Freestream Mach Number Research Articles

Impact of Installation on the Performance of an Aero-Engine Exhaust at Wind-Milling Flow Conditions

Abstract This paper presents a numerical investigation of the effect of wing integration on the aerodynamic behavior of a typical large civil aero-engine exhaust system at wind-milling flow conditions. The work is based on the dual stream jet propulsion (DSJP) test rig, as will be tested within the transonic wind tunnel (TWT) located at the aircraft research association (ARA) in the UK. The DSJP rig was designed to measure the impact of the installed pressure field due to the effect of the wing on the aerodynamic performance of separate-jet exhausts. The rig is equipped with the dual separate flow reference nozzle (DSFRN), installed under a swept wing. Computational fluid dynamic simulations were carried out for representative ranges of fan and core nozzle pressure ratios (CNPR) for “engine-out” wind-milling scenarios at end of runway (EOR) takeoff, diversion, and cruise conditions. Analyses were done for both isolated and installed configurations to quantify the impact of the installed pressure field on the fan and core nozzle discharge coefficients. The impact of fan and core nozzle pressure ratios, as well as freestream Mach number and high-lift surfaces on the installed suppression effect, was also evaluated. It is shown that the installed pressure field can reduce the fan nozzle discharge coefficient by up to 16%, relative to the isolated configuration for EOR wind-milling conditions. The results were used to inform the design and setup of the experimental activity which is planned for 2023.

Shock-Induced Separation and Control in a 4.32-Aspect-Ratio Test Section

Experimental test sections studying shock-wave–boundary-layer interactions are usually right-angled by design to replicate the supersonic engine inlets where these interactions are observed. To avoid flow separation and shock effects on the side walls, investigations are typically performed on the centerline of the test section. However, the centerlines of small-aspect-ratio test sections can be significantly affected by the flow structures generated in the corners. Results using a large-aspect-ratio test section at a freestream Mach number of 1.6 include centerline and corner flow separation topologies, schlieren images of shock structures, total pressure profiles, and surface static pressures throughout the interaction region. These results provide evidence that the large-aspect-ratio test section can produce a large area of centerline flow that is unaffected by the separation and shock structures generated in the corners, which is a significant improvement over most of the smaller-aspect-ratio test sections employed for these types of studies. Microvortex generators are also employed upstream of the interaction, and measurements indicate a five-vortex system that energizes the near-wall boundary layer enough to overcome the shock’s adverse pressure gradient while remaining attached.

Effects of herringbone riblets on shock-wave/turbulent boundary-layer interactions

In the experiment reported in this paper, a spanwise array of herringbone riblets strips is applied upstream of the interaction region between an impinging shockwave and a turbulent boundary layer developing along a flat plate boundary layer at a freestream Mach number of 1.85. High-speed schlieren photography, surface oil flow visualization and PSP are used to examine the effect of herringbone riblets on the characteristics of the shockwave-boundary layer interactions. It shows that despite that the height of the riblets is less than 2 % of the local thickness of the undisturbed boundary layer, a profound modification to the shockwave-boundary layer interaction zone is observed, and the overall size of the separation bubble is decreased. The observed control effects are attributed to the large-scale secondary flow structures produced by the directional riblets. To the best knowledge of the author, this is the first study evaluating the control effect of herringbone riblets on shock wave and turbulent boundary layer interactions in supersonic flow using the experimental method.

Asymptotic boundary condition for numerical modeling of wave packets in a supersonic boundary layer

Within the framework of linear stability theory, a simple non-stationary boundary condition is developed to simulate the far-field asymptotic behavior of linear wave packets propagating in a compressible boundary layer. This condition allows us to skip the linear stage of instability evolution in direct numerical simulations (DNS) of laminar-turbulent transition. It is also suggested to perform numerical simulations of the linear stage without recalculating the Jacobi matrix in the Newton iteration procedure. Robustness and efficiency of the both approaches are evaluated by computations of the first-mode wave packet propagating in the boundary layer on a flat plate at freestream Mach number 2. DNS of the nonlinear stage show that the wave packet quickly breaks down into a turbulent spot, if its hump amplitude is umax′≥0.1U∞. This confirms an amplitude nature of the transition onset criterion. The spectral analysis indicates that the breakdown mechanism differs from the oblique, fundamental or subharmonic resonance and requires additional studies.

Turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers with wall disturbances

Hypersonic turbulence over disturbed walls can be encountered when the fuselage of the vehicles is ablated or installed with transpiration-cooling porous media, resulting in the variation of the wall heat transfer that complicates its accurate predictions. In this paper, we study the turbulent heat flux and wall heat transfer in hypersonic turbulent boundary layers at the free-stream Mach number of 6.0 subject to wall disturbances with different wall temperatures, with our focus on the compressibility effects. We found that the temperature fluctuation intensity and the turbulent heat flux are enhanced in the outer region, which is attributed to the higher mean temperature gradient induced by the wall disturbances. The solenoidal and dilatational components of the turbulent heat flux, obtained by the Helmholtz decomposition that splits the velocity fluctuations into the solenoidal and dilatational components, are of opposite signs, with the latter smaller in magnitude but showing the tendency of mitigating the former. The integration formula that decomposes the wall heat transfer into various physical processes reveals that the viscous dissipation generates the wall heat transfer, while the turbulent heat flux, work of pressure on dilatation and the mean flow convection transport it towards the free stream. The contribution of the dilatational motions to the viscous dissipation and turbulent heat flux is negligible compared with that of the solenoidal components.

Robust Design Optimization of Supersonic Biplane Airfoil Using Efficient Uncertainty Analysis Method for Discontinuous Problem

Busemann’s supersonic biplane airfoil can reduce wave drag through shock interactions at its designed freestream Mach number. However, a choking phenomenon occurs with a decrease in the freestream Mach number, and the drag coefficient increases significantly, resulting in an aerodynamic problem with a discontinuous change in the performance function. In this study, an uncertainty analysis method, the divided inexpensive Monte Carlo simulation (IMCS), is proposed to solve discontinuous problems efficiently and is applied to Busemann’s biplane airfoil. In the divided IMCS, the discontinuity point is determined using a simple sampling method. The uncertainty input space is divided at the detected discontinuity point, and a surrogate model is constructed for each space. Uncertainty analysis was performed using the constructed surrogate models, and the results of the divided IMCS showed qualitative agreement with those of the conventional Monte Carlo simulation, which is the most straightforward uncertainty analysis method. Moreover, the divided IMCS significantly reduced the computational cost of the uncertainty analysis. A robust design optimization of the supersonic biplane airfoil was performed using the divided IMCS, yielding more robust designs than Busemann’s biplane airfoil. The usefulness of the divided IMCS for uncertainty analysis of discontinuous problems was confirmed.

Evaluation of Various Flow Control Methods in Reducing Drag and Aerodynamic Heating on the Nose of Hypersonic Flying Objects

Effective deduction of air heating load and drag is a critical issue in hypersonic vehicle engineering applications. In this research, seven various geometrical models have been proposed to study and compare the effect of each configuration on the flow field, drag, and aerodynamic heating deduction under the same flow conditions. The presented configurations in this study: (a) blunt-body geometry as a reference of comparison, (b) blunt-body geometry with a spike, (c) blunt-body geometry with an counter flow jet, (d) blunt-body geometry with a spike and counter flow jet, (e) blunt-body geometry with a spike and aerodisk, (f) blunt-body geometry with a spike, aerodisk, and root counter flow jet, (g) blunt-body geometry with a spike, four aerodisks and root counter flow jet. The Reynolds-Averaged equations have been solved using the Finite Volume Method (FVM) along with the shear stress turbulence model (k-ω SST). The flow is assumed compressible, steady-state, and axisymmetric with a free stream Mach number of 6. According to the study of each configuration’s performance related to the parameters of drag, maximum pressure, and maximum heat flux factors on the blunt-body walls, (g) configuration with a drag factor of 0.2699, maximum pressure factor of 209.8, and maximum heat flux factor of 25.1, has the most deduction on the blunt-body walls among the seven configurations. The deduction percentage of drag, maximum pressure, and maximum heat flux factors of (g) configuration to (a) configuration are %72.1, %94.5, and %79.9, respectively, which significantly diminished drag and heat flux. Also, the best configuration scenarios for drag and aerodynamic heating deduction are geometrical models of g, f, d, e, c, b, and a, respectively.

Coexistence of different mechanisms underlying the dynamics of supersonic turbulent flow over a compression ramp

Supersonic turbulent flow over a compression ramp is studied using wall-resolved large eddy simulation with a freestream Mach number of 2.95 and a Reynolds number [based on δ0: the thickness of incoming turbulent boundary layer (TBL)] of 63 560. The unsteady dynamics of the present shock wave/turbulent boundary layer interaction (STBLI) flow are investigated by using dynamic mode decomposition techniques, linear and nonlinear disambiguation optimization, local stability analysis (LSA), and global stability analysis (GSA). By analyzing the dynamic system for the STBLI flow, three dynamically important modes with characteristic spanwise wavelengths of 2δ0, 3δ0, and 6δ0 are captured. The 2δ0 mode approximates the spanwise scale of the Görtler-like vortices and Görtler mode of LSA, suggesting the presence of Görtler instability, which is believed to be related to the unsteady motion of streaks downstream of reattachment in the flow. The features of the 3δ0 mode are also observed in large-scale motions of the incoming TBL, implying the existence of a convective mechanism that is excited and maintained by such motions. Additionally, the GSA results show the most unstable mode features a spanwise wavelength of around 6δ0, indicating the existence of global instability that is believed to be related to the oscillating motion of separation shock. The coexistence of these three mechanisms is confirmed. Discussions on the above findings provide an interpretation for low-frequency unsteadiness that the unsteadiness of surface streaks results from the combined effects of the Görtler instability near flow reattachment and the convection of large-scale motions in the incoming boundary layer, while the low-frequency shock motion may be related to a global mode driven by upstream disturbances.

Nonlinear axial-lateral coupled vibration of functionally graded-fiber reinforced composite laminated (FG-FRCL) beams subjected to aero-thermal loads

This paper studies the nonlinear axial-lateral coupled vibration of functionally graded-fiber reinforced composite laminated (FG-FRCL) cantilever beams subjected to aero-thermal loads. The nonlinear partial differential equations governing the problem are determined based on the Euler-Bernoulli beam theory using the von Kármán-type geometrical nonlinearities. The Galerkin method is then applied to discretize the differential equations and to transform them into a nonlinear ordinary differential equation. The coupled ordinary differential equations are solved analytically using the method of multiple time scales (MTS) to study the nonlinear forced vibration time response of the selected FG-FRCL structures, where a large parametric study checks for the effect of power-index, uniform temperature rise, velocity of the free stream air and Mach number on their axial and lateral response, with interesting insights from a scientific and design purposes.

Shock interactions and heating predictions on a V-shaped blunt leading edge at Mach 6–12

V-shaped blunt leading edges (VSBLEs) are usually found at the inlet lips of air-breathing hypersonic vehicles and irregular shape flows. In this work, the VSBLE flows are investigated using numerical simulations and theoretical analysis from Mach 6 to Mach 12. The simulation results show that complex shock–shock interactions around the VSBLE cause extremely high heat flux peaks, which nonlinearly increase with the freestream Mach numbers. To theoretically study the flow mechanism, the shock interactions are divided into large-scale primary shock interactions (PSIs) and micro-scale secondary shock interactions (SSIs). The PSIs are constant, but the SSIs experience a transition from Mach reflection to regular reflection with the Mach number increasing. A transition criterion for the SSIs is established by the shock interaction theory. Furthermore, the increase in the heat flux peaks is proved to be caused by the SSI transition. A semi-empirical heat flux prediction method that relates the shock intensity and heat flux amplification is established. Finally, the transition criterion and the heat flux prediction method are verified by simulations at higher Mach numbers and experiments of VSBLEs with different geometric parameters. This paper develops a theoretical analysis approach for quickly predicting the shock interaction types and heat flux peaks of the VSBLEs under a wide range of Mach numbers.

Dynamic stall characteristics of unswept pitching wing

An experimental investigation of dynamic stall on upswept pitching wing was conducted using Particle Image Velocimetry (PIV) and Pressure Sensitive Paint (PSP) techniques. The wing had an aspect ratio AR = 4 and a NACA 0012 airfoil section profile assembled with a round-tip. The wing motion of interest in this study is pitching at a certain angle of attack range and the wing was robustly designed and machined out of Aluminum to minimize elasticity and tip flapping motions. The freestream Mach number, M∞ = 0.1, and the Reynolds number based on chord length, Rec = 2 × 105, were considered as flow parameters for observing dynamic stall phenomena and for comparison with available numerical simulations from literature. The pitching motion of the wing is sinusoidal with a reduced frequency k = πfc/U∞ = 0.1, and the minimum and maximum angle of attack of the pitching motion were 4° and 22°, respectively. Details of flow structures during pitching at various phase angles were captured using planar two-dimensional (2D) PIV at three spans, x/c = 0.5, 0.75, and 1.0 and the pressure imprint on the surface of the wing was captured by a single shot lifetime method using fast porous pressure-sensitive paint. The initial results show the formation of a separation bubble at a small incident angle and the emergence of a dynamic stall vortex (DSV) after the bursting of the separation bubble. The DSV propagates towards the trailing edge of the wing with its integral scale varying across the three spans of the wing revealing three-dimensionality. The PSP results show a uniform build of suction pressure at low angle of attack which later intensifies in a non-uniform manner due to a circulatory motion of the flow during pitching. After the end of the upstroke phase, the flow starts to reattach to the surface of the wing while the DSV grows and moves away from the surface as it travels downstream along the chord until sheds beyond the trailing edge. The PSP results also capture the tip unloading period during the pitching motion.

Comparison of shock-buffet dynamics on a supercritical airfoil with and without a pitching degree of freedom

With the goal of understanding the dynamics of the transonic flow around an OAT15A airfoil model, velocity field measurements were performed by means of high repetition rate particle image velocimetry. The experiments were performed at free-stream Mach numbers from 0.70 to 0.77 and at a Reynolds number of Rec≈3×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_\ extrm{c}\\approx 3\ imes 10^6$$\\end{document}. The variation of the Mach number allowed for an investigation in the pre-buffet, buffet and close to buffet-offset regime. A fixed version and a spring mounted version of the model were used to investigate the effect of the pitching degree of freedom on the shock buffet. The dominant structural frequency of the airfoil’s pitch motion was adjusted to be in the range of the natural buffet frequency of the flow with inhibited pitching motion of the model. Flow field measurements with an acquisition rate of 4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\\,$$\\end{document} kHz allowed for the detection and analysis of the shape and the motion of the compression shock. With released pitching degree of freedom, shock buffet started at a lower Mach number and showed a larger amplitude for the shock oscillation. Furthermore, the shock motion appeared more harmonic compared to the model without pitching degree of freedom. For a Mach number of M∞=0.72\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M_\\infty =0.72$$\\end{document} and 0.74, the change of the angle of attack and the shock location correlated strongly with each other. From the measurements, the phase lag between both quantities during the coupled motion could be determined. From the correlation of the shock position at different heights, it can be concluded that the shock motion is controlled by events at the shock foot. The movement of the upper shock part is only a reaction to the movement of the lower part.

Numerical investigation on flow and aerothermal characteristics of rarefied hypersonic flows over slender cavities

Flow and aerothermal characteristics of rarefied hypersonic flows passing through slender cavities are investigated comprehensively using the direct simulation Monte Carlo (DSMC) method by various cases, such as the cavity with different depth-to-width ratios and different inclination angles, and the freestream at different altitudes and Mach numbers. The cavity depth-to-width ratio has a great influence on flow structures and gas density inside the cavity, but a slight effect on gas temperature inside the cavity and on heat flux over cavity surfaces. In comparison to the vertical cavity, the upstream-inclined cavity reduces the gas density and the high-temperature area inside the cavity, showing a decrease rate of gas density of about 53 % for φ = -45°, while the downstream-inclined cavity greatly raises the gas density and slightly expands the high-temperature area, reaching a growth rate of gas density of about 114 % for φ = 45°. As the freestream altitude increases from 50 to 80 km, the main vortex expands remarkably while the heat flux near the top of the aft wall decreases sharply, and a noteworthy finding is that the dimensionless temperature contours inside the cavity for the cases of H = 50, 60, and even 70 km seem to be unchanged. Compared with the case of Ma = 6, the maximum density inside the cavity is increased by about 5.5 times for the case of Ma = 30, and it is about 7.3 times for the maximum temperature inside the cavity. However, raising the freestream Mach number seems to not alter the streamline patterns inside the cavity. The three-dimensional effect reduces the maximum density inside the cavity by about 14.5 % to 17.4 % and results in a smaller main vortex compared with the two-dimensional (2D) cavity, and moreover, the slender cavity can weaken the three-dimensional effect due to its larger depth-to-width ratio and the relatively short cavity width. Besides, the vortex-transport theory is proposed, which can well explain the change of gas density inside the cavity for all cases considered in this work.

Kinetic modeling of fluid-induced interactions in compressible, rarefied gas flows for aerodynamically interacting particles

In the study of gas-particulate multiphase systems, the flow of high-speed gas through a distribution of solid particulates is of utmost importance. While these aerodynamically interacting systems have been extensively studied for low-speed gas flows in the gas continuum regime, less attention has been given to high-speed systems where non-continuum effects are significant due to the high flow gradients. To address this, the flow of rarefied gas through an aerodynamically interacting monodisperse spherical particle system is studied using the Direct Simulation Monte Carlo (DSMC) gas-kinetic approach. Since the method provides the best resolution of shocks at supersonic Mach numbers it is used to classify the weak separated shocks and strong collective shocks in these systems based on particle spacing in a two-particulate system at different orientation angles. The study used the two-particle system to help analyze more complex particle distributions of volume fractions, 1%, 5%, and 15%, exposed to gas flows in the slip and transitional gas regime for a free-stream Mach number range of 0.2<Ma∞<2.0. We observe that the weak separated shocks in the 1% distribution allow a higher degree of gas penetration and shock-particle interactions or “hypersonic-surfing”, exposing a major fraction of the particulates to higher force magnitudes. In contrast, the strong collective shock in the 5% and 15% distributions only generates high particulate forces on the flow-facing particles. Finally, a simple stochastic model is proposed for use in large-scale Eulerian–Lagrangian simulations that captures the non-monotonic behavior of average drag and force variability generated by the complicated gas particulate interactions in the compressible gas regime.

Mach reflection of three-dimensional curved shock waves on V-shaped blunt leading edges

Theoretical investigation of the primary Mach reflection (MR) configuration on V-shaped blunt leading edges (VBLEs) forms the focus of this study. By ignoring the secondary interactions, a theoretical method based on a simplified form of the continuity relation is developed to predict the shock configurations, including the detached shock, the Mach stem, the transmitted shock and the triple point. The comparison of the theoretical results with both numerical and previous experimental results shows the reliability of the theoretical approach in predicting shock structures across a wide range of free stream and geometric parameters. The theoretical model provides a detailed comprehension of the occurrence mechanism of inverse MRs on VBLEs and the influence of the free stream and geometric parameters on primary MR configurations. Along with the primary MR configuration, the curved shock or compression waves generated by the crotch are solved and offer insight into the transition from the MR to the regular reflection from the same family (sRR). The increase of the ratio $R/r$ and the free stream Mach number $M_0$ appears to facilitate the transition, while the effect of the half-span angle $\beta$ is non-monotonic. The predicted shock positions allow for the identification of the transition boundary between the primary MR and sRR. It is found that $R/r$ below a threshold (for a set $M_0$ value) produces MR, irrespective of $\beta$ . If this threshold is exceeded, the configuration can transition from the primary MR to sRR and then back to the primary MR as $\beta$ increases.

Global stability of supersonic flow over a hollow cylinder/flare

Supersonic flow over a hollow cylinder/flare with a free-stream Mach number of 2.25 is numerically investigated in this study. Axisymmetric computational fluid dynamics simulations and global stability analysis (GSA) are performed for a wide range of cylinder radii and flare deflection angles. The onset of incipient and secondary separation is delayed as the cylinder radius is decreased due to the axisymmetric effects. The GSA reveals that a decrease in cylinder radius also postpones the emergence of global instability. The GSA results agree well with the results of direct numerical simulations for a supercritical case in the linear stage. The saturated flow exhibits pairs of unsteady streamwise streaks downstream of reattachment. The criterion of the global stability boundary established for supersonic flow over a compression corner (Hao et al., J. Fluid Mech, vol. 919, 2021, A4) is extended to its axisymmetric counterpart.

Numerical simulation of laminar-turbulent transition in a supersonic boundary layer under the action of acoustic disturbances

In low disturbance environment, laminar-turbulent transition (LTT) is associated with excitation of unstable normal modes of small initial amplitudes (receptivity problem). These modes grow exponentially to a critical amplitude in accord with the linear stability theory (LST) and trigger the nonlinear breakdown. In the current study numerical simulation of laminar-turbulent transition (LTT) in the boundary layer on the upper surface of a flat plate in a supersonic free stream of Mach number M∞=3 and Reynolds number Re∞=2 × 107 is carried out. The flow is perturbed by fast or slow acoustic waves of low intensity, which excite unstable waves of the first mode. The latter have frequencies corresponding to the integral amplification N ≈ 9.16 typical for flight conditions. Two cases are considered: the angle of attack AoA=0° at which acoustic waves pass through a weak shock induced by viscous-inviscid interaction; AoA=5° at which acoustic waves pass through the expansion fan emanating from the plate leading edge. A holistic modeling of all stages of the transition from receptivity to the birth of turbulent spots is performed using direct numerical simulations. Linear stability theory is used to interpret the results. Feasibility of practical implementation of the amplitude method for predictions of the LTT onset in the considered and similar cases is discussed. It has been shown that to realize the amplitude method in the considered and similar cases, it is sufficient: to calculate the initial amplitudes of instability in a small vicinity of the leading edge and the propagation of instability from the leading edge to the station where the instability reaches the critical amplitude u′max≈4%. Analysis of known numerical and experimental data showed that this criterion weakly depends on the local Mach number in the range 0<Me<7, and it is acceptable for practical predictions of the transition onset points.

Direct numerical simulation of supersonic boundary layers over a microramp: effect of the Reynolds number

Microvortex generators are passive control devices smaller than the boundary layer thickness that energise the boundary layer to prevent flow separation with limited induced drag. In this work, we use direct numerical simulations (DNS) to investigate the effect of the Reynolds number in a supersonic turbulent boundary layer over a microramp vortex generator. Three friction Reynolds numbers are considered, up to $Re_\tau = 2000$ , for fixed free stream Mach number $M_\infty =2$ and fixed relative height of the ramp with respect to the boundary layer thickness. The high-fidelity data set sheds light on the instantaneous and highly three-dimensional organisation of both the wake and the shock waves induced by the microramp. The full access to the flow field provided by DNS allows us to develop a qualitative model of the near wake, explaining the internal convolution of the Kelvin–Helmholtz vortices around the low-momentum region behind the ramp. The overall analysis shows that numerical results agree excellently with recent experimental measurements in similar operating conditions and confirms that microramps effectively induce a significantly fuller boundary layer even far downstream of the ramp. Moreover, results highlight significant Reynolds number effects, which in general do not scale with the ramp height. Increasing Reynolds number leads to enhanced coherence of the typical vortical structures in the field, faster and stronger development of the momentum deficit region, increased upwash between the primary vortices from the sides of the ramp – and thus increased lift-up of the wake – and faster transfer of momentum towards the wall.

Assessment of heat transfer and Mach number effects on high-speed turbulent boundary layers

High-speed vehicles experience a highly challenging environment in which the freestream Mach number and surface temperature greatly influence aerodynamic drag and heat transfer. The interplay of these two parameters strongly affects the near-wall dynamics of high-speed turbulent boundary layers (TBLs) in a non-trivial way, breaking similarity arguments on velocity and temperature fields, typically derived for adiabatic cases. We present direct numerical simulations of flat-plate zero-pressure-gradient TBLs spanning three freestream Mach numbers $[2,4,6]$ and four wall temperature conditions (from adiabatic to very cold walls), emphasising the choice of the wall-cooling parameter to recover a similar flow organisation at different Mach numbers. We link qualitative observations on flow patterns to first- and second-order statistics to explain the decoupling of temperature–velocity fluctuations that occurs at reduced wall temperatures and high Mach numbers. For these cases, we discuss the formation of a secondary peak of thermal production in the viscous sublayer, which is in contrast with the monotonic behaviour of adiabatic profiles. We propose different physical mechanisms induced by wall-cooling and compressibility that result in apparently similar flow features, such as a higher peak in the streamwise velocity turbulence intensity, and distinct features, such as the separation of turbulent scales.

Propulsion Aerodynamics for a Novel High-Speed Exhaust System

Abstract A key requirement to achieve sustainable high-speed flight and efficiency improvements in space access lies in the advanced performance of future propulsive architectures. Such concepts often feature high-speed nozzles, similar to rocket engines, but employ different configurations tailored to their mission. Additionally, they exhibit complex interaction phenomena between high-speed and separated flow regions at the base, which are not yet well understood. This paper presents a numerical investigation on the aerodynamic performance of a representative, novel exhaust system, which employs a high-speed nozzle and a complex-shaped cavity region at the base. Reynolds-Averaged Navier–Stokes computations are performed for a number of nozzle pressure ratios (NPRs) and freestream Mach numbers in the range of 2.7 &amp;lt; NPR &amp;lt; 24 and 0.7 &amp;lt; M∞ &amp;lt; 1.2, respectively. The corresponding Reynolds number lies within the range of 1.06 × 106 &amp;lt; Red &amp;lt; 1.28 × 106 based on the maximum diameter of the configuration. The impact of the cavity is revealed by direct comparison to an identical noncavity configuration. Results show a consistent trend of increasing base drag with increasing NPR for both configurations, owing to the jet entrainment effect. Cavity is found to have no impact on the incipient separation location of the nozzle flow. At conditions of M∞ = 1.2 and high NPRs, the cavity has a significant effect on the aerodynamic performance, transitioning nozzle operation to underexpanded conditions. This results in approximately 12% higher drag coefficient compared to the noncavity case and shifts the minimum NPR required for positive gross propulsive force to higher values.