This paper presents a comprehensive evaluation of reduced-order models (ROMs) for the determination of pressure coefficient distributions on supersonic and hypersonic bodies. The study investigates the limitations, aerodynamic precision and computational performance associated with various methodologies, ranging from simplistic Newtonian theory-based approaches to more advanced first and second-order shock-expansion theories. Validation is performed by comparing computed results with experimental and computational data for pressure distributions, drag and lift coefficients and centres of pressure for fundamental geometries and authentic vehicle design over a wide range of freestream conditions. The study also includes a comprehensive computational complexity analysis, demonstrating the superiority of finite-element ROM approaches over traditional finite-volume computational fluid dynamics (CFD) simulations. The primary objective of this paper is to scrutinise the extension of these methodological classes to the low supersonic regime. Hence, thermo-chemical reactions within the flow are disregarded, and the ideal gas law is adopted. A value of $\gamma = 1.4$ is chosen for consistency and comparability across the analyses. The proposed ROMs show remarkable potential for reducing high-speed simulation execution times by four orders of magnitude, maintaining accuracy within 20 per cent and as low as 1 per cent. The study unveils three key findings: first, the accuracy degradation of Newtonian-based theories for inclined elements, particularly around 45 degrees, and their reduced dependency on Mach number at large inclination. Secondly, the study presents novel insights into the impact of shock-wave-Mach-wave interactions on pressure distribution calculations, emphasising the Mach number as a crucial metric governing recompression effects. Lastly, the study demonstrates the exceptional accuracy of DeJarnette’s method, providing ${C_P}$ results within 2 per cent for a wide range of conditions, offering an attractive alternative to the Taylor-Maccoll equation.

Reynolds-Averaged Navier–Stokes (RANS) simulations, both steady and unsteady, are used to investigate supersonic, chemically reacting, flow fields inside a strut-stabilised supersonic combustion ramjet (scramjet) engine operating under different fuel flow rates. Fully supersonic, fully subsonic and mixed modes of operations inside the combustor, obtained at different fuel flow rates, are studied numerically through shock wave visualisations and top-wall static-pressure probing. The effect of changing fuel flow rates, imposed both suddenly and gradually, on the behaviour of shock waves and wall pressure profiles are studied in detail. For certain modes of combustion characterised by the presence of oblique shocks at the strut, shockwaves in the combustor respond predictably to an increase or decrease in fuel flow rate attaining the steady state flow fields as predicted by RANS simulations for those fuel flow rates. For certain other modes of combustion, characterised by the presence of shockwaves in the isolator and the absence of oblique shocks at the leading edge of the strut, shockwaves in the flow field appear unstable to fuel flow rate modulations. For such cases, any change in fuel flow rates, sudden or gradual, increase or decrease, causes the isolator shocks to immediately move upstream and eventually out of the isolator. A plausible physics-based explanation of the observed phenomena is presented.

The gas temperature of the supersonic heat airflow simulated test system is mainly determined by the fuel and air flow rates which enter the system combustor. In order to realise a high-quality control of gas temperature, in addition to maintaining the optimum ratio of fuel and air flow rates, the dynamic characteristics of them in the combustion process are also required to be synchronised. Aiming at the coordinated control problem of fuel and air flow rates, the mathematical models of fuel and air supply subsystems are established, and the characteristics of the systems are analysed. According to the characteristics of the systems and the requirements of coordinated control, a fuzzy-PI cross-coupling coordinated control strategy based on neural sliding mode predictive control is proposed. On this basis, the proposed control algorithm is simulated and experimentally studied. The results show that the proposed control algorithm has good control performance. It cannot only realise the accurate control of fuel flow rate and air flow rate, but also realise the coordinated control of the two.

Mach 2 jet from a convergent-divergent elliptical nozzle, of aspect ratio 2, has been controlled with limiting flat and arc tabs. The mixing promoting capability of the flat and arc tabs were studied in the presence of different levels of pressure gradient, at the nozzle exit, corresponding to nozzle pressure ratios of 4 to 8, in steps of one. The geometrical blockage of both the tabs is 5% of nozzle exit area. For the flat tab along the minor axis, the waves in the core become weaker and the core length becomes shorter than the uncontrolled jet, at all the NPRs studied. But the flat tab along the major axis promotes mixing only for some NPRs and retards the mixing for the rest of the NPRs studied. At NPR 5, the flat tab along the minor axis causes the largest core length reduction of 86%. For circular arc tab, along the minor axis, the maximum core length reduction is 55% at NPR 6. Arc tab along the major axis protects the core length for the entire range of the nozzle pressure ratios tested and maximum extension in core length is found at NPR 4, which is 40%.

The gas dynamic laser is numerically studied using quasi-1D and 2D simulations to investigate the effect of diamond pattern of the supersonic flow field (inhomogeneities in density field) on the laser's performance. The system of governing equations is solved with a finite volume approach using a structured grid in which the AUSM+ scheme is used to calculate the convective fluxes. Vibrational temperature of different modes, population inversion and the small signal gain are studied, and the effect of the divergent nozzle's geometry at the maximum gain is analysed.

Direct numerical simulations have been performed by Mayer, Von Terzi & Fasel (J. Fluid Mech., this issue, vol. 674, 2011, pp. 5–42) to demonstrate that oblique-mode breakdown leads to fully turbulent flow for a Mach 3 flat-plate boundary layer. Since very low level of initial disturbances is required for this transition scenario, oblique-mode breakdown is the most potent mechanism for transition in two-dimensional supersonic boundary layers in low-disturbance environments relevant to flight.

The reverse flow pressure limiting aperture is a device that creates and sustains a substantial gas pressure difference between two chambers connected via an aperture. The aperture is surrounded by an annular orifice leading to a third chamber. The third chamber is maintained at a relatively high pressure that forces gas to flow through the annular aperture into the first of said two chambers. The ensuing gas flow develops into a supersonic annular gas jet, the core of which is coaxial with the central aperture. A pumping action is created at the core of the jet and any gas molecules leaking through the aperture from the second chamber are entrained and forced into the first chamber, thus creating a substantial pressure difference between the first and second chamber.