Thermodynamic Exergy Analysis of Launch Vehicles and Spacecraft

1. Engineering Elegant Systems: System Exergy Analysis of Launch Vehicles and Spacecraft Consortium Team UAH George Washington University Iowa State Texas A&M Dependable System Technologies, LLC Multidisciplinary Software Systems Research Corporation (MSSRC) Missouri University of S&T University of Michigan AFRL Wright Patterson 27 August 2019Michael D. Watson, Ph.D.

2. Agenda • Thermodynamic Exergy Relationships • Exergy Analysis of Launch Vehicles • Exergy Analysis of Interplanetary Vehicles • Exergy Analysis of Spacecraft • Un-crewed • Crewed • Capturing Results

3. Thermodynamic Exergy Relationships

4. System Integrating Physics • Consortium identified the significance of understanding and using the System Integrating Physics for Systems Engineering • First Postulate: Systems engineering is system specific and context dependent. • Systems are different, and therefore, the integrating physics for the various systems is different • Second Postulate: The Systems Engineering domain consists of subsystems, their interactions among themselves, and their interactions with the system environment • System interactions among properly defined system functions and with the environment are the basis of systems engineering • Sub-Principle 3(i): Systems engineering seeks a best balance of functions and interactions within the system budget, schedule, technical, and other expectations and constraints. • Sub-Principle (5a): Systems engineering has a physical/logical basis specific to the system • The physics of the specific systems defines the integration relationships • Principle 7: Decision quality depends on system knowledge present in the decision-making process • Understanding of system interactions must be included • Principle 12: Systems engineering solutions are constrained based on the decision timeframe for the system need • Understanding the system interactions shortens the development time and opens design space more for a given timeframe • Thermodynamic Systems • Aircraft • Propeller Driven • Jet Aircraft • Electric • Rotorcraft/VTOL • Gliders • Automobiles • Electrical Systems • Fluid Systems • Launch Vehicles and Spacecraft • Robotic • Integrated through the bus which is a thermodynamic system • Each Instrument may have a different integrating physics but integrates with the bus thermodynamically • Crew Modules • Integrated by the habitable volume (i.e., ECLSS) • A thermodynamic system • Entry, Descent, and Landing (EDL) • Integrated by thermodynamics as spacecraft energy is reduced (i.e., destroyed) in EDL • Power Plants • Ships • Not all systems are integrated by their Thermodynamics • Optical Systems • Logical Systems • Data Systems • Communication Systems • Structural Systems • Biological Systems • System Integrating Physics provides the engineering basis for the System Model

5. Thermodynamics Has Balance Relationships • Energy Balance (First Law of Thermodynamics) • , • + for a control volume • Entropy Balance (Second Law of Thermodynamics) • ), where • Exergy Balance (Integration of First and Second Laws) • ), where ( in Kelvin) • for a control volume • All relationships maintain mass balance

6. Exergy Analysis of Launch Vehicles

7. Exergy Balance Relationship • Exergy Balance for a rocket balances the exergy expended (fluid flow out of the nozzle) with the change in the vehicles kinetic and potential energy • Mass balance is maintained • Rockets are control volumes, not control masses • Each stage is a constant control volume • The vehicle is the integration (addition) of separate control volumes • Staging results in the dropping of a control volume (mass drop) but not a change in the individual stage control volumes • Entropy and Enthalpy of propellant products assumed negligible (are for LOX, LH2) • Represents energy expended in gaining velocity and altitude • Rocket equation can be derived from the exergy balance for a rocket • Orbital mechanics energy balance is also maintained in the exergy balance equation for a rocket • ; Launch Vehicle, Planetary Departure (Accelerating) • ; Lander, Planetary Arrival (Braking)

8. Derivation of Rocket Equation from Exergy Balance Equation • Objective: Determine the relationship between the Exergy Balance Equation and the Rocket Equation. • This derivation starts with the Exergy Balance Equation for a rocket. The derivation makes use of the limiting assumptions contained in the rocket equation: • The Rocket Equation considers only: Mass of the vehicle (Mveh), mass of the propellant (mp), velocity of the vehicle (Vveh), change in the velocity of the vehicle (DVveh), and velocity of the exhaust gas (Ve). • In the Rocket Equation derivation Ve is considered independent of Dt and changes in vehicle mass (i.e. DMveh and Dmpropellant). Ve is measured as the distance from the combustion chamber to the nozzle exit. This velocity does not change over course of the trajectory flight time and therefore can be considered constant over the flight time interval. This ignores start up transients and shut down transients (i.e., modeled as step functions), and assumes no throttling effects on Ve (throttling effects Dmpropellant only). • Engine changes can occur with staging (i.e., different engines and different Ve’s can exist on different stages) which would be handled by breaking the flight trajectory into segments for each stage. Ve can vary between segments but remains constant within the segment. • Note assumptions 2) and 3) make Ve a less reliable variable to differentiate the Exergy Balance Equation with since in some cases it would differentiating with respect to a constant. Therefore differentiation to vehicle velocity is a better choice based on the Rocket Equation limiting assumptions on Ve. • The propellant mass is fully exhausted at the nozzle exit (i.e., 100% efficiency in propellant burning) • Losses are not considered including drag forces, aero thermal heating, gravity, etc. • The trajectory path is not considered.

9. Derivation of Rocket Equation from Exergy Balance Equation • The Exergy Balance Equation for a rocket can be written as: • (1) • Expanding the kinetic energy and potential energy terms yields a more explicit form in terms of velocity: • (2) • Making use of the fact that Exergy is a work relationship and that the derivative of work yields a force relationship, differentiate with respect to the vehicle velocity, Vveh,: • (3) • This yields the following with the potential energy term being represented by: • (4) • (5) • Where since the initial velocity is a constant (fixed starting point).

10. Derivation of Rocket Equation from Exergy Balance Equation • Now, differentiate the Rocket Equation to find the differential relationship (constant C) for. So, • . (6) • Therefore, Equation 5 becomes, • (7) • Now, the Rocket Equation does not contain loss terms (assumption 4 above) and therefore assumes that and. • Applying these assumptions yields, • (8) • Now, taking the limit as Dt -> 0 yields, • (9)

11. Derivation of Rocket Equation from Exergy Balance Equation • Where, • (10) • Since as is a constant, and • (11) • The result of equation 11 is obtained by taking L’Hopitals Rule with the derivative of the top and bottom with respect to time (t). • Now, using, • (12) • Then, • (13) • Since, as is constant. • Therefore, • ` (14) • Grouping terms and integrating, • (15) • Which results in the Rocket Equation, • (16)

12. Orbital Mechanics Relationships in Exergy Balance Equation • Objective: Determine the orbital mechanics energy relationship defined by the Exergy Balance Equation. • If the spacecraft is thrusting, then the exergy balance equation directly contains the relationship between spacecraft energy and thrust. This is seen directly in equation (1) below. • (1) • Now, for a vehicle coasting in orbit around a body (i.e. planet, moon or sun) then the propulsion components are zero and equation (1) reduces to: • . (2) • Combining terms on the right had side of the equation yields: • . (3) • Now, the orbital energy for a spacecraft is: • . (4) • Using this relationship in equation (3) yields, • . (5) • Now, Xdes is zero for a vehicle that is not thrusting and has no other active sources. Treating the spacecraft as a static mass, • . (6) • Which is as expected for a spacecraft in orbit where kinetic and potential energy changes are balanced as the spacecraft orbits the body. • Note that for a vehicle with an active system to stabilization or station keeping (e.g., control moment gyroscope, thrusters, spin stabilization), these systems would be added to the left-hand side of equation (3) and the vehicle orbital energy change would be related to the change induced by the stabilization or station keeping system.

13. Launch Vehicle System Exergy Efficiency . S-II Center Engine Cut-Off S-1C Stage Separation S-II Stage Separation S-1C Center Engine Cut-Off S-IVB Burn 1 Cut-Off LEO Insertion S-IVB Burn 2 Engine Mixture Ratio Shift S-II Engine Mixture Ratio Shift S-IVB Burn 2 Cut-Off Max Q S-!VB Separation

14. Exergy Analysis of Interplanetary Vehicles

15. LEU NTP Mars Transfer Vehicle • Assumptions and Differences • Orion not carried to Mars • Prepositioned tanks in Mars orbit for return trip • Exergy of transfer not calculated • RCS burn data Updated • dropped from 50 kg/s to 7 kg/s to shift • Previous was 40 s, new is 291 s • Large RCS burn ΔVs added into main burn ΔVs • All remaining RCS burns are 40 m/s, fully tangential • No crew member mass in trajectory data vehicle mass • Crew Module exergy not included • Constant mass for high thrust trajectory data • Main Engine Changes • 3 Engines/Core • for LEU CH4 NTP and CHM LOX-LH2 altered to accurately reflect differences from LH2 NTP • changed for all burns to accurately reflect ΔV and

16. Course Shifts NOT TO SCALE

17. Exergy Efficiency

18. SEP TRAJECTORY (MULTI-BODY) Very low SEP performance inside planetary gravity wells SEP should be fired where efficiency curve inflects and turn positive Efficiency oscillates downward after near Mars SOI

19. SEP-CHEM TRAJECTORY (MULTI-BODY) Very low SEP performance inside planetary gravity wells SEP should be fired where efficiency curve inflects and turn positive Efficiency increased when SEP terminated before SOI and system coasts into gravity well until Chemical Engine fired

20. SEP TRAJECTORY (PATCHED CONICS) Very low SEP performance inside planetary gravity wells SEP should be fired where efficiency curve inflects and turn positive

21. SEP-CHEM TRAJECTORY (PATCHED CONICS) Very low SEP performance inside planetary gravity wells SEP should be fired where efficiency curve inflects and turn positive Chemical engine much more efficient inside gravity well

22. Exergy Analysis of Spacecraft

23. Spacecraft Exergy Balance • Spacecraft Bus Propulsion Exergy • (1) • Add attitude control • Kinetic Energy of a rotating body is given by, • (2) • Where, • Ic= moment of inertia about the center of the rotating satellite • w = angular velocity of the satellite • So, rewriting the RHS yields, • (3) • Where, • (where s = distance of thruster from center of mass) • And, (where T = thrust)

24. Spacecraft Exergy Balance • Now, scientific instruments require electrical power and thermal control, so • Where, • q = solar array angle to the sun, and • Where, • hcoverglass = cover glass losses • hcellmismatch = solar cell losses • hparametercalibration = system calibration losses • hUV,micrometeorite= degradation losses by years in flight • Isolar= solar intensity variation • Which yields, • (4)

25. Un-crewed Spacecraft Exergy Balance andOptical Transfer Function Optical Transfer Function Where Over Damped Critically Damped Under Damped Spacecraft Exergy Balance

26. Crewed Module Exergy Balance: ISS ECLSS • Currently using 1998 ISS basic ECLSS to model DSG starting point

27. OGA Reconfiguration Opportunity • Challenge • Exergy is supplied to the electrolyzer cell stack as electrical power. • A portion of this exergy is rejected through the heat exchanger and coolant system. • Design Consideration • Higher temperature electrolyzer operation improves exergy efficiency. • Can we change heat exchanger location to preheat feedwater and improve efficiency?

28. Conclusions

29. Design Analysis Cycle (DAC) • Understanding the systems integrating relationships provides an important advancement in the practice of systems engineering and contribution to the engineering of the system • Provides a complete understanding of the system functions and interactions • Basis to define system GR&A in a way to have a closed set to begin design work • Basis of system closure criteria • Basis for identifying adjustments to the system function design solutions • Basis for determining optimal system performance • Provides a method to quickly compare system configurations and identify best balance result, reducing time necessary for DACs • Analysis complements detailed design work done by the Engineering Disciplines • System Exergy is an integrating relationship • Depends on results from each Engineering Discipline • A positive for systems engineers in conducting system level design • More difficulty to use (depends on results from each Engineering Discipline) for specific components of subsystems

30. Capturing Results • The results of the research conducted by all Consortium members is available on the NASA Portal • https://www.nasa.gov/consortium • “Engineering Elegant Systems: Theory of Systems Engineering” • NASA Technical Publication in work (Due out in October 2019) • “Engineering Elegant Systems: The Practice of Systems Engineering” • NASA Technical Publication in work (Due out in November 2019)