NASA/TP--2001-211274

Prospects For Nuclear Electric Propulsion

Using Closed-Cycle Magnetohydrodynamic

Energy Conversion

R.J. Litchford, L.J. Bitteker, and J.E. Jones

Marshall Space Flight Center, Marshall Space Flight Center, Alabama

October 2001
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NASA/TP--2001-211274

Prospects For Nuclear Electric Propulsion

Using Closed-Cycle Magnetohydrodynamic

Energy Conversion

R.J. Litchford, L.J. Bitteker, and J.E. Jones

Marshall Space Flight Center, Marshall Space Flight Center, Alabama

National Aeronautics and

Space Administration

Marshall Space Flight Center • MSFC, Alabama 35812

October 2001
Acknowledgments

This work was sponsored by the Advanced Propulsion Research Project Office, Advanced Space Transportation Program,

George C. Marshall Space Flight Center (MSFC), National Aeronautics and Space Administration. The authors acknowledge

and thank Tara Poston (MSFC/TD30) for her expert assistance with the trajectory analyses.

The first author expresses special thanks to John W. Cole for many illuminating discussions pertaining to specific energy

requirements for deep space missions. The NASA Principal Investigator was Ron J. Litchford, TD15/ASTR

TRADEMARKS

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NASA Center for AeroSpace Information

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(301) 621 0390

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

(703) 487 4650

ii
TABLE OF CONTENTS

1. INTRODUCTION ......................................................................................................................

2. SYSTEM ANALYSIS ................................................................................................................

2.1

2.2

Thermodynamic Cycle Analysis .....................................................................................

Specific Mass Analysis ...................................................................................................

2.2.1

2.2.2

2.2.3

2.2.4

2.2.5

2.2.6

2.2.7

2.2.8

2.2.9

Fission Reactor ....................................................................................................

Magnetohydrodynamic Generator .......................................................................

Magnet Confinement Structure ...........................................................................

Saddle Coil Winding--Linear Generator ............................................................

Helmholtz Coil Winding--Disk Generator .........................................................

Turbocompressors ................................................................................................

Regenerator ..........................................................................................................

Radiator ...............................................................................................................

Electric Thruster ..................................................................................................

3. SYSTEM ASSESSMENT ..........................................................................................................

4. MAGNETOHYDRODYNAMIC TECHNOLOGY ISSUES .....................................................

4.1

4.2

Conceptual Design of the Nonequilibrium Disk Generator ...........................................

Neutron-Induced Ionization Enhancement .....................................................................

5. MISSION CAPABILITY ASSESSMENT .................................................................................

6. CONCLUSIONS ........................................................................................................................

REFERENCES .................................................................................................................................

4

7

11

12

12

13

14

15

17

17

18

19

20

24

24

27

30

34

35

iii
LIST OF FIGURES

.

2.

.

.

.

.

.

.

.

10.

13.

Schematics of (a) linear and (b) disk MHD generator configurations ....................................... 2

Essential components of a nuclear electrical propelled spacecraft

based on a closed-loop MHD Brayton cycle powerplant .......................................................... 5

Schematic of a closed-loop nuclear MHD Brayton cycle powerplant

with regenerative heating and intercooled multistage compression.

Installation is shown coupled to high-power electric propulsion .............................................. 6

Temperature-entropy diagram for a closed-loop Brayton cycle powerplant

with regenerative heating and intercooled multistage compression .......................................... 7

Illustration of a circular crescent coil cross section for a linear channel of diameter D.

Note that 2a = D + c is a geometric constraint .......................................................................... 14

Illustration of a Helmholtz coil winding for a disk generator of diameter D.

Note that the coils are separated by a distance r = D/2 ............................................................. 16

Thermal efficiency of an MHD generator Brayton cycle using helium

as the working fluid ................................................................................................................... 20

Specific mass characteristics of a disk MHD Brayton cycle powerplant

using helium as the working fluid ............................................................................................. 21

Disk MHD powerplant specific mass attributes for/_N = 40% and l_s,g = 70%.

The working fluid is helium ...................................................................................................... 22

Scaling of MHD powerplant and propulsion system specific mass

with net electrical power ............................................................................................................ 23

Variation in design parameter F with M and T e ......................................................................... 25

Design lofting for a 100-MWth MHD disk generator using cesium-seeded

helium working fluid ................................................................................................................. 26

Computed electrical conductivity versus relative density for pure 3He. Solid

lines correspond to a gas temperature of 1,500 K ..................................................................... 28

V
LIST OF FIGURES (Continued)

14. IMLEO as a function of specific impulse for a 40-MW e nuclear MHD

space power installation delivering a 100-t payload to Mars .................................................... 31

15. Optimal trajectories for 120- and 180-day transits. Assumes

100-t payload and 40-MW e thruster power ............................................................................... 31

16. Optimal power characteristics of a nuclear MHD space power installation

for a 100-t payload ..................................................................................................................... 32

17. Optimized payload for a 40-MW e nuclear MHD space power installation ............................... 33

vi
LIST OF TABLES

°

2.

3.

4.

5.

Virial theorem requirements .................................................................................................

Electric thruster characteristics .............................................................................................

Subsystem technology assumptions .....................................................................................

MHD disk design restrictions ...............................................................................................

Large cross-section neutron interactions ..............................................................................

13

19

21

26

27

vii
LIST OF ACRONYMS, SYMBOLS, AND ABBREVIATIONS

B

emf

H

He

IMLEO

Kr

Li

LMD

MHD

MPD

MSNW

Nb/Ti

Nb3/Sn

NEP

NERVA

STP

U

VASIMR

boron

electromotive force

hydrogen

helium

initial mass in low-Earth orbit

krypton

lithium

log-mean difference

magnetohydrodynamic

magnetoplasmadynamic

Mathematical Sciences Northwest

niobium titanium

niobium tin

nuclear electric propulsion

nuclear engine for rocket vehicle application

standard temperature and pressure

uranium

variable specific impulse magneto plasma rocket

ix
NOMENCLATURE

A C

Arad

Aregen

a

B

BO

Bc

BH

Cp

C

D

Er

F

G

go

h

kent

I,p

Jc

Jlnax

Jx

Jy

Jo

L

M

m

rn

m c

mcomp

mrad

mregen

cross-sectional area

radiator area

regenerator area

radius of crescent coil half-section

magnetic field strength

centerline magnetic field of single loop

magnetic field of circular crescent saddle coils

magnetic field of Helmholtz coils

specific heat at constant pressure

maximum thickness of crescent coil windings

diameter

radial electric field

ratio of the radial electrical field strength to the magnetic flux density

frictional pressure loss ratio

gravitational constant

mean channel height/enthalpy

enthalpy at entrance to device

specific impulse

total current

current density

maximum current density

current density for the x axis

current density for the y axis

circumferential current density

length of the linear generator

Mack number

mass

mass flow rate

mass of magnetic coils

compressor mass

radiator mass

regenerator mass

xi
NOMENCLATURE (Continued)

mstruc

mthrust

n *

Po

P

Pgen

Qrad

Qreactor

Q

regen

qmax, regen

qregen

qrad

qreactor

qregen

R

RL

r

St

T

r0

L

Tc,s

L

Tmax

rmin

H

Uregen

V

Vgen

Wcomp

%

structural mass

thruster mass

number of compressor stages

relative density

stagnation pressure

pressure

generator power density

radiator thermal power

reactor thermal power

regenerator thermal power

theoretical maximum heat transfer for the regenerator

regenerator heat transfer

radiator specific power per unit specific heat

reactor specific power per unit specific heat

regenerator specific power per unit specific heat

gas constant

load resistance

radius of the disk generator

material working stress

temperature

stagnation temperature

compressor stage outlet temperature

compressor stage outlet temperature for isentropic process

electron temperature

bulk gas temperature

maximum operating temperature

minimum operating temperature

velocity

heat transfer coefficient

enclosed volume

volume of magnetic coil winding

working volume of the generator

power consumption of the compressor bank

electrical power

xii
NOMENCLATURE (Continued)

_en

%

Wthrust

^

Wcomp

^

Wgen

acoil

acomp

agen

amagnet

aplant

arad

O_reactor

aregen

astruc

asystem

athrust

/_rad

/_regen

A hcomp

A hcomp,s

A hgen

A hgen,s

AL

A TLMD

8regen

r/N

r/s

_S,C

electrical power output of the generator

magnetic field energy

thruster electrical power

compressor specific power per unit specific heat

generator specific power per unit specific heat

specific mass

specific mass of the coil windings

specific mass of the compressor

specific mass of the generator

specific mass of the magnet

specific mass of the nuclear MHD powerplant

specific mass of the radiator

specific mass of the reactor

specific mass of the regenerator

specific mass of the reactor

specific mass of the entire propulsion system

specific mass of the thruster

Hall parameter

mass per unit area of the radiator

mass per unit area of the regenerator

specific heat ratio

change of enthalpy across the compressor

isentropic change of enthalpy across the compressor

change in enthalpy within the generator

change in enthalpy for ideal isentropic process

eq. (49)

eq. (50)

compressor temperature rise

log-mean temperature difference for the heat exchanger

emissivity

regenerator effectiveness

enthalpy extraction/addition ratio

isentropic efficiency

isentropic efficiency of compressor stage

ooo

Xlll
NOMENCLATURE (Continued)

l_s,g

rlt

r/th

/-to

_c

7Cg

P

Pc

(Y

0

isentropic efficiency of MHD generator

thruster efficiency

thermal efficiency

magnetic permeability

compression ratio

pressure ratio across the generator

material density

magnet material density

bulk electrical conductivity, Stefan-Boltzmann constant

wall angle

specific power (1/c_)

xiv
TECHNICAL PUBLICATION

PROSPECTS FOR NUCLEAR ELECTRIC PROPULSION USING CLOSED-CYCLE

MAGNETOHYDRODYNAMIC ENERGY CONVERSION

1. INTRODUCTION

From the most fundamental perspective, meaningful scientific and human exploration of deep space

will be possible only if there is an abundant source of energy available for propulsion and onboard electrical power production. Furthermore, this energy must be stored in an extremely compact form if it is to be

transported along with the spacecraft since any additional mass increment incurs a corresponding increase

in energy requirement for orbital transfer. These fundamental considerations place a severe constraint on

the minimum acceptable energy density needed for any deep space mission.

To our knowledge, the only plausible means of providing the necessary energy densities, within the

context of currently accepted physics, are beamed energy, nuclear energy (fission and fusion), and matterantimatter annihilation. It should be noted that solar cells may be considered as the onboard conversion

component of a beamed energy system with the caveat that the current specific mass for this technology is

=30 kg/kW e and the perfected value is not expected to fall below 5 kg/kW e. The 1/r 2 decrease in solar

radiation intensity also precludes robust missions beyond Mars.

In principle, any of these energy sources would suffice from the standpoint of energy density alone.

However, there are other attributes such as technical maturity, system complexity, energy conversion efficiency, and system specific mass, which stand to differentiate the various technology readiness levels. In

terms of these broader system level considerations, nuclear fission space powerplants are the clear standout

candidate for near-term realization. This train of thought is by no means unique and can be pursued to

certain logical conclusions, as expounded most recently by Sackheim et al. 1

Given this basic premise, the natural inclination has been toward nuclear-driven, closed-cycle gas

turbine installations, since they represent the nearest evolutionary point beyond the existing technology

base. Turbogenerator cycles, however, are only effective at low-heat rejection temperatures and as a result

require large and massive space radiators. This performance characteristic derives from the fact that practical material limits place severe restrictions on the maximum turbine blade operating temperature, even

when the blades are actively cooled, and this, in turn, restricts the maximum cycle temperature. Despite

this drawback, these systems have good prospects for approaching a powerplant specific mass below the

10-kg/kW e mark.

The major culprit affecting heat engine weight is the space radiator. Because the specific mass of

the radiator is proportional to 1/T 4, the radiator weight can greatly exceed the reactor and energy conversion component weights when forced to operate at a low-heat rejection temperature. Therefore, there is a

strong incentive to break through the 1-kg/kW e barrier by finding an alternative means of elevating the
cycleoperatingtemperatureandtherebyincreasingtheheatrejectiontemperature.Thenaturalalternative

for attainingthis goalismagnetohydrodynamic(MHD) energyconversion.

Theprimary reasonfor consideringMHD is the ability to extractenergyfrom a flowing gasat

arbitrarilyhigh temperatures.As such,anMHD convertercanoperateeffectivelyattemperaturesbeyond

therealmof activelycooledturbinebladetechnology.Usingdemonstratedsolidcoreandfixedparticlebed

reactortechnology,for example,it is possibleto push peak operatingtemperaturesto 2,500K with

minimumdevelopmentrisk, andthisvaluecouldreadilyberaisedto 3,000K with furtherdevelopmentof

advancedhigh-temperaturefissile fuels,particularlyternarycarbideelements.Evenoperatingtemperaturesbeyond3,000K areconceivablewith theintroductionof gascorereactorsin which thefissilefuel is

allowedto circulatethroughoutthepowerconversionsystem.Theusefulupperlimit for gascorereactors

with MHD energyconversionis estimatedto be ashigh as 8,000-10,000K, at which point the rapid

increaseinfreeelectronradiationmakesregenerativecoolingextremelydifficult aswell ascausingthegas

coolingtimescaleto fall--most likely belowthechannelresidencetimescale.

Themostcommonconfigurationsfor MHD generatorsarethe(a)linearchannelandthe(b)radial

disk,asillustratedin figure 1.In eithercase,anexternalmagneticfield, B, is imposed perpendicular to the

flow path and the motion of the electrically conductive gas interacts with the magnetic field to develop a

Faraday electromotive force (emf) orthogonal to both the flow velocity and the magnetic field and a Hall

emf directed along the flow path. The value of the Hall emf relative to the Faraday emf depends upon the

value of the Hall parameter,/3. When/3 is on the order of unity or greater, the Hall configured disk geometry

is used predominately since it avoids the complicated electrode segmentation requirements associated with

the design of linear channels.

(a)

SegmentedAnode

SegmentedCathode

(b) I

!! ::: ,::

',',\\ ;', n ,',' // ',;

ii \\ ii _ i! // !!

,, \\ ',: i ',', // ;;

:: _:,, , ,,,,// ,,:

,, ,,,,

ii Cathode_ I I

o F

/ ol d .,

Figure 1. Schematics of (a) linear and (b) disk MHD generator configurations.

2
TheinducedFaradayandHall emf's resultin acurrentflow in thegas,which is transferredto an

externalloadthroughcontactelectrodesin the channel.Theinteractionof the currentwith themagnetic

field producesa retardingforce on thegas,therebyforcing it to dopushwork asit movesthroughthe

generatorchannel.Therefore,thereis apressuredrop acrosstheMHD converterin directanalogyto that

experiencedby aturbinestage.Thedifferencebeingthatthestationaryandlightly stressedMHD channel

wallscanbecooledto temperaturesmuchlowerthanthecoregastemperatureinthesamemannerthatthe

chamberwallsof achemicalrocketengineareregenerativelycooled.In thiscase,it istheheattransferrate,

notthecoregastemperature,that determinesengineeringfeasibility.

NuclearMHD spacepowersystems,assummarizedabove,werefirst conceivedandconceptually

developedby R.J.Rosain the 1960's.2 8Sincethen,theideahasbeenperiodicallyrevivedandamplified

in relationto variousperceivedspacepowerneeds.9 15Yet,thistechnologyhasneverprogressedbeyond

studiesandlow-priority researchefforts,despiteits manypositiveattributes.Andit remainsto this day,a

potentiallyhighpayoff conceptfor whichtheperceivedrisk far exceedstheactualdevelopmentrisk.

ThisTechnicalPublicationrevivestheconceptoncemoreandamplifiesonthescenariofor anuclear

MHD spacepowerplantcoupledwith high-powerelectricthrusters.Theemphasishereis to demonstrate

thatthesesystemscouldimmenselybroadendeepspacemissioncapabilitywhile adheringto atechnology

developmentpaththatis entirelywithin establishedboundsof engineeringfeasibility.Theseconclusions

areobtainedthroughapreliminarybutthoroughsystemanalysisin whichthevariouscomponentcharacteristicsareestimatedusingestablisheddataor,whenanempiricaldatabaseis unavailable,usingwidely

acceptedextrapolationsfrom current state-of-the-artechnology.Additional technologicaldevelopment

opportunitiesarealsoexaminedin termsof potentialpayoffversusdevelopmentrisk.

3
2. SYSTEM ANALYSIS

Generally speaking, high-power density fission reactors are adaptable to both Brayton and Rankine

energy conversion cycles. For example, Rankine cycles, by taking advantage of the gas-to-liquid phase

transition, provide superior performance for a fixed overall temperature differential, and they can completely avoid the limitations of compressor turbomachinery. Unfortunately, the condensing vapors tend to

be highly corrosive, raising significant design and reliability concerns. Brayton cycles, on the other hand,

are simpler, exhibit only slightly inferior performance, and promise increased reliability in that they are

more suited for utilization of an inert gas working fluid.

Although previous studies have established the fact that Rankine MHD cycles can provide substantially lower system specific mass, 2 8,11,12 the authors take the point of view that Brayton MHD cycles are

more directly compatible with solid-core, gas-cooled reactors and can more effectively leverage the existing technology base. Therefore, they appear to offer a lower risk development path in the near term while

maintaining a significant payoff in comparison to turbogenerator systems. As such, the Brayton MHD

cycle with regenerative heating and intercooled multistage compression forms the focus of attention for

further investigation.

The essential components of a nuclear electric propelled spacecraft based on a closed-loop MHD

Brayton cycle are shown in figure 2. From the perspective of mass distribution, it is useful to lump the

spacecraft subsystems into three categories: the payload, the propellant, and the thrust producing system.

The major thrust of this work was to analyze the specific mass characteristics of the powerplant and the

integrated propulsion system and to make a status/risk assessment of the various enabling technologies.

Since the powerplant is the dominant contributor to overall spacecraft weight, there is intense interest in

obtaining accurate estimates of powerplant specific mass characteristics as a means of delineating

technological capabilities and limitations. Once the specific mass characteristics are quantitatively defined

to a satisfactory degree of accuracy, it becomes possible to comparatively assess various technological

approaches and to identify the major technology development challenges and associated risks.

4
Payload

Communications

and Control

Structures

Propellant

Radiator

Heat Exchanger

Compressor

ElectricThru_

Figure 2. Essential components of a nuclear electrical propelled spacecraft

based on a closed-loop MHD Brayton cycle powerplant.

5
For reference purposes, a schematic of a closed-loop nuclear MHD Brayton cycle powerplant coupled

to high-power electric propulsion is provided in figure 3. The temperature-entropy diagram for the closedloop Brayton power cycle is also shown in figure 4. The thermodynamic cycle is now analyzed assuming

fixed maximum (Tmax) and minimum (Tmin) operating temperatures.

Auxiliary

MHD Generator Power

Nuclear Reactor

Wgen .-_ Power - -

..... , , , I

[ Oro_or I O,.u___N IOon0.t.on.n01 ....

19I

_" " "1

I I

Regenerator I

! !

Qregen I I

b !

I Staged Compressor/Intercooler Bank

L(_J L('_)_J L(_. Electric M°t°r

IIIIIIIIII

Propellant

,1!

L -tm,.-

Electric

Thruster

0 is the Initial

ReferenceState

for the Propellant.

Qrad

Figure 3. Schematic of a closed-loop nuclear MHD Brayton cycle powerplant

with regenerative heating and intercooled multistage compression.

Installation is shown coupled to high-power electric propulsion.
.=.

E

Figure 4.

Entropy

Temperature-entropy diagram for a closed-loop Brayton cycle

powerplant with regenerative heating and intercooled multistage

compression.

2.1 Thermodynamic Cycle Analysis

In the special case where all net power production is used for propulsion, the thermal efficiency

(rlth) of the powerplant is equivalent to the ratio of thruster electric power (Wthruster) to reactor thermal

power (Qreactor):

Wthruster _ Wgen - Wcomp _ (Tma x - T 9 ) - Nc (T2 - Tmin )

rhh - Qreactor Qreactor Tmax _ T7 , (1)

where Wgen is the electrical power output of the generator, Wcomp is the power consumption of the compressor bank, and N c is the number of compressor stages. In addition, it is assumed rmi n = r 1 = T3 = TS...

is the effective radiator temperature.

In analyzing the MHD generator, it is useful to note that any MHD device can be described in terms

of two fundamental process parameters: an enthalpy extraction/addition ratio (rlN) and an isentropic efficiency (rls) which quantifies the degree of departure from an isentropic process.

The enthalpy extraction parameter for the generator is defined as the ratio of the change in enthalpy

Ahgen to the entrance enthalpy bent:

Ahg en h8 - h9 - Tmax - T9 (2)

rlg- hent - h8 - Tmax

7
or

T9 = (1- rlN )Tmax (3)

For an MHD generator (enthalpy extraction), the isentropic efficiency l_s,g is defined as the ratio of

the actual change in enthalpy to that for an ideal isentropic process Ahgen,s:

Ahgen _ h8 - h 9 _ Tmax - T9

rls,g - Ahgen,s - h8- h9, s - Tmax -T9, s

(4)

or

Tmax

"rmax . (5)

Using the isentropic process relationship for an ideal gas, it is possible to write equation (5) in the form:

r 9 = 1- rls,g 1- _g rma x ,

(6)

where 7Vg = P8/P9 is the pressure ratio across the generator and 7is the specific heat ratio. Combining

equations (3) and (6) yields a fundamental relationship between rlN and rls,g:

(7)

The N c compressor stages are assumed to operate with the same temperature rise AT c = T c - rmi n

such that T c = T2 = T 4 = T6... Furthermore, in order to compensate for the net pressure drop in the system,

the pressure ratio across the MHD generator is defined as _g = a_c Nc such that each compressor stage has

a common compression ratio (JVc):

zcc = _ P2 _ P4 _ P6 ... (8)

Pl P3 P5

The parameter G represents a pressure loss ratio due to frictional losses (0<G<I). Thus, for each

compressor stage (enthalpy addition), the isentropic efficiency (rls,c) is defined as
Ahcomp,s _ hc,s - hmi n _ Tc,s - Tmi n

rls, c - Ahcomp - hc _ hmi n -Tc_Tmin , (9)

which can be reformulated in terms of Tc:

+ 1 LT-- in- 1]}Tmill (10)

By using the isentropic process relationship for an ideal gas and using equation (8) to eliminate zcc,

it is possible to write equation (10) in the form:

(11)

Regenerative heating is employed in the cycle to increase thermal efficiency and reduce the amount

of waste heat that must be rejected by the radiator. The regenerator effectiveness is defined as

_ q h7-h6 _ T7-T6

eregen qmaxregen- h9- h6 - T9- T6 '

(12)

which yields

T7 = gregen (T9 - T6 ) + T6 (13)

or, upon substitution of equations (6), (7), and (11),

T7:eregen(1-r#N)Tma x +(1-eregen ) l+--_-,c[t--_- ) -1 Tmin

(14)

A power balance on the regenerator requires that

h9 -hi0 - T9 -T10 - 1

h7-h 6 T7 -T 6

(15)

9
or

-- (16)

Thus, equations (13) and (16) may be combined to obtain the form:

Tlo = (1- eregen)T9 - eregenT6 (17)

Then, substitution for T 9 and T 6 using equations (6), (7), and (11) gives an expression for T10 in terms of the

cycle operating temperatures and process parameters:

{ f 1]t T10= (1-eregen){1-rlN}Tmax +eregen 1+_1 (_g]TN_c -1 Train . (18)

The various thermodynamic states throughout the cycle have now been expressed in terms of the

reactor and radiator operating temperatures and the various component process parameters. This information may further be used to deduce the power per unit mass flow per unit specific heat for each system

component. The results are summarized as follows:

Qreact°r-{1-gregen[1-rlN]}Tmax-(1-gregen) l rls,c[_ " G ) -1 Tmi n

qreactor - _ +

(19)

Wgen

Wgen - rhCp =/]NTmax '

(20)

]

^ Wc°mp - Nc ?'Nc-1 Tmin , (21)

Wc°mp- rhCp rls,c

qregen -

1 (:rcglTN_c_ 1

Qregen =_regen(l_r/N)Tmax__regen l+_,c.t____) Tmin rhC p

(22)

10
and

qrad-_ppQrad-(1-Cregen)(1-17N)Tmax-(1-Cregen ,{1+_ 1 -l Nc -1 ]tTmin

-_s,c _/N c - rmin "

(23)

It is also possible to frame the cycle thermal efficiency in similar terms by substituting equations

(19)-(21) into equation (1):

2.2 Specific Mass Analysis

Thermal efficiency is not the central consideration for space installations. Rather, the entire system

must be examined in terms of its overall mass relative to its performance. This requires a careful evaluation

of all subcomponent mass characteristics in order to obtain an estimate of the aggregate system mass.

The aggregate specific mass of the nuclear MHD powerplant is defined as

aplan t =

_lreactor ÷ °_lge. ÷ °_lcomp ÷ _lrege. ÷ _l_ad

^ ^

Wgen - Wcomp

(25)

The specific mass of the combined powerplant and electric thruster, which is assumed here to

include all necessary power conditioning equipment, is therefore given by

asystem = aplan t + athrust (26)

It is also common practice to define the specific power as ¢ = 1/a. Specification of the subcomponent

specific mass characteristics now follows.

11
2.2.1 Fission Reactor

Ample experience indicates that solid core and fixed particle bed reactors can provide peak temperatures in the 2,500-3,000 K range. The solid-core nuclear engine for rocket vehicle application (NERVA)

engine, for instance, had a design operating temperature of 2,500 K, and a low-risk development path was

identified for increasing this limit to 3,000 K through the development of high-temperature carbide fuels. 16

As such, this technology base can be used to estimate anticipated reactor specific mass. Using the NERVA

technology as an empirical basis, for instance, Holman has developed a 350 MWth reactor design having a

mass of 1,785 kg. This yields a specific power of 0.2 MWth/kg.

Within reasonable bounds, the reactor mass can be assumed independent of reactor power level,

and the authors conservatively estimate a reactor mass of 3,000 kg, which includes margin for shielding.

Thus,

mreacto r 3, 000 kg

areacto r - - (27)

Qreactor Qreactor

2.2.2 Magnetohydrodynamic Generator

There are strong incentives to operate MHD devices at very high magnetic flux densities. For

example, the power density of an ideal MHD generator varies as ou2B 2, where o- is the bulk electrical

conductivity, u is the velocity, and B is the magnetic field strength. Since o-and u have practical limitations,

it is therefore desirable to have B as large as practically feasible. Furthermore, Hall-configured disk generators can exhibit high isentropic efficiency only when the Hall parameter is large (13 >10). 17 Again, high

magnetic flux densities are required since 13 _ B/p, where p is the static pressure in the device.

Because of this basic need for large values of B, the weight of the generator as a whole is dominated

almost exclusively by the weight of the magnet. The magnet weight, in turn, is determined mainly by the

weight of the confinement structure and the weight of the coils. Under these assumptions, the generator

specific mass is defined by

agen = amagne t = astru c + acoil (28)

where _nagnet is the specific mass of the magnet, astru c is the specific mass of the structure, and acoil is the

specific mass of the coil windings.

It is not practical to entertain the utilization of dissipative magnets in space installations, mainly

due to the excessive weight penalties associated with waste heat rejection. Therefore, only supergenic

(i.e., superconducting-cryogenic type coils) are considered in which a high field superconductor

(e.g., Nb3/Sn or Nb/Ti) is embedded in a metal base material (i.e., copper or aluminum) as a means of

providing quench stabilization. It is also assumed that flux pumping techniques will be utilized in order to

minimize the auxiliary equipment needed for magnet power-up.

12
2.2.3 Magnet Confinement Structure

The basic challenge of large-volume, high-field magnet design can be readily summarized.

Because magnetic flux density falls off with distance from the coil as 1/r 2, very large currents are necessary

to fill the working volume, and this, in turn, leads to the exertion of extremely large Lorentz forces on the

coil. Therefore, a large confinement structure is needed to support those forces that the conducting coils

cannot withstand themselves.

The confinement requirements may be fundamentally expressed in terms of the stored magnetic

field energy, Win:

B 2 B 2

%, fff -- dV =

:::V 2f10 2f10

- --V , (29)

where/.t o is the magnetic permeability and V is the enclosed volume. The Virial theorem may then be used

as an estimate of the minimal mass due to structural requirements (i.e., ideal hoop tension to contain the

stored energy):

t) B 2 P

mstru c > _W m =- V , (30)

st st 2f10

where p is the material density and st is the material working stress. Some typical values for W m/m = st p

are summarized in table 1.

Table 1. Virial theorem requirements.

Material Wm/m=st/p(kJ/kg)

Fiber-reinforced composites

Stainless steel (304LN)

Aluminum (2219T851)

Titanium

Beryllium-Copper

10-50

44

107

309

580

At this point, it is convenient to introduce the generator power density, Pgen = Wgen/V, into

equation (30) to arrive at a working specific mass estimate for the confinement structure:

astru c :-

mstruc = P B2/2/'tO (31)

Wgen st Pgen

13
2.2.4 Saddle Coil Winding--Linear Generator

Consider the coil requirements for a linear generator channel. Based on conservative design experience, assume a minimal channel aspect ratio of L/D = 10. This ratio is recommended by Rosa in order to

minimize nonideal losses associated with large surface-to-volume effects. 18 In this case, the working

volume of the generator can be expressed as

Wg en = 4D2L = 5_D3

Vgen - P---_en 2 '

(32)

which yields a nominal generator diameter of

1

2 Wgen (33)

A uniform magnetic field can be produced within the generator volume if the saddle coil windings

approximate a circular crescent cross section of diameter D, as illustrated in figure 5. The total crosssectional area (Ac) of the winding on each side is

Ac = 2ca= 2c(D+2)=c(c + D)=CD(D+ l ) •

(34)

'/7,

Figure 5. Illustration of a circular crescent coil cross section for a linear channel

of diameter D. Note that 2a = D + c is a geometric constraint.

In the limit c/D --+ O, A c _ cD and a uniform constant magnetic field (Bc) is produced which is

defined by

BC m

BO _ ¢toi _ ¢toJcAc _ ¢tOJcC

2 4r 2D 2

(35)

14
wherei is the total current, Jc is the current density, and B 0 = ltoi/2r is the field produced in a loop of

diameter D = 2r. The value forjc can be as high as 109 A/m 2 for Nb3/Sn-based superconductors.

Using equations (33) and (35) to eliminate D and c in equation (34) gives an expression for the

cross-sectional area in terms of the material properties, the generator power characteristics, and the

required magnetic flux density:

Ill 1

2 Wgen

Ac 2Bc 2B c +

- I.toJc [I.toJc 5:rv _gen

(36)

The mass of the magnet coils may now be deduced from the relation:

m c = PcVc = 2pcAcL = 20PcAcD

and the specific mass of the coil windings takes the form:

(37)

mc 20pcAcD (38)

acoil - Wgen - Wgen '

where D is defined by equation (33).

2.2.5 Helmholtz Coil WindingmDisk Generator

Consider the coil requirements for an MHD disk generator of radius r and mean channel height h.

Based on conservative design experience, assume a minimal channel aspect ratio of r/h = 10 in analogy to

the length-to-diameter ratio assumed for the linear configuration. Again, this value is recommended by

Rosa in order to minimize nonideal losses associated with large surface-to-volume effects. 18 Thus, D/h

= 20, and the working volume of the generator can be expressed as

Wgen = 4D2h = _ooD3

Vgen - p--_en

(39)

This yields a nominal disk diameter of

1

D = Pgen

(40)

15
Helmholtzcoil windingsof diameterD, as illustrated in figure 6, can then be used to produce a

uniform magnetic field B H within the disk volume:

BO = I-toi _ I-toLAc (41)

BH = _ 2.q_r - .q_D

This expression can be combined with equation (40) to arrive at an expression for the crosssectional area of the winding in terms of the material properties, the generator power density, and the

required magnetic flux density:

I

-fM

r BH1'

3_ I

N '

1 N

I I

Figure 6. Illustration of a Helmholtz coil winding for a disk generator of diameter D.

Note that the coils are separated by a distance r = D/2.

1

llOJc Pgen

The mass of the magnet coils may now be deduced from the relation:

(42)

m c = PcVc = pc_DAc = "V_pcBH D2

and the specific mass of the coil windings takes the form:

(43)

where D is defined by equation (40).

m c ",J2_PcBH D 2

acoil - Wgen - ].loJcWgen

(44)

16
2.2.6 Turbocompressors

The weight characteristics of the turbocompressors and drive can be accurately estimated from a

broad body of technical experience. Following Rosa, it is assumed that the specific mass of the compressor

group is given by

mc°mp = 2 × 10 -5 kg/W . (45)

acomp - Wcom p

2.2.7 Regenerator

The regenerator is assumed to be a typical compact shell and tube heat exchanger for which the

specific mass attributes can be estimated accurately. A conservative value for the mass per unit area of this

type of heat exchanger is

mregen = 1 kg/m 2 (46)

flregen- Aregen

Assuming a constant value for the overall heat transfer coefficient, Uregen , it is possible to express

the total heat transfer rate in the form:

Qregen = UregenATLMDAregen ,

where ATLMD is the log-mean temperature difference for the heat exchanger and is defined as

(47)

and

aG - aG

ATLMD - in( ATb ] ' (48)

 aG)

ATa = Thot,in - Tcold,out ,

(49)

In the limit IATb/ATal --9 1,

ATb = Thot,out - Tcold,in •

(50)

lim ATb ___>IATLMD -

aG + aG

2

(51)

17
Notethatthetemperaturesusedto calculateATLMDareobtainedfrom thethermodynamiccycleanalysis

basedonanassumedvaluefor theregeneratoreffectiveness.

If equations(46)and(47)arenowcombinedto eliminateA c, the specific mass of the regenerator

takes the form:

mregen flregen

- - (52)

aregen Qregen Uregen ATLMD

2.2.8 Radiator

Space radiators tend to dominate the weight of multimegawatt heat engine installations, and nuclearelectric propulsion systems can quickly become impractical due to the impact on overall system specific

mass. Issues of reliability and survivability also escalate with increasing size. The important design parameter for space radiators is the mass per unit area defined as

firad = mrad = 1 - 0.2 kg/m 2 (53)

Arad

The upper range for/_rad represents projected estimates for conventional radiator design whereas the lower

range for/_rad corresponds to projections for liquid droplet radiator concepts.

The radiative power is given by

4

Qrad = eO-AradTmin , (54)

where e is the emissivity and o-is the Stefan-Boltzmann constant. If equations (53) and (54) are combined

to eliminate Arad, the specific mass of the radiator takes the form:

mrad = flrad (55)

arad = Qrad 4 eOTmi n

18
2.2.9 Electric Thruster

Many nuclear-electric deep space transport missions exhibit optimal results for an idealized thruster

having a specific impulse in the range of 2,500 to 1,500 sec and a thrust in the range of 10 to 1,000 N.

For a thruster efficiency qt = 50%, the fundamental equation of electric propulsion would imply a nominal

power range of

W e = F gOIsp = 0.25 - 15 MW e ,

2qt

(56)

where F is the thrust, Isp is the specific impulse, and go is the Earth's gravitational constant.

In reality, efficient, high-thrust electric propulsion has yet to be demonstrated, and the prevalent

opinion among specialists is that electric thrusters can only be effective at low thrust levels. Nevertheless,

there is some hope that certain electric thruster devices may be scaleable to multimegawatt power levels

and yet remain compact and reliable. The variable specific impulse magneto plasma rocket (VASIMR)

concept even holds the promise of constant power throttling which allows both thrust and specific impulse

to be continuously varied. 19 Extensive calculations by Slavin et al. also indicate that an MHD hightemperature current- (T-) layer type of engine using neon propellant could potentially produce 1,000 N of

thrust at a specific impulse of 2,000 sec with an electrical efficiency of more than 90%. 15

Some representative electric thruster characteristics, including conservative estimates for specific

mass, are summarized in table 2. Note that these are only approximate figures of merit based on a broad

body of technical experience. Here, the specific mass is defined in terms of the plant electrical power

delivered to the thruster:

mthrust mthrust

0¢thrust = Wthrust - Wg en _ Wcomp (57)

Table 2. Electric thruster characteristics.*

Device Isp(sec)

Ion (Kr)

MPD(Li)

MPD(H2)

VASIMR(H2)

qt o_(kg/kWe)

_>5,000 0.8 1.0

4,000-8,000 0.5 0.5

_>8,000 0.5 0.5

3,000-30,000 0.5 0.2-1.0

*Approximatedvalues

19
3. SYSTEM ASSESSMENT

Based on the preceding development, representative system analysis calculations were performed

as a means of assessing system attributes. First, thermodynamic cycle characteristics were investigated

over a practical range of rmi n and JVg; i.e., qN, parameter space. The assumed system characteristics, based

on established bounds of engineering capability, are as follows: Helium working fluid, Tma x = 2,500 K,

6regen = 0.9, iqs,g = 70%, and qs,c = 87%. All calculations were performed assuming no frictional pressure

losses (i.e., G=I).

The resulting thermal efficiency contour map for the MHD Brayton cycle is shown in figure 7. Note

that the peak cycle efficiency moves to larger pressure ratios as the minimum cycle temperature falls. The

highest achievable thermal efficiency approaches 70% as the heat rejection temperature approaches

200 K. For space applications, however thermal efficiency is secondary in importance to system specific

mass.

0.45

0.40

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0

2OO

MHD BraytonCycleThermal Efficiency

Tmax= 2,500 K

............. ....___....___....___....---.---:----- 2 --"

300 400 500 600 700 800

Minimum CycleTemperature (K)

r/th

10 0.65

9 0.60

8 0.55

7 0.50

6 0.45

5 0.40

4 0.35

3 0.30

2 0.20

1 0.10

Figure 7. Thermal efficiency of an MHD generator Brayton cycle using helium as the working fluid.

For demonstration purposes, the authors assumed a reactor power of Wgen = 100 MWth and

explored the specific mass characteristics over a similar range of rmi n and JVg (i.e., qN), parameter space.

Two sets of subsystem technology assumptions were investigated. These assumptions were based on

conservative estimates of near-term and advanced subsystem technologies, as summarized in table 3. The

major anticipated technology advances are as follows: An increase in s t/p through utilization of berylliumcopper material for the magnet structure, a decrease in Pc through utilization of aluminum as the base

material for the supergenic coil, major reduction in radiator specific mass through the introduction of

liquid droplet technology, and slight evolutionary improvements in thruster efficiency and specific mass.

20
Table3.Subsystemtechnologyassumptions.

Parameter Near Term Advanced

mreactor (kg)

Pgen(aWe/m3)

B (tesla)

_/s t (kJ/kg)

Pc(kg/m3)

Jc(A/m2)

Uregen (W/m2K)

]3regen(kg/m2)

'_rad

]3rad (kg/m2)

qthrust(%)

O_thrust(kg/kWe)

3,000

500

8

309

1 xl04

1 xl09

500

1

0.9

1

50

0.5

3,000

500

8

580

3x103

1 xl09

500

1

0.9

0.2

6O

0.4

The resulting contour maps for the disk MHD powerplant specific mass are given in figure 8. For

the near-term technology assumptions, it is found that the powerplant specific mass can be less than

0.4 kg/kW e at a heat rejection temperature of =700 K and an enthalpy extraction ratio of =20%. For the

advanced technology assumptions, the powerplant specific mass approaches 0.2 kg/kW e at a heat rejection

temperature of =500 K and an enthalpy extraction ratio of =30%. Results for the linear MHD channel

configuration display virtually identical quantitative behavior and are not shown.

PowerplantSpecific Mass

0.45 Tmax= 2,500 K Near-TermTechnology

O.4O 9

8 _ J .................................................................

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0

200 300 400 500 600 700

Minimum CycleTemperature(K)

O_plant

(kg/kWe)

9 3.00

8 1.50

7 1.00

6 0.80

5 0.60

4 0.50

3 0.45

: 2 0.40

1 0.38

800

PowerplantSpecific Mass

Tmax = 2,500 K Advanced Technology

0.45 .._.._...:..... ........,,,,, ...

0.40 ii :iii f ................................................. ".................

0.35

o.3o i

0.25 :iii :i_i i :_:i:__;_:_i ii_:i:_i::::_: _::::::_ _:1...... J: !i '_iii:: '_ii::"

0.20 ! ,_: ::::i_:'_i :::::_::_'43 ::. ............................................. _ ] "..

:: h_: :::6 ............ :................... =========================== .................................... J:'

0.10 :_:_87 ..................... "..................................................................................

0.05

0 . . . I . . . I . . . I . . . I . . . I . . . '

200 300 400 500 600 700

Minimum CycleTemperature (K)

Figure 8. Specific mass characteristics of a disk MHD Brayton cycle powerplant

using helium as the working fluid.

O_plant

(kg/kWe)

8 1.00

7 0.60

6 0.40

5 0.30

4 0.26

3 0.24

2 0.22

1 0.21

800

21
In order to keep the powerplant's circulating heat power comparable in magnitude to the generated

electrical power, it is desirable to utilize the highest practical enthalpy extraction ratio consistent with

specific mass optimization desires. Accepting a generator pressure ratio of JVg= 8 as an optimal value yields

an enthalpy extraction ratio design value of qN = 40% when qs,g = 70%. The powerplant and system

specific mass characteristics for this particular case are indicated in figure 9, assuming a target radiator

temperature of 500 K. Note that the propulsion system specific mass is at the 1 kg/kW e mark or less using

very conservative design parameters. Also observe that the thermal efficiency now assumes a respectable

3.0 0.7

2.5

2.0

"_1.5

1.0

value of qth = 40%.

0.5

0

2OO

,\/_ Near-TermSystemsTechnology

1_'k Disk MHD Generator

I\\ -- _ plant

\ i \ .... ucsystem

\_ _ .... r/th

\, _ N _0.,r/th= 40%

_ \ i,,

\ i \ z

k ", " \ z

0_system = 1.1

Tmax=2,500 K _ \\ ]

/min = 500 K I O_plant= 0.61 kg/kWe -':

qW =40% I

rts = 70%

, ,, ,I , , ,,I , ,,,i , , ,,I ,, , ,I , ,, ,

300 400 600 700

0.6

0.5

5OO

/min(K)

0.4

:3-

0.3

0.2

0.1

0

800

1.0

0.9

0.8

0.7

.._ 0.6

0.5

v

0.4

0.3

0.2

0.1

0

200

' AdvancedSystemsTechnology i

\_, DiskMHD Generator /

__ O_plant

0.7

0.6

_\ (Z i

_,\ system /

\ \ /

,, _\ ./ 0.5

qth= 40% \ system= 0.64 kg/k 0.4

\ i \\ /

\ : ",\,, / 03

i

Tm=_ 9 _nn _ ........... ,\\

Tmin max== 2,500 500 KK O_plant = 0.24 kg/kWe \\ 0.1

qN = 40%

_ qs = 70%

.... I .... I ........ I .... I .... 0

300 400 500 600 700 800

/min (K)

:3-

Figure 9. Disk MHD powerplant specific mass attributes for qN = 40%

and qs,g = 70%. The working fluid is helium.

22
Thepredictedscalingof MHD powerplantandpropulsionsystemspecificmasswith netelectrical

power generation, under the assumptionthat qN = 40%, is shown in figure 10 for peak reactor

temperatures of 2,500 and 3,000 K. These estimates turn out to be in substantial agreement with the scaling

results obtained by Rosa and Myrabo. 12 The scaling relationship developed by Mathematical Sciences

Northwest, Inc. (MSNW) for closed-loop Brayton cycle turbogenerator systems is also shown for

comparison. 2° Although the MSNW correlation indicates an economy of scale with increasing power, it is

clear that the MHD Brayton cycle promises much greater payoff for a similar level of development risk.

1.0

0.9

_0.8

_---0.7

0.6

0.5

0.4

.5

_, 0.3

o

O_ 0.2

0.1

0

101

1.8

1.4

1.2

1.o

._o0.8

0.6

E

0.4

i i i i i iii1_ i i i i i iii I i i i i i iii

-- Near-TermMHD Brayton

- -- -- - Advanced MHD Brayton

-. ..... Turbogenerator Brayton -

\_ (MSNW Extrapolation)

*' Tmax=2,500K

-\\ .. Tmax=3,000K

_"_ .... TEl1

"_"_ _. - ax=2,500K

........ Tmax=3,000K

i

'_.

%

%

I I I I Illl I I I I I Illl I I I I I III

10 2 103 10 4

Net Electrical Power Output (MWe)

i i i i i i_ll I i i i i i i i i I i i i i i i i i

Near-TermMHD Brayton

Advanced MHD Brayton

Turbogenerator Brayton

(MSNW Extrapolation)

-- Tmax=2,500K

'_'.. Tmax=3,000K

%

"" "_-_ _ -- -- Tmax=2,500K

......... Tmax=3,000K

0.2

0 , , , , ,,,,I , , , , ,,,,I , , , , ,,,

101 102 103 10 4

Net Electrical Power Output (MWe)

Figure 10. Scaling of MHD powerplant and propulsion system specific

mass with net electrical power.

23
4. MAGNETOHYDRODYNAMIC TECHNOLOGY ISSUES

The success of closed-cycle nuclear MHD powerplants in space will depend on the ability to design

reliable MHD generators with high-efficiency parameters. The previously discussed system analysis

results, for example, depend on assumed values of 40% and 70% for the enthalpy extraction ratio and

isentropic efficiency, respectively. In fact, powerplant specific mass is extremely sensitive to decreases in

isentropic efficiency, and it is possible to assert that these types of installations will be competitive only if

rls,g >- 65%. 15

A critical review of the technology reveals that the greatest hope for attaining these performance

goals lies with nonequilibrium ionization Hall generators. Years of technology development effort in this

arena, mainly by Japanese researchers, have yielded demonstrated efficiency parameters of r/N = 30% and

rls,g = 50%. Clearly, this level of performance is insufficient for space installations, but these results are

based on small-scale experimental facilities, which suffer severe surface-to-volume penalties. Based on

detailed numerical simulations and known scaling laws, these same researchers are confident that the

efficiency parameters can be raised to the necessary level at practical generator scales.

In this section, the conceptual design of a high-performance, seeded nonequilibrium disk generator

is presented. Opportunities for exploiting neutron-induced ionization mechanisms are also discussed as a

potential means of increasing electrical conductivity and enhancing performance and reliability.

4.1 Conceptual Design of the Nonequilibrium Disk Generator

Experience has shown that the successful design of a seeded nonequilbrium disk generator requires

the simultaneous satisfaction of many conflicting restrictions. In addition to keeping the plasma stable and

the isentropic efficiency high, there are practical limits on outlet Mach number, maximum wall divergence

angle, maximum electric field strength, maximum electrode current density, and maximum effective electrode width.

All of these considerations are important from an engineering design perspective. For example, the

outlet Mach number should be only slightly greater than unity in order to obtain good diffuser efficiency,

the maximum wall divergence angle should be maintained less than 10 ° in order to prevent boundary layer

separation, the maximum electric field strength and current density depend on available insulator and

electrode materials, and the effective electrode width is always less than the actual electrode width due to

current concentration.

As previously noted, Hall-configured disk generators can exhibit high isentropic efficiency only

when the Hall parameter is large (13 >10), implying the need for high magnetic flux density. 17 However, it

is just as important to note that nonequilibrium MHD plasmas are subject to ionization instability. This

instability can create inhomogeneous gas dynamic and electrical properties and lead to severe performance

degradation. 21 Past research has shown that this can be avoided in a helium plasma with fully ionized seed

if the temperature is maintained in the 4,000 K < Te < 7,000 K range. 22

24
To estimate the conditions necessary for satisfying this requirement, it is possible to utilize a simplified expression developed by Okuno et al. for a design parameter F defined as the ratio of the radial

electric field strength to the magnetic flux density: 23

(58)

where E r is the radial electric field, R is the gas constant, T e is the electron temperature, M is the Mach

number, and T o is the stagnation temperature.

A plot of this parameter is shown in figure 11 for typical values of M and T 0. From this result, it is

possible to deduce that the electric field strength per unit magnetic flux density must be in the range of

4,000 V/m.T < F < 5,000 V/m.T for the plasma to remain stable. Thus, given a permissible range on

stagnation temperature and electric field strength, specification of B and E r is sufficient to define plasma

stability.

6,000

5,000

4,000

g- 3,000

2,000

1,000

0

2,000

DesignSpaceforCesium-SeededHelium

4,000< F(V/m.T)< 5,000 To= 1,500_...

4,000< Te(K)< 7,000 ..,.,_"/

/,,'"/;'" I

I" ! ' I-- 1.21

{" /" I-- 2"0 I

/ I / I I

! / II

3,000 4,000 5,000 6,000 7,000 8,000

Te(K)

Figure 11. Variation in design parameter F with M and T e.

Inui, Ishikawa, and Umoto have used this basic condition to develop a conceptual design methodology, which avoids the need for trial and error search procedures. 17 Using this methodology, they have

developed a conceptual design for a 100-MWth disk generator consistent with space power installation

requirements. Their assumed design restrictions, based on practical engineering considerations, are

summarized in table 4.

25
Table 4. MHD disk design restrictions.

Parameter Value

Qreactor(MWth)

TO(K)

PO(atm)

rin(m)

qN(%)

B (T)

Mexit

emax(o)

Er,max(kV/m)

Jmax(kA/m2)

EffectiveElectrodeWidth (m)

IO0

2,200

3

0.3

4O

8

1.2

10

35

35

0.025

Their resulting design for disk lofting is shown in figure 12 where the outlet radius is 70 cm, the

inlet height is 5.8 cm, and the exit height is 8.5 cm. For detailed variation in gas dynamic and electrical

properties throughout the channel, the reader is directed to the original reference. 17 The major points to

note are that the plasma is stabilized at an electron temperature of T e = 5,000 K and the isentropic efficiency

is predicted to be qs,g = 83%.

Anode Cathode

R []

U

r= 30 cm

13

I

I

I

I

I

r= 70 cm

Figure 12. Design lofting for a 100-MWth MHD disk generator

using cesium-seeded helium working fluid.

The purpose of this conceptual design exercise is to demonstrate that MHD disk generators can be

developed which exhibit the necessary performance criteria while simultaneously satisfying an array of

practical engineering design restrictions. Unlike many advanced concepts, realization of nuclear MHD

space power does not depend on any assumptions of idealized performance. Certainly, there are major

challenges to be faced in developing this technology, but unlike many advanced concepts, one may proceed

on a sound basis of realism in terms of both performance estimates and engineering feasibility.

26
4.2 Neutron-Induced Ionization Enhancement

Historically, closed-cycle nonequilibrium MHD research has focused on cesium-seeded inert gas

working fluids. However, nuclear reactor thermal sources present opportunities for nuclear-induced

ionization processes, which may greatly enhance electrical conductivity and eliminate the need to circulate

condensable seed material.

In this ionization process, a working medium is either composed of or seeded with an isotope

having a large neutron interaction cross section. The interaction of the neutron and the isotope results in the

production of charged particles with kinetic energy, large compared to the ionization potential of the surrounding medium. These energetic charged particles then excite and ionize the surrounding molecules via

collisions. Secondary ionization processes may also occur due to collisions between the liberated primary

electrons and surrounding molecules. Some examples of interesting interactions with thermal neutrons are

listed in table 5.

Table 5. Large cross-section neutron interactions.

CrossSection KineticEnergy

Interaction at 0.025 eV(barns) Release (MeV)

3He(n,p)3H

l°B(n,(z)7Li

6Li(n,(z)3H

235U(n,fOff*

5,300

3,840

940

580

0.76

2.30

4.78

=170

*ffdenotes fission fragment

The kinetic energy released in nuclear interactions such as these is at least four orders of magnitude

larger than the ionization energy of any molecule. As a result, each nuclear interaction is capable of causing

thousands of ionization events, assuming all of the kinetic energy is transferred to the surrounding

medium. Two mechanisms that can significantly reduce the ionization effectiveness of the nuclear products

are energy loss to walls and excitation without ionization. Nonetheless, for conditions typical of MHD

concepts, namely, characteristic lengths on the order of 10-100 cm and density on the order of 10 3-10

STP density, each nuclear interaction can be expected to produce hundreds to thousands of ionization

events. As a result, a population of free electrons can form which will enhance the electrical conductivity

through electron impact excitation and ionization.

As with most innovative concepts, initial work can be traced back several decades. For example, the

3He neutron interaction was first examined during the mid-1960's at AB Atomenergi in Sweden by Braun

et al. 24 This experimental effort covered a temperature range of 300 to 1,600 K and density ranging from

0.25 to 1 times standard atmospheric density with a maximum thermal neutron flux of 1011/cm 2 sec. 25

Their measurements over this limited range of conditions, however, were not promising; i.e., 0.1 S/m, and

they concluded that the nuclear-induced conductivity enhancement was insufficient for MHD energy

conversion applications.

27
Theseresultsdiscouragedfurtherstudyfor manyyears.Bitteker,however,expandingonthetwotemperaturehelium plasmamodelof Watanabeet al.,26hasrecentlydevelopeda kinetic modelfor 3He

whichindicatesthatthereis aregimeof thermodynamicandneutronflux conditionsfavorablefor meaningful conductivityenhancement. 27

Bitteker'scalculationfor 3Heconductivityis shownin figure 13asafunctionofrelativedensityfor

differentthermalneutronflux levels.It is clearfromtheseplotsthatamaximumconductivityenhancement

existsat somedensityasafunction of neutronflux. At lower density,therateof ionizationis too low to

producesufficientionsto maintaintheconductivityenhancement.At higherdensity,therateofrecombinationoutpacestherateof ionizationwhile simultaneouslythechargemobility decreases,resultingin lower

conductivity.Nonetheless,thesegraphsshowthatnuclear-inducedionizationprocessescanresultin very

significantconductivityenhancementprovideda sufficientneutronflux.

103

102

_" 101

100

8

-_ 10-1

r_q

] 0-2

] 0-a

10-4

10-4

Tg= 1,500 K

__ Neutron Flux

_ _,_'__'_._ Neutr°ns/cm2/sec)

........ I ........ I ........ I ........ I ........ I

10-3 10-2 10-1 10° 101

RelativeDensity,n* = 300 p (atm)/Tg (K)

Figure 13. Computed electrical conductivity versus relative density for pure 3He.

Solid lines correspond to a gas temperature of 1,500 K.

Clearly, nonequilibrium conductivity enhancement requires a continuous input of ionization

energy, in this case, neutrons. This fact would suggest that the entire generator must be located within the

neutron field to operate. However, the rate at which the conductivity enhancement decays after the removal

of the ionizing energy source is a function of the kinetics of the resulting plasma.

28
Theion-electronrecombinationprocessmaytakemanyroutes,dependingontheparticularspecies

involved,butusuallysomeform of three-bodyrecombinationis dominant.In anycase,theserecombinationprocessesareafunctionof theelectronenergy.Formanygasesof interest,thethree-bodyrecombination crosssectiondecreasesasthe electrontemperatureincreasesabovethe bulk temperature,which

decreasesthe rateof recombination,andhence,slowsthe decayof the conductivityenhancement.This

effectbecomesparticularlypronouncedwhentheelectrontemperatureis above0.5-1.0eV for atypical

MHD flow belowa few thousanddegreesKelvin. Undertheseconditions,thedecayof theconductivity

enhancementmay be decreasedby orders of magnitude.This quasi-stabilizedstateof ionization is

sometimestermed"frozeninertgasplasma."

For conditionstypical of conceptsusingnuclear-enhancedconductivity,the durationof useful

conductivityenhancementmaybeextendedto millisecondsto tenthsof secondsafterexitingtheionizing

energysourcewithoutanyadditionalenergyinput.Thistimemaybefurtherextendedif auxiliaryelectron

pumping systemssuchasradio frequencysourcesareemployedto maintainthe electrontemperature

duringtransit.

Theseargumentscombinedwith therecentkinetic calculationsmakeastrongcasefor reinitiating

a vigorousresearchprogramdevotedto neutron-inducedionizationreactions.In fact, NASA Marshall

SpaceFlight Centerstaff aredevelopingdetailedresearchplansthat addressthesecritical technology

issuesonafirm experimentalandtheoreticalbasis.In theauthors'opinion,thepotentialpayoffsfor nuclear

MHD spacepowerin termsof designsimplicity, enhancedperformance,andincreasedreliability more

thancompensatetherisksassociatedwith afocusedresearcheffort.

29
5. MISSION CAPABILITY ASSESSMENT

With the detailed nuclear MHD system analysis results inhand, it was of interest to examine how

this technology could impact deep space mission capability. Because of its widespread benchmark appeal,

the authors selected a piloted Mars mission as a baseline case, even though the technology is fundamentally suited for a much wider range of applications including interplanetary cargo transport, outer planet

exploration, and routine commercial Earth-lunar transport.

In this cursory study, attention was focused on a hypothetical spacecraft using a closed-loop nuclear

MHD Brayton cycle powerplant coupled to high-power electric thrusters. In order to remain consistent

with the previous point design analysis, baseline calculations assumed a 100-MWth, gas-cooled reactor

driving a disk MHD generator having an enthalpy extraction ratio of 40% and an isentropic efficiency of

70%. This implied a thermal efficiency of 40% and a thruster input power of 40 MW e. For near-term

subsystem technology assumptions, this implied an overall propulsion system specific mass of 1.1 kg/kW e

(see fig. 9). The delivered payload was assumed to be 100 t, unless otherwise noted.

Using the widely recognized spacecraft trajectory optimization CHEBY-TOP code, several Mars

trajectories were examined with respect to the 2018 Mars mission opportunities. The basis for this

trajectory optimization algorithm is rooted in the early work of Melbourne at the NASA Jet Propulsion

Laboratory. 28

For all of the results reported here, the code was used to find the optimal departure date that minimized propellant usage for the outbound leg to Mars. A full round trip optimization could change the

departure date and result in increased propellant requirements for the outbound journey, but the present

study did not account for this effect. All trajectories were assumed to start in a 1,000-km circular Earth

orbit (i.e., sufficiently high for safe operation of a nuclear reactor). The spacecraft was then spiraled out

from the Earth, thrusted or coasted through heliocentric space, and spiraled into a 500-km Mars orbit.

Figure 14 shows the initial mass in low-Earth orbit (IMLEO) required to deliver a 100-t payload to

Mars for trip times of 120, 150, and 180 days. The power was held constant at the design point of

40 MW e. These results show that high-power thrusters with specific impulse capabilities between 5,000

and 8,000 sec are attractive for this mission scenario. Within this specific impulse range, it is observed that

the payload can account for as much as half of the IMLEO. The outbound trajectories for the 180- and

120-day transits are shown in figure 15.

30
32O

270

..i-,

O

L.U

J

220

170

',rr:nnSslt t

180-Day Transit

I I I I I

2,000 4,000 6,000 8,000 10,000

Isp(sec)

Figure 14. IMLEO as a function of specific impulse for a 40-MW e

nuclear MHD space power installation delivering a

100-t payload to Mars.

Astronomical Units

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

1.5

0.5

'--'1

-d

"N 0

o

o

-0.5

......... EarthAscention Node

........ MarsAscention Node

.......... Earth Perihelion

....... Mars Perihelion

Figure 15. Optimal trajectories for 120- and 180-day transits.

Assumes 100-t payload and 40-MW e thruster power.

31
Because the CHEBY-TOP code also had the capability of determining the optimal power for a

given system configuration, it was of additional interest to examine those predictions for the 100-t payload.

The predicted optimal power characteristics are shown in figure 16 along with the corresponding system

specific mass and IMLEO. Here, the optimal power for delivering 100 t in 120 days starts out at 13.2 MW e,

at a specific impulse of 2,000 sec, and climbs to 30.6 MW e, at a specific impulse of 10,000 sec. Thus, the

40-MW e point design is substantially greater than the optimal thruster power requirement.

Simply put, the power supply is oversized for the stated mission parameters.

v

.m

E

1.26

250-

1.21 o

I,J,J

J

200-

1.16

1.11 150

I I I I I

(_ -D- System Specific Mass (kg/kWe).

Initial Mass in LEO (t)

i i i i i

2,000 4,000 6,000 8,000 10,000

Isp(sec)

3O

25

"U

o

20

15

10

Figure 16. Optimal power characteristics of a nuclear MHD space

power installation for a 100-t payload.

The 40-MW e installation point design could be used optimally in two alternative ways: faster trip

times and/or larger payloads. For example, if the trip time is held constant at 120 days and the payload is

allowed to vary so that thruster power is optimized at 40 MW e, the results shown in figure 17 are obtained.

In this case, it is possible to deliver 293 t to Mars in 120 days using a thruster having a specific impulse of

2,000 sec; however, the IMLEO, in this case, is a monstrous 880 t. For a thruster having a specific impulse

of 10,000 sec, the delivered payload drops to 132 t, but the IMLEO becomes much more reasonable at

225 t. Note that any high-power thruster technology having specific impulses >6,000 sec will yield a

payload fraction (mass of payload/IMLEO) greater than 0.56. This is a very attractive feature for

fast 120-day transits.

32
v

8

J

9OO

700

5OO

3OO

_ IMLEO(t)

Payload Mass (t)

-3OO

-25O

-2OO

150

100 I I I I I 100

2,000 4,000 6,000 8,000 10,000

"13

m

O

E

,-iv

Isp(sec)

Figure 17. Optimized payload for a 40-MW e nuclear MHD space power installation.

While admittedly incomplete, these mission analyses indicate the enormous potential of nuclear

MHD space power installations when coupled to high-power electric thrusters. The authors strongly

emphasize that these mission capabilities are based on a practical systems level assessment with conservative projections for subsystem technology development.

33
6. CONCLUSIONS

After thoughtfulexaminationof deepspacepropulsionrequirementsandpotentialtechnological

solutions,theauthorsconcludedthatnuclearfissionreactorscoupledwith MHD generatorscouldserveas

suitablelow specificmasspowerplantsfor high-powerelectricpropulsionsystems.Thesesystemsdisplay

thenecessaryenergydensityrequirementswhile alsoremainingentirelywithin therealmof currentengineeringfeasibility.The technologicaldevelopmentrisk for multimegawattinstallationsis only slightly

greaterthan for turbogenerator-basedpowerplants,yet the potentialpayoff is immense--an order of

magnitudeormoredecreasein systemspecificmass.

Basedonthis line ofreasoning,the authorspursueda preliminarysystemanalysisof multimegawatt nuclearelectricpropulsion(NEP)in which a gas-coolednuclearreactoris usedto drive anMHD

generatorin aclosed-loopBraytoncycle.Theprimarypurposeof thisexercisewasto demonstratethatthe

necessarysubsystemtechnologieseithercurrentlyexistorhaveabasisintheexistingtechnologybasewith

cleardevelopmentpathsfor attainingtherequiredperformanceattributes.

Thiswasaccomplishedbyusingathermodynamiccycleanalysisincontextwithathoroughsystem

analysisto exploretheavailabledesignspace.Theresultsof thisanalysisindicatedtheappropriateoperating regimeaswell astherangeof subsystemcomponentperformanceneededto makethesystemviable.

The major technologicalhurdlesmay be summarizedasfollows: Develop reliable, long-life,

high-temperaturefissile fuel elements;demonstrateanincreasein the nonequilibriumMHD generator

enthalpyextractionratiofrom 30%to 40%andisentropicefficiencyfrom 50%to 70%;developefficient

high-power(megawattclass)electricthrustertechnologies;anddemonstratethat the entire systemcan

attainausefuloperatinglifetime.A majoradvantagehereis thatthehigherperformancetranslatesinto a

shorterlifetime requirement(megawattclass)i.e.,daysor monthsinsteadof years.It shouldbenotedthat

improvementsin spaceradiatortechnologywould alsobe immenselybeneficial,but adequatesystems

couldbedevelopedusingtheexistingstateof theart.

Basedon theseresults,the authorsconcludethat MHD NEPtechnologyoffers a pathfor highpayoff,near-termrealizationwith limiteddevelopmentrisk.As such,theauthorsrecommendthatvigorous

technologydevelopmentstepsbeundertaken.

34
REFERENCES

. Sackheim, R.; Van Dyke, M.; Houts, M.; Poston, D.; Lipinski, R.; Polk, J.; and Frisbee, R.: "In-Space

Nuclear Power as an Enabling Technology for Deep Space Exploration," AIAA Paper 2000-3881,

American Institute of Aeronautics and Astronautics, 2000.

2. Rosa, R.J.: "An Electromagnetic Rocket System of High Specific Thrust," Research Report No. 103,

Avco Everett Research Laboratory, April 1958.

3. Rosa, R.J.: "Propulsion System Using a Cavity Reactor and Magnetohydrodynamic Generator," ARS

Journal, Vol. 31, pp. 884-889, July 1961 (see also, ARS Report 1519-60).

4. Rosa, R.J.: "Magnetohydrodynamic Generators and Nuclear Propulsion," ARS Journal, Vol. 32,

pp. 1221-1230, August 1962.

. Rosa, R.J.: "A Discussion of Nuclear Propulsion Using MHD Conversion Techniques," Advanced

Nuclear Propulsion Conference, Los Alamos National Laboratory, April 1964 (see also, AMP 153,

Avco Everett Research Laboratory, February 1965).

6. Rosa, R.J.: "Radiating Space Powerplants Using the MHD Generator," AMP 148, Avco Everett

Research Laboratory, February 1965.

7. Rosa, R.J.: "A High Temperature Radiating Vapor Cycle," Seventh Symposium on Engineering

Aspects of MHD, Princeton, NJ, February 1966.

8. Rosa, R.J.: "Unconventional Propulsion Systems," AAS Paper No. 67-131, American Astronautical

Society, 13th Annual Meeting, Dallas, TX, May, 1-3, 1967.

9. Seikel, G.R.; and Nichols, L.D.: "Potential of Nuclear MHD Electric Power Systems," J. of Spacecraft

and Rockets, Vol. 9, pp. 322-326, May 1972.

10. Thorn, K.; and Schwenk, EC.: "Gaseous-Fuel Reactor Systems for Aerospace Applications,"

J. of Energy, Vol. 1, pp. 267-276, September-October 1977.

11. Rosa, R.J.: "Magnetohydrodynamics Applied to Aerospace and Deep Space Propulsion," AIAA Paper

No. 82-1212, American Institute of Aeronautics and Astronautics, 1982.

12. Rosa, R.J.; and Myrabo, L.N.: "Ultraperformance Closed-Cycle Gas Core Reactors for Orbit Raising," Orbit-Raising and Maneuvering Propulsiorr--Research Status and Needs, AIAA Progress in

Astronautics and Aeronautics, Vol. 89, L.H. Caveny (ed.), pp. 460-476, AIAA, New York, NY, 1983.

35
13. Dias,N.; Anghaie,S.; Dugan,E.T.; and Maya,I.: "GasCore ReactorConceptsandTechnology,"

AIAA Paper91-3582,AmericanInstituteofAeronauticsandAstronautics,1991.

14. Maya,I.; Anghaie,S.;Diaz, N.J.;andDugan,E.T.:"Ultra TemperatureVaporCore--MHD System

for SpaceNuclearElectric Power,"AIAA Paper91-3632,AmericanInstitute of Aeronauticsand

Astronautics,1991.

15. Slavin,V.S.;Danilov,V.V.;andKraev,M.V.:"SpaceTransportSystemontheBasisof MHD Generator andElectricRocketEngine,"Proceedings of the International Conference on MHD Power Generation andHigh Temperature Technologies 1999, Vol. II, Beijing, PRC, pp. 694-707, October 12-15,

1999.

16. Holman, R.R.: "A Critique of NERVA-Based Nuclear Reactor Design and Performance for MMW

Space Propulsion Applications," Space Nuclear Power Systems 1987, Vol. 7, M.S. E1-Genk and

M.D. Hoover (eds.), Orbit Book Company, Malabar, FL, pp. 527-531, 1988.

17. Inui, Y.; Ishikawa, M.; and Umoto, J.: "Proposal for New Conceptual Design Method of Nonequilibrium

Disk MHD Generator," 31st Symposium on Engineering Aspects of MHD, Whitefish, MT,

pp. III.l.l-III.1.8, 1993.

18. Rosa, R.J.: Magnetohydrodynamic Energy Conversion, Revised Printing, Hemisphere Publishing,

New York, NY, 1987.

19. Chang-Diaz, F.; Squire, J.; Bering, E.; George, J.; Ilin, A.; and Petro, A.: "The VASIMR Engine

Approach to Solar System Exploration," AIAA Paper No. 2001-0960, American Institute of

Aeronautics and Astronautics, 2001.

20. Taussig, R.; and Christiansen, W.: "Design Investigation of S olar-Powered Lasers for Space Application," Contract No. NAS3-21134, Mathematical Sciences Northwest, Inc., Bellevue, WA,

November 1978.

21. Kerrebrock, J.L.: "Nonequilibrium Ionization Due to Electron Heating: I. Theory," AIAA J., Vol. 2,

p. 1072, 1964.

22. Nakamura, T.; and Riedmuler, W.: "Stability of Nonequilibrium MHD Plasma in the Regime of Fully

Ionized Seed," AIAA J., Vol. 12, p. 661, 1974.

23. Okuno, Y.; Okamura, T.; and Shioda, S.: "Feasibility of a Disk Type Nonequilibrium MHD Generator

With Subsonic Flow," Transactions oflEE of Japan, Vol. 110-B, p. 603, 1990.

24. Braun, J.; Nygard, K.; and Witalis, E.: "On Plasma Through Neutron Irradiation," International

Symposium on MHD Electrical Power Generation, Paris, France, Vol. 1, pp. 179-194, 1964.

36
25. Braun,J.; andNygard,K.: "Measurementof theElectricalConductivityof 3HePlasmaInducedby

NeutronIrradiation,"Proceedings of the Symposium on MHD Electrical Power Generation, Vienna,

Austria, pp. 557-570, 1966.

26. Watanabe, Y.; Appelbaum, J.; and Maya, I.: "Two-Temperature Model of Helium Plasmas with FastIon Induced Nonequilibrium Ionization," AIAA Paper 90-1613, American Institute of Aeronautics

and Astronautics, 1990.

27. Bitteker, L.: "Nuclear-Induced Electrical Conductivity in 3He," J. App. Phys., Vol. 83, No. 8,

pp. 4018-4023, 1998.

28. Melbourne, W.G.: "Interplanetary Trajectories and Payload Capabilities of Advanced Propulsion

Vehicles," NASA Jet Propulsion Laboratory Technical Report No. 32-68, March 1961.

37
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October 2001 Technical Publication

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Prospects for Nuclear Electric Propulsion Using Closed-Cycle

Magnetohydrodynamic Energy Conversion

6. AUTHORS

R.J. Litchford, L.J. Bitteker, and J.E. Jones

7. PERFORMING ORGANIZATION NAMES(S) AND ADDRESS(ES)

George C. Marshall Space Flight Center

Marshall Space Flight Center, AL 35812

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546 0001

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REPORT NUMBER

M 1027

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AGENCY REPORT NUMBER

NASAfF_2001 211274

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Prepared for the Advanced Space Transportation Program, Space Transportation Directorate

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13. ABSTRACT (Maximum 200 words)

Nuclear electric propulsion (NEP) has long been recognized as a major enabling technology for scientific and human exploration of

the solar system, and it may conceivably form the basis of a cost-effective space transportation system suitable for space commerce.

The chief technical obstacles to realizing this vision are the development of efficient, high-power (megawatt-class) electric thrusters

and the development of low specific mass (<1 kg/kWe) power plants. Furthermore, comprehensive system analyses of

multimegawatt class NEP systems are needed in order to critically assess mission capability and cost attributes. This Technical

Publication addresses some of these concerns through a systematic examination of multimegawatt space power installations in

which a gas-cooled nuclear reactor is used to drive a magnetohydrodynamic (MHD) generator in a closed-loop Brayton cycle. The

primary motivation for considering MHD energy conversion is the ability to transfer energy out of a gas that is simply too hot for

contact with any solid material. This has several intrinsic advantages including the ability to achieve high thermal efficiency and

power density and the ability to reject heat at elevated temperatures. These attributes lead to a reduction in system specific mass

below that obtainable with turbine-based systems, which have definite solid temperature limits for reliable operation. Here, the

results of a thermodynamic cycle analysis are placed in context with a preliminary system analysis in order to converge on a design

space that optimizes performance while remaining clearly within established bounds of engineering feasibility. MHD technology

issues are discussed including the conceptual design of a nonequilibrium disk generator and opportunities for exploiting neutroninduced ionization mechanisms as a means of increasing electrical conductivity and enhancing performance and reliability. The

results are then used to make a cursory examination of piloted Mars missions during the 2018 opportunity.

14. SUBJECT TERMS

nuclear, electric, propulsion, power, magnetohydrodynamics, spacecraft,

Mars mission

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