Michael J. Barrett

Glenn Research Center, Cleveland, Ohio

Paul K. Johnson

Analex Corporation, Brook Park, Ohio

Performance and Mass Modeling Subtleties in

Closed-Brayton-Cycle Space Power Systems

NASA/TM—2005-213985

November 2005

AIAA–2005–5700
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Michael J. Barrett

Glenn Research Center, Cleveland, Ohio

Paul K. Johnson

Analex Corporation, Brook Park, Ohio

Performance and Mass Modeling Subtleties in

Closed-Brayton-Cycle Space Power Systems

NASA/TM—2005-213985

November 2005

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

Third International Energy Conversion Engineering Conference

sponsored by the American Institute of Aeronautics and Astronautics

San Francisco, California, August 15–18, 2005

AIAA–2005–5700
Acknowledgments

NASA's Prometheus Nuclear Systems Program supported the work described within this paper, in whole or part,

as part of the program's technology development and evaluation activities.

Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

This report contains preliminary

findings, subject to revision as

analysis proceeds.

Available electronically at http://gltrs.grc.nasa.gov
Nomenclature 

A = heat transfer area

c = specific heat of solid 

hc = convective heat transfer coefficient 

T = temperature of solid

Te = Far-field fluid temperature 

t = time

V = volume of solid

η = efficiency 

Θ = dimensionless temperature 

ρ = density of solid 

τ = characteristic time scale 

I. Introduction 

LO

B

(Bagge

SED-Brayton-cycle (CBC) power conversion is one method that can be used in space power systems.

rayton system conceptual designs for milliwatt to megawatt power converters have been developed

nstoss and Ashe1

, Harty, et al.2, Shaltens and Mason3, Hyder et al.4, Mason5). When optimizing a CBC-based

power conversion system (PCS), numerous features affect overall system performance; a partial list of influential 

factors includes turbomachinery efficiency, heat exchanger effectiveness, working-fluid composition and cycle 

temperatures and pressures. 

C 

Performance and Mass Modeling Subtleties in 

Closed-Brayton-Cycle Space Power Systems 

Michael J. Barrett 

National Aeronautics and Space Administration 

Glenn Research Center

Cleveland, Ohio 44135 

Paul K. Johnson 

Analex Corporation 

Brook Park, Ohio 44142

Abstract 

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 Tilliette6, Owen7, Baggenstoss and Ashe1, Barrett and Reid8, 

Mason5

 and Johnson and Mason9. 

Tilliette

6

 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. 

Owen7

 evaluated 10-kWe- to 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

1

 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 Reid8

 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. Mason5

 gave an extensive assessment of a 100-kWe CBC design

including system-level optimization results for variations in key design parameters. Johnson and Mason9

 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.10, Traverso11, Ulfsnes et al.12 and Wright13. Using a mass inventory control 

scheme, Traverso et al.10 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,

Traverso11 also showed the importance of thermal energy storage in the turbine wheel of a commercial microturbine. 

Ulfsnes12 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. Wright13 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)8,9,14,15,16, 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

Heat In

Heat Out

Recuperator

TurboAlternator

Gas Cooler

Heat 

Source 

Heat 

Exchanger

(HSHX)

Figure 1. Simple recuperated Brayton cycle. 

HeXe

NaK 393 K 5% Bleed 1150 K 1.22 kg/s

0.82 kg/s 0.138 MPa 0.043 kg/s 0.964 MPa 40.0 mol wt

0.87 kg/s 157 kWt 72% He

 395 K 0% 28% Xe

1150 K (1 of 2)

85.000% 90.000%

1.22 kg/s

400 K 920 K

0.500 MPa 0.515 MPa 313 kWt 320 kWt

CPR 2.00 Speed 45 krpm TPR 1.872

95 kW In EM loss 0.0 kWt 145 kW Out

Brg Loss 0.000 kWt 98%

107 kWt Wnd loss 0.000 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 0.0 kWt

216 kWt Ratio = 1.190 TIT/CIT 2.87

97% Cyc eff 31.90%

110.6 m2 902 K

550 K 222 kWt 0.991 MPa

0.999 MPa

530 K 569 K 95%

Tsink 0.276 MPa 0.506 MPa 920 K

200 K

DP/Pcold = 0.0052

DP/Phot = 0.0150

50.0 kWe

 CT 

100%

1.11 kWe

12.7%

16.1 gpm

DP 138 kPa

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 2. CBC with specified turbomachinery η, 0% compressor bleed, no bearing, windage, or EM losses. 

configuration with each 50-kWe engine running at 31.9% converter efficiency, 

 η converter = alternator electrical output / cycle heat input (1) 

NASA/TM—2005-213985 3
In Fig. 3, we add 2% compressor bleed flow for bearing and rotor cooling. At the entrance to the turbine, the mixing 

of compressor bleed flow with flow from the heat source heat exchanger (HSHX) leads to a lower turbine inlet 

temperature and degraded converter efficiency of 30.1%. Figure 4 shows the effect of using design performance 

maps to estimate turbomachinery efficiencies. (Mean-line design codes are even better estimates of compressor and 

HeXe

NaK 393 K 5% Bleed 1150 K 1.25 kg/s

0.97 kg/s 0.138 MPa 0.051 kg/s 0.963 MPa 40.0 mol wt

1.03 kg/s 166 kWt 72% He

 395 K 2% 28% Xe

1143 K (1 of 2)

85.000% 90.000%

1.27 kg/s

400 K 915 K

0.500 MPa 0.515 MPa 332 kWt 339 kWt

CPR 2.00 Speed 45 krpm TPR 1.869

100 kW In EM loss 0.0 kWt 150 kW Out

Brg Loss 0.000 kWt 98%

116 kWt Wnd loss 0.000 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 0.0 kWt

235 kWt Ratio = 1.347 TIT/CIT 2.86

97% Cyc eff 30.10%

125.3 m2 894 K

550 K 223 kWt 0.992 MPa

0.999 MPa

518 K 575 K 95%

Tsink 0.276 MPa 0.506 MPa 912 K

200 K

DP/Pcold = 0.0050

DP/Phot = 0.0150

1.18 kWe

14.1%

19.1 gpm

DP 138 kPa

50.0 kWe

 CT 

100%

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 3. CBC with specified turbomachinery η, 2% compressor bleed, no bearing, windage, or EM losses.

HeXe

NaK 393 K 5% Bleed 1150 K 1.55 kg/s

1.20 kg/s 0.138 MPa 0.063 kg/s 0.962 MPa 40.0 mol wt

1.26 kg/s 199 kWt 72% He

 394 K 2% 28% Xe

1143 K (1 of 2)

82.051% 86.326%

1.58 kg/s

400 K 925 K

0.500 MPa 0.515 MPa 398 kWt 406 kWt

CPR 2.00 Speed 45 krpm TPR 1.869

128 kW In EM loss 0.0 kWt 178 kW Out

Brg Loss 0.000 kWt 98%

149 kWt Wnd loss 0.000 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 0.0 kWt

301 kWt Ratio = 1.328 TIT/CIT 2.86

97% Cyc eff 25.13%

157.4 m2 903 K

556 K 280 kWt 0.991 MPa

0.999 MPa

524 K 581 K 95%

Tsink 0.276 MPa 0.506 MPa 922 K

200 K

DP/Pcold = 0.0055

DP/Phot = 0.0150

50.0 kWe

 CT 

100%

1.28 kWe

15.9%

23.4 gpm

DP 138 kPa

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 4. CBC with map-based turbomachinery η, 2% compressor bleed, no bearing, windage, or EM losses. 

NASA/TM—2005-213985 4
turbine performance and are preferred to generic conceptual design maps.) Even though the original polytropic 

efficiencies were held to less than 90% (ec = 87%, et = 89%), the design performance maps for the corrected mass 

flow rates, specific speeds and pressure ratios represented reduce each wheel isentropic efficiency by three points or 

more (85% to 82% for the compressor; 90% to 86% for the turbine). The converter efficiency suffers and drops to

25.1%. Figures 5 through 7 display cases that add bearing, windage and electromagnetic losses yielding

progressively more realistic performance estimates. Ultimately, the Fig. 7 converter efficiency falls to 21.7%. The

fidelity increase from Fig. 2 to Fig. 7 revises the efficiency prediction from 31.9% to 21.7% – a relative reduction of

HeXe

NaK 393 K 5% Bleed 1150 K 1.64 kg/s

1.25 kg/s 0.138 MPa 0.066 kg/s 0.962 MPa 40.0 mol wt

1.31 kg/s 210 kWt 72% He

 436 K 2% 28% Xe

1144 K (1 of 2)

82.178% 86.664%

1.67 kg/s

400 K 925 K

0.500 MPa 0.515 MPa 420 kWt 428 kWt

CPR 2.00 Speed 45 krpm TPR 1.868

135 kW In EM loss 0.0 kWt 189 kW Out

Brg Loss 3.922 kWt 98%

157 kWt Wnd loss 0.000 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 3.9 kWt

323 kWt Ratio = 1.310 TIT/CIT 2.86

97% Cyc eff 23.82%

166.5 m2 904 K

556 K 297 kWt 0.991 MPa

0.999 MPa

528 K 581 K 95%

Tsink 0.276 MPa 0.506 MPa 922 K

200 K

DP/Pcold = 0.0056

DP/Phot = 0.0150

1.31 kWe

16.2%

24.4 gpm

DP 138 kPa

50.0 kWe

 C T 

100%

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 5. CBC with map-based turbomachinery η, 2% compressor bleed, bearing losses only. 

HeXe

NaK 393 K 5% Bleed 1150 K 1.75 kg/s

1.34 kg/s 0.138 MPa 0.071 kg/s 0.962 MPa 40.0 mol wt

1.41 kg/s 224 kWt 72% He

 483 K 2% 28% Xe

1145 K (1 of 2)

82.298% 87.084%

1.79 kg/s

400 K 924 K

0.500 MPa 0.515 MPa 447 kWt 456 kWt

CPR 2.00 Speed 45 krpm TPR 1.868

144 kW In EM loss 0.0 kWt 203 kW Out

Brg Loss 4.127 kWt 98%

168 kWt Wnd loss 4.782 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 8.9 kWt

350 kWt Ratio = 1.320 TIT/CIT 2.86

97% Cyc eff 22.35%

180.0 m2 904 K

555 K 318 kWt 0.991 MPa

0.999 MPa

529 K 581 K 95%

Tsink 0.276 MPa 0.506 MPa 923 K

200 K

DP/Pcold = 0.0058

DP/Phot = 0.0150

50.0 kWe

 C T 

100%

1.38 kWe

16.6%

26.3 gpm

DP 138 kPa

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 6. CBC with map-based turbomachinery η, 2% compressor bleed, bearing and windage losses only. 

NASA/TM—2005-213985 5
HeXe

NaK 393 K 5% Bleed 1150 K 1.81 kg/s

1.38 kg/s 0.138 MPa 0.073 kg/s 0.962 MPa 40.0 mol wt

1.45 kg/s 231 kWt 72% He

 507 K 2% 28% Xe

1145 K (1 of 2)

82.348% 87.302%

1.85 kg/s

400 K 924 K

0.500 MPa 0.515 MPa 462 kWt 471 kWt

CPR 2.00 Speed 45 krpm TPR 1.868

149 kW In EM loss 2.6 kWt 211 kW Out

Brg Loss 4.224 kWt 98%

173 kWt Wnd loss 4.704 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 11.559 kWt

365 kWt Ratio = 1.315 TIT/CIT 2.86

97% Cyc eff 21.65%

186.4 m2 905 K

555 K 329 kWt 0.991 MPa

0.999 MPa

531 K 581 K 95%

Tsink 0.276 MPa 0.506 MPa 923 K

200 K

DP/Pcold = 0.0060

DP/Phot = 0.0150

1.39 kWe

16.9%

27.1 gpm

DP 138 kPa

50.0 kWe

 CT 

95%

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 7. CBC with map-based turbomachinery η, 2% compressor bleed, bearing, windage, and EM losses.

32%. As the converter efficiency falls, more heat input is required, more heat rejection is required, cycle state points 

vary, auxiliary loads change accordingly, and system mass estimates increase. Blending empirical and geometric

mass estimators (discussed in section VI.), the combined CBC and HRS subsystem mass estimates increases from

1899 kg to 2308 kg – a jump of nearly 22%. This example suggests that if a designer can tolerate 30% 

overestimation of efficiency or 22% underestimation of subsystem mass, the model of Fig. 2 would be adequate. In

the conceptual design phase, a 22% underestimation of mass could deplete an entire subsystem mass margin

allocation. Additionally, in even the earliest conceptual design for a space power system, 30% error in calculated 

efficiency is unacceptable. Conducting CBC analyses without consideration of realistic turbomachinery 

efficiencies, mechanical losses and electromagnetic losses is at best troublesome and at worst seriously misleading. 

Unfortunately, the fidelity level at which previous “non-CCEP” studies have been conducted is unclear. 

Higher-level system models are often used during the integrated conceptual design of a spacecraft. Estimates

from high-fidelity subsystem models serve as inputs to the larger space-system-level mass and performance

optimization tool. By necessity, parametric representation of the subsystem is frequently used to simplify the 

higher-level model. Caution must be exercised to ensure the representation in the simplified model is relevant to the 

question the larger model is being used to address. At a minimum, design points derived from the simplified

parametric model must be verified using the high-fidelity code. (As a matter of good design practice, the 

parameterization and verification steps inherently require a high-fidelity model exist.) As computing power 

continues to increase, more and more subsystem details can be added to higher-level models, but a fidelity 

difference between subsystem and space system models will likely remain. 

B. Transient 

1. Analytical Formulation 

Integrated transient models are used to evaluate dynamic subsystem interactions such as nuclear reactor and

power conversion control algorithms. When building transient models, the same fundamental issue arises – what 

level of fidelity is required? In the gas-turbine controls community, three levels of transient models are often 

discussed: detailed nonlinear thermodynamic models, linearized dynamic models, and real-time piecewise linear 

dynamic models (RPLDM)

17. The aforementioned CCEP results are examples of detailed thermodynamic nonlinear

model output. Due to the computational complexity of detailed nonlinear models, they are most often used in

NASA/TM—2005-213985 6
engine and subsystem design capacity without real-time implementation. Linearized models are created using the 

detailed nonlinear model for performance characterization around an operating point. By selecting a number of 

discrete operating points, linearized model coefficients can be combined with nonlinear steady-state operating 

curves to create an RPLDM for system control schemes. (A complication to note regarding RPLDM

implementation in a control algorithm is that characteristics of each “as built” engine will differ. Flexibility in early

model architecture must be maintained to allow customization for each engine controller.) 

As it is for any model, the predicted subsystem 

performance from a dynamic model is only as good

as the fidelity captured in the code. In addition to

the aforementioned steady-state fidelity issues 

associated with performance and loss modeling, in a 

transient model, the desired fidelity is often a 

question of what timescales are present in the

problem. Fortunately, in the development of CBC 

subsystems for space applications, at least three 

distinct timescales present themselves and can often 

be used to clarify modeling needs. The 

characteristic electrical, mechanical and thermal 

timescales in a CBC PCS design problem may differ

by orders of magnitude. 

For instance, as user loads are shorted or 

switched on and off, the electrical voltage and 

current transients typically represent millisecond or 

smaller-order timescales. An alternator’s managed 

response to an ion thruster recycle event18 recorded

in Fig. 8 serves as a good example of this type of 

timescale response. As the thruster shorts and resets 

(a recycle), the parasitic load in the system is

adjusted such that the alternator voltage and current 

transients last less than 6 milliseconds. 

Displaying a slightly slower response, dependent

upon component geometries and rotational speeds,

shaft dynamics may be represented by millisecondto-second characteristic times. For instance, a graph 

showing shaft speed of a 2-kWe CBC during

transient testing of commanded shutdown and

restart19 is shown in Fig. 9. 

Slower yet (although there are exceptions), 

subsystem level thermal timescales tend to be the 

longest – ranging from seconds to hours. A Brayton 

solar-dynamic system thermal response to heat flux 

variation during a ground test simulating orbital 

operations3

 is captured in Fig. 10. If through

examination of the governing differential equations, 

an engineer can estimate and isolate the timescales

in the problems of interest, simplifications in

transient modeling may be achieved by separating 

the inconsequential physical phenomenon from the 

relevant factors and removing the unimportant

parameters from the models. 

For example, when trying to estimate the power 

profile and total energy required to start a CBC

converter from rest, the electrical and mechanical

timescales dominate the initial system response. A

multi-kilowatt CBC turboalternator using gas-film,

compliant-foil bearings is easily capable of

Figure 8. Alternator transient during a thruster recycle. 

Figure 9. Shaft speed during transient testing. 

Figure 10. Thermal variation of solar-dynamic Brayton.

NASA/TM—2005-213985 7
achieving “lift-off” (when the foils lift off of the shaft and the shaft is hydrodynamically supported by the gas film)

in less than one second. After lift-off, the system is “motored” (using the alternator as a motor to rotate the shaft) 

until the system reaches a thermofluid transition point at which the converter becomes self-sustaining and power 

producing. Depending on the size and performance characteristics of the converter, the thermal response may take 

minutes. To simplify transient modeling efforts addressing start-up power profiles, a short-time-scale electromechanical model of the turboalternator (including the shaft and bearings but ignoring the thermal response of the 

CBC system) might be adequate to predict the initial power profile in the first second. The short-time model would 

simulate parameters such as motor torque, break-away torque, shaft inertia and bearing contact friction. A second

model considering the subsystem thermal response and motoring time needed until self-sustaining action is reached

would address component mechanical losses and thermal capacitances to allow integration at larger time scales 

thereby completing the power profile and energy estimates. The simplification achieved by timescale identification 

and separation often leads to easier model development and execution. Yet, one must still be sensitive to possible 

exceptions. For instance, if the relatively fast thermal response of the bearing foils is relevant to the contact friction

phenomenon, a locally integrated thermal model may still be needed in the start-up analysis. 

2. Experimental Validation 

As characteristic scales are being evaluated, it is worthwhile to consider what methods will be used to verify 

model predictions. To attain reasonable confidence in predictive capabilities, models (steady-state and transient)

must be validated using empirical data. When planning an experiment to validate a highly integrated dynamic 

model, similitude of critical dimensionless scales is desirable. The degree to which dimensionless scales are not 

matched directly impacts the credibility of the verification. For example, a simple lumped-capacitance thermal

model of an isolated, insulated duct in a Brayton system is characterized by the first-order ordinary differential

equation representing conservation of energy, 

+ hc A(T −Te ) = 0

dt

dT

ρVc (2)

The familiar temperature time-response equation results, 

 (3) /τ ( ) t Θ t e− =

The characteristic time constant, τ, is made up of physically significant duct and flow parameters, 

τ = ρVc hc A (4)

To increase the usefulness of a validation experiment, the experimental apparatus used to generate integrated

duct model verification data should possess a similar time constant to a flight-like system. A 10-cm diameter castiron commercial pipe flowing air with a time constant of 184 s may not be a good representation of a stainless steel

flight-like compressor inlet duct flowing He-Xe with a time constant of 62 s. Certainly, this is an over-simplified

example – an experiment is not needed to provide the first-order solution. However, for components with

complicated geometries and multiple characteristic scales (such as a heat exchanger), the opportunity to achieve

similitude is quickly lost as non-prototypic hardware enters a verification test loop. Even if something as simple as 

the lumped-capacitance time scale is matched, it may be of very limited use. Biot numbers, Bi = hcD/ks, for the 

aforementioned duct cases are significantly greater than 0.1; this invalidates the lumped-capacitance assumption 

altogether. Even as higher-order models are developed, integrated experiments using flight-like components are 

required to verify that modeling assumptions still do not oversimplify the problem.

V. Cycle Sensitivity 

Thermodynamic performance of CBC energy converters can be strongly affected by individual component 

characteristics. Even in the oversimplified Fig. 1 representation, the overall converter efficiency is very sensitive to 

recuperator effectiveness. Turbomachinery efficiencies and heat exchanger effectivenesses are commonly known to

influence cycle performance. However, cycle sensitivity to parameters such as bearing film thickness or alternator

gap size is less recognized. 

NASA/TM—2005-213985 8
Bearing film thickness and alternator gap size

both affect the total frictional losses associated with 

shaft rotation. These viscous losses directly rob the 

turbine of useful shaft work. For a converter that 

runs at 25% efficiency, each kilowatt of viscous loss

can require up to one kilowatt of heat rejection and

4 kWt in additional heat source supply capability (a 

fraction of the viscous heating can be recovered as 

useful work if the heated fluid travels through the 

recuperator or turbine). The selection of an

appropriate design-point bearing film thickness is an 

extremely complicated trade study involving items

such as bearing load capacity, bearing and shaft 

geometry, off-design expectations, thermal 

management and rotordynamics. Likewise, trades

in electromagnetic efficiency, rotordynamics,

material properties, and operating stresses are

needed to set the operating “air” gap distance in the 

alternator. Since the cycle working fluid is sheared in the bearing-film and alternator-gap separations, mechanical 

losses (bearing and windage) are significantly impacted by the separation values. Figure 11 presents a gross 

windage loss estimator as film thickness and peak operating pressure vary for a 100 kWe system. (For thrust and 

journal bearings, effective film thickness and operating pressure cannot be treated as independent parameters; 

bearing load capacity couples the two parameters and requires load estimates to optimize the thickness setting.) In

the windage model results of Fig. 11, loss estimates become significant at the higher pressures. These losses cause

cycle optimized state points to change. The more intricate loss models encompassed in CCEP16 allow us to evaluate 

cycle sensitivities to loss estimates. Comparing Figs. 5-7 and 12 identifies cycle impacts due to mechanical loss 

sensitivities. At a peak operating pressure of 1 MPa, Fig. 7 shows total mechanical losses of approximately 9 kW; at

3 MPa, Fig. 12 totals 23 kW of mechanical losses. Unfortunately, significant variation exists in different loss

models. Figure 13 shows a cycle similar to that of Fig. 12 but using a different empirical loss model.

9

 The

mechanical losses shown in Fig. 13 at 3 MPa are less than 14 kW (a 40% reduction); a related increase in Fig. 12 to

0

5

10

15

20

25

30

35

40

012

Film Thickness, mm

Loss, kW

3 MP

3

a

1 MPa

0.5 MPa

0.1 MPa

Figure 11. Windage loss estimator.

HeXe

NaK 393 K 5% Bleed 1150 K 2.77 kg/s

1.97 kg/s 0.137 MPa 0.104 kg/s 2.888 MPa 40.0 mol wt

2.08 kg/s 339 kWt 72% He

574 K 2% 28% Xe

1147 K

80.269% 83.766%

2.83 kg/s

400 K 934 K

1.500 MPa 1.544 MPa 678 kWt 692 kWt

CPR 2.00 Speed 45 krpm TPR 1.870

234 kW In EM loss 3.3 kWt 310 kW Out

Brg Loss 12.986 kWt 98%

272 kWt Wnd loss 9.820 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 26.140 kWt

582 kWt Ratio = 1.223 TIT/CIT 2.87

97% Cyc eff 14.74%

281.0 m2 915 K

559 K 513 kWt 2.974 MPa

2.994 MPa

547 K 585 K 95%

Tsink 0.275 MPa 1.518 MPa 933 K

200 K

DP/Pcold = 0.0049

DP/Phot = 0.0150

1.55 kWe

21.8%

38.7 gpm

DP 139 kPa

50.0 kWe

 CT 

94%

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 12. CBC at 3MPa peak cycle pressure; includes map-based turbomachinery η, 2% compressor bleed, 

bearing, windage, and EM losses. 

NASA/TM—2005-213985 9
HeXe

NaK 393 K 5% Bleed 1150 K 2.53 kg/s

1.81 kg/s 0.137 MPa 0.095 kg/s 2.888 MPa 40.0 mol wt

1.90 kg/s 311 kWt 72% He

 521 K 2% 28% Xe

1146 K

79.851% 83.408%

2.59 kg/s

400 K 934 K

1.500 MPa 1.544 MPa 621 kWt 634 kWt

CPR 2.00 Speed 45 krpm TPR 1.870

215 kW In EM loss 3.3 kWt 282 kW Out

Brg Loss 5.279 kWt 98%

250 kWt Wnd loss 8.371 kWt DP/P = 0.0270

DP/P = 0.0100 Losses 16.983 kWt

525 kWt Ratio = 1.228 TIT/CIT 2.86

97% Cyc eff 16.09%

255.8 m2 914 K

560 K 466 kWt 2.974 MPa

2.994 MPa

544 K 586 K 95%

Tsink 0.275 MPa 1.518 MPa 933 K

200 K

DP/Pcold = 0.0048

DP/Phot = 0.0150

50.0 kWe

 C T 

94%

1.52 kWe

20.4%

35.5 gpm

DP 139 kPa

Recuperator

TurboAlternator

Reactor

Gas Cooler

HSHX

Main Radiator

ALIP Pump

Figure 13. CBC at 3MPa peak cycle pressure; includes map-based turbomachinery η, 2% compressor bleed, 

and alternate loss model.

Fig. 13 converter efficiency from 14.7% to 16.1% is noted. Not only is converter efficiency affected, but other

design factors are also sensitive to mechanical losses. For example, start-up auxiliary power requirements are 

heavily influenced by mechanical loss and total motoring time estimates. To reduce the uncertainty associated with

loss estimates, a focused research program is currently underway at the NASA Glenn Research Center. The

research will better quantify bearing and windage mechanical losses under different operating conditions in fluids of

various molecular weights and correlate the observed losses with a physics-based loss model. 

VI. Mass Models 

In CBC conceptual design models, two methods of mass estimation are prevalent. The first method uses

empirical curve fits that present “as-built” component masses as a function of a few (frequently one) characteristic 

performance variables. The second method is to have a detailed geometric characterization of the component and 

determine the mass by summing the known volume and material density products. Both methods have advantages

and disadvantages. 

The empirical method is generally simpler and easily included in higher-level integrated system models. For

example, to size a turboalternator or CBC heat exchanger, the specific mass (kg/kW) curves in Figs. 14 and 15 could

be used. The curves are anchored by prototypical hardware built as part of previous research programs.

(Uncertainties due to few “as-built” data points can, of course, propagate to large uncertainties in subsystem mass

estimates.) If the empirical method is used, unjustified extrapolation outside the empirical database must be 

avoided. Additionally, without a more detailed physical model to scale the hardware, the modeler relies on the 

completeness of the independent variables identified. Because of the problems listed, it is often difficult to fully 

assess the impact of advanced technologies using historical hardware-based functional relationships. 

The use of more detailed component design information provides a second mass estimation method. Using this

technique, the CCEP code manipulates information such as that given in Table 1 to estimate the mass of a plate-fin 

counterflow recuperator. The detailed information seems to yield a more fundamental mass calculation, but one 

must recognize that other empirical relationships (such as pressure-drop and heat transfer correlations) are involved

in producing the detailed geometric configuration. If the design details are generated using a fundamental physicsbased algorithm, this method can usually be successfully adapted to investigate advanced technologies (like new 

materials, fabrication methods, etc.). This method is also less constrained by designs that lie outside the historical 

database. However, whenever a conceptual design estimate can be validated with “as-built” reference data in a 

reasonable and unrestrained manner, the hardware-based comparison is usually preferred. 

NASA/TM—2005-213985 10
Figure 14. Figure 15. Specific mass curves for heat exchangers. Specific mass curve for turboalternators. 

VII. Conclusions

Each performance model’s required capabilities are 

driven by the design question being investigated.

However, as a general recommendation, to attain

acceptable results, conceptual design analyses used to size 

closed-Brayton-cycle space power conversion subsystems

must include realistic representations of turbomachinery 

efficiencies, mechanical losses and electromechanical 

losses. Efficiency errors of 30% and mass estimate errors 

of 20% are possible using even moderately unrealistic

representations. 

Transient CBC performance models can benefit from

timescale identification and segregation. Characteristic

electrical, mechanical and thermal timescales in closedBrayton-cycle subsystems can vary from fractions of

milliseconds to hours. Simpler development and use of

integrated dynamic models may be possible using 

timescale separation techniques. 

Dimensionless similitude between ground test units and

flight systems is essential to meaningful experimental 

validation of transient models. Special attention must be

devoted to evaluating ground test hardware with respect to

flight-like characteristic dimensionless scales. 

Cycle energy balances are sensitive to mechanical

losses in bearings and alternators. Comprehensive bearing

and windage loss models are difficult to generate due to

the complexity and number of variables in the related trade 

spaces. Existing loss models yield significantly different 

loss predictions. Using two available models, a 40%

difference in mechanical loss predictions was 

demonstrated for a 100-kWe (two-engine) closed-Braytoncycle subsystem operating at 3 MPa peak pressure. More

research is needed to reduce the uncertainty in journal and 

thrust bearing loss predictions over a range of operating 

conditions using fluids of various molecular weights. 

Closed-Brayton-cycle subsystem mass estimates are

typically empirically based or calculated from more 

detailed component design information. Both methods

Table 1. Recuperator geometric characterization. 

Recuperator

Item Value Units

Total Length = 0.820 m

Total Width = 0.325 m

Total Height = 0.459 m

Divider Plate Thick = 0.000203 m

Sideplate Thick = 0.00254 m

Outer shell Thick = 0.00356 m

Headers

Item Value Units

Inlet Header Length = 0.193 m

Inlet Header Width = 0.248 m

Outlet Header Length = 0.203 m

Outlet Header Width = 0.257 m

Fin Pitch = 197 fins/m

Fin Length = N/A

Fin Thickness = 0.0001524 m

Core General

Item Value Units

Core Length = 0.42418 m

Core Width = 0.313182 m

Fin Pitch = 630 fins/m

Fin Length = 0.00318 m

Fin Thickness = 0.0001524 m

Cold Stream Core (High Pressure)

Item Value Units

Flow Area = 0.0513 m2 

Plate Spacing = 0.00318 m

DHYD = 0.001946 m

# Sandwiches = 60

Heat Xfer Area = 46.5 m2 

Hot Stream Core (Low Pressure)

Item Value Units

Flow Area = 0.0645 m2 

Plate Spacing = 0.00389 m

DHYD = 0.002073 m

# Sandwiches = 61

Heat Xfer Area = 54.9 m2 

 Recuperator mass = 158 kg

NASA/TM—2005-213985 11
have advantages and disadvantages but, if not overly constraining, grounding a mass estimate in “as-built” data is 

frequently advantageous. 

References 

1

Baggenstoss W.G., and Ashe, T.L., “Mission Design Drivers for Closed Brayton Cycle Space Power Conversion 

Configuration,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 114, No. 4, 1992, pp. 721-726. 2

Harty, R.B., Otting, W.D., and Kudija, C.T., “Applications of Brayton Cycle Technology to Space Power,” Proceedings of 

Intersociety Energy Conversion Engineering Conference (IECEC 1993), ACS Publications, Washington, DC, 1993, pp. 463-467. 3

Shaltens R.K., and Mason, L.S., “Early Results from Solar Dynamic Space Power System Testing,” AIAA Journal of 

Propulsion and Power, 1996, pp. 852-858. 4

Hyder, A.K., Wiley, R.L., Halpert, G., Flood, D.J., and Sabripour, S., Spacecraft Power Technologies, Imperial College 

Press, London, 2000, pp. 332-340. 5

Mason, L.S., “A Power Conversion Concept for the Jupiter Icy Moons Orbiter,” AIAA Journal of Propulsion and Power, 

Vol. 20, No. 5, 2004, pp. 902-910. 6

Tilliette, Z.P., “Adaptability of Brayton Cycle Conversion Systems to Fast, Epithermal and Thermal Spectrum Space 

Nuclear Reactors,” Proceedings of Intersociety Energy Conversion Engineering Conference (IECEC 1988), ASME Publications, 

New York, 1988, pp. 197-202. 7

Owen, D.F., “SP-100/Brayton Power System Concepts,” Proceedings of Intersociety Energy Conversion Engineering 

Conference (IECEC 1989), IEEE Publications, Los Alamitos, CA, 1989, pp. 1257-1262. 8

Barrett, M.J., and Reid, B.M., “System Mass Variation and Entropy Generation in 100-kWe Closed-Brayton-Cycle Space 

Power Systems,” Proceedings of Space Technology and Applications International Forum (STAIF-2004), edited by M. El-Genk, 

AIP Conference Proceedings 699, New York, 2004, pp. 445-452. 9

Johnson, P.K., and Mason, L.S., “Design and Off-Design Performance of 100 kWe-Class Brayton Power Conversion 

Systems,” Proceedings of Space Technology and Applications International Forum (STAIF-2005), edited by M. El-Genk, AIP 

Conference Proceedings 746, New York, 2005, pp. 711-718. 10Traverso, A., Calzolari, F., and Massardo, A., “Transient Analysis of and Control System for Advanced Cycles Based on 

Micro Gas Turbine Technology,” Proceedings of ASME Turbo Expo 2003, Vol. 3, ASME, New York, 2003, pp. 201-209. 11Traverso, A., “TRANSEO Code for the Dynamic Performance Simulation of Micro Gas Turbine Cycles,” Proceedings of 

ASME Turbo Expo 2005, ASME, New York, 2005, GT2005-68101. 12Ulfsnes, R.E., Bolland, O., and Jordal, K., “Modeling and Simulation of Transient Performance of the Semi-closed O2/CO2

Gas Turbine Cycle for CO2-capture,” Proceedings of ASME Turbo Expo 2003, Vol. 3, ASME, New York, 2003, pp. 65-74. 13Wright, S.A., “Preliminary Results of a Dynamic System Model for a Closed-loop Brayton Cycle Coupled to a Nuclear 

Reactor,” Proceedings of 1st International Energy Conversion Engineering Conference (IECEC 2003), AIAA, Washington, DC, 

2003. 14Fishbach, L.H., and Caddy, M.J., “NNEP – The Navy/NASA Engine Program,” NASA TM X-71857, NASA Lewis 

Research Center, Cleveland, OH, 1975. 15Klann, J.L., and Staiger, P.J., “Design Tradeoffs for a Space Station Solar-Brayton Power System,” Proceedings of 

Intersociety Energy Conversion Engineering Conference (IECEC 1985), Vol. 1, SAE Publications, Warrendale, PA, 1985, pp. 

84-97. 16Klann, J.L., Closed Cycle Engine Program Operational Manual, NASA Lewis Research Center, Cleveland, Ohio, 1991. 17Kulikov, G.G., and Thompson, H.A. (eds.), Dynamic Modeling of Gas Turbines: Identification, Simulation, Condition 

Monitoring and Optimal Control, Advances in Industrial Control Series, Springer, New York, 2004, pp. 21-25. 18Hervol, D., Mason, L., Birchenough, A., and Pinero, L., “Experimental Investigations From the Operation of a 2 kW 

Brayton Power Conversion Unit and a Xenon Ion Thruster,” NASA TM-2004-212960, NASA Glenn Research Center, 

Cleveland, OH, 2004. 19Le, D.K., and McNelis, A.M., “Validation of a Mechanical Dynamics Model for Closed-Cycle Brayton Engines on a 2-

kWe Unit,” Report No. SSDB-JIMO-2005-003, NASA Glenn Research Center, Cleveland, OH, October 2004. 

NASA/TM—2005-213985 12
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18

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

Power Systems

Michael J. Barrett and Paul K. Johnson

Closed cycles; Nuclear electric power generation; Turbogenerators

Unclassified -Unlimited

Subject Category: 20

Prepared for the Third International Energy Conversion Engineering Conference sponsored by the American Institute of

Aeronautics and Astronautics, San Francisco, California, August 15–18, 2005. Michael J. Barrett, NASA Glenn Research

Center; and Paul K. Johnson, Analex Corporation, 1100 Apollo Drive, Brook Park, Ohio 44142. Responsible person,

Michael J. Barrett, organization code RPT, 216–433–5424.

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.