Effects of Buoyancy on Laminar Flow in Curved Elliptic Ducts

1992 ◽  
Vol 114 (4) ◽  
pp. 936-943 ◽  
Author(s):  
Z. F. Dong ◽  
M. A. Ebadian
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Control Volume ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Uniform Heat Flux ◽  
Published Data ◽  
Circular Duct ◽  
Uniform Wall Temperature ◽  
Wide Range

This paper numerically investigates the effects of buoyancy on fully developed laminar flow in a curved duct with an elliptic cross section. The flow of Newtonian fluids is assumed steady in terms of Boussinesq approximation. The curved elliptic duct is subjected to thermal boundary conditions of axially uniform heat flux and peripherally uniform wall temperature. The numerically generated boundary-fitted coordinate system is applied to discretize the solution domain of the elliptic duct, and the Navier-Stokes equations and the energy equation, including the curvature ratio, are solved by use of the control volume-based finite difference method. The solution covers a wide range of curvature ratios, and Dean and Grashof numbers. The results presented are displayed graphically and in tabular form to illustrate the buoyancy effect. It is further shown that buoyancy acts to increase both the Nusselt number and the friction factor and changes the distribution of the velocity and the temperature. The results for the curved circular duct with and without buoyancy are compared with the data available in the open literature for all cases. Also compared with the published data are the results of laminar flow in a curved elliptic duct, and very good agreement is obtained.

Complex dynamics in a stratified lid-driven square cavity flow

2018 ◽  
Vol 855 ◽  
pp. 43-66 ◽  
Author(s):  
Ke Wu ◽  
Bruno D. Welfert ◽  
Juan M. Lopez
Keyword(s):  
Stokes Equations ◽  
Complex Dynamics ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Stable Temperature ◽  
Wide Range ◽  
Side Walls ◽  
Steady State Solutions

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

Prediction of Cascade Performance Using an Incompressible Navier–Stokes Technique

1991 ◽  
Vol 113 (4) ◽  
pp. 561-571 ◽  
Author(s):  
G. V. Hobson ◽  
B. Lakshminarayana
Keyword(s):  
Stokes Equations ◽  
Control Volume ◽  
Numerical Technique ◽  
Skin Friction Coefficient ◽  
Navier Stokes ◽  
Compressor Cascade ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Distribution Boundary ◽  
Turbulence Effects

A fully elliptic, control volume solution of the two-dimensional incompressible Navier–Stokes equations for the prediction of cascade performance over a wide range is presented in this paper. The numerical technique is based on a new pressure substitution method. A Poisson equation is derived from the pressure-weighted substitution of the full momentum equations into the continuity equation. The analysis of a double circular arc compressor cascade is presented, and the results are compared with the available experimental data at various incidence angles. Good agreement is obtained for the blade pressure distribution, boundary layer and wake profiles, skin friction coefficient, losses and outlet angles. Turbulence effects are simulated by the low-Reynolds-number version of the k–ε turbulence model.

Unsteady evolution of a horizontal jet in a stratified fluid

1976 ◽  
Vol 78 (1) ◽  
pp. 49-63 ◽  
Author(s):  
R. Peyret
Keyword(s):  
Laminar Flow ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Stokes Equations ◽  
Boussinesq Approximation ◽  
Stratified Fluid ◽  
Navier Stokes ◽  
Constant Density ◽  
Navier Stokes Equations ◽  
Implicit Finite Difference

The unsteady laminar flow due to the penetration of a horizontal jet of constant density into a stratified fluid is considered. A numerical solution of the Navier–Stokes equations under the Boussinesq approximation is obtained by means of an implicit finite-difference method. Results for different values of the Reynolds and internal Froude numbers are given and discussed.

Interacting oscillatory boundary layers and wall modes in modulated rotating convection

2009 ◽  
Vol 625 ◽  
pp. 75-96 ◽  
Author(s):  
A. RUBIO ◽  
J. M. LOPEZ ◽  
F. MARQUES
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Large Scale ◽  
Stokes Equations ◽  
Broad Band ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Rotating Convection ◽  
High Modulation ◽  
Wide Range

Thermal convection in a rotating cylinder near onset is investigated using direct numerical simulations of the Navier–Stokes equations with the Boussinesq approximation in a regime dominated by the Coriolis force. For thermal driving too small to support convection throughout the entire cell, convection sets in as alternating pairs of hot and cold plumes in the sidewall boundary layer, the so-called wall modes of rotating convection. We subject the wall modes to small amplitude harmonic modulations of the rotation rate over a wide range of frequencies. The modulations produce harmonic Ekman boundary layers at the top and bottom lids as well as a Stokes boundary layer at the sidewall. These boundary layers drive a time-periodic large-scale circulation that interacts with the wall-localized thermal plumes in a non-trivial manner. The resultant phenomena include a substantial shift in the onset of wall-mode convection to higher temperature differences for a broad band of frequencies, as well as a significant alteration of the precession rate of the wall mode at very high modulation frequencies due to the mean azimuthal streaming flow resulting from the modulations.

scholarly journals Application of Through-Flow Calculation to Design and Performance Prediction of Centrifugal Compressor

1999 ◽  
Vol 5 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Y. S. Choi ◽  
S. H. Kang
Keyword(s):  
Centrifugal Compressor ◽  
Performance Prediction ◽  
Stokes Equations ◽  
Control Volume ◽  
Computer Code ◽  
Secondary Flows ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Simpler Algorithm ◽  
And Performance

A computer code predicting the flows through the centrifugal compressor with the radial vaneless diffuser was developed and applied to investigate the detailed flowfields, i.e., secondary flows and jet-wake type flow pattern in design and off-design conditions. Various parameters such as slip factors, aerodynamic blockages, entropy generation and two-zone modeling which are widely used in design and performance prediction, were discussed.A control volume method based on a general curvilinear coordinate system was used to solve the time-averaged Navier–Stokes equations and SIMPLER algorithm was used to solve the pressure linked continuity equation. The standardk-εturbulence model was used to obtain the eddy viscosity. Performance of the code was verified using the measured data for the Eckardt impeller.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Modeling Of The Alloying Substances Distribution In The Melt During Pulsed Induction Heating Of The Substrate

2017 ◽  
Vol 12 (2) ◽  
pp. 111-118
Author(s):  
Vladimir Popov
Keyword(s):  
Induction Heating ◽  
Stokes Equations ◽  
Substrate Surface ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Empirical Formulas ◽  
Metal Solidification ◽  
Navier Stokes Equations ◽  
High Frequency Electromagnetic Field ◽  
Melting And Solidification

Under study is the applicability of the high-frequency electromagnetic field impulse for metal heating and melting with a view to its subsequent alloying. The processes of heating, phase transition, heat and mass transfer in the molten metal, solidification of the melt are considered with the aid the proposed mathematical model. The substrate surface is covered with a layer of alloying substances. The distribution of the electromagnetic energy in the metal is described by empirical formulas. Melting and solidification of the metal is considered at the Stephan’s approximation. The flow in the liquid is described by the Navier – Stokes equations in the Boussinesq approximation. According to the results of numerical experiments, the flow structure in the melt and distribution of the alloying substances was evaluated versus the characteristics of induction heating

Theory Versus Experiment for the Effects of Pressure Ratio on the Performance of an Orifice-Compensated Hybrid Bearing

1998 ◽  
Vol 120 (4) ◽  
pp. 930-936 ◽  
Author(s):  
P. Mosher ◽  
D. W. Childs
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Load Capacity ◽  
Dynamic Stiffness ◽  
Pressure Ratio ◽  
Navier Stokes ◽  
Rotordynamic Coefficients ◽  
Wide Range ◽  
Bearing Load ◽  
Hybrid Bearing

This research investigates the effect of varying the concentric recess pressure ratio of hybrid (combination hydrostatic and hydrodynamic) bearings to be used in high-speed, high-pressure applications. Bearing flowrate, load capacity, torque, rotordynamic coefficients, and whirl frequency ratio are examined to determine the concentric, recess-pressure ratio which yields optimum bearing load capacity and dynamic stiffness. An analytical model, using two-dimensional bulk-flow Navier-Stokes equations and anchored by experimental test results, is used to examine bearing performance over a wide range of concentric recess pressure ratios. Typically, a concentric recess pressure ratio of 0.50 is used to obtain maximum bearing load capacity. This analysis reveals that theoretical optimum bearing performance occurs for a pressure ratio near 0.40, while experimental results indicate the optimum value to he somewhat higher than 0.45. This research demonstrates the ability to analytically investigate hybrid bearings and shows the need for more hybrid-bearing experimental data.

Closed Form Solution for Outflow Between Corotating Disks

2016 ◽  
Vol 138 (5) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Closed Form ◽  
Stokes Equations ◽  
Closed Form Solution ◽  
Tangential Velocity ◽  
Form Solution ◽  
Navier Stokes ◽  
Published Data ◽  
Rotational Inertia ◽  
Viscous Losses ◽  
Present Solution

Mathematical expressions are derived for flow velocities and pressure distributions for a laminar flow in the gap between two rotating concentric disks. Fluid enters the gap between disks at the center and diverges to the outer periphery. The Navier–Stokes equations are linearized in order to get closed-form solution. The present solution is applicable to the flow between corotating as well as contrarotating disks. The present results are in agreement with the published data of other investigators. The tangential velocity is less for contrarotating disks than for corotating disks in core region of the radial channel. The flow is influenced by rotational inertia and convective inertia both. Dominance of rotational inertia over convective inertia causes backflow. Pressure depends on viscous losses, convective inertia, and rotational inertias. Effect of viscous losses on pressure is high at small throughflow Reynolds number. The convective and rotational inertia influence pressure significantly at high throughflow and rotational Reynolds numbers. Both favorable and unfavorable pressure gradients can be found simultaneously depending on a combination of parameters.

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