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 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.

scholarly journals A semi-analytical solution for the mean wind profile in the Atmospheric Boundary Layer: the convective case

2009 ◽  
Vol 9 (5) ◽  
pp. 19817-19844
Author(s):  
L. Buligon ◽  
G. A. Degrazia ◽  
O. C. Acevedo ◽  
C. R. P. Szinvelski ◽  
A. G. O. Goulart
Keyword(s):  
Boundary Layer ◽  
Analytical Solution ◽  
Wind Profile ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transforms ◽  
Navier Stokes ◽  
Convective Boundary ◽  
Navier Stokes Equations ◽  
Average Wind

Abstract. A novel methodology to derive the average wind profile from the Navier-Stokes equations is presented. The development employs the Generalized Integral Transform Technique (GITT), which joints series expansions with Integral Transforms. The new approach provides a solution described in terms of the quantities that control the wind vector with height. Parameters, such as divergence and vorticity, whose magnitudes represent sinoptic patterns are contained in the semi-analytical solution. The results of this new method applied to the convective boundary layer are shown to agree with wind data measured in Wangara experiment.

Laminar Flow Over Wavy Walls

1991 ◽  
Vol 113 (4) ◽  
pp. 574-578 ◽  
Author(s):  
V. C. Patel ◽  
J. Tyndall Chon ◽  
J. Y. Yoon
Keyword(s):  
Boundary Layer ◽  
Laminar Flow ◽  
Steady Flow ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Regimes ◽  
Navier Stokes ◽  
Wavy Wall ◽  
Fully Developed Flow ◽  
Navier Stokes Equations

The boundary layer over a wavy wall and fully-developed flow in a duct with a wavy wall are considered. Numerical solutions of the Navier-Stokes equations have been obtained to provide insights into the various steady flow regimes that are possible, and to illustrate the nuances of predicting flows containing multiple separation and reattachment points.

Semi-Analytical Method for the Solution of the Poisson Equation Derived From the Navier-Stokes Using Integral Transforms

2014 ◽  
Author(s):  
Daniel J. N. M. Chalhub ◽  
Leandro A. Sphaier ◽  
Leonardo S. de B. Alves
Keyword(s):  
Poisson Equation ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transforms ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Pressure Correction ◽  
Velocity Decomposition ◽  
The Poisson Equation ◽  
New Formulation

The present work proposes two methodologies using the Integral Transform Technique to solve the Poisson equation arising from the incompressible Navier-Stokes equations. The solution of this Poisson equation is very common in the formulations based on pressure-correction and are the main bottleneck of these approaches. The new formulation proposed in this work will allow the elimination of the pressure-velocity decomposition and also eliminate the sub-iterations of the usual pressure-correction methods. The results show a comparison in performance of both proposed approaches.

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.

scholarly journals A semi-analytical solution for the mean wind profile in the Atmospheric Boundary Layer: the convective case

2010 ◽  
Vol 10 (5) ◽  
pp. 2227-2236
Author(s):  
L. Buligon ◽  
G. A. Degrazia ◽  
O. C. Acevedo ◽  
C. R. P. Szinvelski ◽  
A. G. O. Goulart
Keyword(s):  
Boundary Layer ◽  
Analytical Solution ◽  
Wind Profile ◽  
Stokes Equations ◽  
Integral Transform ◽  
Integral Transforms ◽  
Navier Stokes ◽  
Convective Boundary ◽  
Navier Stokes Equations ◽  
Average Wind

Abstract. A novel methodology to derive the average wind profile from the Navier-Stokes equations is presented. The development employs the Generalized Integral Transform Technique (GITT), which combines series expansions with Integral Transforms. The new approach provides a solution described in terms of the quantities that control the wind vector with height. Parameters, such as divergence and vorticity, whose magnitudes represent sinoptic patterns are contained in the semi-analytical solution. The results of this new method applied to the convective boundary layer are shown to agree with wind data measured in Wangara experiment.

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

Burgers turbulence model for a channel flow

1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee
Keyword(s):  
Channel Flow ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Amplitude Equations ◽  
Fourier Amplitude ◽  
Navier Stokes Equations ◽  
Burgers Model ◽  
Model Dynamics

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.

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