Combined Free and Forced Convection of Water Between Horizontal Concentric Cylinders

1983 ◽  
Vol 105 (3) ◽  
pp. 498-504 ◽  
Author(s):  
T. Hung Nguyen ◽  
P. Vasseur ◽  
L. Robillard ◽  
B. Chandra Shekar
Keyword(s):  
Finite Difference Methods ◽  
Axial Flow ◽  
Axial Direction ◽  
Boussinesq Approximation ◽  
Characteristic Parameters ◽  
Governing System ◽  
Concentric Cylinders ◽  
Free And Forced Convection ◽  
Laminar Convection ◽  
Rayleigh Numbers

This paper presents a theoretical study of combined free and forced laminar convection of a mass of water confined between two horizontal concentric cylinders with constant surface temperatures and subject to an externally-imposed constant pressure gradient along the axial direction. The governing system of differential equations is solved, within the Boussinesq approximation, by perturbation and finite difference methods, and the solutions are obtained in terms of the various characteristic parameters of the problem. Essentially, it is found that the flow pattern and the wall shear stress in the axial direction are significantly affected by the Prandtl and the Rayleigh numbers. Thus, the axial flow shows a tendency to develop in two or even three jets, depending on the Rayleigh number. The occurrence of the inversion of density, for water at 4°C, was found to modify completely the convective, or secondary flow, but to have little effect on the main, or axial, flow.

Numerical Investigation of Variable Property Effects on Laminar Natural Convection of Gases Between Two Horizontal Isothermal Concentric Cylinders

1986 ◽  
Vol 108 (4) ◽  
pp. 783-789 ◽  
Author(s):  
D. N. Mahony ◽  
R. Kumar ◽  
E. H. Bishop
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boussinesq Approximation ◽  
Variable Properties ◽  
Transfer Rates ◽  
Concentric Cylinders ◽  
Weighted Mean Temperature ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Gap Width

A numerical finite difference investigation has been conducted to determine the effects of variable properties on the laminar natural convection of gases between horizontal isothermal concentric cylinders. Velocity profiles, temperature profiles, and heat transfer rates have been computed for diameter ratios of 1.5, 2.28, 2.6, and 5.0 and Rayleigh numbers based on gap width up to 1.8 × 105. The temperature difference ratio θo was varied from 0.2 to 3.0, and the range of validity of the Boussinesq approximation was determined to be θo = 0.2. A volume-weighted mean temperature was shown to be the most effective reference temperature to reduce the heat transfer data for each diameter ratio to a single curve of the form keq = C RaLn, for 0.2 ≤ θo ≤ 3.0 and RaL = 2.0 × 105.

Transient, Laminar, Combined Free and Forced Convection in a Duct

1962 ◽  
Vol 84 (2) ◽  
pp. 141-148 ◽  
Author(s):  
S. L. Zeiberg ◽  
W. K. Mueller
Keyword(s):  
Steady State ◽  
Forced Convection ◽  
Wall Temperature ◽  
Axial Direction ◽  
Transient Heating ◽  
Fully Developed Flow ◽  
Fluid Properties ◽  
Free And Forced Convection ◽  
Approach To Steady State ◽  
Rayleigh Numbers

Transient, laminar, combined free and forced convection in a duct is analyzed under the assumptions of constant fluid properties, and fully developed flow. The transient heating is taken to be a result of wall temperature variations; the wall temperatures vary linearly with the axial co-ordinate of the duct (this is shown to be the only permissible axial dependence, other than no wall temperature variation in the axial direction). Numerical results show that for certain combinations of the Prandtl and Rayleigh numbers, an oscillatory approach to steady state exists. This phenomenon can induce a large reduction of the Nusselt number (compared to steady state) during the transient period.

scholarly journals Effect of Rayleigh Number on Internal Eccentricity in a Heated Horizontal Elliptical Cylinder to its Coaxial Square Enclosure

2020 ◽  
Vol 25 (3) ◽  
pp. 17-29
Author(s):  
Abdelkrim Bouras ◽  
Djedid Taloub ◽  
Zied Driss
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Outer Cylinder ◽  
Boussinesq Approximation ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Commercial Code ◽  
Volume Method ◽  
Rayleigh Numbers

AbstractThis paper deals with numerical investigation of a natural convective flow in a horizontal annular space between a heated square inner cylinder and a cold elliptical outer cylinder with a Newtonian fluid. Uniform temperatures are imposed along walls of the enclosure. The governing equations of the problem were solved numerically by the commercial code Fluent, based on the finite volume method and the Boussinesq approximation. The effects of Geometry Ratio GR and Rayleigh numbers on fluid flow and heat transfer performance are investigated. The Rayleigh number is varied from 103 to 106. Throughout the study the relevant results are presented in terms of isotherms, and streamlines. From the results, we found that the increase in the Geometry Ratio B leads to an increase of the heat transfer coefficient. The heat transfer rate in the annulus is translated in terms of the average Nusselt numbers along the enclosure’s sides. Tecplot 7 program was used to plot the curves which cleared these relations and isotherms and streamlines which illustrate the behavior of air through the channel and its variation with other parameters. The results for the streamlines, isotherms, local and average Nusselt numbers average Nusselt numbers are compared with previous works and show good agreement.

scholarly journals Numerical Analysis on Natural Convection Heat Transfer in a Single Circular Fin-Tube Heat Exchanger (Part 1): Numerical Method

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 363 ◽  
Author(s):  
Jong Hwi Lee ◽  
Jong-Hyeon Shin ◽  
Se-Myong Chang ◽  
Taegee Min
Keyword(s):  
Natural Convection ◽  
Heat Exchanger ◽  
Rayleigh Number ◽  
Numerical Method ◽  
Stokes Equations ◽  
Convection Heat Transfer ◽  
Boussinesq Approximation ◽  
Tube Heat Exchanger ◽  
Fin Tube ◽  
Rayleigh Numbers

In this research, unsteady three-dimensional incompressible Navier–Stokes equations are solved to simulate experiments with the Boussinesq approximation and validate the proposed numerical model for the design of a circular fin-tube heat exchanger. Unsteady time marching is proposed for a time sweeping analysis of various Rayleigh numbers. The accuracy of the natural convection data of a single horizontal circular tube with the proposed numerical method can be guaranteed when the Rayleigh number based on the tube diameter exceeds 400, which is regarded as the limitation of numerical errors due to instability. Moreover, the effective limit for a circular fin-tube heat exchanger is reached when the Rayleigh number based on the fin gap size ( Ra s ) is equal to or exceeds 100. This is because at low Rayleigh numbers, the air gap between the fins is isolated and rarely affected by natural convection of the outer air, where the fluid provides heat resistance. Thus, the fin acts favorably when Ra s exceeds 100.

NUMERICAL STUDY OF LAMINAR CONVECTION AND THERMOSOLUTAL CONVECTION IN A TWO-DIMENSIONAL TRAPEZOIDAL CAVITY

1994 ◽  
Vol 18 (3) ◽  
pp. 207-224 ◽  
Author(s):  
M. Lacroix
Keyword(s):  
Schmidt Number ◽  
Numerical Study ◽  
Temperature Gradients ◽  
Thermosolutal Convection ◽  
Governing Equations ◽  
Concentration Gradients ◽  
Height Ratio ◽  
Vertical Walls ◽  
Laminar Convection ◽  
Rayleigh Numbers

Heat transfer driven by temperature gradients and simultaneous temperature and concentration gradients has been studied numerically for horizontal prismatic cavities of trapezoidal section having a hot horizontal base, a cool inclined top and insulated vertical walls. Results are presented for a cavity with width-to-mean height ratio of 4, thermal and concentration Rayleigh numbers up to 106 and 5.105 respectively, and top surface inclinations from 0 to 15 deg to the horizontal. The Prandtl and the Schmidt number used are 0.71 and 0.6 respectively. The governing equations are expressed in terms of stream function and vorticity and body-fitted coordinates are used for mapping the sloping top wall. As the inclination of the top surface is increased, the Nusselt and Sherwood numbers decrease. The effect of opposing thermal and concentration gradients on the Nusselt and Sherwood numbers is however more important than the effect of the inclination of the top surface. Theoretical Nusselt and Sherwood numbers are compared with available experimental data.

Thermal convection of air in a two-layers snow cover of immobile sea ice

2020 ◽  
Author(s):  
Petr Bogorodskii ◽  
Vasilii Kustov ◽  
Tuomas Laurila
Keyword(s):  
Sea Ice ◽  
Boundary Conditions ◽  
Snow Cover ◽  
Thermal Structure ◽  
Boussinesq Approximation ◽  
Cold Season ◽  
Dimensionless Temperature ◽  
Winter Period ◽  
Significant Heterogeneity ◽  
Rayleigh Numbers

<p>Sea ice, as a rule, is covered with a heat-insulating snow cover, consisting of an ice skeleton and air-saturated pores. However, the temperature difference between the sea and the atmosphere during the cold season provides favorable conditions for macroscopic air movement, which significantly reduces the thermal resistance of snow and, thereby, affects the thermal and dynamic interaction of the atmosphere with the upper layers of the sea.</p><p>Actual snow cover accumulating on the surface of sea ice has significant heterogeneity and anisotropy of geometric and thermophysical characteristics conditioned by snow density stratification. Our work is aimed to studying the occurrence of convective instability in a system of two porous layers with permeable common boundary for boundary conditions taking into account the oceanographic aspect of the problem. The analytical solution of the problem in the Darcy-Boussinesq approximation is obtained by the Galerkin method, by selecting approximations of the vertical amplitudes of dimensionless temperature and velocity perturbations that satisfy the boundary conditions of the problem. A qualitative originality of the problem is revealed in comparison with a similar problem for a homogeneous porous layer. It is shown that the stability criteria (critical filtering Rayleigh numbers) due to the difference in the thermophysical and structural properties (coefficients of thermal conductivity, porosity and air permeability) of the layers can significantly differ from each other. According to detailed measurements of the thermal structure and metric characteristics of the fixed snow-ice cover in Amba Bay (Shokalsky Strait, Severnaya Zemlya Archipelago) during Winter 2015-2016, as well as calculations of its thermodynamic evolution, the values and temporal variability of the Rayleigh numbers are estimated. By comparing the observational and modeling data, the reality of the existence of a convective heat transfer regime in the snow cover is revealed. It is concluded that it is necessary to take into account its contribution to the thermal and mass balance of sea ice during winter period.</p>

On the Stability of Taylor - Couette Flow With Axial Flow

2012 ◽  
Author(s):  
Emna Berrich ◽  
Fethi Aloui ◽  
Jack Legrand
Keyword(s):  
Flow Direction ◽  
Axial Flow ◽  
Diffusion Method ◽  
Diffusion Limit ◽  
Taylor Flow ◽  
Concentric Cylinders ◽  
Reflected Light ◽  
Helical Vortices ◽  
Taylor Couette ◽  
The Stability

An experimental investigation of Taylor-Couette flows with axial flow is presented. Two techniques are used: Visualization using the Kalliroscope and Electro-diffusion method using electrochemical probes. The fluid is confined between concentric cylinders. It is constituted by an electrochemical solution seeding with 2% of a rheoscopic liquid AQ-1000 (Kalliroscope Corp., U.S.A.). The rheoscopic liquid contains small particles reflecting light in dependence on their orientation imposed by the flow direction. The reflected light intensity of Kalliroscope flakes allows a qualitative study of the flow. While the polarography technique allows the measurement of diffusion limit current intensities delivered by the electrochemical probes. The frequency responses of the probe to the flow allow the determination of the instantaneous and local mass transfer and the instantaneous wall shear rate. Two protocols were adopted to study the effect of an axial flow superposed to Couette-Taylor flows and the history flow effect. The first one consists to impose an azimuthal flow to the inner cylinder. When the regime was established, we superposed the axial flow. This protocol was named “the direct protocol”. While the second protocol consists to impose firstly the axial flow on the gap of the system then the azimuthal flow. We named it “the inverse protocol”. We demonstrated that the Couette-Taylor flow with axial flow is strongly dependent on the flow history (the protocol). For the same Taylor number and axial Reynolds number, the resulting flow is completely different. An axial flow superposed to Couette-Taylor flow can delay the instabilities apparition; generate the displacement of the Taylor vortices in the same direction as the axial flow or in the opposite direction; and modify the instability character of the flow by developing helical vortices or wavy helical vortices.

scholarly journals Effects of an axial flow on the centrifugal, elliptic and hyperbolic instabilities in Stuart vortices

2014 ◽  
Vol 758 ◽  
pp. 565-585 ◽  
Author(s):  
Manikandan Mathur ◽  
Sabine Ortiz ◽  
Thomas Dubos ◽  
Jean-Marc Chomaz
Keyword(s):  
Axial Velocity ◽  
Local Stability ◽  
Numerical Solutions ◽  
Axial Flow ◽  
Axial Direction ◽  
Threshold Value ◽  
Base Flow ◽  
Centrifugal Instability ◽  
Axisymmetric Vortex ◽  
Stuart Vortices

AbstractLinear stability of the Stuart vortices in the presence of an axial flow is studied. The local stability equations derived by Lifschitz & Hameiri (Phys. Fluids A, vol. 3 (11), 1991, pp. 2644–2651) are rewritten for a three-component (3C) two-dimensional (2D) base flow represented by a 2D streamfunction and an axial velocity that is a function of the streamfunction. We show that the local perturbations that describe an eigenmode of the flow should have wavevectors that are periodic upon their evolution around helical flow trajectories that are themselves periodic once projected on a plane perpendicular to the axial direction. Integrating the amplitude equations around periodic trajectories for wavevectors that are also periodic, it is found that the elliptic and hyperbolic instabilities, which are present without the axial velocity, disappear beyond a threshold value for the axial velocity strength. Furthermore, a threshold axial velocity strength, above which a new centrifugal instability branch is present, is identified. A heuristic criterion, which reduces to the Leibovich & Stewartson criterion in the limit of an axisymmetric vortex, for centrifugal instability in a non-axisymmetric vortex with an axial flow is then proposed. The new criterion, upon comparison with the numerical solutions of the local stability equations, is shown to describe the onset of centrifugal instability (and the corresponding growth rate) very accurately.

Influences of Axial Gap Between Blade Rows on Secondary Flows and Aerodynamic Performance in a Turbine Stage

2009 ◽  
Author(s):  
K. Yamada ◽  
K. Funazaki ◽  
M. Kikuchi ◽  
H. Sato
Keyword(s):  
Flow Field ◽  
Three Dimensional ◽  
Axial Flow ◽  
Axial Direction ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Turbine Stage ◽  
Stator Vane ◽  
Is Design ◽  
Probe Measurements

A study on the effects of the axial gap between stator and rotor upon the stage performance and flow field of a single axial flow turbine stage is presented in this paper. Three axial gaps were tested, which were achieved by moving the stator vane in the axial direction while keeping the disk cavity constant. The effect of the axial gap was investigated at two different conditions, that is design and off-design conditions. The unsteady three-dimensional flow field was analyzed by time-accurate RANS (Reynolds-Averaged Navier-Stokes) simulations. The simulation results were compared with the experiments, in which total pressure and the time-averaged flow field upstream and downstream of the rotor were obtained by five-hole probe measurements. The effect of the axial gap was confirmed in the endwall regions, and obtained relatively at off-design condition. The turbine stage efficiency was improved almost linearly by reducing the axial gap at the off-design condition.

scholarly journals On the Hydromagnetic Stability of a Rotating Fluid Annulus

2010 ◽  
Vol 2 (2) ◽  
pp. 250-256
Author(s):  
H. A. Jasmine
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Velocity Component ◽  
Axial Direction ◽  
Inner Product ◽  
Rotating Fluid ◽  
Concentric Cylinders ◽  
Swirl Velocity ◽  
Product Method ◽  
Mhd Stability

The linear stability of a rotating fluid  in  the annulus  between two concentric cylinders is investigated in the presence of a magnetic field  which is  azimuthal as well as in axial direction. Several results of MHD stability have been derived by using the inner product method. It is shown that when the swirl velocity component is large, the hydromagnetic effects become small compared with those due to swirl. The presence of a velocity field and imposed magnetic field will lead to the basic state to more stability. Keywords: Hydromagnetic Stability; Rotating Fluid. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.3945                 J. Sci. Res. 2 (2), 250-256 (2010) 

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