AIAA 5th Aviation, Technology, Integration, and Operations Conference (ATIO)<br> 26-28 September 2005, Arlington, Virginia AIAA 2005-7411 NAVAJO: Advanced Software Tool for Balloon Performance Simulation Alexey A. Pankine *, Matthew K. Heun, Nam Nguyen, and R. Stephen Schlaifer Global Aerospace Corporation, Altadena, CA, 91001 Global Aerospace Corporation has developed an advanced balloon performance and analysis tool, called Navajo. Navajo advances the state of the art for balloon performance models and can assist NASA and commercial balloon designers, campaign and mission planners, and flight operations staff by providing higher-accuracy vertical and horizontal trajectory predictions than previously possible. Navajo advances the state of the art by employing a highly sophisticated radiative model that accounts for the actual design and shape of the balloon during ascent and float; by treating radiative fluxes in the atmosphere in a realistic manner; and by providing a graphical user interface. Navajo decouples environment and balloon trajectory models to allow a given balloon design to be flown within any number of environment models with different levels of fidelity. Navajo provides integrated vertical and horizontal trajectory modeling and an extensible application architecture to allow different balloon designs and new environments. A = balloon film surface area b = buoyancy b f = buoyancy at float H = balloon altitude m = balloon film mass s = gore length coordinate T A = atmospheric temperature T bb = atmospheric blackball temperature θ = solar elevation angle Σ = balloon shape parameter Σ d = design balloon shape parameter Nomenclature I. INTRODUCTION Prediction of the trajectory of balloon systems is a difficult thermal problem with potentially significant consequences for incorrect results. For zero-pressure balloon systems, radiative and convective heat transfer between the balloon and its environment determines the temperature of the buoyant gas. The temperature of the buoyant gas determines its density and therefore its lifting capacity. A failure to correctly predict in-flight gas temperatures can lead to under-filling or over-filling the balloons at launch. Under-filled systems may not reach the desired float altitude. Overfilled systems will discharge lifting gas if vent ducts are present. For a superpressure balloon system, heat transfer between the balloon and its environment affects the temperature of the lifting gas, which, in turn, determines the pressure of the gas in the balloon. Failure to correctly predict the lifting gas temperature can lead to balloon envelope rupture or non-pressurization at float. Both conditions could lead to potential safety risks. Stratospheric scientific balloons fly in a near-space environment where heat transfer is dominated by radiation and affected by convection. Stratospheric scientific balloon flights have lasted for about 40 days (100 days in the * Project Scientist, 711 W. Woodbury Rd., Altadena, CA, 91001. Senior Engineer, 711 W. Woodbury Rd., Altadena, CA, 91001. Senior Programmer, 711 W. Woodbury Rd., Altadena, CA, 91001. Staff Programmer, 711 W. Woodbury Rd., Altadena, CA, 91001. 1 Copyright 2005 by Global Aerospace Corporation. Published by the, Inc., with permission.
future). And, flight systems can be exposed to continuous sunlight during polar summer flights. In contrast, lowaltitude, non-sun-synchronous satellites fly for years but have short (~45 min) periods of daylight and darkness. Because of the short day-night cycle, satellite component designers can take advantage of thermal inertia and conduct design activities using an orbit-average radiative environment. Satellite designers never have to account for convective effects in their designs. In contrast, balloon performance modelers need to carefully account for all transient thermal effects (such as sunrise) on balloon systems, including the balloon itself. Plus, they need to account for both radiation and convection on very large structures with 100-m characteristic dimensions. A. Navajo Summary The key innovation of this concept is integrated modeling of Earth and planetary balloons and Lighter Than Air (LTA) systems in a single user-friendly desktop computer application. Additional innovations are (a) decoupling of environment and balloon trajectory models to allow a given balloon design to be flown in any number of environments with different levels of fidelity, (b) integrated vertical and horizontal trajectory modeling, (c) integrated safety analysis of Earth balloon flights for in-flight and pre-flight safety calculations, (d) improved fidelity of thermal models, and (e) an extensible application architecture to allow different balloon designs and new environments. History shows that efforts to refine balloon performance models follow a roughly 10-year cycle. The following important models of the performance of stratospheric scientific balloons have been developed: 1974: Kreith and Kreider 1, 1981: THERMTRAJ, Horn and Carlson 2,3, 1989: ALTIME, and 1990: SINBAD 4. The previous state of the art balloon performance model, SINBAD3.1g, cannot simulate balloons on other planets, does not provide multiple environment model types, has tightly coupled balloon and environment models so users cannot change environment submodel types, does not simulate horizontal trajectories, does not have a safety analysis capability, has inaccurate thermal submodels, is not extensible, and does not have a modern graphical user interface. User requirements have outgrown the capabilities of SINBAD. New computer technologies (modern processors and the graphical user interface concepts) provide the opportunity to do more sophisticated analyses in a more userfriendly way. Thus, the time is ripe for the development of an enhanced model of balloon performance. Navajo integrates environment, balloon (or LTA), gondola (for ballast and communications), and trajectory control system submodels to provide rapid and exhaustive evaluation of vertical and horizontal balloon and lighterthan-air vehicle trajectories. The concept utilizes extensible computer application architecture to permit user definition of additional balloons and environments. The Navajo architecture decouples the balloon performance and environment models so that users can swap balloon and environment models easily and assess the capabilities of new balloon technologies in a variety of environments. Navajo is based on an advanced physical model that takes into account changing balloon shape during a flight and provides more realistic representation of the environment. Comparisons of the Navajo simulations to historic flight data show that the model performs very well but that the convective model needs additional improvement. Pankine 5 contains detailed information on the design for the Navajo desktop computer application. It also contains an analysis of numerical issues associated with simulations of balloon performance. 2
B. Navajo User Interface Figure 1 shows the user interface for configuring Navajo simulations. Figure 1. Navajo model configuration interface. II. Navajo s Submodels There are several submodel types in Navajo, including balloon shape models and environment models. A. Sigma Shape Model (SSM) To calculate the time rate of change for buoyant gas or film temperatures, one needs to calculate heat transfer rates at each time step of the numerical simulation. Navajo implements a Floor/Canopy model for the atmospheric radiative fluxes, in which radiation impinging on the balloon is divided into two streams: one consisting of radiation coming from every direction below the equator of the balloon ( Floor ) and the other consisting of radiation coming from above the equator ( Canopy ). Navajo includes two balloon shape models: spherical (as SINBAD) and a new Sigma Shape Model (SSM). SSM utilizes a detailed description of balloon film design. 1. SSM Radiative Modeling The SSM was developed by detailed radiative analyses of balloon characteristics. Figure 2 shows a RadCAD model of the Raven 29.47 MCF fully inflated balloon. Colors indicate model regions with different thermo-optical properties: light blue: one layer of film pink: 2 layers of film (1 cap) dark blue: 3 layers of film (2 caps) 3
Figure 2. RadCAD model of the Raven 29.47 MCF fully inflated balloon. red: 1 layer of film + load tape (all 159 load tapes are combined to create 2 load tapes - on the opposite sides of the balloon, 180 from each other - of equivalent area and constant angular width. Real load tapes are spread uniformly across the balloon envelope at equal distances from each other. To mimic the thermo-optical effects of the uniformly distributed load tapes, the radiative load on the model balloon is azimuthally averaged) yellow - 2 layers of film + load tape green - 3 layers of film + load tape After describing the construction of the balloon, an analysis was performed to determine the solar absorptivity of the Raven 29.47 MCF model. Figure 3 shows the results of that modeling activity. The color scale on the left gives the values of the solar absorptivity of the various regions across the balloon envelope. Figure 4 shows an example comparison of the radiative loads on the Raven 29.47 MCF balloon at 35 km altitude for different solar angles calculated using the RadCAD model and Sinbad. The film thermo-optical properties of the RadCAD model are those from Cathey 6. The film properties in SINBAD are the default Figure 3. Solar absorptivity of Raven 29.47 MCF balloon. 4
Figure 4. Comparison of Radiative loads on Raven 29.47 MCF balloon. properties, suggested by the SINBAD User Manual. The albedo for the comparisons is 0.3. 2. SSM Balloon Shape Modeling With SSM, the shape of the balloon is defined by two parameters Σ d and b/b f. Σ d is the design Σ for the balloon. The specific buoyancy b of the balloon at altitude H and specific buoyancy b f at float altitude are determined. The second parameter is formed by the ratio of these specific buoyancy values. The shape of the balloon for actual off-design, under-inflated conditions is defined through current values of the parameters Σ and b/b f. In-flight balloon shape changes caused by changes in altitude, suspended mass (for example, after a ballast drop), and mass of the buoyant gas (for example, due to a leak) are captured by Navajo. Figure 5 shows the shape of an under-inflated 29.47 MCF Sigma-shape balloon for Σ = 0.2, b/b f = 15. The model simulates the design of the Raven 29.47 MCF balloon: it has 2 caps of similar extent and the same number of load tapes. SSM treats the surface area A(s) and envelope mass m(s) of the balloon as a function of the length along the gore coordinate s so that surface heat transfer phenomena (convective and non-solar radiative terms) are accurately determined in real-time during a simulated flight for both fully inflated and under-inflated conditions. Note that this approach allows one to accurately model the effect of caps or other reinforcements on the balloon envelope in a highly-accurate manner. SSM calculates projected area (for solar radiation) and view factors (to the canopy and to the floor) for the current balloon shape (Σ, b/b f ), solar elevation angle θ, and balloon altitude H in real-time during a simulated balloon flight. SSM calculates effective thermo-optical (TO) properties of the balloon envelope for the current balloon shape during a simulated flight using the balloon design information (number of caps, width of the gore, optical properties of all balloon construction materials, etc.). To perform these calculations quickly, SSM employs an engineering model that approximates the effective properties of the 5 Figure 5. Model of Underinflated 29.47 MCF balloon shape.
balloon envelope to facilitate calculations of the energy balance. The approximation model was validated for Σ- shape balloons with TO properties of typical NASA balloons manufactured by Raven (29.47 MCF and 39.57 MCF). In these tests the TO properties calculated with the Navajo model were within 5% of the TO properties estimated with detailed Thermal Desktop models. Radiative fluxes for the solar elevation angle θ and balloon altitude H are calculated using the user-specified environment, and SSM can work with any number of built-in environments. For a given altitude above the surface H, the volume of the balloon is determined from the temperature and pressure of the buoyant gas at this altitude. Navajo provides user options for variable or constant drag coefficients and added mass coefficients. Navajo s model for vent ducts uses standard equations for flow of gasses and liquids in pipes. The driving force for the flow of the buoyant gas through the vent duct is the pressure difference between the top of the vent duct and the bottom of the vent duct. The bottom of the vent duct is assumed to be open to the atmosphere. The vertical distribution of pressure in both the buoyant gas and the atmosphere is calculated using the hydrostatic equation. It is assumed that gas densities are constant over the relatively short vertical distance between the duct ends. B. Navajo Environment Models Navajo includes a detailed model of radiative fluxes. The upwelling and downwelling solar fluxes for each level of the atmosphere are scaled for each particular solar angle and surface albedo using an engineering model derived from a radiative transfer code called SBDART 7. The solar constant itself is also a parameter that can be adjusted by the user to directly affect solar fluxes. Figure 6 shows the temperature profiles of six atmospheres built into Navajo. (Users can easily define their own atmospheres.) The upwelling and downwelling fluxes in the atmosphere are set by choosing the appropriate built-in atmospheric model (e.g. Tropical Atmosphere). Figure 6. Temperature profiles for 6 built-in atmospheres. 6
Figure 7. Example visible fluxes from a Navajo environmental model. Figure 8. Comparison of Navajo and Sinbad blackball and atmospheric temperature profiles. 7
Figure 7 shows an example of the visible flux model. Shown are the upwelling diffuse flux (visible flux reflected from the surface and back-scattered from the atmosphere, for albedo of 0.3), downward direct flux (solar flux), and the sum of the downward direct (solar) and diffuse fluxes (atmospheric scattering). The reduction of the downward direct flux with decreasing altitude is due to attenuation in the atmosphere. The fluxes shown are for the sun in zenith. The changes in attenuation and scattering with the increasing optical path for solar angles from 0 to 90 are estimated using look up tables that are part of the atmospheric models. Figure 8 compares the atmospheric profiles and the "black-body temperature" (T bb ) profiles in Sinbad and Navajo. In Sinbad a T bb profile defines IR heating in the atmosphere. In Navajo the IR heating in the atmosphere is described in terms of upwelling and downwelling IR fluxes, providing a more detailed and realistic representation of the atmospheric radiative environment. Navajo's T bb profiles were calculated using the IR fluxes in the Navajo model. As can be seen, even for similar temperature profiles the T bb profiles in Sinbad and Navajo differ by as much as 10 K throughout the atmosphere. This figure assists in comparing the results of simulations from Navajo and Sinbad. Figure 9 shows example upwelling and downwelling IR fluxes in the Navajo's tropical atmosphere. The model assumes a cloudless atmosphere. Atmosphere with clouds can be simulated by providing custom profiles of atmospheric fluxes. In the cloudless atmosphere, variation of visible fluxes due to different amounts of water, ozone and aerosol scatterers in the atmosphere is quite small above the tropopause and is not taken into account in this model. Our testing shows that the range of conditions provided by the built-in environmental models is quite exhaustive. If the user is not satisfied with built-in profiles, any environmental profile can be manually adjusted or imported from a tab-delimited file by the user. Atmospheric air properties have been improved relative to SINBAD. Improved curve fits for air thermal conductivity, viscosity, and Prandtl number as a function of temperature are included with Navajo. And, Navajo includes two ways of modeling twilight periods: one based on a linear solar flux within user-defined twilight periods and another based on solar ephemeris information. Figure 9. Upwelling and downwelling IR fluxes in Navajo s tropical atmosphere. 8
III. Navajo Validation To validate the Navajo s physical model we compare simulations to the data from actual high-altitude flights. A given flight is a good candidate for validation purposes if there is sufficient metadata available to describe the balloon construction and flight environment in Navajo. Because Navajo provides much more detail than previous balloon modeling software, much metadata is required. We evaluated many flights for validation candidates. For successful validation, we needed to know the design of the balloon (given in the manufacturer s As-Built Sheet), the balloon shape profile, the in-flight ballasting schedule, and auxiliary information, such as the mass of the payload, the amount of free lift, etc. Our research revealed that we have enough flight balloon construction metadata for 12 recent flights. Many of these flights have additional unknowns (for example, flights 495NT and 496NT used 1.5-mil film, for which we do not have any information on thermo-optical properties). We also desired flights that were longer than one day to evaluate day/night transitions. Unfortunately, we found only three long-duration (longer than a day) flights with complete descriptions for validation purposes: 493N, 494N and 515N. They all took place in Antarctica at about the same time of year. But, at the time this work was performed, ascent information was not available for flights 493N and 494N. Thus, we chose flight 515N for Navajo validation. Navajo was configured with all the metadata information available, but we did not introduce any special fudge factors to the modeling process. We also provided both SINBAD and Navajo with atmospheric temperature and pressure profiles from a radiosonde launch near Flight 515N s launch time. Results of the validation process are shown in the following graphs. A. Balloon Ascent Figure 10 shows a comparison between the actual Flight 515N ascent profile, Sinbad s prediction, and the Navajo result. Note that Navajo provides a very significant improvement over Sinbad in predicting balloon ascent. Navajo accurately represents the time to float. Navajo also accurately represents the flight through the tropopause and it accurately predicts the time that float altitude is reached. The historic data and Navajo lines are nearly coincident throughout the flight while Sinbad predicts a significantly slower vertical velocity. B. Dynamics at Float Figure 11 shows that Navajo accurately reproduces the character of the dynamics of the motion when reaching float. (Note that both the horizontal and vertical scales of Figure are different from Figure, but the data are identical. The SINBAD line is not present, because the SINBAD prediction does reach these float altitudes at the times shown in the graph.) Navajo correctly predicts the growth and later damping of the magnitude of the altitude oscillations upon reaching float altitude, and Navajo comes close to matching the period of the oscillation at float altitude. Navajo over-predicts flight 515N s float altitude by about 160 m on this simulation. C. Climb-out Trajectory Figure 12 compares the historical climb-out trajectory and Navajo s prediction. There is no line representing SINBAD s climb-out trajectory, because SINBAD does not predict horizontal motion. Navajo compares very favorably to the historical trajectory. Differences may be due to mesoscale winds that are not resolved by the wind data set used for the Navajo simulation. D. Large-scale Altitude Excursions After Float Figure 13 shows that the balloon altitude decreases shortly after reaching float (between 25,000 seconds and 50,000 seconds into the flight). (Note that the horizontal and vertical scales of Fig.13 are different from Fig. 10 and Fig. 11, but the data are identical.) This altitude dip occurs because the balloon reaches float just before nightfall. After some venting, the buoyant gas cools due to reduced solar radiation at dusk. The balloon recovers altitude as the gas warms due to solar heating. Navajo correctly predicts the timing and character of this altitude variation, showing a significant improvement over the SINBAD trajectory. However, Navajo predicts a deeper nighttime dip than actually occurred on Flight 515N. 9
Figure 10. Ascent trajectory comparison. Figure 11. Float dynamics. 10
Figure 12. Climb-out trajectory comparison. Figure 13. Day/night transition comparison. 11
Further along the horizontal axis of Fig. 13, nighttime conditions are encountered. Navajo over predicts the altitude effects of day/night transitions: the simulated balloon descends deeper and rises higher than the actual balloon. In this case, SINBAD does a better job of matching the depth of nighttime descent of the balloon. Note, however, that Navajo matches the timing of the peaks and valleys in day/night ascent/descent profiles much better than SINBAD. This is due to Navajo s simulation of the changing geographic position of the Navajo balloon and corresponding change in the timing of the local noon/midnight. The SINBAD model is unable to simulate this effect. Navajo s prediction of deeper descent than SINBAD is due to the deficiencies of the internal natural convective heat transfer model. The model for internal convection is the same as the model for external convection, due to the lack of better data. SINBAD deals with the same problem by introducing an empirical coefficient that can reduce the internal convection by orders of magnitude and make the night height decrease more shallow. In addition, SINBAD s default thermo-optical parameters for the envelope have been chosen over the years to match altitude profiles: they do not correspond to laboratory measurements of film thermo-optical properties. Thus, in Sinbad, the problem of the convective model is masked by the empirical choice of the film TO properties. These simulations indicate that there is, indeed, a problem with the current state of the art in modeling convective heat transfer in large enclosures like a stratospheric balloon. IV. Summary User requirements had outgrown the capabilities of the previous state of the art balloon performance model, SINBAD3.1g. Global Aerospace Corporation has developed an advanced balloon performance and analysis tool, called Navajo. Navajo integrates vertical and horizontal trajectory modeling, decouples environment and balloon trajectory models, improves accuracy of thermal models, and provides an extensible application architecture. Navajo has been validated by comparison to historical balloon flights. Navajo shows improved agreement between historical flights, particularly regarding the ascent profile, dynamic behavior at float, climb-out trajectory, and timing of altitude variations due to altitude excursions. V. ACKNOWLEDGMENTS The authors wish to acknowledge the support of the NASA Small Business Innovation Program (SBIR) program under contracts NAS5-01177 and NAS5-02119 and the advice and assistance of Debbie Fairbrother (NASA/Wallops Flight Facility). VI. REFERENCES 1 Kreith, F. and Kreider, J. F., Numerical Prediction of the Performance of High Altitude Balloons, NCAR Technical Note NCAR-TN/STR-65, Feb. 1974. 2 Carlson, L. A. and Horn, W. J., A Unified Thermal and Vertical Trajectory Model for the Prediction of High Altitude Balloon Performance, Texas Engineering Experiment Station Report TAMRF-4217-81-01, June 1981. 3 Horn, W. J. and Carlson, L. A., THERMTRAJ: A FORTRAN Program to Compute the Trajectory and gas and Film Temperatures of Zero Pressure Balloons, Texas Engineering Experiment Station Report TAMRF-4217-81-02, June 1981. 4 Raque, S. M., SINBAD 3.0, NASA s Scientific Balloon Analysis Model, User s Manual, NASA Goddard Space Flight Center Code 842/Balloon Project Branch, 1993. 5 Pankine, A., M.K. Heun, & R.S. Schlaifer. 2003. Advanced Balloon Performance Simulation and Analysis Tool. AIAA Paper Number 2003-6741 Presented at 3 rd Annual (AIAA) Aviation Technology, Integration, & Operations (ATIO) Forum, Denver, Colorado, 17 19 November. 6 Cathey, H. M. Jr., Transient Thermal Loading of Natural Shaped Balloons, AIAA Paper Number A97-31338, 1997. 7 See http://www.crseo.ucsb.edu/esrg/pauls_dir/ 12