Computation of Velocity Profiles and Pressure Coefficients for a Laminar Flow of Air Over Staggered Array of Tubes

2005 ◽  
Author(s):  
Ramin Rahmani ◽  
Ahad Ramezanpour ◽  
Iraj Mirzaee ◽  
Hassan Shirvani
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Tube Bundle ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Velocity Profiles ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Tube Arrays ◽  
Volume Method

In this study a two dimensional, steady state and incompressible laminar flow for staggered tube arrays in crossflow is investigated numerically. A finite-volume method is used to discretize and solve the governing Navier-Stokes equations for the geometries expressed by a boundary-fitted coordinate system. Solutions for Reynolds numbers of 100, 300, and 500 are obtained for a tube bundle with 10 longitudinal rows. Local velocity profiles on top of each tube and corresponding pressure coefficient are presented at nominal pitch-to-diameter ratios of 1.33, 1.60, and 2.00 for ES, ET, and RS arrangements. Differences in location of separation points are compared for three different arrangements. The predicted results on flow field for pressure coefficient showed a good agreement with available experimental measurements.

On a theory of laminar flow in channels of a certain class. II

1975 ◽  
Vol 77 (1) ◽  
pp. 199-224 ◽  
Author(s):  
L. E. Fraenkel ◽  
P. M. Eagles
Keyword(s):  
Differential Operator ◽  
Laminar Flow ◽  
Mathematical Analysis ◽  
Stokes Equations ◽  
Partial Differential Operator ◽  
Formal Theory ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Curvature Parameter

This paper continues (and concludes) the mathematical analysis begun in (8) of a formal theory of viscous flow in channels with slowly curving walls. In that paper, the theory was shown to yield strict asymptotic expansions, in powers of the small curvature parameter, of exact solutions of the Navier-Stokes equations, but the proofs were restricted to a set of Reynolds numbers and wall divergence angles that is distinctly smaller than the set on which the formal approximation is defined. In the present paper, we study in more detail a certain linear, partial differential operator TN, the invertibility of which is essential to the proofs. This operator is shown to be invertible (and the formal theory is thereby justified) on a parameter domain that is much larger than and may well be the whole of . A key step is to associate with TN a family of operators that approximate TN locally and have much simpler coefficients.

Inward Flow Between Stationary and Rotating Disks

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Achhaibar Singh
Keyword(s):  
Laminar Flow ◽  
Flow Field ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Tangential Velocity ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Rotating Disks ◽  
Navier Stokes Equations

The present study predicts the flow field and the pressure distribution for a laminar flow in the gap between a stationary and a rotating disk. The fluid enters through the peripheral gap between two concentric disks and converges to the center where it discharges axially through a hole in one of the disks. Closed form expressions have been derived by simplifying the Navier– Stokes equations. The expressions predict the backflow near the rotating disk due to the effect of centrifugal force. A convection effect has been observed in the tangential velocity distribution at high throughflow Reynolds numbers.

A Contribution to the Numerical Solution of Developing Laminar Flow in the Entrance Region of Concentric Annuli With Rotating Inner Walls

1974 ◽  
Vol 96 (4) ◽  
pp. 333-340 ◽  
Author(s):  
J. E. R. Coney ◽  
M. A. I. El-Shaarawi
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Stokes Equations ◽  
Complete Solution ◽  
Numerical Differentiation ◽  
Velocity Profiles ◽  
Entrance Region ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Special Case

The boundary layer simplification of the Navier-Stokes equations for hydrodynamically developing laminar flow with constant physical properties in the entrance region of concentric annuli with rotating inner walls have been numerically solved using a simple linearized finite-difference scheme. Additional results to those existing in the literature by Martin and Payne [1–2] will be presented here. An advantage of the analysis used in this paper is that it does not solve for the stream function and vorticity, but predicts the development of tangential, axial and radial velocity profiles directly, thus avoiding numerical differentiation. Results for the development of these velocity profiles, pressure drop and friction factor are presented for five annuli radii ratios (0.3, 0.5, 0.674, 0.727 and 0.90) at various values of the parameter Re2/Ta. The paper may be considered as a direct comparison between the boundary layer solution and the complete solution of the Navier-Stokes equations [1–2] for that special case.

scholarly journals The effort of increasing Reynolds number in POD-Galerkin Reduced Order Methods: from laminar to turbulent flows

2018 ◽  
Author(s):  
Shafqat Ali ◽  
Saddam Hijazi ◽  
Sokratia Georgaka ◽  
Francesco Ballarin ◽  
Giovanni Stabile ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Finite Element ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Reduced Order ◽  
Volume Method ◽  
Reduced Order Methods

We present different strategies to be able to increase Reynolds number in Reduced Order Methods (ROMs), from laminar to turbulent flows, in the context of the incompressible parametrised Navier-Stokes equations. The proposed methodologies are based on different full order discretisation techniques: the finite element method and the finite volume method. For what concerns finite element full order discretisations which in this work aim to be used from low to moderate Reynolds numbers the

Hybrid Solution for Developing Laminar Flow in Wavy-Wall Channels via Integral Transforms

2007 ◽  
Author(s):  
Roseane L. Silva ◽  
Carlos A. C. Santos ◽  
Joa˜o N. N. Quaresma ◽  
Renato M. Cotta
Keyword(s):  
Laminar Flow ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transforms ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Wavy Wall ◽  
Navier Stokes Equations ◽  
Convergence Behavior ◽  
Hybrid Solution

The analysis of two-dimensional laminar flow in the entrance region of arbitrarily shaped ducts is undertaken by application of the Generalized Integral Transform Technique (GITT) in the solution of the steady Navier-Stokes equations for incompressible flow. The streamfunction-only formulation is adopted, and a general filtering solution that adapts to the irregular contour is proposed to enhance the convergence behavior of the eigenfunction expansion. The case of a wavy-wall channel is then considered more closely in order to report some numerical results illustrating the expansions convergence behavior. In addition to reporting results of streamfunction, the product of friction factor-Reynolds number is also calculated and compared against results from discrete methods available in the literature for different Reynolds numbers and amplitudes of the wavy channel.

ON CHAOTIC BEHAVIORS OF INCOMPRESSIBLE FLUID FLOWS IN TRIANGULAR DRIVEN CAVITIES

2005 ◽  
Vol 15 (10) ◽  
pp. 3103-3118 ◽  
Author(s):  
SONG WANG
Keyword(s):  
Incompressible Fluid ◽  
Stokes Equations ◽  
Initial Conditions ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Different Depths ◽  
Incompressible Fluid Flows ◽  
Volume Method

In this paper we investigate numerically chaotic behaviors of incompressible fluid flows at large Reynolds numbers in triangular driven cavities. The problem is first formulated as incompressible Navier–Stokes equations with appropriate boundary and initial conditions. The equations are then solved numerically by an exponentially fitted finite volume method for various Reynolds numbers up to 107. Numerical experiments on flows in triangular cavities with different depths are performed. The numerical results show clearly that the transitions of the flows from lamina to turbulence/chaos follow some conventional routes to chaos.

Numerical Investigation on Shock-Induced Separation Structure of Supercritical Airfoil

2013 ◽  
Vol 756-759 ◽  
pp. 4502-4505 ◽  
Author(s):  
Xin Xu ◽  
Da Wei Liu ◽  
De Hua Chen ◽  
Yuan Jing Wang
Keyword(s):  
Stokes Equations ◽  
Separation Bubble ◽  
Pressure Coefficient ◽  
Reynolds Numbers ◽  
Aerodynamic Characteristics ◽  
Navier Stokes ◽  
Trailing Edge ◽  
Navier Stokes Equations ◽  
Supercritical Airfoil ◽  
Coefficient Distribution

The supercritical airfoil has been widely applied to large airplanes for sake of high aerodynamic efficiency. But at transonic speeds, the complicated shock-induced separation on the upper surface of supercritical airfoil will change the aerodynamic characteristics. The transonic flows over a typical supercritical airfoil CH were numerically investigated in this paper, in order to analyses different shock-induced separation structure. The two-dimensional Navier-Stokes equations were solved with structure grids by utilizing the S-A turbulence model. The computation attack angles of CH airfoil varied from 0oto 4o, Mach numbers varied from 0.74 to 0.82 while Reynolds numbers varied from 3×106to 50×106per airfoil chord. It is shown that with the attack angle increases, the separation bubble occurred on the upper surface first, then the trailing-edge separation occurred, the trailing-edge would separate totally at last. The different separation structure would result in different pressure coefficient distribution and boundary layer thickness.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

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.

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