We describe our 15+ years of experience using Lua as part of the development toolkit for a physics-based simulation code, Eilmer. The code is specialised for the simulation of gas motions at high-speeds and the use of Lua aids to manage complexity and provide flexibility. We discuss our uses of Lua including: userprogrammable input configuration, user-defined run-time customisation, for data description, and as a scripting layer to D language code. The paper presents both user and developer perspectives and experiences. We conclude with some lessons learnt about using Lua in the context of a physics-based simulation code, and close with a recommendation that the inclusion of Lua in our toolkit has been a net positive and fruitful decision.

X3/R is a new large-scale free-piston-driven dual-mode shock expansion tube, developed and operated collaboratively by the University of Queensland (UQ) and Australia’s Defence Science and Technology Group (DSTG). The facility can be converted between a long-duration reflected shock tunnel (RST), a super-orbital expansion tube (X-mode), and a non-reflected shock tube (NRST). In RST mode, the facility is currently capable of producing 600 mm diameter Mach 7 test flows at 25–50 kPa dynamic pressure for more than 10 ms. In expansion tube mode, the facility can reach enthalpies up to 80 MJ/kg for test times on the order of 500–1000 μ s. This paper presents the new facility, summarizes its current operational capabilities, and discusses key the technical challenges overcome during its development.

Pitot pressure is the most common measurement in high total enthalpy shock tunnels for test condition verification. Nozzle calculations using multi-temperature non-equilibrium thermochemistry are needed in conjunction with Pitot measurements to quantify freestream properties. Pitot pressure is typically matched by tuning the boundary layer transition location in these simulations. However, non-equilibrium thermochemistry effects on the Pitot probe are commonly ignored. A computational study was undertaken to estimate the effect of non-equilibrium thermochemistry on Pitot pressure and freestream conditions. The test flow was produced by a Mach 7 nozzle in a reflected shock tunnel for air at a relatively low total enthalpy of 2.67 MJ/kg. Three different thermochemical models (equilibrium, finite-rate chemistry and two-temperature thermochemistry) were employed to compute flow variables at the nozzle exit and Pitot probe. Pitot pressures from these simulations were compared against those obtained via experiments. The results show a departure from the commonly utilized C of 0.92 in the reduced Rayleigh-Pitot equation form for high Mach numbers. Additionally, calculations were done with a sweep of free-stream conditions and resulting in values for one- and twotemperature models to use in future shock tunnel studies. Overall, our results show that the influence of finite-rate thermochemistry should be taken into account, even at relatively low flow enthalpies.

Many production-level hypersonic flow codes employ a defect-correction approach to solving the partial differential equations used to model high-speed thermochemical nonequilibrium flows. Although this approach typically provides fast convergence during the startup phase of a simulation, it is limited to a linear asymptotic convergence rate. Newton-Krylov methods are an alternative approach that can achieve a quadratic asymptotic convergence rate if an exact Jacobian is used in the implicit operator. The challenge is that the derivation of an exact linearization of a hypersonic flow code is non-trivial and prone to human error. In this paper, we present our work towards overcoming this challenge via the Jacobian-Free Newton-Krylov method. The method is Jacobian-free in the sense that the algorithm only requires matrix-vector products which are obtained by Fréchet derivatives. In our solver, we employ complex-step Fréchet derivatives. By doing so the accuracy of our numerical derivatives are not restricted by subtractive floating-point error, and as such we are able to get a Jacobian influence that is effectively as accurate as one that is analytically derived and evaluated. We demonstrate the solver's performance on several test cases that are representative of the type of flows of interest to the hypersonic community. The convergence rate of the developed Newton-Krylov solver is compared against a point-implicit implementation based on a defect-correction method.

A set of experiments was conducted with the aim of evaluating total heat flux mitigation using magnetohydrodynamic flow control over ionized shock layers surrounding planetary entry vehicles. The University of Queensland's X2 expansion tube was used to generate a flow condition representative of a Mars return trajectory. Spherical permanent magnets were fitted into a scaled test model based on NASA's Stardust capsule. Thermocouples located at the stagnation point and shoulder of the test model, as well as thin-film heat transfer gauges located in the aft section, measured total heat flux for both magnetic and nonmagnetic experiments. High-speed imaging of the shock layer showed a significant increase in shock standoff when using the magnet, and polynomial fits were derived, describing standoff distance along the model's forebody. Despite significant noise affecting the heat flux gauges signals for the magnetic experiments, a simple methodology allowed to compare heat flux during the useful test time. It was found that the applied magnetic field significantly reduces total heat flux at the stagnation point and shoulder of the test model, although heat flux to the aft section was found to significantly increase. Reasonable agreement with the numerical predictions was found for the aft section of the test model, but discrepancies were observed at the other locations.

Hypersonic boundary layer transition over slender bodies is initially delayed by blunting of the leading edge, then moving back upstream past a critical bluntness. Transition in the maximum delay regime is not predicted by Linear Stability Theory. In this maximum delay regime, Direct Numerical Simulations are used to investigate instabilities with the entropy layer induced by the bow shock that may contribute to turbulent breakdown. Flow over a 17.78mm (0.7in) nose radius 7 degree half angle cone at Mach 8 is simulated to match experiments of Stetson et al.. The steady base flow is forced by disturbances to excite the instabilities. Multiple distinct instabilities appear within the entropy layer and their characteristics are investigated and compared to experimental results.

This paper introduces Eilmer, a general-purpose open-source compressible flow solver developed at the University of Queensland, designed to support research calculations in hypersonics and high-speed aerothermodynamics. Eilmer has a broad userbase in several university research groups and a wide range of capabilities, which are documented on the project's website, in the accompanying reference manuals, and in an extensive catalogue of example simulations. The first part of this paper describes the formulation of the code: the equations, physical models, and numerical methods that are used in a basic fluid dynamics simulation, as well as a handful of optional multi-physics models that are commonly added on to do calculations of hypersonic flow. The second section describes the processes used to develop and maintain the code, documenting our adherence to good programming practice and endorsing certain techniques that seem to be particularly helpful for scientific codes. The final section describes a half-dozen example simulations that span the range of Eilmer's capabilities, each consisting of some sample results and a short explanation of the problem being solved, which together will hopefully assist new users in beginning to use Eilmer in their own research projects.

One of the most dramatic effects of vibrational and chemical non-equilibrium in hypersonic flows occurs in the bow-shock detachment process in flow over a wedge. This was shown theoretically and in reflected shock tunnel experiments by Hornung & Smith (J. Fluid Mech., vol. 93, 1979, pp. 225–239). In the present work, the effect is first demonstrated by computation of two-dimensional non-equilibrium flows. The effect of the finite transverse extent of the wedge is then studied by three-dimensional computations of non-relaxing flows. An analytical formula is obtained that gives the shock detachment distance of a finite wedge for ideal-gas and equilibrium flows. In the experiment, the finite transverse extent of the wedge competes with the non-equilibrium effects, as each introduces a new length scale. The carbon dioxide and nitrogen flows of the experiment are therefore computed in three dimensions and with two-temperature chemistry accounting for vibrational and chemical non-equilibrium. In the case of nitrogen flow, the agreement between experiment and computation is not good, the experimental detachment distance being larger. A number of possible reasons are quantitatively examined. A conclusive resolution of the discrepancy is considered to require a repeat of the experiment with more accurately characterized conditions. In the case of the carbon dioxide experiments, the computed results agree remarkably well with experiment. This is partially due to the fact that the condition is very close to equilibrium, where the sensitivity of the detachment process to relaxation effects is small. The analytical expression for the dimensionless detachment distance agrees very well with all the three-dimensional computations of non-relaxing flows.

The aerodynamic heating experienced by capsules entering into the atmospheres of Saturn, Uranus, and Neptune is greatly affected by chemically nonequilibrium processes occurring in the shock layers. There are several reaction schemes available in numerical predictions for hydrogen dissociation and ionization, and more experimental data would assist verifying these existing models. This paper reports the results of electron number density measurements conducted in the X2 expansion tube at the University of Queensland using a condition representative of a proposed Saturn entry, where significant nonequilibrium effects in the shock layer are expected. Electron number density along the stagnation streamline was obtained from Stark broadening. The data presented here provide independent measurements for evaluating the reaction schemes for the conditions created. It was found that the experimental data were qualitatively modeled by a contemporary kinetic model. Quantitative agreement between experimental and numerical data was found by adjusting the ionization rate coefficients from an existing reaction scheme by a factor of 25. This updated reaction rate set was also cross-validated with electron number density measurements in NASA’s shock tube tests. The adjusted rates had better agreement than using the original rates, and quantitative agreement can be found in the high-density cases.

This paper reports on an experimental study of magnetohydrodynamic aerobraking using an expansion tube facility, which can generate the correct electrodynamic boundary conditions for spacecraft atmospheric entry. Argon test gas was selected for its relatively simple chemistry, making it well suited to develop experimental test cases for numerical code development. Test models were constructed from either spherical neodymium permanent magnets or steel balls. Ceramic paint was used as an electrically insulating surface boundary condition for experiments where this was required. Finite-rate reacting computational fluid dynamics of the experimental configuration indicates that relatively long duration argon relaxation times lead to a highly nonequilibrium shock layer in which a significant Hall effect arises. This is important because it is expected that future flight vehicles using magnetohydrodynamic aerobraking technology will also be operated at flight conditions where Hall effect is strong. Shock stand-off was measured using high-speed luminosity imaging for various magnetic and nonmagnetic model configurations. Experimental results in this paper support previous numerical studies that found that only an electrically insulated model surface can generate a significant magnetohydrodynamic interaction when Hall effect is strong.

A set of magnetohydrodynamic (MHD) aerobraking experiments was conducted with the aim of simulating the Earth reentry environment for Mars return trajectories, and to study the effects of MHD flow control on the ionizing shock layer surrounding a planetary entry vehicle. The X2 expansion tube of the University of Queensland was used, which could provide realistic flowfield boundary conditions, where ionization is spontaneously generated within the shock layer as in true flight and the freestream is nonconducting. Suitable flow conditions providing strong MHD interaction at superorbital Earth reentry velocities were developed. Steel ball and neodymium permanent magnet models were tested, both uncoated and coated with electrically insulating high-temperature epoxy. Shock-layer high-speed imaging showed a significant increase in shock standoff distance for the magnetic models. The experimental shock standoff results generally agreed well with analytical and numerical shock standoff predictions. These experiments demonstrate that a strong MHD interaction can be generated for a Mars return trajectory with moderate magnetic field strengths. Furthermore, they provide a promising framework for future MHD aerobraking experiments to investigate MHD drag force and heat-flux mitigation.

A computational parameter study of the viscous axisymmetric supersonic flow over a double cone is made with a view to determining the boundary of the region in which such flows are unsteady. The study is restricted to the case when the boundary layer is laminar. The features of both the steady and unsteady flows in different characteristic regions of the parameter space are described. In particular, the phenomenon of pulsating flow typical of spiked blunt bodies (small first-cone angle, theta(1), and large second-cone angle, theta(2)), is shown to be inviscid in nature. In theta(1)-theta(2) space, the region of unsteady flow is enclosed in a loop with a lower and an upper theta(2) branch with a maximum theta(1) between. The location of the lower theta(2) branch is determined by the second-cone detachment angle theta(2d). For this reason, the gas model in one of the conditions is chosen to be thermally perfect carbon dioxide (at Mach number 8) for which theta(2d) is quite large. In the other cases, the gas model is perfect-gas nitrogen at Mach numbers 2, 4 and 7.7. In the hypersonic range, within the uncertainties, and in the parameter range covered, the unsteadiness boundary is shown to depend on only three dimensionless parameters.

In this work, near-infrared and ultraviolet spectroscopic data collected during the Hayabusa spacecraft reentry is used as the basis for validating numerical and experimental studies using the compressible flow computational fluid dynamics codeEilmer3and the University of Queensland's X2 expansion tube. Spectra generated numerically from simulations of the full-scale vehicle at the selected trajectory point at 1 s after peak total heating were compared with experimentally captured spectra over a binary-scaled and total-enthalpy-matched radiating shock layer around a 1/5-scale Hayabusa model, and both sets of data were compared with spectra obtained from flight. For the infrared results, experimental and simulated spectra, as well as simulated and flight spectra, compared well within an uncertainty margin of between 20 and 90% depending on the particular case being compared. Experimental and simulated ultraviolet results did not compare well; however, comparisons between simulated and flight ultraviolet spectra were more favorable, comparing well within an uncertainty of around 50%.

Nitrogen is proposed as a suitable driver gas candidate for the operation of free-piston-driven shock tunnels at low total enthalpies. When compressed adiabatically, nitrogen has a lower speed of sound than the commonly used driver gases, e.g., argon and helium, thus providing the ability to achieve tailored conditions and longer test durations at lower enthalpies. This paper describes the methodology used to design operating conditions using nitrogen as the driver gas and presents an experimental and numerical demonstration of its use to achieve tailored conditions in a free-piston-driven shock tunnel. In this demonstration, the useful test flow duration was extended from less than 0.5 ms to 4 ms based on a constant-nozzle-supply-pressure criterion for tests at total enthalpies of 1.6 MJ/kg. The same design methodology was then used to develop different nitrogen–argon driver conditions for tailored operation in the free-piston-driven shock tunnel T4 for enthalpies spanning from 1.6 to 3.2 MJ/kg. With a nitrogen driver gas, T4, which was originally designed for operation up to Mach 25 flight conditions, can now operate at conditions as low as an equivalent flight Mach number of 5.5. This is significant because the experimental results, supported by numerical simulations, clearly demonstrate that nitrogen can be used as a driver gas in free-piston-driven shock tunnels to maximise the duration at which test conditions are held constant when testing at low total enthalpies.

This paper explores the operating envelope for the University of Queensland's free-piston driven X2 expansion tube to determine if flow conditions can be produced that generate a significant magnetohydrodynamic interaction. Numerical calculations are presented to demonstrate the existence of viable operating conditions to study magnetohydrodynamics. Argon is selected as the test gas due to its simple chemistry and low ionization enthalpy. A candidate flow condition is selected for detailed analysis and experimental validation. Finite-rate reacting argon numerical simulations indicate that relatively short shock-layer length scales for the models tested in X2 limit the degree of argon ionization that is generated. However, a strong interaction remains available, and use of a larger facility can fully mitigate this issue. It is shown that expansion tubes are capable of generating the required flowfield for these experiments, and important considerations for design of suitable test flows are identified.

Experiments were performed using the University of Queensland's X2 expansion tube with the aim of measuring stagnation point radiative heat flux to a blunt reentry body in superorbital Earth reentry air test flow. The selected flow condition produced a flight equivalent velocity of 14.9 km/s, representative of a Mars return trajectory. A radiation gauge was developed which consisted of a thin-film heat flux gauge placed behind an optical window, enabling isolation of the radiative heat flux component. Magnesium fluoride and B270 windows were used which made it possible to isolate the vacuum ultraviolet and infrared contributions, which are the main radiating wavelength regions at Mars return conditions. Absorbance calibration of the gauges had to account for the spectral dependence of the Nickel sensing element, and relied on radiation simulations using NEQAIR to predict the spectral distribution of the radiative heat flux. Experimental measurements yielded an average calibrated radiative heat flux of 10.7 MW/m2 over the 120 - 7000 nm wavelength range, of which 60% was predicted to be in the vacuum ultraviolet. Experimental radiative heat flux was around four times higher than the NEQAIR prediction, which, based on CFD did not, however, account for precursor radiation and excitation of the high temperature freestream.

Magnetohydrodynamic (MHD) aerobraking experiments were conducted in the large-scale X3 expansion tunnel at the University of Queensland. The test gas was argon flowing at approximately 5.7 km . s(-1) for a quasi-steady period of 500 mu s. A neodymium spherical permanent magnet, suspended by string and enclosed within a 65-mm-diameter spherical forebody, was used to generate the magnetic field. An accelerometer was attached to the rear of the magnet to measure streamwise motion, allowing the Lorentz force on the magnet to be deduced according to Newton's second law. The stagnation point magnetic flux density was varied by changing the internal streamwise location of the magnet within the forebody. Experimental results demonstrate a linear increase in MHD drag with magnetic field strength, which is in agreement with previous results from arcjet facilities. However, the MHD drag force was much lower in these experiments, even after accounting for shock density ratio and viscosity differences. This discrepancy could be due to the different freestream state generated by the two types of facilities.

Shape optimization of modern three-dimensional hypersonic inlets requires many geometric design parameters. Because the flow physics is complex, a Reynolds-averaged Navier-Stokes (RANS) analysis is also desirable when performing optimization. A computationally efficient means of handling many-parameter optimization with expensive cost functions is to use gradient-based searches informed by an adjoint flow solution. In this work, a discrete adjoint method for high-speed flows is documented. It is implemented in the open-source compressible-flow solver Eilmer. One difficulty with extending a hypersonic flow solver to include an adjoint solver is the differentiation of complex, nonlinear (and sometimes nondifferentiable) algorithms. Here, it is shown that difficulty can be overcome using flow Jacobians constructed with finite differences based on complex variables. The coupled flow and adjoint solvers are packaged together with a gradient-based optimizer. The flow and adjoint solvers are verified and validated for high-speed RANS analysis. The discrete adjoint method for optimization is demonstrated using the NASA P2 hypersonic inlet as a test case. The results show that the optimization method can remove an undesirable shock present in the original geometry, while achieving the desired compression ratio and improving overall performance metrics.

X3R is a new, large-scale free-piston driven reflected shock tunnel designed and operated at the University of Queensland, Australia. The facility is a derivative of the X3 super-orbital expansion tube, which uses a combination of new and pre-existing hardware. It is capable of generating 600 mm diameter Mach 7 test flows at 25 kPa and 50 kPa dynamic pressure for durations of approximately 12.5 ms. Previously, hypersonic testing in Australia was limited in both scale and duration, due to the size of the local facilities capable of experimentation in this regime. This paper presents the new facility and summarizes its current operational capabilities. This includes a description of the facility geometry, and details of the two currently available operating conditions. These conditions were specifically designed to overcome the drawbacks of the tunnel’s relatively short free-piston driver, and use a high helium fraction driver gas to produce a long duration but low compression ratio driver response.