Linear stability of WENO schemes coupled with explicit Runge–Kutta schemes

Hermes, Viktor; Klioutchnikov, Igor; Olivier, H.

doi:10.1002/fld.2626

Cited by 8 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A sixth-order central-difference scheme is used to approximate the viscous fluxes. Details about the numerical schemes may be found in Hermes, Klioutchnikov & Olivier (2012), Gageik, Klioutchnikov & Olivier (2015) and Cao (2021). The DNS solver has been validated and successfully applied to study hypersonic compression-ramp flows (Cao, Klioutchnikov & Olivier 2019;Cao 2021;Cao et al 2021a,b).…”

Section: Dns Of the Compression-ramp Flowmentioning

confidence: 99%

Transition to turbulence in hypersonic flow over a compression ramp due to intrinsic instability

et al. 2022

View full text Add to dashboard Cite

In this work, a transition process in a hypersonic flow over a cold-wall compression ramp is studied using direct numerical simulation (DNS) and global stability analysis (GSA). The free-stream Mach number and the Reynolds number based on the flat-plate length are 7.7 and $8.6 \times 10^5$ , respectively. The shock-induced pressure rise causes the boundary layer to separate on the flat plate, forming a separation bubble around the corner. Without introducing any external disturbances, the DNS captures the transition to turbulence downstream of flow reattachment. The DNS results agree well with the experimental data as well as theoretical predictions. To uncover the intrinsic instability in the flow system, GSA is employed to investigate the three-dimensionality of the two-dimensional base flow. Several stationary and oscillatory unstable modes are revealed, which result in spanwise periodicity inside and downstream of the separation bubble. The GSA and DNS results indicate that the intrinsic instability of the flow system triggers the formation of streamwise counter-rotating vortices and boundary-layer streaks near reattachment. The downstream transition to turbulence starts from the breakdown of the streamwise vortices and streaks. Moreover, the second harmonic of the most unstable global mode and a broadband low-frequency unsteadiness occur in the saturated flow, which has a significant influence on the transition process. In summary, the present study demonstrates a transition process in a hypersonic compression-ramp flow as a result of the intrinsic instability of the flow system.

show abstract

Section: Dns Of the Compression-ramp Flowmentioning

confidence: 99%

Transition to turbulence in hypersonic flow over a compression ramp due to intrinsic instability

et al. 2022

View full text Add to dashboard Cite

show abstract

Section: Hypersonic Flow Over a Curved Compression Rampmentioning

confidence: 99%

Stability of hypersonic flow over a curved compression ramp

Hao¹,

Guo²,

Wen³

et al. 2023

J. Fluid Mech.

View full text Add to dashboard Cite

In this work, the stability of hypersonic flow over a curved compression ramp is studied using several stability analysis tools and direct numerical simulations (DNS). The free-stream Mach number and the unit Reynolds number are 7.7 and $4.2 \times 10^6$ m $^{-1}$ , respectively. Corner rounding is considered to alter the separation bubble flow so as to suppress the intrinsic instability of the compression-ramp flow. The variation of intrinsic instability is confirmed by global stability analysis. Subsequently, resolvent analysis is employed to examine the response of intrinsically stable flows to external disturbances. It is shown that the considered flows strongly amplify low-frequency streamwise streaks with a preferential spanwise wavelength. This result is verified using DNS by introducing a random forcing upstream of the separation point. Furthermore, both resolvent analysis and DNS demonstrate that the separation bubble contributes little to the selection of the spanwise wavelength of streamwise streaks. The combined effects of convective and intrinsic instabilities are also explored using DNS. A better agreement with experimental data is achieved after introducing upstream disturbances in an inherently unstable flow.

show abstract