Development and Testing of an Ablation Model Based on Plasma Wind Tunnel Experiments Alessandro Turchi∗, Bernd Helber†, Alessandro Munaf`o‡, Thierry E. Magin§ von Karman Institute for Fluid Dynamics, Rhode-Saint-Gen`ese, Belgium,1640 Ablative materials are extensively used in several aerospace applications. Their employ as heat shield for re-entry capsules enables to survive re-entry conditions that would be otherwise unfeasible. The coupled experimental-numerical work is fundamental to grow the understanding of their behavior in operative conditions. This work deals with the development and testing of an ablation model able to reproduce the stagnation-point gas-surface interaction over non-charring carbon-based ablative materials. Numerical tools, specifically developed at the von Karman Institute for Fluid Dynamics for re-entry application studies, are used together in the analysis to obtain relevant quantities as the stagnationpoint surface mass blowing rate and temperature. Data from the experiments performed in the von Karman Institute Plasmatron in both air and nitrogen environment are used to compare with the numerical results and to tailor the ablation model. Test results in nitrogen environment prove that active surface nitridation takes place, and a proper nitridation reaction probability is extracted from the tests using the developed model with a reverse approach. Comparisons with the measured surface temperatures suggest that additional surface phenomena can occur in the low cold-wall heat flux tests. Surface nitrogen recombination, identified as one of these possible mechanisms, is analyzed.
Nomenclature ρ E H h p Q u ud v M R ω˙ m ˙ q˙cond q˙rad
= = = = = = = = = = = = = = =
density, kg/m3 total energy, J/kg total enthalpy, J/kg static enthalpy, J/kg pressure, Pa radial component of molecular flux vector, W/m2 radial velocity, m/s radial diffusive velocity, m/s circumferential velocity, m/s molecular mass, kg/mol universal gas constant, 8.314 kJ/(mol K) surface source term, kg/(m2 s) mass blowing rate, kg/(m2 s) solid conduction, W/m2 radiative heat flux, W/m2
∗ Postdoctoral
Fellow, Aeronautics and Aerospace Department, Chauss´ ee de Waterloo 72, AIAA Member;
[email protected]. Candidate, Aeronautics and Aerospace Department, Chauss´ ee de Waterloo 72, AIAA Student Member;
[email protected] ‡ Ph.D. Candidate, Aeronautics and Aerospace Department, Chauss´ ee de Waterloo 72, AIAA Student Member; currently Postdoctoral Fellow, Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, 306 Talbot Lab, 104 S. Wright St. Urbana, IL 61801, US;
[email protected]. § Associate Professor, Aeronautics and Aerospace Department, Chauss´ ee de Waterloo 72, AIAA Member;
[email protected]. † Ph.D.
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s˙ γ λ Fd F S U σ τ θ ε A k
= = = = = = = = = = = = =
recession velocity, m/s reaction probability thermal conductivity, W/(m K) viscous flux vector inviscid flux vector source term vector conservative variable vector Stefan-Boltzmann constant, 5.670 373 × 10−8 W/(m2 K4 ) viscous stress tensor, N/m2 polar angle, rad integral emissivity area, m2 reaction ve
Ns r T t
locity, m/s = number of species = radial distance, m = temperature, K = time, s
Subscripts b i s w
= = = =
material backside surface species solid material gas-surface interface
Superscripts r
= reaction
I.
Introduction
During the last decades, space agencies have sent landers to the Moon, Mars, and Venus, as well as atmospheric probes to Jupiter, Venus, and Titan. When entering a planetary atmosphere, these probes need to be protected from the extremely harsh conditions characterized by high temperature and high heat flux. Thermal protection system (TPS) materials are used to build the heat shield that protects the vital structure from the severe heating encountered during hypersonic flight through a planetary atmosphere. The TPS is a single point-of-failure subsystem. It is critical and its performance needs to be validated through ground tests and analyses. For present and future space exploration missions, TPS can be mission enabling, significantly impacting the launch mass or scientific and instrumental payload. Therefore, it is of fundamental importance to advance the development, design, and analysis of TPS materials. The von Karman Institute (VKI) Plasmatron is a state-of-the-art inductively coupled plasma (ICP) torch.1, 2 The facility was developed during the 90s to fulfill the need of specific tools for the development and testing of new TPS within Europe. As the gas is heated by induction through a coil, one of the advantages of ICP torches, with respect to Arcjet facilities, is the high purity of the plasma flows produced thanks to the absence of electrodes and their associated erosion. This particular characteristic makes the ICP plasma generators a perfect facility for the study of the complex gas-surface interaction, such as ablation and catalysis, where the chemical interaction between the gaseous species, and the solid material constituents is the driving phenomenon and a precise control of the flow conditions is sought. For these reasons, several simulation campaigns took place at the VKI over the past years to advance the fundamental knowledge of ablation phenomena; ablation tests of several materials, from pure graphite to newer low-density pyrolyzing materials, have been carried out in air/nitrogen plasmas in the VKI Plasmatron.3, 4 The fully instrumented Plasmatron test chamber allows for the accurate monitoring of the freestream conditions during the tests, as well as the measurements of interesting quantities as sample recession rate, surface temperature, and spectrally resolved boundary-layer emission.5 These features make the data collected from the ablation experiments rather unique, generating a wide dataset for ablation model validations and updating.
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Recently, several numerical tools were developed at the VKI in order to be used in the investigation of reentry-related phenomena. A new thorough library (Mutation++ ) for the evaluation of thermal and transport properties of gas mixtures, and the calculation of both finite-rate gas-phase chemistry and homogeneous/heterogeneous gas/gas-solid equilibrium chemistry has been developed.6 Also, a stagnation-line code able to reproduce the flow along the stagnation line of spherical and cylindrical bodies, by solving the dimensionally reduced Navier-Stokes equations, has been developed.7 The approach, based on the local similarity of the stagnation-streamline area in the considered flow, simplifies the Navier-Stokes equations by reducing the number of the independent variables, ending up in a quasi-one-dimensional system that conserves the main physics of the original systems in a less computationally expensive framework.8 The modeling of the carbon-based ablative material behavior in the VKI Plasmatron environment is the goal of the present analysis. The common approaches for the macroscopic modeling of the TPS material are mainly of three different types. The first approach is based on the one- or multi-dimensional transient computation of the conduction inside the material.9 A lot of complexity can be added to the modeling if the accurate resolution of the processes taking place inside the material is sought.10 However, simplified boundary conditions are normally used for the gas–solid interface in this kind of approach.9 For instance, inviscid boundary-layer edge conditions are taken from separate simplified flowfield simulations, and the surface conditions (i.e., temperature or convective heat flux) are obtained by means of semi–empirical relations. In the second approach the surface ablation is treated using a dedicated boundary conditions in the CFD simulation of the flow field. This approach has been used extensively in a wide range of applications (i.e., heat shields, solid rocket nozzles, etc. . . ) to study both charring and non-charring materials using either equilibrium or finite-rate surface chemistry giving satisfactory results.11–17 The last, most complex, can be described in short as a combination of the previous two. It can be performed either by coupling together two distinct solvers designed to compute the solid- (first approach) and the gas-side (second approach) of the problem,18, 19 or by directly developing a unified numerical tool capable of computing the flow through the material accounting also for ablation of the material fibers from within.20 The latter, in particular, is very promising for the study of highly porous materials for which, under certain conditions, the hypothesis of a mere surface ablation is not accurate enough. In the present work, we focus on the second type of approach. The numerical tools developed in-house at the VKI, and introduced previously, are used here together with experimental data produced from the VKI Plasmatron experiments. The developing, the testing and the tailoring of the ablative boundary condition with the objective of a higher fidelity representation of the actual tests and material are discussed in detail in the analysis.
II.
Theoretical Modeling
The study of the carbon-based non-charring material behavior in plasma wind tunnel conditions is addressed in the present analysis by focusing on the gas-surface interface. In this section, the fluid governing equations and a simplified version of the solid-phase conservation equations are presented together with the interface balances that represent the link between the flow and the material side of the problem. A.
Stagnation-Line Fluid Governing Equations
The conservation form of the stagnation-line governing equations for spherically shaped blunt bodies can be obtained, as described in [8], by taking the following steps: i) perform a coordinate transformation to recast the original equations (written in the cartesian reference frame) in spherical coordinates originating in the ˆ θ) = φ(θ) ¯ φ(r)) iii) take the limit θ → 0. In the case body center ii) apply a separation of variables (i.e., φ(r, of thermal equilibrium and chemical non equilibrium flows these equations read: ∂U ∂F ∂Fd + − =S ∂t ∂r ∂r
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(1)
where the vectors of the conservative variables, the inviscid fluxes and the diffusive fluxes are: h iT U = i = 1, Ns ρi ρu ρv ρE h iT F = ρi u p + ρu2 ρuv ρuH h iT Fd = i = 1, Ns −ρi udi τrr τrθ τrr u − Q
(2) (3) (4)
The vectors in Eqs. (2)-(4) are unaltered with respect to the original system except that for: i) the variables ˆ θ), which depends only u, v, udi , τrr , and τrθ represent that part, φ(r), of the original generic variable, φ(r, on the radial distance from the spherical coordinate system origin ii) only the radial component of the viscous fluxes is considered because of the flow-field symmetry constraints taken in the ansatz derivation.8 The source term vector on the right-hand side of Eq. (1) contains, together with the chemical source terms, also the convective and diffusive metric terms arising from the transformation in spherical coordinates. The original derivation of the stagnation-line equations given in [8] assumed the Newtonian theory to express the pressure distribution around the body: p − p∞ =
1 ρ∞ u2∞ cos2 θ 2
(5)
As it is known this assumption provides a good approximation only in the case of hypersonic flows (Ma 1). However, the subsonic pressure distribution around a sphere derived from potential flow theory is: p − p∞ =
5 1 ρ∞ u2∞ (cos2 θ − sin2 θ) 2 4
(6)
Equation (6) reduces to Eq. (5) on the stagnation line (θ → 0). Therefore, Eq. (1) still holds in the case of subsonic flows. B.
Solid-Phase Governing Equations for Non-Charring Ablative Materials
When a non-pyrolyzing ablative material is exposed to the extreme conditions typical of a plasma wind tunnel experiment, or of an atmospheric re-entry, its surface can recede because of the interplay of several phenomena (e.g., thermo-chemical ablation, mechanical ablation, etc. . . ). The solid-phase energy conservation equation written in the reference frame fastened to material surface, moving at a constant speed s, ˙ reads:21 ∂ ∂ ∂Ts ∂ (ρs hs A) = Aλs + s˙ (ρs hs A) (7) ∂t ∂r ∂r ∂r where the terms represent, from left to right, the temporal variation of the material sensible energy, the conduction inside the material, and the convected energy due to the coordinate motion. By integrating Eq. (7) between the moving surface (w) and the backside surface (b) one can obtain the following closed expression for the steady-state solid conductive heat flux: ∂T q˙cond = λs = s˙ ρs (hsw − hsb ) (8) ∂r s in which the surface has been considered planar, the recession velocity constant, the material thick enough for the back surface to remain at the initial temperature, and both the solid density ρs and the solid thermal conductivity λs constant across the material. Hence, Eq. (8) states that if the considered material is thick enough, such that the temperature variation does not reach the backside surface, the temperature profile inside the material does not vary over the time in the moving coordinate system. C.
Gas-Solid Interface Governing Equations for Non-Charring Ablative Materials
In the case of non-pyrolyzing ablative materials, if one assumes that no material can be removed in a condensed phase, the species conservation equation written in the control volume limited to the thin lamina representing the gas-surface interface takes the form of a surface balance:22 (ρi u)w + ρi udi w = ω˙ iw i = 1, Ns (9) 4 of 18 American Institute of Aeronautics and Astronautics
where the species convective flux (ρi u), due to the non-zero surface velocity caused by the material recession that injects mass in the system (blowing), and the diffusive flux generated by the concentration gradient PN (ρi udi ) equate the source term due to all the surface reactions involving the ith species (ω˙ iw = i r ω˙ irw ). Equation (9) reduces to the well known catalytic balance in which the diffusive flux equates the homogeneous source term if no ablation occurs (zero blowing velocity). Since the surface heterogeneous reactions are the only responsible for the mass injections, summing up Eq. (9) over all the species in the mixture one obtains: (ρ u)w = m ˙s
(10)
PNs ˙ iw is the mass loss of the ablated material. that is the global surface mass balance, where m ˙s = i ω Similarly, the global energy conservation equation can be derived by writing the balance of the energy fluxes at the surface: Ns X ∂T λw − ˙ s hsw = (h ρ u)w + m ˙ s (hsw − hsb ) (11) hi ρi udi w + q˙radnet + m ∂r w i where the left-hand side contains the energy fluxes entering the surface because of the gas conduction, diffusion, radiation and surface material consumption; and on the right-hand side the exiting energy fluxes due to the gas blowing and the solid conduction are listed instead. Since no coupling with a material solver is considered at this stage, Eq. (8) has been used to express the solid conductive heat flux at steady state (note that s˙ = m ˙ s /ρs ). In the present formulation the gas radiative heat flux in Eq. (11) is neglected, since no coupling with a radiation code is performed. The material is assumed to have a constant integral emissivity (εs ) evaluated experimentally. Therefore, the net radiative heat flux can be expressed as: q˙radnet = q˙radin − q˙radout = −σεs Tw4
(12)
A set of surface reactions is needed to compute the surface source terms in Eq. (9) and evaluate the material consumption. If the surface reactions are assumed to be uncoupled and first order in reactant concentrations, the surface reaction velocity of each reaction is evaluated by multiplying the number flux of the reactant species arriving at the surface, given by the kinetic theory, by the probability of each reaction to take place:23 r γir 8 R Tw r ki = (13) 4 π Mi Reaction probabilities (γir ) are needed for both the ablative and the catalytic surface reactions. Data from [23] are used as baseline values for the ablative reactions in the present analysis. Two oxidation reaction (Cs + O → CO, and 2Cs + O2 → 2CO), one nitridation reaction (Cs + N → CN), and one sublimation reaction (3Cs → C3 ) are considered. The total mass blowing rate (m ˙ s ) can be evaluated by summing up the contributions of each of these reactions: ω˙ O 2ω˙ O2 ω˙ N ω˙ C3 m ˙s=m ˙ O+m ˙ O2 + m ˙ N+m ˙ subl = + + + MC (14) MO MO2 MN MC Further considerations on the baseline reaction set and its applicability for the present study will be given in section IV.
III.
Numerical Modeling
The VKI stagnation-line code was developed at the VKI by Munaf`o.7 In the solver, the spatial discretization of Eq. (1) is performed by means of a cell-centered finite volume method.24 The numerical convective fluxes are computed by means of a Roe’s approximate Riemann solver,25 using the linearization proposed in [26] to evaluate the Roe’s averaged state. Second order accuracy in space is achieved by using an upwind reconstruction to obtain the cell interface variables. The diffusive fluxes and source terms are both evaluated in terms of primitive variables: ρi , u, v, T . The value of the primitive variables and their gradients at the volume interface are computed by a weighted average and a central finite difference approximation, respectively. The cell center value of the primitive variables to be used in the evaluation of the diffusive source terms are computed using a two-point central finite-difference approximation. Both fully implicit and fully 5 of 18 American Institute of Aeronautics and Astronautics
explicit time-integration schemes are implemented in the code. An explicit scheme is used for the present analysis. More details about the code implementation can be found in [7]. The VKI stagnation-line code is coupled with the Mutation++ library, designed at the VKI and here used for the computation of the thermodynamic and transport properties as well as for the evaluation of the gasphase chemical source terms.6 Species thermodynamic properties for the present analysis are obtained from the NASA 9-coefficient polynomials, and relative mixture quantities are derived from pure species quantities through mixing rules. The transport properties are derived from kinetic theory, which provides relationships for macroscopic transport coefficients based on microscopic collision integrals. The chemical production rates for species, based on elementary chemical reactions including third body, are calculated by taking the forward reaction rate coefficients specified by the user in an Arrhenius law form. The backward rate coefficient is determined by satisfying the equilibrium relation. The library has been designed, implemented and extensively tested to ensure high fidelity together with low computational costs. The ablative boundary condition, based on the formulation described in section II.C, has been implemented in the code following the approach proposed by several authors for different kind of applications and both equilibrium and finite-rate surface chemistry.11, 12, 14, 15 The convective and the diffusive fluxes at the gas-surface interface are obtained by solving the surface species mass balance, Eq. (9), and the surface energy balance, Eq. (11). A Newton’s method is used to solve for the surface temperature in Eq. (11).
IV.
Experimental Contributions to Modeling
Ablation tests were conducted in the VKI Plasmatron in both air and nitrogen plasmas to characterize ablative material behaviors. For the present study we focus on analyzing the response of a non-charring carbon fiber preform. This material consists of a compound of 2-D randomly oriented carbon fibers with an average density of 215 kg/m3 and a porosity of typically 90%.27 The ablative test samples are hemispherical probes of 50 mm length with 2.5 cm nose radius, satisfying the geometrical constrains for the applicability of the stagnation-line formulation described previously. During each test the stagnation-point recession was tracked by means of a high speed camera with about ±0.1 mm accuracy (depending on the test-specific optical configuration of the camera). With this approach the local mass blowing rate at the stagnation point can be evaluated by using the recorded centerline recession thickness, the recession time and the material density. Any further considerations or uncertainties on the surface area variation due to the shape change in the case of non-uniform ablation of the test sample, needed if the mass blowing rate was evaluated by simply measuring the sample mass loss after the test, is therefore avoided. Moreover, with this technique the actual steadystate recession time can be considered by neglecting the initial transient phase when non-linear recession or swelling can occur.28 The surface temperature is measured, independently of the surface emissivity, by a two-color pyrometer with an accuracy of ±20 K. Additionally, an infrared radiometer is used to give an independent measurement of the surface temperature and, together with the pyrometer measurements, to evaluate the material emissivity. Further details on the experimental setup and measurement post processing can be found in [27]. Beside their straightforward use for model validation purposes, the described measurements of the mass blowing rate and the surface temperature can contribute actively to update and tailor some baseline model parameters if different kinds of material and/or conditions are investigated. The baseline ablation model composed of two oxidation, a nitridation and a sublimation reactions was introduced in the previous section.23 The reaction probabilities of this model were evaluated by fitting the data collected over different experiments mainly focused on the combustion of graphite. As described previously, the material under investigation is rather different than a single compact piece of graphite. Therefore, the application of the baseline ablation model to the actual investigation has to be assessed. Among the considered surface heterogeneous reactions, oxidation by atomic oxygen represents by far the prime contribution to the material consumption in air plasma conditions that aim at simulating high-speed entry. For the majority of the plasmatron testing conditions, however, this reaction appears to be limited by the diffusion of the atomic oxygen through the boundary layer up to the surface where the reaction takes place. For this reason, the accurate evaluation of the oxidation reaction probability does not represent an issue for the proper estimation of the related mass blowing rate. Moreover, since the oxygen is almost fully dissociated, the molecular oxygen oxidation reaction is practically inhibited. Sublimation, unless very high heat fluxes are achieved, is also unlikely to occur in the considered cases because the surface temperature is not high enough. On the other hand, surface nitridation, as pointed out in [29], has been found to increase rapidly when the temperature exceeds 1373 K and it has been
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10
Table 1: Freestream conditions for the Arcjet test case from [34]. Value
Velocity, m/s Density, kg/m3 Temperature, K yO2 yN2 yNO yO yN
5354 0.003 1428 0.000 0.617 0.005 0.121 0.257
N2 O
species mass fractions
Property
0
10
-1
10
-2
10
-3
N
C3 CO
CN
10
-4
10
-5
O2
Ref. [34] VKI S-L w/ nitridation 10
-6
0
0.1
0.2
0.3
0.4
distance from stagnation point, cm
Figure 1: Stagnation streamline species mass fraction distribution for the Arcjet test case.
the subject of several investigations over the last decade.28–30 The reaction probability originally evaluated in [31] was found to be excessively high when compared with other investigations.28–30, 32 Therefore, carbon fiber preform testing in pure nitrogen environment represents a good opportunity to investigate the nitrogencarbon interaction. In this environment, if sublimation does not occur, the described gas-surface interaction model has to account for the sole nitridation reaction. Hence, the carbon mass blowing rate in Eq. (14) reduces to: CN MN m ˙ s = ω˙ N (15) MC and it is directly linked to the measured recession rate through the known material density. The superscript CN in Eq. (15) indicates the source terms for atomic nitrogen due to the nitridation reaction (Cs + N → CN). Then, recalling the definition of the surface source term per unit area: ω˙ ir = kir ρi
(16)
Eq. (13) can be rewritten, by using Eq. (15), to express the unknown nitridation reaction probability as: CN γN =
m ˙ s MC ρN MN
R Tw 2π MN
−1/2 (17)
At this point, by imposing the experimental mass blowing rate in Eq. (17), one can evaluate the nitridation reaction probability through the gas-surface interaction model where the unknown nitrogen density is computed taking into account the surface mass balance in Eq. (9). Furthermore, if the test conditions allow for the hypothesis of steady-state ablation (Eq. (8)) to hold true, Eq. (11) can be used to compute the steadystate surface temperature. By comparing this result with the experimental measurements, a reasonable agreement should be expected. If this is not the case, the cause can be attributed to the possible catalytic efficiency of the ablative material that can favor the highly exothermic atomic nitrogen recombination affecting considerably the surface temperature.33
V.
Arcjet Model Preliminary Test
A first test case is presented in this section to test the ablation model behavior. Data were taken from [34] where a numerical study on an experimental test conducted in the Interactive Heating Facilities at NASA Ames Research Center was presented. The original graphite body was a 10-deg, one-half-angle sphere cone with a radius of 1.905 cm. Its approximation to a sphere of the same radius to study the stagnation-point flux through the stagnation-line code is quite straightforward and it is expected to not introduce any significant 7 of 18 American Institute of Aeronautics and Astronautics
10
0
N2
species mass fractions
O
10
-1
10
-2
10
-3
10
-4
10
-5
N
C3 CO
CN O2
VKI S-L w/ nitridation VKI S-L w/o nitridation 10
-6
0
0.1
0.2
0.3
0.4
distance from stagnation point, cm
Figure 2: Stagnation streamline species mass fraction distribution for the Arcjet test case with and without surface nitridation.
error in the simulation results. The rebuilt freestream enthalpy was reported to be approximately 27 MJ/kg, and the measured stagnation-point pressure and stagnation-point cold-wall heat flux were 81 kPa and 21 MW/m2 , respectively. These conditions correspond to the calculated freestream conditions given in Table 1. A mesh composed of 100 cells, clustered in the wall region to ensure a good resolution of the stagnation point, has been selected after a grid convergence study was performed. A mixture composed of 11 gasphase species was considered: C, C2 , C3 , CN, CO, CO2 , N, N2 , NO, O, and O2 . A subset of the gas-phase reactions given in [35], involving only the selected species, was used to compute the gas-phase chemistry through the Mutation++ library.6 The obtained results are here compared with those presented in [34] where the Gauss-Seidel Implicit Aerothermodynamic Navier-Stokes with Thermochemical Surface Boundary conditions (GIANTS) code was used to perform the analysis.36 Figure 1 shows the mass fraction profiles along the stagnation line obtained from the present simulation, together with the values extracted from [34]. The two simulations qualitatively agree and the mass fraction profiles show the same behavior despite the stagnation-line reduction, the differences in the diffusion modeling, small discrepancies in the gas-phase chemical reaction rates and the thermal equilibrium assumption in the present calculation. More importantly, the species involved in the gas-surface interaction process follow the same behavior giving the qualitative evidence of the right implementation of the ablative boundary condition in the VKI stagnation-line code. It is worth noting that the results shown in [34] were obtained by specifying the experimentally measured surface temperature. Differently, in the present calculation the surface temperature was directly computed by solving Eq. (11). A further code-to-code comparisons (not reported here) with the results published in [37], where simulations of the same test case were performed, showed the same satisfactory agreement. The results shown in Fig. 1 were obtained using the complete Park’s ablation model with surface nitridation. Figure 2 shows a comparison between the VKI stagnation-line code results obtained either by considering or not this surface reaction. The boundary-layer species distributions for the species containing nitrogen obviously quite differ between the two cases. Furthermore, small disparities for other species as atomic oxygen and carbon monoxide also show up. This comparison highlights the strong interaction between the different surface heterogeneous reaction products within the boundary layer. In Table 2 the computed surface temperature and mass blowing rate are compared with the experimental results given in [34]. As seen, the computed surface temperature reasonably agrees with the experimental value. The major contributions of the total mass blowing rate, computed by using Eq. (14), are also listed. When surface nitridation is considered, the total mass blowing rate is significantly enhanced. Moreover, although the steady-state surface temperature is only marginally affected (the nitridation reaction is slightly exothermic, with a reaction energy of 0.34 eV), the atomic oxygen oxidation contribution is almost halved. This is an evidence of the diffusion-limited regime of the oxidation reaction for the actual conditions. In fact, its con-
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Table 2: stagnation-point results for the Arcjet test case and comparison with the experimental data. m ˙ s , kg/m2 s
m ˙ O , kg/m2 s
m ˙ N , kg/m2 s
m ˙ subl , kg/m2 s
Tw , K
0.192 0.319 0.213
— 0.084 0.166
— 0.185 —
— 0.049 0.047
3540 3496 3488
Experimental data [34] VKI S-L w/ nitridation VKI S-L w/o nitridation
Table 3: Nominal Plasmatron Test Conditions and Rebuilt Boundary-Layer Edge Conditions. Test
N-1
N-2
A-1
A-2
Nominal test conditions
Working gas Working power, kW Mass flow rate, kg/s Static pressure, kPa Cold-wall heat flux, MW/m2
N2 154 16 1.5 1
N2 350 16 1.5 3
Air 166 16 1.5 1
Air 365 16 1.5 3
Rebuilt edge conditions
Velocity, m/s Temperature, K Density, kg/m3
734 6413 0.00045
1739 10805 0.00019
759 6228 0.00048
1887 10587 0.00022
tribution to the total mass blowing rate is strongly affected by the boundary layer modification induced by the surface nitridation. Carbon sublimation has a non-negligible contribution to the total mass blowing rate because of the considerably high surface temperature in the present conditions. As reported in [34], the observed behavior of the gas-surface interaction model underlines the importance of a better understanding of the nitrogen-carbon interaction.
VI.
Results and Discussion
A total of four tests performed in the VKI Plasmatron are considered in the present analysis. Two different working fluids, nitrogen and air, were tested in the same conditions of cold-wall heat flux, mass flow rate and static pressure. The nominal test conditions are listed in Table 3. More details about the testing procedure can be found in [27]. A.
Definition of Plasmatron Test Case Conditions
In order to simulate these experimental tests, the inlet conditions for the stagnation-line simulations were obtained through the standard procedure used at the VKI to rebuild the boundary-layer edge conditions by means of the VKI Rebuilding code.38 This procedure involves both numerical simulation of the ICP flow field and experimental measurements. After a literature survey, the reference catalycity of the copper calorimeter, which is a necessary input parameter for the VKI Rebuilding code, was set to 0.019.39–41 This catalycity value was used without modifications for both nitrogen and air tests. With the rebuilding procedure, edge temperature, velocity and equilibrium composition were obtained by matching the cold-wall heat flux and dynamic pressure measurements. Table 3 lists the velocity boundary-layer edge conditions for the analyzed test cases. For the nitrogen tests, a mixture of 4 species was considered: N, N2 , N+ , e− . For the air tests, 15 species were used: C, C2 , C3 , CN, CO, CO2 , N, N2 , NO, O, O2 , C+ , N+ , O+ , e− . Both the gas-phase mixtures and the gas-phase reaction mechanisms were selected from a subset of those used in [35].
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10
0
10
N
0
N N
O -1
10
species mass fractions
species mass fractions
10
N2
10-2
10-3 N+ +
O
10
-4
CO C
NO
10
-5
10
-6
CN
+
O
-1
+
O
10-2
10-3
CO C
10
-4
10
-5
10
-6
NO
C3 N2
e-
O2
CN
CO2
0
0.5
1
1.5
2
O2
0
0.5
1
1.5
distance from stagnation point, cm
distance from stagnation point, cm
(a) Test case A-1-a
(b) Test case A-2-a
2
Figure 3: Stagnation streamline species mass fraction distributions for the air test cases without surface nitridation.
B.
Air Test Cases Without Surface Nitridation and Catalycity
The experimental tests in air environment, labeled as A-1 and A-2 in Table 3, are first analyzed. From now on, to distinguish between different numerical test cases that aim at simulating the same experimental test, a trailing character is added to the name of the corresponding experimental test case. In this first series of two simulations, Park’s ablation model without surface nitridation is used. As reported in Table 3, the two test cases present quite different freestream conditions generated by different working powers. The major species stagnation-line profiles are shown in Fig. 3 for both the test cases. For test case A-1-a the presence of ionized species is very limited, whereas the higher freestream temperature of test A-2-a generates a considerably ionized gas. To satisfy the condition that no electrical current flows across the surface, the ionized species are forced to recombine at the wall with a neutralization probability of 1.23 Recombination of both atomic oxygen and nitrogen through the boundary layer is very low, especially for case A-1-a because of the low stagnation-point pressure. Therefore, the effect of this weak recombination on the species mass fractions is altered by the total mass increase caused by the blowing, and a small drop of both atomic and molecular nitrogen appears although the mole fraction ratio between N and N2 is decreasing. For test A-2-a, the quite large amount of N+ that recombines to the neutral species in the boundary layer, increases the mass fraction of the atomic nitrogen. Atomic oxygen decreases in both cases because of the heterogeneous reaction with the surface carbon that creates CO. Although surface nitridation is not considered here, CN is created through the boundary layer by the gas-phase reactions and peaks around the midpoint of the chemical boundary layer. For test A-2-a a small quantity of C3 shows up because of the higher temperature. Table 4 shows the computed mass blowing rate and surface temperature together with the experimental results. The uncertainty in the experimental mass blowing rate is primarily due to the uncertainty on the material density. Numerically computed mass blowing rates substantially agree with the measured ones for both tests. Therefore, the fact that surface nitridation was not considered seems not to have a strong impact on the numerical–experimental comparison of this quantity. However, there is experimental evidence that active nitridation occurs when carbon-based materials are exposed to a pure nitrogen flow. For this reason, the mere omission of this surface reaction from the model seems quite rough and will be better analyzed in the following section. Comparison of the surface temperatures shows a different situation. For test A-2-a the numerical value essentially agrees with the experimental one. The obtained difference (of the order of 100 K) is in line with the level of fidelity expected when using the steady-state ablation approximation to compute the solid conduction term in Eq. (11). Differently, for test A-1-a an underestimation of almost 300 K appears rather 10 of 18 American Institute of Aeronautics and Astronautics
Table 4: Stagnation-point results for the Plasmatron tests in air and comparison with the experimental data. Test ID
A-1-a A-2-a
Experimental
Numerical
m ˙ sexp , kg/m2 s
Twexp , K
m ˙ snum , kg/m2 s
Twnum , K
0.0086–0.01034 0.0082–0.01006
2160–2200 2828–2868
0.0075 0.0082
1845 2712
Table 5: Experimental values of stagnation-point mass blowing rate and temperature together with the numerical values of the stagnation-point temperature, and the evaluated reaction probabilities for nitridation and catalycity. Test ID
N-1-a N-1-b N-1-c N-2-a
Experimental
Numerical
m ˙ sexp , kg/m2 s
Twexp , K
Twnum , K
CN γN
N2 γN
0.00025–0.0014 0.00025–0.0014 0.00025–0.0014 0.0015–0.0044
2010–2050 2010–2050 2010–2050 2624–2664
1722 2080 2049 2635
0.00049 0.00068 0.00065 0.003200
— 0.035 0.030 —
large. Experimental evidence of a constant surface temperature, and a linear recession of the stagnation point, claim that the steady state was reached during the test.27 Furthermore, if that had not been the case, a higher solid conductive heat flux, resulting in a lower surface temperature, should have been expected during the transient phase. Therefore, this would eventually justify a numerical overestimation rather than an underestimation. It can be also argued that, if the “thermal wave” had reached the backside of the sample, the steady-steady state ablation approximation would not have been longer valid. In this situation, the solid conductive heat flux starts decreasing and a higher surface temperature can be observed. However, this scenario is expected to give a highly unsteady trend of the surface temperature that was not observed during the test. Last, the good agreement obtained for test A-2-a, which presents harsher conditions and a similar mass blowing rate, discredits this hypothesis. For the reasons explained above, the discrepancy in the surface temperature for test A-1-a is considered here to be related to the exclusion from the model of some other phenomenon taking place over the surface. In this view, surface catalysis is the prime suspect because it affects directly the surface temperature and would cause no significant change of the mass blowing rate if the so called diffusion limited ablation regime is achieved. From Fig. 3 one can see that the atomic oxygen mass fraction is sensibly reduced next to the surface, therefore only a small amount of atomic oxygen would be available to recombine on the surface. Differently, the high content of atomic nitrogen can theoretically supply a large amount of energy if recombination to molecular nitrogen occurs on the surface. To verify this hypothesis, tests N-1 and N-2, performed in pure nitrogen environment, are analyzed in the next section. C.
Nitrogen Test Cases: Assessment of the Nitridation and Catalycity Reaction Probabilities
The two experimental test cases N-1 and and N-2, using pure nitrogen as working fluid, are analyzed here to better understand the possible interaction between atomic nitrogen and the carbon fiber preform. As reported in Table 3, these two tests were conducted in the same exact nominal conditions of test A-1 and A-2. The procedure described in section IV is applied here to retrieve the nitridation reaction probability CN (γN ). In this analysis, the uncertainty on the experimental mass blowing rate, that has to be imposed in the numerical simulation to calculate the nitridation reaction probability by means of Eq. (17), is mainly due to the spatial resolution of the high speed camera (∼ ±0.1 mm) that was of the same order as the 11 of 18 American Institute of Aeronautics and Astronautics
10
Ref. 28 Ref. 29 Ref. 30 Ref. 30 Ref. 31 Ref. 32 Ref. 32 Present work
-1
nitridation probability
10
0
10-2
10-3
10-4
10
-5
0
400
800
1200
1600
2000
2400
2800
temperature, K
Figure 4: Active nitridation reaction efficiency comparison with data from the literature.
tiny receded thickness. In particular, for test case N-1, the stagnation-point recession was lower than the high speed camera resolution. Nevertheless, microscope post test analyses revealed the evidence of chemical attack on the surface and spectroscopy measurements of CN detected a mole fraction on the order of 10−4 − 10−6 . Therefore, a value of 0.1 mm recession was guessed on the basis of intrusive caliper measurements to obtain the experimental mass blowing rate. Numerical tests N-1-a and N-2-a in Table 5 show the obtained reaction probabilities evaluated without considering any additional phenomenon than the carbon nitridation on the surface. For these two numerical tests, when comparing the numerical and the experimental surface temperatures (also shown in Table 5) a substantial difference is found again for the lower cold-wall heat flux case (N-1-a). Differently, test case N-2-a, like test A-2-a, shows a good agreement with the experimental value. Thus, likewise the behavior observed for the air test case A-1-a, for the lowest of the two analyzed heat fluxes the model considerably under predicts the surface temperature. As anticipated in the previous section, a phenomenon that has been neglected and that could explain the underestimation of the surface temperature is the catalytic efficiency of the ablative material. However, if this hypothesis is correct, a reason should be found for this phenomenon to take place only in the low cold-wall heat flux tests (A-1 and N-1). A literature survey on the catalytic phenomenon revealed that many models describing the evolution of the recombination efficiency with temperature, consider a strong decrease of this efficiency for temperatures above a particular threshold value (depending on the analyzed material).42–44 A similar phenomenon was also observed experimentally in [45].This behavior can be ascribed to the change of the recombination reaction order, that above a critical value of the temperature can switch from first to second order with a squared dependence on pressure.43 Alternatively, it can be attributed to a stronger thermal desorption of the absorbed atoms at higher temperature that can deplete significantly the surface coverage.42, 44 For ablative materials, it is normally assumed that the catalytic recombination is negligible with respect to the heterogeneous reactions such as oxidation and nitridation, reasoning with the assertion that these processes dominate over the catalytic recombination on highly rough surfaces.46, 47 However, the possibility of having catalytic recombination over an ablative surface was already considered in the past33 and not valid reasons have been found to unconditionally exclude this phenomenon that theoretically can be even enhanced on surfaces with a preeminent roughness.48 N2 For the reasons above, several recombination efficiencies (γN ) were investigated for the catalytic reaction N + N → N2 until the experimental surface temperature and the numerical one matched for case test N-1 (see N2 Table 5). This resulted in a value of γN of 0.03. Obviously, the addition of the recombination mechanism affect both the boundary-layer species profile and the surface temperature. This, in turn, results in a CN modification of the nitridation reaction probability γN which increases from 4.9 × 10−4 , for case N-1-a, to −4 6.5 × 10 for case N-1-c. Figure 4 shows the computed nitridation probabilities for the experimental tests N-1 and N-2 together with values from the literatures.28–32 The red dots indicate the values that corresponds
12 of 18 American Institute of Aeronautics and Astronautics
10
0
10
N
0
N N
O N2
-1
10
species mass fractions
species mass fractions
10
w/o nitirdation and catalycity w/ nitridation and catalycity
10-2
10-3 N+ +
O
10
-4
C NO
10
-5
10
-6
CO
CN
+
O
-1
+
O
w/o nitridation and catalycity w/ nitridation and catalycity
10-2
10-3
CO C
10
-4
10
-5
10
-6
NO
C3 N2
e-
O2
CN
CO2
0
0.5
1
1.5
2
O2
0
0.5
1
1.5
distance from stagnation point, cm
distance from stagnation point, cm
(a) Test case A-1-a and A-1-b
(b) Test case A-2-a and A-2-b
2
Figure 5: Stagnation streamline mass fraction distributions for the air test cases without and with surface nitridation and catalycity.
to the nominal value of the calculated reaction probabilities. Error bars associated with those values are also shown. It is worth noting that, for test N-1, only an upper bound is shown because the lower one would have been associated with no ablation, conflicting with the material post test measurements. As shown, the probabilities fall in the range of the values obtained by other researchers although the actual structure of the analyzed material is rather more complex than that of a simple graphite piece. Unfortunately, the error bars associated to these values, due to the poor resolution of the high speed camera (compared to the actual recession of the material for the presented tests), are quite large and further investigations with an increased resolution are required to obtain a better characterization of the nitridation reaction probability. However, the obtained “educated guess” are considered suitable for the purposes of the present analysis. D.
Air Test Cases with Surface Nitridation and Catalycity
The results obtained from the analysis performed in pure nitrogen environment and described in the previous section are used here to update the gas-surface interaction model to be used in air environment. As explained previously, the computed nitridation reaction probabilities are prone to a series of uncertainties that have to be reduced in order to obtain more accurate values. However, the present data are the only ones giving a clue of the possible nitridation reaction probability value up to the temperatures of interest in the present study (see Fig. 4). Furthermore, they have been evaluated specifically for the material under investigation. Arrhenius type law are normally used to represent the reaction probability behavior with temperature.30 For these reasons, an Arrhenius type law, generated considering the nominal values of the evaluated reaction probabilities (red dots in Fig. 4), has been assumed to describe the behavior of the nitrogen carbon interaction CN with temperature: γN = A exp(−B/Tw ). The A and B coefficients for this law are 8.1×10−1 and 1.46×104 , respectively. Concerning the assumed material catalytic efficiency, if the supposed catalycity drop takes place, the behavior will depart substantially from an Arrhenius type law. Therefore, the most reasonable choice seems to distinguish between low- and high cold-wall heat flux tests, applying the same values obtained for N2 N2 N-1 (γN = 0.03) and N-2 (γN = 0.0) to test cases A-1 and A-2, respectively. Figure 5 shows a comparison of the boundary-layer species profiles with and without the updated reaction probabilities for the surface nitridation and recombination for both test cases A-1 and A-2. For the low heat flux test case (Fig. 5(a)), the differences between the profiles of the species containing nitrogen are evident. The imposed surface recombination, whose evaluated reaction probability is approximately two order of magnitudes higher than the one for the nitridation, increases the molecular nitrogen content approaching the surface and, consequently, reduces the atomic nitrogen one. Furthermore, an interesting coupling shows up between the nitridation products, CN, and atomic carbonC. The latter in fact, not considered directly 13 of 18 American Institute of Aeronautics and Astronautics
Table 6: Stagnation-point results for the Plasmatron tests in air without and with surface nitridation and catalycity, and comparison with the experimental data. Test ID
A-1-a A-1-b A-2-a A-2-b
Experimental
Numerical
m ˙ sexp , kg/m2 s
Twexp , K
m ˙ snum , kg/m2 s
m ˙ O , kg/m2 s
m ˙ N , kg/m2 s
Twnum , K
0.0086–0.01034 0.0086–0.01034 0.0082–0.01006 0.0082–0.01006
2160–2200 2160–2200 2828–2868 2828–2868
0.0075 0.0082 0.0082 0.0098
0.0075 0.0080 0.0082 0.0082
— 0.0002 — 0.0015
1845 2067 2712 2719
as a possible ablation product, is increased next to the surface by the dissociation of CN that, after being produced at the surface, is quickly depleted in the boundary layer. This process takes place in a very thin region of the boundary layer and pushes down the CN mass fraction to the value obtained when surface processes involving nitrogen species were neglected. Similar considerations still hold for the high power test A-2. Concerning the product of the surface oxidation, CO, it results poorly affected by the additional surface phenomena that have been considered here. For test A-1-b, a small departure from the profile obtained in test A-1-a is observed, whereas the profile obtained for test A-2-b is indistinguishable from that of test A-2-a. More importantly, both simulations A-1-b and A-2-b show a negligible departure of the CO surface mass fraction from the values obtained in tests A-1-a and A-2-a. This is confirmed when the surface mass blowing rate contributions are analyzed in detail. Table 6 lists these contributions together with the total numerical mass blowing rate and the experimental one (numerical contribution from sublimation is omitted since is alway less than 10−4 ). The new values of the total mass blowing rate agree slightly better with the experimental ones. As seen the atomic oxygen oxidation contribution to the total mass blowing rate is marginally affected (case A-1-b) or even unaffected (case A-2-b). Therefore, one can conclude that the big influence that was observed in section V and in [34] was a consequence of the excessively high nitridation reaction probability. In fact, the value from [31] is approximately two order of magnitude higher than the one evaluated in the present work (see also Fig. 4). A similar comment can be made on the results shown in [23] where a big influence of the surface nitridation on the total mass blowing rate was shown. Figure 6(a) shows a comparison of the diffusive fluxes of the species involved in the relevant surface processes for test A-1 (atomic oxygen oxidation, nitridation and nitrogen recombination). Negative values indicate the species diffusing towards the surface whereas positive values indicate those diffusing away from the surface. Molecular oxygen and carbon monoxide fluxes follow the same trend even when nitridation and recombination are included in the analysis. The small discrepancy in the diffusive fluxes justifies the slightly different value of the mass blowing rate contribution associated to the oxidation reaction (m ˙ O in Table 6). In fact, this reaction is supposed to be diffusion limited in the present test conditions. The temperature increase caused by the nitrogen surface recombination in case A-1-b is on the order of 200 K. The new value of the computed surface temperature approaches the experimental measure presenting a more reasonable difference of about 100 K (see Table 6). Figure 6(b) shows that this increase of the surface temperature also affects the boundary-layer temperature profile and a difference of around 100 K is found up to a distance of about 2 mm from the surface. This temperature change, coupled with the surface production of CN and N2 is the responsible for the small variation of the diffusive flux of atomic oxygen. However, the contribution of CN produced in the surface nitridation is considered to be very small since its diffusive flux is almost unchanged and its mass fraction profile quickly approaches the one obtained without considering the surface nitridation. Therefore, the boundary layer modification can be ascribed mainly to the surface catalysis. For test A-2-b the small difference in the surface temperature (Table 6) is caused by the small exothermicity of the surface nitridation only, since no surface recombination was considered. As it was pointed out previously, in these conditions recombination of ionized species to the neutral ones takes place in the boundary layer and the diffusive flux profile of N substantially differs from that of test case A-1. When nitridation is considered, the atomic nitrogen diffusive flux inversion obtained for case A-1-a (solid line in Fig. 7(a)) disappears, and the atomic nitrogen diffuses only away from the surface. The diffusive flux of molecular oxygen is unchanged by the addition of the surface nitridation. As it was presumable, Figure 7(b)
14 of 18 American Institute of Aeronautics and Astronautics
reveals that this tiny variation of the surface temperature does not affect the boundary-layer temperature distribution. 6500
0.02 w/o nitridation and catalycity w/ nitridation and catalycity CO
0.01 2
diffusive flux, kg/m s
stagnation-line temperature, K
0.015
0.005 CN
N2
0 -0.005
N
O
-0.01
5500 w/o nitridation and catalycity w/ nitridation and catalycity 4500
3500
2200 2000
2500
1800
-0.015 -0.02
0
0.005
1500 0
0.5
1
0
0.5
1
1.5
2
distance from stagnation point, cm
distance from stagnation point, cm
(a) Diffusive fluxes
(b) Temperature
Figure 6: Diffusive fluxes of the species involved in the surface reactions and boundary-layer temperature profile for test case A-1 without and with surface nitridation and catalycity.
11000
0.02 w/o nitridation and catalycity w/ nitridation and catalycity CO
0.01 2
diffusive flux, kg/m s
10000
stagnation-line temperature, K
0.015
CN
0.005 N2
0 N
-0.005 O
-0.01 -0.015
9000
w/o nitridation and catalycity w/ nitridation and catalycity
8000 7000 6000
3000
5000
2800
4000
2600 0
0.005
3000
-0.02
2000 0
0.5
1
0
0.5
1
1.5
2
distance from stagnation point, cm
distance from stagnation point, cm
(a) Diffusive fluxes
(b) Temperature
Figure 7: Diffusive fluxes of the species involved in the surface reactions and boundary-layer temperature profile for test case A-2 without and with surface nitridation and catalycity.
VII.
Conclusions
An ablative model able to reproduce the gas-surface interaction of a carbon-based non-charring material in plasma wind tunnel test conditions has been implemented in a stagnation-line code. The model allows to study the steady-state surface ablation of the stagnation point of hemispherical samples that are typically used for the ablation tests in the von Karman Institute Plasmatron. Comparisons with similar models in the literature have shown a good agreement despite the stagnation-line approximation introduced in the flow 15 of 18 American Institute of Aeronautics and Astronautics
governing equations and the simplified approach to treat the solid material steady-state conduction. Several tests on a carbon fiber preform, performed in the von Karman Institute Plasmatron in both nitrogen and air environment, have been analyzed. Thanks to the available experimental data, the original heterogeneous surface reaction dataset, taken from the literature, has been critically reviewed and its applicability to the material under investigation has been investigated. Emphasis has been given to the gas-surface interaction processes involving atomic nitrogen as active nitridation and catalytic recombination. Data from pure nitrogen tests have been used to update the surface nitridation reaction probability up to temperature of about 2650 K. Also, by comparing the experimental and numerical values of the surface mass blowing rate and temperature, a catalycity of the carbon fiber preform at surface temperature around 2000 K has been hypothesized. The calculated reaction probabilities for the surface nitridation and the nitrogen catalytic recombination have been used to simulate tests performed in air environment at the same conditions of mass flow rate, pressure and cold-wall heat flux of the nitrogen ones. The agreement with the experimental data on the surface mass blowing rate and temperature has been improved using the updated reaction probabilities. Further analysis and comparison with more experimental data will be addressed in the future to better characterize the behavior of these probabilities with the test conditions.
VIII.
Acknowledgments
The research of A. Turchi, A. Munaf` o and T. E. Magin is sponsored by the European Research Council Starting Grant No. 259354: “Multiphysics models and simulations for reacting and plasma flows applied to the space exploration program.” The research of B. Helber is supported by the fellowship of the Agency of Innovation by Science and Technology (IWT, dossier No. 111529).
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