Background:
For hypersonic vehicles, the transition in external airflow from laminar to turbulent has significant impacts on drag, heating, velocity, and overall performance. Strategic vehicle surface heating may offer control over this process, but this requires simulation/experimental validation. For a given cylindrical vehicle model, the lab ran high-fidelity CFD simulations using a structured grid providing mean flow fields as functions of location along the vehicle. Using a given modified linear stability theory-based (LST) code, I processed the CFD output data for two thermal cases—one with the wall temperature at +50 K above adiabatic and one at –50 K below.
LST examines how small disturbances in the airflow around a vehicle grow or decay. Here, eigenvalues represent the growth rates (how quickly disturbances amplify) and phase speeds indicate how fast these disturbances travel. First-mode disturbances are lower-frequency, shear-driven instabilities with longer wavelengths, whereas second-mode (Mack mode) disturbances are high-frequency instabilities with shorter wavelengths that typically drive the transition to turbulence in hypersonic boundary layers (Fig. 1), thereby increasing drag and heating.
Objective:
Identify the dominant instability modes (first‐ and second‐mode waves) in the hypersonic flow around a cylindrical vehicle geometry and determine how surface heating or cooling influences their growth rates, informing strategies for improving hypersonic vehicle performance by delaying transition to turbulence.
Methodology:
I imported CFD data from a cylinder (with specified half-angle and nose radius) at 0° AoA in a hypersonic freestream with specified Mach and Reynolds numbers. I configured the LST code in MATLAB that analyzed the CFD data to quantify second-mode instabilities and disturbance growth rates, analyzing disturbances with frequencies ranging from 5 kHz to 200 kHz (in 20 kHz increments) at a fixed spanwise wavenumber (β = 0). I executed the LST code on mean flow profiles extracted at streamwise slices from 545 to 650 (in increments of 20), extracting eigenvalues and eigenfunctions. This was performed for the +50K and -50K vehicle surface temperature cases.
The eigenvalues provide information about the growth rates and phase speeds of the disturbances, while the eigenfunctions represent the mode shapes in the wall-normal direction. The unstable modes are identified based on the sign of the imaginary part of the eigenvalue, with positive values indicating growing disturbances. The mode shapes are used to classify the instabilities as first mode or second mode based on their wall-normal structure. I then analyzed growth rates and phase speeds of the unstable modes as a function of frequency and streamwise location in the two temperature cases.
Key Results:
The LST analysis showed that for the +50 K condition (Fig. 2), the dominant instability is the second mode (Mack mode), with peak growth rates of approximately 0.0008 s⁻¹ in the frequency range of 40–80 kHz. In contrast, the –50 K case (Fig. 3) exhibited significantly lower growth rates (around 0.0002 s⁻¹), indicating a stabilizing effect of wall cooling on the hypersonic boundary layer. This revealed a a fourfold reduction in turbulence-inducing disturbance growth via surface cooling.
Lower frequencies are more unstable compared to the higher frequencies. This suggests that the dominant instability modes in the boundary layer are associated with low-frequency disturbances. The boundary layer is more receptive to the growth of low-frequency perturbations, which is a characteristic of the first and second mode instabilities in hypersonic flows.
Analysis across multiple streamwise slices (Fig. 4, 5) revealed a downstream decay in disturbance growth rates, suggesting that as the boundary layer thickens, its stability improves. First-mode (shear-driven) disturbances were also observed but were less significant compared to the dominant second-mode instabilities.
Conclusion:
The stability analysis confirms that the second-mode instabilities—critical in triggering turbulence in hypersonic flows—are highly sensitive to surface temperature. The data clearly indicate that a cooler wall (–50 K) significantly suppresses the growth of these instabilities compared to a heated wall (+50 K). This result has practical implications for hypersonic vehicle design, as it supports the development of thermal management strategies to delay transition, reduce aerodynamic drag, and lower thermal loads. My role in processing and analyzing the CFD output with the provided LST code produced essential quantitative insights that can be directly applied to improve predictive transition models and inform the design of more efficient hypersonic vehicles.