Aerothermodynamic Analysis of Aerocapture and Ballistic Entry Flows in Neptune’s Atmosphere

Mom, dad, sister, thank you for everything you have done for me: all the efforts, all the trips, all the phone calls, all the hugs, all the kisses, all the goodbyes and all the reunions. To Professor M ´ario Lino da Silva, to Duarte Gonc¸alves, to Beatriz Oliveira and In ˆes Cardoso, thank you very much for all the patience and help during these long months.

Declaration

Nomenclature

That Coefficient for Gupta-Yos species formulation [m s kg−1] Coefficient aav in Gupta-Yos formulation [m s kg−1]. Js Species mass diffusion flux vector[kg m−2s−1] jν Emission spectral coefficient [W m−3sr−1Hz−1] kb,r Reactor back-reaction rate[mol m3s−1] kf, r Forward reaction rate of reactant[mol m3s−1] Keq,r Equilibrium constant of reaction.

Acronyms

Introduction

Motivation

Atmospheric Entry Overview

Chemistry model

• Neptune Mission Overview
• Mission
• Aerocapture/Aerobraking
• Capsule design
• Trim tab design
• Objectives
• State of the Art
• Thesis Outline

A visit to Neptune (and Triton) is of great interest because of its proximity to the Kuiper Belt, Figure 1.2, which could increase our knowledge of the formation of the Solar System and the origin of life. Aerocapture (Figure 1.3b) is based only on a single-shot maneuver, where the spacecraft descends deeper into the planet's atmosphere with increased drag and aerodynamic heating, but also has a very narrow flight corridor, which increases the risk of the mission.

Governing Equations

• Fluid Models
• Governing Equations
• Thermodynamic Models
• Chemical Kinetics
• Transport Properties
• Aerodynamic Forces and Moments
• Coordinate system
• Forces and Moments
• Radiation
• Emission and Absorption Coefficients
• Radiative Energy Transfer
• Linear Interpolation Approach

Depending on the geometry of the species, the rotational and vibrational degrees of freedom can vary. Where εk is the energy associated with each thermal mode and ε0 is the zero point energy of the series. The transport coefficients appear as a function of the collision terms ∆(1)ij and ∆(2)ij , defined as

There is also an influence of the electric field present in plasmas, which contributes to the mass diffusion fluxes [27]. Near the shoulder and in the regions behind the body, the flow fails to exhibit tangent plate-like properties, and the accuracy of the approximation is correspondingly compromised. Regarding the computational implementation of the method, a structured mesh is assumed to discretize the flow domain in this work.

Its application to the calculation of the radiation source term in the energy equation is usually neglected, since the radiation calculation is usually fully or partially decoupled from the field calculation.

Numerical Modeling

• CFD Solver - SPARK
• SPARK Line by Line Code
• Ray Tracing - Ray Distribution
• Trajectory Point
• Aerocapture Trajectory Point
• Ballistic atmospheric Entry Trajectory Point
• Atmosphere
• Chemical Model Database
• Transport Models Database
• Radiation Models Database
• Mesh Study
• Mesh Boundary Conditions
• Mesh Convergence Study
• Mesh Refinement
• Numerical Issues

Using this ESA's CDF study on The Mission to the Ice Giants [2], accurate values ​​(velocity, pressure and density) can be found for the point where the wall heat flux is estimated to reach maximum values ​​in a ballistic atmospheric entry, which is the most critical point of the mission. Regarding the transitions used for the spectral database, most of the validation work has already been done by Fernandes [7], which makes this step easier. The mesh considered in this work consists of a structured mesh of 70x60 cells: 60 cells on the tangential direction of the wall and 70 on the normal direction of the wall.

This is explained by the minor influence of the boundary layer on the pressure, in contrast to the important influence of this layer on the temperature. This singularity does not arise from the physical model, nor from the geometric shape of the wall. For the shock refinement, a routine looked for abrupt (but significant) changes in these properties, and there was a clustering of the cells around this area.

However, the aspect ratio of the cells from the considered grid was already too large, making them very elongated in the tangential direction.

Results

Problem Description

• Test case 1 - Aerothermodynamic analysis of Entry Trajectory Point and Aerocapture Trajectory PointAerocapture Trajectory Point
• Test case 2 - Aerodynamic analysis of Aerocapture Trajectory Point

Secondly, an aerodynamic analysis will be performed on the Aerocapture TP, studying the influence of the capsule design (θ = 60◦ and θ = 45◦), the influence of considering the presence of CH4 and finally, the influence of the sweep angle η under the assumption of a constant area ratio. The main goal will be to calculate the aerodynamic coefficients and describe how these parameters behave for all different scenarios.

Computational framework

• Computational Domain
• Ray Tracing Convergence

The computational domain was extended beyond the end of the capsule shoulder to account for the hypothetical location of the trim flaps (considered for Test Case 2). Since the Ray Tracing model calculates the wall heat from all the visible rays, truncation of the domain to the boundary of the shoulder will underestimate the radiative wall heat at these last wall points, since the downstream proximity of these points would otherwise lie outside the calculation domain. Also, although the swing of the shoulder is not considered for the solutions, this should not significantly affect the results as long as the sound line is reattached to the body before the shoulder (which is the case for both capsule configurations for the Entry TP, shown in Figure 4.1).

For this reason, modeling the expansion is not necessary if we only care about the front body solution. This means that for each case the distance of the impact to the wall must be overestimated when calculating the first solutions without refinement. Before choosing the number of rays per hemisphere used for radiation analysis, we performed some convergence tests (global and local) with 50, 75 and 100 rays for a given case.

However, this increase adds considerable additional time for the Ray Tracing Procedure calculation as will be shown in Table 4.4.

Run Time Considerations

• CFD Solver - SPARK
• Radiative Solver - SPARK LbL

Test Case 1

• Entry Trajectory Point
• Stagnation Line analysis
• Aerocapture Trajectory Point
• Stagnation Line analysis
• Sonic line transition
• Wall Heating
• Convective Wall Heat Fluxes
• Total Wall Heat Fluxes
• Radiative Model Influence
• Literature Comparison

For the Aerocapture TP there is a significant increase in temperature after the shock, reaching values ​​above 15,000 K, see Figure 4.9. Forθ = 60◦ in Entry TP the flow already experiences this change in the attachment of the sonic line to the wall towards the shoulder. For the Entry TP, the heat flux profile shows higher values ​​on the order of 700 W/cm2 in the nose region compared to Aerocapture TP.

The Aerocapture TP shows only the final increase, without a sudden decrease in the convective heat flux. For the Entry TP with chemical composition A (with CH4), the radiant heat flux near the stagnation point has a relatively low value (only about 20% and 15% of the total heat flux for θ= 60◦ and θ= 45◦, respectively), but grows along the wall and reaches values ​​around 60% of the total heat flux in the shoulder region (Figure 4.16a and Figure 4.16b). This justifies the different shape (ignoring the magnitude difference) of the radiative heat flux profiles for this trajectory point for the different chemical compositions, while for composition B there are larger values ​​of radiative heating in the stagnation region.

Aerocapture TP, there is no significant change in the dominant species distribution, and the decrease in the radiative heat flux comes mainly from the significant decrease in temperature.

Test Case 2

• Aerodynamic coefficients

The frontal area of ​​the flap is kept constant at a value of 5% of the frontal area of ​​the main body. The projection of the forces in the flap area multiplied by the area will thus always produce the same force in the x-direction, and will result in the same drag, since the pressure in the flap area is almost constant. This projection is independent of the sweep angle and depends only on the angle θc, Figure 4.31a.

As far as lift is concerned, the scenario is different, since the projection of the forces in the y direction will depend not only on θc (Figure 4.31b), but also on φ (Figure 4.31c), and consequently η. The higher values ​​of CD for θ = 60◦ are expected as there is a significant increase in the wall pressure in the conical part of the capsule for this capsule design. This is a result of the results not being completely correct (since the shoulder extension is not implemented), but also because this Newtonian theory loses some of its accuracy when θc > θs(check.

Another fact that should be highlighted is the small influence of the chemical composition on the results.

Conclusions

Achievements

In terms of stability, the 45◦ configuration should generally be more favorable, as it is easier to move the aerodynamic center behind the center of gravity. In addition, and due to the chemical composition of Neptune, the high post-suckγ for the stream contributes to possible instabilities for the 60◦ configuration. It was found that for cone angles greater than 46°, the transition of the sound line from the nasal cap (in the spherical part of the capsule) to the shoulder is numerically proven.

Successful use of control surfaces, such as the trim tab mentioned in this work, becomes even more difficult to achieve for larger angles. Regarding the use of the trim tab, aerodynamic analysis concluded that low lift coefficients CL.

Future Work

Bibliography

In-flight experience with the Mars Science Laboratory Guidance, Navigation, and Control system for entry, descent, and landing. A review of reaction rates and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations up to 30,000 K, 1990. Uncertainty determination for aeroheating in probe entries of Uranus and Saturn by the Monte Carlo method.

N2 - CH4 - Ar chemical kinetic model for simulations of Titan's atmospheric intrusion. Journal of Thermophysics and Heat Transfer, 2007. The effect of Reynolds number on the hypersonic flow around faceted shapes. 22nd AIAA International Space Planes and Hypersonics Systems and Technologies Conference, (September), 2018.

Appendix A

Pressure Forces

Finally, the correction function K(¯t) (see Fig. A.4) must be considered for the flap part, as explained in [59]. D is the total width of the border with a constant distance to the beginning of the flap. Now the forces in their direction will not cancel out, since the flap only moves at a certain angle.

But in the z-direction the same applies as before, since we can consider the flap as symmetrically located in relation to the planxy. Now the forces in their direction will not be equalized, since the flap only sweeps over a certain angle. However, the same applies as before in the z-direction, since we can consider the flap as symmetrically located in relation to the planxy.

I would like to make one final comment: the pressure correction was only performed for θ= 45◦ because at the trajectory point where this was implemented the results for θ = 60◦ were poor physical and the flow near the flap is subsonic. approach makes no sense.

Viscous Forces

Appendix B

Chemical Dataset

Appendix C

Database from NASA’s Neptune GRAM

Appendix D

Numerical Problems

Appendix E

Results Aerothermodynamic Analysis