DEKAF: spectral multi-regime basic-state solver for boundary layer stability

Abstract

As the community investigates more complex flows with stronger streamwise variations and uses more physically inclusive stability techniques, such as BiGlobal theory, there is a perceived need for more accuracy in the base flows. To this end, the implication is that using these more advanced techniques, we are now including previously neglected terms of Op1{Re 2 q. Two corresponding questions follow: (1) how much accuracy can one reasonably achieve from a given set of basic-state equations and (2) how much accuracy does one need to converge more advanced stability techniques? The purpose of this paper is to generate base flow solutions to successively higher levels of accuracy and assess how inaccuracies ultimately affect the stability results. Basic states are obtained from solving the self-similar boundary-layer equations, and stability analyses with LST, which both share Op1{Req accuracy. This is the first step toward tackling the same problem for more complex basic states and more advanced stability theories. Detailed convergence analyses are performed, allowing to conclude on how numerical inaccuracies from the basic state ultimately propagate into the stability results for different numerical schemes and instability mechanisms at different Mach numbers.

Ionization and dissociation effects on boundary-layer stability

“…Equation (3.3) is obviously not necessary for the flow assumptions (CPG, TPG or LTE) where the species mass fractions are not system state variables. The resolution of the base-flow problem is carried out with the DEKAF flow solver (see Groot et al (2018), Miró Miró et al (2018a) or § 7 of Miró Miró (2020)). It employs a pseudo-spectral collocation method in the wall-normal direction and a second-order finite-difference method in the marching direction.…”

“…The laminar base-flow field is obtained using the DEKAF solver (see Groot et al (2018), Miró Miró et al (2018a) or § 7 of Miró Miró (2020)). As laid out in § 3.1, the inviscid flow region is characterized by solving the corresponding shock-jump relation for each flow assumption, and then employing a one-dimensional Euler solver for the CNE cases.…”

Decoupling ablation effects on boundary-layer stability and transition

“…(2018) or Groot et al (2018). The value of y i in (5.1) corresponds to approximately 2.5 times the BL height, which was heuristically seen to provide a good resolution both in the BL and out of it.…”

“…The resolution of the base-flow problem is carried out with the DEKAF flow solver (see Groot et al 2018 or § 7 of Miró Miró 2020). It employs a pseudo-spectral collocation method in the wall-normal direction, and a second-order finite-difference method in the marching direction.…”

“…where q e are the BL edge quantities, q w are the wall quantities and ξ is the marching variable (see Groot et al 2018or White 1991, dξ = ρ e u e μ e dx. (4.…”