Flow-induced oscillation in rectangular cavities is a captivating phenomenon in fluid dynamics with implications for many engineering applications. The oscillations can cause increased drag, noise, and structural vibrations, making their study crucial for fields like aerospace engineering. Understanding and controlling these oscillations is essential for optimizing designs across different applications. Hopefully, a thorough study was conducted on the same topic in a paper entitled “ Numerical Identification of Flow-Induced Oscillation Modes in Rectangular Cavities using URANS”, which is our reference paper in this exploration.

• Reference [1]: Mesbah, M., and S. Majidi. “Numerical identification of flow-induced oscillation modes in rectangular cavities using urans.” Journal of Applied Fluid Mechanics2 (2020): 703-713.

Figure 1: Reference Paper`s designed computation domain

Simulation Process

The set of governing equations is numerically solved in the computational domain shown in Fig. 1. The cavity has a length to depth ratio (L/D) of 4, and simulations are performed. It is then converted into cells using ANSYS Meshing, regarding a denser grid near the walls. Overall, 290500 cells establish the structured grid. As mentioned above, the application in the aerospace industry leads to assuming high Mach number flow. Further, the Transition SST 4 equation turbulence model is utilized.

Figure 2: the produced Structured grid with denser cells near the critical regions

Post-processing

The velocity patterns in our rectangular cavity show something really amazing about how fluid flow creates spinning motions! When fast-moving air passes over the top of the open cavity, it creates a special zone where the air spins in circles inside. Our simulation captured extremely high speeds of 105.4 meters per second in the main flow region above the cavity. Also, we can see a clear spinning pattern (called a vortex) forming inside the cavity where the fast top flow drags the slower cavity air along. Furthermore, this spinning motion isn’t standing still – it moves and changes strength over time! This movement creates the oscillations that make noise and vibrations in real-world applications like car windows and airplane wheel wells. Most importantly, this perfect capture of the shear layer at the cavity opening shows exactly where flow instability begins and why it creates such strong self-sustained oscillations.

Figure 3: Velocity distribution in and around the rectangular cavity

The temperature patterns tell us even more about what happens in the rectangular cavity! The air moving past the top of the cavity creates a mixing zone that changes heat patterns in interesting ways. Our analysis shows temperature variations from 280K to 343K (that’s a difference of 63 degrees!) with the highest temperatures appearing at the leading edge of the cavity. Additionally, we can see how the spinning vortex inside the cavity pulls warmer air from the main flow down into the cavity along the back wall. Most importantly, this temperature pattern matches perfectly with the velocity field and confirms that our simulation correctly captures how heat transfer happens in these oscillating flows. The temperature gradient at the cavity opening creates density changes that affect pressure fluctuations and can trigger acoustic resonance – the main cause of unwanted noise in many engineering applications! This clear connection between flow patterns and temperature helps engineers design quieter and more efficient vehicles, buildings, and industrial equipment.

Figure 4: Temperature distribution