NOMENCLATURE

I

Current

V

Applied voltage

R

Resistance

k

Thermal conductivity of material

dT/dr

Temperature gradient in the radial direction

A

Area of heat application

h

Convective heat transfer coefficient

T

Surface temperature

$T_\infty $

Ambient temperature

$ \rho $

Density

$ c_p $

Specific heat capacity

$ \varepsilon $

Emissivity

$ \sigma $

Stefan-Boltzmann Constant

dr

Arbitrary radius

$ A_{cs} $

Cross-sectional area

$ \mu $

Resistivity

q(r)

Net flux

$ Q_{max} $

Maximum heat intensity

$ Q_{Net} $

Net heat flux

2.0 OVERVIEW

Reliable heat-shielding is essential, physical re-entry processes are complicated, experiments are needed to support model development and hypersonic impulse facilities cannot perform ablation tasks if cold-walled. The aim of the current work is to achieve high thermal and aerodynamic performance at lower cost. The Next-Generation Experimental Model (NGEM) presented in this work is very similar to the European standard probe but comes with six degrees of freedom to account for the variable angle-of-attack for better manoeuvrability during re-entry, descent and landing. This increased operational capability represents a milestone achieved by the NGEM. Recent experiments based on Orion re-entry conditions used a surface temperature of about 2800K [Reference Glass24] and the Apollo 4 lunar return speed of 11 km/s reportedly resulted in a surface temperature of about 2400K [Reference Dec and Braun25], while typical re-entry surface temperatures for Space Shuttles were about 1740K [Reference Glass24]. The author had previously used the new plasma preheating test device to achieve a surface temperature of about 2500K on a preheated graphite surface [Reference Iyinomen26]; the surface temperature profile was then used to assess the mass loss through ablation in a Mach 4.5 flow [Reference Iyinomen27]. The use of this invention as a means of heating the disk has been proven to be effective for reaching temperatures of this magnitude [Reference Iyinomen, Malpress and Buttsworth28], and the process has potential to be used more widely for ablation experiments [Reference Iyinomen29]. This innovative research work makes a significant contribution to hot-wall testing of carbon-based materials for ablation and re-entry studies in hypersonic impulse facilities.

The aim of the present work is to improve the setup for generating the plasma to enable the components to tolerate higher temperatures and improve the aerothermodynamic capability of future experimental programs. The advantages associated with the new plasma preheating technique include (1) the light weight and portability of the model, (2) the control over the surface temperature to replicate re-entry conditions, (3) the excellent temperature profile across the surface of the sample, (4) the ability to replicate entries for different planetary missions due to its capability to perform well in all types of re-entry gases such as O₂, N₂, Air, CO₂, He, Ne, Ar, H₂, CH₄, NH₃, etc.; (5) the ability to be applied to different types of heatshield materials such as PICA, SIRCA, Avecoats, C/C composites, graphite, etc.; (6) the ability to be used for different axisymmetric probe geometries such as Stardust, Orion, Hayabusa, SpaceX-dragon, etc.; (7) the ability to perform well in both short- and long-duration wind tunnels; and (8) its highly economical nature, as the operational costs are less than 10% of those of running the high-enthalpy plasmatron and NASA Ames arc-jet facilities. In addition to the above-mentioned advantages, this present work optimised the aerothermodynamic efficiency for future experimental tests and can now generate stagnation point temperatures above 3000K. The two major improvements associated with the NGEM are: (a) a reduction of the heat losses via conduction on the heatshield sample by incorporating a thermal barrier between the test sample and the backshell, and (b) the incorporation of six degrees of freedom to account for variable angle of attacks for better manoeuvrability during re-entry, descent and landing. These modifications enable the NGEM to be smarter and more practically replicate real flight vehicles, as shown in Fig. 3.

Figure 3. Sectional view showing improved operational capabilities for the NGEM (see Appendixes for details).

4.0 ESTIMATING POWER REQUIREMENTS

The heat flux has a direct correlation with the surface temperature, which follows a Gaussian distribution from the stagnation point to the edges [Reference Bag and De45]. As shown in Fig. 6, the method consists of splitting a heatshield sample along the axisymmetric plane (OA) and measuring the heat flux to one of the edges as a function of radius (r) relative to the splitting plane. The radial heat distribution can then be derived using Abel transformation of the heat flux measurements [Reference Tsai and Eagar46].

Figure 6. Schematic heat flux domain with boundary conditions in the plasma preheating test device.

4.2. Governing heat equation

An analytical method was used to estimate the power requirements for preheating the samples. For this analysis, electrical power is the dominant source of energy input. The governing heat equation for the heatshield material sample is given by Equation (1).

(1) $$\matrix{ {Rate\;of\;energy\;input = thermal\;energy\;transfer + thermal\;energy\;storage} \hfill \cr } $$

(2) $$\matrix{ {\therefore\;Electrical\;power = \;thermal\;\left[ {conduction + convection + radiation} \right] + energy\;storage} \hfill \cr } $$

(3) \begin{align}{I^2}R = {\textrm{}}\overbrace {{\delta \over {\delta r}}{\textrm{}}k{\textrm{}}{{dT} \over {dr}}}^{Conduction} + {\textrm{}}\overbrace {A{\textrm{}}h{\textrm{}}\left( {T - {\textrm{}}{T_\infty }} \right)}^{Convection} + {\textrm{}}\overbrace {A\varepsilon \sigma \left( {{T^4} - {\textrm{}}T_\infty ^4} \right)}^{Radiation} + \overbrace {\rho {c_p}{{dT} \over {dt}}}^{Storage}\end{align}

where I represents the current rating, $R$ is the resistance of specimen, k is the thermal conductivity of the material, $\;\frac{{dT}}{{dr}}$ is the temperature gradient in the radial direction, A is the area of heat application, h is the convective heat transfer coefficient, T is the surface temperature, ${T_\infty }$ is the ambient temperature, $\rho $ is the density of the material sample and ${c_p}$ is the specific heat capacity of the material sample. Conductive heat transfer from the disk to the backshell can be neglected due to thermal barrier/insulation. The convective heat transfer can also be neglected due to the vacuum conditions as the convective heat transfer coefficient approaches zero prior to flow. Also prior to flow, the heatshield material is thermally soaked and a steady-state condition is achieved as $\frac{{dT}}{{dt}}$ approaches zero. Hence, Equation (3) reduces to Equation (4). This approximation is reasonable because, at temperatures in excess of 2000K, the conductive and radiative heat transfers become increasingly negligible compared with radiative heat transfer.

(4) \begin{align}{I^2}R = \overbrace {A\varepsilon \sigma \left( {{T^4} - T_\infty ^4} \right)}^{Radiation}\end{align}

Considering a disk of arbitrary radius $dr$ and uniform cross-sectional area ${A_{cs}}$ with resistivity $\mu $ , the electrical resistance is given by Equation (5):

(5) $$\matrix{ {R = \;\mu {{dr} \over {{A_{cs}}}} = \;\mu {{dr} \over {\pi {r^2}}}\;} \hfill \cr } $$

The surface temperature of the sample can then be estimated based on radiative heating from the plasma. Equating the total electrical power to the radiative heating, where the source of heat flux for the heatshield is the plasma inside the probe, yields Equation (6), where $I$ is the current, R is the resistance of material sample, $\varepsilon $ is the emissivity of the sample material, $\;A$ is the total surface area of sample being exposed, $\sigma $ is the Stefan–Boltzmann constant and T is the surface temperature.

(6) $${{I^2}R = \;A\varepsilon \sigma \left( {{T^4} - \;T_\infty ^4} \right)\;}$$

Taking A to be $2\pi {r^2}$ for the front and back side of the disk and substituting the value for R in Equations (5) into (6), it can be shown that the temperature T is given by Equation (7):

(7) $$\matrix{ {T = \;{{\left[ {{I^2}\mu {{dr} \over {2{\pi ^2}\varepsilon \sigma {r^4}}}\; + T_\infty ^4\;} \right]}^{0.25}}} \hfill \cr } $$

Similarly, the temperature variation with radius of the Orion sample can be calculated by substituting $\pi \left( {{d^2}r + \;{h^2}} \right)$ for the front surface area, where h is the maximum height of the spherical cap perpendicular to the base. Also, the surface area of the stardust geometry can be obtained from literature. This simple One-Dimensional (1-D) analysis appeared to be reasonable for estimation purposes because it showed good correlation to calibrated data. Figure 7 shows the surface temperatures estimated using Equation (7), and by substituting $28\; \times {10^{ - 4}}$ Ohm.m for electrical resistivity, 0.9 for emissivity $\;and\;{5.68^{ - 8}}$ W/m⁴K for the Stefan–Boltzmann constant, the non-linear relation between the current rating and surface temperature is shown in Fig. 7, which is the average power requirement for all three sample. The heating started from ambient temperature ( ${T_\infty }$ ) and shows good agreement with calibrated data. Temperature calibration was carried out using currents of 200A, 250A, 300A, 350A and 400A. The calibration was limited to a maximum current of 400A during preliminary tests because of the limitations in the material thermal capabilities [Reference Iyinomen, Malpress and Buttsworth28]. With the present material selection as presented in Table 2 for the experimental model, a current of 600A can be practically applied to achieve stagnation point temperatures in excess of 3000K.

Figure 7. Average power requirements for preheating surface temperatures.

The present work adopts heatshields of constant thickness of 2 mm, considered suitable for ablation experiments. Using graphite material and a current rating of 400A, it took about 15s for the plain disk sample to attain steady state. The present work is designed for a current rating of 600A. Using this current and invoking the graphite material properties from Table 1 in a Finite-Element Analysis (FEA) simulation using Ansys, it took about 8s for the samples to attain steady-state temperatures, as shown in Fig. 8. The apparatus development for the new preheating methodology, the camera and spectrometer calibration, and the FEA simulations show that the determined temperature profile of the heated disc is suitable to continue with mass loss assessments [Reference Iyinomen, Malpress and Buttsworth28]. This work focuses on ground-based characterisation techniques for thermal protection material analysis, thus making it a valuable tool for to study aerothermodynamics during re-entry. The presented technology is useful for detailed material characterisation, for example, in the context of material response model validation.

Figure 8. Transient simulation of stagnation surface temperatures with heatshields of 2mm thickness.

4.3. Abel’s transformation for heat flux distributions

Suppose that ( ${y_1},\;{y_2}$ ) are linearly independent solutions of a homogeneous second-order differential equation given by Equation (8) on ( $a,\;b$ ), where $A\left( x \right),\;B\left( x \right)$ are continuous on ( $a,\;b$ ), then the round scheme $W\left( x \right)$ is either always zero on ( $a,\;b$ ) or never zero on ( $a,\;b$ ). For $x\; \in \left( {a,b} \right)$ , this can be mathematically analysed as follows:

(8) \begin{align}y'' + A\left( x \right)y' + B\left( x \right)y = 0\end{align}

(9) $$\matrix{ {{\rm{Set \,}}{\mkern 1mu} W = W\left( {{y_1},\;{y_2}} \right) = \;\left| {\matrix{ {{y_1}} & {{y_2}} \cr {y_1^\prime } & {y_2^\prime } \cr } } \right| = \;{y_1}y_2^\prime - {y_{\rm{2}}}y_1^\prime } \hfill \cr } $$

Differentiating Equation (9) using the product rule produces Equation (10)

(10) $$\matrix{ \therefore{{W^\prime } = \left[ {{y_1}y_2^{\prime \prime } + \;y_2^\prime y_1^\prime } \right] - \;\left[ {{y_2}y_1^{\prime \prime } + \;y_1^\prime y_2^\prime } \right] = \;{y_1}y_2^{\prime \prime } - \;{y_2}y_1^{\prime \prime }\;} \hfill \cr } $$

Since ( ${y_1},\;{y_2}$ ) are solutions, they can independently fit into Equation (8), resulting in

(11) $$\matrix{ {{y_1}^{\prime \prime } + A\left( x \right){y_1}^\prime + B\left( x \right){y_1} = 0\;} \hfill \cr } $$

(12) $$\matrix{ { \to \;{y_1}^{\prime \prime } = - A\left( x \right){y_1}^\prime - B\left( x \right){y_1}} \hfill \cr } $$

Also,

(13) $$\matrix{ {{y_2}^{\prime \prime } = - A\left( x \right){y_2}^\prime - B\left( x \right){y_2}} \hfill \cr } $$

Substituting the expressions for ${y_1}^{\prime\prime}$ and ${y_2}^{\prime\prime}$ in Equation (12) and Equation (13) into the Right-Hand Side (RHS) of Equation (10) gives

(14) $$\matrix{ {W' = {y_1}\left[ { - A\left( x \right){y_2}^\prime - B\left( x \right){y_2}} \right] - \;{y_2}\left[ { - A\left( x \right){y_1}^\prime - B\left( x \right){y_1}} \right]\; = A\left( x \right){y_2}y_1^\prime - \;A\left( x \right){y_1}y_2^\prime } \hfill \cr } $$

(15) $$\therefore{W' = A\left( x \right){y_2}y_1^\prime - \;A\left( x \right){y_1}y_2^\prime = A\left( x \right)\left( {{y_2}y_1^\prime - \;{y_1}y_2^\prime } \right) = A\left( x \right)\left( { - W} \right)}$$

(16) $$\matrix{ { \to {{dW} \over {dx}} = \; - A\left( x \right)\left( W \right) \to \;{{dW} \over W}\; = \; - A\left( x \right)dx} \hfill \cr } $$

Integrating both sides of Equation (16) will produce Equation (17), where C is the constant of integration:

(17) \begin{align}\ln W = - \mathop \smallint \nolimits_{{x_0}}^x A\left( x \right)dx + C \end{align}

Taking the exponential of both sides of Equation (17) yields

\begin{align*}W = \; ex{p^{ - \mathop \smallint \nolimits_{{x_0}}^x A\left( x \right)dx}} + \; ex{p^C} = \; ex{p^{ - C\mathop \smallint \nolimits_{{x_0}}^x A\left( x \right)dx}} = Cex{p^{ - \mathop \smallint \nolimits_{{x_0}}^x A\left( x \right)dx}} \; \end{align*}

Hence,

(18) \begin{align}W\left( r \right) = \; W\left( {{r_0}} \right)ex{p^{ - \mathop \smallint \nolimits_{{r_0}}^r A\left( r \right)dr}}\end{align}

Equation (18) shows the initial boundary conditions, where the constant C represents $W\left( {{r_0}} \right)$ . If C is zero, then the whole expression for $W\left( r \right)$ will be zero. Alternatively, if C is not zero, then the whole expression for W(r) can never be zero because the value of an exponential function does not reach zero. The distribution of the net heat flux reaching the heatshield is taken to be a Gaussian distribution, where the net flux falls onto an area of heat application of a given radius (AB), as shown in Fig. 6. The spatial variation of the net flux, q(r), falling onto a workpiece from the arc source as a function of the (heat) flux distribution parameter in the radial direction, r, had similarly been reported by Goldak et al. [Reference Goldak, Chakravarti and Bibby47], as presented by Arul and Sellamuthu [Reference Arul and Sellamuthu48], where ${Q_{max}}$ is the maximum heat intensity for a stationary heat source.

(19) $$\matrix{ {{q_r} = \;{Q_{max}}ex{p^{ - \;\left[ {{{6{r^2}} \over {A{B^2}}}} \right]\;}}} \hfill \cr } $$

The arc efficiency is expressed as $\mu = \;\frac{{{Q_{Net}}}}{{I \times V}}$ , where ${Q_{Net}}$ is the net heat flux, I is the current and V is the applied voltage. The arc length is the primary parameter governing the heat distributions, while the current dominates the magnitude of the heat flux on the anode surface [Reference Tsai and Eagar46].

5.0 PREHEATING TIME VERSUS THICKNESS OF HEATSHIELD SAMPLES

Simulations from other work have shown that the time required to reach steady state became longer as the heatshield thickness increased, as shown in Fig. 9. The time evolution of the heatshield thickness along the stagnation line was investigated through numerical simulations, where ${n_{solid}}$ is the heatshield thickness (0.05, 0.1 and 0.2m), Rn is a constant nose radius of 1m, and t is the heating time in seconds. Using constant heating, the 0.05m sample (red line) attained a steady-state condition at about 450s, the 0.1m sample (green line) attained steady state at about 1100s and finally the 0.2m sample (blue line) attained its steady state at about 1500s.

Figure 9. Ablation of graphite in dissociating air with different thicknesses [Reference Scala49].

Figure 10. Temperature contours of selected heatshield samples from FEA simulations showing heatshield thermal spread for the NGEM at no-flow conditions.

Figure 11. Spatial temperature profiles showing heatshield thermal spread [Reference Iyinomen, Malpress and Buttsworth28].

The decision about the thickness should be properly considered to balance the preheating costs and the aerodynamic loads. Although thinner samples save time and operational costs, the aerodynamic loading on a sample supported around the edges with a very small thickness will likely be too high, and the sample will break, thereby rendering the experiments useless. The thermal expansion loads needed to maintain electrical conductivity between the heatshield and electrode, unavoidable aerodynamic forces and other constraints resulting from holding the samples will exacerbate any potential for failure of the specimens.

6.0 SIMULATION RESULTS FROM PLASMA PREHEATING

The temperature contours displayed in Fig. 10 show that the thermal distribution was highly axisymmetric with minimal edge effects. The temperature distributions of the experimental probes were simulated using Three-Dimensional (3D) FEA with Ansys. The simulation was for no-flow, and the heat flux inputs were tuned to produce the surface temperatures at 600A current rating. For the computational setup, the grid resolution was smooth and the meshing adaptive. The boundary conditions were mainly applied to the heatshield samples, and the heat gradually flowed towards the surrounding materials. The simulation results correspond to a heating duration of 10s. Although steady-state conditions were attained at about 8s, the additional preheating time provided room for any noticeable thermal soak after the solution reached steady state. As the solutions run beyond 8s, additional thermal soak was not really an issue in the present work (Fig. 8). The surface temperatures of the samples exceeded 3000K at the stagnation point, decreasing non-linearly from the stagnation point to about 2600K at the edges, as shown in Fig. 11.

Figure 10 shows the temperature contour from the FEA simulation using Ansys Workbench. The contact regions in the present work have been designed to minimise conduction losses at the heatshield edges (shoulder regions) using a thermal barrier material (zirconia). The improvement of the surface temperature profile in the present work can be seen in Fig. 11. For the present work, Fig. 11 shows the surface temperature profile of a graphite heatshield at the stagnation point in excess of 3000K, gradually decreasing to about 2550K at the shoulder regions (points A and B). Beyond the shoulder regions a holding ring is in contact with the heatshield (points E and F), where the temperature first experiences a drastic drop (to about 1500K) due to the low conductivity across the contact and the high thermal diffusivity of metallic material, and further experiences a thermal drop to about 1300K on surfaces in contact with the environment (points G and H). Details regarding the spatial temperature profiles have been exhaustively published by the author [Reference Iyinomen, Malpress and Buttsworth28,Reference Iyinomen29].

7.0 SPATIAL TEMPERATURE DISTRIBUTION

Axisymmetric heatshield samples must have a good temperature distribution for accurate aerothermodynamics quantification of ablation rates in hypersonic impulse facilities. One of the fascinating advantages of this new plasma preheating technique is the surface temperature control of the ablation sample in a hypersonic flow field. The surface temperatures can be regulated to replicate re-entry requirements in hypersonic impulse facilities. Due to the strong coupling between surface temperatures and boundary-layer species, the surface temperature profile needs to be well established to be able to reflect the boundary-layer characteristics. Figure 12 shows the temperature contours of a 50mm-diameter axisymmetric heatshield sample predicted using MATLAB Simulink. The thermal spread efficiency is a very important aspect of surface temperature control. The top left of Fig. 12 shows a very poor temperature distribution from the stagnation point to the edges. At the top right, the spatial temperature distributions of the axisymmetric heatshield sample are improved but still show a poor profile from the stagnation point to the edges. The temperature profile is further improved at the bottom left, and finally, the bottom right image shows a very good temperature profile across the disk because of the good thermal spread efficiency from the stagnation point to the edges. It is interesting to note that all four images in Fig. 12 have the same temperature of about 3100K at the stagnation point. Obtaining a good stagnation point temperature without reference to the overall surface temperature profile will be completely unreliable for any re-entry aerothermodynamics studies. A good surface temperature coupled with aerodynamic pressure, oxidiser composition, flow strain rate (as functions of model shape and amount of burn-off) and material properties always results in a good boundary-layer characteristic due to the strong coupling between the gaseous and surface kinetics.

Figure 12. Temperature distributions of axisymmetric heatshields (viewing normal to the surface).

8.0 PHYSICAL EXPLANATIONS

The CFD results using an axisymmetric graphite sample showed a good temperature distribution for ablation rate experiments in hypersonic impulse facilities. Figure 13 illustrates the flow dynamics and associated aerothermodynamic gradient along the surface, where the source of heat flux for the heatshield is the plasma inside the probe. The temperature is driven by the plasma at the back side of the experimental sample, while the aerodynamic flow is driven by the forced convection from the hypersonic impulse facility at the front side of sample (heatshield specimen). The aerodynamic flow velocity at the surface of the experimental sample increases from the stagnation point to the edges, while the surface temperature decreases from the stagnation point to the edges.

Figure 13. Schematic illustration of surface aerothermodynamic flow properties.

While the aerothermodynamic flow (cooling of sample) occurs at the front, the plasmadynamic flow (heating of sample) occurs at the back side of the disk. The plasma zone is a term used to describe the region occupied by the plasma. At steady-state condition, the inert gas flows through the shroud, gains some heat energy from the centralised hot tungsten electrode, then experiences a drastic rise in enthalpy as it passes through the hot plasma towards the heatshield, before finally exiting via the exhaust/vent.

Some preliminary experiments were carried out to validate this novel plasma preheating test device. A 50mm disk sample was heated with plasma in a vacuum of 500Pa, then the hot sample was subjected to Mach 4.5 flow for 0.5s, as shown in Fig. 14(a). The Schlieren technique based on the principle of the changing density of the gas was used to identify the establishment of the bow shock and therefore the commencement of Mach 4.5 flow. The high-speed camera was set at a frame rate of 2500fps. Detailed numerical analyses have been provided extensively by the author in other publications [Reference Iyinomen26–Reference Iyinomen29], where the ablation rate gradually decreased from the stagnation point to the edges of the disk. CO formation was the major contributor to graphite mass loss, while the contributions from all other carbonaceous species were relatively insignificant. All carbonaceous species shoed peak values around the stagnation region at the wall. The sample data from simulations using Stardust and Orion MPCV show general agreements with that of the disk. Due to the good thermal coupling between the surface and the flow, the present work has potential to be a better analytical/experimental research tool for simulating reaction species for different planetary missions.

Figure 14. Preliminary experiments conducted at Mach 4.5 to validate plasma preheating invention [Reference Iyinomen26,Reference Iyinomen, Malpress and Buttsworth28].

9.0 FUTURE WORK

This novel invention can accurately replicate planetary re-entry surface temperatures and any associated hypersonic flow characteristics within the boundary layer. The NGEM has been fully developed for series of ablation tests in any reliable aerospace laboratory. The fact that the NGEM can replicate surface temperatures in excess of 3000K, will encourage the use of spectroscopic measurements of ablation species and spatial microstructural studies using X-ray microtomography. Infrared pyrometers and thermo-cameras are also needed to adequately monitor the surface temperature profiles across experimental samples.