Bottom Endwall Research Articles

Comparing endwall heat transfer among staggered pin fin, Kagome and body centered cubic arrays

Truss-type lattices present good mechanical and thermal properties and are regarded as promising structures for internal cooling. This study presents a systematic comparison of thermo-fluid behaviors among staggered pin fin array, Kagome lattice array and Body Centered Cubic (BCC) lattice array in a rectangular channel under an identical porosity. Transient liquid crystals (TLC) and numerical methods were utilized to explore the flow and endwall heat transfer characteristics in structures. The results reveal that, due to stronger flow mixing and more irregular vortices, the endwall-averaged Nusselt number of the Kagome array and the BCC array is 17–24% and 26–41% higher than that of the pin fin array, respectively. The similar topology results in similar heat transfer characteristics between the Kagome array and the BCC array, and an arc-shaped high heat transfer wake region outside the vertex is induced by the horseshoe vortex and the secondary flow washing the endwall. Meanwhile, for the Kagome array, a strong counter rotating vortex is formed near the bottom endwall, while in contrast, there is no obvious similar flow behavior near the top endwall. This leads to a 46–54% difference in the Nusselt number between the bottom endwall and the top endwall of the Kagome. In addition, the relationship between the element-averaged Nusselt number and Reynolds number of each array is obtained to guide practical applications. This research indicates that BCC or Kagome lattices may become a potential alternative to conventional pin fins due to their higher thermal efficiency.

Analytical and experimental study of the substance transport in the vortex flow

The characteristics of the vortex flow with a free surface formed in a vertical cylindrical container filled with water, where the source of motion is the disk at the bottom endwall, are studied experimentally and analytically. Different types of oils and petroleum are used in experiments as admixtures. The problem of an “oil body” form in a complex vortex flow is considered on the basis of the analysis of equations for the mechanics of immiscible liquids of different densities with physically based boundary conditions. The calculations of the free surface forms are carried out in cases of one- and two-component fluid. The relations obtained are in satisfactory agreement with the experimentally registered forms of the interfaces. The flow structure near a rotating disk is studied, the shapes of the trajectories of moving liquid particles in the water column near the disk are determined. The coincidence of the types of spiral movement of liquid particles on the surface and near the disk indicates that the characteristic features of the vortex flow are determined in the boundary layer on the rotating disk and then transferred to the entire spatial region occupied by the liquid. Experimental and theoretical study of the vortex flow showed that the trajectories of moving liquid particles near the water surface are spatial spirals along which these particles move from the periphery to the center. The expressions obtained for the form of trajectories of liquid particles accelerated by the rotating disk coincide with the type of registered tracers’ trajectories in the depth of liquid and on the free surface of the flow.

Three dimensional analysis of natural convection in a narrow vertical annulus closed at top and opened at bottom

Natural convection flow and heat transfer in a narrow vertical annulus located centrally above a reservoir has been studied. The fluid in the reservoir is heated up by a hot, isothermal bottom end wall. The flow characteristics has been analysed by observing flow topologies and contours of temperature. Results are presented for Rayleigh numbers in the interval [2000–20000]. The flow consist of steady, periodic and quasi periodic regimes. The stream trace plot in each case is found to contain correct number of singularities of different types, which is required for satisfying the Hunts criterion. The annulus geometry selected for the study is a simplified model of the narrow annulus of a typical nuclear reactor design. The variation of circumferential temperature obtained from the study provides a relevant data for the design of nuclear reactors and similar systems.

Design and cold flow testing of a Gas-Solid Vortex Reactor demonstration unit for biomass fast pyrolysis

Innovative gas-solid fluidized beds with process intensification capabilities are among the most promising alternatives for the current state of the art in the chemical industry. In the present work the advantages of such a reactor that sustains a rotating fluidized bed with gas-solid slip velocities much higher than those in conventional fluidized beds are illustrated computationally and experimentally. A Gas-Solid Vortex Reactor (GSVR) demonstration unit is designed to operate at typical biomass fast pyrolysis conditions targeting the production of chemicals and fuels from renewable feedstocks. For the demonstration unit preheated N2 supplies the thermal energy required by the fast pyrolysis process but alternative sources can also be evaluated. A broad range of operation conditions in the 80mm diameter and 15mm height GSVR can be evaluated: N2 mass flow rates of 5–10gs−1 and biomass feed mass flow rates of 0.14–1.4gs−1. Particle-free and particulate flow experiments confirmed that the carrier gas is evenly distributed around the GSVR cylindrical chamber as anticipated by computational fluid dynamic simulations. The latter also supported the inclusion of a profiled bottom end wall and a diverging exhaust. Cold flow experiments with biomass confirmed that the GSVR sustains a rotating fluidized bed with average bed height of 10mm and solids azimuthal velocities of 6–7ms−1.

Three-dimensional instabilities and inertial waves in a rapidly rotating split-cylinder flow

The nonlinear dynamics of the flow in a differentially rotating split cylinder is investigated numerically. The differential rotation, with the top half of the cylinder rotating faster than the bottom half, establishes a basic state consisting of a bulk flow that is essentially in solid-body rotation at the mean rotation rate of the cylinder and boundary layers where the bulk flow adjusts to the differential rotation of the cylinder halves, which drives a strong meridional flow. There are Ekman-like layers on the top and bottom end walls, and a Stewartson-like side wall layer with a strong downward axial flow component. The complicated bottom corner region, where the downward flow in the side wall layer decelerates and negotiates the corner, is the epicentre of a variety of instabilities associated with the local shear and curvature of the flow, both of which are very non-uniform. Families of both high and low azimuthal wavenumber rotating waves bifurcate from the basic state in Eckhaus bands, but the most prominent states found near onset are quasiperiodic states corresponding to mixed modes of the high and low azimuthal wavenumber rotating waves. The frequencies associated with most of these unsteady three-dimensional states are such that spiral inertial wave beams are emitted from the bottom corner region into the bulk, along cones at angles that are well predicted by the inertial wave dispersion relation, driving the bulk flow away from solid-body rotation.

Use of a Cavity Resonator for Measuring Free Water in Fuels

The possibility, in principle, of determining the content of undissolved water in fuels with high precision using high-quality super-high frequency (SHF) resonance systems (microwave cavity resonator) is substantiated. Results of experimental study of a cylindrical cavity resonator with a thin layer of water on the bottom-end wall are adduced. The proposed method is analyzed using simulation by the finite-element method in the ANSYS system. Results of this research can be of practical use for determining deposited water in jet fuels.

The Taylor-Proudman column in a rapidly-rotating compressible fluid II. asymptotic analysis

A matched asymptotic analysis is conducted for compressible rotating flow in a cylindrical container when a mechanical and/or a thermal disturbance is imposed on the wall. The system Ekman number is assumed to be very small. The conditions for the Taylor-Proudman column in the interior, which were also given in the companion paper (Ref. [1]) for energy transports by means of the energy balancing analysis, have been re-derived. The concept of the grouping of variables, the energy flux content e ≡ T + 2α2rv, is reformulated, and its effectiveness in characterizing the energy transport mechanism is delineated. It is seen that, under the condition of the Taylor-Proudman column, there exist numerous admissible theoretical solutions for interior flow pertinent to the imposed wall boundary condition. Some canonical examples are illustrated. The differential heating problem on the top and bottom endwall disks is revisited by using the concept of the energy flux content. The results are shown to be in line with the previous findings.

An experimental study of regime transitions in a differentially heated baroclinic annulus with flat and sloping bottom topographies

Abstract. A series of laboratory experiments has been carried out in a thermally driven rotating annulus to study the onset of baroclinic instability, using horizontal and uniformly sloping bottom topographies. Different wave flow regimes have been identified and their phase boundaries – expressed in terms of appropriate non-dimensional parameters – have been compared to the recent numerical linear stability analysis of von Larcher et al. (2013). In the flat bottom case, the numerically predicted alignment of the boundary between the axisymmetric and the regular wave flow regime was found to be consistent with the experimental results. However, once the sloping bottom end wall was introduced, the detected behaviour was qualitatively different from that of the simulations. This disagreement is thought to be the consequence of nonlinear wave–wave interactions that could not be resolved in the framework of the numerical study. This argument is supported by the observed development of interference vacillation in the runs with sloping bottom, a mixed flow state in which baroclinic wave modes exhibiting different drift rates and amplitudes can co-exist.

Rapidly rotating cylinder flow with an oscillating sidewall

We present numerical simulations of a flow in a rapidly rotating cylinder subjected to a time-periodic forcing via axial oscillations of the sidewall. When the axial oscillation frequency is less than twice the rotation frequency, inertial waves in the form of shear layers are present. For very fast rotations, these waves approach the form of the characteristics predicted from the linearized inviscid problem first studied by Lord Kelvin. The driving mechanism for the inertial waves is the oscillating Stokes layer on the sidewall and the corner discontinuities where the sidewall meets the top and bottom end walls. A detailed numerical and theoretical analysis of the internal shear layers is presented. The system is physically realizable, and attractive because of the robustness of the Stokes layer that drives the inertial waves but beyond that does not interfere with them. We show that the system loses stability to complicated three-dimensional flow when the sidewall oscillation displacement amplitude is very large (of the order of the cylinder radius), but this is far removed from the displacement amplitudes of interest, and there is a large range of governing parameters which are physically realizable in experiments in which the inertial waves are robust. This is in contrast to many other physical realizations of inertial waves where the driving mechanisms tend to lead to instabilities and complicate the study of the waves. We have computed the response diagram of the system for a large range of forcing frequencies and compared the results with inviscid eigenmodes and ray tracing techniques.

The influence of a sloping bottom endwall on the linear stability in the thermally driven baroclinic annulus with a free surface

We present results of a linear stability analysis of non-axisymmetric thermally driven flows in the classical model of the rotating cylindrical gap of fluid with a horizontal temperature gradient [inner (outer) sidewall cool (warm)] and a sloping bottom endwall configuration where fluid depth increases with radius. For comparison, results of a flat-bottomed endwall case study are also discussed. In both cases, the model setup has a free top surface. The analysis is carried out numerically using a Fourier–Legendre spectral element method (in azimuth and in the meridional plane, respectively) well suited to handle the axisymmetry of the fluid container. We find significant differences between the neutral stability curve for the sloping and the flat-bottomed endwall configuration. In case of a sloping bottom endwall, the wave flow regime is extended to lower rotation rates, that is, the transition curve is shifted systematically to lower Taylor numbers. Moreover, in the sloping bottom endwall case, a sharp reversal of the instability curve is found in its upper part, that is, at large temperature differences, whereas the instability line becomes almost horizontal in the flat-bottomed endwall case. The linear onset of instability is then almost independent of the rotation rate.

Two-fluid confined flow in a cylinder driven by a rotating end wall

The flow of two immiscible fluids completely filling an enclosed cylinder and driven by the rotation of the bottom end wall is studied numerically. The simulations are in parameter regimes where there is significant advection of angular momentum, i.e., the disk rotation rate is fast compared to the viscous diffusion time. We consider two classes of scenarios. The first consists of cases that are straightforward to reproduce in physical experiments where only the rotation rate and the viscosity ratio of the fluids are varied. Then we isolate different forces acting on the system such as inertia, surface tension, and gravity by studying variations in individual governing parameters. The viscosity ratio determines how quickly the upper fluid equilibriates dynamically to the flow in the lower fluid and plays a major role in determining how vortex lines are bent in the neighborhood of the interface between the two fluids. This in turn determines the structure of the interfacial layer between the two swirling fluids, which is responsible for the flow in the upper fluid. The simulations show that even when there is significant interfacial deformation, both the dynamics and the equilibrium flow are dominated by vortex bending rather than vortex stretching. The simulations show that for the range of immiscible fluids considered, surface tension effects are significant. Increased surface tension reduces the degree to which the interface is deformed and the limit of zero surface tension is not an appropriate approximation.

Vertical Taylor–Couette flow with free surface at small aspect ratio

The free surface flow between two concentric cylinders with vertical axes is investigated using numerical and experimental approaches. The bottom end wall of the cylinders and the outer cylinder are stationary and fixed, and the inner cylinder is allowed to rotate. In such a case, an odd number of Taylor vortices is usually formed (normal mode). However, we found that anomalous modes with outer flow near the bottom end wall or inner flow at the free surface appear in some conditions. Further, we determined bifurcation diagrams between the normal three-cell mode and normal one-cell mode and between the normal five-cell mode and the normal three-cell mode.

Optimal harmonic response in a confined Bödewadt boundary layer flow

The Bödewadt boundary layer flow on the stationary bottom end wall of a finite rotating cylinder is very sensitive to perturbations and noise. Axisymmetric radial waves propagating inward have been observed experimentally and numerically before the appearance of spiral three-dimensional instabilities. In this study, the sensitivity and response of the finite Bödewadt flow to a harmonic modulation of the rotation rate are analyzed. A comprehensive exploration of response to variations in the amplitude and frequency of the forcing has been carried out. There are sharply delineated linear- and nonlinear-response regimes, with a sharp transition between them at moderate amplitudes. The periodic forcing leads to a steady-streaming flow, even in the linear-response regime, and to a period-doubling bifurcation in the nonlinear regime. Frequency response curves at different forcing amplitudes over a wide range of frequencies have been computed and used to identify the frequency band that excites the axisymmetric radial waves and the forcing frequency that elicits the strongest response. Finally, we have shown that the axisymmetric waves always decay to the steady basic state when the harmonic modulation is suppressed, and conclude that the experimentally observed persistent circular waves are not self-sustained.

Crossflow instability of finite Bödewadt flows: Transients and spiral waves

The flow in an enclosed rotating cylinder with a stationary lower end wall is investigated numerically. For fast rotation rates, the flow in the interior is primarily in the azimuthal direction, with an angular momentum distribution very close to that corresponding to solid-body rotation for about the inner-half radius. The differential rotation sets up a large-scale circulation that is primarily present in the boundary layers on the rotating top and sidewalls and the stationary bottom wall, with a very weak effusive component throughout the bulk interior providing a matching between the boundary layer flows on the top and bottom. The top end wall boundary layer has a profile that very closely matches the von Kármán solution for a rotating disk boundary layer; it is stable and very robust to finite disturbances for all rotation rates considered. The boundary layer on the stationary bottom end wall has a profile that agrees with the Bödewadt solution for a stationary disk with an ambient flow in solid-body rotation. This boundary layer is not robust, suffering crossflow instability to multiarmed spiral waves via a supercritical Hopf bifurcation, as well as being susceptible to axisymmetric circular waves that travel radially inward where the boundary layer profile is most inflectional. In the absence of any external forcing, the circular waves are transitory, but low amplitude forcing can sustain them indefinitely, whereas the spiral waves are essentially unaffected by the external forcing.

Unsteady transitional swirling flow in the presence of a moving free surface

Unsteady incompressible viscous flows of a fluid partly enclosed in a cylindrical container with an open top surface are presented in this article. These moving free-surface flows are generated by the steady rotation of the solid bottom end wall. Such type of flows belongs to a group of recirculating lid-driven cavity flows with geometrical axisymmetry. The top surface of the cylindrical cavity is left open so that the free surface can freely deform. The Reynolds regime corresponds to unsteady transitional flows with some incursions in the fully laminar regime. The approach taken here revealed new nonaxisymmetric flow states that are investigated based on a fully three-dimensional solution of the Navier–Stokes equations for the free-surface cylindrical swirling flow without resorting to any symmetry property unlike all other results available in the literature. The results are compared with those of Bouffanais and Lo Jacono [“Transitional cylindrical swirling flow in presence of a flat free surface,” Comput. Fluids 38, 1651 (2009)] corresponding to the exact same parameters but with a flat-and-fixed top free surface. These solutions are obtained through direct numerical simulations based on a highly accurate Legendre spectral element method combined with a moving-grid technique.

Low pressure acoustic pyrometer signal generator

An acoustic pyrometer measures the average gas temperature across a space of known distance, especially turbulent, high temperature gas loaded with caustic particulates. It includes an acoustic signal generator that generates a high amplitude acoustic signal with a short rise time The acoustic signal generator includes an outer tank closed at top and bottom ends by top and bottom end walls and enclosing an outer chamber. A cylinder is supported within the tank and has top and bottom opposed ends. A mid-plate extends across the cylinder and defines the bottom end, and an axial opening in the mid-plate receives a shaft of a piston assembly having an upper piston and a lower piston at ends of the shaft. A throat is attached to the bottom end, and receives the lower piston. The lower piston seals the throat when received in the throat. The upper piston is slidable in the cylinder under influence of air pressure. A pneumatic operating system for charging said cylinder and said outer chamber with gas at a moderate pressure includes a coupling for connection to a source of gas pressure and a remotely operated vent to allow pressurized gas in the cylinder to escape, thereby allowing the piston assembly to open said throat and allow pressurized gas to escape and produce a shock wave for use by the acoustic pyrometer.

Mode formation of free surface rotating flow between concentric vertical cylinders

Mode exchanges of flows between concentric and rotating cylinders with vertical axes have been studied by numerical and experimental approaches. The lengths of the cylinders are finite, and the inner cylinder rotates and the outer cylinder is stationary. The bottom end wall of the annulus is a fixed solid wall and the top is a free surface between a working liquid and the air, and the wall condition is axially asymmetric. This gives one of the modifications of Taylor-Couette system. In this system, the normal mode flow has an inward flow on the lower end wall and an outward flow near the free surface. In experiment, visualized flows are observed from the top and the side of the cylinders, and the position of the free surface is measured. Numerical methods are based on the unsteady axisymmetric equations, and the gravitational acceleration and the surface tension are considered to formulate the dynamics of the free surface. The experimental result and numerical result show the primary mode, the secondary normal mode and the anomalous mode, which are similar to the modes found in the symmetric system. The regions where the primary modes and the normal secondary modes appear are determined in the space spanned by the Reynolds number and the aspect ratio.

Buoyant convection in a parallelogrammic enclosure filled with a porous medium – General analysis and numerical simulations

A numerical study is made of buoyant convection in a parallelogrammic enclosure, which is filled with a porous medium. The enclosure is equipped with insulated non-vertical sidewalls and isothermal horizontal endwalls. The temperature at the top horizontal endwall is higher than the temperature at the bottom horizontal endwall. This provides a generally stable fluid stratification in the interior. Emphasis is given to the explicit role of local baroclinicity, which is induced in the immediate neighborhood of the non-vertical portions of the sidewalls. Comprehensive numerical solutions to the governing equations are acquired. The Boussinesq-fluid assumption is used, and the Brinkman-extended Darcy flow model is adopted in the momentum equation. In order to represent local thermal non-equilibrium, the two-equation model is utilized in the energy equation. A systematic scale analysis is performed, which produces descriptions of general flow and heat transport characteristics. These results are shown to be consistent with the detailed numerical solutions. Enhancement of heat transfer through the cavity is more pronounced as the inclination angle of the non-vertical sidewall increases.

Cell pattern and stagnation ring of the flow driven by the counter-rotation in a fluid-filled cylinder

For the flow driven by the counter-rotation between the top and bottom endwalls in a fluid-filled cylinder, a stagnation ring can be observed on the slower rotating endwall in experiment. Its appearance corresponds to a two-cell flow pattern in the meridional plane, where a flow separation forms in the Ekman boundary layer. In this paper we numerically show that, in addition to the single-cell and two-cell patterns previously studied, there exist more complex cell patterns, namely, three-cell and merged-cell patterns, when the flow is driven under differently counter-rotating manner that is realized between the top and bottom endwalls as a whole against the sidewall. Such a counter-rotating flow makes the stagnation ring to appear simultaneously on both top and bottom endwalls rather than just on the slower rotating endwall. Moreover, the three-cell and merged-cell patterns, which are formed by a combination of the Ekman layer separation with the “vortex breakdown bubble”, are unique characteristics. The appearance of the cell pattern and stagnation ring is primarily decided by the counter rotation-rate ratio s, but is also affected by the Reynolds number Re and height-to-radius aspect ratio Λ, so a cell-pattern zone and a stagnation ring zone are proposed numerically as a function of s and Re for a given Λ.

Vortex Breakdown in a Cylindrical Container with Rotating Top and Bottom Endwalls

Experimental and numerical studies are reported on the vortex breakdown phenomenon in an enclosed cylindrical container in which a top endwall rotates at an angular velocity Ω, and a bottom endwall rotates at an angular velocity Ωb, and a colinder sidewall is stationary. Regime boundaries for the vertex breakdown, the location of the stagnation point of breakdown bubble and the attendant global flow features are in good agreement between the experimental and numerical results. The flow behavior is examined an |Ωb/Ω| was varied for several combinations of the cylinder aspect ratios and the rotational Reynolds numbers based on Ω. For a co-rotation (Ωb/Ω>0), the breakdown bubble is located closer to the bottom endwall. For sufficiently large values of Ωb/Ω, the bubble adheres to the bottom endwall. When Ωb/Ω becames close to 1, the meridional-plane flow tends to become antisymmetric with respect to the midplane of the cylinder. For a counter-rotation (Ωb/Ω<0), the bubble moves toward the top endwall. Finally, as|Ωb/Ω| is further increased, the bubble ceases to exist. The Brown and Lopez criterion based on the production of the negative azimuthal vorticity is considered using the present numerical results.