Outer Cylindrical Wall Research Articles

Linear stability analysis of thermocapillary flow in a slowly rotating shallow annular pool using spectral element method

The stability of thermocapillary flow in a slowly rotating shallow annular pool was investigated by using the Legendre spectral element method. The silicon melt (Pr=0.011), filling in a pool with adiabatic free surface and bottom, was heated at the outer cylindrical wall and cooled at the inner cylindrical wall. The critical stability conditions for different dimensionless rotation rates ω, ranging from 0 to 2000, were determined by linear stability analysis. Moreover, the energy analysis was applied to further illustrate the underlying mechanism of the flow instability. The results indicate that there is one Hopf bifurcation for ω<940 and ω>1185. Thermocapillary flow is the dominant factor of the instability for ω<940, and the pool rotation becomes the key role for the first instability for ω>1185. Three turning points were observed in the interval 940⩽ω⩽1185, corresponding to three transitions between two-dimensional steady flow and three-dimensional oscillatory flow, owing to the competition of two driving forces with increasing Marangoni number at a fixed ω. With pool rotation, the results exhibit that the flow instability is deduced to occur initially in the zone near the cold wall with the evidence of the extreme velocity gradient and also the distribution of the local kinetic energy.

Linear-stability analysis of thermocapillary-buoyancy convection in annular two-layer system with a radial temperature gradient

In this paper, we present a set of linear-stability analysis results of the thermocapillary-buoyancy convection in an annular two-layer system of 5cSt silicone oil and HT-70 with a radial temperature gradient. The annular two-layer system is heated at the outer cylindrical wall and cooled at the inner wall. The effects of the depth ratio, the radius ratio and the aspect ratio of the annular pool on the critical conditions for the convection transition are analyzed. The flow destabilizing mechanism is identified. Results indicate that the hydrothermal wave, or the combined hydrothermal wave and three-dimensional oscillatory flow, should be responsible for the flow destabilization when the stable thermocapillary-buoyancy convection transits to the three-dimensional oscillatory convection. With the increase of the radius ratio of the annular pool, the critical Marangoni number, wave number and phase velocity all decrease. With the increase of the depth ratio η, the critical Marangoni number initially increases before a dramatic decrease. The maximum value of the critical Marangoni number locates in the range of η=0.625–0.833.

Two-Dimensional Numerical Simulation for Flow Pattern Transition of Thermal-Solutal Capillary Convection in an Annular Pool

In order to understand the transition characteristics of the thermal-solutal capillary convection in an annular pool, a series of two-dimensional numerical simulations were conducted. The bottom of the pool is adiabatic rigid wall and the top is adiabatic and non-deformable free surface. The inner and outer cylindrical walls maintain at constant temperature and solute concentration, respectively. The thermo-capillary force is supposed to equal to the solute-capillary force, but their directions are contrary. Results show that the thermal-solutal capillary convection is steady at a small Reylonds number. When the capillary Reynolds number exceeds a critical value, the steady flow transits into unstable thermal-solutal capillary convection. The transition from the steady to oscillatory flow undergoes a Hopf bifurcation. Furthermore, the effects of the liquid layer aspect ratio, the radius ratio, the Prandtl number and the Lewis number on the onset of flow pattern transition are discussed. The physical mechanism of the unstable thermal-solutal capillary convection is also analyzed.

HVI Ballistic Performance Characterization of Non-parallel Walls

The parallel, Double Wall, hypervelocity impact shield configuration has been heavily tested and characterized for ballistic performance for normal and oblique impacts for the ISS and other programs. However, in many locations with spacecraft designs, the rear wall cannot be modeled as being parallel or concentric with the outer bumper wall and in cases with a cylindrical outer wall, the effective non-parallel angle commonly varies as the outer wall impact location changes. This complicates micrometeoroid and orbital debris assessment of critical spacecraft components located within outer spacecraft walls. Based on a study combining hypervelocity impact testing and hydrodynamic impact simulations on multiple shield configurations including non-parallel first and rear walls, this paper provides equation adjustments for use with the double wall Ballistic Limit Equation (BLE) for a variety of impact speeds, non-parallel wall angles and impact obliquities.

Statistics of confined turbulent flows with and without rotation effects

A volume penalization method is implemented in a tri-periodic pseudo-spectral code. The numerical stability constraint of the method is studied and released with an original implicit formulation of the penalization term. The accuracy of the method in representing no-slip boundaries is tested by considering the impact of a three-dimensional vortex ring on a wall. This technique is then used to assess the influence of cylindrical boundaries on turbulent flow fields and on their structure at given radial positions. The Lagrangian study shows that the axial direction of the open-ends cylinder is privileged for the orientation of the turbulent structures. After these cases in which kinetic energy decays, we finally test rotating the outer cylindrical walls to force "naturally" the flow towards kinetic energy statistical equilibrim.

Linear-stability Analysis of Thermocapillary Flow in an Annular Two-layer System with Upper Rigid Wall

The linear-stability analysis of thermocapillary flow in the annular immiscible two-layer system of 5cSt silicone oil and HT-70 with a radial temperature gradient was carried out. The annular two-layer system is heated at the outer cylindrical wall and cooled at the inner wall, the bottom and top surfaces are bounded by two rigid and heat-insulated walls. The influences of the liquid layer depth and radius ratio between the cold inner wall and the hot outer wall on stability are thoroughly investigated. The critical Marangoni number, critical wave number and critical phase velocity are obtained. In addition, the mode of bifurcation for the hydrothermal wave is predicted at different liquid layer depth, and the temperature disturbance pattern of hydrothermal wave at interface is also exhibited.

Thermocapillary-Buoyancy Convection in Annular Two-layer System with a Radial Temperature Gradient

In order to understand the characteristics of thermocapillary-buoyancy convection in the annular two-layer system of 5cSt silicone oil and HT-70 with a radial temperature gradient, a set of two-dimensional numerical simulations are carried out using the finite-volume method. The annular two-layer system is heated from the outer cylindrical wall and cooled at the inner cylindrical wall. The radius ratio and the aspect ratio of the system are 0.2 and 0.05–0.1, respectively. Results show that the flow is steady for sufficiently small Marangoni number. When the Marangoni number exceeds a critical value, the additional cells appear near the interface and the cold inner wall, and then an unsteady multi-cellular structure is developed. The temperature fluctuation wave propagates from the cold inner wall to the hot outer wall. And the critical Marangoni number decreases with the increase of the aspect ratio.

Effect of magnetic field on the buoyancy and thermocapillary driven convection of an electrically conducting fluid in an annular enclosure

The main objective of this article is to study the effect of magnetic field on the combined buoyancy and surface tension driven convection in a cylindrical annular enclosure. In this study, the top surface of the annulus is assumed to be free, and the bottom wall is insulated, whereas the inner and the outer cylindrical walls are kept at hot and cold temperatures respectively. The governing equations of the flow system are numerically solved using an implicit finite difference technique. The numerical results for various governing parameters of the problem are discussed in terms of the streamlines, isotherms, Nusselt number and velocity profiles in the annuli. Our results reveal that, in tall cavities, the axial magnetic field suppresses the surface tension flow more effectively than the radial magnetic field, whereas, the radial magnetic field is found to be better for suppressing the buoyancy driven flow compared to axial magnetic field. However, the axial magnetic field is found to be effective in suppressing both the flows in shallow cavities. From the results, we also found that the surface tension effect is predominant in shallow cavities compared to the square and tall annulus. Further, the heat transfer rate increases with radii ratio, but decreases with the Hartmann number.

Experimental and numerical analysis of thermo-magnetic convection in a vertical annular enclosure

In the present paper an experimental and numerical analysis of a thermo-magnetic convective flow of paramagnetic fluid in an annular enclosure with a round rod core and a cylindrical outer wall is presented. It is complemented by an experimental analysis of natural convection depending on the inclination angle to show the stability of the present configuration. Convection in an annulus between two vertical co-axial cylinders resulting from gravitational and magnetic environments has been investigated. A strong magnetic field can be an alternative to heat transfer enhancement. The effect of the magnetic field on the convection of the paramagnetic fluid in the annular vessel in various positions was compared. The numerical analysis was done based on the continuity, momentum and energy equations. A term related to the magnetic buoyancy force was added to the momentum equation. The distributions of Nusselt number present minima in two positions of the enclosure, which depends on the reciprocal relationship between the gravitational and magnetising forces.

Asymptotic solution of thermocapillary convection in two immiscible liquid layers in a shallow annular cavity

The steady laminar two-dimensional thermocapillary convection of two superposed horizontal liquid layers in a shallow annular cavity was investigated using asymptotical analysis. The liquids were supposed to be immiscible with a nondeformable interface. The cavity was heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces were rigid and adiabatic. Asymptotic solutions were obtained in the core region in the limit as the aspect ratio, which was defined as the ratio of the lower layer thickness to the gap width, and trended to zero. The numerical experiments were also carried out to compare with the asymptotic solution of the steady two-dimensional thermocapillary convection. It is found that the expressions of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio.

A numerical study of the flow of Bingham-like fluids in two-dimensional vane and cylinder rheometers using a smoothed particle hydrodynamics (SPH) based method

In this paper, a Lagrangian formulation of the Navier–Stokes equations, based on the smoothed particle hydrodynamics (SPH) approach, was applied to determine how well rheological parameters such as plastic viscosity can be determined from vane rheometer measurements. First, to validate this approach, a Bingham/Papanastasiou constitutive model was implemented into the SPH model and tests comparing simulation results to well established theoretical predictions were conducted. Numerical simulations for the flow of fluids in vane and coaxial cylinder rheometers were then performed. A comparison to experimental data was also made to verify the application of the SPH method in realistic flow geometries. Finally, results are presented from a parametric study of the flow of Bingham fluids with different yield stresses under various applied angular velocities of the outer cylindrical wall in the vane and coaxial cylinder rheometers. The stress, strain rate and velocity profiles, especially in the vicinity of the vane blades, were computed. By comparing the calculated stress and flow fields between the two rheometers, the validity of the assumption that the vane could be approximated as a cylinder for measuring the rheological properties of Bingham fluids at different shear rates was tested.

Asymptotic solution of thermocapillary convection in thin annular two-layer system with upper free surface

The steady laminar two-dimensional thermocapillary convection in the thin annular two superposed horizontal liquid layers with one free surface, one liquid/liquid interface subjected to a radial temperature gradient was investigated using asymptotical analysis. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the lower layer thickness to the gap width, goes to zero. The numerical experiments are also carried out to compare with the asymptotic solution of the steady two-dimensional thermocapillary convection. The asymptotic results indicate that the expressions of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio.

Stability of Thermocapillary Convection in Annular Pools with Low Prandtl Number Fluid

In order to understand the stability characteristics of thermocapillary convection in an annular pool with low Prandtl number (Pr = 0.011) fluid, a linear stability analysis had been performed. The annular pool was heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surface were adiabatic. The results show that the critical Marangoni number and the critical wave number decrease with the increase of the aspect ratio, which is defined as the ratio of the depth to the gap width of the annular pool. When the aspect ratio exceeds 0.12, the critical wave number keeps almost constant. As the radius ratio increases, the critical Marangoni number decreases slightly, while the critical wave number increases. In the gravity condition, the effect of the buoyancy on the critical Marangoni number and wave number increases gradually with the increase of the aspect ratio.

Asymptotic solution of thermocapillary convection in a thin annular pool of silicon melt

The free surface of the silicon melt in a thin annular pool is subjected to a radial temperature gradient. Since the surface tension depends on the temperature, it will create a thermocapillary force on the free surface and, in turn, yield to thermocapillary convection in the bulk of the liquid by the viscous traction. This paper presents an investigation on the steady two-dimensional thermocapillary convection in a differentially heated annular pool of the silicon melt using the asymptotical way. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the pool height to the gap width, goes to zero. The numerical experiments are also carried out to compare to the asymptotic solution of the steady two-dimensional thermocapillary convection. The results indicate that the expressions of velocity and temperature fields in the core region from the asymptotic solution are found to be valid in the limit of small aspect ratio.

Experimental investigation of a rotating fluidized bed in a static geometry

Rotating fluidized beds in a static geometry are based on the new concept of injecting the fluidization gas tangentially in the fluidization chamber, via multiple gas inlet slots in its cylindrical outer wall. The tangential injection of the fluidization gas fluidizes the particles tangentially and induces a rotating motion, generating a centrifugal field. Radial fluidization of the particle bed is created by introducing a radially inwards motion of the fluidization gas, towards a centrally positioned chimney. Correctly balancing the centrifugal force and the radial gas–solid drag force requires an optimization of the fluidization chamber design for each given type of particles. Solids feeding and removal can be continuous, via one of the end plates of the fluidization chamber. The fluidization behavior of both large diameter, low density polymer particles and small diameter, higher density salt particles is investigated at different solids loadings in a 24 cm diameter, 13.5 cm long non-optimized fluidization chamber. Scale-up to a 36 cm diameter fluidization chamber is illustrated. Provided that the solids loading is sufficiently high, a stable rotating fluidized bed in a static geometry is obtained. This requires to minimize the solids losses via the chimney. With the polymer particles, a dense and uniform bed is observed, whereas with the salt particles a less dense and less uniform bubbling bed is observed. Solids losses via the chimney are much more pronounced with the salt than with the polymer particles. Slugging and channeling occur at too low solids loadings. The hydrostatic gas phase pressure profiles along the outer cylindrical wall of the fluidization chamber are a good indicator of the particle bed uniformity and of channeling and slugging. The fluidization gas flow rate has only a minor effect on the occurrence of channeling and slugging, the solids loading in the fluidization chamber being the determining factor for obtaining a stable and uniform rotating fluidized bed in a static geometry.

Sound resistant enclosure

A sound resistant enclosure apparatus adapted for a person have access to an environment that reduces sound from ambient noise. More particularly, the invention relates to a manner in which to use common fabrication materials and method to construct a sound resistant enclosure or booth for use to make or receive cellular telephone calls in relative quiet. The apparatus include among its essential elements, a cylindrical outer wall, a cylindrical inner wall, a door, a top or roof, a floor and sound resistant material mostly deposited between the inner and outer walls. Sound resistant material can also be found in the door, roof and walls. The sound resistant enclosure blocking much of the ambient environmental noise such that the occupant of the enclosure can make or receive a cellular phone call more effectively and efficiently without having distracting unwanted extraneous environmental noise interrupting their conversation.

Experimental and Numerical Study of Rotating Fluidized Beds in a Static Geometry

The new concept of a rotating fluidized bed in a static geometry was numerically and experimentally studied. The particle bed can be both tangentially and radially fluidized by injecting the fluidization gas tangentially in the static fluidization chamber via multiple gas inlet slots located in its outer cylindrical wall. The tangential fluidization of the particles induces a rotating motion of the particle bed. As a result of the particle bed rotational motion, the solids experience a radially outwards centrifugal force. A radially inwards gas-solid drag force and radial fluidization of the particle bed can be introduced by forcing the fluidization gas to leave the fluidization chamber via a chimney with one or multiple gas outlet slots, positioned at the axis of the fluidization chamber. The solids can be continuously fed and removed in and out of the fluidization chamber via solids inlet and outlet holes in the front or back ends of the fluidization chamber.The fluidization patterns of low-density polymer particles with a large diameter and of high-density salt particles with a small diameter were experimentally studied in a 24-cm diameter, 13.5-cm long non-optimized static fluidization chamber at different solids loadings. Scale-up to a 36-cm diameter fluidization chamber was also studied. With both types of particles, a rotating fluidized bed and an acceptable gas-solid separation was obtained provided that the solids loading was sufficiently high. Slugging and channeling and a non-uniform distribution of the gas over the gas inlet slots to the fluidization chamber may occur at low solids loadings and can be detected via well-chosen pressure measurements. The fluidization patterns observed in the same fluidization chamber were completely different with the polymer particles and with the salt particles. The polymer particles tend to form a dense and uniform bed, its behavior being mainly characterized by tangential fluidization. The salt particles tend to form a less dense, bubbling fluidized bed that is both tangentially and radially fluidized.Computational fluid dynamics simulations give an improved insight in the gas and solid phase flow pattern.

NUMERICAL INVESTIGATION OF SILICON MELT FLOW IN A SHALLOW ANNULAR POOL UNDER AN AXIAL MAGNETIC FIELD

In order to understand the effect of the magnetic field on surface patterns on semi-conducting silicon melt in industrial Czochralski furnaces, we conducted a series of unsteady three-dimensional numerical simulations of silicon melt flow in a shallow annular pool under the axial magnetic field for the magnetic field strength from 0 to 0.1T. The pool is heated from the outer cylindrical wall and cooled at the inner wall. Bottom and top surfaces are adiabatic. When the magnetic field is weak, the simulation can predict various three-dimensional oscillatory flows depending on the radial temperature difference. With the much larger magnetic field, three-dimensional flow becomes axisymmetric steady flow. Details of flow and temperature disturbances are discussed and the critical magnetic field strengths for the onset of axisymmetric steady flow are determined.

Experiments on instabilities of thermocapillary convection in shallow annular liquid layers

An experimental study of thermocapillary convection of silicone oil (the Prandtl number Pr ≈ 18) was conducted in a shallow annular cavity with outer radius Ro = 55 mm and inner radius Ri = 15 or 27.5 mm for liquid heights H in the range 1–3 mm. The liquid layer is heated from the outer cylindrical wall and cooled at the inner wall. The experiments were performed over a wide range of Marangoni numbers, 400 < Ma < 10000. The measurement of surface temperatures and observation of instability structures were made by using an IR thermography technique. As Ma exceeded a critical value, hydrothermal waves were observed for thin liquid layers, H ⩽ 2.5 mm, of both the inner radii. These waves are characterized by curved spoke patterns propagating in the azimuthal direction. For thicker layers, H > 2.5 mm, multicell patterns were dominant. At low Ma, the multicell patterns were steady, toroidal rolls. As Ma was increased, the rolls began to rotate around the centre of the cavity and unsteady longitudinal rolls appeared. In the range 2.5 ⩽ H ⩽ 2.8 mm, hydrothermal waves and multicell coexisted. The transition map is presented in terms of Ma and Bod (the dynamic Bond number).

Rotating fluidized beds in a static geometry: Experimental proof of concept

AbstractThe new concept of a rotating fluidized bed in a static geometry (RFB‐SG) is presented. The rotating motion of the particle bed and the tangential fluidization of the solids are obtained by the tangential injection of the fluidization gas via multiple gas inlet slots in the outer cylindrical wall of the fluidization chamber. The solids experience a radially outwards centrifugal force. The gas, on the other hand, is forced to move radially inwards towards a chimney with one or more outlet slots, creating a radially inwards gas‐solid drag force and fluidizing the solids radially. The new fluidization concept is experimentally investigated and proven using one and the same non‐optimized fluidization chamber design with either large diameter, low density polymer particles or small diameter, higher density Alumina particles. The fluidization chamber is operated in continuous mode, at different solids loadings and in the vertical and horizontal position. © 2007 American Institute of Chemical Engineers AIChE J, 2007