scholarly journals Numerical study of the thermosolutal convection in a 3-D cavity submitted to cross gradients of temperature and concentration

2019 ◽  
Vol 23 (3 Part B) ◽  
pp. 1923-1933
Author(s):  
Meriem Ouzaouit ◽  
Btissam Abourida ◽  
Lahoucine Belarche ◽  
Hicham Doghmi ◽  
Mohamed Sannad
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stokes Equations ◽  
Numerical Study ◽  
Thermosolutal Convection ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Conservation Of Momentum ◽  
Prandtl Numbers

This study is a contribution to the numerical study of the thermosolutal convection in a 3-D porous cavity filled with a binary fluid submitted to cross gradients of temperature and concentration. The Navier-Stokes equations, mass and energy governing the physical problem are discretized by the finite volume method. The equations of conservation of momentum coupled with the continuity equation are solved using the SIMPLEC algorithm, then the obtained system is solved using the implicit alternating directions method. The numerical simulations, presented here, correspond to a wide range of thermal Rayleigh number (103< Ra < 106) and buoyancy ratio (1 < N < 12). The Lewis and Prandtl numbers were fixed respectively at 5 and 0.71 and the sections dimension ? = D / H = 0.4. The temperature distribution, the flow pattern and the average heat and mass transfer are examined. The obtained results show significant changes in terms of heat and mass transfer, by proper choice of the governing parameters.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

Simulation of Fluid Flow Through a Granular Bed

2006 ◽  
Author(s):  
Arezou Jafari ◽  
S. Mohammad Mousavi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Packed Bed ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Duct Geometry ◽  
Flow Through

Numerical study of flow through random packing of non-overlapping spheres in a cylindrical geometry is investigated. Dimensionless pressure drop has been studied for a fluid through the porous media at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), and numerical solution of Navier-Stokes equations in three dimensional porous packed bed illustrated in excellent agreement with those reported by Macdonald [1979] in the range of Reynolds number studied. The results compare to the previous work (Soleymani et al., 2002) show more accurate conclusion because the problem of channeling in a duct geometry. By injection of solute into the system, the dispersivity over a wide range of flow rate has been investigated. It is shown that the lateral fluid dispersion coefficients can be calculated by comparing the concentration profiles of solute obtained by numerical simulations and those derived analytically by solving the macroscopic dispersion equation for the present geometry.

Numerical Study of Incompressible Flow About Transversely Oscillating Cylinder Pairs

2004 ◽  
Vol 126 (4) ◽  
pp. 310-317 ◽  
Author(s):  
W. Jester ◽  
Y. Kallinderis
Keyword(s):  
Incompressible Flow ◽  
Stokes Equations ◽  
Numerical Study ◽  
Structural Response ◽  
Secondary Peak ◽  
Navier Stokes ◽  
Flow Induced Vibration ◽  
Oscillating Cylinder ◽  
Navier Stokes Equations ◽  
Wide Range

A numerical investigation of incompressible flow about transversely oscillating cylinder pairs is performed. Both tandem and side-by-side arrangements undergoing both flow-induced and forced transverse oscillations are considered. A second-order projection scheme is used to solve the 2-D incompressible Navier Stokes equations and a staggered approach is used to couple flow and structural response. Automatic mesh deformation and adaptation are used to handle arbitrary motion of the bodies. Comparisons with experimental results indicate that the present numerical method can capture complex interference and flow–structure interaction phenomena. Specifically, results are presented that demonstrate wake galloping effects, in which a cylinder in the wake of another experiences large flow-induced vibration over a wide range of flow velocities, and the presence of an experimentally observed secondary peak in the flow-induced vibration of rigidly connected cylinders in a tandem arrangement. An explanation of this secondary peak is provided by employing appropriate visualization of the unsteady flow. Results for forced oscillation of a pair of cylinders in a side-by-side arrangement are also presented that show the effect of phase angle on the wake structure behind the cylinder pair.

scholarly journals Dynamics of Single Droplet Splashing on Liquid Film by Coupling FVM with VOF

Processes ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 841
Author(s):  
Yuzhen Jin ◽  
Huang Zhou ◽  
Linhang Zhu ◽  
Zeqing Li
Keyword(s):  
Liquid Film ◽  
Weber Number ◽  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Single Droplet ◽  
Navier Stokes Equations ◽  
Volume Method ◽  
The Relationship

A three-dimensional numerical study of a single droplet splashing vertically on a liquid film is presented. The numerical method is based on the finite volume method (FVM) of Navier–Stokes equations coupled with the volume of fluid (VOF) method, and the adaptive local mesh refinement technology is adopted. It enables the liquid–gas interface to be tracked more accurately, and to be less computationally expensive. The relationship between the diameter of the free rim, the height of the crown with different numbers of collision Weber, and the thickness of the liquid film is explored. The results indicate that the crown height increases as the Weber number increases, and the diameter of the crown rim is inversely proportional to the collision Weber number. It can also be concluded that the dimensionless height of the crown decreases with the increase in the thickness of the dimensionless liquid film, which has little effect on the diameter of the crown rim during its growth.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

Numerical Study of Viscous Flows Inside Partially Filled Spinning and Coning Cylinders

1996 ◽  
Vol 118 (2) ◽  
pp. 335-340 ◽  
Author(s):  
Mohamed Selmi
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Center Of Mass ◽  
Steady Motion ◽  
Practical Interest ◽  
Nonlinear Effects ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Practical Applications ◽  
Analysis And Design

This paper is concerned with the solution of the 3-D-Navier-Stokes equations describing the steady motion of a viscous fluid inside a partially filled spinning and coning cylinder. The cylinder contains either a single fluid of volume less than that of the cylinder or a central rod and a single fluid of combined volume (volume of the rod plus volume of the fluid) equal to that of the cylinder. The cylinder rotates about its axis at the spin rate ω and rotates about an axis that passes through its center of mass at the coning rate Ω. In practical applications, as in the analysis and design of liquid-filled projectiles, the parameter ε = τ sin θ, where τ = Ω/ω and θ is the angle between spin axis and coning axis, is small. As a result, linearization of the Navier-Stokes equations with this parameter is possible. Here, the full and linearized Navier-Stokes equations are solved by a spectral collocation method to investigate the nonlinear effects on the moments caused by the motion of the fluid inside the cylinder. In this regard, it has been found that nonlinear effects are negligible for τ ≈ 0.1, which is of practical interest to the design of liquid-filled projectiles, and the solution of the linearized Navier-Stokes equations is adequate for such a case. However, as τ increases, nonlinear effects increase, and become significant as ε surpasses about 0.1. In such a case, the nonlinear problem must be solved. Complete details on how to solve such a problem is presented.

Experimental and Numerical Study of Vortex Induced Vibrations on a Spool Model

2018 ◽  
Author(s):  
David Gross ◽  
Yann Roux ◽  
Benjamin Rousse ◽  
François Pétrié ◽  
Ludovic Assier ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Dynamic ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Perturbation ◽  
Industry Standards ◽  
Vortex Induced Vibrations ◽  
Recommended Practices ◽  
Decay Tests

The problem of Vortex-Induced Vibrations (VIV) on spool and jumper geometries is known to present several drawbacks when approached with conventional engineering tools used in the study of VIV on risers. Current recommended practices can lead to over-conservatism that the industry needs to quantify and minimize within notably cost reduction objectives. Within this purpose, the paper will present a brief critical review of the Industry standards and more particularly focus on both experimental and Computational Fluid Dynamic (CFD) approaches. Both qualitative and quantitative comparisons between basin tests and CFD results for a 2D ‘M-shape’ spool model will be detailed. The results presented here are part of a larger experimental and numerical campaign which considered a number of current velocities, heading and geometry configurations. The vibratory response of the model will be investigated for one of the current velocities and compared with the results obtained through recommended practices (e.g. Shear7 and DNV guidelines). The strategy used by the software K-FSI to solve the fluid-structure interaction (FSI) problem is a partitioned coupling solver between fluid solver (FINE™/Marine) and structural solvers (ARA). FINE™/Marine solves the Reynolds-Averaged Navier-Stokes Equations in a conservative way via the finite volume method and can work on structured or unstructured meshes with arbitrary polyhedrons, while ARA is a nonlinear finite element solver with a large displacement formulation. The experiments were conducted in the BGO FIRST facility located in La Seyne sur Mer, France. Particular attention was paid towards the model design, fabrication, instrumentation and characterization, to ensure an excellent agreement between the structural numerical model and the actual physical model. This included the use of a material with low structural damping, the performance of stiffness and decay tests in air and in still water, plus the rationalization of the instrumentation to be able to capture the response with the minimum flow perturbation or interaction due to instrumentation.

Numerical Prediction of Turbulent Wakes Behind a Square Cylinder

1998 ◽  
Vol 14 (1) ◽  
pp. 23-29
Author(s):  
Robert R. Hwang ◽  
Sheng-Yuh Jaw
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Wall Region ◽  
Square Cylinder ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Turbulent Vortex Shedding ◽  
Model Equations ◽  
Good Agreement

ABSTRACTThis paper presents a numerical study on turbulent vortex shedding flows past a square cylinder. The 2D unsteady periodic shedding motion was resolved in the calculation and the superimposed turbulent fluctuations were simulated with a second-order Reynolds-stress closure model. The calculations were carried out by solving numerically the fully elliptic ensemble-averaged Navier-Stokes equations coupled with the turbulence model equations together with the two-layer approach in the treatment of the near-wall region. The performance of the computations was evaluated by comparing the numerical results with data from available experiments. Results indicate that the present study gives good agreement in the shedding frequency and mean drag as well as in some phase profiles of the mean velocity.

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