Transpiration cooling is an active methodology in reducing surface heat flux for hypersonic vehicles, which offers the possibility of reducing nose bluntness and, therefore, increasing aerodynamic performance. This paper presents a numerical analysis of transpiration-cooled sharp leading edges made from ultra-high-temperature ceramics. The structural integrity of a 10 mm radius wedge leading edge is investigated numerically with regard to different coolant plenum geometries and pressurization magnitudes. It is found that the close spacing of individual plenum chambers reduces the stress in the material significantly and provides the maximum possible coolant mass flux. An optimization procedure of plenum pressure distribution is carried out using an analytical description of the porous flow in the leading edge. It is found that there exists an optimum plenum pressure that minimizes the probability of failure of the leading-edge model. Nitrogen coolant requires less pressure than helium to reach this criterion and, furthermore, requires less pressure to displace the air freestream and thus protect the leading edge from oxidation.

Shock tube experiments are essential in understanding the environment encountered by hypersonic vehicles. Such experiments provide information used to determine rate constants of chemical, relaxation and radiative processes taking place in non-equilibrium plasmas. These constants are significant drivers of uncertainty in surface heat flux predictions. Recent work has shown that flow non-uniformities in real shock tube experiments can be misinterpreted as a need to alter these parameters; however, no comprehensive model exists to decouple the effects. We show that there is a rigorous method to achieve this by using experimental measurements as boundary conditions and including their effects via reverse time integration. This method improves over previous implementations by rigorously enforcing conservation laws, incorporating two-temperature, non-equilibrium thermochemistry and explicitly modelling both forward- and backward-running sound waves in the shock tube test slug through a method of characteristics formulation. This approach allowed the effect of shock speed variation in highly non-equilibrium tests, specifically those relevant to Titan entry, to be studied for the first time. A validation study showed that properties predicted by the method were found to agree with results from a viscous, two-dimensional axisymmetric Navier-Stokes solver within 1.5 %. When applied to shock tube test cases from the EAST and T6 facilities for simulation of lunar return and Titan entry representative conditions, the method offered improved agreement with experimentally measured oxygen 777 nm and 240-440 nm radiance, respectively, when compared with previous implementations, particularly towards the rear of the test slug where forward-running sound waves from the driver become influential.

Sharp leading edges offer aerodynamic and observability advantages in hypersonic flight. The reduction in standoff distance resulting from the adoption of sharp edges, however, results in increased convective heating that needs to be managed. Transpiration cooling is an attractive option in terms of aerothermal performance, reusability, and complexity. In this study, a method is presented for the numerical simulation of transpiration cooling at the stagnation point of sharp leading edges or tips. The method is suited to both equilibrium and nonequilibrium flow and is based on Cheng's stagnation line theory. The method explicitly models coolant flow through the porous medium. Detailed temperature profiles and mass fractions in the shock layer and within the porous medium are computed. The sensitivity of these profiles to coolant flow rate and nature, wall thermal boundary conditions, and catalytic activity is studied. The ability of different coolant mixtures to limit the transport of reactive species to the surface is assessed. It is found that low-molecular-weight injectants provide better shielding of the surface at moderate to high blowing. At low blowing, low-molecular-weight injectants are less effective because of the increased diffusivity of shock layer species through the injectant. The effect of wall catalycity is found to be localized to the wall and of secondary importance to thermal boundary condition and blowing rate.

Extreme heat loads during flight constrain the design of hypersonic vehicles. Further, certain missions necessitate the use of sharp leading edges, which enhance aerodynamic performance. Sharp leading edges decrease the shock standoff distance, which increases temperature gradient and thus surface heat flux. Additionally, reduced standoff distance introduces non-equilibrium phenomena into the near-surface gas mixture, which may result in high catalytic heating. Transpiration cooling is a method for reducing surface heat loads, preventing oxidative damage, and maintaining leading-edge geometry during flight, while also providing reusability. This paper investigates the application of transpiration cooling to stagnation points in hypersonic flight, across a wide parameter space. Results are generated from a stagnation line solver, applying Park two-temperature nonequilibrium thermochemistry and rigorous multicomponent evaluations for transport properties. This study explores a range of freestream altitudes and velocities, leading-edge radii, injectants, and surface properties. Correlations for both heat and mass Stanton numbers are presented and compared to existing correlations. Injectants similar to the shock-layer gas align with correlations established with equilibrium assumptions and mixture definitions for transport properties. However, wall catalycity, wall temperature, and dissimilar injectants modify the cooling behavior. These effects are due to alterations in near-wall mixing that can only be captured with nonequilibrium thermochemistry and multicomponent transport properties.

Shock tube experiments allow interrogation of nonequilibrium thermochemistry relevant to hypersonic flow conditions. Two-dimensional effects such as shock curvature and boundary-layer growth influence shock tube flows, yet their influence on measured data is unknown. Due to shot-to-shot variability and computational limitations, a priori numerical methods are unsuitable. Existing a posteriori methods are one-dimensional, requiring correlations for problem closure. This work develops a novel method for conducting a posteriori, two-dimensional, viscous, reacting gas analysis of shock tube flows, removing the requirement for self-similar boundary-layer correlations. This method is enabled by an additional equation fixing the shock to a desired location. Using the outflow pressure as a system variable, the problem is stabilized in the shock frame of reference. Comparisons to a reference case of argon and an experimental synthetic air condition in Oxford's T6 tunnel have excellent agreement in regions where shock trajectory effects are minimal. A 1.33 Pa 8.18 km/s synthetic air experiment in NASA EAST highlights the influence of two-dimensional effects. Peak integrated radiance is decreased by 10% due to shock curvature from the quasi-one-dimensional result, improving experimental agreement. Additionally, a 40% difference in centerline axial velocity and a 15% radiance increase are predicted when modeling two-dimensional effects.

The systems of non-linear ordinary differential equations governing reactive flows in thermochemical nonequilibrium are computationally demanding due to their high dimensionality and severe numerical stiffness, caused by the wide range of inherent kinetic spatio-temporal scales. Reduced-order models (ROMs) seek to reduce this computational cost whilst retaining sufficient accuracy. Projection-based ROMs such as Galerkin and Petrov-Galerkin (PG) have recently emerged as promising methods for compressible reactive flow simulations. However, being typically based on data-driven techniques such Proper Orthogonal Decomposition, such projection methods require offline training data, enforce a fixed reduction size and cannot guarantee a priori stability. Moreover, lacking any physical knowledge of the system dynamics, they cannot guarantee sitffness reduction. This work introduces a novel, physics-based Petrov-Galerkin ROM framework grounded in Computational Singular Perturbation (CSP) theory. The proposed CSP-PG method adaptively constructs trial and test bases online using the instantaneous eigen-decomposition of the system’s right-hand-side Jacobian. This enables dynamic tracking of the evolving time-scale structure, ensuring effective reduction in both dimensionality and stiffness through time-scale separation. Application of the CSP-PG method to a 1D two-temperature post-shock plasma flow demonstrates improved accuracy and numerical stability over standard PG projections. Although the eigen-decomposition increases the per-iteration cost, it enables adaptive time-stepping that yields an overall speedup exceeding 130%. The method demonstrates robust scalability to higher-dimensional systems, with reduction in dimensionality of up to 43%, leading to a reduction in numerical stiffness by up to two orders of magnitude.

This article presents the commissioning of two blowdown modes of operation in the Oxford High Density Tunnel (HDT) at Mach 7: Extended Ludwieg Mode (ELM) and Plenum Augmented Ludwieg Mode (PALM). ELM is a quasi-steady blowdown mode, producing a steady decrease in supply pressure to the facility nozzle, whilst PALM offers steady supply conditions at the expense of total pressure capability. Theory of operation of the modes, quasi-1D numerical simulations and experimental results are presented, as well as a PALM performance map for HDT. ELM has been commissioned across the full range of HDT's current operating pressures, whilst PALM has been demonstrated for 3 fill pressures: 14 bar, 30 bar and 55 bar. Test times in both modes were limited by facility unstart to at most 400 ms, greater than a factor of 10 improvement relative to Ludwieg Mode, though for the 14 and 30 bar PALM cases this came with a reduction of Unit Reynolds capability of 40% and 30%, respectively. The 55 bar PALM case demonstrated a test time of 160 ms for a 20% reduction in unit Reynolds number capability. Theoretical performance maps predict that operation in PALM can provide a factor of 10 improvement to the test time capability for HDT for all M7 unit Reynolds numbers run to date in the facility without any upgrades. Hence, this article presents a significant improvement of the capability of the HDT to investigate unsteady and long duration flow phenomena relative to standard Ludwieg Mode operation.

Polar species appear in several planetary entry problems in both the shock-heated gas and its interaction with the ablative heat shield or other active cooling systems. Typically, the contributions of polar species to plasma transport properties are evaluated using spherical phenomenological potential functions or, more recently, with ab initio computations. Limited consideration has been given to the use of nonspherical potential functions for polar species. The Stockmayer potential is a Lennard–Jones potential function modified to account for polar interactions. In this paper, the Stockmayer potential is used to compute collision integrals for NO, CN, CO, and CH. Additionally, a methodology applicable to potential functions similar in form to the Lennard–Jones potential is developed to determine scaling laws that describe the asymptotic behavior of the orbiting boundary at low energies. The use of the nonspherical Stockmayer potential function preserves agreement with the Lennard–Jones potential at moderate to high temperatures (above 5000 K) when potential parameters are selected consistently. This indicates that the polarity of species at these temperatures does not strongly impact transport properties.

High altitude ice crystals have led to instances of ice accretion on stationary compressor surfaces in aeroengines. Rollback, surge and stall events are known to have been instigated through such accretions due to aerodynamic losses related to ice growth, damage and flameout due to ice shedding. The prevalence of these events has led to a change in certification requirements for icing conditions. Development of accurate numerical models allows the costs of certification and testing to be minimised. Ice crystal icing (ICI) accretion is modelled as a coupled heat transfer and phase change continuity and energy balance at the surface. The Extended Messinger Model (EMM) incorporates a temperature gradient across the ice and water layers. This model was updated previously to model mixed phase ICI with an additional water layer at the surface to generate a temperature gradient from a warmed surface to the ice interface (> 0 degrees C), the updated model is EMM-Crystals (EMM-C). Within this paper, the EMM-C is modified to generate unsteady ice accretion. This update is relevant due to the intrinsic 3D flows present in a compressor stage and documented testing of engine stages and flight tests showing the complex 3D shapes of mixed phase warmed surface ICI accretion. A substrate heat transfer model is implemented for turbomachinery specific flow cases. This work has been validated against ICI experiments comprising of a cantilevered prismatic stator test piece, a swan neck duct linear cascade and existing experimental results from test campaigns performed at the Research Altitude Test Facility (RATFac) in Canada.

Abstract The secondary air system and cooling passages of gas turbine components are prone to blockage from sand and dust. Prediction of deposition requires accurate models of particle transport and thermo-mechanical interaction with walls. Bounce stick models predict whether a particle will bounce or stick upon impact and calculate rebound trajectories if applicable. This paper proposes a bounce stick model that uses analytical solutions of adhesion, plastic deformation and viscoelasticity to time-resolve collision physics. The Discrete-Element Methods (DEM) model shows good agreement when compared to experimental studies and FEA simulations, requiring minimal parametric fitting. Further comparison is made to the best resolved and industry standard models available. In addition to coefficients of restitution, other variables crucial to modelling rebound, for example angular velocity, are predicted. The time-stepping explicit approach allows coupling between internal processes during contact and shows that viscoelasticity plays a significant role in adhesion. Modelling time-dependent internal variables like wall-normal force allow the modelling of non-spherical particles, the physics of which has been shown by previous work to differ significantly from that of spheres. These effects have not been captured well, if at all, by other models. The spherical version of this model has previously been shown to produce good predictions of deposition distribution in CFD. The developments presented here allow the inclusion of more complex collision physics which will improve numerical predictions of deposition. The accompanying second part to this paper demonstrates this with the addition of surface roughness modelling.

The propagation of sound waves in high-temperature and plasma flows is subject to attenuation phenomena that alter both the wave amplitude and speed. This finite change in acoustic wave properties causes ambiguity in the definition of sound speed travelling through a chemically reactive medium. This paper proposes a novel computational study to address such a dependence of sound-wave propagation on non-equilibrium mechanisms. The methodology presented shows that the equations governing the space and time evolution of a small disturbance around an equilibrium state can be formulated as a generalised eigenvalue problem. The solution to this problem defines the wave structure of the flow and provides a rigorous definition of the speed of sound for a non-equilibrium flow along with its absorption coefficient. The method is applied to a two-temperature plasma evolving downstream of a shock, modelled using Park’s two-temperature model with 11 species for air. The numerical absorption coefficient at low temperatures shows excellent agreement with classical theory. At high temperatures, the model is validated for nitrogen and argon across wide temperature ranges with experimental values, showing that classical absorption theory is insufficient to characterise high-temperature flows due to the effect of finite-rate chemistry and vibrational relaxation. The speed of sound is verified in the frozen and equilibrium limits and its non-equilibrium profile is presented with and without viscous effects. It is furthermore shown that the variation in the speed of sound is driven by the dominating reaction mechanisms that the flow is subject to at different thermodynamic conditions.

Porous and dense zirconium diboride (ZrB 2 ) materials are promising ultra‐high‐temperature ceramics (UHTCs) for transpiration cooling in hypersonic applications, providing an effective means to reduce component temperatures and mitigate oxidation effects. While porous ZrB 2 enables coolant flow, dense ZrB 2 offers structural integrity. However, achieving a reliable ceramic‐to‐metal connection remains a significant challenge due to the inherent differences in their physical, chemical, and mechanical properties. This study investigates the brazing process of both porous and dense ZrB₂ UHTCs to zirconium metal (Zr). Zr was selected due to its thermal expansion properties closely matching those of ZrB₂, reducing thermal stress at the interface and enabling coolant transfer into porous ZrB₂ from the supply reservoir. The brazing temperature of 1650°C was selected based on the Zr–ZrB₂ phase diagram to ensure eutectic melting without compromising the structural integrity of the base materials, and the filler composition was selected to enhance wetting and spreading. The results demonstrate that dense ZrB₂ forms robust and continuous interfaces with Zr metal, while porous ZrB₂ presents greater challenges due to thermal expansion mismatches and paste infiltration. These findings provide valuable insights into ceramic–metal joining for aerospace high‐performance thermal protection systems under extreme conditions, which would reinforce the real‐world impact.

Abstract Cooling passages and the secondary air system of gas turbine components are prone to blockage from sand, dust and ash. The ability to model deposition of non-spherical particles accurately using CFD would allow the prediction of in-service performance degradation and the design of deposition-tolerant hardware. This paper implements a Continuous Random Walk (CRW) transport model with a Discrete Elements Methods (DEM) based bounce stick model to predict deposition in CFD. These are the first such simulations in the open literature to incorporate particle shape and surface roughness. The resulting spatial trends of deposition are compared with experimental data of particle deposition in an S-bend. The case considered is representative of the flow and metal conditions, particle size and loading distribution, and passage geometry seen in HPT blade cooling passages. Numerical predictions of deposition distribution show good qualitative agreement with experiments. The approach is therefore suitable to assess and compare the susceptibility of components to particulate damage in industry. To the authors' knowledge, this is the first example in the open literature of experimental comparison of deposition trends in CFD. The approach provided reasonable first-order estimations of quantitative deposition heights, which may be used to estimate component-level degradation in-engine. More accurate quantitative predictions of deposition will require a suitable deposit evolution and erosion model and improved material data, which are not yet available in the literature. The performance of the DEM bounce stick model was favourable compared to energy-based alternatives.

Accurate prediction of shedding in ice crystal icing (ICI) in turbomachinery remains a challenge, particularly due to limitations of current 3D numerical accretion models in capturing realistic shapes and sub-surface conditions. This study presents an experimentally grounded approach to assess shed potential using laser-scanned ice accretion geometries and time-resolved wall thermal data. Experiments were conducted using a vaned test article exposed to ice crystal conditions at the NRC's ICE-MACR facility, for inlet temperatures in the range T-0, (in) is an element of [-6.0, -2.0] degrees C. End-of-test freeze-out accretions were recorded using a handheld laser scanner. Despite occlusions from vanes and accumulated ice along the line of sight, usable ice accretion profiles were extracted without the need for scan repair. Cases with warmer inlet temperatures exhibit larger ice accretions, with circumferentially averaged blockage up to 3.16 times the dry vaned baseline. A vaneless reference case exhibits only light frosting under the same conditions. The scanned accretions are used in conjunction with experimental wall thermal histories to identify regions of shedding by advancing thermal boundary conditions and resolving the likely impact on subsurface water films. This hybrid experimental-numerical approach offers a robust framework for informing future shed models with realistic thermal boundary conditions and accretion geometries.