Computational Modeling of Gas-Surface Interactions

Many of the missions aimed towards space exploration require an entry into the atmosphere of Earth or another planet at hypersonic speeds. These atmospheric entry probes, i.e. hypersonic vehicles use a Thermal Protection System (TPS) to shield them from aerodynamic heating experienced during (re-)entry. Aerothermal heating of the vehicle TPS is directly affected by the gas-surface interaction processes that occur between the vehicle surface and the atmospheric gas. 

Catalycity of a TPS material and surface-participating reactions that lead to surface recession are the key gas-surface interaction processes that impact the heating of the vehicle surface. Aerodynamic heating causes very high temperatures in the boundary layer which can lead to dissociation of molecular gas species. If the heated TPS material acts as a catalyst and dissociated atoms diffuse to the surface, it can promote recombination of dissociated boundary layer species which increases the convective heating to the surface. Thus, a less catalytic surface is desirable to minimize this additional heating. Also, when the vehicle surface is heated, the surface material may chemically react with the boundary layer gases and can lead to surface recession as a result of surface material consumption. Detailed studies of these interactions are required for the accurate prediction of aerothermal heating of the vehicle TPS and in characterizing TPS materials. The objective of our research study is to assess the effect of different gas-surface interaction models and processes on the boundary layer species concentration and temperature gradients near the material surface, and on the heat transfer to the material surface. The study examines the effects of gas-surface interactions for graphite exposed to high enthalpy reacting nitrogen flow. The numerical simulations in this study are conducted using the Michigan Aerothermodynamic Navier-Stokes computational fluid dynamics (CFD) code LeMANS developed at the University of Michigan.

To study the effects of these processes, the entry flight environment considered represents the post shock subsonic high-enthalpy gas flow. To determine the properties of a TPS material, it is required to be tested in an experimental facility that can create conditions similar to real entry flight conditions. Reproducing these conditions in existing ground facilities is both challenging and expensive. Therefore, a partial simulation of the flight conditions that involves subsonic high-enthalpy flow for the purpose of this study is considered. Computational models can be used for predicting the aerothermal environment of the vehicle TPS during (re)-entry but the computational models can be used to perform such analysis only after they have been validated to accurately predict the flow in the test facility and are validated with experimental results from the facility.

The computational results are evaluated using the experimental tests conducted in the 30 kW Inductively Coupled Plasma (ICP) Torch Facility [1] at the University of Vermont. It is designed to test scaled material samples in subsonic high enthalpy gas flows for simulation of atmospheric (re-)entry trajectory heating conditions. In our work, experimental results from POCO graphite grade DFP2 samples tested in the nitrogen plasma stream are used. The experimental tests were aimed at measuring the relative nitrogen atom number density and translational temperature in the reacting boundary layer above the graphite surface using a two-photon laser induced fluorescence (LIF) technique.

The test article is a 25 mm diameter graphite sample mounted in the test chamber at a distance of 90 mm from the ICP torch exit. Fig. 1a shows a photograph of the graphite sample during exposure to the nitrogen plasma in the test chamber of the ICP Torch Facility. Hot nitrogen plasma flows out (shown by green arrows in Fig. 1a) through the quartz tube of the ICP torch at a mass flow rate of 0.83 g/s. The section in the box is the portion simulated using the CFD code LeMANS. An example of the simulation of this experimental configuration is shown in Figure 1(b) where the translational temperature contours are presented.

Figure 1 (a): Experimental set up with graphite sample in nitrogen plasma in the test chamber of the ICP torch facility (section in box is the portion simulated using the CFD code LeMANS)(Courtesy : Prof. D.G. Fletcher (UVM)). (b) Simulation of experimental configuration: Translational temperature contours

The boundary conditions at the test article wall are defined by a gas-surface interaction model implemented in LeMANS. It is a general finite rate surface chemistry (FRSC) model [2-4] that can be used to investigate the effects of surface catalysis as well as surface participating reactions. The model can simulate the chemical interaction between the hypersonic gas and surface of the vehicle during planetary entry. A simplified binary catalytic atom recombination model [5] is also implemented in LeMANS and can be used to study the effects of surface catalysis. It could only be applied to a binary gaseous mixture of atoms and molecules whereas the FRSC model can be applied to multiple gaseous species.

The gas-surface interaction processes studied are the recombination of nitrogen atoms to molecules at the surface due to catalysis, and carbon nitridation where nitrogen atoms react with the surface carbon to form gaseous CN. Carbon nitridation is studied as sample mass loss is observed in the experiment. The surface reaction types considered are adsorption and Eley-Rideal (E-R) recombination. The E-R mechanism involves the reaction of a gas-phase species with an adsorbed species to form a gas-phase product. Two sets of surface reactions are taken into account. The first set is the surface reaction (shown in Eq. 1) that accounts only for the nitrogen atom recombination on the wall due to surface catalysis.

N + (s) N(s) : Adsorption (1)
N + N(s) N2 + (s) : Eley-Rideal recombination

The second set (shown in Eq. 2) takes into account the nitrogen atom recombination on the wall due to surface catalysis along with the carbon nitridation reaction where the carbon from the surface reacts with the impinging nitrogen atoms. The Eley-Rideal recombination reaction is used to represent the process of carbon nitridation.

N + (s) N(s) : Adsorption (2)
N + N(s) N2 + (s) : Eley-Rideal recombination
N +(s) + Cb CN + (s) : Eley-Rideal recombination

Detailed description of this work can be found in the conference papers enlisted below. The results obtained from recent simulations are shown here. All the test cases are investigated for constant reaction efficiency 𝛾 and the flow physics model chosen for all test cases is thermochemical nonequilibrium flow. The production and consumption of a species as a result of a surface reaction is a function of the reaction efficiency 𝛾 that lies within the range 0 to 1. The reaction efficiency 𝛾 for surface catalysis, also referred to as catalytic efficiency of nitrogen atoms, is denoted by 𝛾N. It is the ratio of the flux of nitrogen atoms that recombine on the surface to form nitrogen molecules to the total flux of nitrogen atoms that impinge on the surface. The reaction efficiency for carbon nitridation, also referred to as carbon nitridation efficiency, is denoted by 𝛾CN. It is the ratio of nitrogen atoms reaching the surface and combining with surface carbon atoms to the ratio of the total flux of nitrogen atoms that impinge on the surface. It is assumed that all the carbon mass loss occurs due to the carbon nitridation reaction. 


Case 1 represents a wall where no surface chemistry is accounted for and is treated as non-catalytic. The surface chemistry for Cases 2 and 4 is defined by the reactions shown in Eq. 1 and for Case 3, it is defined by Eq. 2. The values for reaction efficiency are set based on experimentally determined values. The comparisons between the numerical results and experimental LIF measurements are presented for translational temperature and normalized nitrogen atom density in the test sample boundary layer along the stagnation streamline in Fig. 2(a) and 2(b), respectively. The results from the simulations show that the temperature in the boundary layer is not significantly affected by different surface reactions whereas the nitrogen atom density decreases in the boundary layer when surface chemistry is included. The nitrogen atom number density profiles are relatively insensitive to the surface chemistry parameters, and all three cases show good agreement with the experimental measurements.  The carbon mass removal rate is also computed and compared to the measured value. The experimentally determined value of mass loss rate of carbon is 0.61 mg/s whereas the computationally calculated value for mass loss rate of carbon for Case 3 is 0.92 mg/s.

Figure 2 : Comparison of translational temperature and normalized N-atom density along the stagnation line between the computational and experimental data.

The total heat flux and the diffusive heat flux are shown in Figs. 3a and 3b, respectively. As expected, there is an increase in the total heat flux for all the cases with surface reactions as compared to the non-catalytic wall. There is a significant increase in the total heat flux for the cases with surface reactions as compared to the non-catalytic wall case. This increase is explained by the contribution from diffusive heat flux for the cases with surface reactions which is zero for a non-catalytic wall as shown in Fig. 3b. Currently, a sensitivity analysis on the ICP torch exit chemical composition is being performed to evaluate its effect on the flow around the graphite sample and its mass loss.

Figure 3: Comparison of wall heat flux between the computational results for different test conditions.

Acknowledgments

This work is funded by the Air Force Office of Scientific Research Grant FA-9550-11-1-030. The critical information provided for this research by Professor Doug Fletcher and his graduate students at the University of Vermont is also greatly acknowledged. 

References

  1. Owens, W. P., Uhl, J., Dougherty, M., Lutz, A., Meyers, J., and Fletcher, D. G., “Development of a 30kW Inductively Coupled Plasma Torch for Aerospace Material Testing,” AIAA Paper 2010-4322, June 2010.
  2. Marschall, J. and MacLean, M., "Finite-Rate Surface Chemistry Model, I: Formulation and Reaction System Examples," AIAA Paper 2011-3783, June 2011.
  3. MacLean, M., Marschall, J., and Driver, D. M., "Finite-Rate Surface Chemistry Model, II: Coupling to Viscous Navier-Stokes Code," AIAA Paper 2011-3784, June 2011.
  4. Alkandry, H., Farbar, E. D., and Boyd, I. D., "Evaluation of Finite-Rate Surface Chemistry Models for Simulation of the Stardust Reentry Capsule," 43rd AIAA Thermophysics Conference, 25-28 June 2012, New Orleans, Louisiana, AIAA Paper 2012-2874.
  5. Scott, C. D., “Wall Catalytic Recombination and Boundary Conditions in Nonequilibrium Hypersonic Flow - With Applications,” The Third Joint Europe/US Short Course in Hypersonic Flow, October 1990.

Recent Publications

  1. Anna, A., Alkandry, H. and Boyd, I.D., “Computational modeling of gas-surface interactions for high-enthalpy  reacting  flows,” AIAA Paper 2013-0187, January 2013.
  2. Anna, A., Boyd, I.D., Colombo V., Ghedini E., Sanibondi P., Boselli M. and Gherardi M. “Computational modeling of surface catalysis for graphite exposed to high-enthalpy nitrogen flow,” Specialists Meeting- AVT-199 /RSM-029, VKI, Belgium, October 2012.
  3. Anna, A. and Boyd, I.D., “Computation of surface catalysis for graphite exposed to high-enthalpy nitrogen flow,” AIAA Paper 2012-0534, January 2012.