Significant Supersonic Modes and the Wall Temperature Effect in Hypersonic Boundary Layers

Abstract

Note the importance of the relative sonic line y s , indicated by My s −1, where My uy − c ay where uy is the local mean flow velocity tangential to the wall, c ω∕ β 2 α 2 p is the disturbance propagation speed (with ω the circular frequency, β the spanwise wave number, and α the streamwise wave number), and ay is the local mean flow speed of sound. The disturbance propagation speed c is constant in the wall-normal direction for the entire disturbance structure at a fixed frequency and location. Between the sonic line and the wall, the disturbance is propagating downstream supersonically with respect to the mean flow velocity, resulting in the acousticlike behavior. Again, the acoustic description of the flow is only exact in very particular circumstances [6-8] but provides a qualitatively similar description of the flow in reality. Outside of the sonic line, the disturbance propagates subsonically. At the critical layer [ My c 0], ropelike structures are observed both numerically [9-11] and experimentally [12,13]. Because the disturbance travels subsonically in the freestream [ My < 1], the traditional second mode is referred to as a subsonic mode. When the phase speed of the disturbance is supersonic with respect to the mean flow in the freestream [ My > 1], the mode is known as a supersonic mode, and additional physical phenomena are encountered. A schematic similar to Fig. 1 is presented in Fig. 2 for the supersonic mode, which shows the same structures near the wall as the subsonic mode. Below the first sonic line [ My s1 −1], the disturbance propagates downstream supersonically with respect to the mean flow, and the critical layer [ My c 0] is outside of this first sonic line. However, with the supersonic mode, a second relative sonic line is included [ My s2 1], outside of which the disturbance travels upstream supersonically with respect to the mean flow. The three distinct regions (two supersonic, one subsonic) have also been described by Mack [6]. In the outer supersonic region, because there

Ionization and dissociation effects on boundary-layer stability

“…Also, as seen in § 4.2.4, the most unstable perturbation is a supersonic mode over a large fraction of the streamwise range. Supersonic modes are known to have a non-exponential decay in the free-stream region (see Knisely & Zhong 2019 a , b , c ), further increasing the amplitude with which they reach the shock.…”

“…They also concluded that the second mode's characteristic time scale is much shorter than the dissociation/recombination time. Bitter & Shepherd (2015) performed an extensive parametric study on supersonic modes in TNE conditions (yet with frozen chemistry), being later extended to TCNE conditions by Knisely & Zhong (2019 a , b , c ). Their main finding was that unstable supersonic modes generally appeared as a consequence of highly cooled walls.…”

Dense-gas effects on compressible boundary-layer stability

“…At M ∞ = 4.5 and 6, the amplification curves exhibit a kink (indicated by a + symbol in figure 7), at which the decreasing phase speed reaches the value c r = 1 − 1/M ∞ , meaning that the wave travels supersonically relative to the free stream. These features are typical of the so-called supersonic mode (Bitter & Shepherd 2015;Mortensen 2018;Knisely & Zhong 2019a). It is worth pointing out that this mode emerges in a frequency range well above the slow-mode one (which is not the case for the first and second perfect-gas modes).…”

Numerical Study of Hypersonic Boundary-Layer Transition Delay through Second-Mode Absorption

“…Figure 11 presents snapshots of static pressure perturbations p illustrating the strong growth of waves by many orders of magnitudes over a few tens of centimeters only. Pressure oscillations also appear around the sonic line which is often observed and indicative of secondmode transition 27,46 Finally, Fig. 12 quantifies the growth of wall pressure perturbations and provides a comparison with the previously discussed LST results.…”