Large Eddy Simulation Modeling in 2D Lid-Driven Cavity
Primitive variable formulation of Navier–Stokes equation is solved in a lid-driven cavity using SIMPLE algorithm. The equations are discretized using finite volume method in a staggered grid mesh. The turbulence flow phenomena are observed in a 2D lid-dri
- PDF / 1,045,337 Bytes
- 10 Pages / 439.37 x 666.142 pts Page_size
- 18 Downloads / 264 Views
Abstract Primitive variable formulation of Navier–Stokes equation is solved in a lid-driven cavity using SIMPLE algorithm. The equations are discretized using finite volume method in a staggered grid mesh. The turbulence flow phenomena are observed in a 2D lid-driven cavity using large eddy simulation modeling of flow. Smagorinsky model is applied for the formulation of eddy viscosity. The solution is obtained upto maximum Reynolds number 4500 using grid sizes 66 × 66, 81 × 81, 101 × 101 and 121 × 121. A comparison has been drawn between turbulence model and without turbulence model. The study of comparison between two models consists of velocity profiles along the center of the cavity, location of primary and secondary eddies, velocity vector plot and pressure contours. Keywords SIMPLE · FVM · Staggered grid · LES · Smagorinsky model
1 Introduction Two-dimensional lid-driven cavity is a square cavity having all the walls except top wall which is rigidly fixed and stationary as shown in Fig. 1. The top wall is allowed to move toward right or left with non-dimensional speed unity. Non-dimensional length of each side of the wall is unity. Initially, the cavity is filled with fluid which is at rest. As the lid starts moving toward right with uniform velocity unity, the fluid flow in the cavity is set up. As the Reynolds number gradually increases, the number of primary and secondary eddies increases in the cavity. The large eddy which appears at Re = 0.00001 is called primary eddy. With increase of Reynolds number, levels of corner eddies gradually grow in the cavity [1, 2]. B. Dalai (B) Faculty, Mechanical Engineering, College of Engineering and Technology, Bhubaneswar, Biju Patnaik University of Technology, Rourkela, Odisha, India e-mail: [email protected] M. K. Laha Faculty, Aerospace Engineering, Indian Institute of Technology, Kharagpur, West Bengal, India e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2021 S. Revankar et al. (eds.), Proceedings of International Conference on Thermofluids, Lecture Notes in Mechanical Engineering, https://doi.org/10.1007/978-981-15-7831-1_1
3
4
B. Dalai and M. K. Laha
Fig. 1 Schematic diagram of a lid-driven cavity
According to the appearance of the eddies, these are named as secondary, tertiary and so on. The present work contains large eddy simulation modeling of Navier– Stokes equation in the lid-driven cavity to study the effect of chaos and turbulence at higher Reynolds number flow. Primitive variable form of Navier-Stokes equation is preferred than the stream function-vorticity form because of simplicity of incorporating the eddy viscosity term in the governing equation. Few literatures regarding the chaos effect in the cavity are discussed below. Ghia et al. studied the primitive variable formulation of Navier–Stokes equation using multigrid method in a lid-driven cavity [3]. They were successful to solve the N–S equation upto Re = 10,000 in the grid sizes 129 × 129 and 257 × 257. Chen solved the large eddy simulation modeling of stream fu
Data Loading...
