Prediction of bypass transition in hypersonic blunt-plate boundary layers subject to noisy conditions

TL;DR

This work addresses bypass transition in hypersonic boundary layers over blunt bodies by introducing a hybrid framework that couples shock-driven receptivity (SF-HLNS), nonlinear streak evolution (NPSE), and secondary-instability growth (BSA) to predict transition onset via an amplification factor $N$ and threshold $N_{tr}$. The method captures the transition-reversal phenomenon observed experimentally for large nose radii and demonstrates quantitative agreement with transition locations across multiple cases, while accounting for realistic wind-tunnel noise levels $Q$ and their impact on receptivity. The key contributions are a principled, three-stage model linking freestream disturbances to nonlinear streaks and their instabilities, a practical transition predictor, and validation against experimental data, highlighting robustness to noise and parameter variations. The approach offers a computationally efficient pathway to design hypersonic blunt bodies with controlled transition behavior and emphasizes the need for facility-noise characterization in interpreting transition experiments.

Abstract

In hypersonic boundary-layer flows over blunt bodies, laminar-turbulent transition exhibits two distinct regimes: for small nose radii, increased bluntness delays transition; beyond a critical radius, further increasing bluntness reverses this trend. The latter regime corresponds to a bypass transition route, whose onset remains challenging to predict. The primary difficulty lies in capturing the excitation of non-modal streaks in the nose region, which is strongly affected by the bow shock and entropy layer effects. Recently, Zhao & Dong (J. Fluid Mech., 2025, 1013: A44) develops a high-efficient, high-accuracy shock-fitting harmonic linearised Navier-Stokes (SF-HLNS) approach to quantify the excitation of linear non-modal perturbations. In this paper, we present a predictive framework for bypass transition by integrating the SF-HLNS approach with the nonlinear parabolised stability equations (NPSE) and the bi-global stability analysis (BSA). The NPSE is employed to track the nonlinear evolution of the streaky perturbations up to nonlinear saturation, while the BSA approach is used to capture the high-growth secondary instabilities. By integrating the growth rates of these secondary instability from their neutral positions, an amplitude amplification factor is obtained, enabling the prediction of transition onset. Under slow-acoustic forcing conditions drawn from wind-tunnel experiments, the present hybrid framework successfully reproduces the transition-reversal phenomenon at large nose radii, and yields quantitative agreement with measured transition locations, thereby validating its predictive capability.

Figures (20)

• Figure 1: $(a)$ Sketch of the physical model. $(b)$ Side view of computational domains for (I) SF-HLNS, (II) NPSE and (III) BSA.
• Figure 2: ($a$) Contours of the local Mach number $\bar{M}$ and the entropy increment $\Delta s$ in the $x-y$ plane for case A (not to scale). ($b$) and ($c$) Wall-normal profiles of $u_B$ and $T_B$ in regular and logarithmic scales, respectively. $\delta_{EL}$ and $\delta_{BL}$ mark the edges of the entropy and boundary layers, respectively.
• Figure 3: Properties of entropy-layer modes. $(a,b)$ Contours of $-\alpha_i$ in the $\beta$-$\omega$ plane at ${x}=25$; $(c,d)$ contours of $N$-factor of the 2-D entropy-layer modes in the ${x}$-$\omega$ plane. Left column: case A; right column: case E.
• Figure 4: Validation of (\ref{['eq:PSD']}) by the wind-tunnel-noise measurements of PSD duan2019characterization, where two levels of $Q$ are selected.
• Figure 5: Dependence of $\chi$ defined in Eq.(\ref{['eq:sf-hlns_relation']}) on ($a$) $\omega$ (for $k_3=4$) and ($b$) $k_3$ (for $\omega=0$).