[Paper Review] Numerical simulations of fluid flow and heat transfer in a four-sided, lid-driven rectangular domain

V. Ambethkar, Durgesh Kushawaha|arXiv (Cornell University)|Apr 26, 2017

Heat Transfer and Optimization15 citations

TL;DR

This study presents a numerical investigation of unsteady, incompressible fluid flow and heat transfer in a four-sided lid-driven rectangular cavity using the SIMPLE algorithm and QUICK finite volume scheme. Results show that increasing Reynolds number enhances both local and average Nusselt numbers, indicating improved overall heat transfer, despite a decreasing horizontal temperature gradient near vertical walls.

ABSTRACT

Numerical simulations for 2-D unsteady, incompressible flow with heat transfer in a four-sided lid-driven rectangular domain are reported in the present study. For the four-sided lid-driven rectangular domain, the lower wall is moved to the left, the upper wall is moved to the right, while the right wall is moved upwards and the left wall is moved downwards. All four walls move with equal speed. Different constant temperatures are applied to the left and right moving walls, and thermal insulation is applied to the upper and bottom moving walls. The governing equations are discretized using the QUICK scheme of finite volume methods. The SIMPLE algorithm is adopted to compute the numerical solutions of the flow variables, $u$-velocity, $v$-velocity, $P$, and $θ$ as well as local and average Nusselt numbers for $50 \le Re \le 1500$ and $Pr=6.63$. Due to the force generated by moving fluid, the direction of moving walls and the Reynolds number affect fluid flow in the rectangular domain in addition, at different Reynolds numbers along the cold wall of the domain, the variation in average and local Nusselt numbers reveals that overall heat transfer increases isotherms showed that as Reynolds numbers increase, the horizontal temperature gradient near the vertical walls decreases, because of which heat transfer decreases.decreases.

Motivation & Objective

• To investigate fluid flow and heat transfer characteristics in a four-sided lid-driven rectangular cavity with moving walls and asymmetric thermal boundary conditions.
• To analyze the influence of Reynolds number and wall motion direction on flow patterns and heat transfer mechanisms.
• To numerically solve the Navier-Stokes and energy equations for a wide range of Reynolds numbers (50 ≤ Re ≤ 1500) and Prandtl number Pr = 6.63.
• To quantify local and average Nusselt numbers to assess heat transfer performance under varying flow conditions.
• To validate the numerical model by comparing results with published data for special cases of lid-driven cavity flow.

Proposed method

• Governing equations—steady, incompressible Navier-Stokes and energy equations—are solved using the finite volume method with the QUICK scheme for spatial discretization.
• The SIMPLE algorithm is employed to couple pressure and velocity fields and ensure mass conservation in the pressure-velocity correction loop.
• Boundary conditions include: all four walls move with equal speed (lower wall left, upper wall right, right wall up, left wall down), with constant temperatures on left (hot) and right (cold) walls and thermal insulation on top and bottom walls.
• Simulations are performed at time t = 0.001 s for Reynolds numbers ranging from 50 to 1500 and Prandtl number Pr = 6.63.
• Flow variables (u-velocity, v-velocity, pressure, temperature) and heat transfer metrics (local and average Nusselt numbers) are computed and visualized.
• Streamlines and isotherms are used to analyze flow structures and thermal gradients, respectively.

Experimental results

Research questions

• RQ1 How does increasing Reynolds number affect the velocity profiles and flow structure in a four-sided lid-driven cavity?
• RQ2 What is the impact of wall motion direction and magnitude on the formation of primary and secondary vortices in the cavity?
• RQ3 How does the local Nusselt number vary along the cold wall, and what does this imply about heat transfer distribution?
• RQ4 How does the average Nusselt number change with Reynolds number, indicating overall heat transfer performance?
• RQ5 What is the relationship between the horizontal temperature gradient near vertical walls and the resulting heat transfer efficiency at different Reynolds numbers?

Key findings

• As Reynolds number increases from 50 to 1500, the average Nusselt number increases, indicating enhanced overall heat transfer in the cavity.
• The local Nusselt number along the cold wall decreases with increasing Reynolds number, suggesting a decay in heat transfer rate at the wall surface despite overall improvement.
• The horizontal temperature gradient near the vertical walls decreases with increasing Reynolds number, which correlates with reduced heat transfer efficiency near the walls.
• v-velocity profiles become more negative and exhibit oscillatory behavior with increasing Reynolds number, indicating complex unsteady flow dynamics.
• Streamline patterns show a primary central vortex and two weaker secondary vortices near the left and right moving walls at Re = 500, while at higher Re (1000, 1500), the flow structure stabilizes with denser streamlines near the moving walls.
• u-velocity increases with Reynolds number from bottom to top wall, reflecting stronger flow intensity due to enhanced wall-driven forces.