Theoretical study on regular reflection of shock wave–boundary layer interactions

Abstract

Abstract

A study on the RR-to-MR transition of shock wave reflections near the leading edge in hypersonic flows

“…The three minimum values ofS MR which fulfil (2.14) for M ∞ = 2, 2.5 and 3 exist at α s = 14.4 • , 16.4 • and 17.1 • , respectively, corresponding to β s = 44.6 • , 38.5 • and 34.5 • . Comparing the three angles to the separation shock angles close to the interaction point of MR measured on the pictures in several recent studies: in the study of Tao et al (2014), the measured angle is β s ≈ 34 • for M ∞ = 3 and in the study of Matheis & Hickel (2015), the measured angles are β s ≈ 41 • for M ∞ = 2 and β s ≈ 34 • for M ∞ = 3; in the study of Grossman & Bruce (2018), the measured angle is β s ≈ 42 • for M ∞ = 2; and in the study of Xue et al (2020), the measured angles are β s ≈ 43 • for M ∞ = 2 and β s ≈ 37 • for M ∞ = 2.5. The comparisons are summarised in table 1.…”

“…Several recent studies (see Matheis & Hickel 2015;Giepman et al 2018;Xue et al 2020) found that the size of the separation bubble is strongly related to the incident shock strength. In the study of Xue et al (2020), it was observed that the separation shock strength close to the interaction point was positively correlated with incident shock, and the separation shock strength in MR was stronger than that in RR, causing difficulty in predicting the RR-to-MR transition. Even though the shock reflection region is so close to the plate leading edge that the boundary layer almost disappears, a separation bubble still exists (see Sriram et al 2016).…”

“…Notably, in both the works of Li & Ben-Dor (1996a,b) and Wang et al (2018), the influence of the boundary layer did not have to be taken into consideration. However, in the study of Xue et al (2020) on shock wave-boundary layer interactions, the boundary layer could not be neglected. Thus, both FIT and the MEP principle were employed, resulting in curved separation shocks owing to various combinations of FIT solutions and MEP solutions, while the RR-to-MR transition was not predicted well.…”

“…Because, in the MR configuration, the polar lines show that α r2 does not affect α r1 , the whole flow field can be treated as three flow fields: Flow I, which is an inviscid flow determined by the Mach number and incident shock; Flow II, which is a very strong curved shock; and Flow III, which is a separation flow determined by the Mach number and separation shock, as shown in figure 6(a). A non-dimensional factorS (see Wang et al 2018;Xue et al 2020) is employed to measure the total entropy production, as follows…”

“…2018; Xue et al. 2020) found that the size of the separation bubble is strongly related to the incident shock strength. In the study of Xue et al.…”