Automatic derivation of stability equations in arbitrary coordinates and for different flow regimes

Pinna, Fabio; Groot, Koen J.

doi:10.2514/6.2014-2634

Cited by 23 publications

(13 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Introducing (2.4) and the quantities' decomposition into the flow equations, one obtains the stability equations, which reduce to a generalized eigenvalue problem once completed with the appropriate set of boundary conditions. Stability equations are derived within the Automatic Derivation and Implementation module (ADIT) of the VESTA toolkit (Pinna & Groot 2014) from the compressible Navier-Stokes equations in cylindrical coordinates. The influence of the magnetic field is ignored as it is mainly confined to the torch section of Plasmatron.…”

Section: Stability Modelmentioning

confidence: 99%

Local analysis of absolute instability in plasma jets

2020

View full text Add to dashboard Cite

show abstract

Section: Stability Modelmentioning

confidence: 99%

Local analysis of absolute instability in plasma jets

2020

View full text Add to dashboard Cite

show abstract

“…If the pseudo-basic-state quantities satisfy system (5), R evaluates to zero and the invertibility of A then implies thatF " 0. If R ‰ 0, a Newton-Raphson iteration yields the fluctuation vectorF " A´1R, which represents the required distortion of the pseudo-basic-state variables to bring R closer to zero.…”

Section: Iiid Equation Set-up and Solution Methodsmentioning

confidence: 99%

“…The ξ-derivatives, forming the right hand side terms of system (5), encode the solutions' streamwise history. Self-similar solutions are sought in this study, which requires dropping these terms.…”

Section: Iia Self-similar Boundary-layer Equationsmentioning

confidence: 99%

“…If θ " 0, this behavior is nullified. g Note that this variable does not appear in system (5), but it does in the stability problem.…”

Section: Iib Stability Problemmentioning

confidence: 99%

“…The BiGlobal approach accounts for all effects due to higher order streamwise derivatives of the flow and hence does not introduce a model error. In fact, the term with the smallest order of magnitude in the BiGlobal system of equations for compressible flow is: 5…”

mentioning

confidence: 99%

See 2 more Smart Citations

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

Groot

Miró

Beyak

et al. 2018

2018 Fluid Dynamics Conference

Self Cite

View full text Add to dashboard Cite

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.

show abstract