Laminar–turbulent transition induced by a discrete roughness element in a supersonic boundary layer

Abstract

The linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach 2.5, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most unstable wake mode is of the varicose type and grows on average ∼17 % faster than the most unstable sinuous mode and ∼30 times faster than the most unstable boundary layer mode occurring in the absence of a roughness element. Due to the high growthrates registered in the presence of the roughness element, an amplification factor of N = 9 is reached within ∼50 roughness heights from the roughness trailing edge. The independently performed Navier-Stokes, spatial BiGlobal and PSE-3D stability results are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages of the laminar-turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate similar to that observed in the case of compressible turbulent spots for the same Mach number.

Investigation on the wake flow instability behind isolated roughness elements on the forebody of a blunt generic reentry capsule

“…The N -factor increases with roughness height for both dominant modes leading to a maximum N -factor for the S1 and A1 modes of N max ≈ 7.8 and ≈ 3.6 for k = 150 µm, respectively. Within this work, the symmetric mode always leads to the highest integrated ampli¦cation rate, which is in close agreement to the ¦ndings of [12,24,25,28] for the near ¦eld around the roughness element in a zero pressure gradient §ow. The authors of [12,24,25,28] report that depending on the aspect ratio [25], the symmetric mode is the leading mode at ¦rst and leads to transition in supercritical cases, where the amplitude of the disturbance caused by the roughness element is su©cient to promote turbulence [29].…”

“…The spectrum is obtained for the conditions given in [24] for F = 0.08 at x = 93.66: 1 ¡ present results; and 2 ¡ De Tullio et al [24] results from a di¨erent solver, which has been extensively validated [22,23]. Details on the base §ow computations, as well as on the instability characteristics of the wake modes, studied by DNS and an instability solver, are given in [24]. Figure 6 depicts the spatial eigenspectrum obtained for F = 0.08 at x = 93.66.…”

“…For the spectrum shown in Fig. 6, De Tullio and coauthors [24] discretized the whole spanwise extend of the computational domain with standard ¦nite di¨erence schemes and imposed periodic boundary conditions. The wall-normal direction was discretized using the FD-q method.…”

Acoustic Leading-Edge Receptivity for Supersonic/Hypersonic Flows over a Blunt Wedge

“…A validation of the code can be found in the work of De Tullio et al [21]. A grid study relevant for the current problem is presented in Section IV.A of this paper.…”

A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue

“…Asai, Minagawa & Nishioka 2002, Wu & Luo 2003, but there also exists experimental evidence suggesting that streaks generated by roughnesses of suitable form and height may stabilize planar and oblique T-S waves (Fransson et al 2005;Shahinfar, Sattarzadeh & Fransson 2014). The evolution and instability of roughness-induced streaks in supersonic boundary layers have been studied recently; see Kegerise, Owens & Rudolf (2010), Wheaton & Schneider (2012, Choudhari et al (2010Choudhari et al ( , 2013, Iyer et al (2011) andDe Tullio et al (2013). Klebanoff & Tidstrom (1972) carried out the first experimental investigation of physical mechanism causing earlier transition in a boundary layer perturbed by an isolated twodimensional roughness with h * /δ * = 0.7 − 0.8, where δ * is the displacement thickness of the smooth boundary layer.…”