Free Convection in a Two-Dimensional Porous Loop

1986 ◽  
Vol 108 (2) ◽  
pp. 277-283 ◽  
Author(s):  
L. Robillard ◽  
T. H. Nguyen ◽  
P. Vasseur
Keyword(s):  
Steady State ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Outer Boundary ◽  
Convective Motion ◽  
Steady State Solution ◽  
Temperature Fields ◽  
Maximum Temperature ◽  
Two Dimensional ◽  
Convective Cells

A study is made of the natural convection in an annular porous layer having an isothermal inner boundary and its outer boundary subjected to a thermal stratification arbitrarily oriented with respect to gravity. For such conditions, no symmetry can be expected for the flow and temperature fields with respect to the vertical diameter and the whole circular region must be considered. Two-dimensional steady-state solutions are sought by perturbation and numerical approaches. Results obtained indicate that the circulating flow around the annulus attains its maximum strength when the stratification is horizontal (heating from the side). This circulating flow is responsible for an important heat exchange between the porous layer and its external surroundings. The flow field is also characterized by the presence of two convective cells near the inner boundary, giving rise to flow reversal on this surface. When the maximum temperature on the outer boundary is at the bottom of the cavity, the convective motion becomes potentially unstable; for a Rayleigh number below 80, there exists a steady-state solution symmetrical with respect to both vertical and horizontal axes; for a Rayleigh number above 80, an unsteady periodic situation develops with the circulating flow alternating its direction around the annulus.

scholarly journals Two-Dimensional Convection Induced by Gravity and Centrifugal Forces in a Rotating Porous Layer Far Away from the Axis of Rotation

1998 ◽  
Vol 4 (2) ◽  
pp. 73-90 ◽  
Author(s):  
Peter Vadasz ◽  
Saneshan Govender
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Temperature Fields ◽  
Wave Number ◽  
Marginal Stability ◽  
Two Dimensional ◽  
Wide Range ◽  
Gravity Driven ◽  
Gravity Driven Flow ◽  
The Stability

The stability and onset of two-dimensional convection in a rotating fluid saturated porous layer subject to gravity and centrifugal body forces is investigated analytically. The problem corresponding to a layer placed far away from the centre of rotation was identified as a distinct case and therefore justifying special attention. The stability of a basic gravity driven convection is analysed. The marginal stability criterion is established in terms of a critical centrifugal Rayleigh number and a critical wave number for different values of the gravity related Rayleigh number. For any given value of the gravity related Rayleigh number there is a transitional value of the wave number, beyond which the basic gravity driven flow is stable. The results provide the stability map for a wide range of values of the gravity related Rayleigh number, as well as the corresponding flow and temperature fields.

The Effects of Energy Dissipation on the Transition to Planing of a Boat

1989 ◽  
Vol 33 (01) ◽  
pp. 35-46
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Steady State ◽  
Energy Dissipation ◽  
Detailed Analysis ◽  
Leading Edge ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Spray Formation ◽  
Propulsion Force

The problem of the transition to planing of a boat, in the presence of the effect of spray formation at the boat's leading edge, is investigated using a nonlinear steady-state solution of the equations of the theory of a directed fluid sheet for two-dimensional motion of an incompressible inviscid fluid. The motion of the fluid is coupled with the motion of the free-floating boat and detailed analysis is undertaken pertaining to such features as trim angle, sinkage, and propulsion force. The effects of the rate of energy dissipation arising from spray formation at the boat's leading edge, and changes in equilibrium depth, propulsion angle, and the boat's weight, are studied and shown to significantly influence the boat's planing characteristics.

Bifurcations of Numerically Simulated Marangoni Flows in Floating Zones

1997 ◽  
Vol 07 (06) ◽  
pp. 1295-1305
Author(s):  
C. Menke
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Marangoni Number ◽  
Control Parameter ◽  
Thermocapillary Convection ◽  
Period Doubling ◽  
Time Dependent ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Period Doubling Bifurcations

Marangoni or thermocapillary convection in a two-dimensional cylindrical half zone configuration under microgravity is studied numerically. The time-dependent simulations take into account convection and conduction in the melt, heat transfer between the melt and the ambient, and deformations of the free melt/gas surface of the half zone. A modified Marker and Cell (MAC) method is used to compute the flow and the temperature fields. The algorithm is applied especially to silicon melts. Above a critical temperature difference in the melt, the steady state becomes unstable and oscillatory thermocapillary convection occurs. The relevant control parameter for the onset of oscillations is the Marangoni number. As the Marangoni number increases, the phenomenon of period doubling is observed in the simulations. After a sequence of period doubling bifurcations, the flow becomes turbulent.

An Experimental and Numerical Study of the Isothermal Flowfield Behind a Bluff Body Flameholder

1997 ◽  
Vol 119 (2) ◽  
pp. 328-339 ◽  
Author(s):  
C. N. Raffoul ◽  
A. S. Nejad ◽  
R. D. Gould ◽  
S. A. Spring
Keyword(s):  
Steady State ◽  
Bluff Body ◽  
Recirculation Zone ◽  
Numerical Study ◽  
Steady State Solution ◽  
Accurate Solution ◽  
State Solution ◽  
Laser Doppler Velocimeter ◽  
Two Dimensional ◽  
Reynolds Stresses

An experimental and numerical investigation was conducted to study the turbulent velocities and stresses behind a two-dimensional bluff body. Simultaneous three-component laser-Doppler velocimeter (LDV) measurements were made in the isothermal incompressible turbulent flowfield downstream of a bluff body placed at midstream in a rectangular test section. Mean velocities and Reynolds stresses were measured at various axial positions. Spanwise velocity measurements indicated that the flow is three dimensional in the recirculation zone of the bluff body. Confidence in the accuracy of the data was gained by calculating the mass fluxes at each axial station. These were found to agree with each other to within ±3 percent. A parallel Computational Fluid Dynamics (CFD) study was initiated to gage the predictive accuracy of currently available CFD techniques. Three solutions were computed: a two-dimensional steady-state solution using the standard k-ε model, a two-dimensional time-accurate solution using the standard k-ε model, and a two-dimensional time-accurate solution using a Renormalized-Group (RNG) k-ε turbulence model. The steady-state solution matched poorly with the data, severely underpredicting the Reynolds stresses in the recirculation zone. The time-accurate solutions captured the unsteady vortex shedding from the base of the bluff body, providing a source for the higher Reynolds stresses. The RNG k-ε solution provided the best match to the data.

Flow Past Rotating Cylinders: Effect of Eccentricity

2000 ◽  
Vol 68 (4) ◽  
pp. 543-552 ◽  
Author(s):  
S. Mittal
Keyword(s):  
Steady State ◽  
Stokes Equations ◽  
Lift Coefficient ◽  
Steady State Solution ◽  
Rotating Cylinder ◽  
Computational Results ◽  
Two Dimensional ◽  
Dimensional Solution ◽  
Mean Values ◽  
Flow Past

Computational results are presented for flows past a translating and rotating circular cylinder. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. To validate the formulation and its implementation certain cases, for which the flow visualization and computational results have been reported by other researchers, are computed. Results are presented for Re=5, 200 and 3800 and rotation rate, (ratio of surface speed of cylinder to the freestream speed of flow), of 5. For all these cases the flow reaches a steady state. The values of lift coefficient observed for these flows exceed the limit on the maximum value of lift coefficient suggested by Goldstein based on intuitive arguments by Prandtl. These observations are in line with measurements reported, earlier, by other researchers via laboratory experiments. To investigate the stability of the computed steady-state solution, receptivity studies involving an eccentrically rotating cylinder are carried out. Computations are presented for flow past a rotating cylinder with wobble; the center of rotation of the cylinder does not match its geometric center. These computations are also important from the point of view that in a real situation it is almost certain that the rotating cylinder will be associated with a certain degree of wobble. In such cases the flow is unsteady and reaches a temporally periodic state. However, the mean values of the aerodynamic coefficients and the basic flow structure are still quite comparable to the case without any wobble. In this sense, it is found that the two-dimensional solution is stable to purely two-dimensional disturbances.

Numerical Simulations Using TVD Schemes of Two-Dimensional Supersonic Flow in Chemical Equilibrium

2017 ◽  
Vol 14 (02) ◽  
pp. 1750020
Author(s):  
J. Saldía ◽  
S. Elaskar ◽  
J. Tamagno
Keyword(s):  
Steady State ◽  
Chemical Equilibrium ◽  
Blunt Body ◽  
Steady State Solution ◽  
Two Dimensional ◽  
Tvd Schemes ◽  
Adaptive Use ◽  
Contact Discontinuities ◽  
Yee Scheme ◽  
Accuracy Of Results

A numerical scheme for the solution of both unsteady and steady-state, two-dimensional Euler equations considering gas in chemical equilibrium, is presented. Three alternatives of the Total Variation Diminishing (TVD) Harten–Yee scheme are implemented. One of them is a technique based on the adaptive use of different limiter functions in each wave of the inter-cell Riemann problem. With this technique, the undesirable effects of the artificial viscosity on the capture of contact discontinuities are reduced, without loss of robustness in nonlinear waves resolution. In order to verify the accuracy of the proposed scheme, results of the unsteady flow in cylindrical explosions, and of the steady-state solution of hypersonic flow over a blunt body, are presented. Finally, comparisons considering accuracy of results and convergence properties between the three Harten–Yee schemes are carried out.

Investigation of High Performance Heat Sink Characteristics in Forced Convection Cooling of Power Electronic Systems

2011 ◽  
Author(s):  
Giti Karimi-Moghaddam ◽  
Craig Rende ◽  
Richard D. Gould ◽  
Subhashish Bhattacharya
Keyword(s):  
Nusselt Number ◽  
Steady State ◽  
Forced Convection ◽  
Heat Sink ◽  
High Performance ◽  
Temperature Limit ◽  
Simulation Software ◽  
Temperature Fields ◽  
Junction Temperature ◽  
Maximum Temperature

This study presents the experimental performance of a high fin density heat sink for semiconductor power modules — such as IGBTs. As a case study a commercially available extruded heat sink has been chosen. By analyzing the steady-state maximum temperatures as well as various geometric orientations, Nusselt number correlations were found experimentally, which can be used to predict the performance of the heat sink. It was found that the experimental Nusselt number correlations can predict the performance of the heat sink to within a 10%. Furthermore, steady-state maximum temperature results showed that for low fan speeds (2 m/s–3 m/s), the device junction temperatures achieved a value no higher than 80°C, which is well below the junction temperature limit for 125°C for silicon power semiconductor devices. Furthermore, it was shown that for two heat sinks in series forced convection tests, gap spacing between the devices has a minimal effect on the overall performance. Also, a numerical simulation study using COMSOL Multiphysics simulation software to study flow and temperature fields has been conducted. These modeling results the thermal behavior of heat sink are validated by experimental measurements.

Convection and Stability in a Magnetic Fluid Saturated Rotating Porous Layer

2005 ◽  
Author(s):  
S. Saravanan ◽  
H. Yamaguchi
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Stability Analysis ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Magnetic Fluid ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Magnetic Field ◽  
Critical Wavenumber

The influence of magnetic field on the onset of centrifugal convection in a magnetic fluid filled differentially heated porous layer is studied theoretically using linear stability analysis. The resulting eigenvalue problem is solved using the Galerkin technique. The critical centrifugal Rayleigh number, the critical wavenumber and the eigenfunctions corresponding to two-dimensional flow pattern at the threshold are calculated. It is found that the magnetic field has a destabilizing effect and can be suitably adjusted depending on particle magnetization to enhance convection. This phenomenon can be utilized to increase the efficiency of heat transfer devices.

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