LIMITS OF SIMULATING GAS GIANT ENTRY AT TRUE GAS COMPOSITION AND TRUE FLIGHT VELOCITIES IN AN EXPANSION TUBE

Transcription

1 LIMITS OF SIMULATING GAS GIANT ENTRY AT TRUE GAS COMPOSITION AND TRUE FLIGHT VELOCITIES IN AN EXPANSION TUBE C.M. James 1, D.E. Gildfind 1, R.G. Morgan 1, S.W. Lewis 1, E.J. Fahy 1, and T.J. McIntyre 2 1 The Centre for Hypersonics, The School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia, c.james4@uq.edu.au, d.gildfind@uq.edu.au, r.morgan@uq.edu.au, s.lewis6@uq.edu.au, e.fahy@uq.edu.au 2 The School of Mathematics and Physics, The University of Queensland, Brisbane, QLD, 4072, Australia, mcintyre@physics.uq.edu.au ABSTRACT Atmospheric entry to the Gas Giants involves velocities of the order of km/s, which is mostly beyond the capabilities of current ground testing facilities. This paper details an investigation exploring the operating limits of the X2 superorbital expansion tube at the University of Queensland (UQ) for the simulation of radiating gas giant entry flow conditions. Theoretical calculations show that the X2 expansion tube can simulate a proposed Uranus entry at 22.3 km/s but is unable to recreate the necessary 26.9 km/s velocity to simulate a proposed Saturn probe mission. Further theoretical analysis shows that with an increased amount of helium diluent in the test gas, similar shock layer conditions to the proposed 26.9 km/s Saturn entry could be achieved in the X2 expansion tube. Due to the current interest in sending atmospheric entry probes to Uranus and Saturn, this is a useful conclusion, demonstrating that there are experimental facilities capable of producing aerodynamic test flows for simulating gas giant entry conditions. 1. INTRODUCTION The Galileo probe s 47.5 km/s entry into Jupiter on December 7th, 1995 was an engineering triumph. The probe survived its entry into the atmosphere of the largest gas giant planet in the solar system, and achieved the full scientific mission that it was built for. However, analysis of the in-flight ablation of the Galileo probe s heat shield by Milos [1] showed that the ablation on both the stagnation point and the frustum of the probe s sphere-cone heat shield differed from what had been predicted, and that only half of the heat shield ablated during the entry. This indicated that the heat shield design could have been optimised further. The Galileo probe s heat shield was designed using two separate state-of-the-art, for their time, Computational Fluid Dynamics (CFD) codes [2] and three different types of experiments to validate the simulations and some of the parameters used. Laser irradiation experiments were performed on ablating models using a gas dynamic laser [3]. 1/24 scale ablating Galileo probe models were flown in a ballistic range at 4 5 km/s [4] with an air test gas used to study convective heating and an argon test gas used to study radiative heating. It had been concluded that radiative heat transfer at the stagnation point of an 89%H 2 /11%He (by volume) Jupiter entry test-flow could be approximated by the heat transfer from Argon due to the theoretical similarity between the spectral lines of each gas [5]. Ablating models were also tested in a 50%H 2 /50%He (by volume) arc-jet flow in NASA s Giant Planets Facility at 15 km/s [6]. The experiments indicated that the probe design was suitable. However, disagreement between what the simulations predicted and the flight test data indicated that improvements to both experimental and simulated modelling could be made. Following the Galileo mission, several CFD studies have aimed to recreate the ablation of the Galileo probe s heat shield, but no experimental studies have been performed. The work of Matsuyama et al in 2005 [7] succeeded in re-creating the recession of the frustum region (i.e. the conical sides of the probe s sphere-cone heat shield) of the probe closely by using a radiative energy transfer calculation that was tightly coupled to the flow-field solver and Park s injection-induced turbulence model. However, stagnation point recession was overestimated. A study by Park in 2009 [8] was able to recreate the stagnation point recession fairly closely by implementing a model that was focused on correctly modelling the interaction between the flow-field and the spallating carbon particles from the heat shield. Park s model calculated the thermochemical state of the gas more accurately than had been achieved previously, included the effects of vacuum ultraviolet (VUV) radiation absorption, and the effects of spallation. While the majority of gas giant entry research in the past was either performed for the design of the Galileo probe, or to analyse issues associated with it, there is currently renewed interest in future gas giant entry probe missions. The US National Research Council Vision and Voyages for Planetary Science in the Decade report

2 identified probes to Uranus [9] and Saturn [10, 11] as high priorities for future space missions due to the large scientific questions that remain unanswered: Firstly, gas giant planets contain matter produced early in the solar system that can be used to improve models of solar system formation and evolution; the gas giants provide a valuable link to extrasolar planetary systems, where gas giant planets are common; and lastly, Jupiter and Saturn are fundamentally different planets to Neptune and Uranus. The latter planets are known as ice giants due to heavy elements trapped in their atmospheres in an ice-like state. It is hoped that by entering the atmosphere of an ice giant planet, humankind can then better compare gas giant and ice giant planets. The proposed probe entry velocities were 22.3 km/s for Uranus [9] and 26.9 km/s for Saturn [10, 11]. Within this new context, which may see the design of two new gas giant probe missions in the foreseeable future, it is worth considering how ground testing can aid the development of this next generation of gas giant entry probes. Due to the extreme cost of performing real flight tests, ground tests have been essential to the design of planetary entry vehicles, but they have their limitations. Because of the total pressure requirements of planetary entry, it is impossible in practice to run continuous duration planetary entry wind tunnel experiments on a test model, and decisions must be made about what to simulate. Most test facilities which are used to simulate planetary entry are either relatively low velocity and long duration (i.e. arcjets and plasma torches) where often neither the velocity nor the enthalpy of the true flight condition are re-created but the test time is long enough for the model to reach sufficient temperatures at which hot-wall and ablation tests can be carried out; or high velocity, impulse facilities (i.e. shock tunnels and expansion tubes) where the velocity and Reynolds number of the true flight condition can be re-created, but the test times are extremely short (10 s or 100 s of microseconds) and experiments are performed on a cold model. The aforementioned three sets of experiments performed for the design of the Galileo probe all fell into the low velocity and long duration category. None of the experiments were able to re-create the velocity of the Galileo probe s entry, but in various ways, and at various velocities, each experiment aimed to re-create the heating environment for a duration long enough to study the recession of an ablating model. This paper focuses on the situation where velocity is high and test times are short, and it examines the opportunities and limitations of studying gas giant entry in an expansion tube, namely the X2 expansion tube at the University of Queensland (UQ). Expansion tubes are used principally for studying planetary entry phenomena from 6 12 km/s, but this paper examines whether they are able to simulate the flow conditions of planned missions to Uranus and Saturn, due to the excess performance available from their high powered free-piston drivers, and the extra performance gained by using a light hydrogen/helium test gas. This paper aims to establish theoretically the limits of what gas giant entry experiments can be performed at true gas composition and true flight velocity in the X2 expansion tube, before examining other avenues that can be explored to allow gas giant entry to be simulated in an expansion tube when true flight velocity is not achievable. It provides the first step down a path of experimentation that has never been performed before, the conclusion of which will be the ability to simulate radiating, aerodynamic gas giant entry flows over scaled models into all of the gas giant planets in the solar system. This data will inform the design of the next generation of gas giant entry probes by providing fundamental information for the development of improved gas dynamics models. This data will help to reduce the mass of future gas giant entry vehicles while also improving reliability, leading to decreased costs and engineering safety factors for future gas giant entry missions. 2. THE X2 EXPANSION TUBE Shock tubes and reflected shock tunnels powered by freepiston drivers have been used for the study of hypervelocity flows since 1960 [12]. However, they are traditionally limited to velocities up to, and including, Earth orbit velocities (around 8 km/s) [13]. Due to the fact that all the energy is added to the flow across a shock wave, both reflected and non-reflected shock tunnels are limited in the total enthalpy that they can simulate [13]. This is because at very high shock speeds, the test flow exists as a highly dissociated plasma, which is useful to study high temperature effects, but not for aerodynamic testing. The expansion tube, a concept proposed by Resler and Boxsom in the 1950 s [14], circumvents the limitation discussed above by only adding part of the required energy to the flow with a shock wave. The rest of the energy is added by processing the test gas with an unsteady expansion. At the expense of test time, total enthalpy and total pressure are added to the flow without the flow dissociation that would occur in a shock tunnel [13]. The X2 expansion tube at the University of Queensland has been used extensively to simulate and measure radiating test flows for several planetary bodies in the solar system, including Earth, Mars, Titan, and Venus [15, 16], at velocities ranging from km/s. However, when considering simulating entries into the gas giant planets in the outer reaches of the solar system, velocities range from km/s, pushing the performance envelope limits of these facilities as they are currently configured. The short test time duration of the X2 expansion tube ( µs), and expansion tubes in general, means that the test flow itself does not have the time to sufficiently heat the test model during the experiment, and the experiment is performed on a cold model. However, if the enthalpy

3 of the test flow can be matched, andρl scaling is used to match the Reynolds number of the scaled model to that of the flight vehicle, then the flight aerodynamics of a vehicle can be studied, and so can the radiation of the entry. The work of Zander et al [17] examined electrical pre-heating of reinforced-carbon-carbon (RCC) models in the X2 expansion tube to allow experiments to be performed on models at temperatures up to 2,500 K. Surface thermochemistry was found to increase with surface temperature, and it was found that it was possible to observe these effects during the test time of the experimental facility. This is an example of a technique that reduces the limitations of expansion tube research by allowing experiments to be performed with a hot model, where model heating is accomplished by a different mechanism to the true flight condition. A schematic of an expansion tube operating with a shock heated secondary driver tube is shown in Figure 1. The figure shows the longitudinal wave processes that occur as a function of time during an experiment. Prior to the experiment, each section of the tube downstream of the primary diaphragm is filled to a set pressure, while upstream a set driver gas and reservoir fill condition are established. Figure 1. Distance-time (x-t) diagram of a free-piston driven expansion tube operating with a shock heated secondary driver tube. (Adapted from Gildfind et al [18].) After each section of the tube is filled to the required conditions, the piston is released. The piston rapidly accelerates, compressing the primary driver gas in front of it from its initial fill pressure to the burst pressure of the primary diaphragm, at which point the pressure and temperature of the driver gas are both very high (10 s of MPa, 1000 s of K). This hot, high pressure pocket of driver gas is used to drive shock waves through the driven sections of the tube and over a test model. In its simplest configuration, the expansion tube has two driven sections: a shock tube, and a lower pressure downstream tube called an acceleration tube that is used to accelerate the shocked test flow through an unsteady expansion. The configuration shown in Figure 1 features a compound driver where an extra section called a secondary driver tube is added between the primary diaphragm and the shock tube. This section is filled with a light gas (generally helium) and is used to augment or tune the performance of a set driver condition. The use of a compound driver adds more complexity to what is already a complicated experiment, but if tuned correctly, the compound driver allows the facility to drive a more powerful shock through the test gas than it could have done otherwise. Fully characterising an expansion tube test flow is a costly computational process, requiring complex compressible, high temperature, transient two-dimensional axisymmetric CFD. UQ has developed a one-dimensional CFD code, L1d3 [19], that can perform a simulation of the facility in a matter of hours, but it is still not fast enough to be used as a parametric design tool for the design of new test conditions. To allow for the preliminary design and approximate characterisation of new expansion tube test conditions within a reasonable time frame, it is important to have simple, approximate design tools which allow experimenters to design new test conditions quickly and easily, while incorporating a sufficient level of flow physics to provide sufficiently accurate predictions. For this paper, an in-house expansion tube and shock tunnel simulation code, PITOT [20], has been used to conduct a parametric study of the performance of the X2 expansion tube. PITOT uses isentropic and compressible flow gas processes to quickly simulate flow conditions. It uses NASA s Chemical Equilibrium with Applications (CEA) [21] code to account for high-temperature gas effects, while also incorporating a perfect gas solver. PITOT has been used in this paper to conduct a parametric study of the performance of the X2 expansion tube. Due to the high temperatures reached in the acceleration tube of an expansion tube, where shock speeds usually range from 6 12 km/s, and for gas giant entry can exceed 20 km/s, it is important for an expansion tube simulation tool to incorporate real gas effects, and for this reason equilibrium gas properties are used in PITOT. Equilibrium gas effects are used for all calculations in this paper. Generally PITOT simulates the driver, secondary driver, and shock tube performance very closely, and it is usually only in the acceleration tube, where due to boundary layer effects and the low density nature of the tube, that experiment and theory can begin to differ significantly. The driver conditions used for this study can be seen in Table 1. Table 1. X2 expansion tube driver conditions used for this study[18]. Driver case Diaphragm Rupture Rupture Reservoir Driver ID thickness pressure temp. fill fill pressure pressure - mm MPa K MPa kpa X2-LWP-2.0 mm X2-LWP-2.5 mm

4 3. EXPANSION TUBE CONDITION ANALYSIS All conditions discussed in this analysis use a simulated Uranus entry test gas composition of 85%H 2 /15%He (by volume) based on values from the work of Conrath et al [22] that were found from Voyager fly by measurements. They found a helium mole fraction in the upper troposphere of Uranus (where methane is insignificant) of 0.152± For this paper, the error has been ignored, and the amount of significant figures reduced to two. The work of Palmer et al [23] also performed simulations with a 85%H 2 /15%He (by volume) gas composition based on the mole fraction from Conrath et al [22]. Stagnation enthalpy (H t ) is used to compare the performance of all test conditions in this paper because it gives a measure of energy contained in a gas due to both its gas state and its velocity (see the two terms in Equation 1). The stagnation enthalpy of the planetary entries were calculated using only the velocity component of the stagnation enthalpy because the real planetary entry conditions have a freestream temperature that is not significant compared to the free stream velocity. This is not true of expansion tube test flows where the freestream temperature can be several 1000 K, and the flow may be partially dissociated. H t = h+ U2 2 (1) It should be noted that while the maximum enthalpy can be given to the test flow by expanding it to as close to zero pressure as possible by using the lowest acceleration tube fill pressure possible, the analysis in the following section is generally limited to an acceleration tube fill pressure of 0.5 Pa for several reasons. Operationally, it can be difficult to maintain the pressure in the acceleration tube at below 0.5 Pa long enough to perform an experiment, and the low starting pressure can make it difficult to obtain accurate shock speed measurements for the conditions. The low density shock tube effects ( Mirels effects ) mentioned previously also become more pronounced when extremely low acceleration tube fill pressures are used Conditions Without a Secondary Driver Figure 2 shows how different shock tube fill pressures affect the performance of the facility when both driver conditions (X2-LWP-2.0 mm-0 and X2-LWP-2.5 mm-0) are used without a secondary driver. Six conditions are shown in the figure, using both driver conditions and acceleration tube fill pressures of 0.1, 0.5, and 1.0 Pa. (Details of the two driver conditions used can be found in Table 1.) Figures 2(a) and (b) show how the stagnation enthalpy and acceleration tube shock speed of the different conditions changes when the shock tube fill pressure is varied from kpa. All curves are normalised by their maximum value. &%'()$'%*'#*+$ &%'()$'%'#*+$ &%'()$'%*'#*+*$ &%'()$'%'#*+*$ &%'()$'%*'#*+$ &%'()$'%'#*+$ % " #$ 0. - % -%&%'()$'%*'#*+$ -%&%'()$'%'#*+$ -%&%'()$'%*'#*+*$ -%&%'()$'%'#*+*$ -%&%'()$'%*'#*+$ -%&%'()$'%'#*+$ % " #$ Figure 2. Effects of shock tube fill pressure on the performance of six conditions without a secondary driver. a) How performance (measured in terms of stagnation enthalpy) changes with varying shock tube fill pressure. b) How acceleration tube shock speed changes with varying shock tube fill pressure. It can seen in Figures 2(a) and 2(b) that there is a relationship between the shock tube and acceleration tube fill pressures (p 1 and p 5 ). As the acceleration tube fill pressure is increased from 0.1 to 0.5, and then to 1.0 Pa, a higher shock tube fill pressure is required to achieve both maximum performance (Figure 2(a)) and maximum velocity (Figure 2(b)). Taking the conditions using X2- LWP-2.5 mm-0 as an example, with an acceleration tube fill pressure of 0.1 Pa, to achieve maximum performance a 1.0 kpa shock tube fill pressure is required, while to achieve maximum velocity 1.5 kpa is required. As the acceleration tube fill pressure is raised to 0.5 and then 1.0 Pa, to achieve maximum performance shock tube fill pressures of 1.8 and 2.3 kpa are required respectively, and for maximum velocity shock tube fill pressures of 3.1 and 4.3 kpa are required. Overall, the plot demonstrates why a parametric study is important: the condition that maximises performance in terms of stagnation enthalpy is not the fastest condition (as may have been expected), and the fastest condition does not occur when the shock tube fill pressure is minimised to maximise shock speed in the shock tube (which may also have been expected). The best performing condition with an acceleration tube fill pressure of 0.5 Pa has a stagnation enthalpy of 173 MJ/kg, giving it a flight equivalent velocity of 18.6 km/s Conditions With a Secondary Driver Figure 3 shows the performance of various conditions using a pure helium secondary driver tube. Both driver conditions are shown (Figure 3(a) uses X2-LWP-2.0 mm-0 and Figure 3(b) uses X2-LWP-2.5 mm-0) and the accel-

5 eration tube fill pressure has been fixed at 0.5 Pa. Each curve represents a different shock tube fill pressure from kpa, and the secondary driver fill pressure has been varied from kpa. The same axes have been used for both plots to better illustrate the difference in performance between the two driver conditions. In Figure 3 it can be seen that for both driver conditions, the maximum secondary driver performance point shifts to the right as the shock tube fill pressure increases, meaning that a higher secondary driver fill pressure (p sd1 ) is required to maximise performance with a higher shock tube fill pressure (p 1 ). It can also be seen that the maximum stagnation enthalpy appears to asymptote toward a shock tube fill pressure of 0 kpa. This occurs because when a lower secondary driver fill pressure is used, the corresponding secondary driver shock speed (V sd ) is higher, meaning that the temperature (and sound speed) of the shocked secondary driver gas (T sd2 ) is higher, increasing it s performance. If there is enough pressure behind that shock (p sd2 ) to provide maximum performance to the shock tube in front of it, the overall performance multiplication will be higher. However, other limitations need to be considered here. Clearly, an experiment cannot be performed with zero pressure in the shock tube, and therefore a minimum shock tube fill pressure has to be established. If the fill pressure is reduced too far there is a point where the condition will not have sufficient test gas to produce a usable test flow. Test conditions also become more susceptible to leaks in the shock tube with lower fill pressures because there is less test gas in the shock tube to begin with. For these reasons, 2 kpa was chosen as the shock tube fill pressure for both secondary driver conditions as a compromise between maximising performance, and achieving a usable test flow. In Figure 3 it can be seen that for both conditions performance is maximised (within 0.4% of the maximum) when the secondary driver fill pressure (p sd1 ) is in the range kpa, with a maximum between kpa for both conditions. A secondary driver fill pressure of 21 kpa was selected for use with the driver condition X2-LWP-2.5 mm-0, and a secondary driver fill pressure of 25 kpa was selected for use with X2-LWP-2.0 mm- 0. The maximum performance of these two conditions is 235 MJ/kg for X2-LWP-2.0 mm-0, and 270 MJ/kg for X2-LWP-2.5 mm-0. This corresponds to maximum flight equivalent velocities of 21.7 km/s and 23.2 km/s respectively. This means that the velocity of the proposed 22.3 km/s Uranus entry could be simulated with the X2 expansion tube with the driver condition X2-LWP-2.5 mm-0 and a secondary driver section. 4. OTHER AVENUES TO EXPLORE Due to the fact that the previous theoretical analysis shows that the X2 expansion tube cannot currently simulate the 26.9 km/s entry velocity required to simulate Saturn entry, it is important that other avenues be explored to potentially allow the simulation of these conditions in the facility in the future. This section examines how utilising a higher amount of helium diluent than the actual entries allows hotter shock layers to be simulated at achievable shock speeds Higher Amounts of Helium diluent In 1998, Stalker and Edwards [24] proposed a test gas substitution for the study of gas giant entry conditions in ground testing facilities. They showed that for inviscid gas giant entry flows the helium acted as an inert diluent and collision partner for the hydrogen molecules and atoms in the flow-field. They found that the amount of inert diluent in the flow-field, and even the type of inert diluent, did not affect the ionising relaxation of the test flow. This means that when more flow energy is required and the facility cannot provide it through velocity, the amount of helium diluent in the test flow can be increased, and when even more flow energy is required beyond that, the helium diluent can be replaced with the heavier Neon. Both of these substitutions produce stronger shock waves in the test flow, and more particle collisions, producing a far hotter post-shock flow. This allows hotter shock layers to be simulated when the facility is not able to produce enough stagnation enthalpy to reproduce the conditions directly. The substitution has not yet been validated experimentally for the study of radiating gas giant entry flows, and therefore it is currently unclear how the addition of more Helium will affect the radiating flow-field in practice. However, it is a promising line of investigation for the study of gas giant entry in a ground testing facility that will potentially allow proposed gas giant entries to be examined in the X2 expansion tube. Figure 4 shows how a differing percentage of helium diluent in the test gas (by volume) affects the flow condition in various ways. The results shown are based on a simple test condition using the X2-LWP-2.5 mm-0 driver condition, no secondary driver, a 2 kpa shock tube fill pressure, and a 0.5 Pa acceleration tube fill pressure. All values are normalised by the results for 10% He (by volume). Figure 4(a) shows how a differing amount of helium diluent affects the gas properties of the test gas. Over the range shown on the figure, it can be seen that the molecular weight (MW 1 ) and density (ρ 1 ) of the test gas increase by a maximum amount of around 72% above the value with 10% He diluent (by volume). The specific heat ratio (γ 1 ) increases by a maximum amount of around 13%, and the specific gas constant of the gas (R 1 ) decreases by a maximum amount of around 42%. The result shown in Figure 4(b) is very interesting. It can be seen that over the full range from 10 90% He diluent, the performance of the conditions in terms of stagnation enthalpy is almost constant, with a maximum deviation of less than 0.2%. The acceleration tube shock speed (V s2 )

6 Stagnation enthalpy (Ht, MJ/kg) a) X2-LWP-2.0 mm-0 Conditions p 1 = 0.25 kpa p 1 = 0.5 kpa p 1 = 0.75 kpa p 1 = 1 kpa p 1 = 1.25 kpa p 1 = 1.5 kpa p 1 = 1.75 kpa p 1 = 2 kpa p 1 = 2.5 kpa p 1 = 3 kpa p 1 = 4 kpa p 1 = 5 kpa Secondary driver fill pressure (p sd1, kpa) Stagnation enthalpy (Ht, MJ/kg) b) X2-LWP-2.5 mm-0 Conditions p 1 = 0.25 kpa p 1 = 0.5 kpa p 1 = 0.75 kpa p 1 = 1 kpa p 1 = 1.25 kpa p 1 = 1.5 kpa p 1 = 1.75 kpa p 1 = 2 kpa p 1 = 2.5 kpa p 1 = 3 kpa p 1 = 4 kpa p 1 = 5 kpa Secondary driver fill pressure (p sd1, kpa) Figure 3. Effect of secondary driver fill pressure (p sd1 ) on performance for different shock tube fill pressures (p 1 ). Each condition has a set acceleration tube fill pressure (p 5 ) of 0.5 Pa. increases over the whole range shown on the figure, but it is a very small increase of 0.8%. The shock tube shock speed decreases by around 4% before rising again. This behaviour is explained by Figures 4a and 4c. In general, the similarity begins with what can be seen in Figure 4(a), where it is shown that over the full range of helium diluent values shown, the initial gas properties are not changed by more than around 72%. No gas properties have changed significantly. This is also seen in Figure 4(c), where the effect that the differing amount of helium has on various post-shock variables in the shock tube are shown. The maximum variation of any postshock variable over the whole range is the density (ρ 2 ), with an increase of 65%. Examining the unsteady expansion equation (Equation 2), it can be seen that an unsteady expansion is a function of velocity (V 2 and V 7 ), sound speed (a 2 ), pressure (p 2 and p 7 ), and specific heat ratio (γ 2 ), and in terms of post-shock shock tube variables, none of them show a large variation over the 10 90% He diluent range shown. It appears that overall the unsteady expansion is not sensitive to any of the changes seen in the figure, and the performance remains very similar for every amount of diluent. V 7 = V 2 + 2a 2 γ ( p2 p 7 ) γ 2 1 2γ 2 (2) Figure 4(c) shows how the composition of the shocked gas in the shock tube at equilibrium changes with differing amounts of helium diluent. The blue curve shows the percentage of H 2 that has been dissociated with that amount of diluent, with 0 corresponding to no dissociation, and 1 corresponding to all the H 2 being dissociated. It is important to examine the dissociation in the shock tube because while the equilibrium assumptions used in PITOT indicate that the dissociated shock tube gas will have recombined fully by the time it exits the acceleration tube for all conditions, this would be difficult to quantify in practice, so it is a parameter that should be minimised. It can be seen in the figure that with 10% helium diluent less than 5% of the H 2 is dissociated in the shock tube, and with 90% helium diluent less than 5% of the H 2 is not dissociated in the shock tube. It can also be seen that the amount of dissociation in the shock tube starts to increase rapidly above around 40 50% helium diluent. Figure 5 shows how a differing amount of helium diluent affects the gas flow in the test section. Figure 5(a) shows how differing diluent affects the temperature along the stagnation streamline over the test model for both frozen and equilibrium flow. Figure 5(b) shows how the species in the shock layer at equilibrium change as the amount of helium diluent increases. In Figure 5(a) it can be seen that the temperature behind both the frozen and equilibrium normal shock waves increase fairly linearly with the amount of helium diluent. The frozen temperature ranges from 13,400 K with 10% He diluent to 29,000 K with 90% He diluent. The equilibrium temperature increases from 3,500 to 14,300 K over the same range. To understand what this means practically, it is useful to compare these numbers to proposed gas giant entries. Looking at the first Uranus entry point investigated by Palmer et al [23] (ρ = 2.04e-5 kg/m 3, T = K, U = 22,503 m/s) a CEA calculation performed by the authors gave an equilibrium temperature behind the shock wave of 5,700 K. This temperature could be recreated with a 35 36% helium fraction in the test gas. Looking at the first Saturn entry point investigated by Palmer et al [23] (ρ = 1.80e-5 kg/m 3, T = K, U = 26,316 m/s) a CEA calculation performed by the authors gave an equilibrium temperature behind the shock wave of 8,700 K. This temperature could be recreated with a 49 50% helium fraction in the test gas. It should be noted that the theoretical freestream density of the expansion tube conditions (4.30e e- 5 kg/m 3 ) are of the same order of magnitude as the freestream density of the entry trajectory points (2.04e-5 kg/m 3 and 1.80e-5 kg/m 3 ), so thermochemical relaxation would be expected to be similar for both the experiments and the actual entries. Figure 5(b) shows how the composition of the shocked test gas along the stagnation streamline at equilibrium

7 #++ )) ) )( ) -. /0 1 & ' ( ) " #$%" -.2 * * & ' ( ) " #$%" * + *,* & ' ( ) " #$%" 3 & ' ( ) " #$%" Figure 4. How a differing percentage of helium diluent (by volume) affects the test conditions. a) shows how it affects the test gas gas properties. b) shows how it affects the performance of the conditions. c) How it affects various shock tube variables, and d) How it affects the composition of the shocked test gas at equilibrium. All values are normalised by the results for 10% He (by volume). changes with differing amounts of helium diluent. The mole fractions of various species at equilibrium are shown (H 2, H, He, H+, e-, He+) as well as the percentage of H 2 that is dissociated and then the percentage of H that is ionised. (0 corresponds to no dissociation or ionisation, and 1 corresponds to full dissociation or ionisation.) As the percentage of helium increases it can be seen that levels of dissociation continue to rise until around 30% He where all of the hydrogen molecules in the flow-field are dissociated and ionisation begins. It can be seen that with a helium fraction of above around 80% it is expected that all of the hydrogen atoms in the flow-field will be ionised at equilibrium. 5. CONCLUSIONS This paper has shown theoretically that experiments to simulate a proposed 22.3 km/s Uranus entry could be performed in the X2 expansion at the University of Queensland using the true gas composition of the atmospheric entry if a secondary driver section was used, or with a higher amount of helium diluent (35 36%) if a secondary driver section was not used. The paper also showed that a proposed 26.9 km/s Saturn entry could be simulated in the X2 expansion tube without a secondary driver section if an even higher amount of helium diluent was used (49 50%). This theoretical analysis will be examined experimentally over the coming months. REFERENCES Overall, Figure 5 shows the full extent of what is possible with the Stalker substitution. Figure 5(a) shows how by increasing the amount of He diluent in the flowfield an approximately 19km/s flight equivalent velocity flow condition can be used to simulate the shock layers of Uranus entry at 22.5 km/s or Saturn entry at 26.3 km/s, while still having the ability to increase the helium fraction further to allow hotter shock layers to be simulated. Figure 5(b) shows how over the full range from 10 90% the test condition can simulate everything from a shock layer where at equilibrium the hydrogen molecules in the flow-field are not fully dissociated to a shock layer where at equilibrium all of the hydrogen in the flow-field is dissociated and ionised. [1] F.S. Milos. Galileo probe heat shield ablation experiment. Journal of Spacecraft and Rockets, 34: , [2] R.N. Talley. Galileo Probe Deceleration Module Final Report. Re-Entry Systems Operations, General Electric Co., Rept. 84SDS2020, January [3] J.H. Lundell. Spallation of the galileo probe heat shield. In AIAA Paper , June [4] C. Park and A. Balakrishnan. Ablation of galileo probe heat-shield models in a ballistic range. AIAA Journal, 23: , [5] C. Park. Calculation of radiation from argon shock

8 -. %/ '0 (0 0 (0 0 ( " " " "+, "+ "## "# ' ( ) * "#$%& ' ( ) * "#$%& Figure 5. How a differing percentage of helium diluent (by volume) affects the gas properties of the gas along the stagnation line over the test model. a) shows the temperature behind the shock along the stagnation line for both frozen and equilibrium flow, and b) shows what is in the stagnation streamline gas at equilibrium. The Uranus and Saturn entry temperatures in a) were calculated using the first values in Tables 4 and 8 in the work of Palmer et al [23] and a CEA normal shock calculation performed by the authors. layers. Journal of Quantitative Spectroscopy and Radiative Transfer, 28:29 40, [6] C. Park, J.H. Lundell, M.J. Green, W. Winovich, and M.A. Covington. Ablation of carbonaceous materials in a hydrogen-helium arcjet flow. AIAA Journal, 22: , [7] S. Matsuyama, N. Ohnishi, A. Sasoh, and K. Sawada. Numerical simulation of galileo probe entry flowfield with radiation and ablation. Journal of Thermophysics and Heat Transfer, 19:28 35, [8] C. Park. Stagnation-region heating environment of the galileo probe. Journal of Thermophysics and Heat Transfer, 23: , [9] W.B. Hubbard. Ice giants decadal study. In Vision and Voyages for Planetary Science in the Decade , pages National Academy Press, Washington, D.C., [10] T. R. Spilker. Saturn atmospheric entry probe trade study. In Vision and Voyages for Planetary Science in the Decade , pages National Academy Press, Washington, D.C., [11] T. R. Spilker. Saturn atmospheric entry probe mission study. In Vision and Voyages for Planetary Science in the Decade , pages National Academy Press, Washington, D.C., [12] R.J. Stalker. Isentropic compression of shock tube driver gas. ARS Journal, 30:564, [13] R.G. Morgan. A review of the use of expansion tubes for creating superorbital flows. In AIAA 35th Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 6-10, [14] E.L. Resler and D.E. Boxsom. Very high mach number principles by unsteady flow principle. Cornell University Graduate School of Aerodynamic Engineering, [15] U.A. Sheikh, R.G. Morgan, F. Zander, T.N. Eichmann, and T.J. McIntyre. Vacuum ultraviolet emission spectroscopy system for superorbital reentries. In 18th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Tours, France, [16] T.N. Eichmann. Radiation Measurements in a Simulated Mars Atmosphere. PhD thesis, the University of Queensland, St. Lucia, Australia, [17] F. Zander, R.G. Morgan, U.A. Sheikh, Buttsworth. D.R., and P.R. Teakle. Hot-wall reentry testing in hypersonic impulse facilities. AIAA Journal, 51: , [18] D.E Gildfind, R.G. Morgan, M. McGilvray, P.A. Jacobs, R.J. Stalker, and T.N. Eichmann. Free-piston driver optimisation for simulation of high mach number scramjet flow conditions. Shock Waves, 21: , [19] P.A. Jacobs. L1d: A computer program for the simulation of transient-flow facilities. Report 1/99. Department of Mechanical Engineering, University of Queensland, Australia, [20] C.M. James, D.E. Gildfind, R.G. Morgan, P.A. Jacobs, and F. Zander. Designing and simulating high enthalpy expansion tube conditions. In 2013 Asia-Pacific International Symposium on Aerospace Technology, Takamatsu, Japan, [21] D.J. McBride and G. Gordan. Computer Program for Calculations of Complex Chemical Equilibrium Compositions and Applications II. Users Manual and Program Description. Nasa Lewis Research Center, Cleveland, OH, U.S.A., [22] B. Conrath, D. Gautier, R. Hanel, G. Lindal, and A. Marten. The helium abundance of uranus from voyager measurements. Journal of Geophysical Research, 92:15,003 15,010, [23] G. Palmer, D. Prabhu, and B.A. Cruden. Aeroheating uncertainties in uranus and saturn entries by the monte carlo method. Journal of Spacecraft and Rockets, 51: , [24] R.J. Stalker and B.P. Edwards. Hypersonic bluntbody flows in hydrogen-neon mixtures. Journal of Spacecraft and Rockets, 35: , 1998.