Charring Material Ablation Research Articles

Identification of the surface heat flux of charring ablative materials using dynamic Bayesian network based on multisource information fusion

In order to solve the dual uncertainty problem between heat flux and thermophysical properties in the identification of the heat flux of charring ablative materials, a dynamic Bayesian network (DBN) based on multisource information fusion is proposed. The method is divided into two stages, with thermophysical properties identified in the former stage and the heat flux identified in the latter stage. A one-dimensional pyrolysis layer model is adopted to characterize the ablation process of materials. In the DBN, the multisource information of surface recession and temperature history data are considered as observation nodes. Sensitivity analysis is used to determine the key parameters in each time step in the DBN, and only key parameters are identified in the corresponding time step. Thus, with the increase of types of information and the decrease of the number of simultaneous identification parameters, the identification accuracy can be improved. The method was verified by numerical and experimental cases. In the numerical cases with noise and experimental cases, the maximum error of using the proposed method was 3.27% and 2.55%, respectively. Compared with only considering the temperature information, the relative errors of the identification results considering multisource information fusion were reduced by 83.95% and 47.53%, respectively.

Conjugate flow-thermal analysis of a hypersonic reentry vehicle in the rarefied flow regime

A conjugate thermal analysis is performed for a charring ablative material by coupling an in-house direct simulation Monte Carlo flow solver with an in-house material thermal response solver at the fluid–solid interface. The coupling is achieved by exchanging and updating the interface properties (convective heat flux and wall temperature) between the flow and thermal solvers at certain anchor points along the reentry trajectory. Iterative and non-iterative coupling techniques are studied in this work and discussed. In-house flow-thermal code is validated by comparing surface heat flux and temperature variation with those obtained from an open-source code, Stochastic PArallel Rarefied-gas Time-accurate Analyzer, from Sandia National Laboratories, USA. The effect of introducing pyrolysis gas at the interface in the flow-thermal analysis is studied by applying a blowing correction function in an iterative manner. The effect of surface recession is also studied by enabling material degradation due to thermal ablation.

Effect of Thermal Ablation at the Fluid-Solid Interface of a Hypersonic Reentry Vehicle in Rarefied Flow Regime

The present work aims to develop a coupled flow-thermal solver to study atmospheric reentry phenomenon in the rarefied regime. Conjugate thermal analysis is performed for a charring ablative material by coupling a direct simulation Monte Carlo flow solver with an in-house material thermal response solver at the fluid-solid interface. The coupling is achieved by exchanging and updating the interface properties (convective heat flux and wall temperature) between the two solvers in a loosely coupled manner at certain anchor points along the reentry trajectory. Iterative and non-iterative coupling techniques are studied in this work and discussed. The effect of introducing pyrolysis gas at the interface in a loosely coupled flow-thermal analysis is studied by applying a blowing correction function to the heat flux obtained using iterative method. The results show that the blowing gas has an appreciable effect in reducing the surface heat flux that can significantly impact the TPS design.

Insight into chemical reaction kinetics effects on thermal ablation of charring material

Thermal ablation plays an important role in the aerospace field. In this paper, to study the chemical kinetics effects on heat transfer and surface ablation of the charring ablative material during aerodynamic heating, a charring ablation model was established using the finite element method. The AVCOAT 5026-39H/CG material, one typical thermal protection material used in thermal protection system, was employed as the ablative material and heated by aerodynamic heating condition experienced by Apollo 4. The finite element model considers the decomposition of the resin within the charring material and the removal of the surface material, and uses Darcy?s law to simulate the fluid-flow in the porous char. Results showed that the model can be used for the ablation analysis of charring materials. Then effects of chemical kinetics on ablation were discussed in terms of four aspects, including temperature, surface recession, density distribution, and mass flux of pyrolysis gas. The pre-exponential factor and activation energy have different effects on ablation, while the effect of the reaction order is little. This paper is helpful to understand the heating and ablation process of charring ablative materials and to provide technical references for the selection and design of thermal protection materials.

Two-dimensional study of charring ablative materials using finite volume method

Numerical simulation of charring ablative materials using finite volume (F.V) method is presented in this paper and a new modeling approach for pyrolysis gas mass flux production for multi-dimensional analyses is proposed. Pyrolysis gas mass flux produced in carbon-phenolic ablation process is solved by a user defined transport equation. User defined functions (UDFs) are developed in FLUENT 6.3 to consider the equilibrium surface thermochemistry (EST) model of carbon ablation in air including the diffusion and sublimation. Source terms of energy and pyrolysis gas equations, temperature-dependent boundary conditions, material properties variations and wall recession are all implemented in these UDFs. Also, Spring-based smoothing method is utilized as the grid motion technique. Furthermore, one-dimensional (1D) thermal response of the stagnation point is investigated using a finite difference (F.D) FORTRAN code. To ensure the accuracy of the proposed multi-dimensional modeling, a comparison is made between the published data and the computational results achieved by 2D F.V method at the stagnation point and the 1D F.D outcome. It is found that the predictions for the centerline temperature rise in the 2D analysis is generally higher than those of the 1D code. Also, the maximum ablation mass flux and the maximum recession are smaller compared to 1D predictions. This approach provides an in-depth study of a charring material under heat loads in situations where the classical 1D approach fails, e.g. anisotropic materials, sharp geometries and insulator-backup material interface.

Application of Levenberg–Marquardt Method for Estimation of the Thermophysical Properties and Thermal Boundary Conditions of Decomposing Materials

This study is devoted to inversely estimating the thermophysical properties and thermal boundary conditions of a carbon-phenolic composite, which is one of the widely used charring ablator. Conventional and modified Levenberg–Marquardt methods are applied to determine the unknown parameters and functions, respectively. The unknown parameters include specific heat and thermal conductivity over a wide temperature range, and the unknown functions are the time-varying cold-wall heat flux and surface temperature. Before inverting the data, a correlation analysis is performed to demonstrate the dependency of the unknown quantities and also to determine the number and locations of sensors. An in-house version of charring material ablation code is used to both compute the sensor measurements and invert the data. The current study pursues three scenarios, including avoiding crime in the inversion, adding random errors to the simulated measurements and using different decomposition models to generate the measurement temperatures and invert the data. The obtained results demonstrate the efficiency of the proposed method in retrieving the boundary conditions at the receding surface of charring composites, as well as, the temperature dependent thermophysical properties.

One-Dimensional Thermal Analysis Model for Charring Ablative Materials

This paper presents a one-dimensional model for the analysis of the charring ablative materials used in spacecraft thermal protection systems. The numerical method is based on an implicit finite difference formulation of the governing equations written for a system of mobile coordinates that accounts for the possible presence of surface recession. The maximum allowable operating temperature for the adhesive layer of the junction between the heat shield and the substructure is used as a design parameter for determining the minimum heat shield thickness. A case study on the re-entry of the Stardust capsule is presented. The model proposed as a useful dimensioning tool for the preliminary design phase of the heat shields of spacecraft entering the atmosphere. The model was validated through a survey of the literature related to the dimensioning of thermal shields but based on numeric programs of highly representative industrial standards.

Thermal Analysis of Honeycomb Sandwich Panels as Substrate of Ablative Heat Shield

This study describes a method to extend the one-dimensional charring material ablation code developed by Aerotherm Corporation to simulate honeycomb sandwich panels protected by ablative heat shields. Modeling of one-dimensional elements with a variable surface area was embedded in the original charring material ablation code to model nonplanar surfaces. This feature was used in the current study to simulate conductive heat transfer through honeycomb sandwich panels. For internal radiation exchanges, a useful form of steady-state radiation heat flux is derived from an energy balance inside enclosed honeycomb cells. This form makes the system of equations appropriate to be solved by a Gauss–Seidel iterative method. Furthermore, comprehensive formulations are provided to calculate internal radiation view factors between the faces of right prisms with an arbitrary polygon base. The results are presented in two parts. First, the thermal response of metallic sandwich panels as a hot structure is investigated. The thermal behavior of the panel is compared with that of the familiar Swann–Pittman model. Second, the thermal response of stainless-steel panels that are protected by a carbon-phenolic ablative heat shield is determined. In this part, a parametric study is conducted to quantify some important geometrical factors that influence the thermal analysis and performance. The results from both parts provide verification for the simulation tool developed in this study.

Effects of gradient density on effective heat capacity of charring ablative material for re-entry vehicles

Purpose – The effective heat capacity is a key index to estimate the thermal protection performance of charring ablative materials in reentry vehicles subjected to aerodynamic heat loads. The purpose of this paper is to investigate the effects of gradient density on the effective heat capacity. Design/methodology/approach – Based on the Fourier law and the pyrolysis interface model, the authors establish the governing equations for the transient heat conduction with variable density, and then simulate one-dimensional transient thermal behavior of a homogeneous and three types of non-homogeneous charring ablative material in reentry capsules by using the implicit numerical method. Findings – The moving rate of pyrolysis interface and the surface temperature of charring ablative material depend on not only the surface heating history, but also the gradient density. And the gradient density can improve the insulation performance of charring materials, e.g. the effective heat capacity in the bilinear design is larger than that in the homogeneous design under a given heat flux condition. Originality/value – This study will help the design of the thermal protection system in reentry vehicles.

Numerical Investigation of Thermal Response Using Orthotropic Charring Ablative Material

An orthotropic material model is implemented in a three-dimensional material response code, and numerically studied for charring ablative material. Model comparison is performed using an iso-Q sample geometry. The comparison is presented using pyrolysis gas streamlines and time series of temperature at selected virtual thermocouples. Results show that orthotropic permeability affects both pyrolysis gas flow and thermal response, but orthotropic thermal conductivity essentially changes the thermal performance only. The pyrolysis gas flow is hypothesized to contribute to the thermal response of the material as it convects energy through the porous medium.

Numerical study of iso-Q sample geometric effects on charring ablative materials

Abstract The geometric effects of iso-Q sample – a geometry that is widely used in arc-jet experiments – were numerically studied on charring ablative materials under arc-jet conditions. The objective was to investigate how the sample diameter, thickness, and sample holder affect the pyrolysis gas transport, thermal, and material response within the material. A series of three-dimensional (3D) simulations was performed on different iso-Q samples. Identical conditions were applied on the same low-density charring ablative material, but with different sample diameters and thicknesses. The results indicate that the sample diameter influences both side-wall heating behavior and the amount of gas blowing through the front surface; the sample thickness significantly affects the side-wall blowing pattern. In addition, two types of impermeable sample holders were studied. Sample holders which sheath the outside of the sample were found to result in effects similar to shortening the depth of the sample. Moreover, for samples with high diameter-to-depth ratio, the sample holder was found to increase the blowing rate at the stagnation point. These results can be used as general guidelines for choosing model geometries in future arc-jet experiments. The importance of 3D modeling and the limit of the one-dimensional (1D) assumption made in most material response codes, are also addressed.

Multidimensional Modeling of Pyrolysis Gas Transport Inside Charring Ablative Materials

The behavior of pyrolysis gas transport in arcjet test samples is numerically studied. The simulation of the pyrolysis gas flow inside a porous material is presented, using two different geometries. The effects of allowing the gas to flow out of the sidewall are especially highlighted. Results show that the flow inside the test article is complex, and that the zero-dimensional or one-dimensional assumption made in most material response codes are not necessarily valid for certain geometries. The importance of three-dimensionality for modeling an ablative test article is addressed.

Numerical Modeling of Charring Material Ablation with Considering Chemical-Reaction Effects, Mass Transfer and Surface Heat Transfer

The numerical solution of governing equations for charring material ablation for anticipating the recession rate and the heat response of charring heat shields is presented. The governing equations are nonlinear because of changing thermodynamic properties ρ, Cp, k according to temperature. The nonlinear equations are linearized by the new method which is developed in this research and this method is based on Newton–Raphson method, and the TDMA algorithm (Thomas algorithm) is used for solving these new linear equation systems. Using Newton–Raphson method is one of the advantages of the solving method, because it is very simple and it can be easily generalized to more difficult problems. The obtained results are compared with reliable sources to examine the accuracy of writing code.

NUMERICAL MODELING OF CHARRING MATERIAL ABALATION WITH CONSIDERING CHEMICAL REACTION, MASS TRANSFER AND SURFACE HEAT TRANSFER EFFECTS

Presently there is a little information that relates to heat shield systems. Also this information is not certain in so many cases. The main reason is that accurate calculations for measuring the sacrificing rate of various materials have not been obtained yet. Additionally, the real scale test has two disadvantages: high cost and low flexibility, and for each case we must perform a new test. So having a reliable numerical program that calculates the surface recession rate and interior temperature history is necessary. In this study numerical solution of governing equations for charring material ablation are presented in order to anticipate the recession rate and the heat response of charring heat shields. Thermodynamic properties , ,k changes relative to the temperature accompany the nonlinear nature of the governing equations and the Newton-Rafson method along with TDMA algorithm is used to solve this nonlinear equation system. Using Newton- Rafson method is one of the advantages of the solving method because it is relatively simple and it can be easily generalized to more difficult problems. In Newton-Rafson method the nonlinear equations complexity is not a dominating effect because by differentiation relative to every independent variable the structural coefficients of the governing equations system are obtained. Moreover the most important feature of the obtained equation system is that we can obtain the value of every independent variable in each iteration and by adding this amount of change in every variable to the previous one, the new variable value appears in governing equation structural coefficients and it continues up to complete convergence. The obtained results are compared with reliable sources in order to examine the accuracy of compiling code.

Ablative Materials' Boundary Condition Simulation by Applying Inverse Approach and Euler Solver

Anovel numerical approachis proposedfor determination of the surfaceconditions of ablative materials thatcan be considered as a counterpart of previous studies. The proposed technique benefits from the Euler solver that calculates the flowfield outside the boundary layer. The Euler solver is coupled with the charring material ablation code that accounts for unsteady ablation. In the current study, there is no need for determination of the flow and thermal fieldsintheadjacentboundarylayers.Theproposedapproachapproximatestheboundary-layereffectsand determines the surface conditions of ablators with minimal complexity and computational memory usage. The conjugate gradient method is also employed to estimate the boundary conditions at the ablator’s surface from the measured temperature histories. Two test cases are analyzed using numerical experiments with simulated exact and noisy measurements, which illustrate the advantages of the proposed method applied to such problems.

Multi-scale simulations of in-depth pyrolysis of charring ablative thermal protection material

Charring ablative thermal protection systems have been commonly used to protect the payload of a hypersonic or space exploration vehicle from exposure to high heat loads. The physical phenomena associated with the pyrolysis of the charring ablative material are very complex. The existing surface ablation models were built upon various assumptions, which introduce large uncertainties in the engineering design process and disable the direct assessment of uncertainties at engineering level. The current study proposes a multi-scale numerical model to simulate the in-depth pyrolysis process of a charring ablator. First, a numerical model for simulating the transport and chemical reactions of the pyrolysis gas as a continuum through the porous char layer of an ablative material is developed, validated, and verified. The continuum numerical model is designed to account for the effects of in-depth heat and mass transfer, and chemical kinetics of the pyrolysis gas, which are missing from the existing surface ablation models. Next, atomistic simulations are used as a tool to determine the pyrolysis gas composition entering the char layer from the virgin material, and to identify the main reaction pathways for the interaction between the pyrolysis gases. The pyrolysis gas composition and kinetic chemistry model are intended to be used to reduce the uncertainty associated with the continuum numerical model used to simulate transport and reaction of the pyrolysis gas through the char in the surface ablation process. The current status of the multi-scale pyrolysis model development and results from the validation and verification studies are presented in the paper.

Inverse Identification of Thermal Properties of Charring Ablators

The modified Levenberg-Marquardt method is used for simultaneous estimation of decomposition kinetic coefficients and temperature-dependent thermophysical properties of charring ablators with a moving boundary over a wide temperature range. No prior information is used for the functional forms of the unknown thermal conductivity and specific heat. The procedure used differs from the traditional one in that it does not require prescribed time-dependent surface heat flux, recession rate, and pyrolysis gas mass flow rate. These time-dependent quantities may recover during an iterative procedure. The measured temperatures are simulated numerically by the Charring material ablation code, which accounts for unsteady ablation. The method can determine unknown parameters in an efficient manner with reasonable accuracy, without exact advance knowledge about the net surface heat flux, surface recession, and gas flux through the material.

Estimation of Temperature-Dependent Thermophysical Properties of Noncharring Ablators

heat flux and ablative mass flux are unknown a priori and must be determined at each time step. The measured temperatures are simulated numerically by the Charring Material Ablation code that accounts for unsteady ablation. Particular emphasis is placed onthe sensitivity analysis, in which the role of sensor location andnumber of sensors in the estimation of thermal properties can be best appreciated. Considering the nonlinear nature of the proposed inverse problem, it is shown via simulated experiment that unknown parameters can be achieved with reasonable accuracy using this method despite the correlation of the involving parameters and the existing noises in the measurement data.

Performance Analysis of Thermal Protection System of a Solid Rocket Nozzle

A coupled approach is adopted to solve the conjugate problem of fluid flow and heat transfer in solid rocket nozzles in order to achieve an optimum thermal protection system (TPS). The computational fluid dynamics (CFD) code to solve the Navier-Stokes equations for fluid flow in a rocket nozzle is coupled with the charring material ablation code through an energy balance at the active surface of the wall material. The present analysis compares well with the test results generated in-house as well as those reported in the literature.

Evaluation and Mapping of Heat-Shield Flight Temperature and Composition with Raman Spectroscopic Techniques

A Raman spectroscopic technique has been developed which can measure the maximum temperatures experienced by charring heat-shield materials and determine their post-test compositions (char, pyrolysis zone, and virgin resin). The technique has the capabilities of analyzing circular areas less than 0.1 mm in diameter or rectangles 0.1 mm in width and 2 mm in length. It can provide fine detailed surface and internal mappings and perform the analyses rapidly and conveniently in the laboratory following testing or flight recovery. Representative plots of temperature and composition profiles are provided. The data are compared with computations from the Charring Material Ablation (CMA) code.