorphoses occur as the water height, Hw, and the bottom-sidewall angle, α, vary. It is found that the sidewall convergence (divergence) from the top to the bottom stimulates (suppresses) the development of vortex breakdown (VB) in both water and air. At α = 60°, the flow topology changes eighteen times as Hw varies. The changes are due to (a) competing effects of AMF (the air meridional flow) and swirl, which drive meridional motions of opposite directions in water, and (b) feedback of water flow on AMF. For small Hw, the AMF effect dominates. As Hw increases, the swirl effect dominates and causes VB. The water flow feedback produces and modifies air eddies. The results are of fundamental interest and can be relevant for aerial bioreactors.

The lower and upper boundary approximation for describing the yield condition of porous bodies whose behavior is sensitive to a third strain rate invariant is obtained. Together with porosity the constitutive equations contain a material parameter that is responsible for the change in pore shape. This approach makes it possible to present the macroscopic yield condition in a compact form convenient for analysis and various applications. In particular, generalization of well-known plasticity conditions of Gurson and Green-Shima is presented. The lower estimate generalizes the Gurson model and the upper estimate corresponds to the Green-Shima model. Octahedral contours of the loading surface are constructed that agree with experimental data for loose materials and porous powder bodies.

This experimental study describes a hysteresis—a vivid manifestation of strongly nonlinear flow physics. A sealed vertical cylindrical container of radius 45 mm and height 90 mm is filled with water and sunflower oil. The rotating lid drives swirl and the meridional circulation of both fluids. As the rotation strength Re increases, the oil-water interface rises near the axis, touches the lid at Re = Re1, and moves toward the container sidewall. Then as Re decreases, the interface returns to the axis and separates from the lid at Re = Re2 < Re1. At each Re from the range, Re2 < Re < Re1, two different stable steady flow states are observed that is typical of hysteresis. The hysteresis only occurs if a volume fraction of oil is small. The hysteresis disappears as the oil fraction exceeds a threshold, which is around 0.4.

New exact solutions, obtained for centrifugal convection of a compressible fluid in pipes and annular pipes, explain axially elongated counterflow and energy separation—poorly understood phenomena occurring in vortex devices, e.g., hydrocyclones and Ranque tubes. Centrifugal acceleration (which can be up to 106 times gravity in practical vortex tubes), combined with an axial gradient of temperature (even small), induces an intense flow from the cold end to the hot end along the pipe wall and a backflow near the axis. To account for large density variations in vortex devices, we use the axial temperature gradient as a small parameter instead of the Boussinesq approximation. For weak pipe rotation, the swirl is of solid-body type and solutions are compact: vz/vza=1−4y2+3y4 and (T−Tw)/(Ta−Tw)=(1−y2)3; where y=r/rw, the subscripts w and a denote values of axial velocity vz, temperature T, and radial distance r, at the wall and on the axis. The axial gradient of pressure, being proportional to 3y2−1, has oppos...