  Due to the thick boundary layers in hypersonic flows, the state of the
boundary layer significantly influences the whole flow field as well as surface
heat loads. Hence, for engineering applications the efficient numerical
prediction of laminar-to-turbulent transition is a challenging and important
task. Within the framework of the Reynolds averaged Navier-Stokes equations,
Langtry/Menter [1] proposed the $\gamma$-$Re_{\theta_t}$ transition model using
two transport equations for the intermittency and $\gamma$-$Re_{\theta_t}$
combined with the Shear Stress Transport turbulence model (SST) [2]. The
transition model contains two empirical correlations for onset and length of
transition. Langtry/Menter [1] designed and validated the correlations for the
subsonic and transonic flow regime. For our applications in the hypersonic flow
regime, the development of a new set of correlations proved necessary, even
when using the same SST turbulence model [3]. Within this paper, we propose a
next step and couple the transition model with the SSG/LRR-$\omega$ Reynolds
stress turbulence model [4] which we found to be well suited for scramjet
intake simulations. First, we illustrate the necessary modifications of the
Reynolds stress model and the hypersonic in-house correlations using a
hypersonic flat plate test case. Next, the transition model is successfully
validated for its use coupled to both turbulence models using a hypersonic
double ramp test case. Regardless of the turbulence model, the transition model
is able to correctly predict the transition process compared to experimental
data. In addition, we apply the transition model combined with both turbulence
models to three different fully 3D scramjet intake configurations which are
experimentally investigated in wind tunnel facilities. The agreement with the
available experimental data is also shown.
