Discussions on driven cavity flow

Ertürk, Ercan

doi:10.1002/fld.1887

Cited by 149 publications

(85 citation statements)

References 51 publications

(214 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Results associated with the secondary vortices are listed in Table 6, which also includes relevant results obtained by Erturk (2009) for two different Re numbers of 10000 and 20000. It should be pointed out that, in the latter, a uniform mesh size of 1025x1025 was used, as opposed to the non-uniform mesh of 768x768 used in this study.…”

Section: Reynolds Numbersmentioning

confidence: 99%

“…Recently, physical, mathematical and numerical aspects of the steady incompressible lid-driven cavity flow were discussed in detail by Erturk (2009). The findings of the study were also compared with those of earlier publications.…”

Section: Introductionmentioning

confidence: 98%

“…On the other hand, 2-D incompressible steady driven cavity flow can be computable at high Re (Erturk, 2009) with its peculiar computational challenges. Therefore, steady lid-driven cavity flow, especially at high Re (Re ≥ 10000), has been exploited by many researchers in order to test and improve robustness and stability of their computational methods (Erturk, 2009;Erturk et al, 2005;Ramšak and Škerget, 2004;Erturk and Gökçel, 2006;Sahin and Owens, 2003;Barragy and Carey, 1997;Schreiber and Keller, 1983;Ghia et al, 1982).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

Yapıcı

Uludağ

2013

Braz. J. Chem. Eng.

View full text Add to dashboard Cite

-In this work, computer simulation results of steady incompressible flow in a 2-D square lid-driven cavity up to Reynolds number (Re) 65000 are presented and compared with those of earlier studies. The governing flow equations are solved by using the finite volume approach. Quadratic upstream interpolation for convective kinematics (QUICK) is used for the approximation of the convective terms in the flow equations. In the implementation of QUICK, the deferred correction technique is adopted. A non-uniform staggered grid arrangement of 768x768 is employed to discretize the flow geometry. Algebraic forms of the coupled flow equations are then solved through the iterative SIMPLE (Semi-Implicit Method for PressureLinked Equation) algorithm. The outlined computational methodology allows one to meet the main objective of this work, which is to address the computational convergence and wiggled flow problems encountered at high Reynolds and Peclet (Pe) numbers. Furthermore, after Re ≥ 25000 additional vortexes appear at the bottom left and right corners that have not been observed in earlier studies.

show abstract

Section: Reynolds Numbersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

Yapıcı

Uludağ

2013

Braz. J. Chem. Eng.

View full text Add to dashboard Cite

show abstract

“…The (9,5) HOC formulation for the transient Navier-Stokes equations in primitive variable was discussed by Kalita and Sen [18]. Discussion of transition from laminar to turbulent flow at Reynolds number starting from 1000 has been investigated by Erturk [21]. Hou [22] studied stable fourth-order streamfunction method for incompressible flow with boundaries.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solutions of 2-D Unsteady Incompressible Flow in a Driven Square Cavity Using Streamfunction-Vorticity Formulation

Ambethkar¹,

Kumar²,

Srivastava³

2016

Int. J. of Appl. Math.

View full text Add to dashboard Cite

In this paper, we have used a streamfunction-vorticity (ψ − ξ) formulation to investigate the problem of 2-D unsteady viscous incompressible flow in a driven square cavity with moving top and bottom walls. We used this formulation to solve the governing equations along with no-slip and slip wall boundary conditions. A general algorithm was used for this formulation in order to compute the numerical solutions for the flow variables: streamfunction ψ, vorticityfunction ξ for low Reynolds numbers Re ≤ 50. We have executed this with the aid of a computer programme developed and run in C++ compiler. We have proved the stability and convergence of the numerical scheme using matrix method. Following this, the stability conditions obtained for the time and space steps have been used in numerical computations to arrive at the numerical solutions with desired accuracy. Also investigated was the variation of u and v components of velocity at points closed to left side, top and bottom walls of the square cavity at different time levels for Reynolds number 50. Based on the numerical computations of u-velocity, we found: (i) the u-velocity is almost same near the top and bottom wall of the square cavity above and below the geometric center for Re=15 and 30; (ii) the absolute value of the u-velocity first decreases, then increases, and finally decreases, near top and bottom wall of the square cavity. Based on the numerical computations of the v-velocity, we found: (i) the absolute value of the v-velocity increases uniformly as time level increases' (ii) the v-velocity at the right wall of the square cavity attains a maximum value, and then, decreases towards the geometric center. The numerical solutions of the vorticity vector ξ at Re=50 for different times along the horizontal line through geometric center of the square cavity indicate the following: (i) the vorticity contours decreased in between the left wall boundary to the midpoint of the square domain; (ii) it, then, increased in between the midpoint to the right wall boundary. Based on the numerical solutions of streamfunction ψ, we found: (i) the size of streamline contours decreased when the time increased; (ii) two streamline contours are generated, one above the geometric center, and the other, below the geometric center in clockwise direction.

show abstract

“…E. Erturk recommends to reduce a mesh step for overcoming this instability (see, for example, [5]). But in this case, the systems of the linear algebraic equations (SLAE) with huge number of unknowns are generated, and more effective methods are needed to solve them.…”

Section: Introductionmentioning

confidence: 99%

On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step

Alexander

Liubov

2017

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki

View full text Add to dashboard Cite

Use of the all-Russian mathematical portal Math-Net.Ru implies that you have read and agreed to these terms of use http://www.mathnet.ru/eng/agreement Download details: IP: 52.36.4.81 May 12, 2018, 09:52:56 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2017, vol. 21, no. 2, pp. 362-375 ISSN: 2310-7081 (online), 1991 http://doi. AbstractThe stable stationary solutions of the test problem of hydrodynamics and heat transfer in a plane channel with the backward-facing step have been considered in the work for extremely high Reynolds numbers and expansion ratio of the stream ER. The problem has been solved by numerical integration of the 2D Navier-Stokes equations in 'velocity-pressure' formulation and the heat equation in the range of Reynolds number 500Re 3000 and expansion ratio Introduction. Permanent improvement of numerical techniques for modeling fluid dynamics and heat transfer requires adequate methods to assess their effectiveness. For these purposes, consideration of well-known test problems which solutions have all main features of real fluid flows is the best approach. On the one hand, for these problems the huge volume of experimental and theoretical results is saved up that provides their maximum reliability. On the other hand the critical parameters are unambiguously determined for them. The 'intensification' of these parameters increases the complexity of the problems. The efficiency evaluation of a new computing technology follows from this: the more critical parameters of the problem are 'intense', the more the technology is effective. The well-known example of such problem of hydrodynamics of incompressible viscous liquids is the classical lid-driven cavity problem. Reynolds number is the critical parameter for this problem.The problem of separated flow in a 2D channel with backward-facing step is one more such a problem [1]. The problem is characterized by a simple geometry. Its solution, in general, depends on two parameters: Reynolds number Re and expansion ratio ER, where ER is defined as the ratio of the full height of the channel to the height of its inlet segment. Prandtl number Pr is added when heat transfer is taken into account. Change of these few input parameters allows to receive radically various solutions of the problem-namely, separated flow patterns, which are characterized by the quantity, form, size, and position of the vortices. Furthermore, they can have a very complex structure. The maximum value of Reynolds number (Re = 3000 at ER = 2) was reached in the article [2], and expansion ratio (ER = 4 at Re 300) was reached in the works [3,4].Further increase in these parameters causes computational instability which, in particular, is discussed in [2]. E. Erturk recommends to reduce a mesh step for overcoming this instability (see, for example, [5]). But in this case, the systems of the linear algebraic equations (SLAE) with huge number of unknowns are generated, and more effective methods are needed to solve the...

show abstract

Discussions on driven cavity flow

Cited by 149 publications

References 51 publications

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

Finite volume simulation of 2-D steady square lid driven cavity flow at high reynolds numbers

Numerical Solutions of 2-D Unsteady Incompressible Flow in a Driven Square Cavity Using Streamfunction-Vorticity Formulation

On the solution of fluid flow and heat transfer problem in a 2D channel with backward-facing step

Contact Info

Product

Resources

About