Rodger W. Dyson, Barry Penswick, Malcolm Robbie, and Steven M. Geng

Glenn Research Center, Cleveland, Ohio

Investigation of Liquid Metal Heat Exchanger

Designs for Fission Surface Power

NASA/TM—2009-215505

March 2009

AIAA–2008–5733
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Rodger W. Dyson, Barry Penswick, Malcolm Robbie, and Steven M. Geng

Glenn Research Center, Cleveland, Ohio

Investigation of Liquid Metal Heat Exchanger

Designs for Fission Surface Power

NASA/TM—2009-215505

March 2009

AIAA–2008–5733

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

Sixth International Energy Conversion Engineering Conference (IECEC)

sponsored by the American Institute of Aeronautics and Astronautics

Cleveland, Ohio, July 28–30, 2008
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Level of Review: This material has been technically reviewed by technical management. 

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ideas from a technical peer group.

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
Fission surface power is an option for future Moon and Mars surface missions. High

power nuclear reactor heated Stirling convertors are an option to provide reliable power

for long duration outpost operations. This report investigates various design approaches

for the liquid metal to acceptor heat exchange and clarifies the details used in the analysis.

Nomenclature

∆T Difference in Temperature between solid surface and surrounding film area, K

m ̇ Mass Flow Rate, kg s−1

μ Water Viscosity, kg m−1s

−1

A Outside Solid-Fluid Contact Surface Area, m2

Ac Cross-sectional Area of Flow, m2

Cp Heat Capacity at Constant Pressure, Jmol−1K−1

dh Hydraulic Diameter, m

h Overall Heat Transfer Coefficient, W

m2K

kw Thermal Conductivity of Water, Wm−1K−1

P r Prandtl Number, Cp·μ

kw

Q Power input or heat lost, W

qi Heat Flux from the Wall, W m−2

Re Reynolds Number, m ̇ ·DH

μ·Ac

I. Introduction

S

tirling thermal energy conversion in space, heated via a liquid metal cooled reactor is anticipated

to be an efficient and reliable provider of power on the surface of the Moon and elsewhere. NASA’s

Exploration Technology Development Program Fission Surface Power Systems Project plans to perform a

non-nuclear laboratory demonstration of fission surface power technology using Stirling or Brayton thermal

energy conversion. A notional design1is shown in Fig. 1. The technology demonstration will include a liquid

metal loop to transport the heat to a power conversion unit for electrical energy production. The waste heat

is rejected via heat pipe radiator panels to the walls of a thermal vacuum chamber. Initial demonstration

testing will utilize electric heating elements to simulate a nuclear reactor. Prior to conducting a full-scale

test, smaller sub-scale testing is planned to demonstrate feasibility. A specific test that is currently being

assembled involves the integration of two 1 kW Stirling convertors from GRC and a NaK heating loop at

MSFC.

Investigation of Liquid Metal Heat Exchanger Designs 

for Fission Surface Power 

Rodger W. Dyson, Barry Penswick, Malcolm Robbie, Steven M. Geng 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

NASA/TM—2009-215505 1
A. Fission Surface Power Test Circuit

Figure 1. NaK heated Stirling Convertors Notional

Layout (Langlois1)

The test rig shown in Fig. 2 supplying the heated

liquid metal to the Stirling convertors in this initial

demonstration can at most heat the NaK to 800K

at 1 kg/sec,2, 3 although an actual reactor could provide more heat than that safely. It also operates

in a vacuum chamber at a pressure of 10−5 torr or

lower. Natural convective cooling is eliminated leaving thermal radiation as the primary energy loss.

The actual reactor temperature and mass flow

can be adjusted via fuel rod selection and electromagnetic pumping, but for this demonstration

project we assume the coolant has an exit temperature of 798K. Notice the overall pyramid configuration in Fig. 1 due to the required radiation shielding

of components. The Stirling linear alternator magnets are located at the outer edge of the pyramid and hence it is imporant to reduce the ”footprint” of the

dual-opposed Stirling convertors.

Reactors can be cooled with liquids or gases. Water cannot be used with fast spectrum reactors since it

acts as a moderator slowing neutrons. Liquid metals have been used in the past for reactor cooling. This

demonstration project utilizes NaK which is an alloy of sodium (Na) and potassium (K) that is commercially

available. Alloys with between 40% and 90% potassium by weight are liquid at room temperature. The

mixture (NaK-78) with the lowest melting point (the eutectic mix), consisting of 78% potassium and 22%

sodium, is liquid from 260 K to 1058 K. This allows for convenient frequent shutdown of the reactor since

with higher melting point coolants continual heating would be required to prevent freezing of the coolant.

NaK also has a very low vapor pressure (high boiling point temperature) making it a good choice for

the vacuum environment of space. Previous Soviet RORSAT radar satellites were powered by NaK-cooled

reactors. Sodium potassium (NaK) was also used in the U.S. SNAP-10A fission reactor.

Figure 2. Fission Surface Power Test Circuit (Garber2, 3)

The test circuit was originally intended to operate with liquid Lithium and has been modified to

account for the additional expansion rate of NaK.

Since NaK will react with air and water to produce potentially explosive hydrogen reactions, it is

important to maintain safe handling prodecures for

filling and draining. The entire test is mounted on

a tilt table to ensure complete draining. However,

the wetted walls will remain wet due to surface tension and a process of ”steam cleaning” is envisioned.

Gaseous Nitrogen is used to cool the pump to keep

the magnetics healthy.

B. Heat Exchanger Design Requirements

The actual demonstration convertors are manufactured by Sunpower, Inc. notionally shown in Fig. 3

in their dual opposed configuration and a single convertor with the heat acceptor highlighted.

The ideal P2A liquid metal heat exchanger will

have the following properties:

• Provide 4180 W thermal energy to the convertor

• Minimize mechanical joints

• The liquid metal reactor coolant should drain due to the forces of gravity on the Earth, Moon, and

Mars.

NASA/TM—2009-215505 2
,

Figure 3. Dual Opposed and Single 1177 W Stirling Convertors (Penswick4, 5)

• Maintain a minimum flow velocity to reduce the impact of impurity settling

• Provide a symmetric heat flux to the convertor

• Minimize the temperature difference across the heater head wall (reduce stresses)

• Minimize stresses on the heater head due to differing coefficients of thermal expansion (CTE)

• Minimize pressure drop to reduce the pumping power required

• Account for and mitigate abrasion/erosion both at joints and on the heater head

• Provide long-lived reliable brazes/welds by reducing stresses along these joints/interfaces

• Inexpensive to manufacture

• Reduce the ”footprint” of the dual convertors to reduce required radiation shielding for potential future

nuclear applications

• Minimize flow direction changes in the supporting plumbing (T’s encourage erosion, impact reliability)

This report provides a comparison of various design concepts as they address these criteria by utilizing

advanced fluid heat transfer analysis techniques

II. Heater Head Heat Flux Assumptions

The accuracy of our model (and effectiveness of our design) is only as good as the assumptions used

in the analysis. One of the challenges in this design project is a lack of heat transfer profiles expected

at the boundary of the domain. One could model the entire convertor,6to determine the exact heat flux

distribution but current time limitations require an engineering estimate of these conditions (i.e. Note that

a complete power convertor has many geometric details that effect its peformance and heating requirements)

A number of previous studies have assumed either a constant temperature along the acceptor or a constant

heat flux. For example, a previous analysis for a thermal vacuum test rig assumed a 15K temperature drop

along the length of the acceptor and a constant heat flux.7In Fig. 4(a) heat conduction from an electric

source is used to heat the acceptor. In Fig. 4(b), a uniform flux is assumed a distance away from the wall to

minimize the effect of boundary condition errors.

Also, Sage8 analysis (a globally implicit harmonic one-dimensional Navier-Stokes solver and Stirling

engine optimizing software package) assumes a temperature difference along the acceptor. And the expansion

NASA/TM—2009-215505 3
(a) Electric Heating Configuration (b) Wall Temperature Distribution (c) Heat Flux into Regenerator

Figure 4. Delta Temperaure Along Acceptor (Oriti7)

space is often treated with only a few cells, each with a single temperature resulting in an approximate heat

flux profile.

In Fig. 5(a) is shown the heat flux profile predicted from a Sage/FEA analysis. Again, the temperature

distribution is assumed at the wall, not the heat flux, resulting in a large heat flux at the dome end of

the acceptor to maintain the high temperature. Notice in the graph that when a 20K temperature drop is

assumed this results in a lower heat flux at the dome end. Since the delta T is being provided as an input,

the resulting heat flux profile is again only an approximation. The slight increase in the heat flux profile

near the regenerator can be observed in Fig 4(c) to be due to the increased conduction along the wall and

radial conduction into the regenerator.

In recent whole engine simulations, a constant temperature was assumed on the heat exchanger and the

resulting oscillating heat flux is shown in Fig. 5(b). Typically a time average of this profile is assumed for

the purposes of designing the heat supply interface to the acceptor.

(a) Wall Heat Flux (Wood9) (b) Wall Heat Flux Oscillation (Dyson10)

Figure 5. Heater Head Wall Flux

Also, under the assumption of fixed wall temperature, notice the temperature profile through the entire

engine in Fig. 6. Notice the dome temperature becomes essentially uniform. In our current analysis of the

liquid metal heat exchanger, we assume a fixed temperature along the dome as well. If we assume only

10% heat transfer in through the dome, the effective dome temperature must be higher than the acceptor

temperature because the liquid metal cools upon impinging the dome (in the case of axially entering flow).

Notice that the dome wall becomes much cooler than the acceptor when the convertor is operating in reverse

NASA/TM—2009-215505 4

as a cooler (i.e. piston leads the displacer).
as a cooler (i.e. piston leads the displacer).

(a) Heater and Cooler Profiles Shown

Figure 6. Typical Fluxes Through the Heater Head

Experimental evidence11 indicates that the heater head dome is actually slightly cooler than the acceptor

region when the heat is delivered directly to the acceptor. Once we apply liquid metal to the dome this

condition may no longer be true, but more heat transfer overall is possible into the Stirling heater head in

this circumstance due to effectively more heat transfer surface area.

These previous studies indicate a variety of approximations which are often applied to estimate the

effective heat flux and serve to bracket the variability expected in our analysis. In Fig. 7, the effects of

assuming either a constant heat flux or a constant temperature along the acceptor are shown including the

liquid metal temperature profile and heat flux axially along the acceptor. For example, if the NaK is flowing

at a rate of .17 kg/s and the heat flux profile is assumed to be constant, then the temperature profile shown in

Fig. 7(a) of the liquid metal gradually cools along the length. In contrast, when the temperature is assumed

constant, then the liquid metal must quickly cool near the surface as shown in 7(b) resulting in a spiking

higher heat flux at the entrance. For our final heat exchanger design both assumptions were made to bracket

the predicted performance.

A. Correlations

Traditionally, engineers have relied on empirical correlations of heat transfer coefficients (HTC) to estimate

convection heating (fluid to solid). Those correlations are valid only in a particular flow regime and only under

developed flow conditions. Interestingly, the correlations themselves are based on a non-dimensionalization

of the Navier-Stokes equations (Buckingham-PI rule) and then experiments are performed to attempt to fit

a curve to the data.

For example, the heat lost from a hot tube to the surrounding area:

Q = h · A · ∆T (1)

The unknown is always the heat transfer coefficient, h, until experiments can be performed, and then only

for specific fluids, flow regimes, and thermodynamic conditions. The Dittus-Boelter heat transfer relation12

NASA/TM—2009-215505 5
(a) Heater Head-Constant Heat Flux, Varying Temperature

Mass Flow .17 kg

s

, Heat Transfer 4165W, ∆P 7.6 Pa

(b) Heater Head-Constant Wall Temperature, Varying Flux

Mass Flow .17 kg

s

, Heat Transfer 3676W, ∆P 7.6 Pa

Figure 7. Effects of Heat Exchanger Heat Transfer Assumptions

is valid for a wide range of fluids, including water, in a circular pipe with Reynolds numbers between 10,000

and 120,000 and Prandtl numbers in the range between 0.7 and 120. The heat transfer coefficient (HTC) is:

h =

kw · Nu

Dh

(2)

Nu = 0.024 · Re0.8· P r0.4(3)

B. Annular Heat Exchanger Correlation

For the case of an annular heat exchanger, with inner Diameter, Di, and outer diameter, Do, with an

insulated outer wall and constant temperature inner wall, the heat flux transfer from the wall is:

qi = hi (Ti − Tf luid) (4)

and the Nusselt number:

Nui =

hiDh

k

(5)

where Dh = Do − Di.

Di/Do Nui

0 NA

0.05 17.46

0.10 11.56

0.25 7.37

0.50 5.74

1.00 4.86

Table 1. Laminar Developed

Flow Annular Duct Heating

The heat transfer coefficient for fully developed

laminar flow may be found by the Table 1. Clearly,

the heat transfer cofficient increases as the outer

diameter decreases. This implies the flow volume

should decrease in the direction of the flow if it is

desired to increase the heat transfer coefficient to

maintain a uniform heat flux since the NaK’s temperature is decreasing along the acceptor as it releases heat.

Other heat transfer coefficients for liquid metal

may be found in Weisman.13 The limitation of the

heat transfer coefficients is they typically apply only

in very specialized flow regimes and entrance effects are typically not accounted for. Fortunately,

by solving the Navier-Stokes equations directly we don’t need the empirical heat transfer correlations since

NASA/TM—2009-215505 6
we are effectively performing the experiment that the correlations would have been derived from while

simultaneously including the entrance and exit effects.

For the case of constant or variable heat flux, more complicated influence coefficients are employed,

further exacerbating the difficulty of validating the results. A fully computational fluid dynamic analysis is

employed instead, and its formulation is detailed next.

III. Numerical Approach

(a) Segregated Solver (b) Computer Cluster

Figure 8. Solver Tools

There are a number of computational fluid

dynamics tools available for accomplishing this

work including Modified CAST, CFD-ACE, Fluent,

STAR-HPC, CFX/ANSYS, and many others that

are all low order accuracy solver based. Some new

high-order codes are being developed that are less

stable, but provide faster solution times. The low

order methods seem to be able to use about 30 processors efficiently. So it is important to run many

cases at once to fully utilize a large computer cluster. In this work, many design optimizations were

tested simultaneously.

A. Solver

A pressure based solver is used where the NavierStokes equations are solved sequentially (segregated

from one another) as outlined in Fig. 8(a). The

pressure derivatives are discretized using a bodyweighted formulation. The face pressure is determined by assuming that the normal gradient of the

differences between pressure and body forces is constant. This is used due to the large body forces

occuring in the high density liquid metal (especially

when compared to water or Helium) The gravity

forces are added as a source term as well for this

reason. It is assumed the liquid metal is flowing in

the laminar regime. The thermodynamic fluid properties assumed are shown in the Appendix Fig. 16.

Some of the designs examined contained unsteady flow features such as vortices, mixing, and reversed

flow. It was necessary to solve the unsteady Navier-Stokes equations in those cases. Also, since the heat

flux at the acceptor actually oscillates during the cycle (see Fig. 5(b)), a more exact analysis would require

accounting for unsteady heat flux effects in an complete unsteady analysis. And, such effects as the reactor

startup impulse are currently ignored but would require an unsteady analysis as well.

The current heat exchanger analysis was carried out on a 374 processor cluster as shown in Fig. 8(b).

The solution process involves:

• Meshing Technique

– avoiding tetrahedral cells during meshing,

– matching cell sizes across non-conformal regions,

– smoothly expand/shrink cells through domain,

– utilizing double-sided boundary layers,

• Geometry Technique

– including as much geometry as is practical,

– cleaning up the geometry in CAD rather than using virtual geometry, Solver Technique

NASA/TM—2009-215505 7
– over-converge the steady solution to improve grid (by identifying local instability regions),

– maximize the energy under-relaxation factor,

– disable secondary temperature gradients,

– emphasize the course multigrid to avoid round-off error,

– utilize explicit under-relaxation of temperature,

– utilize higher space and time accuracy whenever possible,

• Optimization

– utilize parallel processing to perform design optimization.

– bound the results with both constant heat flux or temperature assumptions

– apply about 30 processors per design, but solve many parametric cases at a time

IV. Design Evolution

This effort is the first time that a Stirling engine will be directly heated with single-phase liquid metal

NaK-78 and careful attention was given to accounting for the very high thermal conductivity and viscous,

body force dominated convective motions. A number of conceptual designs were analyzed computationally

as shown in Fig. 9. The designs are first characterized by either a predominantly axial or radial motion of

the liquid metal past the acceptor surface. Secondarily, the angle at which the flow enters or exits the heat

exchanger further delineates the categories.

Each of the following design concepts will be described fully in subsequent sections:

• The axially slanting entrance and exit case was first examined (Fig. 9(a)) with the arrows indicating direction of flow and the overall flow pattern being both radial and axial (diagonally across the

acceptor).

• The second concept (Fig. 9(b)) resulted in purely radial flow but minimized erosion on the heater head.

• The third concept (Fig. 9(c)) produced very symmetrical axial flow at the entrance, but somewhat

eratic heat fluxes due to excessive back pressures.

• The fourth concept (Fig. 9(d)) produced purely radial flow with a surprisingly symmetric heat flux.

• The fifth concept (Fig. 9(e)) resulted in very uneven heat fluxes due to vortical flow structures.

All of these concepts eventually lead to our final design that is very similar to Fig. 9(c)), but that is

presented later in section VI.

A. Angled Entrance, Angled Exit

The first conceptual design considered and its predicted performance is shown in Fig. 10. The liquid metal

is assumed to enter the tube at 798K and the walls are assumbed to be perfectly insulated (adiabatic).

The first column in the figure represents the originally desired performance of the heat exchanger across

the Stirling acceptor. The heat flux was assumed to be constant, thus allowing the temperature to vary.

Notice the mass flow rate in was reduced by 30% under this heat flux assumption. A constant temperature

assumption requires the higher flow rate.

The overall heat flux was at the correct level, but the heat flux profile was very unsymmetrical and would

have potentially caused performance degradation of the Stirling convertors due to non-symmetrical thermal

energy input through the heat acceptor. Also, the overall temperature drop across the acceptor was 50K

which is large compared to previous analysis and experimental results.

NASA/TM—2009-215505 8
Figure 9. Preliminary Cases Considered a). Angled Entrance, Angled Exit b). Radial Flow with Split

Entrance/Exit c). Symmetric Entrance, Toroidal Back-End, Conical Drain, d). Radial Flow with Single

Entrance/Exit, e). Radial to Axial

,

Figure 10. Flooded Dome, Angled Inlet/Outlet, Nominal VS. Achieved Performance

B. Radial Flow with Split Entrance/Exit

Results for the radial flow concepts (Figs. 9(b) are shown in Fig. 11 and in this case consists of two inlet

channels that enters radially from the top of the heater head. The two inlets force the metal to collide,

thereby reducing the impact force on the heater head. A copper spreader is used to more evenly distribute

the heat circumferentially. A thin insulating shield is shown in Fig. 11 and it serves to protect the copper from

erosion and with proper thickness ”tuning” the heat flux and temperature can be made radially symmetric

about the acceptor. The exit consists of two radially extended outlet tubes.

Since the effects of radially/circumferentially uneven heating (though axially uniform) of the Stirling

convertor are not presently characterized, a more conservative axially varying, circumferentially uniform

heat flux profile is desired.

C. Symmetric Entrance, Toroidal Back-End, Conic Drain

The third design under consideration is one in which the flow directly impinges the dome axially and then

evenly spreads around the dome and over the heat exchangers. With a NaK-78 mass flow of .24kg/s and

assumed inlet temperature of 798K, the expected outlet average temperature is 779K with a total energy

delivery of 3885 W.

These results are shown in Figs. 12. Note that the temperature along the acceptor wall is assumed

NASA/TM—2009-215505 9
(a) Side (b) Symmetric Temperature Distribution

(c) Temperature Acceptor (d) Heat Flux Constant Temperature

Figure 11. Radial Concentric

constant at 768 K. But as shown in Fig. 12(d), the heat flux is not symmetrical around the acceptor. This

is partly explained by the unsymmetrical pressures shown in Fig. 12(e) in which a back pressure is forcing a

reversed flow on the top half of the heat exchanger. If the dome is not considered adiabatic and some of the

liquid metal heat energy conducts into the expansion space then the total energy delivered is a little higher

at 4070 W.

Since the heat flux is not symmetrical about the acceptor, this design was considered inadequate; however

the final design is most similar to this one.

D. Radial Flow with Single Entrance/Exit

This concept is a refinement of the Split Entrance/Exit concept shown in Fig. 9 (b). Rather than attempt

to minimize the impact of the liquid metal on the heater head through split entrance collision, an insulating

shield is used to both protect the head from impact and spread the heat flux appropriately. This concept

appears promising but it is not clear how the Stirling engine would respond to this axially symmetric,

circumferentially varying heat flux.

E. Radial to Axial

The radial to axial concept in Fig. 9(e) appeared promising since it shared many of the features with the

Symmetric Entrance, Toroidal Back-End, Conical Drain case (Fig. 9(c)) and it appeared to provide good

drainage of the liquid metal. Unfortunately, the required tight angle at the entrance forced most of the flow

downward upon impact resulting in very uneven heating.

NASA/TM—2009-215505 10
(a) Side View (b) Velocity (c) Bottom View – Acceptor colored

blue

(d) Heat Flux (e) Pressure (f) Temperature

Figure 12. Axially Flooded Entrance, Toroidal Exit - Constant Temperature Along Acceptor

V. Initial Reference Concept & Summary

A preliminary concept design is shown in Fig. 13(a) and was the first to include a full stress analysis

and ease of manufacturing in its design. Unfortunately, the liquid metal analysis indicated this was actually

the worst performing due to extremely uneven heating. Some areas around the top of the acceptor did not

receive any liquid metal heating!

A summary of the predicted performance of the candidate designs is shown in Fig. 13(b). Interestingly,

a good candidate design is the radial heat exchanger (Fig. 9(d)); however, a final axial design is presented

next that matches this performance and provides a more conservative axial flow across the acceptor.

VI. Final Configuration & Fabrication

The final design is shown in Fig. 14. Notice the similarity with the third case shown in Fig. 9(c). The

primary difference is the larger torus (now shaped elliptically for stress management) and the inner curved

lip that prevents the NaK from backflowing into the acceptor region.

A comparison of the original design goal with the final design’s performance is shown in Table 2. The

total pressure drop is about 820 Pa, the maximum flow velocity is 1.874 m/s, the NaK-78 mass flow rate is:

.24 kg/s, the total heat accepted into the Stirling convertor is: 4659 W, and the enthalpy flux into the inlet

of the heat exchanger is: 107,888 W.

Notice the entrance and exit heights correspond to the radial gap along the acceptor. Originally it was

anticipated that as the temperature of the liquid metal dropped along the length of the acceptor that the

heat transfer coefficient would need to be gradually increased to maintain a constant temperature along the

acceptor. Since this would have resulted in difficulties with gravity draining the NaK-78 the same entrance

and exit height was used instead with little impact upon the performance of the heat exchange system.

A picture of the as fabricated heat exchanger and the very uniform heat flux is shown in Fig. 15. All

performance goals are achieved with this design.

NASA/TM—2009-215505 11
(a) Preliminary Design (b) Summary of Preliminary Designs

Figure 13. Preliminary Design Summary

Property Design Goal Achieved Performance

Wall Temperature 768K 768K

LM Inlet Temp. 798K 798K

LM Temp. Drop 20K 22K

Thermal to Conv. 4180W 4659W

LM Flow Rate .24 kg/s .24 kg/s

LM Volume Rate 3.18e-4 m3/s 3.18e-4 m3/s

Avg. HX Heat Flux 28.7 W/cm2 31.8 W/cm2

Entrance Height 4.5 mm 3.45 mm

Exit Height 3.45 mm 3.45 mm

LM Pressure Drop 55 Pa 820 Pa

Table 2. Final Design, Nominal VS. Achieved Performance

NASA/TM—2009-215505 12
(a) Final Design Layout (b) Cut-Away View

(c) Stress (d) Deformation

(e) Velocity (f) Pressure

Figure 14. Final Liquid Metal Heat Exchanger Design: Stress, Deformation, Velocity, and Pressure

NASA/TM—2009-215505 13
,

Figure 15. Final Design as Fabricated

NASA/TM—2009-215505 14
VII. Conclusion

The final heat exchanger design is being fabricated from stainless steel and will be tested at NASA

Marshall’s Fission Test Power Circuit facility. It utilizes a flooded axial entrance to achieve uniform flow

around the heater head acceptor. It provides some heating through the dome and the balance enters through

the acceptor with the NaK temperature dropping about 22K along the acceptor length. After several design

iterations, it was found that an elliptical torous with an inner curved lip reduced uneven back pressures to

achieve an essentially perfect heat flux distribution across the acceptor.

Despite the variability in the heat flux profile assumed, the reactor coolant mass flow can be adjusted

to compensate for any minor inaccuracies to ultimately deliver acceptable heat energy to the convertor. At

most, the mass flow rate would need to be adjusted up or down approximately 30% from the mean of .24

kg/s to achieve this.

A. APPENDIX: Sodium Potassium Thermodynamic Properties

The density, specific heat, conductivity, and viscosity for the eutectic mixture of liquid Sodium Potassium

is shown in Fig. 16. Notice that for the temperature range the heat exchanger operates in the properties are

essentially constant. However, the fully variable property characteristics were included in the computational

fluid dynamic analysis of the exchanger system.

(a) (b)

(c) (d)

Figure 16. NaK-78 Properties

NASA/TM—2009-215505 15
References

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Internation Energy Conversion Engineering Conference (IECEC), 25027 June 2007, St. Louis, Missouri, AIAA-2007-4774

2Garber, A.E. ”Capabilities and Testing of the Fission Surface Power Primary Test Circuit (FSP-PTC)”, Space Nuclear

Conference 2007, Boston, MA, June 24-28, 2007, Paper 2030

3Garber, A.E., Godfroy, T. ”Design, Fabrication and Integration of a NaK-Cooled Circuit”, ICAPP ’06, Reno, NV, June

4-8, 2006, Paper 6331

4Penswick, B. ”Liquid metal heater head / HX information”, Memo Dated: 13 July 2007

5Penswick, B. ”Liquid metal heater head modeling ”, Memo Dated: 12 July 2007

6Dyson, R.W., Geng, S. M., Tew, R.C., Adelino, M. ”Towards Multiphysics Analysis of Stirling Convertors”, Engineering

Applications of Computational Fluid Mechanics, 2008

7Oriti, S., Schreiber, J.G. ”Design and Fabrication of a Stirling Thermal Vacuum Test”, 2nd Int. Energy Conversion

Engineering Conference, AIAA 2004-5561, 16-19 Aug. 2004, Providence, RI

8Gedeon, D., ”Sage - Stirling-Cycle Model-Class Reference Guide”, Version 4, Gedeon Associates, 2006

9Wood, J.G. ”Actual Heat Flux Results”, Memo, Aug. 2007

10Dyson, R.W., Wilson, S.D., Tew, R.C., Demko, R. ”Fast Whole-Engine Stirling Analysis”, 3rd Int. Energy Conversion

Engineering Conference, AIAA 2005-5558, 15-18 Aug. 2005, San Francisco, CA

11Jiang, N., Simon, T. ”Heat Transfer and Fluid Dynamics Measurements in the Expansion Space of a Stirling Cycle

Engine”, IMECE 2006-15631, NASA/CR-2006-214454, Dec. 2006

12Incropera, F. P., DeWitt, D.P. ”Fundamentals of Heat and Mass Transfer”, John Wiley & Sons, 2002.

13Weisman, J., ”Elements of Nuclear Reactor Design”, Elsevier: New York, 1977

14Burdi, G.F. ”SNAP Technology Handbook” Volume I, Liquid Metals, Atomic International Report No. NAA-SR-8617,

August, 1964

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4. TITLE AND SUBTITLE

Investigation of Liquid Metal Heat Exchanger Designs for Fission Surface Power 

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6. AUTHOR(S)

Dyson, Rodger, W.; Penswick, Barry; Robbie, Malcolm; Geng, Steven, M. 

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WBS 463169.02.03.02.01 

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14. ABSTRACT

Fission surface power is an option for future Moon and Mars surface missions. High power nuclear reactor heated Stirling convertors are an 

option to provide reliable power for long duration outpost operations. This report investigates various design approaches for the liquid metal 

to acceptor heat exchange and clarifies the details used in the analysis. 

15. SUBJECT TERMS

Stirling cycle power convertors; Fission surface power; Liquid metal heat; Thermal energy conversion 

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