Laminar-turbulent transition prediction for hypersonic vehicle with RANS-based models.

Laurent MUSCAT¹, Marina OLAZABAL¹

¹CEA CESTA, 15 Avenue des Sablières CS60001, 33116 Le Barp CEDEX, France.

E-mail: laurent.muscat@cea.fr

Keywords: RANS-based transition method, crossflow, hypersonic experimental vehicle.

Abstract

The prediction of the boundary layer transition has a significant impact on the design of hypersonic aircraft. Indeed, the transition to turbulence increases the skin friction and the heat transfer, which involves the necessity to use thermal protection materials in order to ensure structural safety of the vehicle. Nevertheless, these systems cannot cover the entirety of the vehicle because of their prejudicial influence on the drag resistance.

To understand the fundamental problems in hypersonic laminar-turbulent boundary layer transition for three-dimensional complex vehicles, several research programs and flight tests have been pursued, such as HiFiRE (US-Australia cooperated), HyBoLt (US) and BOLT (US) [1-4].

As the viscous and acoustics instabilities mainly identified (named as 1^st and 2^nd Mack mode), are preponderant in 2D hypersonic configurations, for 3D configurations, the presence of an inflection point in the spanwize velocity profile can trigger crossflow instabilities that also disturb the boundary layer. Moreover, through the panels of research programs, it appears that these crossflow instabilities may involve transition onset earlier than the streamwize instabilities due to favorable pressure gradients.

Many prediction methods based on correlation have been widely used in an engineering framework but their validity domains are generally restrained to 2D configurations.

The stability analysis methods as linear stability theory (LST), parabolic stability equation (PSE) and global stability analysis (BiGlobal/TriGlobal) represent the highest fidelity analysis tools to predict transition but for a too large amount of computation cost regarding industrials constraints.

Several Reynolds Averaged Navier-Stokes (RANS) framework models based on experiment, DNS results and stability analysis have emerged as the Fu-Wang Model [5], γ-Re_θ [6] or Qiao et al. one [7]. This last one is formulated in the ν_L-γ framework where ν_L corresponds to eddy-viscosity coefficient of laminar fluctuation and γ to the intermittency factor. The equation on laminar fluctuation depends on the characteristic timescales of the different instabilities previously introduced.

In this study, the Qiao et al. [7] transition model is modified thanks to Wang et al. [8] approach to tackle effects of nose bluntness. Indeed, a correlation based on the ratio between local unit Reynold number and freestream Reynolds number is introduced in the time scale of the 2^nd mode and crossflow one, in order to implicitly introduce the local effect of nose bluntness. Moreover, this transition model is validated on 2D/3D hypersonic test cases, including an investigation of transition prediction with this RANS-based transition model on the HyTRV research vehicle [9].

Fig. 1: Skin friction obtained with transition model on the windward side of HyTRV at 2° attack angle.

Fig. 2: Skin friction obtained with transition model on the leeward side of HyTRV at 2° attack angle

References

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[8] Wang, G., Yang, M. and Xiao, Z., “Improved k-ω-γ transition model by introducing the local effects of nose bluntness for hypersonic heat transfer”, IJHMT, 2018, Vol. 119, 185-198, https://doi.org/10.1016/j.ijheatmasstransfer.2017.11.103.

[9] Liu, S., Yuan, X., Liu, Z., Yang, Q., Tu, G., Chen, X., Gui, Y., “Design and transition characteristics of a standard model for hypersonic boundary layer transition research”, AMS, 2021, Vol. 37, 1637-1647, https://doi.org/10.1007/s109409-021-01136-5.