A Numerical Simulation of Unsteady Lid Driven Cavity Flow With Moving Boundaries Using CMSIP

2020 ◽  
Author(s):  
K. M. Akyuzlu ◽  
A. Antoniou
Keyword(s):  
Reynolds Numbers ◽  
Linearization Method ◽  
Finite Difference Schemes ◽  
Algebraic Equations ◽  
Driven Cavity ◽  
Computational Mesh ◽  
Proposed Model ◽  
Unsteady Characteristics ◽  
Strongly Implicit Procedure ◽  
Secondary Vortices

Abstract A two-dimensional, mathematical model is adopted to investigate the development of circulation patterns for compressible lid driven flows inside a rectangular cavity where the bottom of the cavity is free to move at a specified speed. A time and space dependent transformation is applied to the governing equations to obtain a rigid (non-moving) solution domain. The transformed equations are discretized for a uniform and orthogonal computational mesh using second order in space and first order in time finite difference schemes. The resulting nonlinear equations are then linearized using Newton’s linearization method. Finally, the set of algebraic equations that result from this process are put into a matrix form and solved using the Coupled Modified Strongly Implicit Procedure (CMSIP). Numerical experiments are carried out for various Reynolds numbers to verify the accuracy of the solution algorithm. Then the numerical simulations of lid driven flow inside the cavity is carried out for the unsteady case where the aspect ratio of the cavity is changed from 1 to 1.5 at a constant speed. It is concluded that the proposed model is successful in predicting the unsteady characteristics of the primary vortex and the secondary vortices inside a cavity with moving bottom.

Numerical Assessment of Turbulent Flow Driving in a Two-Sided Lid-Driven Cavity with Antiparallel Wall Motion

2021 ◽  
Vol 406 ◽  
pp. 133-148
Author(s):  
El Amin Azzouz ◽  
Samir Houat ◽  
Ahmed Zineddine Dellil
Keyword(s):  
Flow Characteristics ◽  
Turbulence Models ◽  
Reynolds Numbers ◽  
Systematic Evaluation ◽  
Driven Cavity ◽  
Rans Turbulence Models ◽  
Calculation Results ◽  
Two Dimensional Flow ◽  
Rsm Model ◽  
Secondary Vortices

In this paper, the case of the steady two-dimensional flow in a two-sided lid-driven square cavity is numerically investigated by the finite volume method (FVM). The flow motion is due to the top and bottom horizontal walls sliding symmetrically in the opposite direction with equal velocities, UT and UB, obtained through three respective Reynolds numbers, Re1,2=10000, 15000, and 20000. Due to the lack of availability of experimental results in this Reynolds number margin for this type of flow, the problem is first examined by considering that the flow is turbulent with the inclusion of four commonly used RANS turbulence models: Omega RSM, SST k-ω, RNG k-ε and Spalart-Allmaras (SA). Next, the regime is considered being laminar in the same range of Reynolds numbers. A systematic evaluation of the flow characteristics is performed in terms of stream-function contour, velocity profiles, and secondary vortices depth. Examination of the calculation results reveals the existence of a great similarity of the predicted flow structures between the Omega RSM model and those from the laminar flow assumption. On the other hand, the computed flow with the SST k-ω model, the RNG k-ε model, and the SA model reveals a remarkable under-prediction which appears clearly in the size and number of secondary vortices in the near-wall regions. Various benchmarking results are presented in this study.

scholarly journals Simulation of Lid-Driven Cavity Flow with Internal Circular Obstacles

2020 ◽  
Vol 10 (13) ◽  
pp. 4583 ◽  
Author(s):  
Tingting Huang ◽  
Hee-Chang Lim
Keyword(s):  
Reynolds Number ◽  
Solid Wall ◽  
Vortex Formation ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Time Model ◽  
Cross Sectional ◽  
Driven Cavity ◽  
Secondary Vortices ◽  
Boltzmann Method

The Lattice Boltzmann method (LBM) has been applied for the simulation of lid-driven flows inside cavities with internal two-dimensional circular obstacles of various diameters under Reynolds numbers ranging from 100 to 5000. With the LBM, a simplified square cross-sectional cavity was used and a single relaxation time model was employed to simulate complex fluid flow around the obstacles inside the cavity. In order to made better convergence, well-posed boundary conditions should be defined in the domain, such as no-slip conditions on the side and bottom solid-wall surfaces as well as the surface of obstacles and uniform horizontal velocity at the top of the cavity. This study focused on the flow inside a square cavity with internal obstacles with the objective of observing the effect of the Reynolds number and size of the internal obstacles on the flow characteristics and primary/secondary vortex formation. The current LBM has been successfully used to precisely simulate and visualize the primary and secondary vortices inside the cavity. In order to validate the results of this study, the results were compared with existing data. In the case of a cavity without any obstacles, as the Reynolds number increases, the primary vortices move toward the center of the cavity, and the secondary vortices at the bottom corners increase in size. In the case of the cavity with internal obstacles, as the Reynolds number increases, the secondary vortices close to the internal obstacle become smaller owing to the strong primary vortices. In contrast, depending on the sizes of the obstacles ( R / L = 1/16, 1/6, 1/4, and 2/5), secondary vortices are induced at each corner of the cavity and remain stationary, but the secondary vortices close to the top of the obstacle become larger as the size of the obstacle increases.

Numerical analysis and explore of asymmetrical fluid flow in a two-sided lid-driven cavity

2020 ◽  
Vol 14 (3) ◽  
pp. 7269-7281
Author(s):  
El Amin Azzouz ◽  
Samir Houat
Keyword(s):  
Velocity Ratio ◽  
Two Dimensional ◽  
Lower Side ◽  
Square Cavity ◽  
Driven Cavity ◽  
Parallel Motion ◽  
Bottom Cavity ◽  
Secondary Vortices ◽  
Volume Method ◽  
Fluid Characteristics

The two-dimensional asymmetrical flow in a two-sided lid-driven square cavity is numerically analyzed by the finite volume method (FVM). The top and bottom walls slide in parallel and antiparallel motions with various velocity ratio (UT/Ub=λ) where |λ|=2, 4, 8, and 10. In this study, the Reynolds number Re1 = 200, 400, 800 and 1000 is applied for the upper side and Re2 = 100 constant on the lower side. The numerical results are presented in terms of streamlines, vorticity contours and velocity profiles. These results reveal the effect of varying the velocity ratio and consequently the Reynolds ratio on the flow behaviour and fluid characteristics inside the cavity. Unlike conventional symmetrical driven flows, asymmetrical flow patterns and velocity distributions distinct the bulk of the cavity with the rising Reynolds ratio. For λ>2, in addition to the main vortex, the parallel motion of the walls induces two secondary vortices near the bottom cavity corners. however, the antiparallel motion generates two secondary vortices on the bottom right corner. The parallel flow proves affected considerably compared to the antiparallel flow.

The two-sided lid-driven cavity: experiments on stationary and time-dependent flows

2002 ◽  
Vol 450 ◽  
pp. 67-95 ◽  
Author(s):  
CH. BLOHM ◽  
H. C. KUHLMANN
Keyword(s):  
Three Dimensional ◽  
Standing Waves ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Flow State ◽  
Incompressible Fluid Flow ◽  
Velocity Measurements ◽  
Driven Cavity ◽  
Rectangular Container ◽  
Hot Film

The incompressible fluid flow in a rectangular container driven by two facing sidewalls which move steadily in anti-parallel directions is investigated experimentally for Reynolds numbers up to 1200. The moving sidewalls are realized by two rotating cylinders of large radii tightly closing the cavity. The distance between the moving walls relative to the height of the cavity (aspect ratio) is Γ = 1.96. Laser-Doppler and hot-film techniques are employed to measure steady and time-dependent vortex flows. Beyond a first threshold robust, steady, three-dimensional cells bifurcate supercritically out of the basic flow state. Through a further instability the cellular flow becomes unstable to oscillations in the form of standing waves with the same wavelength as the underlying cellular flow. If both sidewalls move with the same velocity (symmetrical driving), the oscillatory instability is found to be tricritical. The dependence on two sidewall Reynolds numbers of the ranges of existence of steady and oscillatory cellular flows is explored. Flow symmetries and quantitative velocity measurements are presented for representative cases.

scholarly journals Entropy generation of a hybrid nanofluid on MHD mixed convection is a lid-driven cavity with partial heating having two rounded corners

2021 ◽  
Vol 321 ◽  
pp. 02004
Author(s):  
Zakaria Korei ◽  
Smail Benissaad
Keyword(s):  
Thermal Conductivity ◽  
Reynolds Number ◽  
Mixed Convection ◽  
Entropy Generation ◽  
Volume Fraction ◽  
Object Oriented ◽  
Reynolds Numbers ◽  
Hybrid Nanofluid ◽  
Driven Cavity ◽  
Partial Heating

This research aims to investigate thermal and flow behaviors and entropy generation of magnetohydrodynamic Al2O3-Cu/water hybrid nanofluid in a lid-driven cavity having two rounded corners. A solver based on C ++ object-oriented language was developed where the finite volume was used. Parameter’s analysis is provided by varying Reynolds numbers (Re), Hartmann numbers (Ha), the volume fraction of hybrid nanofluid (ϕ), radii of the rounded corners. The findings show that reducing the radii of the rounded corners minimizes the irreversibility. Furthermore, the thermal conductivity and dynamic viscosity of hybrid nanofluid contribute to increasing the irreversibility. Finally, the entropy generation is decreased by increasing the Hartman number and increases by rising the Reynolds number.

scholarly journals Modeling the Multicommodity Multimodal Routing Problem with Schedule-Based Services and Carbon Dioxide Emission Costs

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Yan Sun ◽  
Maoxiang Lang
Keyword(s):  
Carbon Dioxide ◽  
Carbon Dioxide Emissions ◽  
Transportation Network ◽  
Linearization Method ◽  
Mixed Integer ◽  
Multicommodity Flow ◽  
Routing Problem ◽  
Multimodal Transportation ◽  
Proposed Model ◽  
Freight Routing

We explore a freight routing problem wherein the aim is to assign optimal routes to move commodities through a multimodal transportation network. This problem belongs to the operational level of service network planning. The following formulation characteristics will be comprehensively considered: (1) multicommodity flow routing; (2) a capacitated multimodal transportation network with schedule-based rail services and time-flexible road services; (3) carbon dioxide emissions consideration; and (4) a generalized costs optimum oriented to customer demands. The specific planning of freight routing is thus defined as a capacitated time-sensitive multicommodity multimodal generalized shortest path problem. To solve this problem systematically, we first establish a node-arc-based mixed integer nonlinear programming model that combines the above formulation characteristics in a comprehensive manner. Then, we develop a linearization method to transform the proposed model into a linear one. Finally, a computational experiment from the Chinese inland container export business is presented to demonstrate the feasibility of the model and linearization method. The computational results indicate that implementing the proposed model and linearization method in the mathematical programming software Lingo can effectively solve the large-scale practical multicommodity multimodal transportation routing problem.

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