Turbulent spots in hypersonic transitional planar and axisymmetric boundary layers

TL;DR

The study addresses turbulent spot dynamics in hypersonic transitional boundary layers over planar and axisymmetric surfaces at $M=5.85$, using heat-transfer intermittency measured by platinum sensors to quantify transition and spot properties. It introduces a modified detector framework and analyzes leading/trailing edge speeds, streamwise length scales, and spot generation rates, finding $U_{le}\approx0.9\,U_e$ for both geometries while $U_{te}$ is lower on the planar surface, leading to faster planar spot growth. Planar boundary layers generate more spots than axisymmetric ones at matched edge Reynolds numbers, though the two geometries converge in spot generation rates at sufficiently high $Re_e$. The results explain the shorter transition length observed on flat plates and provide a validated, heat-transfer–based intermittency methodology applicable to hypersonic boundary-layer design and analysis.

Abstract

Experiments were conducted to investigate characteristics of turbulent spots formed in transitional boundary layers developed over a flat plate and an axisymmetric cone placed in similar hypersonic freestream environment of Mach number 5.85. The freestream Reynolds number in the present work varied between $3.0-6.0\times10^6$/m. Heat transfer measurement along the surface of both the test models was used to ascertain the state of boundary layer and to calculate the intermittency associated with transitional boundary layer. Turbulent spots generated in the transitional boundary layer were characterized in terms of their leading-trailing edge velocities, their streamwise length scales and their generation rates on both the test models. Leading edge of the turbulent spots developed over both the test models were found to be convecting at a speed equivalent to 90\% of the boundary layer edge speed. The trailing edge of the spots developed on a planar boundary layer traversed at a lower speed than its axisymmetric counterpart. Streamwise length scales of a turbulent spot developed in a planar boundary layer grew at a higher rate when compared with axisymmetric boundary layer. Turbulent spot generation rates for both planar and axisymmetric boundary layers was found to be in the range of $1000000-3000000$ spots/m/s.

Figures (9)

• Figure 1: Figure depicting schematic of HST4
• Figure 2: Figure depicting schematics of flat plate and cone used in present work.
• Figure 3: (a) Typical raw signal and post-processed heat transfer time history obtained through a thin film sensor. (b) Zoomed in view of a turbulent spot identified from heat transfer time history and its association with various features of a typical turbulent spot. $U_{le}$ and $U_{te}$ are speeds assciated with the leading and trailing edge of the turbulent spots respectively.
• Figure 4: (a) Work flow involved in Intermittency calculation from heat transfer time history. $D_{i}$ and $C_{i}$ are detector function and criterion function for $i^{th}$ data point respectively. $\gamma_{e}$ is intermittency calculated from experimental measurement of surface heat transfer. (b,c,d,e) Typical heat transfer time histories along with criterion function (${\mathinner{\cdotp\cdotp\cdotp\cdotp\cdotp\cdotp}}$) and intermittency (- - - -) time histories from sensors placed in transitional boundary layers developed over flat plate (d,e) and cone (b,c).
• Figure 5: Spatial distribution of intermittency along the length of (a) flat plate (b) cone for all the experimental runs. (--- $\cdot$$\cdot$ ---) line represents universal intermittency for one of the shots for every experimental condition.