1. Modeling two-phase cryogenic flow for autonomous control of loading operation E. Ponizovskaya-Devine b, D.G. Luchinsky a, M. Khasin b,J.Perotti d, J. Sass d and B. Brown d a Mission Critical Technologies, Inc., El Segundo, CA, USA b SGT, Inc., Greenbelt, MD, USA c Ames Research Center, NASA, Moffett Field, CA, USA d Kennedy Space Center, NASA, Moffett Field, CA, USA Cryogenics Engineering Conference 2015 Tucson, TX

2. Outline NASA plans for autonomous cryogenics transfer Hierarchy of two-phase models for cryogenics flow – Separated nt model (equations) – Homogeneous moving front model (equations) – Correlations – Algorithm Validation – NIST experiment 1966 – KSC CryoTestBed setup 2015 Learning – NIST experiment: leaning the correlation parameters – Fault evaluation Conclusions Cryogenics Engineering Conference 2015 Tucson, TX

3. NASA: autonomous health management and control of cryogenics systems Statement A: Approved for public release; distribution is unlimited Cryogenic fluid loading system health management and control ground systems space systems Autonomous health management Fault detection Fault localization Fault evaluation Recovery Requires Accurate and fast models On-line Optimization Learning

4. Two-phase separated flow equations Cryogenics Engineering Conference 2015 Tucson, TX For each components the mass, momentum and energy conservation equations for separated model are: Energy conservation equation for the wall: Variables: Temperature T g, T l, Velocity u g, u l, Pressure P, Density  g,  l Energy e g, e l, Enthalpy h g, h l,

5. Set of correlations for cryogenic flow Cryogenic heat transfer module (in progress):  Experimental results about two-phase boiling flows were accumulated in the form of correlations over decades;  Fidelity of the boiling two-phase flow models is determined by their ability to incorporate flow-boiling correlations;  Micro-G phenomena in the flow are primarily determined by the changes in correlations in microgravity; Knowledge of flow-boiling correlations for cryogenic fluids remain limited Successful development of the autonomous CFM in space and on the ground depends on the efficient optimization and learning framework Figure: (top) heat transfer correlations for liquid nitrogen boiling curve. (bottom) Cryogenic boiling correlations currently included into cryogenic heat transfer module for stratified flow. Cryogenics Engineering Conference 2015 Tucson, TX Forster-Zuber Gorenflo Dittus-Boelter Frost-Dzokawic Bjornard and Griffith Bromley Experiment Dittus-Boelter PhD_Thesis-Thermal_Bubble_Behaviour_in_Liquid_Nitrogen_under_Electric_Fields Flow maps

6. Separated model semi-implicit algorithm Cryogenics Engineering Conference 2015 Tucson, TX At the first step of the NI algorithm – The expanded (non-conservative) set of equations for the mass and energy conservations is solved to express pressure in terms of new velocities. – new velocities are found by solving coupled momenta equations. – next, new pressure is calculated using new velocities – finally so-called provisional values of the energy, density, and the void fraction are found by substituting new pressure and velocities into the expanded set of mass and energy conservation equations At the second step of the NI algorithm – corrected values of the void fraction, density, and energy for each phase are found using unexpanded (conservative) set of equations for the mass, and energy conservations. First step: expanded energy and mass conservation equations are used are used to express new pressure in terms of velocities

7. Two-phase homogeneous flow equations Cryogenics Engineering Conference 2015 Tucson, TX Homogeneous u g = u l = u Equilibrium T g =T l Variables: Temperature T Velocity u Pressure P, Void fraction  Density  g,  l Energy e g, e l, Enthalpy h g, h l, For each components the mass, momentum and energy conservation equations for separated model are: Energy conservation equation for the wall: Works at least 2000 times faster than real time

8. Governing equations for loading operation model Selection of state variables: pressure P and specific enthalpy h NIST data for LN2 Ordinary differential equation (ODE) for loading operation density internal energy T w1 T w3 L1L1 L2L2 P, h Cryogenics Engineering Conference 2015 Tucson, TX

9. Second step: solve quasi-steady momentum equation, Mass conservation (6) Energy conservation (7) Vapor flow in control volume: solution Cryogenics Engineering Conference 2015 Tucson, TX Third step: solve equations for the wall temperature First step: solve coupled expanded energy and density equations is the pressure drop in case of abrupt pipe contraction or expansion given by correlations (0 if pipe diameter is the same)

10. Correlations in homogeneous model Cryogenics Engineering Conference 2015 Tucson, TX Pipe contraction (Collier and Thome): Pipe expansion (Romie correlation ): 1. Correlations for friction losses defined by Colebrook equation for gas or liquid for two-phase For the heat transfer coefficient the Dittus- Boelter approximation was used: (Re > 2300) The boil enhancement factor was introduced the same way as in the Gungor-Winterton (1987) correlation. 3. Pipe abrupt expansion or construction 2. Heat transfer correlations we use slip ratio correlations for void fraction  and mass quality x

11. Hierarchy of cryogenic flow models embedded into learning and optimization framework Cryogenics Engineering Conference 2015 Tucson, TX On-line and offline learning and optimization loop I.The models are combined within one physics module Ranges from separated non-equilibrium flow model to single phase isothermal model Includes extended correlations module for cryogenic flow boiling Embedded into external optimization and learning framework Fast and time-accurate II. Capabilities Modeling and simulations Offline development of D-matrix and Fault Tree Online fault detection, isolation and evaluation Virtual sensors and Sensor consistency check Offline learning of correlations Optimization including design optimization Training

12. Cryogenics Engineering Conference 2015 Tucson, TX NIST chilldown test NIST experiment of chilldown of 60 m long pipe with ¾ inch diameter was performed in 1966 at NBS (new NIST). The temperature, pressure, and wall temperature were measured at 4 locations (see top figure) We use NIST experimental data to validate both homogeneous and separated models In the bottom figure the separated model of the NIST experiment is shown. The pipe was divided into 30 control volumes. We use NIST model to develop learning and optimization applications of physics models J. A. Brennan et al, “COOLDOWN OF CRYOGENIC TRANSFER LINES‐‐AN EXPERIMENTAL REPORT,” NBS (now NIST) Report 9264, November 7, 1966.

13. KSC Criogenic TestBed Cryogenics Engineering Conference 2015 Tucson, TX Kashani, A., Ponizhovskaya, E., Luchinsky, D., Smelyanskiy, V., Sass, J., Brown, B., and Patterson-Hine, A., Physics based model for online fault detection in autonomous cryogenic loading system, AIP Conference Proceedings 1573, 1305- 1310 (2014).

14. Separated model validation: NIST data Cryogenics Engineering Conference 2015 Tucson, TX Figure: experimental data (black lines) obtained in NIST chilldown experiment at four stations are compared with model predictions (colored lines) for: (a) fluid temperature; (b) wall temperature; (c) liquid heat transfer coefficient to the wall; (d), (e), and (f) pressure at three different stations. The separated code validation using NIST chilldown experimental data. There are only a few control parameters: input valve and exit losses. The chilldown dynamics almost entirely depends on the heat transfer correlations. Experimental data include fluid temperature, wall temperature, pressure, and heat transfer to the wall. We use these data to study extensively 33 parameters of the current heat transfer correlations used in separated model. Time, s (a) (b) (c) (d) (e) (f) Time, s

15. Separated model of cryogenic flow Separated model Is robust and runs 500 times faster than real-time It captures pressure and material waves of the cryogenic flow in the transfer line and can reproduce sharp temperature variations IMPORTANTLY, it includes extended set of correlations for one-dimensional flow-boiling of cryogens It was used to demonstrate complex faults in the system including Phase separation Vapor lock Liquid holdup induced by valve operation  It was validated using NIST chilldown data and using new and old KSC test bed data Figure: (top) Geometry of the transfer line (height vs length along the pipe) divided into 24 control volumes; (bottom) The model predictions (blue lines) as compared to the measured time-series data (black lines) for the temperature. Cryogenics Engineering Conference 2015 Tucson, TX

16. Homogeneous model validation against CryoTestBed data Comparison with the testbed data at the pressure and temperature sensors: experiment-black, simulations –red. Model includes : pipes of different diameter Control valves Dump valves Pump Moving front homogeneous model simulates 6000 sec of loading operation in less than 3 sec and shows good accuracy for the temperature dynamics and slow changing in pressure. Cryogenics Engineering Conference 2015 Tucson, TX Time, s

17. Sensitivity Test for Correction Parameters A large number of the important design parameters (e.g. heat and mass transfer coefficients in various flow regimes, pressure and heat losses in the pipe components, two-phase valve flow coefficients etc.) are only approximately known for two-phase cryogenics flows. As one of the first steps in developing a learning framework we performed sensitivity test of the 33 parameters of the chilldown model of the NIST experiment. Example of the sensitivity tests for two parameters Gwsc changing by 10% changes cost function by 25% Kex changing by 16% changes cost function by 63% Main Conclusion: We see that the model predictions are very sensitive with respect to changes in the correlation parameters. Therefore physics models allow to develop a unique model-based machine learning approach to learn important parameters of boiling cryogenics flows. We are currently studying a possibility to develop off-line supervised learning capability as an extension of the work on optimization tools. Cryogenics Engineering Conference 2015 Tucson, TX

18. Learning correlations using global optimization Cryogenics Engineering Conference 2015 Tucson, TX In this test we demonstrate the capability of learning unknown correlation parameters using unconstrained global optimization Experimental results are taken from the NIST chilldown Separate model is used to obtain predictions Global optimization is performed using MCMC algorithm The cost function is sqared sum of deviations of the model predictions from the experimental data Main Conclusion: physics models allow to develop a unique model-based machine learning approach to learn important parameters of boiling cryogenics flows. J. Brennan et al, "Cooldown of Cryogenic TransferLines - an Experimental Report", NBS (now NIST) Report 9264, November 7, 1966. Figure: video demonstrating convergence of the model predictions towards experimental data for the fluid and wall temperature

19. Fault identification and evaluation Cryogenics Engineering Conference 2015 Tucson, TX

20. Sensitivity of chilldown regime to pressure variation Cryogenics Engineering Conference 2015 Tucson, TX Nominal regime –black, storage tank pressure at the time within the range 917<t<1993 s is changing from 7 to 17 psi (nominal is around 10psi). 7 psi is solid red, 17 psi is dashed green. Time, s

21. Tradeoff between commodity and loading time Cryogenics Engineering Conference 2015 Tucson, TX The optimization based on homogeneous model for the loading operation: Top fig. shows that the bigger pressure (green dashed line) results in more commodity spent during childown and faster chilldown. Bottom fig shows that the bigger valve opening (green dashed line) results in more commodity spent during childown and faster chilldown. Left fig. shows commodity, right fig. shows the temperature at the sensor closest to the vehicle tank. Storage tank pressure variation Valve opening variation Time, s Series of simulations were performed on sensitivity to valve opening and storage tank pressure to optimize the loading operation regime. The experiments were proposed based on the simulations and they sow agreement with simulations

22. Conclusions Cryogenics Engineering Conference 2015 Tucson, TX The hierarchy of two-phase flow models was proposed for health management and control of cryogenic loading operation Two models for two-phase flow were studied: Separated model is able to simulate pressure and material wave and fast enough to predict flow parameters in real time Moving front homogeneous model is at least 2000 time faster than real time and predicts accurately slow changes in pressure and temperature The models were validated using the KSC CryoTest Bed experimental data and NIST experimental data The model can be used for online learning the correlation parameters for cryogenic fluids on the ground and in microgravity. The models can be used to learn unknown system parameters and optimize the loading regime