Performance and Mass Modeling Subtleties in Closed-Brayton-Cycle Space Power Systems

A number of potential NASA missions could benefit from closed-Brayton-cycle (CBC) power conversion systems. The human and robotic mission power applications include spacecraft, surface base, and rover scenarios. Modeling of CBC subsystems allows system engineers, mission planners and project managers to make informed decisions regarding power conversion system characteristics and capabilities. To promote thorough modeling efforts, a critical review of CBC modeling techniques is presented. Analysis of critical modeling elements, component influences and cycle sensitivities is conducted. The analysis leads to quantitative results addressing projections on converter efficiency and overall power conversion system mass. Even moderate modeling errors are shown to easily over-predict converter efficiencies by 30 percent and underestimate mass estimates by 20 percent. Both static and dynamic modeling regimes are evaluated. Key considerations in determining model fidelity requirements are discussed. Conclusions and recommendations are presented that directly address ongoing modeling efforts in solar and nuclear space power systems. NASA/TM—2005-213985 1 II. Literature Review More than 270 works on Brayton-related space power system topics appear in the literature over the last 30 years. Six examples of steady-state analyses are Tilliette, Owen, Baggenstoss and Ashe, Barrett and Reid, Mason and Johnson and Mason. Tilliette examined 25-kWe-class Brayton systems. Liquid metal cooled and direct gas cooled reactors were evaluated as heat sources; fast and thermal spectrums were included. Recuperated and non-recuperated Brayton systems were evaluated. Tilliette demonstrated that a CBC was adaptable for all 10 of the configurations examined. Owen evaluated 10-kWeto 100-kWe-class CBC concepts using pumped loop, heat pipe and direct gas reactor cooling schemes. Thermoelectric conversion was also examined; comparative advantages of a CBC system were given. Baggenstoss and Ashe detailed key mission design requirements for CBC systems. They examined power outputs from 0.5 to 3,300 kWe. Heat sources considered included isotope, solar and reactor; liquid-metal-cooled and direct-gas-cooled reactors were examined. Barrett and Reid evaluated CBC performance as influenced by working fluid molar mass and cycle peak pressure. Their results indicated performance degradation due to increased mechanical losses at higher operating pressures. Mason gave an extensive assessment of a 100-kWe CBC design including system-level optimization results for variations in key design parameters. Johnson and Mason evaluated design-point CBC performance as number of converters, cycle peak pressure and shaft speed varied. Off-design operating modes that reduced reactor heat input were also assessed. Compared to steady-state assessments, far fewer CBC transient analyses have been published. Four relevant recent evaluations are Traverso et al., Traverso, Ulfsnes et al. and Wright. Using a mass inventory control scheme, Traverso et al. showed stable behavior of a 24-kW solar-dynamic CBC converter with heat rejection radiators subjected to orbital sink temperature periodicity. In a description of a transient code validation case, Traverso also showed the importance of thermal energy storage in the turbine wheel of a commercial microturbine. Ulfsnes studied the transient behavior of a semi-closed O2/CO2 gas turbine. The study confirmed the highly integrated complexity of component interactions in a closed cycle system. With the exception of shaft speed calculations, transient variations in gas constant and specific heat ratio were found to have only minor effects on overall cycle performance. Wright modeled an integrated closed-Brayton-cycle and gas-cooled fission reactor power system. The model demonstrated stable behavior and showed that the system was capable of load following. Wright showed that temperature feed back mechanisms in reactor control caused what he labeled “counterintuitive” behavior; his model response to a step decrease in electrical load was an increase in reactor power output. III. Present Objectives Cast in the context of previous studies, the present work has three principal objectives: to demonstrate the system-level impacts of differing levels of refinement in modeling closed-Brayton-cycle power conversion systems, to recommend a minimum CBC modeling fidelity for conceptual design studies, and to identify issues related to mass estimation and transient modeling related to the conceptual design of CBC energy conversion systems for space applications. IV. Fidelity Necessity System and subsystem models are tools used to aid in answering engineering design questions. The requisite fidelity of a model depends on what questions are being considered. Different constraints exist for the development, execution and validation of steady-state versus transient simulations. For conceptual design and sizing of CBC power systems, steady-state thermofluid design models are typically used to generate performance and mass estimates. If dynamic interactions with other subsystems are of interest, an integrated transient model is needed to conduct the investigation. In either case, there exists a minimum set of component and subsystem models that are needed to adequately characterize the system. If one oversimplifies the models, erroneous conclusions may be drawn from the analysis results. Elaboration on some key influential factors is warranted. A. Steady State Many engineers are familiar with the thermodynamics of the ideal Brayton cycle. The cycle is frequently introduced in the first thermodynamics course of an undergraduate mechanical or aerospace engineering curriculum. ‡ In actuality, by its definition the Brayton cycle must be an ideal set of thermodynamic state paths that result in a closed process. The “closed-Brayton-cycle” vernacular is used to distinguish a closed-loop converter from an openloop gas-turbine engine. The nomenclature “ideal” Brayton cycle clarifies that real (non-ideal) component performance is not considered. In practice, real performance is included in many “Brayton” analyses. NASA/TM—2005-213985 2 At first introduction, an instructor may also cover realbehavior of compressors, turbines and heat exchangers. From an introductory course then, we might model a recuperated CBC as shown in Fig. 1. This configuration shows the basic elements of a CBC, but it omits bearings, compressor bleed flow paths (used to cool bearings and the alternator rotor), heat exchanger details, and elements of other subsystems that directly influence CBC performance. Parameters needed to solve the simple cycle thermodynamics of the Fig. 1 representation include turbomachinery efficiencies, recuperator effectiveness and irreversible component flow losses (or “pressure drops”). These performance parameters must be carefully selected to preserve the realness of the model. Overestimation of performance capability can yield unrealistic cycle efficiencies; underestimation can forecast detrimentally heavy subsystem masses. As an illustration, we use a pedigreed high-fidelity CBC modeling code, the NASA Closed Cycle Engine Program (CCEP), to explore the effects of overestimating performance. Figure 2 shows a more realistic CBC diagram that includes heat rejection subsystem (HRS) information; inclusion of this subsystem is key to understanding gas cooler performance and auxiliary load requirements such as required pumping power. For convenience, the heat source subsystem is shown as a generic system because vastly different models are required for different heat sources such as solar, chemical, or nuclear. However, for the same reasons HRS definition is needed, some detailing of the heat source subsystem is also mandatory to complete a thorough power system analysis. Since we are not actually conducting a system analysis but instead are seeking to illustrate CBC modeling issues, the generic source subsystem will suffice for the present work. A 100-kWe, two-engine configuration is presented in Fig. 2; numerical values in the figure are multiplied or divided accordingly. Figure 2 represents the first oversimplified case in which we zero the compressor bleed flows, mechanical losses (bearings and windage) and electrical (EM) losses. Unrealistically optimistic turbomachinery efficiencies are also selected. The result is a Power Out