Modeling Of Material Response Research Articles

Chemical Kinetics and Thermal Properties of Ablator Pyrolysis Products During Atmospheric Entry

Legacy and modern-day ablation codes typically assume equilibrium pyrolysis gas chemistry. Yet, experimental data suggest that speciation from resin decomposition is far from equilibrium. A thermal and chemical kinetic study was performed on pyrolysis gas advection through a porous char, using the Theoretical Ablative Composite for Open Testing (TACOT) as a demonstrator material. The finite-element tool SIERRA/Aria simulated the ablation of TACOT under various conditions. Temperature and phenolic decomposition rates generated from Aria were applied as inputs to a simulated network of perfectly stirred reactors (PSRs) in the chemical solver Cantera. A high-fidelity combustion mechanism computed the gas composition and thermal properties of the advecting pyrolyzate. The results indicate that pyrolysis gases do not rapidly achieve chemical equilibrium while traveling through the simulated material. Instead, a highly chemically reactive zone exists in the ablator between 1400 and 2500 K, wherein the modeled pyrolysis gases transition from a chemically frozen state to chemical equilibrium. These finite-rate results demonstrate a significant departure in computed pyrolysis gas properties from those derived from equilibrium solvers. Under the same conditions, finite-rate-derived gas is estimated to provide up to 50% less heat absorption than equilibrium-derived gas. This discrepancy suggests that nonequilibrium pyrolysis gas chemistry could substantially impact ablator material response models.

Experimental investigation on the validity of the local thermal equilibrium assumption in ablative-material response models

Thermal Protection Systems (TPS) material response models rely on the assumption of local thermal equilibrium (LTE) between the solid phase and the gas phase. This assumption was challenged and investigated by several authors but a sufficiently precise knowledge of heat transfer coefficients in TPS materials was lacking to reach final conclusions. The objective of this work is to contribute to filling this gap by providing a literature review of available data in other communities (thermal energy storage, heat exchangers) and by performing an experimental characterization of Calcarb, a commercial carbon preform used for manufacturing thermal protection systems. Heat transfer within Calcarb was studied experimentally in the Through-Thickness and in the In-Plane directions for Reynolds numbers of 1 to 4 - representative of the TPS application - using the transient single-blow technique. Numerical parameter estimation was performed using the Porous material Analysis Toolbox based on OpenFoam (PATO) and the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA). The heat transfer coefficient hv is found to be greater than or equal to 108 W/(m3K) and the LTE assumption is shown to be valid in the conditions of the experiment. To assess the validity of the LTE assumption for other conditions, the above bound of hv may now be used in combination with a local thermal non-equilibrium model.

Two-temperature ablative material response model with application to Stardust and MSL atmospheric entries

Ablative material response codes currently in use consider local thermal equilibrium between the solid phases and the pyrolysis gases. For typical entry conditions, this hypothesis may be justified by the fact that the thermal Peclet number within the pores is small, which is a necessary condition for thermal equilibrium in non-reactive materials. However, the validity of this analysis may fall under some circumstances. The thermal Peclet number may become large due to high pyrolysis gas velocities. Additional physical phenomena not accounted for in the Peclet analysis may become non-negligible, such as the change of enthalpy due to chemical reactions. The objective of this study is two-fold. First, a detailed two temperature material response model for porous reactive materials is presented. This model has been implemented and made available in the Porous material Analysis Toolbox based on OpenFOAM (PATO). Second, the model is applied to the Theoretical Ablative Composite for Open Testing (TACOT) in a wide range of conditions to assess the true range of validity of the thermal equilibrium hypothesis. Simulations are carried out on the Stardust and Mars Science Laboratory (MSL) atmospheric entries. The main design variables have been monitored and compared between the two models: temperature evolution and species concentration within the material, pyrolysis gas blowing rate, extension of the pyrolysis zone, and wall recession due to ablation. Results show that under chemical equilibrium conditions, no significant deviation in the monitored quantities are observed, while under chemical non-equilibrium conditions there is a large impact on the species concentration.

Assessment of a 3D ablation material response model for lightweight quartz fiber reinforced phenolic composite

AbstractTo understand the ablation mechanism of materials is crucial for the design of thermal protection system (TPS) for manned reentry vehicles. To investigate the thermal behavior of lightweight quartz fiber reinforced phenolic (LQP) composite subjected to an aerodynamic hyper‐thermal environment, a 3D ablation material response model for the LQP composite is developed with surface and volume ablation in consideration. It is used to predict surface and back temperature, linear ablation velocity, and quality loss rate of the material. The 3D temperature field, pyrolysis degree, gas flow, and pressure field are analyzed as well. To evaluate the accuracy of the model, an ablation test of oxyacetylene flame is adopted on the LQP composite. In the ablation process, the pyrolysis gases propagate primarily through the surface primarily and through the sidewall afterwards. The gas pressure peaks at the early stage rather than increasing constantly. The analysis of thermal insulation mechanism of the LQP composite indicates that the radiation and heat blockage effect are the primary factors to improve the ablation resistance, accounting for 50.0% and 37.3% of the improvement, respectively. The low thermal conductivity determines the admirable thermal insulation performance. The surface temperature of material can be reduced by introducing high emissivity powder into the material, preparing coating on the surface, and adjusting the content of phenolic and silica fiber.

Monte Carlo Sensitivities and Performance of Woven Deployable Entry Systems

A material response model is developed for the determination of erosion rates and thermal response of woven materials to enable accurate thermal protection material sizing and future missions to Venus and giant planets. The stagnation-point thermal response is evaluated using the model developed in Icarus, a material response finite volume solver. A Monte Carlo global sensitivity analysis is further performed using a stand-alone Python wrapper script developed to determine the interactions between key parameters in the material surface energy balance of the one-dimensional simulation, such as the convective blowing correction parameter and weave material properties. The time-accurate material response for the dual-weave erosion and surface temperatures show good agreement with stagnation flat face arcjet tests involving time-varying aeroheating–cooling cycles. The high-fidelity Monte Carlo sensitivity analysis technique was used to address challenges in thermal protection sizing for the Adaptive Deployable Entry and Placement Technology (ADEPT) system, a low ballistic coefficient hypersonic decelerator. The results provide new correlations for such weaves involving carbon–air equilibrium oxidation and wall enthalpy imposition through a B-prime formalism. Through the multivariate regression analyses and uncertainty rankings performed, only two properties were found to largely contribute to the transient thermal response of the gore, with emissivity contributing up to of the total output uncertainty at the front face and at the back face.

Performance of cork-based thermal protection material P50 exposed to air plasma

Cork P50 thermal protection material was characterized under the Earth atmospheric entry conditions in the framework of the in-flight experiment QARMAN. A total of 25 P50 samples were exposed to air plasma ranging the chamber static pressure values of 1500, 4100, 6180, and 20,000 Pa and heat fluxes between 280 and 3250 kW/m^2. The sample radius was also varied between 11 and 25 mm radius to investigate the effects of the stagnation line velocity gradient. The experimental results on heat flux, pressure, surface and in-depth temperatures, surface emissivity, swelling and recession rates, and computed boundary layer profiles as well as the mass blowing rates are presented. A material characterization data suite is also provided including thermogravimetric analysis, specific heat, and thermal conductivity. Overall, a wide range of experimental data of Cork P50 material in Earth atmospheric entry conditions is made available to modelers and engineers for improved material response models and heat shield design consolidation.

Toward an In-Depth Material Model for Cermet Nuclear Thermal Rocket Fuel Elements

The development and qualification of nuclear thermal propulsion (NTP) fuel element technologies would be aided by an in-depth model of material response and failure modes at operating conditions. Integrated computational materials engineering techniques have the potential to provide such a model, as demonstrated here through three case studies focused on a tungsten–uranium mononitride (UN) cermet fuel. The first case focuses on the erosion of tungsten (also named wolfram), a nominal coating/cladding and fuel element matrix material, in hot hydrogen. Ab initio techniques are used to calculate erosion rates and thermal expansion at NTP operating conditions. The second focuses on the stability of UN fuels at high temperature and in the presence of hydrogen. Phase diagram techniques augmented with ab initio thermodynamic data reveal potential instabilities and decomposition pathways at high hydrogen concentrations. The third focuses on using microstructure information to predict high-temperature mechanical response and failure of tungsten. Combined finite element and discrete dislocation dynamics techniques provide mechanical properties in agreement with experimental methods. The integration of these techniques for an all-encompassing material model is discussed.

Computational modeling of viscoplastic polymeric material response during micro-indentation tests

The computational modeling of instrumented indentation tests used to characterize material properties is challenging. It is mainly due to the computational techniques demanded to couple the complex physical mechanisms involved, such as, for example, the time-dependent inelastic material response to loads during contact. Therefore, this work aims to simulate the mechanical response of the poly vinylidene fluoride (PVDF) during a micro-indentation test considering a viscoplastic material model, and a prescribed load approach, using the finite element method. Further, model validation is performed based on experimental data measured during the contact between the indenter and the PVDF. Numerical analyses were performed using COMSOL Multiphysics finite element software considering the loading scheme of the experimental tests of 800 mN/min rate during loading and unloading, and a 400 mN constant load, held by 30 s. Finally, a viscoplastic Chaboche constitutive model is presented considering two cases: (1) a perfectly plastic behavior, and (2) a nonlinear isotropic hardening behavior based on Voce and Hockett–Sherby exponential laws. While the latter models exhibit some discrepancy in capturing the experimental behavior, the former one has shown excellent agreement with the load-depth curves obtained experimentally, achieving the best fitting for the set of Chaboche parameters: $$A=1\,{\mathrm{{s}}}^{-1}, {n}=4.62$$ and $$\sigma _\mathrm{{ref}}=132$$ MPa. Moreover, several phenomenological features of viscoplastic behavior such as rate dependence, plastic flow (or creep) and stress relaxation were accurately provided by the Chaboche model when describing the behavior of the PVDF material.

A strongly objective, robust integration algorithm for Eulerian evolution equations modeling general anisotropic elastic-inelastic material response

A background to the constitutive modeling of elastic-inelastic material response is provided to highlight the uniqueness of the Eulerian formulation of general nonlinear fully anisotropic thermoelastic-inelastic materials proposed in Rubin (1994) [1]. This model introduced Eulerian evolution equations for a triad of microstructural vectors that characterize elastic deformations and anisotropic orientations. Components of tensors which transform like the Cauchy stress referred to these vectors are insensitive to superposed rigid body motions so they can be used to formulate general elastically and inelastically anisotropic constitutive equations. This paper develops a strongly objective, robust numerical algorithm for integrating the evolution equations for the microstructural vectors. This algorithm can easily be implemented into computer codes to simplify the use of general anisotropic constitutive equations for thermoelastic-inelastic material response.

An Arbitrary Lagrangian-Eulerian, coupled neutronics-shock physics model for the analysis of shockwave implosion of solid fissile materials

The aim of this work is to present a coupled neutronics-shock physics model for the study of shockwave compression of solid fissile materials. The shock-physics solver implements multi-material continuum mechanics balance equations, a hydrodynamic material response model and a dynamic mesh to describe shock-induced deformations in solid bodies. In addition, an Arbitrary Lagrangian-Eulerian (ALE) formulation of the governing equations is adopted, in order to avoid mesh distortion and tangling problems in case of large deformations. As for neutronics, a multigroup SP3 neutron transport model is selected for the estimation of the neutron flux.Several case studies are presented to validate the developed models, demonstrate the coupling between the two physics and highlight the advantages of the ALE approach.The proposed model can be a useful tool for the simulation of shock implosion of fissile materials, such as in subcritical plutonium experiments or in reactivity accidents initiated by strong energetic events.

Long-term evolution of spherical shell with boron carbide layer after explosive compression

Predictive simulation of the long-term response of multilayer targets with ceramics layers to shock compression demands appropriate material models. Because ceramics are complex brittle materials, which tend to lose their strength under heavy loads, such simulation requires the failure models well-proven for a wide range of strains and strain rates. Standard plate impact experiments provide the main data utilized for developing and validating the mechanical models of material response to shock compression. However, apart from the fact that such experimental data are inherently one-dimensional, they can be insufficient to verify the failure model at relatively low strain rates typical for long unloading waves. Here, we present the experimental results for explosive compression of a spherical multilayer shell initiated by a single detonator. The explosive-coated shell consists of the nested spherical layers: the outer made of boron carbide and the inner of lead. X-ray images showing the evolution of those layers after detonation are then compared with simulation results. Propagation of the compression wave through the layers resulting in ceramics damage is analyzed in detail. We demonstrate that the failure model of boron carbide should be adjusted for compressions below 10 GPa to achieve a good agreement with our experimental images. Such an improved failure model provides the predictive simulation of long-term dynamics of targets after unloading, and it has almost no effect on wave profiles after plate impact.

Assessment of a one-dimensional finite element charring ablation material response model for phenolic-impregnated carbon ablator

In this study, mathematical formulations to model charring ablation problems were numerically implemented using finite element analysis (FEA) with ABAQUS, which account for the material decomposition and progressive surface removal in the heat conduction and the surface energy balance equations. FEA was performed for a one-dimensional model to predict the temperature and ablation histories of a phenolic-impregnated carbon ablator sample (i.e., a common heat shield material for hypersonic vehicles and spacecraft) subjected to oxy-acetylene torch flame (i.e., 0.8 SLPM acetylene gas to 2.7 SLPM oxygen gas). The recovery enthalpy and convective heat transfer coefficient for the ablation model were calculated based on gas compositions and two assumed surface conditions (i.e., equilibrium and frozen). Simulations using the calculated recovery enthalpy and convective heat transfer coefficient resulted in a recession rate of 6.38 times (equilibrium) and 14.08 times (frozen) higher than the experimental data, despite fair agreement of the surface temperature. In addition, the effect of the heat transfer coefficient was investigated through a steady-state ablation analysis. The results of the analysis indicate that there is not one single value for the heat transfer coefficient that would allow the prediction to match both measured recession rate and surface temperature. Possible reasons for such an inconsistency are provided and discussed.

Analysis of Meteoroid Ablation Based on Plasma Wind-tunnel Experiments, Surface Characterization, and Numerical Simulations

Abstract Meteoroids largely disintegrate during their entry into the atmosphere, contributing significantly to the input of cosmic material to Earth. Yet, their atmospheric entry is not well understood. Experimental studies on meteoroid material degradation in high-enthalpy facilities are scarce and when the material is recovered after testing, it rarely provides sufficient quantitative data for the validation of simulation tools. In this work, we investigate the thermo-chemical degradation mechanism of a meteorite in a high-enthalpy ground facility able to reproduce atmospheric entry conditions. A testing methodology involving measurement techniques previously used for the characterization of thermal protection systems for spacecraft is adapted for the investigation of ablation of alkali basalt (employed here as meteorite analog) and ordinary chondrite samples. Both materials are exposed to a cold-wall stagnation point heat flux of 1.2 MW m−2. Numerous local pockets that formed on the surface of the samples by the emergence of gas bubbles reveal the frothing phenomenon characteristic of material degradation. Time-resolved optical emission spectroscopy data of ablated species allow us to identify the main radiating atoms and ions of potassium, calcium, magnesium, and iron. Surface temperature measurements provide maximum values of 2280 K for the basalt and 2360 K for the chondrite samples. We also develop a material response model by solving the heat conduction equation and accounting for evaporation and oxidation reaction processes in a 1D Cartesian domain. The simulation results are in good agreement with the data collected during the experiments, highlighting the importance of iron oxidation to the material degradation.

Rationally Derived Three-Parameter Models for Elastomeric Suspension Bushings: Theory and Experiment

Abstract Linear, causal, and time-invariant viscoelastic material response models are of practical interest in many areas, including our interest in automotive suspension bushings. Empirical fits to experimental data may involve several fitted parameters which, if chosen arbitrarily, violate theoretical restrictions derived from causality, linearity, and time invariance. Here, we retain a correction term in an asymptotic expansion for Bode’s representation of the famous Kramers-Kronig relations. We then derive two new mathematical forms that both satisfy theoretical restrictions and fit experimental data well. Both forms proposed in this article have three free parameters each. The first form has logarithms and power law terms and is valid if the index in the power law is small. The second form has only logarithmic terms and satisfies restrictions exactly. Both forms successfully fit the test data for four different automotive suspension bushings in a frequency range of 1–30 Hz. The first form, with the power law, is more complicated but fits the data slightly better. Because the frequency response involves both a real and imaginary part, simultaneously fitting both parts well with merely three parameters validates the approximations proposed in this article.

Multidimensional material response simulations of a full-scale tiled ablative heatshield

The Mars Science Laboratory (MSL) was protected during Mars atmospheric entry by a 4.5 meter diameter heatshield, which was constructed by assembling 113 thermal tiles made of NASA's flagship porous ablative material, Phenolic Impregnated Carbon Ablator (PICA). Analysis and certification of the tiles thickness were based on a one-dimensional model of the PICA response to the entry aerothermal environment. This work provides a detailed three-dimensional heat and mass transfer analysis of the full-scale MSL tiled heatshield. One-dimensional and three-dimensional material response models are compared at different locations of the heatshield. The three-dimensional analysis is made possible by the use of the Porous material Analysis Toolbox based on OpenFOAM (PATO) to simulate the material response. PATO solves the conservation equations of solid mass, gas mass, gas momentum and total energy, using a volume-averaged formulation that includes production of gases from the decomposition of polymeric matrix. Boundary conditions at the heatshield forebody surface were interpolated in time and space from the aerothermal environment computed with the Data Parallel Line Relaxation (DPLR) code at discrete points of the MSL trajectory. A mesh consisting of two million cells was created in Pointwise, and the material response was performed using 840 processors on NASA's Pleiades supercomputer. The present work constitutes the first demonstration of a three-dimensional material response simulation of a full-scale ablative heatshield with tiled interfaces. It is found that three-dimensional effects are pronounced at the heatshield outer flank, where maximum heating and heat loads occur for laminar flows.

Ablative thermal protection systems: Pyrolysis modeling by scale-bridging molecular dynamics

Pyrolysis of a phenolic polymer is a well-known heat removal mechanism in charring ablators, but the process has not been well-quantified. Here, we perform scale-bridging molecular dynamics (MD) simulations based on a reactive-force-field (ReaxFF) potential to elucidate the pyrolysis kinetics of a highly crosslinked phenolic formaldehyde resin. We show that bulk pyrolysis starts at temperatures of ∼500 K, and exhibits a temperature dependence that follows the Arrhenius law. The pyrolysis process initiates with the removal of –OH functional groups and –H atoms from aromatic C rings within the bulk phenolic resin to release H2O, followed by breaking of these C rings to release C-based fragments. Using the pyrolysis rates from MD simulations, we develop a thermal material response model applied to predict the heat transfer within a charring syntactic foam ablator. Our model predictions of the char thickness and temperature distributions, under a variety of heat loads, are in good agreement with prior experiments.

Decomposition of Phenolic Impregnated Carbon Ablator (PICA) as a Function of Temperature and Heating Rate.

Material response models for phenolic-based thermal protection systems (TPSs) for atmospheric entry are limited by the lack of knowledge of the nonequilibrium processes that may govern the decomposition pathways of phenolic resin at heating rates up to tens of degrees Celsius per second. We have investigated the pyrolysis of phenolic impregnated carbon ablator (PICA) by measuring the molar yields of the volatile decomposition products as a function of temperature at four nominal heating rates of 3.1, 6.1, 12.7, and 25 °C s-1, over the temperature range of 100-1200 °C. A mass spectrometer was used to probe the 14 significant gaseous products directly as PICA samples were heated resistively in vacuum. Four products, H2, CH4, H2O, and CO, overwhelmingly dominated the molar yields. However, in terms of mass yield, phenol and its methylated derivatives, cresol and dimethyl phenol, were significant. The temperature-dependent molar yields of the observed products exhibited a marked dependence on heating rate. The heating-rate-dependent behavior of the molar yields has been attributed to two main competing decomposition processes that occur as the temperature passes from roughly 300 to 500 °C: (1) cross-linking reactions that produce ether functional groups and carbon-carbon bonds and eliminate H2O and (2) breakdown of the polymer backbone through scission of methylene bridges and liberation of phenol and its methylated derivatives. The latter process competes more effectively with the former as the heating rate increases. The relative rates of these processes appear to have a significant effect on the molar yields of volatile products from subsequent decomposition processes as the temperature is increased further. Thus, the heating rate strongly affects the pathways taken during the pyrolysis of the phenolic resin in PICA. The new data may be used to test nonequilibrium models that are designed to simulate the response of TPS materials during atmospheric entry of spacecraft.

Use of a Quasi-Steady Ablation Model for Design Sensitivity With Uncertainty Propagation

Sensitivity analysis and design calculations are often best performed using low-order models. This work details work done on adding complementary pieces to a low-order, quasi-steady-state ablation model to facilitate uncertainty propagation. The quasi-steady-state ablation model is a one-dimensional, quasi-steady-state, algebraic ablation model that uses finite-rate surface chemistry and equilibrium pyrolysis-gas-production submodels to predict surface recession rate. The material response model is coupled to a film-transfer boundary layer model to enable the computation of heat and mass transfer from an ablating surface. For comparison to arcjet data, a simple shock heated gas model is coupled. A coupled model consisting of submodels for the shock heated gases, film heat and mass transfer, and material response is exercised against recession rate data for surface and in-depth ablators. Comparisons are made between the quasi-steady-state ablation model and the unsteady ablation code, Chaleur, as well as to other computations for a graphite ablator in arcjet facilities. The simple models are found to compare reasonably well to both the experimental results and the other calculations. Uncertainty propagation using a moment based method is presented. The results of this study are discussed, and conclusions about the utility of the method as well as the properties of the ablation code are drawn.

Detailed analysis of species production from the pyrolysis of the Phenolic Impregnated Carbon Ablator

Many modern materials that are being developed to protect space vehicles entering planetary atmospheres use phenolic impregnated carbon fiber substrates as the basic material architecture. To mitigate the heat flux into the material, the decomposition of phenolic phase generates protective gases that blow into the boundary layer and help shield the material. The goal of this paper is to measure the decomposition products of cross-linked phenolic as used in the NASA's Phenolic Impregnated Carbon Ablator (PICA). A custom batch reactor was designed to quantitatively determine detailed species production from the pyrolysis of PICA. A step-wise heating procedure using 50K increments from room temperature up to 1250K was followed. An initial PICA mass of 100mg was loaded in the reactor, and the mass loss was measured after each 50K step. Species production after each step was quantified using gas-chromatography techniques. The quantitative molar yields of pyrolysis products as a function of reaction temperature are compared to those from resole phenol-formaldehyde resin pyrolysis reported in the literature. The differences in product distributions between PICA pyrolysis and resole phenol-formaldehyde pyrolysis confirm that the decomposition products are sensitive to the composition of the material and the cross-linking process. These results indicate that characterizations need to be performed for all variations of phenolic-matrix based ablators. Such information is also critical for the development of next generation material response models.

Simple implementation of plain woven polypropylene fabric

With increased utilisation of simple fabrics in technical engineering and manufacturing environments the need for suitable, easy to implement material representations in simulation software has increased. A simple implementation of plain woven polypropylene fabric for inflation simulation of dunnage bags is developed. Only standard finite element software packages and a simple material calibration protocol based on numerical optimisation were used to generate a homogenised material representation for the in-plane properties of plain woven polypropylene undergoing both loading and unloading. This is achieved by performing a simple material test that represents the in situ loading state of the material, measuring the applied load and material deformation in response to that load, and mapping that response to a simulation of the same test by means of an inverse problem statement. Following the proposed method, a material response model for plain wove polypropylene was developed that captures the major responses of a measured woven test specimen.