Design of a passive safety system for a nuclear thermal rocket

Annals of Nuclear Energy 111 (2018) 536–553

Contents lists available at ScienceDirect

Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene

Design of a passive safety system for a nuclear thermal rocket Jivan Khatry a, Fatih Aydogan b,⇑, Muhammad Ilyas a, Michael Houts c a

Center for Advanced Energy Studies (CAES), University of Idaho, 995 University Blvd., Idaho Falls, ID 83401, USA Center for Advanced Energy Studies (CAES), Idaho State University, 995 University Blvd., Idaho Falls, ID 83401, USA c NASA Marshall Space Flight Center, 4200 Rideout Rd, Huntsville, AL 35808, USA b

a r t i c l e

i n f o

Article history: Received 24 May 2017 Received in revised form 7 September 2017 Accepted 15 September 2017

Keywords: RELAP5 NASA Pewee I LOFA Safety system

a b s t r a c t Long-term high payload missions necessitate the need for nuclear space propulsion. Several nuclear reactor types were investigated by the Nuclear Engine for Rocket Vehicle Application (NERVA) program of National Aeronautics and Space Administration (NASA). Study of planned/unplanned transients and their impact on nuclear thermal rockets is important due to the need for long-term missions. It has been determined that a loss-of-flow-accident (LOFA) is the most serious design basis accident that will affect nuclear thermal rockets. A safety system is needed to respond to a LOFA and to prevent the core from melting. In this paper, a special secondary loop has been designed that utilizes the existing components of the Pewee I reactor. In particular, the tie rod tubes are connected to a secondary loop with radiator tubes. A check valve is also present in the circuit to help facilitate natural circulation in one direction in the absence of gravity. The radiator tube heat transfer surface area was increased to the following specifications: (i) 2 times the heat transfer surface area (HTSA) of the tie rod tubes, (ii) 4 times the HTSA of the tie rod tubes, (iii) 6 times the HTSA of the tie rod tubes, (iv) 8 times the HTSA of the tie rod tubes, and (v) 10 times the HTSA of the tie rod tubes. The following expected results were achieved: (i) during both steady-state operation and post-LOFA decay heat removal, temperature of the tie rod can be kept below the material melting point; (ii) during both steady-state operation and post-LOFA decay heat removal, natural circulation can be facilitated with a decent flow rate; (iii) during post-LOFA decay heat removal, the coolant temperatures in the tie rod tubes decreases and the mass flow rate increases; and (iv) in the secondary system, the heat sinks are able to remove the heat generated by the heat sources, during both steady-state and transient operation. As far as minimum radiator HTSA is concerned, the radiator tubes need to have a HTSA of approximately twice of that of the tie rod tubes. This ensures the tie rod tubes won’t melt and there is a decent natural circulation flow rate. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction A nuclear thermal rocket (NTR) is a vehicle, powered by nuclear fission, which travels into space for long-term space missions. Typically, NTRs are open-cycle reactor designs and consist of a propellant tank, pump, and reactor vessel. The reactor core serves as the engine of the rocket and heats the coolant (also referred to as propellant or working fluid) and then releases it an exhaust pressure. The reactor vessel of the NTR houses the core barrel, neutron reflector, control drum mechanisms, and core support plates/structures. Instead of control rods, NTRs have control drums to control the reactivity. These drums are rotated to keep the reactor critical. Historically, NTRs have used various propellants such as ammonia, nitrogen, and hydrogen. The KIWI reactors of Los Alamos ⇑ Corresponding author. E-mail address: [email protected] (F. Aydogan). https://doi.org/10.1016/j.anucene.2017.09.025 0306-4549/Ó 2017 Elsevier Ltd. All rights reserved.

Scientific Laboratory (LASL) used ammonia as the propellant. The Tory reactors of Lawrence Livermore Laboratories used nitrogen as the propellant. The Rocketdyne Division of North American Aviation identified hydrogen as a more suitable propellant than ammonia and nitrogen (Gunn, 2001). Among the advantages of NTRs as opposed to chemical combustion rockets is that they need less fuel per payload. In addition, they can diminish travel time and cut down on risks to nearearth objects and Mars (Akyuzlu, 2014). NASA anticipates that NTRs can travel to Mars by taking 50% of the time than envisioned (Russon, 2015). The learning experience from NTR studies can be used in improving the design of terrestrial nuclear reactors, especially that of safety systems. Aside from NTRs, rockets powered by nuclear electric fission reactors (NEFRs) have also been devised. In contrast to NTRs, NEFRs have similar fundamentals to those of nuclear power plants such as a reactor core, an energy conversion system, and a heat rejection

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

537

Abbreviations BM-PeBR Bimodal Pellet Bed Reactor CBC Closed Brayton Cycle FSOR Flexible Solar Optical Reflector HCC Hot Coolant Channels HS RELAP Heat Structure HV RELAP Hydrodynamic Volume HTSA Heat Transfer Surface Area ISNPS Institute for Space Nuclear Power Studies ICC Inner Coolant Channels ML Multilayer Insulation NASA National Aeronautics and Space Administration NbC Niobium Carbide NERVA Nuclear Engine Rocket Vehicle Application NTR Nuclear Thermal Rocket P Pressure (Pa) in Fig. 1 PeBR Pellet Bed Reactor PCC Peripheral Coolant Channels PVA Photovoltaic Array RELAP Reactor Excursion Leak Analysis Program SOFI Spray-On Foam Insulation Stdy-st Steady-state problem type declaration in RELAP T Temperature (K) in Fig. 1 TDJ Time Dependent Junction TDV Time Dependent Volume TREAT Transient Reactor Test Facility (U-Nb)C Uranium-Niobium Carbide VCHP Variable Conductance Heat Pipe W Mass flow rate (kg/s) in Fig. 1 WANL Westinghouse Astronuclear Laboratory ZBO Zero-Boiloff ZrC Zirconium Carbide ZrH Zirconium Hydride Symbols Ac performance factor in specific impulse equation ad payload ratio

system. NEFRs generate electricity to operate the instruments pertaining to the vehicle and also for the electric propulsion system. The following NEFRs have operated in space: (i) the BUK and TOPAZ reactors of Russia, and (ii) the SNAP-10A reactor of the United States. (Summerer and Stephenson, 2011). Nuclear reactors for space exploration have design criteria that share similarities and differences with those of terrestrial nuclear reactors. According to De Grandis et al. (2004) and Finzi et al. (2007), nuclear reactors for space exploration have the following design criteria: (i) produce required electrical power (most relevant for NEFRs), (ii) need to last for the required time period sans human intervention and refueling, (iii) limited mass and volume of design due to payload, (iv) meet safety requirements of the terrestrial nuclear reactors, (v) less maintenance and repair procedures than terrestrial reactors, and (vi) prevent leakage of fluids and possess safety systems to address these. Summerer and Stephenson (2011) list the following design criteria: (i) sufficient efficiency concerning heat removal in space and launch environments, (ii) very small and compact reactor cores, (iii) very high enrichment ratios, (iv) high core temperatures, and (v) low core power densities to enable long usage times. The NERVA program of NASA investigated several NTR designs from 1959 to 1973. The first NTR design developed was the KIWI B4D in 1964. The last NTR design developed was the Nuclear Furnace-1. Aside from these, prototype designs of NERVA NTRs include NRX, Phoebus, Pewee, and XE Prime. Out of these designs,

Aout At bs C1 cp cv Du F th g Isp M md Me mf M molar mp ms Pamb P0 Pout P t0 T Tc Th T in T out ts u

v v eq v in v out

flow area of the nozzle exit flow area of the nozzle throat structural ratio thrust coefficient in specific impulse equation specific heat capacity at constant pressure specific heat capacity at constant volume change in rocket velocity thrust of the rocket gravitational constant of earth specific impulse molecular weight of the exhaust gas payload mass Mach number full mass of the rocket is the molar mass propellant mass structural mass ambient pressure reactor power prior to shutdown pressure of the propellant at the nozzle exit time-dependent power reactor operation time prior to shutdown temperature of the fluid cold surface temperature hot surface temperature exit temperature of the propellant from the core/combustion chamber, temperature of the propellant at the nozzle exit time elapsed since shutdown rocket velocity speed of the fluid equivalent exhaust velocity velocity from the core/combustion chamber exhaust velocity at the nozzle exit

the Pewee had the highest operating temperature of greater than 2500 K and the Nuclear Furnace-1 had the longest reactor operation time of approximately 160 min (Houts, 2014). Nuclear reactors, especially terrestrial nuclear reactors, have active and passive safety systems. Active safety systems are those that require electric/mechanical inputs or human intervention to operate. Passive safety systems are those that depend on natural processes such as gravity or natural circulation and don’t need human intervention or electric/mechanical inputs to run. Modern day boiling water reactors and pressurized water reactors have mostly active safety systems. Many of the proposed Generation III+ reactors such as the Westinghouse Advanced Passive 1000 (AP1000), General Electric Economically Simplified Boiling Water Reactor (ESBWR), Molten Salt Reactor (MSR), European Leadcooled System (ELSY) reactor, High Temperature Gas Reactor (HTGR), and Sodium Advanced Fast Reactor (SAFR) have new passive safety systems. Safety systems that operate in response to an accident have not been designed for nuclear space vehicles. In this paper, we have selected the Pewee I Test Reactor to use for our safety system design. We have assumed the safety system will act in response to a design basis accident such as a LOFA. In this paper, the following will be presented: (i) a description of the Pewee I Test Reactor, (ii) a description of the fundamental formulae relevant to rockets (iii) a literature review of safety systems in space nuclear reactors, (iv) a literature review of nonforced circulation systems in space, (v) a presentation of the safety

538

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

system design, (vi) modeling of Pewee with safety system in RELAP5, (vii) operation of the Pewee I with secondary system in steady-state mode, (viii) operation of the Pewee I with secondary system in response to a transient, and (ix) conclusions to summarize the findings of this work.

2. Description of the Pewee I Test reactor The Pewee I Test Reactor, was a design that had 25% of the fuel elements of the Phoebus design. It was constructed to examine the fuel elements of the latter. The Pewee I never operated in space (Finseth, 1991). The Phoebus design was constructed under Project Rover, which was a joint project managed by Atomic Energy Commission, Los Alamos Scientific Laboratory (LASL), and NASA. The Copernicus Spacecraft, designated by NASA to take humans to Mars in the 2030’s, has been designed assuming three Peweetype engines are utilized. Pewee type engines each have a thrust of 111.21 KN (Borowskiet al., 2012). The Pewee I (Fig. 1) primarily consists of the reactor pressure vessel and the exhaust nozzle. Bear in mind that Fig. 1 assumes the Pewee I operated in space. Hence, the propellant tank and pump are presented. In reality, the propellant tank is much larger than the reactor vessel and nozzle. Table 1 presents the dimensions concerning the Pewee I. Fig. 1 presents the coolant parameters across the Pewee I with information such as mass flow rate (W), pressure (P), and temperature (T). The propellant tank holds all the propellant for the mission. The propellant is liquid hydrogen. Stored at a pressure of

Table 1 Specifications of the Pewee I design. Particulars

Details

Core diameter (m) Ratio of support elements to fuel elements No of fuel elements

0.53 1:3 402 (390 nineteen-hole type and 12 twelve-hole type) 1.32 36.42 0.1 0.20 0.08 0.15 0.41

Height of fuel elements (m) Total uranium-inventory in the core (kg) Control drum diameters (m) Reflector thickness (m) Aluminum support plate thickness (m) Nozzle throat diameter (m) Nozzle exit diameter (m)

0.5 MPa, the pump is used to raise the pressure to near 6.92 MPa. From the pump, most of the flow enters the propellant line, and the rest enters via the tie rod manifolds. From the propellant line, part of the flow goes to the pressure vessel bolt cooling, part of the flow goes to the nozzle bolt cooling, and the majority enters via the propellant inlet. There are 120 coolant tubes inside the shell of the nozzle chamber. The propellant travels via these tubes and then mixes with the small portion of the propellant that enters via the nozzle bolt cooling. The propellant continues through an annular expansion region and then through the coolant holes of the beryllium reflector. The beryllium reflector consists of an inner and an outer reflector. The inner reflector has small coolant holes, and the outer reflector has large coolant holes (see Fig. 2). The outer reflector also houses the control drum cylinders with their poison

Fig. 1. Pewee flow diagram (not drawn to scale).

539

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

the 19-hole fuel elements and are neighbors to both types of fuel elements. The propellant through the core mixes after exiting the annulus, slats, M1 elements, tie rods, and fuel elements. The total flow rate adds up to 18.59 kg/s. The temperature of the coolant entering the

Fig. 2. Quarter of top part of beryllium reflector.

plates for long-term reactivity control. Upon exiting the beryllium reflector, the propellant mixes with the coolant from the pressure vessel bolt cooling passage. The flow continues through the reactor vessel dome and then into the core. Within the core region shown in Fig. 3, there are four major channels that handle the coolant flow. The following are the 4 major coolant channels located in the core: the fuel elements (includes 19 and 12-hole fuel elements), which handles most of the flow; the ‘‘once-through” tie rods, which receive coolant directly via the tie rod manifolds and contain the zirconium hydride moderator sleeves; the M1 elements, which are unloaded peripheral elements; and the slats, which are tubes with rectangular-like geometry. The 120 tie rod tubes in the core receive coolant directly from the three tie rod manifolds. The tie rod tubes have both an outer tube and an inner tube as shown in Fig. 4. In the Pewee design, the coolant flows through both tubes in the same direction. Also, notice the layers of ZrH, ZrC, gap, and graphite in Fig. 4. There is a bypass to the core known as the annulus. The annulus surrounds the slats. Between the slats and the uncooled filler elements is the Invar wrapper, which has pyrographite strips on the outside. These are used for heat insulation. The annulus is surrounded by the beryllium reflector. The M1 elements have the same hexagonal shape as

Fig. 3. 60° slice of core.

Fig. 4. Tie rod tube top view (Fittje and Schnitzler, 2008).

Fig. 5. 19-hole fuel element.

Fig. 6. Top of pressure dome.

540

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

nozzle inlet is 1755.23 K. The coolant flows through the nozzle and is then released into the atmosphere as thrust. The coolant pressure of 3.26 MPa at the nozzle exit (in Fig. 1) is not provided in the original report by LASL (1969). This pressure was calculated using pressure drop relations and was used to model the pressure profile throughout the rocket in RELAP5. Fig. 5 presents a side view of a 19-hole fuel element. The hydrogen coolant passes through these holes. The diameter of each of these holes is 0.00279 m (LASL, 1969). Fig. 6 presents the top of the pressure vessel dome and shows the control drum knobs and support rod coolant manifolds (also known as tie rod manifolds).

Here, we present some of the equations relevant to both chemical and nuclear rockets. These equations are taken from NASA (2014). Fig. 7 presents a simple drawing of a rocket with mass partitions. The payload is the mass of the cargo or civilians the rocket is carrying. It is also referred to as the mass of the rocket with the propellant and structure subtracted. The propellant as mentioned in the introduction is the working fluid of the rocket. The structure is the part of the rocket that includes the engine/booster system. The rocket is partitioned into three mass systems such as payload mass md , propellant mass mp , and structural mass ms . The full mass of the rocket mf is given by

ð1Þ

The empty mass of the rocket me is given by

me ¼ md þ ms :

md md ¼ : mf  md mp þ ms

ad ¼

ð3Þ

The structural ratio bs is given by

bs ¼

ms ms ¼ : ms þ mp mf  md

ð4Þ

The propellant mass ratio MR is given by

mf mp 1 þ ad ¼1þ ¼ : me me bs þ ad

MR ¼

3. Fundamental formulae relevant to rockets

mf ¼ md þ mp þ ms :

Notice that the empty mass is basically the mass of everything inside the rocket, excluding the propellant. The payload ratio ad is given by

ð5Þ

In reality, a high ad implies a large payload can be handled by a small amount of propellant. A low bs indicates a good booster design. A high MR indicates a large increase in rocket velocity. All of these are desired for rockets in general, regardless of propulsion type. The Mach number is the ratio of the speed of the gas to the speed of sound in the gas. Mathematically, it is given by

Me ¼

v

v

a

¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; cRspec T

ð6Þ

where

c¼

cp cv

ð7Þ

is the ratio of specific heats,

ð2Þ

Rspec ¼

R ¼ c p  cv M molar

ð8Þ

is the specific gas constant, R is the molar gas constant, cp is the specific heat capacity at constant pressure, cv is the specific heat capacity at constant volume, M molar is the molar mass, v is the speed of the fluid, T is the temperature of the fluid, and a is the speed of sound. For dry air, Rspec has the value of 287.058 J/Kg K or 287.058 m2/s2 K. The Mach number is very important since compressibility effects need to be considered when a fluid is passing through a duct with contracting/expanding flow area. Table 2 shows the various domains of the Mach number. _ is Fig. 8 presents a small diagram of the rocket nozzle. Here, m the mass flow rate of the propellant, v in is the velocity from the core/combustion chamber, T in is the exit temperature of the propellant from the core/combustion chamber, P in is the exit pressure of the propellant from the core/combustion chamber, Aout is the flow area of the nozzle exit, At is the flow area of the nozzle throat, v out is the exhaust velocity at the nozzle exit, T out is the temperature of the propellant at the nozzle exit, P out is the pressure of the propellant at the nozzle exit, and P amb is the ambient pressure. The mass flow rate through the rocket nozzle is given by

A Pin _ ¼ ptffiffiffiffiffiffi m T in

rffiffiffiffiffiffiffiffiffiffi

cþ1Þ ð 2ðc1Þ

c

cþ1

Rspec

2

:

ð9Þ

Table 2 Ranges of the Mach number.

Fig. 7. Diagram of rocket with various mass partitions.

Mach # domain

Classification

Me < 1

Subsonic

Notes – Compressibility is neglected – Happens at rocket nozzle inlet

Me ¼ 1

Transonic

– Compressibility effects are significant – Happens at rocket nozzle throat

Me > 1

Supersonic

– Compressibility effects significant – Happens at rocket nozzle exit

more

541

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

Fig. 8. Diagram of the rocket nozzle with important variables.

The ratios of the flow areas, Aout to At , is given by

  cþ1 c1 2 2ðc1Þ  ðcþ1Þ Aout c þ 1 2ðc1Þ 1 þ 2 Me ¼ : 2 At Me

ð10Þ

The temperature leaving the nozzle is given by

T out T in

  c  1 2 1 Me ¼ 1þ 2

Fig. 9. Graph of specific impulse compared with thrust for several propulsion systems (Source: NASA Jet Propulsion Laboratory, ND).

ð11Þ Table 3 Ranges of specific impulse for propulsion systems.

and the pressure leaving the nozzle is given by

  c Pout c  1 2 c1 Me ¼ 1þ : 2 Pin

ð12Þ

The exhaust velocity of the propellant is given by

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

v out ¼ Me cRspec T out :

ð13Þ

Propulsion type

Isp range

Chemical Augmented N2H4, NH3 H2 Electrothermal NH3, N2H4 Solar H2 Nuclear, antimatter, laser (H2) Electric propulsion

230–500 320–330 600–1200 800–1000 800–1000 1400–3100

The thrust of the rocket is given by

_ v eq ¼ m _ v out þ ðPout  Pamb ÞAout ; F th ¼ m

ð14Þ

where v eq is the equivalent exhaust velocity. The specific impulse is given by the total impulse divided by the weight of the propellant. Mathematically, we have the equation

R

Isp ¼

_ v eq v eq F th dt m ¼ ¼ : _ mg g mp g

ð15Þ

Another expression for the specific impulse is given by

Isp ¼

F th ¼ Ac C 1 _ m

rffiffiffiffiffiffi T in ; M

ð16Þ

where Ac is the performance factor, C 1 is the thrust coefficient, and M is the molecular weight of the exhaust gas (Kulcinski, 1996). The equivalent exhaust velocity v eq is given by

v eq

ðPout  Pamb ÞAout ¼ v out þ : _ m

ð17Þ

The Tsiolkovsky rocket equation, also known as the ideal rocket equation, is given by

Du ¼ v eq ln



mf me



¼ v eq lnðMRÞ ¼ ðIspÞg ln MR:

ð18Þ

The significance of Eq. (18) is that a high change in the rocket velocity is needed to travel from the earth to the cosmos and beyond. This equation can be re-arranged to get Du

MR ¼ eðIspÞg or

ð19Þ

Du mp ¼ eðIspÞg  1: me

ð20Þ

Fig. 9 shows a plot of the specific impulse for several types of rockets. From Fig. 9, we can summarize the specific impulse ranges as shown in Table 3. As noticed, nuclear rockets have a higher specific impulse than chemical rockets. This is desired because a higher specific impulse implies a higher rocket equivalent exhaust velocity. If both the chemical rocket and nuclear rocket were to have the same propellant mass ratio ðMRÞ, the nuclear rocket would have the higher Du. Of course, the higher the Du, the greater the probability of exiting the earth’s atmosphere and entering the cosmos. 4. Literature review of safety systems in space nuclear reactors NASA came up with a Mars Design Reference Architecture (DRA) 5.0 study (Borowski et al., 2009). This study investigated the mission, payload, and transportation system requirements for a civilian expedition to Mars, scheduled for the 2030s. In this particular study, they considered a rocket with three NERVA-derived NTR engines, each with a resulting thrust of 111.21 KN (like the Pewee design). The fuel in the core is NERVA-derived/UC-ZrC in graphite ‘‘composite”. The propellant of this rocket is liquid hydrogen. The core has a propellant exit temperature of 2650–2700 K. The engine chamber pressure is 1000 psi. The nozzle area ratio is 300:1 to 500:1 and the specific impulse is 900–910 s. The length of the engine is 7.01 m. The safety system in this spacecraft is not intended to respond to accidents. Rather, it is meant for

542

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

preventing abnormalities. The safety systems associated with this design involve the multilayer insulation (MLI) that surrounds the liquid hydrogen tanks for passive thermal protection. The cryogenic tanks are manufactured using aluminum/lithium and have a diameter of 8.2–8.9 m. Typical insulation consists of 100 spray on foam insulation (SOFI) (0.78 kg/m2) plus 60 layers of MLI (0.90 kg/m2). The active zero-boiloff (ZBO) cryocooler is used to limit/eradicate boil-off when the propellant tank is exposed to the climate of the planet. The cryocooler is powered by photovoltaic array (PVA) primary power system. Similar to the design presented by Borowski et al. (2009), Christie and Plachta (2006) presented a bimodal NTR (BNTR) design. In addition to thrust, BNTRs also provide electricity for instruments and other systems of the spacecraft. This BNTR design has liquid hydrogen stored in the core stage tank, in-line tank, and four drop tanks. These tanks each have a diameter of 7.5 m. The core stage tank has a length of 20 m, whereas the in-line tanks and drop tanks are each 10 m long. The truss structure, which is composed of 24 struts, connects the walls of the core stage and in-line tanks to the rest of the vehicle. The transhab is an

Fig. 10. Bimodal NTR spacecraft (Christie and Plachta, 2006).

air-inflatable habitat for the crew members to board in during the mission. The safety systems in this BNTR are similar to those presented by Borowski et al. (2009). Here, all the hydrogen storage tanks are surrounded by multilayer insulation (MLI), flexible optical solar reflector (FSOR), and spray-on foam insulation (SOFI). In order of appearance, SOFI is covered by MLI and then covered by FSOR. The core stage tank and in-line tank each have two cryocoolers. The purpose again is to keep the hydrogen in its liquid state during inter-planetary missions. Malloy (1994) designed a passive cooling system for an open cycle nuclear reactor, like those found in nuclear rockets (see Fig. 10). In this particular design, the passive cooling system consists of passive coolant tanks, flow rate regulators, and checks valves. During normal operation, propellant flows to the reactor and also to the coolant tanks. When the reactor and pump are shut down, the pressure at the pressure coolant tanks is greater than the pressure at the reactor inlet. Hence, the coolant can flow naturally from the tanks to the reactor inlet. The flow rate regulator determines the flow rate based on decay heat needs (see Figs. 11–13). The Pellet Bed Reactor (PeBR) is a design that was initiated at the University of New Mexico’s Institute for Space Nuclear Power Studies (ISNPS) and is deemed sufficient for both thermal and electric propulsion missions. The concepts of the PeBR build-up on previous designs such as the pebble bed reactor, high temperature gas-cooled reactors for space propulsion, and NERVA reactors. The PeBR is a hydrogen-cooled reactor with an annular core and with (U-Nb)C microspheres with ZrC spherical fuel pellets. The PeBR design has both active and passive safety systems, which operate after the reactor has been shut down. These safety systems are needed to remove the decay heat. The active safety systems involve passing the propellant through the core. However, the drawback here is that additional propellant inventory is needed to cool down the reactor post-shutdown. The passive safety

Fig. 11. Decay heat removal system of open cycle reactor (Malloy, 1994).

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

Fig. 12. Simple diagram of a heat pipe (Lienhard and Lienhard, 2016).

system here involves the reactor core cooling down naturally via conduction/radiation, where the decay heat is gradually rejected to the surroundings. Morley and El-Genk (1992) did a multidimensional transient heat conduction/radiation model of the PeBR core and surrounding structures. Their analysis shows that total passive cooling of the reactor core isn’t possible for decay heat removal. Instead, using active cooling for 600–1000 s from shutdown, followed by passive cooling is sufficient to remove the decay heat. Another design of the PeBR is known as the bimodal PeBR (BMPeBR). Like the PeBR design, the BM-PeBR uses UC as fuel and hydrogen as propellant. Distinct from the PeBR, this utilizes a helium-xenon (He-Xe) closed Brayton cycle (CBC) engine and has structural materials consisting of super-alloys, and hydrogen The objectives of the BM-PeBR are as follows: (i) ability to deliver

543

electric power and thermal propulsion needs, (ii) have an annular reactor core design and several CBC engines as back-up components, in the event of failure in the coolant loop, (iii) maintain a maximum fuel temperature less than 1600 K (applicable for power generation and propulsion modes), (iv) have fuel pellets that retain the fission products, (v) have two independent reactor control systems that support each other, (vi) facilitate passive decay heat removal, (vii) have a negative temperature reactivity feedback to assist with stable reactor operation and safety, (viii) have a high specific impulse (650–750 s) and (ix) obtain specific power densities of 11.0–21.9 We/kg that are feasible at power ranges of 10– 40 kWe. The potential uses of the BM-PeBR are as follows: (i) powering surveillance satellites for planetary exploration, world-wide air traffic control; and (iii) to transport payloads to higher orbits, while trimming down on launch cost to geosynchronous orbits. The reactor vessel is surrounded by a radial reflector, which is thermally insulated and utilizes multi-foil insulation to avert greater than normal temperatures in the reflector by the hot HeXe working fluid. There is a sodium heat pipe radiator that is coupled to the reactor vessel via conduction and is suited for passive decay heat removal. Similar to the PeBR, the BM-PeBR has a large height-to-diameter ratio. The radial heat transfer path and large outer surface area of the reactor make passive cooling and decay heat removal possible.

5. Literature review of non-forced circulation systems in space As mentioned in Section 1, passive safety systems have been devised for terrestrial reactors. Many of these passive safety systems depend on natural circulation. Natural circulation is achieved due to fluid density differences or phase differences in the heat source and heat sink. Among the benefits of natural circulation include simplicity of design, less maintenance needed, no risk of

Fig. 13. Diagram of proposed safety system.

544

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

pump/compressor related accidents, and the flow rate increases with power (especially, two-phase flow). One of the drawbacks of natural circulation is the low flow head. Due to the low flow head, the size of the closed loop must be increased, or the flow resistance in the loop must be decreased, to maximize the flow rate (International Atomic Energy Agency, 2005). It is generally accepted that natural circulation doesn’t work without gravity. However, non-forced circulation systems for use in space have been devised. In particular, heat pipes have been used. A heat pipe has closed ends and allows two-phase flow to transpire between a heat source and a heat sink. The heat source is at one end of the pipe and evaporates the fluid. The vapor flows to the condenser on the opposite end of the pipe. The condensed fluid returns to the evaporator via a wick structure using capillary motion. Hall and Doster (1986) report that heat pipes have been used to transfer heat in space reactor designs for civilian/military needs. In such heat pipes, lithium is the coolant since it transitions from liquid to vapor at the preferred operating temperature. In addition, heat pipe reactors have been proposed for in-space electrical power production and planetary electrical power (Wright et al., 2005; Elliot et al., 2003; Houts et al., 2003; El-Genk and Tournier, 2004). These are the benefits of heat pipe reactors: (i) fluid motion is independent of pumps/compressors and is facilitated by vaporization, condensation, and wicking processes; and (ii) heat pipes can deal with the freezing and thawing in the absence of gravity. Walker et al. (2013) have designed and tested high-temperature alkali metal heat pipes for space fission power. In particular, they designed a self-venting arterial heat pipe and a grooved heat pipe. A self-venting arterial pipe contains a screen artery. Inside this screen artery, there are small venting pores in the evaporator section that permit trapped vapor or non-condensable gas to escape. Grooved heat pipes are designated for spacecraft thermal control since non-condensable gas in grooves can easily escape. El-Genk and Tournier (2004) came up with a conceptual design of a heat pipe-segmented thermoelectric module converters space reactor power system, which can deliver a net power of 110 KWe. This particular reactor has a hexagonal core with 126 heat pipe modules and uses uranium nitride fuel pins with rhenium cladding. This design is part of NASA’s goals to develop designs of space reactor power systems (SRPSs) for future missions to planets. Ideally, these SRPSs provide 50 to 300 KWe to operate multiple units of electric thrust engines. According to Shukla (2015), plenty of heat pipes have been designated for space applications. The following are examples of heat pipes: (i) variable conductance heat pipe (VCHP), (ii) cryogenic heat pipe, (iii) vapor chamber heat pipe, and (iv) loop heat pipe. The VCHP is a capillary driven heat pipe that utilizes a noncondensable gas in addition to the default coolant. Communication technology satellites are one area where VCHPs are favored (Mock et al., 1975). Cryogenic heat pipes have been favored for use in thermal control of charge-coupled device (CCD) cameras, which are utilized for the NASA-space interferometry mission (Bughy et al., 2011). A vapor chamber heat pipe is a flat-plate heat pipe with a small aspect ratio. Vapor chamber heat pipes are used in flight-sensitive applications, for example, avionics packages, computers, and surface mount circuit board cores. Loop heat pipes are currently favored to serve as thermal control devices for high powered telecommunication satellites (Shukla, 2015). 6. Design of the secondary system loop In this section, we describe the design of the secondary system loop shown in Fig. 16. This secondary loop is connected to the tie rods in the core. By default, the inlet of the tie rod tubes is connected to a manifold at the entrance. This manifold receives part

Table 4 Tie rod tube materials melting points. Material

Melting point (K)

Reference

ZrC Graphite Zirconium (II) Hydride (ZrH2)

3795.15 3773.15 1073.15

AZO Materials (2016) Entegris (2013) US Nano, ND

of the propellant from the propellant tank (see Fig. 1). The original system doesn’t have manifolds at the exit. In Fig. 16, we have added manifolds at the exit, and this will send the coolant to the radiator. The check valve is located after the tie rod exit manifold and is needed to make sure the secondary system coolant will flow in just one direction. Checks valves depend on flow in order keep them open or closed. The internal disc inside the check valves permits coolant to pass through it in the forward direction, hence opening the valve. The internal disc starts to close as the flow rate declines or the flow moves in the opposite direction (Johnson, 2006). There are various kinds of check valves: (i) ball check valve, (ii) dual plate valve, (iii) in-line check valve, (iv) piston check valve, and (v) swing check valve. Without the check valve, there will be conflicting flow. Check valves are available in the market for aerospace applications. For example, Valcor Engineering Corporation manufactures check valves that can be used in the spacecraft’s reaction control systems or altitude control systems (Valcor Engineering Corporation, 2017). CIRCOR Aerospace also manufactures check valves for space applications (Circor Aerospace, 2017). The hydrogen from the propellant tank will no longer flow through the tie tubes. Instead, the hydrogen will all be sent through the main propellant line in Fig. 1. However, the total flow of 18.59 kg/s going through the rocket is still the same as before. This secondary circuit needs to be operated such that the melting points of the tie rod tube materials aren’t exceeded. In particular, the melting points are presented in Table 4. We don’t have the melting point of ZrH, but we do have that of zirconium (II) hydride (ZrH2). Hence, we are assuming the melting point of ZrH is comparable to ZrH2. From Table 4, 1073.15 K is the maximum temperature permitted for the secondary system. The other temperature constraint is the freezing point of hydrogen, which is 14.01 K. Given that the tie rods are scattered around the core, it is important to pass coolant through them during normal operation. Hence, this secondary system should cool the ZrH moderator in normal steadystate operation and remove decay heat in a post-LOFA accident. In designing the secondary loop, the dimensions of the tie rod tubes and the tie rod manifolds will be kept the same as the default design. The dimensions we are left to determine are that of the radiator and the outside pipes. Such will be discussed in the proceeding section. The radiator will be assumed to be a collection of tubes rather than just a single tank. In this way, the radiator will have better heat transfer with the surroundings due to its high HTSA.

7. System modeling of Pewee I with secondary system To model the LOFA on the Pewee I, we need to create a Reactor Excursion Leak Analysis Program (RELAP) model of the rocket. In particular, RELAP is a special thermal hydraulics computer code developed by the Idaho National Laboratory in 1997. Since then, it has been used to model terrestrial nuclear power plants. Here, the model is described briefly. The Pewee nodalization diagram is presented in four parts in Figs. 14–17. First, we will describe the nodalization diagram for the original Pewee design presented in Fig. 14. As per tradition with most RELAP5 normalization diagrams,

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

Fig. 14. Original RELAP5 nodalization diagram of the Pewee I.

Fig. 15. Overall RELAP5 nodalization diagram of the Pewee I with secondary system.

545

546

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

Fig. 16. Pewee I detailed nodalization diagram of core components.

Fig. 17. Pewee I radial nodalization diagram of core/reflector region.

components are represented as pipes and volumes (including single volumes and time-dependent volumes) and have a unique three-digit number for identification. In this particular example, time-dependent volumes serve as boundary conditions for the

propellant inlet, nozzle bolt cooling, pressure vessel bolt cooling, and tie rod manifold. The time-dependent junctions (TDJ) connect the time-dependent volumes to the main circuit. The major components are numbered and labeled in Figs. 14–17. The whole

547

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

RELAP5 model is oriented horizontally, such that the gravity effects are neglected. Fig. 16 presents each of the different core channels shown in Fig. 1, such as the fuel elements, slat, annulus, tie rod tubes, and M1 elements. The coolant channels within the fuel elements were divided into three main RELAP5 pipes: hydrodynamic (HV) 430 for inner coolant channels (ICC), HV 432 for peripheral coolant channels (PCC), and HV 431 for the hot coolant channels (HCC). Because the fuel elements neighbor the tie rods, M1 elements, and an inner core boundary wall; it was justified to model the fuel elements as separate pipes with corresponding heat structures. Similar to light water reactors in RELAP5, it is not unusual to model a hot fuel element, a cold fuel element, and average temperature fuel elements. The hot and cold fuel elements are needed for the extreme situations. Since the Pewee is a hydrogen-cooled design, a hot fuel element is modeled for our extreme situations. The fuel elements have a total of 7554 coolant channels, and so HV 430 represents the 7175 ICC holes, HV 431 represents 19 HCC holes, and HV 432 represents the remaining 360 PCC holes. There are heat structures attached to the core channels and reflector, and they serve the purpose of modeling heat generation in fuel elements and heat transfer between fuel elements and neighboring structures. Since not all components appear on a single RELAP5 diagram (as shown in Fig. 14), connections to the unseen parts are indicated with HV number, volume number, and face number in the form CCCVV000F (CCC for hydrodynamic volume (HV) number, VV for volume number, and F for face number ranging from 1– 6) near each circular node. For example, HV 430 is divided into 12 volumes and is connected to HV 417 at the front and HV 465 at the rear. The pipe obtains input from 417010002 (HV 417, volume 1, face 2) and transfers its output to 465010001 (HV 465, volume 1, face 1). In this work, face 1 of a pipe/single volume/timedependent volume was designated as the inlet and face 2 was designated as the outlet. Fig. 17 presents a radial nodalization diagram of the Pewee design. Here, various channels in the core and the reflector with the appropriate HV #, HS #, and temperatures from the literature are presented. With modeling the secondary system in Fig. 15, the HV 520 and HV 530 are retained from the original RELAP model (Fig. 14). We have added HV 540 (tie rod manifold exit), the check valve, HV 550 (pipe between tie rod manifold exit and radiator inlet tubes), HV 560 (radiator inlet tubes), HV 570 (radiator tubes), HV 580 (radiator exit tubes) and HV 590 (pipe between radiator exit tubes and tie rod manifold entrance). In this secondary loop design, HV 530 is the main heat source, and HV 570 is the main heat sink. Aside from these, there are other structures that handle heat transfer: (i) HV 520 and HV 540 as minor heat sources, and (ii) HV 560 and HV 580 as minor heat sinks. In reality, the minor heat source HV 520 will absorb some heat via convection with the main propellant. In the same manner, the minor heat source HV 580 will absorb some heat via convection with the propellant entering the nozzle inlet. As for heat sinks HV 560, HV 570, and HV 580; these have a temperature boundary condition, where the outside is held at a constant temperature.

The RELAP5 model presented in Figs. 14, 16 and 17 has been tuned as best as possible to match the parameters shown in Fig. 1. Table 5 presents some sample tuned parameters. 8. Testing of secondary system during steady-state operation As mentioned earlier, the secondary system has to be operated during steady-state operation to keep the tie rods cooled. Hence, we adjusted the dimensions of the radiator (HV 570), radiator inlet (HV 560), and radiator outlet (HV 580); such that we can keep the tie rod temperatures from melting and achieve natural circulation. We can’t adjust the dimensions of the tie rod tubes (HV 530) and the tie rod manifolds (HV 520 and HV 540) as these are fixed. The main quantity that will be adjusted is the HTSA of HV 560, HV 570, and HV 580. In RELAP5, this is easily done by increasing the total heat transfer length of the respective hydrodynamic volume in the corresponding heat structure. Table 6 presents a summary of cases that were considered. Table 7 presents sample dimensions and materials used in the RELAP model. As with the total flow areas of the tie rod tubes (HV 530) and tie rod manifolds (HV 520 and HV 540), the default values were retained. The materials and dimensions of HV 545, HV 550, HV 560, HV 570, HV 580, and HV 590 were freely decided. With the choice of material for HV 545, HV 550, HV 560, HV 570, HV 580, and HV 590; graphite was selected. Graphite has a very low service temperature of 0 K and a high melting point of 3773.15 K. This temperature range makes it suitable for operation in space, where temperatures are as low as 3 K. In addition, the M1 elements and the slat tubes were manufactured from graphite in the original Pewee design.

Table 6 Sample cases to run. Case ID

Heat transfer surface area of heat sinks

1 2 3 4 5

2*(HTSA of secondary loop heat sources) 4*(HTSA of secondary loop heat sources) 6*(HTSA of secondary loop heat sources) 8*(HTSA of secondary loop heat sources) 10*(HTSA of secondary loop heat sources)

Table 7 Sample dimensions used in RELAP model for Case 1. HV #

Flow area (m2)

Length (m)

Materials

520 530 540 545 550 560 570 580 590

7.09e3 8.44e3 7.09e3 7.09e3 7.09e3 7.09e3 8.44e3 7.09e3 7.09e3

1.34 1.32 1.34 4.02e-1 9.38e-1 1.34 1.32 1.34 1.34

Graphite Default as shown in Fig. 4 Graphite Graphite Graphite Graphite Graphite Graphite Graphite

Table 5 Sample tuned parameters against design parameters (in parenthesis). Component

Mass flow rate (kg/s)

Temperature (K)

Pressure (MPa)

Reflector exit Core inlet Nozzle inlet Fuel element exit (includes ICC, HCC, PCC)

13.65 14.06 18.60 11.86

126.27 (125.00) 118.50 (127.78) 1767.08 (1755.23) 2619.53 (2555.56)

5.58 5.44 4.19 4.19

(13.65) (14.06) (18.59) (12.13)

(5.71) (5.56) (4.28) (4.28) Fig. 18. Spacecraft for 2037 Nuclear Thermal Propulsion Mission (Kos and Russell, 2014).

548

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

Fig. 20 presents the mass flow rates from Case 1. As expected, the mass flow rates through the fuel elements, M1 elements, slat, and annulus are greater than normal. This time, the mass flow rate through the tie rod tubes is 4.67 kg/s. This flow rate is almost close to the original flow rate of 4.54 kg/s as shown in Fig. 1. Fig. 21 shows that the heat sinks can remove the heat generated by the heat sources in the secondary system. Fig. 22 presents the temperatures from Case 2. There is a major difference in the tie rod tube exit temperatures as compared to Case 1. Here, the coolant exiting the tie rod tubes is at a reduced temperature of 87.92 K.

Fig. 19 presents the temperatures from Case 1. Here, the coolant exiting the tie rods is at a temperature of 247.95 K. Note that this temperature is below the original temperature of 260 K shown in Fig. 1. The temperature leaving the radiator is 15.67 K. The temperature leaving the fuel elements is 2026.44 K. Note that this temperature is less than the fuel element temperature shown in Fig. 1. This is because more coolant is being sent through the fuel elements. The overall temperature of the hydrogen coolant entering the nozzle is 1739.87 K. This temperature is almost 15 K less than the temperature of 1755.23 K shown in Fig. 1.

2500

Temperature (K)

2000 1500

Nozzle inlet Fuel element exit

1000

Tie rod tube exit Radiator exit

500 0 0

100

200

300

400

500

600

700

800

900

1000

Time (s)

Mass flow (Kg/s)

Fig. 19. Steady-state temperatures for Case 1.

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0

Primary system Tie rod tubes M1 elements Slats Annulus Fuel elements 0

100

200

300

400

500

600

700

800

900

1000

Time (s)

Fig. 20. Steady-state mass flow rates for Case 1.

35000000 30000000

Duty (W)

25000000 20000000 Heat generated in secondary loop Heat removed in secondary loop

15000000 10000000 5000000 0 0

200

400

600

800

1000

Time (s)

Fig. 21. Comparison of heat source and heat sink duty for Case 1.

549

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

2500

Temperature (K)

2000 1500

Nozzle inlet Fuel element exit

1000

Tie rod tube exit Radiator exit

500 0 0

100

200

300

400

500

600

700

800

900

1000

Time (s)

Fig. 22. Steady-state temperatures for Case 2.

The coolant exiting the radiator is at a temperature of 16.62 K. Fig. 23 presents the mass flow rates from Case 2. As expected, there is minimal difference in the mass flow rates in the fuel elements, M1, slat, and annulus as compared to Case 1. However, the mass flow rate through the tie rod tubes is now 32.56 kg/s as opposed to 4.67 kg/s. Fig. 24 also shows a 1-to-1 correlation between heat generated and heat removed. In Table 8, we summarize the temperatures obtained from these steady-state cases. In Table 9, we summarize the mass flow rates from these steady-state cases. From Tables 8 and 9, we can see that the performance of the secondary system doesn’t improve drasti-

Table 8 Temperature results from steady-state cases. Case ID

1 2 3 4 5

Temperature (K) Fuel elements exit

Nozzle inlet

Tie rod tubes exit

Radiator exit

2026.44 2018.46 2015.08 2018.44 2015.21

1739.87 1738.20 1739.39 1738.21 1739.71

247.95 87.92 85.83 86.71 86.75

15.67 16.61 16.16 15.96 15.69

50 45

Mass flow (Kg/s)

40 35

Primary system

30

Tie rod tubes

25 M1 elements

20

Slats

15

Annulus

10

Fuel elements

5 0 0

100

200

300

400

500

600

700

800

900

1000

Time (s)

Fig. 23. Steady-state mass flow rates for Case 2.

40000000 35000000

Duty (W)

30000000 25000000 20000000 Heat generated in secondary loop

15000000

Heat removed in secondary loop

10000000 5000000 0 0

200

400

600

800

1000

Time (s)

Fig. 24. Comparison of heat source and heat sink duty for Case 2.

550

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

Table 9 Mass flow rates from steady-state cases. Case ID

1 2 3 4 5

Mass flow (kg/s) Mass Fuel elements

Mass M1 elements

Mass Slats

Mass Annulus

Mass Tie rod tubes

15.73 15.77 15.80 15.77 15.80

0.20 0.20 0.20 0.20 0.20

1.99 1.98 1.97 1.98 1.96

0.67 0.65 0.63 0.65 0.63

4.67 32.56 31.34 34.68 34.18

qffiffiffiffiffiffiffi T loop Isploop Ac C f M q ffiffiffiffiffiffi ¼ T org Isporg Ac C f M

Table 10 Masses of components in Fig. 18 (Kos and Russell, 2014). Spacecraft components

Mass (metric tons)

Mass of one NTR Mass of one external radiation shield Mass of three NTRs Mass of three external radiation shields Unloaded mass of core propulsion stage tank Usable liquid hydrogen propellant mass Reactor coolant system usable propellant load Total in-line tank mass Total saddle truss and liquid hydrogen drop tank Total payload mass Total spacecraft mass

4.11 2.15 12.32 6.45 27.42 47.27 15.58 108.21 118.41 78.48 414.15

ð21Þ

where Isploop is the specific impulse with the secondary system, Isporg is the specific impulse in the original design, T loop is the overall temperature of the hydrogen leaving the core in the design with the secondary system, and T org is the overall temperature of the hydrogen leaving the core in the original design. Assuming the Ac and C f coefficients are the same in both cases, Eq. (21) simplifies to

pffiffiffiffiffiffiffiffiffiffi Isploop T loop ¼ pffiffiffiffiffiffiffiffi : Isporg T org

Table 11 Events scheduled for the RESTART problem. Time (s)

Event

0 500 560 1600

Steady-state operation Flow rate throughout system is decreased Scram is initiated Transient run ends

Table 12 Decay heat equation constants. Time after shutdown (s)

a

b

0.1 to 10 10 to 150

12.05 15.31 27.43

6.39e2 18.07e2 29.62e2

150 to 8  108

entering the nozzle is 1739 K, which is almost 15 K less than the default temperature shown in Fig. 1. This loss of temperature will result in a lower specific impulse, which is often thought of as a measure of effectiveness. With a lower temperature, this will result in a lower fluid velocity, as per Eq. (13). A lower fluid velocity will also result in lower thrust, as per Eq. (14). Here, we will attempt to estimate the loss in the specific impulse. Referring to Eq. (16), the ratio of the specific impulse in the rocket with the secondary loop to the original design, is given by

cally from Case 2 and beyond, as the temperatures and mass flow rates have minor differences. One of the drawbacks of this secondary system design is the loss of thermal efficiency. Recall that the overall temperature

ð22Þ

The temperature of the hydrogen entering the nozzle in the original system is 1755.23 K. The temperature of the hydrogen entering the nozzle in the new system is 1739.23 K. Using Eq. (22), the specific impulse decreases by 0.46%. The secondary system adds an estimated weight of 0.540 metric tons to the Pewee. Table 10 presents some masses of a model spacecraft with three Pewee-type engines, shown in Fig. 18. Given that there are three NTRs, there will be three safety system loops. The total mass added by these loops is 1.62 metric tons. The total mass of the spacecraft is 414.15 metric tons. The safety loops add 0.39% of mass to the default spacecraft design. 9. Testing of LOFA and SCRAM on secondary system The transient runs were initiated on the completed steady-state runs. Transient runs in RELAP5 require a RESTART problem to be resumed from the end-time of the steady-state run. Figs. 26–31 present the graphs resulting from these runs. These figures are a continuation of the steady-state cases presented in Figs. 19–24. In these figures, the LOFA occurs at a time of 500 s. At a time of 560 s, the scram is initiated. Part of the steady-state data is

455000000 405000000

Heat (W)

355000000 305000000 255000000 RELAP decay heat

205000000

Original decay heat

155000000 105000000 55000000 5000000 0

500

1000

23 1500

Time (s)

Fig. 25. Decay heat curve.

2000

551

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

where P0 is the power prior to shutdown, P is the time-dependent power, t s is the time since shutdown, and t 0 is the time prior to shutdown. with the time-dependent values of a and b presented in Table 12. Fig. 25 shows a graph of the calculated decay heat with the RELAP decay heat. In this work, it was assumed the reactor was in operation for 50 min.

presented in these transient runs to show the change from steadystate to transient. Tables 11 and 12 shows a summary of the events relevant to Figs. 25–31. The decay heat profile used for these transients was calculated using the following relation provided by Glasstone and Sesonske (2010). The decay heat is given by the relation

P b  5  103 a½t b s  ðt 0 þ t s Þ ; P0

ð23Þ

2500

Temperature (K)

2000 1500 Tie rod exit 1000

Radiator exit Fuel element material

500 0 0

500

1000

1500

2000

2500

Time (s)

Fig. 26. Transient temperatures for Case 1.

45 40

Mass flow (Kg/s)

35 30 25 20

Primary system

15

Secondary system

10 5 0 -5 0

200

400

600

800 1000 Time (s)

1200

1400

1600

1800

Fig. 27. Transient mass flow rates for Case 1.

40000000 35000000

Duty (W)

30000000 25000000

Heat generated in secondary loop

20000000

Heat removed in secondary loop

15000000 10000000 0

500

1000

1500

2000

Time (s)

Fig. 28. Comparison of heat source and heat sink for Case 1.

552

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

2500

Temperature (K)

2000 1500 Tie rod exit 1000

Radiator exit Fuel element material

500 0 0

500

1000

1500

2000

2500

Time (s)

Fig. 29. Transient temperatures for Case 2.

50 45 40 Mass flow (Kg/s)

35 30 25

Primary system

20 Secondary system

15 10 5 0 -5 0

200

400

600

800 1000 Time (s)

1200

1400

1600

1800

Fig. 30. Transient mass flow rates for Case 2.

45000000 40000000

Duty (W)

35000000 30000000

Heat generated in secondary loop

25000000

Heat removed in secondary loop

20000000 15000000 0

500

1000

1500

2000

Time (s)

Fig. 31. Comparison of heat source and heat sink for Case 2.

We start by looking at the Case 1 results. Looking at Fig. 26, the temperature of the coolant exiting the tie rod tubes decreases when the LOFA occurs. Referring to Fig. 27, the mass flow rate in the secondary system has increased while the mass flow rate in the primary system has decreased. The maximum flow rate in the secondary system has reached 40.52 kg/s. From Fig. 28, the heat sink is removing all of the heat in the heat source in response to the LOFA. The trends noted in Figs. 29–31 for Case 2 were also present in Cases 3–5. Hence, graphs from these cases have not been presented. However, the temperature drop in the tie rods is not as significant as compared to Case 1. Based on observations from both

the steady-state and transient runs, Case 1 has the minimum radiator heat transfer surface area needed to prevent the tie rod tubes from melting and to ensure a suitable natural circulation. 10. Conclusions The secondary system in the Pewee design was designed and tested using RELAP5. This secondary system keeps the moderator cool during normal operation and acts as a passive decay heat removal system in an emergency situation such as a LOFA. The design assumes the radiator consists of several tubes rather than just a single pipe. The dimensions of the tie rod tubes were left

J. Khatry et al. / Annals of Nuclear Energy 111 (2018) 536–553

unchanged, whereas the dimensions of the radiator tubes were increased. In particular, the heat transfer surface area of the radiator was increased each time. At minimum, the radiator tubes must have twice the heat transfer surface area as the tie rod tubes. This is necessary to keep the tie rod temperatures less than 1073 K (melting point of zirconium hydride) and also have a decent flow rate through the secondary system. Upon receiving the steadystate results, a LOFA transient was run by cutting off the mass flow rate of the propellant. Then, the reactor was scrammed. The results show that the secondary system can remove the decay heat. The disadvantage of the secondary system is that it decreases the specific impulse and thrust of the rocket. Acknowledgements The authors would like to thank the NASA EPSCOR Space Grant Consortium for supporting this research. In addition, the authors would like to thank the Center for Space Nuclear Research personnel for providing materials helpful to this research. References Akyuzlu, K.M., 2014. A numerical study of high temperature and high velocity gaseous hydrogen flow in a cooling channel of a nuclear thermal rocket core. In: ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, pp. 1–13). AZO Materials, 2016. Zirconium Carbide. Retrieved August 27, 2016, from AZO Materials website: http://www.azom.com/properties.aspx?ArticleID=261. Borowski, S.K., McCurdy, D.R., Packard, T.W., 2012Nuclear Thermal Propulsion (NTP): a proven growth technology for human NEO/Mars exploration missions. In: Aerospace Conference, 2012 IEEE, pp. 1–20. Borowski, S.K., McCurdy, D.R., Packard, T.W., 2009Nuclear thermal rocket/vehicle characteristics and sensitivity trades for NASA’s mars design reference architecture (DRA) 5.0 study. In: Proceedings of Nuclear and Emerging Technologies for Space. Bugby, D.C., Cepeda-Rizo, J., Rodriguez, J.I., 2011. Thermal Switching Cryogenic Heat Pipe. Georgia Institute of Technology. Christie, R.J., Plachta, D.W., 2006. Zero boil-off system design and thermal analysis of the bimodal thermal nuclear rocket. In: El-Genk, M.S. (Ed.), AIP Conference Proceedings, vol. 813(1). AIP, pp. 494–501. CIRCOR Aerospace, 2017. Check valves. Retrieved April 1, 2017, from CIRCOR Aerospace website: http://www.circoraerospace.com/products-check-valves. asp. De Grandis, S., Finzi, E., Lombardi, C., Mandelli, D., Padovani, E., Passoni, M., et al., 2004. A feasibility study of an integral PWR for space applications. In: Proceedings of the ICAPP, vol. 4. El-Genk, M.S., Tournier, J.M., 2004. Conceptual design of HP-STMCs space reactor power system for 110 kWe. In: El-Genk, M.S., Bragg, M.J. (Eds.), AIP Conference Proceedings, vol. 699(1). AIP, pp. 658–672. Elliot, J.O., Lipinski, R.J., Poston, D.I., 2003. Design concept for a nuclear reactorpowered Mars Rover. Entegris, 2013. Properties and Characteristics of Graphite. Retrieved August 27, 2016, from Entegris website: https://www.entegris.com/resources/assets/ 6205-7329-0513.pdf. Finseth, J., 1991. Overview of Rover Engine Tests. Final Report, Sverdrup Corporation for NASA MSFC.

553

Finzi, E., Lombardi, C.V., Summerer, L., 2007. An integrated PWR for planetary exploration. In: Proceedings of the ICAPP, vol. 7. Fittje, J., Schnitzler, B., 2008. Evaluation of Recent Upgrades to the NESS (Nuclear Engine System Simulation) Code. In: 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. p. 4951. Retrieved from https:// ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20090004441.pdf. Glasstone, S., Sesonske, A., 2010. Nuclear Reactor Engineering: Reactor Systems E, third ed. XanEdu Publishing Inc., pp. 78. Gunn, S., 2001. Nuclear propulsion—A historical perspective. Space Policy 17 (4), 291–298. Hall, M.L., Doster, J.M., 1986. Transient modeling of the thermohydraulic behavior of high temperature heat pipes for space reactor applications. Houts, M., 2014. Space Fission Power and Propulsion. Retrieved January 30, 2017, from NASA website: https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/ 20150002600.pdf. Houts, M., Van Dyke, M., Godfroy, T., Martin, J., Bragg-Sitton, S., Dickens, R., et al., 2003. Hardware based technology assessment in support of near-term space fission missions. In: AIP Conference Proceedings, vol. 654(1). AIP, pp. 784–789). International Atomic Energy Agency, 2005. Natural circulation in water cooled nuclear power plants (Rep. No. IAEA-TECDOC-1474). (2005). Retrieved January, 2016, from IAEA website: http://www-pub.iaea.org/MTCD/Publications/PDF/ TE_1474_web.pdf. Johnson, M., 2006. The misunderstood check valve. Valve Mag., 28–34 Kos, L., Russell, T., 2014. Nuclear cryogenic propulsion stage conceptual design & mission analysis. Retrieved August 28, 2017, from NASA website: https:// ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20140008793.pdf. Kulcinski, G.L., 1996. Nuclear power in space. Retrieved September 5, 2017, from the University of Wisconsin-Madison Nuclear Engineering and Engineering Physics website: http://fti.neep.wisc.edu/neep602/lecture25.html. Lienhard VI, J.H., Lienhard V, J.H., 2016. A Heat Transfer Textbook. Phlogiston Press, Cambridge, MA. Malloy III, J.D., 1994. U.S. Patent No. 5,329,564. U.S. Patent and Trademark Office, Washington, DC. Mock, P.R., Marcus, D.B., Edelman, E.A., 1975. Communications technology satellite: a variable conductance heat pipe application. J. Spacecraft Rockets 12 (12), 750– 753. Morley, N.J., El-Genk, M.S., 1992. Passive decay heat removal in the PeBR concept for nuclear thermal propulsion. In: AIP Conference Proceedings, vol. 246(1). AIP, pp. 955–966. NASA, 2014. Rocket Thrust Summary. Retrieved November 10, 2015, from NASA website: https://spaceflightsystems.grc.nasa.gov/education/rocket/rktthsum. html. Russon, M., 2015. NASA Cutting mars travel time in half using solar-electric engines and nuclear rockets. International Business Times. Retrieved August 27, 2016, from http://www.ibtimes.co.uk/nasa-cutting-mars-travel-time-half-usingsolar-electric-engines-nuclear-rockets-1504450. Shukla, K.N., 2015. Heat pipe for aerospace applications—An overview. J. Electron. Cooling Therm. Control 5 (01), 1. Summerer, L., Stephenson, K., 2011. Nuclear power sources: a key enabling technology for planetary exploration. Proc. Inst. Mech. Eng., Part G: J. Aerospace Eng. 225 (2), 129–143. Valcor Engineering Corporation, 2017. Aerospace check valves. Retrieved April 1, 2017, from Valcor Engineering Corporation website: http://www.valcor.com/ missiles-and-aerospace/aerospace-check-valves/. Walker, K.L., Tarau, C., Anderson, W.G., 2013. Alkali metal heat pipes for space fission power. Nuclear and Emerging Technologies for Space (NETS-2013), Albuquerque, NM. Wright, S.A., Lipinski, R.J., Pandya, T., Peters, C., (2005). Proposed design and operation of a heat pipe reactor using the Sandia National Laboratories annular core test facility and existing UZrH fuel pins. In: El-Genk, M.S., Bragg, M.J. (Eds.), AIP Conference Proceedings, vol. 746(1). AIP, pp. 449–460.