Development and Verification of Improved Composite Material Demise Models for Ground Risk Prediction Software Tools

University of Pisa

Department of Civil and Industrial Engineering

Faculty of Aerospace Engineering

Development and verification of composite

material demise model for ground risk

prediction software tools

Master Thesis developed at the Institute of Space System (IRS) of the

University of Stuttgart in cooperation with the University of Pisa

Master Student Advisor

Serena Pirrone Professor Sauro Filippeschi

Supervisors

Abstract

The Carbon Fiber Reinforced Polymer (CFRP) represents an example of complex, non-monolithic compounds, which are becoming progressively more prevalent in many aerospace applications.

This work of thesis develops a numerical model describing the CFRP ablation behavior during an atmospheric uncontrolled reentry on Earth from Low Earth Orbits (LEO) regions. The modelling results are compared to the results that have been obtained experimentally at the Institute of Space Systems (IRS) of the University of Stuttgart.

This work is part of the Clean Space initiative promoted by the European Space Agency (ESA): this initiative aims to maintain the Earth’s orbital environment as a safe area and debris free (https://www.esa.int/Our_Activities/Space_Safety/Clean_Space). In order to achieve this objective, a new approach, known as Design for Demise (D4D), has been introduced: it refers to the intentional design of space system hardware that at the end of their life cycle have the characteristic to completely burn up or “ablate” during an atmospheric uncontrolled reentry decreasing, therefore, the amount of surviving parts reaching the ground and the correlated casualty risk.

In the demisable behavior’s analysis of the CFRP, a cylindrical disk of 0,00407 m length and 0,02655 m diameter has been examined in three different simulation cases: a) low heat fluxes conditions (the reference value used for the aerothermal heat flux is 260 kW/m2_),

where the sample is subjected mainly to pyrolysis outgassing; b) medium heat fluxes conditions (the reference value used for the aerothermal heat flux is 520 kW/m2), where the sample presents an initial pyrolysis outgassing followed by a gradual oxidation; and c) high heat fluxes (the reference value used for the aerothermal heat flux is 1400 kW/m2) where both the pyrolysis of the epoxy matrix and the oxidation process of the char proceed at higher rate. The aerothermal heat flux reference values are in good agreement with the values that have been adopted during the experiments at IRS.

its thickness. Particular attention has been addressed to analyze the trends of the temperature profiles related to the temperature’s growth on the sample’s boundary surfaces which includes: a) the surface that appears to be directly exposed to the aerothermal heat flux (surface referred in the following chapters as “front surface”), and b) the rear surface, that is not directly exposed to the flux (surface known in the following study as “back surface”). The modelled temperature profiles have been found to be in good agreement with that obtained experimentally. In particular, the modelled vs. laboratory tests comparison showed a good agreement in terms of temperature profile’s growth rates and highest temperature values achieved at the end of exposition time to heat flux conditions that are similar to those that would be observed during an uncontrolled reentry to the Earth from LEO regions.

The second part of the analysis is focused on modelling the reduction of the CFRP sample’s thickness during different reentry conditions: the sample thickness’s reduction is primarily due to the oxidation process of the carbon char that takes place when the CFRP is under high temperatures conditions (temperatures higher than the activation temperature of the oxidation process, which is 1160 K). This additional analysis concerns the cases when the sample is exposed to medium and high heat fluxes, that are conditions during which the oxidation process takes place: a) in the medium heat flux case, the thickness’s decrease results to be equal to 46,81% at the end of the test, whereas b) in the high heat flux condition, about 60% of the thickness is lost at the end of the simulation.

Table of Contents

1. Introduction 1

2. State of Art 4

2.1 Background 4

2.2 Design for demise D4D 7

2.3 Composite materials used in the aerospace industry 8

2.4 Ablation models for CFRP material 11

3. Facilities at IRS and past studies 20

3.1 IRS Experimental facilities 20

3.2 Emissivity investigation 22

3.3 Plasma Wind Tunnel investigation 25

3.4 Steady-state thermal material response 27

3.5 Transient material response 27

3.5.1 Testing CFRP EX1515/M5JJ in Low Heat Flux regime 28

3.5.2 Testing CFRP EX1515/M5JJ in Medium Heat Flux regime 30

3.5.3 Testing CFRP EX1515/M5JJ in High Heat Flux regime 33

4. Numerical ablation model 36

4.1 Energy balance equation 37

4.2 Boundary conditions 40

4.3 Input data for the numerical model 42

4.4 Initial condition 42

4.5 Solver PDEPE 43

4.6 Numerical solution 45

4.6.1 Low Heat Flux 45

4.6.2 Medium Heat Flux 48

4.6.3 High Heat Flux 51

4.7 Additional calculations 53

4.7.1 Medium Heat Flux 54

5. Sensitivity analysis 59

5.1 Background 59

5.2 Sensitivity analysis results 60

6. Results 67

6.1 Discussion of the modelling results 67

6.2 Comparison between modelling and experimental results 69

6.2.1 Low Heat Flux condition for radiative and adiabatic back surface case-study 69

6.2.2 Medium Heat Flux condition for radiative and adiabatic back surface case-study 70

6.2.3 High Heat Flux condition for radiative and adiabatic back surface case-study 72

6.3 Variation of sample’s thickness 73

6.4 Sources of uncertainty 74

7. Conclusions 77

8. Acknowledgement 80

9. Cited Litterature 81

Appendix-A: List of Tables 83

Appendix-B: List of Figures 84

1.

Introduction

A significant number of satellites are located in orbits around the Earth in order to perform measurements of physical and chemical parameters that are needed to support key domains of investigation such as space science, human space exploration, Earth observation, climate research, meteorology and telecommunication, among others. The gathering of high-quality data is a top priority in advancing our knowledge in the functioning of the Earth’s system, in ensuring an efficient globally distributed telecommunication system and for national security.

During the last decade in Europe a large-scale Earth Observation programme was developed, known as Copernicus programme to support the European strategy aiming to improve our knowledge of the Earth’s system. The seven ESA’s satellite missions called Sentinels represent the core of Copernicus, these ESA’s missions were designed to provide information on the functioning of the Earth’s system with special focus on climate changes and its variability with changing environmental pressures caused by human activities through the monitoring of chemical and physical parameters of oceans, land and atmosphere. The Copernicus programme is also aimed to support national and international emergency response systems for the management of the risk caused by natural extreme events (i.e., hurricanes, typhoons, earthquakes) and national security programs.

Four Sentinel satellites have been successfully launched and the Sentinel-4 mission will be the next one. The Sentinel-4 will be placed on a geostationary orbit equipped with instruments that will allow the monitoring of air quality, stratospheric ozone, solar radiation and climate over Europe and Northern Africa. The Sentinel-4 satellite consists of a) the Sentinel-4 space element, which will be launched in 2019, and b) the Sentinel-4 ground segment elements, for a total expected mission time of about 15 years.

The Copernicus programme represents only a small part of the recent space activities’ expansion. During the last two decades the problem of the space debris gained a significant attention due to the growing effort in space research and technological development. In the

are in the Low Earth Orbit (LEO), whereas objects larger than 30 cm – 100 cm are in the Geostationary Earth Orbit (GEO) with an estimated total mass of about 7500 tons. This significant amount of debris that can be found in LEO and GEO regions is primarily originated by a number of sources which include a) past collisions between satellites, b) the explosion of satellites and rocket bodies, and c) the release by solid rocket motor firings of aluminum oxide Al2O3 in the form of dust and slag particles.

As the debris population grows, more collisions will occur and this could be particularly critical for the LEO regions: about the 43% of the total amount of objects orbiting around Earth is located in the Low Earth Orbit region and it is distributed in a not uniform way. In particular, the three major peaks are placed near 600, 800 and 1000 km respectively: the 600 km peak is dominated by spacecraft while the other two peaks are dominated by rocket bodies (Liou, 2011). Recent studies have estimated that over the next 200 years in the Medium Earth Orbit (MEO) and Geostationary Earth Orbit (GEO) the debris population growths will be significantly lower than that will occur in the LEO zones (Liou, 2011). Therefore, in the last years space agencies have developed ad-hoc programs to face this issue in order to avoid future risks associated with uncontrolled flying objects in the LEO region. In this context, the European Space Agency (ESA) developed its space debris mitigation strategy by promoting the Clean Space initiative which represents an eco-friendly approach to the space activities having as overarching goal that of maintaining the Earth’s orbital environment as a safe area and debris free. This approach is structured along two main actions which are a) the removal of the already existing debris, and b) the design of non-debris creating missions. In particular the removal of existing non-debris is driven through an active removal, i.e. deorbit of the dead satellites through service vehicles and capture of the debris through nets, whereas for future missions the approach is based on the Design for Demise (D4D) which refers to the intentional design of space system hardware that at the end of their life cycle have the characteristic to completely burn up or “ablate” during an atmospheric uncontrolled reentry which would lead to a reduction of the amount of surviving parts reaching the ground and the correlated casualty risk.

The ablation of materials is a very complex process, it is well understood for the metallic materials that ablate through melting process, while for the Carbon Fiber Reinforce Polymer like materials the ablation process is more complex. The behavior of these materials is

influenced by manifold physical mechanisms such as the endothermic pyrolysis process and the exothermic oxidation process (Fritsche, 2017).

The goal of the Design for Demise approach is to obtain a well demisability of the spacecraft components (i.e. the spacecraft design and the materials adopted in its manufacturing must be demisable). Recent studies have demonstrated that a spacecraft is ideally well demisable if it is characterized by a) thin walls, b) no large, heavy, monolithic and temperature resistant components, c) break-up time as early as possible during the reentry which would imply an early exposure of parts to the atmosphere (i.e. high ballistic coefficient and high break-up altitude are needed) (Pagan and Herdrich, 2017). Therefore, a spacecraft material is ideally well demisable if it is characterized by a) resistance against the LEO environment (i.e. resistance against corrosion caused by atomic oxygen, resistance against ionizing radiation, resistance against micro-debris impact), b) prone behavior to thermomechanical failure in order to break-up early, c) limited thermal resistance, d) neither radioactivity or toxicity, in case of survival to impact (Pagan and Herdrich, 2017).

The analysis of the aerospace materials’ behavior during the reentry phase on Earth is very complex and requires the knowledge of parameters that can be measured in chamber-controlled experiments by testing samples of aerospace materials in experimentally simulated reentry conditions. An example of experimental simulations is represented by those executed in the Plasma Wind Tunnel (PWT or PWK) facilities located in the Institute of Space Systems (IRS) of the University of Stuttgart. The materials that have been tested at PWT facility include metallic alloys, ceramics and composites.

In this context, it is important to have numerical models able to simulate the ablation behavior of materials subjected to reentry conditions.

The aim of this thesis is to develop a numerical ablation model to study the behavior of composite material in different reentry conditions. The study focused on the demise’s analysis related to the Carbon Fiber Reinforced Polymer (CFRP) and experimental data

2.

State of Art

2.1 Background

In the last 60 years, about 4800 launches have placed 6000 satellites into orbit, less than a thousand are still operational today (ref). About 23000 objects orbiting the Earth have been tracked, this large amount of objects has sizes larger than 5 cm - 10 cm in Low Earth Orbit (LEO) and 30 cm – 100 cm in Geostationary Earth Orbit (GEO) and it has a total mass of about 7500 tons (https://www.esa.int/Our_Activities/Space_Safety/Space_Debris/About_space_ debris).

Space debris is considered a high-risk issue for future space missions: for example, a debris of just 1 cm size can expend the energy of an exploding hand-grenade when impacting a satellite. Moreover, because of the huge quantity of debris orbiting the Earth, some Space’s regions (in particular, LEO areas) could become inaccessible for centuries. Therefore, ESA is trying to mitigate the space debris through the Clean Space initiative (https://www.esa.int/Our_Activities/Space_Safety/Clean_Space) which represents an eco-friendly approach to the space activities, i.e. maintaining the Earth’s orbital environment as a safe area (free of debris) through the following techniques (Pagan and Herdrich, 2017): a) Debris reduction, through the debris’ capture using nets and service vehicles in order to

deorbit the defunct satellites; these are classified as active measures.

b) Debris restriction, through the 1) monitoring and tracking the existing debris, 2) passivation of volatile systems, 3) evasive maneuvers of active vehicles, and 4) deorbiting in decay orbits satellites at their End-Of-Life (EOL).

c) Ultimate neutralization of defunct vehicles and debris through destructive re-entry.

During uncontrolled re-entry, the spacecraft are exposed to high aerothermal heating and, therefore, the components and substructures may break-up and as consequence the risk of impact of surviving debris on ground appears possible: this happens to components that are very heavy or to parts that have very compact structures or to parts with late exposure; typically, they represent a mass fraction of 10% to 40% of the original spacecraft mass. Examples are represented by entering space stations like Skylab-1 or Salyut-7.

The following scheme (Figure 2.1) illustrates different patterns involved in uncontrolled and controlled re-entries (Pagan and Herdrich, 2017):

The controlled re-entry (as in the case of crew missions) requires active deorbiting and it is identified by a well-defined control procedure that requires the knowledge of the point of re-entry, altitude, flight path and impact region. Therefore, it is characterized by a low risk of harm to human life and property if it is well performed. Differently, during uncontrolled re-entry, random deorbiting following orbital decay is executed and no control flight path is possible to secure, therefore, it is difficult to accurately predict the point of impact. This latter case is characterized by high risk for people life and properties (Pagan and Herdrich, 2017).

In detail, an uncontrolled re-entry in atmosphere (see Figure 2.2) involves several events such as (Pagan and Herdrich, 2017):

a) the solar arrays break-off, where they together with other similar structures break-off due to aeromechanical forces;

b) the fragmentation of the vehicle, due to aerothermal heating and aeromechanical forces; c) the demise of objects produced by the fragmentation, due to aerothermal heating;

Figure 2.2: Uncontrolled re-entry, (Pagan and Herdrich, 2017)

The possible impact of surviving debris on the ground represents a high risk for properties and human life. The primary risk is related to the possibility of a direct hit of people, the secondary risk concerns the potential debris hit on buildings, industrial plants, vehicles. Several models are adopted to predict number, flight path, size and mass of the surviving debris but the prediction of the point of impact on the ground is characterized by a high uncertainty in the case of uncontrolled re-entry. The impossibility to predict correctly and with an acceptable uncertainty the trajectory of survival debris moving earthwards to the final impact on the ground is due to several factors, including:

- the inaccurate tracking data;

- the complex and irregular shape of the re-entering object;

- the uncertainty in the computation of the atmospheric density at the altitudes of the flying object;

- the error associated to the predicted magnitude and variability of solar and geomagnetic activity which may likely lead to an increase of the error associated to the gas-surface interaction and drag coefficients estimate;

- the local wind can influence significantly the trajectory in the lower atmosphere (troposphere) before the impact on the ground;

- the impacted Earth’s surface area by these flying objects reentering from space may be as large as several hundred squared kilometers.

2.2 Design for Demise D4D

Having in mind the background briefly described above, a new philosophy in designing space vehicles is gaining a growing attention in the international scientific community which is known as the Design for Demise (D4D) approach.

The D4D consists in the intentional design of space systems hardware in order to have a complete burn up or ‘ablation’ of materials during an uncontrolled re-entry (https://www.esa.int/Our_Activities/Space_Engineering_Technology/Design_for_Demise_ ITT_issued_aiming_for_safer_satellites). This new approach is required in order to reduce substantially the amount of surviving parts reaching the ground and the correlated risk for human life and properties.

The D4D study started in September 2004 by analyzing the risk factors associated to the re-entry from LEO regions: the study started with the re-re-entry analysis using the SCARAB (Spacecraft Atmospheric Re-Entry and Aerothermal Break-Up) tool on the spacecraft of the Sentinel fleet. In particular, the spacecraft Sentinel-1 has been deeply studied in relation to the reduction of re-entry risk because of its mass and the presence of a high payload (Grassi et al., 2017).

The D4D approach is a recent concept and, therefore, important gaps still exist. The following factors represent a major challenge for improving the D4D approach:

- the process of the spacecraft demise is a complex challenge due primarily to a) the complex thermo-mechanical environment that the satellites are part of during their re-entry, and to b) the difficulty on predicting the fragmentation events during the demise which represent a source of important errors in the estimation of the casualty risk; - how and to what extent the structural design influences the vehicle’s demisability;

In detail, a spacecraft design is ideally well demisable if it is characterized by a) thin walls, b) no large-, no heavy-, no monolithic- and no temperature resistant-components, c) break-up time as early as possible during the reentry and this means an early exposure of parts to the atmosphere (i.e. high ballistic coefficient and high break-up altitude are needed).

A spacecraft material is ideally well demisable if it is characterized by a) resistance against the LEO environment (i.e. resistance against corrosion through the action of atomic oxygen, resistance against ionizing radiation, resistance against micro-debris impact), b) prone behavior to thermomechanical failure in order to break-up early, c) limited thermal resistance, and d) neither radioactivity or toxicity, in case of survival to impact (Pagan and Herdrich, 2017).

2.3 Composite materials used in the aerospace industry

The composite materials play a significant role in the aerospace industry due to their exceptional strength and stiffness-to-density ratios and superior physical properties.

The composite materials are formed by two or more constituents differing in form and/or material composition. They consist of fibers bonded by a resin matrix: the fibers represent the strong and stiff elements, whereas the resin matrix is needed in order to a) keep together the fibers, b) distribute the load to the fibers in equal way in order to have a uniform deformation under mechanical stress, and c) protect the fibers from the action of the external environment. Therefore, considering all the above, the resin matrix is required to have advanced mechanical properties.

The composite materials are preferred in the aerospace industry because provide many advantages such as (Nayak, 2014):

- light weight due to high specific strength and stiffness; - high fatigue and corrosion resistance;

- low thermal dilatation coefficient, guaranteeing a high dimensional stability during thermal excursions;

- high mechanical properties;

However, these materials have also some disadvantages including the following (Nayak, 2014):

- high cost;

- laminated structure with weak interfaces causing poor resistance to out of plane tensile loads;

- sensitivity to impact damage and high possibility of internal damage going unnoticed.

The composite materials are not conventional: they are anisotropic, inhomogeneous and they have a complex behavior when subjected to high loads and, therefore, to better understand and predict their behavior in different working conditions complex numerical mathematical models are required.

Thanks to their characteristics the composite materials are largely used in many applications in the aerospace sector. There are many different typologies of composite materials which differ on the basis of the type of fibers and resin matrices used. In particular different typologies of resin matrixes are summarized in the following Table 2.1.

Metal matrix (MMC) Ceramic matrix (CMC) Polymer matrix (PMC)

Strong, conductive and high temperature capable Examples: titanium, aluminum, magnesium

Strong, tough, high temperature capable

Examples: silicon carbide, alumina

Strong, stiff, low weight, good wear resistance

Examples: epoxy, polyester

Table 2.1: Different typologies of matrixes used in the aerospace sector (Nayak, 2014)

The Tables 2.2 and 2.3 reported below are reported the predominant fibers and the predominant polymeric matrices mostly used in the aerospace applications (Nayak, 2014).

Polymeric Matrices

Epoxy Phenolic Polyester Polyimide

- 80% of total composite use - Used at moderately high temperatures - Expensive - Low shrinkage - No release of volatile during curing - Good storage stability to make prepregs - Sensitive to moisture, causing swelling and degradation of properties - Lower viscosity - Used at high temperatures - Cheaper - High shrinkage - Release of volatile during curing - Inherent stability for

thermal oxidation - Brittle if compared to

epoxy

- Less storage stability - Absorbs moisture but the effects in working service are not significant - Cheap - Easy to use - Used at ambient temperature - High shrinkage - Good chemical resistance - Brittle - Difficult to prepreg - Less sensitive to moisture if compared to epoxy - High temperatures application - Difficult to process - Brittle

Table 2.3: Polymeric matrices

The carbon fibers are the most used in aerospace applications because of their light weight (it is lighter than both aluminum and steel), high strength and stiffness and modulus, long durability, elevated fatigue and creep resistance. A carbon fiber is composed by carbon

Fiber Density

[g/cc]

Modulus [GPa]

Strength

[GPa] Application areas

Glass - E-glass - S-glass 2.55 2.47 65-75 85-95 2.2-2.6 4.4-4.8

Rocket motor casings Parts subjected to high loads Aramid - Low modulus - Intermediate modulus - High modulus 1.44 1.44 1.48 80-85 120-128 160-170 2.7-2.8 2.7-2.8 2.3-2.4

Not load bearing parts Rocket motor casings Parts subjected to high loads Carbon - Standard modulus (high strength) - Intermediate modulus - High modulus - Ultra-high strength 1.77-1.80 1.77-1.81 1.77-1.80 1.80-1.82 220-240 270-300 390-450 290-310 3.0-3.5 5.4-5.7 2.8-3.0 4.0-4.5 7.0-7.5

Used in almost all parts of satellites

Primary structural parts in high performance fighters Space structures

Primary structural parts in spacecraft

atoms bonded together aligning parallel to the longitudinal axis. This fiber is approximately 0.005-0.010 mm in diameter and the degree of alignment is the reason of its high strength. The carbon fibers contain a minimum of 92% carbon, when the amount is ≥ 99%, the fiber is considered to be a graphite fiber.

The advantage of the carbon fiber is the high fatigue and corrosion resistance properties, if combined with appropriate resins: the materials deriving from this combination are known as Carbon Fiber Reinforced Polymers (CFRP) and they show particularly high performances when the carbon fibers are bonded using the epoxydic matrix, because of all the important advantageous of this resin as exposed in the table reported above. The CFRP is extensively used for a variety of applications in the aerospace sector, due to its favorable strength-to-weight ratio compared to metal alloys that have been traditionally used. In this context, the numerical methods developed in the past for metallic components to model their behavior under various stress conditions is not applicable. Therefore, in recent years several studies focused on the development of CFRP ablation behavior’s models in order to understand its demise processes during uncontrolled re-entry on Earth. This research activities addressed to improve our understanding of physical and chemical processes affecting the CFRP ablation behavior is one of the objectives of the ESA Clean Space Initiative.

2.4 Ablation models for CFRP material

This section provides a detailed literature review of previous studies related to the ablation behavior of carbon fiber/epoxy composite materials.

One of the first important analysis on the ablation behavior of the CFRP has been conducted by Quintiere et al. (2007), who analyzed the key factors affecting the properties of the composite material when exposed to fire events with aircraft operations. The analyzed composite’s sample has a thickness of 3.2 mm and it is represented in Figure 2.3.

During the sample’s heating, the resin evaporates and escapes through the carbon fibers introducing important internal pressure in the material and, consequently, the expansion of the composite. As consequence of the sharp increase of the sample’s temperature, the material’s density decreases while the thermal conductivity of the resin increases. During the resin’s evaporation, the remaining char burns as a consequence of the surface oxidation producing carbon monoxide. Typically, the burning activation temperature for the char is in the range of 300 °C to 500 °C.

Quintiere et al. (2007) modeled the composite’s decomposition with a one-step first-order model characterized by the following governing equation:

𝑑𝛼 𝑑𝑡

=

1−𝛼 1−𝜇

𝑘(𝑇)

(2.1) where 𝛼 = 𝑚− 𝑚𝑖 𝑚𝑓− 𝑚𝑖= 𝑚 𝑚𝑖 −1

𝜇−1 represents the mass loss rate, 𝑘 = 𝑎𝑃exp (− 𝐸𝑎

𝑅 𝑇) is the Arrhenius

rate, 𝐸_𝑎 is the decomposition’s activation energy, 𝑎_𝑃 is the pre-exponential factor, m is the mass, the subscripts i and f are respectively the initial and final conditions, whereas μ is the mass residue fraction.

The equation has been solved in the term m

𝑚𝑖 and the results have been compared to that

obtained experimentally.

Quintiere et al. (2007) observed that the resin completely evaporates for heat fluxes above 25 𝑘𝑊

𝑚2: in these conditions, the heat of combustion for the evolved resin vapors was about 20 𝑘𝐽

𝑔−𝑣𝑎𝑝𝑜𝑟, the yield of CO in flaming was about 0.48 𝑔−𝐶𝑂

𝑔−𝑣𝑎𝑝𝑜𝑟, the mass fraction μ of remaining

residue was about 0.74, the energy activation 𝐸_𝑎 for the decomposition process resulted 182

𝑘𝐽

𝑚𝑜𝑙 and the pre-exponential factor 𝑎𝑃 was 9.67x10

10 _𝑠−1_{. Moreover, it was observed that}

the sample can swell to over twice its volume by increasing its porosity by about 65% of its initial value.

In all the analysis, Quintiere et al. (2007), considered both thermal conductivity and specific heat at constant pressure in function of the temperature as illustrated in Figure 2.4.

Therefore, the thermal properties have been expressed as empirical expressions in function of the temperature, simulating a model where there is no need to know the properties of each constituent; this represents an important future of their modelling approach because to model

This study represented the scientific basis on which other studies based their numerical models on the ablation behavior of the carbon fiber reinforced polymer. Among different studies that by Tranchard et al. (2015) on the decomposition of the T700 carbon fiber reinforced M21 epoxy resin composite during a severe fire event represents an important milestone. The decomposition mechanism has been examined as a two-step process where the material is transformed from an initial (‘virgin state’) to a final stage (‘degraded state’) which is composed by a carbonaceous residue and carbon fiber. Therefore, in this model the degradation of the composite material involves a multi-species decomposition process.

This model is based on the following heat balance equation:

𝜌 𝑐𝑃 𝑑𝑇 𝑑𝑡 = ∇ ( Λ ∇T ) − [ℎ − ℎ𝑔] 𝑑𝜌 𝑑𝑡 − [ 𝑚_𝑔𝑥 𝑚_𝑔𝑦 𝑚_𝑔𝑧 ] ∇ℎ𝑔 (2.2)

where (a) is the heat transfer, (b) is the anisotropic heat conduction, (c) is the composite’s decomposition, and (d) is the gas transport which is linked to the internal pressure. In the heat balance equation 𝜌 is the material’s density, which is expressed in function of the time t (𝑑𝜌

𝑑𝑡 density rate) assuming that the volume of the sample does not change significantly over

time. 𝑐_𝑃 is the specific heat at constant pressure, Λ is the thermal conductivity tensor, h is the enthalpy of decomposition of each step i, hg is the gaseous’ enthalpy, the vector [

𝑚_𝑔𝑥 𝑚_𝑔𝑦 𝑚_𝑔𝑧] represents the three components (x,y,z) of the gas mass transport vector.

In the model, the temperature dependent parameters are 𝜌, 𝑐_𝑃, Λ, 𝑑𝜌

𝑑𝑡 which have been

expressed as function of the decomposition degree 𝛼 defined as:

𝛼 =

𝜌𝑉− 𝜌

𝜌_𝑉− 𝜌_𝐸 (2.3)

where 𝜌𝑉 and 𝜌𝐸 are the densities of the virgin and degraded material, respectively.

Along with the heat balance equation, Tranchard et al. (2015) considered a set of additional equations in order to characterize the boundary conditions which include: a) an equation

comprising the heat fluxes acting at the surface exposed to the heat source and b) an equation related to the heat fluxes concerning the surface unexposed of the composite material.

They solved the heat balance equation in function of the mass’s evolution, the time to ignition and the temperature profile along the material’s sample. The theoretical results have been compared with the experimental results and major findings are:

1) the mass that has been obtained during the experiment by exposing the CFRP sample to a controlled heat flux was found in good agreement (maximum error ±3%) with that obtained theoretically by applying the heat balance equation;

2) in relation to the dependence with time-to-ignition, the modelled value of 40 s is higher of the 25 s obtained in the laboratory tests. Considering the complexity of the laboratory tests and the assumption adopted in solving the heat balance equation (i.e., low accuracy of the input parameters used in the model), the difference between modelled and measured time-to-ignition has been considered acceptable for the purposes of the study;

Another important example of ablation behavior’s modelling is the work published by McKinnon et al. (2016), who considered a carbon fiber laminate composite with a layup made of 16 plies with orientation described by (-45, 0, 45, 90)2s. In each layer, this layup

features fibers that are rotated by 45 degrees with respect to the previous layer producing quasi-isotropic thermal transport properties through the plane of the material. The laminae are composed of continuous carbon fibers and the matrix material is an epoxy resin. McKinnon et al. (2016) assumed the thermal degradation of the carbon fiber composite to be described by a 4 consecutive chemical reactions mechanism formed by first-order reactions except the last one that is a second-order reaction. The reactions are summarized in Table 2.4.

# Reaction equation 𝐴 [(𝑚3 _𝑘𝑔−1₎𝑛−1_𝑠−1_{] 𝐸 [} 𝐽

𝑚𝑜𝑙] ℎ [

𝐽 𝑘𝑔] 1 Compositevirgin = 0.989Compositeint1

+ 0.011Compositevol1 4.09 10

5 _{9.18 10}4 _{−1.8 10}4

2 Compositeint1 = 0.902Compositeint2

+ 0.098Compositevol2 6.16 10

19 _{2.78 10}5 _{−3.8 10}4

3 Compositeint2 = 0.911Compositeint3

+ 0.089Compositevol3 1.23 10

21 _{3 10}5 _{1.8 10}4

4 0.5Compositeint3 + 0.5Compositeint4 =

0.888Compositeresidue+ 0.112Compositevol4 8.00 10

5 _{1.5 10}5 _{1.0 10}4

Table 2.4: Four-reactions process for CFRP degradation

The subscripts used in Table 2.4 have the following meaning: a) virgin is related to the initial unreacted material component, b) residue refers to the final product of the degradation which means a component composed of undegraded carbon fibers with a minor contribution from the char formed from degradation of the epoxy resin, c) int corresponds to the intermediate component formed by the reaction which is followed by a index representing the number of the reaction that forms the intermediate product, 4) vol refers to the mixture of gaseous volatile compounds produced by the pyrolysis which is followed by a second index referring to the type of chemical reaction involved.

McKinnon et al. (2016)’s study was observed a gradual increase in the sample’s thickness during the laboratory test, in accordance with the observations made by Quintiere et al. (2007) that found a 100% increase of the original thickness value for the carbon fiber composite at the end of the simulation. The four-reactions mechanism with a relative experimental vs. theoretical difference as low as 7%, on average, may be considered a suitable mechanism scheme to model the mass loss process of the carbon fiber composite due to thermal degradation.

In this context, an important contribution to our knowledge on the CFRP behavior in different conditions is represented by the analysis conducted by Fritsche (2000) that improved the modeling performance of CFRP properties during the re-entry of a spacecraft containing parts made in CFRP. The decomposition by an endothermic pyrolysis and the burning through an exothermic oxidation were the two main processes considered in analyzing the CFRP behavior. When exposed to high heat fluxes, the CFRP undergoes to a degradation of its chemical and physical characteristics primarily driven by two main

processes: 1) the phenolic resin on the outer layers decomposes producing a mixture of volatile gaseous compounds due to the endothermic pyrolysis process that takes place and the decomposition layer migrates inside the CFRP “virgin material” with increasing temperature; 2) on the backside of this decomposition there is a carbon char through which the mixture of gaseous compounds produced by the pyrolysis process escapes and the outflow of the pyrolysis’ gaseous products in the hot boundary layer causes a decrease of the aerodynamic heat transfer rate. Moreover, on the surface the carbon char is also oxidized by the impinging high temperature oxygen adding heat. Therefore, all these processes through which the composite materials decompose have been formulated mathematically, as discussed below.

The local heating in the material due to incoming heat 𝑞̇_ℎ is described by the equation: 𝑑𝑞_ℎ̇

𝑑𝑥 = 𝜌 𝑐𝑝𝑇̇ (2.4)

where ρ, cp and T are the local values of density, specific heat at constant pressure and temperature.

The surfaces at temperature T re-radiate the heat to the outside as: 𝑞𝑟̇ = 𝜀 𝜎 𝑇4 (2.5)

where σ = 5.67 · 10−8 w/(m2k4) is the Stefan-Boltzmann constant and 𝜀 is the emissivity of the material.

Between the internal surfaces the heat qc is exchanged through a conductive mechanism: 𝑞̇_𝑐 = 𝜆𝑑𝑇

𝑑𝑥 (2.6)

where 𝜆 is the thermal conductivity of the material.

The pyrolysis process is an endothermic process which adds a negative contribution to the heat fluxes balance and decreases the density of the resin 𝜌_𝑝 as it follows:

𝜌̇_𝑝 = −𝐹 𝜌_𝑝 (2.7) where F is the pyrolysis reaction rate.

𝑞̇_𝑔 = 𝑚̇_𝑔 𝑐_𝑝,𝑔𝑑𝑇

𝑑𝑥 (2.8)

Where 𝑚̇_𝑔 is the mass flux and 𝑐_𝑝,𝑔 represents the specific heat at constant pressure of the pyrolysis gas mixture.

On outflow through the frontal surface the pyrolysis gaseous mixture will cause a change in the heat flow field in front of the surface and the external aerodynamic heat input 𝑞̇∞: this

can be accounted by a blowing factor, which is a measure for the reduction of the effective aerothermal heat flux. However during the outflow through the front surface the pyrolysis gaseous mixture can blow apart small carbon fibers which is difficult to model with available data. The correlation for the mass loss by erosion (𝑚̇_{𝑏𝑙𝑜𝑤}) was found empirically using experimental data:

𝑚̇_{𝑏𝑙𝑜𝑤} = 𝑚̇𝑔

𝑥𝑏𝑙𝑜𝑤

(2.9)

where 𝑚̇_𝑔 is the pyrolysis gaseous mass flux and 𝑥_{𝑏𝑙𝑜𝑤} is a constant parameter determined by experimental tests.

After the decomposition of the resin, a carbon char layer remains and it is subjected to oxidation due to the impinging oxygen. This process is exothermic and the oxidation heat flux 𝑞̇_𝑜𝑥 is represented by the following equation:

𝑞̇_𝑜𝑥 = 𝑚̇_𝑜𝑥 ℎ_𝑜𝑥 (2.10) where ℎ_𝑜𝑥 is the heat of oxidation and 𝑚̇_𝑜𝑥 is the oxidation rate.

Considering the processes that take place in the CFRP material in various heat flux conditions, in order to model the behavior of the material a numerical model was formulated in order to study the temporal evolution of processes that may affect the CFRP mechanical properties. Therefore the numerical approach is structured by considering 1) a discretization in space, where the spatial derivatives that are in the differential equations have to be approximated by spatial differences and 2) discretization in time, that is needed because it is not feasible to calculate the change of the temperature and heat flux at the same time, therefore the temperature distribution at a given time is used as known input data to calculate the corresponding heat flux.

In the numerical algorithm Fritsche (2000) considered the 1D wall divided in N layers and applied this scheme for a sample of 20 mm thickness divided in 10 layers characterized by

a constant thickness. The multi-step calculation is executed for each layer in order to obtain the temperature profile along the CFRP sample thickness accounting for the contribution of conduction, radiation, pyrolysis and oxidation processes.

3.

Experimental facilities and experimental studies at IRS

The experimental data used in this work of thesis were obtained at the Plasma Wind Tunnel (PWT or PWK) facilities located in the Institute of Space Systems (IRS) of the University of Stuttgart, Germany. Therefore, in this chapter the IRS facilities and the experimental set up have been described in order to provide a better inside on the experimental data used in our modeling vs. experimental data comparison discussed in Chapter 6.

3.1 IRS Experimental facilities

The facilities that are available at IRS are the PWK1 and the PWK4, which differ for the typology of their plasma generator as illustrated in Figure 3.1 and Figure 3.2.

Figure 3.1: Plasma Wind Tunnel 1 (PWK1) and Plasma Wind Tunnel 4 (PWK4) facilities located at IRS (Pagan et al., 2017)

Both the facilities have the vacuum vessels constituted by steel tanks having 6 m length, 2 m diameter and a double wall cooling system. Both the PWK tanks end in a hemispherical dome that is connected to the vacuum system and protected against the heat by water-cooled copper shields. The vacuum chamber can be opened by moving the lid on a guide rail and the plasma source is flanged on a conical element at the lid’s center. In both PWK1 and PWK4 the probes and the specimen support system are mounted on a 4-axis positioning system: therefore, it is possible to simulate parts of the re-entry trajectories through the specimen’s movement in different plasma flow regimes. The optical glass windows allow pyrometric temperature measurements on the front side of the specimen at distances from the plasma source between approximately 50 mm and 1 m. Concerning the electric power, it is supplied by a current-regulated thyristor rectifier that consists of six identical units supplying 1 MW each that can be connected in series or parallel, thus varying the desired output level of current, voltage, and power (Pagan et al., 2017).

The main differences between the PWK1 and PWK4 are reported in Table 3.1.

PWK1 PWK4

Plasma generator Magnetoplasmadynamic

generator Thermal plasma generator

Heat flux [𝒌𝑾

𝒎𝟐 ] 125-20000 250-5000

Mass specific enthalpies (air) [ 𝑴𝑱

𝒌𝒈 ]

7-150 2-30

Working gaseous N2+O2(+Ar), Ar, Ar+O2,

N2, H2, He

N2+O2, Ar, Ar+O2, N2, H2, N2+CH4, Ar+CO2, He Table 3.1: Characteristics of PWK1 and PWK4

Thanks to the PWK facilities at IRS the experimental behavior of materials’ samples during simulated uncontrolled re-entry conditions from Low Earth Orbit (LEO) regions has been studied. In particular, the following case-studies have been conducted:

- Optical properties (emissivity);

- Steady-state thermal responses in the PWK; - Transient testing to full demise in PWK.

In this context, the tested materials include metallic alloys, ceramics, composites and COPV segments:

This work of thesis focused on composite materials with a special attention to the Carbon Fiber Reinforced Polymer (CFRP) that has been described in the previous chapter.

3.2 Emissivity investigation

Particular attention has been focused on the study of the emissivity with changing heat flux conditions. The temperature-dependent emissivity coefficient has been analyzed through the Emissivity Measurement Facility (EMF). The EMF consists of a chamber containing a black body cavity, where an inert gas atmosphere is maintained. A graphite tube with ε = 0.9 effects the black body cavity and a resistive heating heats up the black body cavity for the measurements: the resulting configuration presents ε > 0.999 and, therefore, it can be considered a black body (Pagan et al., 2017).

The EMF facility is showed in the Figure 3.4 and Figure 3.5 reported below.

With reference to the figures reported above, because of the geometrical setup of the cavity, a heating of itself and the sample in the initial Position-1 is possible, therefore, the resulting black body temperature is measured and monitored using a pyrometer positioned in front of the window while the heating power is regulated manually. When the temperature of interest has been reached, the sample is rapidly shifted to the Position-2 by a piston, in this position the sample does not result to be embedded in a black body radiation environment. Assuming that the transition from Position-1 to Poition-2 is sufficiently fast, the temperature of the sample can be considered constant for the time interval. Therefore, the grey body emissivity of the sample can be found as a function of the measured sample temperature adopting as reference value, the black body temperature that has been measured previously (Pagan et al., 2017). The total emissivity

𝜀

_𝑡𝑜𝑡 of the sample at a temperature TBB=TPOS1 can be expressed

as:

𝜀

𝑡𝑜𝑡,𝑇_𝐵𝐵

= (

𝑇𝐺𝐵 𝑇_𝐵𝐵

)

4

= (

𝑇𝑃𝑂𝑆2 𝑇_{𝑃𝑂𝑆1}

)

4 (3.1)

where TGB = TPOS2 is the measured grey body temperature.

In relation to the CFRP, a sample has been pyrolyzed for 2 hours at 1000 K before the emissivity measurement shots were performed at intervals of 300 K up to a temperature’s value of 1900 K. Figure 3.6 shows the calculated total and spectral emissivity curves.

As suggested by Figure 3.6 the CFRP sample cools down very rapidly when it is not exposed to the heating environment within the graphite tube, this effect was not observed during similar tests executed on metals and ceramics samples. Therefore, it is assumed that the low density influences the materials’ incompetence to retain a high temperature in a cool environment (Pagan et al., 2017).

In order to obtain more realistic emissivity values, it would be necessary to conduct an empirical study aimed to evaluate the measured temperature history around the measurement shot considering the cooling of the sample during the shifting motion from Position-1 to Position-2. In addition, the analysis on the thermal environment and behavior of the sample at different positions would be certainly contribute to improve our knowledge on this specific process (Pagan et al., 2017).

3.3 Plasma wind tunnel investigation

In the PWK facilities the specimens have been tested in different heat flux regimes which are:

- Low heat flux regime ( 260 𝑘𝑊

𝑚2 );

- Medium heat flux regime ( 520 𝑘𝑊

𝑚2 );

- High heat flux regime ( 1400 𝑘𝑊

𝑚2 ).

These conditions have been characterized by the use of copper heat flux probes, as it is the standard procedure at IRS. Considering that the copper is much catalytic if compared to the other materials, some of the tested materials experienced a heat flux deviated from the given reference value: in relation to the test performed on the CFRP samples, the illustrated

The tested CFRP sample, as the other materials’ samples, has the following geometry:

As showed in Figure 3.7 the sample has a conical disk geometry; this geometry has been chosen in order to be compatible with the specimen support system riported in Figure 3.8.

This is a support system that has been designed to create a well insulated, near 1D wall heat conduction scenario through the material sample’s thickness. During the experiments, several analysis have been executed.

Figure 3.7: CFRP analyzed sample and its geometry (Pagan et al., 2017)

First, the temperature profile on the surface exposed to the plasma jet (front surface) has been investigated using the following equipment and devices:

- Linear Pyrometer LP3: calibrated for 958.1 nm, very reliable, precise focusing, highly linear I/O signal relation (irradiance / current).

- LumaSenseMCS640 Thermographic Imaging Camera: 640x480 resolution, 60 fps, calibrated for 960 ±5 nm.

- Maurer TMR95-EA narrowband pyrometer: calibrated for 1.5 μm to 2.6 μm, for low-temperature applications (e.g. aluminum).

The temperature profile has been computed also on the rear surface of the sample through the Mini-PYREX: optical signal collimated and transferred to InGaAs(P) detector diode via optical fiber, calibration at black body radiator setup. Black body conditions assumed (εMP3=

1) (Pagan et al., 2017).

Furthermore, the following studies have been executed:

- Physical examination: compution of the thickness and the mass at the center of the disk conical sample pre and post-test;

- Microscopic analysis: examination of notable and prominent post-test surface structures and patterns (up to 5x optical magnification).

3.4 Steady-state thermal material response

The CFRP shows the tendency to experience the pyrolysis process under moderate heat flux conditions altering significantly the composite material without necessarily affecting its structural integrity. This suggests that the steady-state plasma exposure condition is not feasible before having undergone a complete char-through; this scenario is considered to be not important. Therefore, the steady-state thermal response has not been investigated for our CFRP case-study.

Before activating the plasma generator, in the PWK facility the sample is positioned perpendicularly with respect to the generator axis. In the case of the CFRP, because of its low critical temperatures, the sample holder bearing the specimen prone to an early demise is rotated by 180° in order to attenuate the exposure and the pre-heating of the sample. When the test conditions have been set, the material’s sample is rotated back and moved in the centerline of the plasma plume; once the rotation of the probe is completed, the sample is moved laterally in the center of the plume (Pagan et al., 2017).

In detail, at IRS the tested sample of CFRP is the coded as CFRP EX1515/M55J with a conical disk shape of 26.5 mm frontal diameter and 4.2 mm thickness. During the ablation behavior test in the three heat flux conditions, it appeared clear that the aerothermal demisability of the organic composites is not a straightforward issue. The CFRP behaves as a classical ablator when exposed to atmospheric re-entry, charring and releasing syngases in the boundary layer, which results in a convective blockage. Furthermore, it behaves as an insulator, blocking the internal conductive heat transport very effectively for long durations. In general, the rate of ablation for CFRP appeared to be directly related to the reference heat flux (Pagan et al., 2017).

3.5.1 Testing CFRP EX1515/M55J in Low Heat Flux regime

When the CFRP is tested in the Low Heat Flux regime, the test conditions are the following:

Heat flux 260 𝑘𝑊

𝑚2

Pressure 15 Pa

Test Time 375.3 s

During the test time, the sample expands and loses mass. The mass loss is due primarily to the outgassing process: this is evident from the little structural damage that can be observed on the sample’s surface at the end of the test. In this heat flux condition, delamination, ablation nor spallation are observed (Pagan et al., 2017).

Table 3.3 provides the thickness and mass of the CFRP sample at the end of the test.

Pre-test Post-test Absolute difference Relative difference Thickness [mm] 4.06 6.38 +2.32 +57.14% Mass [g] 4.1882 3.0563 -1.1319 -27.03%

Table 3.3: Evolution of CFRP thickness and mass

The pre-test, during-test and post-test specimens located respectively on the left side, in the bottom and on the right side are shown in Figure 3.9.

Figure 3.9: CFRP EX1515/M55J specimen tested. Left: pre-test, right: post-test, bottom: mid-test, indicating the sample’s outward expansion (Pagan et al., 2017)

Figure 3.10 shows the temperature profiles of the sample’s surface exposed to the plasma jet (frontal surface) and of the sample’s rear surface.

The Figure 3.10 suggests that:

- The frontal surface reaches a temperature value of about 1500 K after 100 s and then it remains constant at this value for all the test time;

- In the first 2 minutes the rear surface reaches temperatures that are too low to be registered and after about 150 s it rapidly rises, increasing linearly within the first few seconds and following then an exponential trend until the end of the experiment;

- At the end of the test, the temperature gradient between the frontal and the rear surface (about ΔT = 400 K) is significant and this is primarily due to the material’s low thermal conductivity through its thickness.

3.5.2 Testing CFRP EX1515/M55J in Medium Heat Flux regime

When the CFRP is tested in the Medium Heat Flux regime, the test conditions are that reported in Table 3.4.

Heat flux 520 𝑘𝑊

𝑚2

Pressure 415 Pa

Test Time 972.7 s

When the composite’s sample is under medium heat flux conditions, its degradation is very rapid and it is the result of two processes: pyrolysis decomposition and surface ablation. After 16 minutes of testing, losses in both mass and thickness have been noticed and a large crater depression in the center part of the sample has been found, however, the overall structure integrity has been maintained (Pagan et al., 2017). With respect to Low Heat Flux conditions the test executed in Medium Heat Flux conditions show a higher degradation rate of the sample.

The Table 3.5 provides the variation of the thickness and mass of the CFRP sample during the test and for the entire test period:

As expected, the losses in thickness and mass are important and they are higher than that obtained in low heat flux conditions.

The sample conditions after the pre-test, during-test and post-test treatment with medium heat flux are illustrated respectively on the left side, in the bottom and on the right side of Figure 3.11.

Pre-test Post-test Absolute difference

Relative difference

Thickness [mm] 4.06 0.51 -3.55 -87.44%

Mass [g] 4.1896 0.7984 -3.3912 -80.94%

Table 3.4: Test conditions in Medium Heat Flux regime

The Figure 3.12 provides the temperature profile on the sample’s surfaces exposed to the plasma jet (front surface) and on the sample’s back surface are shown:

Figure 3.11: CFRP EX1515/M55J specimen tested. Left: pre-test, right: post-test, bottom: mid-test, indicating the sample’s outward expansion (Pagan et al., 2017)

From the analysis of the temperature trend reported in Figure 3.12 the following findings can be highlighted:

- On the frontal surface, the temperature grows at a higher rate than the growth rate of the medium heat flux and reaches the peak value of about 1800 K within three minutes and then decreases to about 1600 K;

- The gradual decrease of the temperature on the frontal surface after reaching a peak value is related to the influence of the surface ablation, a process that does not take place when the material is tested at low heat flux condition; in this latter case no reduction of the surface temperature has been observed;

- On the back surface, within the first 300 s the temperature is too low in order to be measured with available instrument, whereas after 300 s the temperature follow an exponential upward trend until the end of the experiment;

- During the test, the temperatures’ profile on the front and rear surfaces became quite similar towards the end of the experiment.

3.5.3 Testing CFRP EX1515/M55J in High Heat Flux regime

When the CFRP sample is tested in the High Heat Flux regime, the test conditions are those reported in Table 3.6.

Heat flux 1400 𝑘𝑊

𝑚2

Pressure 1900 Pa

Test Time 391.7 s

As in the medium heat flux condition, during the test the CFRP is subjected to both pyrolysis and surface ablation processes. The outgassing takes place within the first 10 s and very little delamination appears within the first 30 s because of structural constriction (Pagan et al., 2017).

When the composite carbon fiber/epoxy is exposed to High Heat Flux, a thickness’s

therefore, it is observable the time range within which the CFRP demises depends on the heat flux.

The CFRP sample has burnt through completely at its central point of measurement; therefore, the post-test thickness can’t be established. At the end of the experiment, almost the 84% of the sample’s original mass results ablated (Pagan et al., 2017).

The Table 3.7 provides the thickness and mass in pre- and post-test conditions.

Pre-test Post-test Absolute difference

Relative difference Thickness [mm] 4.08 _through) (burn- -4.08 -100%

Mass [g] 4.2071 0.6831 -3.5240 -83.76%

Figure 3.13 illustrates the sample surface observed at different time step of the test, whereas Figure 3.14 provides the temperature profile of CFRP when exposed to high heat flux conditions.

Table 3.7: Evolution of CFRP thickness and mass

Figure 3.13: From left to right: CFRP EX1515/M55J specimen surface at 1 s, after 30 s, example of delamination after 83 s, and after 300 s (Pagan et al., 2017)

The analysis of Figure 3.14 suggests that:

- On the frontal surface, the temperature growth rate is higher than that observed for low and medium heat flux conditions reaching a peak temperature value of about 1900 K within the first 100 s followed by a downward trend reaching the value of about 1700 K; - Following a similar behavior of that observed for the Medium Heat Flux case, the temperature decreases from its peak value due to the effect of ablation process that takes place on the surface’s sample;

- On the back surface, the temperature trend follows an exponential trend within the first 200 s and then an almost linear law until the end of the test;

- During the test, the temperatures curves of the front and back surface tend gradually to converge and the rate of convergency increases towards the end of the experiment.

4.

The numerical ablation model

As highlighted in the previous sections, in order to study the composite materials’ behavior during the atmospheric reentry of a space vehicle on Earth from LEO regions, a numerical ablation model has been developed, tested and validated for different thermodynamic conditions on the basis of experimental simulations performed at the Plasma Wind Tunnel facilities located in the Institute of Space Systems (IRS) of the University of Stuttgart, Germany.

The numerical code is structured in order to analyze the CFRP (Carbon Fiber Reinforced Polymer) composite material’s ablation behavior when it is exposed to a given heat flux hitting the external surface. In order to simplify the scheme of the energy and mass balance during in the numerical simulation, the shape of the CFRP sample was a cylindrical disk, instead of the conic shape of the sample examined experimentally.

The following picture shows, with reference to the considered CFRP sample, the key processes that take place in the CFRP during the reentry phase:

During the atmospheric reentry, the material is exposed to high thermal loads which determine the occurrence of important transformation processes of the CFRP from its surface

Figure 4.1: Ablation processes that take place in the CFRP during the reentry phase of a vehicle in the atmosphere

X-axis [m] X = 0,00407

to its innermost layers that may change its mechanical characteristics. These processes include the following mechanisms:

a) the Pyrolysis: the epoxy matrix is decomposed in a mixture of gaseous species as products of the endothermic chemical process of pyrolysis. The decomposed CFRP layer extends its volume in the virgin material;

b) the Oxidation: the carbon char located on the backside of this decomposition is the region through which the gaseous species produced by pyrolysis diffuse through and it is subject to oxidation in its superficial layer primarily due to the impinging oxygen (Fritsche, 2017).

In order to analyze the temperature’s profile along the sample’s thickness when exposed to reentry conditions, the CFRP sample (cylindrical disk) has been discretized spatially and temporally i.e. the structure has been split along the x-axis in many layers (N) for which was assumed constant the physical and chemical properties and its thickness. In our numerical simulation we have discretized the thickness’ sample in N=15 layers (CFRP sample divided in 15 layers along the X-axis direction).

4.1 Energy Balance Equation

In accordance with the approach proposed by Tranchard et al. (2015), the energy balance equation (Equation (4.1)) has been studied for each N-layer and it considers the heat stored in the material (I), the heat due to conduction (II), the pyrolysis contribution (III) and the heat exchanged between pyrolysis gases and charred region within this region (IV):

(4.1)

The parameters 𝜌, 𝑐_𝑃 , 𝜆 represent density, specific heat at constant pressure and thermal conductivity of the CFRP sample, respectively; during the test time (t) these parameters vary

Figure 4.3: Specific Heat at constant pressure in function of the Temperature y = 1941,9e-4E-04x 1500 1550 1600 1650 1700 1750 1800 0 100 200 300 400 500 600 700 D ens ità , [K g/ m ^3 ] Temperatura, [K]

Figure 4.2: Density in function of the Temperature

y = 867,03ln(x) - 4032,1 0 200 400 600 800 1000 1200 1400 1600 0 100 200 300 400 500 600 700 Spec if ic H eat at C o ns ta nt P res sur e, [ 𝐽/( 𝐾 𝑔 𝐾 ) ] Temperature, [K]

Therefore, the parameters adopted in the numerical simulations are the following:

𝜌 = 1941,9 e−0,0004 𝑇

𝑐_𝑃 = 867,03 log(𝑇) − 4032,1 (4.2) 𝜆 = 2,1045 𝑒−0,002 𝑇

-

The term F represents the reaction rate of the pyrolysis process and it is expressed as:

𝐹 = 𝛴 𝐴𝑖𝑒𝑥𝑝(−_{𝑅 𝑇}𝐸𝑖

𝑃) (4.3)

where 𝑖 is a given step-process of the pyrolysis.

In our work the pyrolysis process is considered to be composed by one chemical process. Therefore, the reaction rate has been calculated using the following equation:

y = 2,1045e-0,002x 0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 0 100 200 300 400 500 600 700 Ther m al c o ndu cti vi ty, [ W /m K ] Temperature, [K]

where A = the preexponential factor, Ep = the activation energy of pyrolysis process, R =

the universal gas constant = 8.314 𝐽

𝑚𝑜𝑙 𝐾 , 𝑇𝑃 = the activation temperature of the pyrolysis

process.

-

The term 𝜌_𝑃 represents the pyrolysis density of the epoxy matrix, it depends strongly on the temperature. This parameter is constant when the temperature is lower than the temperature at which the pyrolysis process starts (from experimental evidence this temperature is 𝑇_𝑃 = 600 𝐾). Therefore the density decreases when the temperature is higher than 600 K.

The Table 4.1 shows an approximated parametric solution that has been chosen to calculate the pyrolysis density in our numerical model:

T <

𝑻

_𝑷

T >

𝑻

_𝑷

𝜌_𝑃 = 1170 𝐾𝑔

𝑚3 𝜌𝑃 = −0,0003 𝑇2+ 0,3592 𝑇 + 1047,5

-

The term ℎ𝑃 is the enthalpy of the pyrolysis process.

-

𝜌_𝑔 represents the density of the gas mixture produced by the pyrolysis, the latter has been considered formed primarily by a mixture of carbon monoxide (CO) and carbon dioxide (CO2).

-

The term 𝑏 is the thickness of the 15 layers composing the sample.

During the simulation, in first approximation b has been considered constant during the entire simulation period i.e. 𝑏 = 2,7 10−4 m for each N-layer during the entire test time (t). Then, in an improvement of the model the gradual decrease of the thickness of each N- layer due to the oxidation process of the carbon char has been examined.

-

The parameter 𝑐𝑃,𝑔 is the specific heat at constant pressure of gas mixture produced by

the pyrolysis.

4.2 Boundary conditions

Together with the Energy balance Equation (1), the heat fluxes related to the sample’s frontal surface (surface located in x=0) have been considered.

The heat loads at the boundary region (qBC) are described in the Equation (2), where the

aerothermal heat flux(I), the heat flux radiated from the frontal surface to the external environment (II), the heat flux due to the oxidation of the carbon char layer’s surface (III) and the heat flux exchanged between pyrolysis gas mixture and charred regions are considered:

(4.5)

-

The term 𝑞_{𝐴𝐸𝑅𝑂} is the aerothermal heat flux.

Values related to low, medium and high heat flux have been considered during the experimental and numerical simulations. In all experimental conditions that have been analyzed, the heat flux measured during the experimental tests was found different from its reference value; this difference can be explained considering that the reference values of heat fluxes are related to hemispherical probes while during the experimental tests flat probes have been utilized (Pagan et al., 2017).

Assuming a fully or near continuous flow regime, heat fluxes as measured with a flat or hemispherical head calorimeter probes can be correlated with one another using the following equation (Pagan et al., 2017):

𝑞 _{𝑓𝑙𝑎𝑡} = 𝑞ℎ𝑒𝑚𝑖

√2,3 (4.6)

This explains the values of 𝑞_{𝐴𝐸𝑅𝑂} considered in the numerical code.

-

The term σ = 5,670367 10−8 𝑊

𝑚2_𝐾4 is the Stefan Boltzmann’s constant.

-

The parameter ε is the emissivity; ε = 0.85 has been adopted.

-

The parameter ℎ_𝑔 = 𝑐_𝑃,𝑔𝑇_𝑃 is the enthalpy of the gas mixture produced by the pyrolysis.

-

The term 𝜌_𝐶 is the char density.