This paper is concerned with modeling of ablation behavior of carbon-carbon composites used in hot spot areas of reentry space and hypersonic vehicles. Of the three modes of ablation (thermal, chemical and mechanical), the chemical (oxidation) is considered to influence the performance of the material. Aerodynamic heat flux need to be computed separately and is the input for this. The thermal field is obtained by 3D finite element method. Nonlinear transient thermal analysis is carried out, as the material properties are dependent on temperatures. Oxidation rates are computed using the analytical relations available in literature. The oxidation is divided into two regimes: reaction rate and diffusion rate controlled. Mainly the surface temperature controls the regime. The oxidation protected materials are considered by using the parameter “activation energy.” The variations of ambient temperature, pressure and oxygen concentration with altitude are taken into consideration. As the recession takes place, newer surfaces are exposed to aerodynamic heating. Numerical examples are presented to show the effects of: heat flux, altitude and oxidation protection on the recession characteristics. Change of regime from reaction to diffusion rate control depends on parameters such as flow velocity and altitude. The latter has significant influence on ablation rate.

Hypersonic and reentry vehicles are subjected to intense aerothermal loads. The loads consist of external surface pressure,
skin friction, and aerodynamic heating. The latter is the predominant one. The heating rates vary with the type of mission, as low as 0.57 to as high as 57 W/

A review of fifty years of hypersonic vehicles has been presented [

As mostly

Variable node 3D solid element.

8 nodes

12 nodes

21 nodes

3D

Figure

Chemical ablation and boundary movement.

The molar oxidation rate is given by [

The Oxidation rate is given by

The oxidation rate is given by [

Figure ^{3}. If carbon fiber and carbon matrix do not oxidize simultaneously, the value of

Oxidation behavior of C/C composite.

With reference to Figures

Boundary movement Scheme.

Numerical examples are presented to bring out the effects of: reradiation, heating rate, altitude, and oxidation protection. The problem considered is that of rectangular slab of thickness equal to 150 mm, assumed to be made of

The heat transfer from the hot body by radiation is governed by fourth power law and is usually neglected in many cases as seen from the literature. However, in the case of aerospace vehicles subjected to aerodynamic heating of higher intensity, the radiation from the hot body needs to be considered. In order to show this effect, problem is analysed with and without radiation boundary condition on the heated surface. Figure

Surface temperature versus time

In aerospace vehicles, the intensity of heat flux varies as function of surface coordinates and time with maximum value at the stagnation point, as the vehicle moves in its flight path. Here, heat fluxes,

Surface recession with time at sea level,

Surface recession with time at altitude,

The altitude has greater influence on the oxidation. The variations of ambient temperature, pressure and density of air with altitude are the influencing factors. A study has been carried out for three altitudes,

Recession depth at different altitudes

The results presented in the earlier three sections are for the cases of unprotected

Effect of Oxidation protection at sea level,

Effect of Oxidation protection at higher altitude,

Finite element method-based software with boundary movement capability for modeling of oblation behavior of carbon-carbon composites has been developed. Analytical expressions for oxidation rates have been taken from literature. Based on the numerical studies on example problems, a few conclusions are drawn. The change of regime from reaction to-diffusion-rate controlled oxidation takes place at different temperatures depending on parameters such as velocity, altitude. The altitude has got significant influence on the recession. The protected material offers much better oxidation resistance compared to the unprotected material. It may be observed that in the present work, the oxidation protection has been modeled using the parameter, “activation energy.” This term appears only in the expression for the reaction rate controlled regime. However, a similar term for the protected material is not present in the expression for the diffusion controlled regime. This calls for improvement in the presently available model. With this software available, it is possible to model the ablation behavior of nose tips and leading edges used in the reentry space vehicles with aerodynamic loads computed separately. However, if the present software is integrated with a suitable aerothermodynamic package, it becomes possible to cocompute the aerodynamic loads along with the shape change due to ablation, taking in to account the varying local atmospheric data, as the vehicle moves in its trajectory.

Derivative matrix

Specific heat

Characteristic dimension

Altitude, heat transfer coefficient

Reaction rate

Material conductivity matrix

Diffusion rate of oxygen

Pressure of oxygen

Heat flux per unit area

Load vector in transformed eqn.

Temperature

Time

Global coordinates

Time step

Density of air

Emissivity

Ratio of

High temperature ablators

Carbon–carbon composite

Capacitance matrix

Concentration of oxygen

Activation energy

Load vector

Conductivity matrix

Direction cosines

Total pressure of local atmosphere

Logarithmic pressure of inerts

Universal gas constant

Molar oxidation rate

Temperature of medium

Flow velocity

Change in temperature

Surface recession

Density of material

Stephen-Boltzmann const.

Natural coordinates

Low temperature ablators.

Chemical, composite, conductivity

Diffusion

Surface

Transpose

Radiation, reaction

Heat flux

Time derivative.

The author expresses his thanks to Defence Research and Development Laboratory, Hyderabad, for sponsoring the project “Erosion Modeling of HSTDV Nose tip,” particularly to Dr. Panneerselvam, Technology Director, Aerodynamics. The author acknowledges the research contributions of (i) P. Ramesh, Project Officer, (ii) Suman Babu, (iii) J.G. Dhanamgaya, and (iv) G. Harishankar, graduate students.