Have you ever wondered how fluids behave when they're dragged by a moving surface? Or how a thin layer of oil lubricates machinery? These phenomena, and many more, can be understood through a fundamental concept in fluid mechanics called Couette Flow.
Today, we're going to explore Couette flow, not just theoretically, but also through the lens of Computational Fluid Dynamics (CFD) using a simulation result visualized in ParaView.
What is Couette Flow?
Imagine two parallel plates. One plate is stationary, and the other is moving at a constant speed, dragging a viscous fluid between them. This is the essence of Couette flow. It's one of the simplest forms of fluid motion, driven purely by the shear stress exerted by the moving plate on the fluid.
Key Characteristics:
Steady-state: The flow doesn't change with time.
Laminar: The fluid moves in smooth, parallel layers, without turbulence.
Incompressible: The fluid density remains constant.
Constant Viscosity: The fluid's resistance to flow doesn't change.
No Pressure Gradient: The flow is solely driven by the moving plate, not by a pressure difference.
Under these conditions, the velocity of the fluid varies linearly from zero at the stationary plate to the speed of the moving plate at its surface. This linear velocity profile is the hallmark of Couette flow.
Bringing it to Life with CFD
While analytical solutions for Couette flow exist, using CFD allows us to simulate and visualize these principles, even for more complex scenarios. Our image showcases the results of a CFD simulation for a Couette flow case.
Let's break down what we see in the ParaView visualization:
The image shows a fluid between two plates, with the top plate moving and the bottom one stationary. This setup creates a shear flow, where the fluid velocity varies linearly between the plates.
The smaller plot on the right, labeled "LineChartView1," is the most telling part. It shows the velocity profile along the vertical axis (Y-axis). The X-axis of this plot represents the velocity component U_X, and the Y-axis represents the vertical position.
The plot starts at zero velocity at the bottom (Y = 0).
It increases linearly with height. It reaches a maximum velocity at the top of the domain. This straight, diagonal line is the signature linear velocity profile of a simple, incompressible Couette flow.
I am happy to analyse a completely new subject - the Fluid Mechanics...
Jai hind...
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