This paper presents progress towards a transition modelling capability for use in the numerical solution of the Reynolds-averaged Navier-Stokes equations that provides accurate predictions for transonic flows and is thus suitable for use in the design of wings for aircraft flying at transonic speeds. To this end, compressibility corrections are developed and investigated to extend commonly used empirical correlations to transonic flight conditions while retaining their accuracy at low speeds. A compressibility correction for Tollmien-Schlichting instabilities is developed and applied to a smooth local correlation-based transition model and a stationary crossflow instability compressibility correction is included by adding a new crossflow source term function. Two- and three-dimensional transonic transition test cases demonstrate that the Tollmien-Schlichting compressibility correction produces substantially improved agreement with the experimental transition locations, particularly for higher Reynolds number applications where the effects of flow compressibility are expected to be more significant, such as the NASA CRM-NLF wing-body configuration, while the crossflow compressibility correction prevents an inaccurate, upstream transition front. The compressibility corrections and modifications do not significantly affect the numerical behaviour of the model, which provides an efficient alternative to non-local and higher-fidelity approaches, and can be applied to other transport-equation-based transition models with low-speed empirical correlations without affecting their predictive capability in the incompressible regime.

This article focuses on the aerodynamic design of a morphing aerofoil at cruise conditions using computational fluid dynamics (CFD). The morphing aerofoil has been analysed at a Mach number of 0.8 and Reynolds number of $3 \times 10^{6}$ , which represents the transonic cruise speed of a commercial aircraft. In this research, the NACA0012 aerofoil has been identified as the baseline aerofoil where the analysis has been performed under steady conditions at a range of angles of attack between $0^{^{\kern1pt\circ}}$ and $3.86^{^{\kern1pt\circ}}$ . The performance of the baseline case has been compared to the morphing aerofoil for different morphing deflections ( $w_{te}/c = [0.005 - 0.1]$ ) and start of the morphing locations ( $x_{s}/c = [0.65 - 0.80]$ ). Further, the location of the shock wave on the upper surface has also been investigated due to concerns about the structural integrity of the morphing part of the aerofoil. Based upon this investigation, a most favourable morphed geometry has been presented that offers both, a significant increase in the lift-to-drag ratio against its un-morphed counterpart and has a shock location upstream of the start of the morphing part.

Experiments are performed to study the unsteadiness of rectangular cavity flows at Mach 0.325, 0.620 and 0.818. Typical characteristics of mean surface pressure distributions show a slight pressure variation near the front face, a local peak surface pressure ahead of the rear corner and a low pressure at immediate downstream of the cavity. Larger peak pressure and pressure variation near the cavity rear face are observed as the length-to-depth ratio increases. Surface pressure fluctuation distribution shows an increase toward the cavity rear face and reaches a peak value. At further downstream locations, the level of surface pressure fluctuation approaches the value of incoming flow. The amplitude of peak surface pressure fluctuation is associated with length-to-depth ratio and reaches the maximum at length-to-depth ratio of 8.60. This is considered due to intermittent switching between open- and closed-cavity flows. Higher moments of surface pressure signal at immediate downstream of the cavity show a similar trend. More negative skewness coefficient and larger deviation of flatness coefficient indicate the presence of more large negative events, which is mainly corresponding to mass removal process (breath-out phase). This unsteady mass flow is more pronounced at higher Mach number.