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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Computation of Optimal Interplanetary Low-Thrust Trajectories With Bounded Thrust Magnitude By Means of the Generalized Newton-Raphson Method

The generalized Newton-Raphson method, an iterative procedure for solving nonlinear operator equations, has been extended in application to variational problems with bounded control variables. A minimum fuel interplanetary low thrust orbital transfer problem is worked out in detail to demonstrate the practical aspects of the algorithm as well as its computational effectiveness. The control variables are the thrust magnitude, limited from zero to some prescribed maximum value, and the thrust steering angle.

Computation

Nickel-Cadmium Battery Operation Management Optimization Using Robust Design

In recent years following several spacecraft battery anomalies, it was determined that managing the operational factors of NASA flight NiCd rechargeable battery was very important in order to maintain space flight battery nominal performance. The optimization of existing flight battery operational performance was viewed as something new for a Taguchi Methods application.

NiCd rechargeable battery Taguchi Methods applicat

Multidisciplinary Design Optimization and Analysis of an Open Rotor Stage: Part 1

Successful design of open rotor propulsors requires effective analysis across multiple disciplines, including aerodynamics, acoustics, and structures. A viable design must not only be efficient but must also produce an acceptable level of noise and meet all static and dynamic structural requirements. For design and optimization, this is especially challenging because running high fidelity analyses is resource-intensive, and optimizing a design may require many thousands of cases to be analyzed. For this reason, the NASA team has applied design methodology that utilizes low-cost aerodynamic methods, machine learning models, and high-fidelity analyses when necessary. This includes standard two-dimensional methods such as throughflow analysis and quasi-3D blade-to-blade CFD, as well as some newly developed methods. Optimization using 3D CFD is necessary to maximize performance, and this is considered as well. All optimizations are carried out subject to structural constraints evaluated using finite element analysis. Doing this accurately requires a robust trunnion design, capable of pitching the blade between cruise and takeoff conditions while maintaining acceptable factor of safety. Hot to cold analysis must also be applied in order to correctly determine the as-manufactured shape. For acoustics, the unsteady pressures on the blade surfaces must be predicted, and this can be done either through full-annulus unsteady CFD or through a nonlinear harmonic method (NLH). NLH can run much faster, allowing some acoustic considerations to be made earlier in the design process. The design process is ongoing, and this presentation will review the current status and planned next steps. This part of the talk will focus on aerodynamic performance and be followed by a talk on structures and acoustics.

Design

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions to the finite element problem, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. The transient finite-element analysis is done using TACS, and the cell-discharge battery model uses OpenMDAO and dymos. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization

Development of a Thermal Radiator Optimization Tool with Alternate Coolants

The development of a modeling tool to optimize the design of a thermal radiator based on capacity, rejection temperature, geometry, type and coolant is presented. The radiator size is determined from the desired capacity, environmental conditions and rejection temperature. Flow through the radiator is derived from the overall heat load and prescribed inlet to outlet delta temperature for a given coolant. The tool considers radiator geometry (i.e., tube spacing and diameter, face-sheet thickness, overall size, etc.) and general type (i.e., parallel/manifold versus serpentine) in the optimization. Selection from a handful of potential coolants is also available in the tool which primarily affects necessary tube diameter to maintain turbulent flow and minimize pressure drop. An Equivalent System Mass (ESM) approach is utilized to include pump power in the optimization. Results from the tool and potential future enhancements are also discussed.

Coolant

Benchmarking Bayesian Optimization Frameworks and Acquisition Strategies for Materials Discovery and Autonomous Laboratories

Bayesian optimization (BO) can accelerate materials discovery by guiding expensive experiments toward the most promising processing conditions. We systematically compare five BO surrogate and framework combinations (Gaussian processes in Ax, Gaussian processes and Monte-Carlo neural networks in BayBE, random forests in Lolopy, and tree-structured Parzen (TPE) estimators in Hyperopt) on three benchmarks that mimic common materials design tasks (a discrete solid-electrolyte composition space, a hybrid discrete/continuous laminate-composite design problem solved with micromechanics modeling, and the continuous Ishigami analytic function which is a standard optimization benchmark). Each BO surrogate is paired with posterior mean, probability of improvement, and expected improvement acquisition functions and run for 100 trials from randomized initial samples with uniform random search providing a control. Across five random seeds per setting, BayBE’s Gaussian-process surrogate with expected improvement consistently reached ≥95 % of the known optimum in the fewest evaluations, while Lolopy’s random forest matched or exceeded GP performance on purely categorical or mixed spaces at a higher computational cost. Posterior mean alone often stagnated at local optima, underscoring the need for exploration, whereas probability and expected improvement balanced exploration and exploitation leading to better optimization in fewer trials. Execution times ranged from milliseconds for TPE to minutes for neural-network and random-forest surrogates. These results establish baseline expectations for BO in automated materials laboratories and highlight expected improvement with Gaussian processes as a reliable first choice, with random forests offering a strong alternative when categorical variables dominate. The benchmark suite and code are released to facilitate future surrogate, acquisition, and constraint-handling research in data-driven materials optimization.

Bayesian optimization

Design and Optimization of an Open Rotor Stage

Open rotor propulsors enable greatly increased effective bypass ratios over current aircraft engines, resulting in significantly improved efficiencies. One of the most promising of these geometries is the “open fan”, which consists of a single rotor followed by a single stator. This configuration will be referred to as an “open rotor stage” for design work at NASA. In this work we consider the multidisciplinary design and optimization of an open rotor stage using a variety of 2D and 3D techniques. The 2D aerodynamic techniques used for design include a 2D Trefftz plane method, axisymmetric throughflow, and quasi-3D blade-to-blade CFD. Aerodynamic performance is prioritized, while structural requirements are met and some acoustic considerations are included. Between the rotor, stator, and hub profiles, a total of 101 design variables are used. Differences in the process of designing an open rotor stage vs. designing other high-speed propellers are also discussed. The current design, the NASA Optimized Propulsor for Efficiency and Noise (N-OPEN-1), achieves 84.7% net efficiency as predicted by 3D CFD, with further improvements expected to be possible. This design makes effective use of a slower rotor and a less tip-loaded work distribution than typical single-rotation propellers, allowing the stator to produce 14.8% of the thrust. Laminar flow on the blades was responsible for a 1.7% efficiency benefit and warrants further study.

Open rotors

Design and Optimization of an Open Rotor Stage

Open rotor propulsors enable greatly increased effective bypass ratios over current aircraft engines, resulting in significantly improved efficiencies. One of the most promising of these geometries is the “open fan”, which consists of a single rotor followed by a single stator. This configuration will be referred to as an “open rotor stage” for design work at NASA. In this work we consider the multidisciplinary design and optimization of an open rotor stage using a variety of 2D and 3D techniques. The 2D aerodynamic techniques used for design include a 2D Trefftz plane method, axisymmetric throughflow, and quasi-3D blade-to-blade CFD. Aerodynamic performance is prioritized, while structural requirements are met and some acoustic considerations are included. Between the rotor, stator, and hub profiles, a total of 101 design variables are used. Differences in the process of designing an open rotor stage vs. designing other high-speed propellers are also discussed. The current design, the NASA Optimized Propulsor for Efficiency and Noise (N-OPEN-1), achieves 84.7% net efficiency as predicted by 3D CFD, with further improvements expected to be possible. This design makes effective use of a slower rotor and a less tip-loaded work distribution than typical single-rotation propellers, allowing the stator to produce 14.8% of the thrust. Laminar flow on the blades was responsible for a 1.7% efficiency benefit and warrants further study.

turbomachinery

Aerothermal Shape Optimization of Actively-Cooled Battery Packs Using Conjugate Heat Transfer

Thermal management for battery is important for electric aircraft because battery temperature is critically important to vehicle safety, and it also has direct impact on the efficiency of the battery system. Because ambient air is a readily available resource for aircraft, this paper considers an active cooling concept with forced convection of ambient air through the battery pack. Conjugate heat transfer analysis is used to solve the coupled aero-thermal problem, which consists of a finite-volume computational fluid dynamics solver for the fluid domain, and a conduction heat transfer solver for the solid domain. A mixed Neumann and Dirichlet boundary condition is developed for the fluid-solid interface, which allows the solid domain to completely submerge in the fluid domain. A gradient-based optimization method is adopted, and the discrete adjoint approach implemented in DAFoam is used to efficiently compute the gradients. The aero-thermal coupling for primal analysis and gradient computation is handled using the OpenMDAO-based MPhys framework. A constant heat source is prescribed for the battery cells, and the battery shape (design variable) is optimized to minimize cooling pump power and battery weight (composite objective function) while keeping the battery temperature below a threshold (constraint). The optimized design achieves a 44.6% and 1.5% reduction in the cooling pump power and battery weight, respectively, and the maximal temperature constraint is satisfied. This work has the potential to reduce battery-pack weight, improve performance, and reduce the weight of thermal management systems for electric vertical take-off and landing aircraft.

heat transfer

Aerothermal Shape Optimization of Actively-Cooled Battery Packs using Conjugate Heat Transfer

Thermal management for battery is important for electric aircraft because battery temperature is critically important to vehicle safety, and it also has direct impact on the efficiency of the battery system. Because ambient air is a readily available resource for aircraft, this paper considers an active cooling concept with forced convection of ambient air through the battery pack. Conjugate heat transfer analysis is used to solve the coupled aero-thermal problem, which consists of a finite-volume computational fluid dynamics solver for the fluid domain, and a conduction heat transfer solver for the solid domain. A mixed Neumann and Dirichlet boundary condition is developed for the fluid-solid interface, which allows the solid domain to completely submerge in the fluid domain. A gradient-based optimization method is adopted, and the discrete adjoint approach implemented in DAFoam is used to efficiently compute the gradients. The aero-thermal coupling for primal analysis and gradient computation is handled using the OpenMDAO-based MPhys framework. A constant heat source is prescribed for the battery cells, and the battery shape (design variable) is optimized to minimize cooling pump power and battery weight (composite objective function) while keeping the battery temperature below a threshold (constraint). The optimized design achieves a 44.6% and 1.5% reduction in the cooling pump power and battery weight, respectively, and the maximal temperature constraint is satisfied. This work has the potential to reduce battery-pack weight, improve performance, and reduce the weight of thermal management systems for electric vertical take-off and landing aircraft.

thermal management

Optimal Battery Charging for Damage Mitigation

Our control philosophy is to charge the NiH2 cell in such a way that the damage incurred during the charging period is minimized, thus extending its cycle life. This requires nonlinear dynamic model of NiH2 cell and a damage rate model. We must do this first. This control philosophy is generally considered damage mitigating control or life-extending control. This presentation covers how NiH2 cells function, electrode behavior, an essentialized model, damage mechanisms for NiH2 batteries, battery continuum damage modeling, and battery life models. The presentation includes graphs and a chart illustrating how charging a NiH2 battery with different voltages and currents affects damages the battery and affects its life. The presentation concludes with diagrams of control system architectures for tracking battery recharging.

Hartley, Tom T.

Nickel-cadmium Battery Cell Reversal from Resistive Network Effects

During the individual cell short-down procedures often used for storing or reconditioning nickel-cadmium (Ni-Cd) batteries, it is possible for significant reversal of the lowest capacity cells to occur. The reversal is caused by the finite resistance of the common current-carrying leads in the resistive network that is generally used during short-down. A model is developed to evaluate the extent of such a reversal in any specific battery, and the model is verified by means of data from the short-down of a f-cell, 3.5-Ah battery. Computer simulations of short-down on a variety of battery configurations indicate the desirability of controlling capacity imbalances arising from cell configuration and battery management, limiting variability in the short-down resistors, minimizing lead resistances, and optimizing lead configurations.

Zimmerman, A. H.

Photophoretic Propulsion Enabling Mesosphere Exploration NIAC Phase I Final Report

This Phase I report presents a comprehensive study on photophoretic flyers—innovative, ultralight, solar-powered vehicles that harness photophoretic forces generated via Knudsen pumping to achieve sustained flight in the mesosphere (50–80 km altitude). By integrating advanced materials such as nanocardboard— characterized by its extremely low areal density (~1 g/m²) and high bending stiffness—with ultrathin light-absorbing coatings, the project converts incident solar radiation directly into a directed thrust. Extensive experimental investigations, coupled with high-fidelity computational fluid dynamics (CFD) simulations using ANSYS Fluent, validate the concept across various three-dimensional geometries, including spherical, conical, and rocket-shaped configurations. These simulations bridge the gap between free-molecular and continuum flow regimes, demonstrating that optimized designs can generate lift forces sufficient to support kilogram-scale payloads even in low-pressure environments. At the heart of this innovation is the use of Knudsen pumping, where temperature gradients across porous surfaces induce directional gas flow, creating a modest overpressure that provides lift. The report introduces an analytical framework that interpolates between the well-known low-Reynolds number drag regime and the high-Reynolds number momentum theory. This model accurately predicts lift based on design parameters such as microchannel dimensions, porous wall geometry, areal density, and nozzle exit area. For instance, simulations indicate that 10-meter-scale structures with carefully engineered porous walls can achieve the necessary pressure differential to support scientifically significant payloads (~1 kg). The study also explores a hybrid propulsion approach that combines solar buoyancy with photophoretic lift. Initially, solar heating creates a buoyant force that elevates the flyer to mesospheric altitudes. Once in the optimal pressure range, the photophoretic mechanism—powered by Knudsen pumping—takes over as the primary source of lift, ensuring stable, long-duration flight. This dual-mode operation not only facilitates the deployment of photophoretic flyers but also broadens the potential applications for mesospheric exploration. In addition to propulsion, the report investigates the integration of photophoretic thrusters for trajectory control of existing research balloons in the upper stratosphere. By dynamically adjusting the nozzle orientation and controlling the flow-through velocity, these thrusters provide precise maneuverability, enabling the flyers to counteract atmospheric disturbances and adjust their flight paths in real time. For example, a photophoretic thruster approximately 7.5 by 7.5 meters in size could be unfolded below a payload gondola of a 60 million-cubic-foot zero-pressure balloon. Such a thruster can provide horizontal speed control of approximately 1 m/s using only sunlight and no moving parts (except those needed to track the Sun and control the jet direction). Importantly, photophoretic thrusters operate more efficiently at higher altitudes, which is complementary to known trajectory control techniques, such as propellers and tethered wings, which are more effective at lower altitudes. Finally, the report identifies three scientific research thrusts where mesospheric aircraft technology can have a profound impact: atmospheric tides, characterization of gravity waves, and investigation of mesospheric instabilities. Overall, the findings of this Phase I project represent a significant advancement in photophoretic propulsion technology. By demonstrating that large-scale, ultralight structures can be powered solely by solar radiation—via carefully engineered Knudsen pumping—this work lays a robust foundation for scalable, near-space flight architectures. Future refinements in material fabrication, structural optimization, and integrated trajectory control are expected to further enhance performance, paving the way for operational demonstrations that could revolutionize atmospheric science, remote sensing, and communication networks.

Knudsen Pump

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry

Mission Design Considerations for a Low-Thrust Spacecraft

Developing an executable low-thrust trajectory for use in a spaceflight mission requires the design and optimization of a deterministic trajectory as well as the validation that the selected architecture is robust to some set of uncertainties, execution errors, and potential contingencies. Uncertainty in the ability of the spacecraft and its launch vehicle to execute a trajectory as well as potential deviations such as in-flight anomalies combine with design-to constraints and requirements to complicate the optimization problem. The approach by which robust mission design was accomplished for the initial capability of NASA’s Gateway is presented as well as associated results.

NRHO

Mission Design Considerations for a Low-Thrust Spacecraft

Developing an executable low-thrust trajectory for use in a spaceflight mission requires the design and optimization of a deterministic trajectory as well as the validation that the selected architecture is robust to some set of uncertainties, execution errors, and potential contingencies. Uncertainty in the ability of the spacecraft and its launch vehicle to execute a trajectory as well as potential deviations such as in-flight anomalies combine with design-to constraints and requirements to complicate the optimization problem. The approach by which robust mission design was accomplished for the initial capability of NASA’s Gateway is presented as well as associated results.

mission design

Comparison and Application of Battery Modeling Methods for Conceptual Electric Aircraft

Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.

power