- Email: [email protected]
Preliminary design and thermal analysis of a liquid metal heat pipe radiator for TOPAZ-II power system
Annals of Nuclear Energy 97 (2016) 208–220
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Preliminary design and thermal analysis of a liquid metal heat pipe radiator for TOPAZ-II power system Wenwen Zhang, Chenglong Wang, Ronghua Chen, Wenxi Tian, Suizheng Qiu ⇑, G.H. Su School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
i n f o
Article history: Received 2 October 2015 Received in revised form 14 March 2016 Accepted 6 July 2016 Available online 21 July 2016 Keywords: TOPAZ-II power system Heat pipe radiator design Numerical analysis
a b s t r a c t An alkali metal heat pipe radiator is proposed for the Russian TOPAZ-II space reactor power system to replace the original pumped loop radiator with three advantages. First, the single point failure problem of the original radiator can be avoided. Second, because only the NaK manifold needs to be armored, the specific mass would be reduced and the reliability and survivability can be improved. Third, the heat pipe has nearly isothermal characteristics and high heat transfer capabilities. In the present paper, the high temperature heat pipes using potassium as working fluid, wire screen mesh as wick layer, made of stainless steel are adopted to remove waste heat by radiation. An integral carbon-carbon fin covering and connecting heat pipes as whole heat transfer radiator is selected for its higher thermal conductivity and lower self-weight. A detailed steady state numerical calculation using the finite element method coupled with finite difference method is performed to predict the heat rejection characteristics of the heat pipe radiator. Heat transfer performances of the new concept heat pipe radiator and the pumped loop radiator are compared with key parameters. The results show that the designed heat pipe radiator satisfies the waste heat rejection requirements of the TOPAZ-II power system under the normal operating conditions and has an ideal redundancy. The isothermal and safety of heat pipe radiator is also better than that of pumped loop radiator. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Future space transportation and planet surface power applications will require small nuclear reactors for power generation due to unavailable or limited solar power in harsh space environment. Nuclear power can serve as a compact durable energy source that can operate for a long-term. Both the United States and the Russia have developed several types of space reactor power systems, including thermionic conversion reactor, thermoelectric conversion reactor and some dynamic conversion reactors using Stirling or Brayton cycles. The Russian TOPAZ-II power system is the most technologically advanced and experienced thermionic system ever built (Bennett et al., 1996). It provides electricity by means of thermionic energy conversion and releases the waste heat by a pumped loop radiator. As shown in Fig. 1, the heat radiator is designed as the shape of a truncated cone and the surface of this cone is formed from steel coolant tubes welded to circular manifolds at the top and bottom of the radiator (Paramonov and ⇑ Corresponding author at: School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China. E-mail address: [email protected] (S. Qiu). http://dx.doi.org/10.1016/j.anucene.2016.07.007 0306-4549/Ó 2016 Elsevier Ltd. All rights reserved.
El-Genk, 1995). Radiators in orbit around the Earth are exposed to an environment of micro-meteoroids and space debris particles. Although the pumped loop radiator has a simple structure and good heat rejection performance, it has potential single point failure, which means the rupture of any radiation tube would lead to LOCA for the whole system. And for the space power system, once this accident happens, the entire system would be damaged forever for no possibility of repairing. The heat rejection system employing heat pipe technology has become the main design selection for the space power system. The growing dependency on heat pipes is due to the isothermal characteristics and high heat transfer capabilities inherent in the heat pipe concept. Another reason is the fact that each heat pipe of the radiator can be considered as an independent entity. Heat pipe failures due to environmental hazards wouldn’t mean the overall heat rejection system failure. These features show that the heat pipe radiator is typically lighter and smaller than a conventional pumped loop radiator. Several space reactor power system concepts have been developed with a liquid metal or water cooled heat pipe radiator for the waste heat rejection or the passively energy transport of the fission power generated in reactor. The American SPACE-R thermionic reactor system employs a
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
209
Nomenclature Q A h hfg M T D p
m r l
m X V f Rv Z g m U
heat power (W) area (m2) enthalpy (jkg1) latent heat (jkg1) molecular weight (mol1) temperature (K) diameter (m) pressure (Pa) specific volume (m3kg1) radius (m) length (m) specific volume (m3kg1) quality of vapor average velocity at cross-section (ms1) view factor perfect gas constant, radial position (m) axial position (m) gravitational acceleration (ms2) mass (kg) z-component of velocity (ms1)
Geek symbols q density (kgm3) c specific heat ratio r Surface tension (Wm2K4) Stefan-Boltzmann constant (Wm2K4) l viscosity (Pas)
radiator including 100 finned carbon-carbon heat pipes which uses potassium as working fluid (Von Arx et al., 1999). The thermocouple reactor system SP-100 has 12 radiator panels which is thermally coupled with the secondary coolant duct (El-Genk and Seo, 1990). The heat pipes applied for the radiator also use the potassium as working fluid. Several other conceptual designs, such as SCoRe (sectored compact reactor) system (Tournier and El-Genk, 2006), SAIRS (scalable AMTEC integrated reactor space power sys-
k e h
s t d
P
heat conductivity (Wm1K1) porosity emissivity angle (°) shear stress specific volume (m3kg1) thickness (m) nonuniform factor
Subscripts v vapor l liquid c capillary e entrainment b boiling, bubble s sonic, solid, surrounding g gravity eff effective w wick fin fin wc welded fin pw pipe wall sin inner surface sout outer surface ave average
tem) (El-Genk and Tournier, 2004a), heat pipe-segmented thermoelectric module converters (HP-STMCs) space power system (ElGenk and Tournier, 2004b), also adopt the alkali liquid metal heat pipes. Several models or codes have been developed to design or analyze the heat pipe and the heat pipe radiator. Tournier and El-Genk (1992, 1995, 2002) developed a two-dimensional heat pipe transient analysis model (HPTAM) to simulate the transient operation of fully-thawed heat pipes and the startup of heat pipes from a frozen state. A heat transfer analysis computer code HEPSPARC was developed by the NASA Lewis Research Center to analyze a radiator comprised of a pumped fluid in a transport duct that moves across the evaporator section of a heat pipe array (Hainley, 1991). NASA Glenn Research Center (GRC) developed the LERCHP code which can predict the steady state performance, including the determination of operation temperature and operation limits which might occur under specified conditions (Tower et al., 1992). Based on the design of existing space power system radiators, an alkali metal heat pipe radiator is preliminarily designed to improve the safety and heat transfer performance of the TOPAZII system. Meanwhile, using the numerical simulation method, the designed heat pipe radiator is analyzed under steady state. The model contains the heat pipe flow and heat transfer process, the fin heat transfer with radiation and conduction and a coolant transport duct calculation. The original pumped loop radiator is also modeled and calculated and the results are compared with that of the heat pipe radiator calculation.
2. Thermal design of the heat pipe radiator 2.1. Heat pipe material selection
Fig. 1. Schematics of TOPAZ-II power system and its pumped loop radiator.
Generally speaking, heat pipe mainly consists of three parts, working fluid, wick or capillary structure and container. The
210
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
optimized choices of working fluid, wick geometry and structural materials can maximize the various operation limits of the heat pipe and minimize the mass of the system. This criteria is particularly important for space applications to reduce launch cost. 2.1.1. Working fluid The first consideration is the operating temperature range. Table 1 shows the applicable temperature range of water and alkali metals which are widely used in space technology (Faghri, 2014). The operation temperature of TOPAZ-II system coolant is in the range of 700–900 K, so the potassium and cesium can both be employed for the designed heat pipe. During heat pipe design process, the working fluid with high surface tension is desirable in order to generate an ideal capillary driving force and wet the wick and container material. A high latent heat of vaporization is preferred in order to transfer enough heat with a minimum fluid flow, reaching lower pressure drop in the heat pipe. The flow resistance will be minimized by choosing working fluid with low viscosity. If the vapor pressure loss and gravitational head can be neglected, the properties of the working fluid which determine the maximum heat transport can be attributed to the figure of merit as shown follows:
M¼
ql rl hfg ll
ð1Þ
The value of M varying with temperature for some given working fluids (El-Genk and Tournier, 2011) is shown in Fig. 2. As we can see, unlike water, the curves of alkali metals are quite flat which means a wide range of applicable operating temperature that can be chosen with an ideal merit number. In addition, the table inserted in Fig. 2 presents the main properties of the two candidate metals, cesium and potassium. The merit number of potassium is much larger than that of cesium for the higher values of surface tension and latent heat and lower liquid viscosity. As a result, potassium is more preferable than cesium. The final fluid selection is also based on cost, availability, compatibility and the other factors such as thermal stability. In this paper, the potassium is preliminarily selected as the working fluid for its suitable working temperature range and higher merit number. 2.1.2. Structural materials The pipe container is used to isolate the working fluid from the outside environment. Therefore, it has to be leak-proof, maintain the pressure difference across its walls. Selection of the container material depends on several factors, such as the compatibility with working fluid, strength to weight ratio, thermal conductivity and ease of fabrication. A high strength to weight ratio is more important in space applications, and a high thermal conductivity ensures the minimum temperature drop between the heat source and the wick. The candidate materials includes titanium alloys, stainless steel, refractory metals (W, Nb, Mo), inconel et al. (Hainley, 1991). In the reference Dunn and Reay (2012), stainless steel and inconel are recommended while the titanium is not recommended
Table 1 Applicable temperature range of the heat pipe working fluids. Medium
Melting point/K
Boiling point/K
Feasible temperature range/K
Water Lithium Sodium Potassium Cesium
273 452 371 335 302
373 1613 1165 1047 943
303–473 1273–2073 873–1473 773–1273 723–1173
Fig. 2. Merit number of working fluid candidates.
for the short life time with potassium under high temperature. Meanwhile, considering that the radiator operates in a neutron irradiation from the reactor, the inconel is finally selected. The prime purpose of the wick is to generate capillary action to transport the working fluid from the condenser to the evaporator. There are two categories of the wick structure: homogeneous and composite wicks (Merrigan, 1984). Homogeneous wick is relatively simple to design and manufacture. The composite wick can significantly increase the capillary limit of the heat pipe, but high manufacturing costs are needed. As a preliminary design, the wire screen mesh wick which belongs to the homogenous structures is chosen, and stainless steel is selected as the wick material, which is commercially available and compatible with the potassium working fluid. There is no need to develop any advanced wick materials, because the wick only provides thermal features and does not need to bear any structural loads. An integral copper fin is applied in the TOPAZ-II system, but in the advanced space radiator designs, graphite-carbon composite (i.e., carbon-carbon (C-C)) technology has been developed and tested(Juhasz, 2008, 2002), and it was utilized in the SP-100 power system design. Heat pipes with carbon-carbon fins and armor are the preferred choice for these radiators for the high thermal conductivity, efficient spreading and inherent redundancy. It would further reduce the area density of spacecraft radiators (Tournier and El-Genk, 2005). As a result, the integral C-C fin is applied to improve the TOPAZ-II system radiator in this paper. 2.2. Operation limits of heat pipes Although the heat pipe has an excellent performance of heat transfer, there are a series of limitations to heat transport. The operation limits of a heat pipe, in the order of increasing power throughput and temperature, are the viscous, sonic wicking or capillary, entrainment, boiling etc. These limits are affected by the size and shape of heat pipe, working fluid, temperature and other related parameters, and they are important criteria for the design and verification of the heat pipe (Ivanovskii et al., 1982). These limits are illustrated in Fig. 3. It is necessary for the operating point to be chosen in the area lying below these curves. The actual shape of this area depends on the working fluid and wick material and varies appreciably for different heat pipes. 2.2.1. Sonic limit The heat pipe has a constant diameter and the steam accelerates due to the adding steam in the evaporation section, and decelerates for the vapor condensation in the condensation section. At a
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
211
The friction coefficient of liquid can be expressed as follows:
Fl ¼
ll
ð7Þ
KAW ql hfg
The friction coefficient of vapor has different forms of expressions under different flow conditions, as shown in Table 2. During the process of calculation, the Fv will be selected based on the Reynolds number and Maher number.
Fig. 3. Limitations to heat transport in the heat pipe.
somewhat higher temperature choking at the evaporator exit may limit the total power handling capability of the pipe. When the steam reaches the sonic velocity in the evaporation section, critical flow will occur. Changes in the condenser heat rejection rate cannot be transmitted upstream to the evaporator section. It means the further reduction in the condenser temperature and pressure will not increase the vapor flow rate, but will cause the vapor velocity to become supersonic in the condenser section. The sonic limit, is always dominant at low temperatures, should be avoided. The heat pipe sonic limit can be expressed as:
Q s;max ¼
dv ¼
Av qo hfg M v
1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cv Rv T o 1 þ cv21 M2v 1 þ cv M 2v
20Q s;max pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pqo hfg cv Rv T o
ð2Þ
ð3Þ
where, Av is the cross sectional area of vapor region, hfg is the latent heat of potassium, Mv is the molecular weight of the vapor, cv is the vapor specific heat ratio, Rv is the ideal gas constant, T o is potassium heat pipe operating temperature. 2.2.2. Capillary limit The capillary operation limit is encountered when the maximum capillary capability of the porous wick cannot overcome the combined liquid and vapor pressure losses along the heat pipe. The capillary pressure head for circulating the heat pipes working fluid will be higher if increases the liquid surface tension and decreases the radius of the liquid-vapor meniscus in the surface pores of the wick. When the capillary limits occurs, liquid cannot be pumped to the surface. Dry out will occur and the heat pipe may overheat. In order for the heat pipe to operate normally, Eq. (4) must be satisfied, namely
Dpc;max P Dpl þ Dpv þ Dpg
ð4Þ
When the capillary heat transfer limit occurs, the maximum theoretical capillary pressure can be expressed as:
Dpc;max ¼ Q c;max ðF l þ F v Þ þ Dpg
ð5Þ
where, F l is the friction coefficient of liquid, F v is the friction coefficient of vapor, DPg is the gravitational pressure drop, which is determined by the deploying planet or zero in the weightless space condition. Combing the capillary pressure and the other three pressure drops, the capillary limit can be derived. The equation is written as follow:
Q c;max ¼
2r=r c ql gdv cos h ql gl sin h ðF l þ F v Þleff
ð6Þ
2.2.3. Entrainment limit In the heat pipe, the vapor flows from the evaporator to the condenser and the condensed liquid returns through the wick structure. At the interface of the wick and vapor, the vapor exerts a shear force on the liquid in the wick. The magnitude of the shear force depends on the vapor properties and velocity. The force drives the droplets into the steam flow and transport them to the condensation section. This tendency of droplets to entrain the steam is resisted by the surface tension of the liquid. When the vapor flow at the evaporator section is chocked, the entrainment limit will encountered. Entrainment will prevent the heat pipe operating normally. The following equation gives the entrainment limiting flux as:
Q e;max ¼ Av hfg
qv r
1=2
2r w
ð8Þ
where, r is the surface tension of the liquid potassium, r w is the hydraulic radius of the capillary wick. 2.2.4. Boiling limit Boiling in wicks is a topic of considerable interest. Burnout will occur at the evaporator at high radial fluxes. A similar limit on peak radial flux will also occur at the condenser. The boiling limit will become effective only when the bubbles generated within the wick become trapped there, forming a vapor blanket. The growing bubbles block the flow of the liquid in the wick and it would cause the heat pipe to burn up. The following equation gives the boiling limiting flux:
Q b;max ¼
2ple keff T v 2r Dpc hfg qv lnðri =rv Þ r b
ð9Þ
where, le is the length of the evaporator, r b is the vaporization center radius of bubbles, DPc is the maximum capillary pressure, ri =r v is the ratio between the heat pipe diameter and the vapor cavity diameter, keff is the effective thermal conductivity and it can be expressed as:
keff ¼
kl ½ðkl þ ks Þ ð1 eÞðkl ks Þ ½ðkl þ ks Þ þ ð1 eÞðkl ks Þ
ð10Þ
2.3. Design parameters and materials of the radiator The nominal thermal power of TOPAZ-II reactor is 115 kW and the electric power is 5 kW, so about 110 kW waste heat should be rejected by the radiator. With reference to the similar radiator design, five design schemes are chosen and analyzed. The number of the heat pipes is 140, 160, 180, 200 and 220, respectively. Fig. 4 shows the design flow chart. According to the operation requirements, the working fluid and structure materials are selected firstly. Then the geometric parameters are determined by the heat transfer limits. The lower limit of vapor region is determined by the sonic limit and the thickness of the wick is determined by the capillary limit. Because the friction coefficient of vapor has different expressions under varies conditions, as shown in Table 2 previously, so the Reynolds number should be checked whether it is suitable for the equation chosen to calculate the capillary limit.
212
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220 Table 3 Design parameters and materials of radiator components. Parameter
Value design A design B design C design D design E
Number of heat pipes Average heat pipe power/W Pipe wall material Porous wick material/type Working fluid Heat pipe total length/mm Evaporator length/mm Condenser length/mm Radius of vapor space/mm Wick average porosity/mm Wick thickness/mm Pipe wall thickness/mm Heat pipe total mass/kg Fin material Fin width(average)/mm Fin thickness/mm Effective surface emissivity Fin total mass/kg Transport duct wall material Length of cross section/mm Width of cross section/mm Transport duct total mass/kg
140 160 180 786 688 611 Inconel Stainless Steel/mesh Potassium 780 720 660 130 120 110 650 600 550 8.97 8.39 7.90 0.6 0.6 0.6 0.57 0.55 0.52 1.0 1.0 1.0 73.06 71.75 68.92 Carbon-Carbon 20 20 20 0.4 0.4 0.4 0.9 0.9 0.9 3.34 3.48 3.55 Stainless steel 140 130 120 46.2 43.8 41.7 41.33 44.09 46.16
200 550
220 500
600 100 500 7.50 0.6 0.5 1.0 65.70
540 90 450 7.15 0.6 0.47 1.0 61.25
20 0.4 0.9 3.56
20 0.4 0.9 3.49
110 40.0 47.58
100 38.5 48.32
Fig. 4. The heat pipe radiator design flow chart.
Table 2 The expressions of Fv under different flow conditions. Flow condition
F v expressions
Rev 6 2300; Mv 6 0:2
Fv ¼ A
8lv 2 v rv qv hfg
Fv ¼ A
8lv 2 v rv qv hfg
Rev 6 2300; Mv > 0:2 Rev > 2300; M v 6 0:2 Rev > 2300; M v > 0:2
1=2 c 1 1 þ v2 M 2v 3=4
0:038lv 2 v rv qv hfg
F v ¼ 2A Fv ¼
0:038lv Av r2v qv hfg
2r hv Q Av hfg lv
2r v Q Av hfg lv
3=4 3=4 c 1 1 þ v2 M 2v Fig. 5. Mass and operation limit redundancy changes with the number of heat pipes.
If the Reynolds number is not in the required range, the thickness of the wick will be adjusted. The design values of the parameters is shown in Table3. As shown in Table 3, the design parameters of the five schemes are summarized. The average heat pipe power is used as the nominal design power. The C-C fins of the five radiators have the same width and thickness. The masses of heat pipe, fin and transport duct are also calculated and shown in Table 3. Fig. 5 presents the radiator mass and heat pipe operation limit redundancies of the five designs. The radiator mass here is the sum of heat pipe, fin and transport duct, not including the support frame and radiator armor. As we can see, the mass of the radiator using 160 heat pipes is maximum and declines when the heat pipe number increases. As shown in Table 3, although the mass of transport duct increases with the increasing number of heat pipes, he mass of heat pipes decreasing at the same time. The operation limit redundancy is defined as (QlimitQhp)/Qhp. The radiator average temperature is used as the reference temperature to calculated the limits. As shown in Fig. 5, both the capillary limit and the sonic limit increases with the number of heat pipes and the entrainment limit is almost stable. Based on the radiator mass and the operation
limit, it is better to choose the bigger heat pipe number. But if choose the 220 heat pipes design scheme, the diameter of the transport duct becomes too large and cannot match with the other components of the system, so the 200 heat pipes design scheme is selected. 3. Steady state analysis model of the heat pipe radiator 3.1. Mathematical models of the heat pipe radiator steady analysis Based on the design of the radiator of SPACE-R reactor power system, combined with the original TOPAZ-II radiator features, a truncated cone radiator using heat pipe is designed, as shown in Fig. 6. An annular transport duct which has a rectangular cross section is employed. The heat pipes can simply be attached to the surface of the duct or actually penetrate the duct wall. Here, we take the latter design choice for the better heat transfer capability. In this situation the pipes are coupled by forced convection with the duct fluid. The heat pipes actually penetrate the duct wall from
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
213
action causes pressure and density to decrease. As a result, the compressibility should be considered. The vapor pressure drop due to friction cannot be recovered completely in the condenser section. Therefore, the temperature distribution along the length of the heat pipe are not isothermal. Studies of the distributions of temperature, pressure, and velocity in the vapor passage are essential to predict correct heat pipe performance. Thus, compressible, one-dimensional laminar flow in the vapor passage is considered. For the purpose of formulating the mass, momentum, and energy equations in one-dimensional form, the average velocity is taken. In addition, friction at the liquid-vapor interface, and momentum and energy factors are similarly calculated. Mass, momentum and energy conservation equations are given as follows:
D
d _0 ðqVÞ ¼ m dZ
dp d F qV 2 þ ðM f qV 2 Þ ¼ dZ dZ 8D " !# ! E V2 d V2 _ 0 h0 þ 0 qV h þ f ¼m D dZ 2 2
ð12Þ ð13Þ
ð14Þ
A friction factor for the surface is written as
F¼
8sv qV 2
ð15Þ
Momentum and energy factors are expressed as
Mf ¼ Fig. 6. Structure of the designed heat pipe radiator.
Ef ¼
both the top and bottom sides with a staggered arrangement. The transport duct carries the fluid heated by the reactor core to the evaporator section of heat pipes. 3.1.1. Heat pipe container and capillary wick structure The liquid potassium in the wick structure flows very slow for the much larger density of the liquid potassium than that of vapor. In addition, the thermal conductivity of liquid sodium is large and the thickness of the wick is very thin. It is then assumed that influence of the liquid flow in the wick is negligible and the pure conduction model is applied in the wick. Therefore, heat transfer through the wick structure can be analyzed using heat conduction model. The governing equations for the container and wick heat conduction is expressed as follows:
1 @ @T i @ @T i þ ¼ 0 i ¼ 1; 2 Rki ki R @R @Z @R @Z
ð11Þ
Z
1 DV
2
1 DV 3
D
U 2 dy
ð16Þ
0
Z
D
U 3 dy
ð17Þ
0
Bankston and Smith (1972) ever did a research on the vapor flow in the heat pipe, and obtained the value of the coefficients in the above equations. Shear stress at the interface, ant the momentum and energy factors are shown in Fig. 7. During the heat pipe operation, the potassium droplet would be entrained into the vapor space. As a result, two-phase flow occurs in the vapor region and the quality of vapor is taken into account. The specific volume and the enthalpy are expressed as
t ¼ tl þ Xðtg tl Þ
ð18Þ
h ¼ hl þ X hfg
ð19Þ
The specific volume of the saturated potassium vapor can be approximately expressed as
tg ¼
Ru T PM
ð20Þ
where, the subscriptsi ¼ 1 and i ¼ 2 denote the pipe container and the capillary structure, respectively.
The Clausius-Clapyron equation is applied to obtain the relationship between temperature and pressure, which is shown as follows:
3.1.2. Vapor region During the operation of the heat pipe, the vapor zone may be free molecular, choked, and continuum flow at various times. The present work just calculates and analyzes the steady state of the heat pipe after startup, so only the continuum stage was modeled. Even though the Reynolds number depends on the geometry of the heat pipe and the actual heat transfer rate, the results cited from the reference (Bowman, 1987) show that the vapor flow in heat pipe can be assumed laminar. The vapor with small density has a very low pressure. Even for relatively small heat flux, the vapor will flow very fast, accelerating towards sonic velocity because viscous
dP hfg M dT ¼ P Ru T 2
ð21Þ
Based on Eqs. (12)–(17), Eqs. (18)–(21), the gas state equation and other constitutive equations, the following equations can be derived. These equations are solved to obtained the vapor flow characteristics in the code. The axial gradient for vapor density:
dq 1 dX q tg X q Ru T dp ¼ 2 ðtg tl Þ þ 1 hfg M dZ dZ t dZ p
ð22Þ
214
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
Fig. 7. Variations of friction, momentum and energy factors.
The axial gradient for vapor quality:
dX q t2 ¼ dZ ðtg tl ÞV 2
ðtg
("
1 V 2Xq þ Mf p
tg Rv T 1 hfg M t2
#
dp FV 2 dy 8DtMf
)
Q i4 ¼ f pw epw r
_0 2m tl Þ DV
t2
ð23Þ The axial gradient for vapor velocity:
_ 0 Vðtg tl Þ dX q VX q dV tm ¼ þ þ dZ D t dy p
tg Ru T dp 1 dZ t hfg M
ð24Þ
The axial gradient for vapor pressure: Mf m _0 VD
dp Ef ¼ dZ
h
2hfg þ
ðtg tl Þ
t
þ E1 f
i E V2 h V2 ðt t Þ F h0 h þ f2 þ 20 E1 tfg 8D gt2 l f 2 M h X t M ðt t Þ c R T E f gt2 l hp Mv Tp E f fgp q t2g 1 hRv M
ðtg tl Þ
t hfg V2
f
fg
f
FV 2 8D
li ðT 4wci T 4s Þ
phðD þ dfin Þ 360
ð360 hÞpD li ðT 4pwi T 4s Þ 360
ð27Þ
ð28Þ
where, f wc and f pw are the geometric view factors of the welded strip and the naked pipe, respectively; T wci and T pwi are the temperature of the welded strip and the naked pipe wall associated to the control volume i of the pipe. The T wci is obtained by one-dimension conduction calculation of the welded strip with a radiation boundary of the outer surface. Since the fin is very thin, the temperature distribution is assumed to be two-dimensional. In order to simplify the calculation, a quasi steady-state thermal model is developed to analyze the heat transfer of the fin. The energy balance equation of the flat strip is given as:
fg
ð25Þ
2
d T fin 2
dx
The axial gradient for vapor temperature:
dT Rv T 2 dp ¼ dZ hfg Mp dZ
Q i1 ¼ f wc ewc r
ð26Þ
3.1.3. Numerical method For the container and capillary wick of the heat pipe, the FEM (finite element method) is adopted to calculated the conduction. The one-dimensional vapor flow model is used to analyze the central vapor passage and a series of first-order differential nonlinear equations are obtained. The Runge–Kutta method is employed to solve these equations. The equations of container, wick and vapor region are solved separately. In the interface between the wickliquid and vapor, coupling is implemented. Fig. 8 shows the twodimension mesh of the heat pipe.
¼
ðf sout esout þ f sin esin ÞrðT 4fin T 4s Þ Q i2 þ Q i3 ¼ dx k dfin li kdfin
ð29Þ
Considering the symmetry of the fin between the adjacent pipes, just half of it is modeled. The finite difference method (FDM) is used to discretize the Eq. (29) and the discrete equations obtained are calculated by Newton iterative method. The schematic of fin solution is presented in Fig. 9. The number of axial control volumes equals to that of the heat pipe. The root temperature of fin is assumed to equal to the temperature of pipe wall. A nonuniform factor is defined here to present the temperature nonuniform of the integrated fin, which can be written as follows:
P¼
T max T min T av e
ð30Þ
where, T max and T min are the maximum temperature and the minimum temperature of the integrated fin, respectively; T av e is the average temperature of the fin.
3.2. Mathematical model of the carbon-carbon fin 3.3. Mathematical model of the transport duct The basic mechanism of heat transfer in the space radiator is conduction combined with radiation. A radiating element consists of a heat pipe, the carbon-carbon strip welded to it and two half part of the flat fin. For each radiating element, the radiation can also be divided into four parts: heat dissipated from the welded strip, naked part of the heat pipe wall and two surfaces of the flat carbon-carbon fin. The radiation of the welded fin and naked part of the heat wall can be estimated by
The transport duct in the middle of the radiator is designed with two entrances and two exits. It carries the fluid heated by the heat source to the evaporative section of the heat pipe. Just a quarter of the radiator is taken to be analyzed for its symmetry. One-dimensional flow and heat transfer model is established. The control volume division is shown in Fig. 10. To simplified the calculation, each five adjacent heat pipes are considered to have the same flow and heat transfer performance and only
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
215
Fig. 8. Two-dimensional mesh used to represent the heat pipe.
3.4. Mathematical model of the pumped loop radiator The TOPAZ-II radiator consists of the following elements: upper header, lower header, radiating elements and supporting frame. This radiator is shaped as a truncated cone, whose bases are formed by upper and lower headers. The headers, 24 mm outer diameter and a 1 mm thick, stainless steel wall, are connected by the radiation elements. Different from the heat pipe radiator, the radiating element of the pumped loop radiator consists of a stainless steel coolant pipe and a copper strip welded to the pipe. Considering the symmetry of this tube-fin radiator, only a quarter is analyzed, as shown in Fig. 11. To simplify the calculation, four radi-
Fig. 9. Two-dimensional mesh of the carbon-carbon fin.
one is calculated for each pipe group. Therefore, ten heat pipes are modeled, and each one represents five adjacent heat pipes of the actual radiator. The coolant temperature and the convective heat transfer coefficient are obtained by the transport duct calculation, and they are used as the evaporator convection boundary of the heat pipe. The heat pipe and fin calculation will return dissipation heat to the transport duct model as its inner heat source. The heat transfer coefficient to determine the temperature drop from the transport duct fluid to a heat pipe immersed in the fluid is determined by standard empirical relationships. The following equation is used to obtain the heat transfer coefficient of which the liquid metal flows across a heat pipe evaporator is described below (Hainley, 1991):
h ¼ ðl=lw Þ0:14 Dout ½5:0 þ 0:025ðRePrÞ0:8
ð31Þ Fig. 11. Calculating schematic of the pumped loop radiator.
Fig. 10. Control volume division of the transport duct.
216
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
ating elements are modeled, and each one represents the actual five adjacent elements. One-dimensional analysis model is established for the coolant tube and heat transfer in the copper fin is modeled by the same way in Section 3.2.
4. Radiator performance analysis 4.1. Analysis of the radiator under nominal condition Select the first heat pipe near the coolant inlet (heat pipe1) in the calculation model to analyze in detail. From the temperature contour of heat pipe shell and wick in Fig. 11, we can see that the temperature in the outer part is higher than that of inner in the evaporator and the temperature difference between the out surface of the shell and inner surface of the wick is about 5 K. In the condensing section, the temperature of the inner surface is higher than that of the outer part and the temperature difference is about 0.7 K. This difference is caused by the length difference between the condenser and evaporator. Meanwhile, as shown in Fig. 12, the condensing section has a good isothermal performance. Fig. 13 shows the variation of the vapor parameters in the pipe length direction. It can be seen that the vapor pressure, temperature and density all reduce from evaporator to condenser. The vapor pressure drop along the whole length is 25 Pa, the temperature difference is 0.6 K and the density decreases by 0.2 g/m3. Meanwhile, these variables drops fast in the evaporator section and slow in the condenser section. This is because the vapor accelerates to the maximum velocity in the evaporator section with
mass adding and slows down with mass removal in the condenser section, as shown in Fig. 17. Fig. 14 compares the temperature distributions of the heat pipe radiator fin and the pumped loop radiator fin. The left one is the former and the right one is the latter. Both are the hottest fins in the calculation models. As we can see, the temperature of heat pipe radiator fin reduces in the direction vertical to the heat pipe and has a good isothermal performance in the pipe length direction which is related to the almost constant temperature of the vapor. Meanwhile, the temperature difference between the hottest point and the coldest point is also small. The maximum temperature is 792 K while the minimum is 764 K in this fin and the temperature difference is just 28 K. But from the temperature contour of the pumped loop radiator fin, we can see that it has a much larger temperature difference. The maximum temperature is 833 K while the minimum is 735 K and the temperature difference is 98 K. The reason is that the copper fin of the pumped loop radiator is in connection with the coolant tube which has a large temperature difference between the coolant inlet and outlet. Therefore, for a single fin, the heat pipe radiator has a better isothermal performance and smaller thermal stress. Figs. 15–17 show the calculating results of a quarter of the radiator. Fig. 15 shows the variation of average temperature of the coolant, evaporator and condenser along the coolant flow direction. After extension, the coolant temperature decreases from 839 K to 740 K which coincides with the TOPAZ-II design values. So the heat pipe radiator has the same heat dissipation capability as the pumped loop radiator under the nominal condition. It also can be seen that the main heat resistance locates between the cool-
Fig. 12. Temperature distribution of the heat pipe wall and wick.
Fig. 13. Axial variation of vapor temperature, pressure and density.
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
217
Fig. 14. Temperature distribution of the fins.
Fig. 15. Average temperature variations of the coolant, evaporator and condenser in the coolant flow direction.
ant in the transport duct and outer surface of evaporator. The maximum temperature difference between them is 20 K (the coolant inlet side) and the minimum temperature difference is 13 K (the coolant outlet side). The temperature difference between the evaporator and condenser is just about 3 K. Hence, the convectional heat transfer enhancement between the coolant and the heat pipe is meaningful to improve the heat dissipation capability of radiator. Fig. 16 presents the variations of average temperature, pressure, density and velocity of the vapor along the transport duct. As we can see, the average temperatures of the working fluid in different heat pipes decrease from 809 K to 731 K. The pressures and densities also decrease following the temperature drop. But the velocities of the heat pipes increase along the transport duct. Although the powers of heat pipes reduce gradually along the coolant flow direction, the lower temperature causes reducing of the vapor density so that the vapor velocity becomes larger. Fig. 17 shows the axial distributions of vapor velocity of the selected five heat pipes. As we can see, the vapor velocity of the heat pipe near the coolant outlet is larger than that of the heat pipe
Fig. 16. Average temperature, pressure, density and velocity variations of vapor in the coolant flow direction.
218
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
Fig. 20. The comparison of the radiation powers and coolant outlet temperatures of the two radiators. Fig. 17. Axial variations of vapor velocity of different heat pipes.
Fig. 21. Fin temperature distribution. Fig. 18. The heat pipe power variation along the transport duct.
Fig. 19. Heat transfer limitation changes with the coolant inlet temperature.
Fig. 22. The maximum temperature and minimum temperature of the radiator fins.
near the inlet. In each heat pipe, the vapor velocity increases from zero to the maximum value and then decreases to zero. In the evaporator section, the vapor accelerates due to the mass adding
while in the condenser section the vapor slows down with the vapor condensing. Meanwhile, the maximum velocity of the first heat pipe reaches 42 m/s, and the maximum Mach number is about
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
Fig. 23. Temperature nonuniform factor of the integrated fins.
0.1. As a result, the power throughput of the heat pipe is still much lower than its sonic limit.
4.2. Analysis of the radiator with different coolant inlet temperatures Selecting five coolant inlet temperatures, 750 K, 800 K, 843 K, 900 K and 950 K, the heat pipe radiator was calculated to predict its heat rejection performance. Fig. 18 shows the heat throughput variation along the transport duct. As we can see, the power of the first heat pipe near coolant inlet decreases from 1030 W to 455 W while that of the last heat pipe near the outlet decreases from 629 W to 331 W. It can be seen that the magnitudes of thermal power of all the heat pipes drop to nearly half. Consequently, the coolant temperature has a great effect on the radiator heat rejection power. The sonic, capillary and entrainment limits of the potassium heat pipe near the transport duct inlet are calculated at different coolant inlet temperature, as shown in Fig. 19. As we can see, the sonic limit is the smallest at 750 K, but it rises very fast with the increasing of coolant temperature and becomes much larger than heat pipe power. As a result, at high working temperature, the sonic limit has the minimal threat to the heat pipe operation. The capillary limit keeps at a low level in different coolant temperatures. Therefore, when the heat pipe works at a high temperature, the capillary limit would be encountered first. Fig. 20 compares the radiating power and coolant outlet temperatures of pumped loop radiator and heat pipe radiator. As we can see, there is little difference between the heat rejection capabilities of the two radiators. They have almost the same heat rejection power under the nominal condition which is one of the design criteria. Because the fin of pumped loop radiator is directly connected to the coolant tube, the thermal resistance of the pumped loop radiator is smaller than that of the heat pipe radiator. As a result, when the coolant inlet temperature increases, the radiating power of the former becomes larger than that of the latter. When the radiator works at a low temperature, however, the radiating power of the heat pipe radiator becomes larger than that of the pumped loop radiator for its isothermal character. Fig. 21 shows the average fin temperature distribution of the selected heat pipes along the direction vertical to the heat pipe at different coolant inlet temperatures. As we can see, the total temperature difference of the same fin increases following the coolant temperature. For instance, the temperature difference of the heat pipe fin near the coolant entrance increases from 18 K
219
to 38 K. For each fin, the temperature gradient is larger near the root than that of the outer part. Fig. 22 compares the maximum temperature and minimum temperature of the radiator fins. As we can see, the highest temperature of pumped loop radiator fin is obviously higher than that of heat pipe radiator fin and the lowest temperature of pumped loop radiator is also slightly larger than that of heat pipe radiator. With the increasing of coolant inlet temperature, the difference becomes larger and larger. This phenomenon is also related to the thermal resistances of radiators and the heat pipe radiator has a larger thermal resistance for its complicated heat rejection process. Fig. 23 compares the temperature nonuniform factors of the two integrated fins. As we can see, the nonuniform factor of the heat pipe radiator fin is much smaller than that of the pumped loop radiator fin. And with the increasing of the coolant inlet temperature, the difference also becomes larger and larger. Therefore, it is proved that the heat pipe radiator has a better isothermal performance than the pumped loop radiator and it leads to a smaller integral thermal stress of the heat pipe radiator. 5. Conclusions In this paper, a new concept heat removal system using heat pipe radiator was proposed for the TOPAZ-II reactor power system to overcome the single point failure problem of the original pumped loop radiator. Steady-state numerical calculations were conducted to analyze the heat transfer performances of two types of radiators. Several conclusions are summarized as follows: (1) The radiator design scheme using 200 heat pipes are selected from the candidates, because of the lower mass, higher operational limit redundancies and suitable size. This heat pipe radiator has a good isothermal performance that the maximum temperature difference of a single fin is just 30 K while that of the pumped loop radiator is about 100 K. As a result, the heat pipe radiator will have a smaller thermal stress. (2) The sonic limit of the heat pipe rises fast with the temperature increase, while the capillary limit changes a little with the temperature and keeps at a low level under 2000 W. Capillary limit has a greater harm to heat pipe than sonic limit, especially at high working temperature. (3) The heat pipe radiator has a more complex heat transfer process than the pumped loop radiator. There are several thermal resistances in the heat transfer process. The thermal resistance between the coolant of duct and outer surface of evaporator is the largest.
Acknowledgements The present study is support by the National Natural Science Foundation of China (no. 11505134) and by the China Postdoctoral Science Foundation (no. 2015M572568). References Bankston, C.A., Smith, H.J., 1972. Incompressible Laminar Vapor Flow in cylindrical Heat Pipes[R]. Los Alamos Scientific Lab, N. Mex.. Bennett, G.L., Hemler, R.J., Schock, A., 1996. Space nuclear power – An overview[J]. J. Propul. Power 12 (5), 901–910. Bowman, W.J., 1987. Simulated Heat Pipe Vapor Dynamics (Ph. D. Dissertation). Air Force Institute of Technology. Dunn, P.D., Reay, D., 2012. Heat Pipes[M]. Elsevier. El-Genk, M.S., Seo, J.T., 1990. Study of the SP-100 radiator heat pipes response to external thermal exposure[J]. J. Propul. Power 6 (1), 69–77.
220
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
El-Genk, M.S., Tournier, J.M.P., 2004a. ‘‘SAIRS”-Scalable AMTEC integrated reactor space power system[J]. Prog. Nucl. Energy 45 (1), 25–69. El-Genk, M.S., Tournier, J.M., 2004b. Performance analysis of potassium heat pipes radiator for HP-STMCs space reactor power system[C]. In: AIP Conference Proceedings. IOP Institute of Physics Publishing Ltd, pp. 793–805. El-Genk, M., Tournier, J.M., 2011. Uses of Liquid-metal and water heat pipes in space reactor power systems[J]. Front. Heat Pipes (FHP) 2 (1). Faghri, A., 2014. Heat pipes: review, opportunities and challenges[J]. Front. Heat Pipes (FHP) 5 (1). Hainley, D.C., 1991. User’s manual for the heat pipe space radiator design and analysis code (HEPSPARC)[J]. Ivanovskii, M.N., Sorokin, V.P., Vagodkin, I.V., 1982. The Physical Principles of Heat Pipes[J]. Oxford University Press. Juhasz A J. Design Considerations for Lightweight Space Radiators Based on Fabrication and Test Experience With a Carbon-Carbon Composite Prototype Heat Pipe. Revised[J]. 2002. Juhasz, A.J., 2008. High conductivity carbon-carbon heat pipes for light weight space power system radiators[J]. Merrigan, M.A., 1984. Heat Pipe Technology Issues[R]. Los Alamos National Lab, NM (USA). Paramonov, D.V., El-Genk, M.S., 1995. A detailed thermal-hydraulic model of the TOPAZ-II radiator[C]. Proceedings of the 12th symposium on space nuclear power and propulsion: conference on alternative power from space; conference
on accelerator-driven transmutation technologies and applications, vol. 324(1). AIP Publishing, pp. 485–493. Tournier, J.M., El-Genk, M.S., 1992. ‘‘HPTAM” heat-pipe transient analysis model: an analysis of water heat pipes[C]. Proceedings of the ninth symposium on space nuclear power systems, vol. 246(1). AIP Publishing, pp. 1023–1037. Tournier, J.M., El-Genk, M.S., 1995. HPTAM for modeling heat and mass transfers in a heat pipe wick, during startup from a frozen state[C]. Proceedings of the 12th symposium on space nuclear power and propulsion: conference on alternative power from space; conference on accelerator-driven transmutation technologies and applications, vol. 324(1). AIP Publishing, pp. 123–134. Tournier, J.M., El-Genk, M.S., 2002. Current capabilities of ‘‘HPTAM: for modeling high temperature heat pipes’ startup from a frozen state[C]. In: AIP Conference Proceedings. IOP Institute of Physics Publishing Ltd, pp. 139–147. Tournier, J.M., El-Genk, M., 2005. Radiator heat pipes with carbon-carbon fins and armor for space nuclear reactor power systems[C]. Space Technology and Applications Int, vol. 746(1). AIP Publishing, p. 935–945. Tournier, J.M.P., El-Genk, M.S., 2006. Liquid metal loop and heat pipe radiator for space reactor power systems[J]. J. Propul. Power 22 (5), 1117–1134. Tower, L.K., Baker, K.W., Marks, T.S., 1992. NASA Lewis steady-state heat pipe code users’ manual[J]. Von, Arx, Alan, Vincent, 1999. System simulation of a multicell thermionic space power reactor[M].
Contents lists available at ScienceDirect
Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Preliminary design and thermal analysis of a liquid metal heat pipe radiator for TOPAZ-II power system Wenwen Zhang, Chenglong Wang, Ronghua Chen, Wenxi Tian, Suizheng Qiu ⇑, G.H. Su School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
a r t i c l e
i n f o
Article history: Received 2 October 2015 Received in revised form 14 March 2016 Accepted 6 July 2016 Available online 21 July 2016 Keywords: TOPAZ-II power system Heat pipe radiator design Numerical analysis
a b s t r a c t An alkali metal heat pipe radiator is proposed for the Russian TOPAZ-II space reactor power system to replace the original pumped loop radiator with three advantages. First, the single point failure problem of the original radiator can be avoided. Second, because only the NaK manifold needs to be armored, the specific mass would be reduced and the reliability and survivability can be improved. Third, the heat pipe has nearly isothermal characteristics and high heat transfer capabilities. In the present paper, the high temperature heat pipes using potassium as working fluid, wire screen mesh as wick layer, made of stainless steel are adopted to remove waste heat by radiation. An integral carbon-carbon fin covering and connecting heat pipes as whole heat transfer radiator is selected for its higher thermal conductivity and lower self-weight. A detailed steady state numerical calculation using the finite element method coupled with finite difference method is performed to predict the heat rejection characteristics of the heat pipe radiator. Heat transfer performances of the new concept heat pipe radiator and the pumped loop radiator are compared with key parameters. The results show that the designed heat pipe radiator satisfies the waste heat rejection requirements of the TOPAZ-II power system under the normal operating conditions and has an ideal redundancy. The isothermal and safety of heat pipe radiator is also better than that of pumped loop radiator. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction Future space transportation and planet surface power applications will require small nuclear reactors for power generation due to unavailable or limited solar power in harsh space environment. Nuclear power can serve as a compact durable energy source that can operate for a long-term. Both the United States and the Russia have developed several types of space reactor power systems, including thermionic conversion reactor, thermoelectric conversion reactor and some dynamic conversion reactors using Stirling or Brayton cycles. The Russian TOPAZ-II power system is the most technologically advanced and experienced thermionic system ever built (Bennett et al., 1996). It provides electricity by means of thermionic energy conversion and releases the waste heat by a pumped loop radiator. As shown in Fig. 1, the heat radiator is designed as the shape of a truncated cone and the surface of this cone is formed from steel coolant tubes welded to circular manifolds at the top and bottom of the radiator (Paramonov and ⇑ Corresponding author at: School of Nuclear Science and Technology, Xi’an Jiaotong University, Xi’an 710049, China. E-mail address: [email protected] (S. Qiu). http://dx.doi.org/10.1016/j.anucene.2016.07.007 0306-4549/Ó 2016 Elsevier Ltd. All rights reserved.
El-Genk, 1995). Radiators in orbit around the Earth are exposed to an environment of micro-meteoroids and space debris particles. Although the pumped loop radiator has a simple structure and good heat rejection performance, it has potential single point failure, which means the rupture of any radiation tube would lead to LOCA for the whole system. And for the space power system, once this accident happens, the entire system would be damaged forever for no possibility of repairing. The heat rejection system employing heat pipe technology has become the main design selection for the space power system. The growing dependency on heat pipes is due to the isothermal characteristics and high heat transfer capabilities inherent in the heat pipe concept. Another reason is the fact that each heat pipe of the radiator can be considered as an independent entity. Heat pipe failures due to environmental hazards wouldn’t mean the overall heat rejection system failure. These features show that the heat pipe radiator is typically lighter and smaller than a conventional pumped loop radiator. Several space reactor power system concepts have been developed with a liquid metal or water cooled heat pipe radiator for the waste heat rejection or the passively energy transport of the fission power generated in reactor. The American SPACE-R thermionic reactor system employs a
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
209
Nomenclature Q A h hfg M T D p
m r l
m X V f Rv Z g m U
heat power (W) area (m2) enthalpy (jkg1) latent heat (jkg1) molecular weight (mol1) temperature (K) diameter (m) pressure (Pa) specific volume (m3kg1) radius (m) length (m) specific volume (m3kg1) quality of vapor average velocity at cross-section (ms1) view factor perfect gas constant, radial position (m) axial position (m) gravitational acceleration (ms2) mass (kg) z-component of velocity (ms1)
Geek symbols q density (kgm3) c specific heat ratio r Surface tension (Wm2K4) Stefan-Boltzmann constant (Wm2K4) l viscosity (Pas)
radiator including 100 finned carbon-carbon heat pipes which uses potassium as working fluid (Von Arx et al., 1999). The thermocouple reactor system SP-100 has 12 radiator panels which is thermally coupled with the secondary coolant duct (El-Genk and Seo, 1990). The heat pipes applied for the radiator also use the potassium as working fluid. Several other conceptual designs, such as SCoRe (sectored compact reactor) system (Tournier and El-Genk, 2006), SAIRS (scalable AMTEC integrated reactor space power sys-
k e h
s t d
P
heat conductivity (Wm1K1) porosity emissivity angle (°) shear stress specific volume (m3kg1) thickness (m) nonuniform factor
Subscripts v vapor l liquid c capillary e entrainment b boiling, bubble s sonic, solid, surrounding g gravity eff effective w wick fin fin wc welded fin pw pipe wall sin inner surface sout outer surface ave average
tem) (El-Genk and Tournier, 2004a), heat pipe-segmented thermoelectric module converters (HP-STMCs) space power system (ElGenk and Tournier, 2004b), also adopt the alkali liquid metal heat pipes. Several models or codes have been developed to design or analyze the heat pipe and the heat pipe radiator. Tournier and El-Genk (1992, 1995, 2002) developed a two-dimensional heat pipe transient analysis model (HPTAM) to simulate the transient operation of fully-thawed heat pipes and the startup of heat pipes from a frozen state. A heat transfer analysis computer code HEPSPARC was developed by the NASA Lewis Research Center to analyze a radiator comprised of a pumped fluid in a transport duct that moves across the evaporator section of a heat pipe array (Hainley, 1991). NASA Glenn Research Center (GRC) developed the LERCHP code which can predict the steady state performance, including the determination of operation temperature and operation limits which might occur under specified conditions (Tower et al., 1992). Based on the design of existing space power system radiators, an alkali metal heat pipe radiator is preliminarily designed to improve the safety and heat transfer performance of the TOPAZII system. Meanwhile, using the numerical simulation method, the designed heat pipe radiator is analyzed under steady state. The model contains the heat pipe flow and heat transfer process, the fin heat transfer with radiation and conduction and a coolant transport duct calculation. The original pumped loop radiator is also modeled and calculated and the results are compared with that of the heat pipe radiator calculation.
2. Thermal design of the heat pipe radiator 2.1. Heat pipe material selection
Fig. 1. Schematics of TOPAZ-II power system and its pumped loop radiator.
Generally speaking, heat pipe mainly consists of three parts, working fluid, wick or capillary structure and container. The
210
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
optimized choices of working fluid, wick geometry and structural materials can maximize the various operation limits of the heat pipe and minimize the mass of the system. This criteria is particularly important for space applications to reduce launch cost. 2.1.1. Working fluid The first consideration is the operating temperature range. Table 1 shows the applicable temperature range of water and alkali metals which are widely used in space technology (Faghri, 2014). The operation temperature of TOPAZ-II system coolant is in the range of 700–900 K, so the potassium and cesium can both be employed for the designed heat pipe. During heat pipe design process, the working fluid with high surface tension is desirable in order to generate an ideal capillary driving force and wet the wick and container material. A high latent heat of vaporization is preferred in order to transfer enough heat with a minimum fluid flow, reaching lower pressure drop in the heat pipe. The flow resistance will be minimized by choosing working fluid with low viscosity. If the vapor pressure loss and gravitational head can be neglected, the properties of the working fluid which determine the maximum heat transport can be attributed to the figure of merit as shown follows:
M¼
ql rl hfg ll
ð1Þ
The value of M varying with temperature for some given working fluids (El-Genk and Tournier, 2011) is shown in Fig. 2. As we can see, unlike water, the curves of alkali metals are quite flat which means a wide range of applicable operating temperature that can be chosen with an ideal merit number. In addition, the table inserted in Fig. 2 presents the main properties of the two candidate metals, cesium and potassium. The merit number of potassium is much larger than that of cesium for the higher values of surface tension and latent heat and lower liquid viscosity. As a result, potassium is more preferable than cesium. The final fluid selection is also based on cost, availability, compatibility and the other factors such as thermal stability. In this paper, the potassium is preliminarily selected as the working fluid for its suitable working temperature range and higher merit number. 2.1.2. Structural materials The pipe container is used to isolate the working fluid from the outside environment. Therefore, it has to be leak-proof, maintain the pressure difference across its walls. Selection of the container material depends on several factors, such as the compatibility with working fluid, strength to weight ratio, thermal conductivity and ease of fabrication. A high strength to weight ratio is more important in space applications, and a high thermal conductivity ensures the minimum temperature drop between the heat source and the wick. The candidate materials includes titanium alloys, stainless steel, refractory metals (W, Nb, Mo), inconel et al. (Hainley, 1991). In the reference Dunn and Reay (2012), stainless steel and inconel are recommended while the titanium is not recommended
Table 1 Applicable temperature range of the heat pipe working fluids. Medium
Melting point/K
Boiling point/K
Feasible temperature range/K
Water Lithium Sodium Potassium Cesium
273 452 371 335 302
373 1613 1165 1047 943
303–473 1273–2073 873–1473 773–1273 723–1173
Fig. 2. Merit number of working fluid candidates.
for the short life time with potassium under high temperature. Meanwhile, considering that the radiator operates in a neutron irradiation from the reactor, the inconel is finally selected. The prime purpose of the wick is to generate capillary action to transport the working fluid from the condenser to the evaporator. There are two categories of the wick structure: homogeneous and composite wicks (Merrigan, 1984). Homogeneous wick is relatively simple to design and manufacture. The composite wick can significantly increase the capillary limit of the heat pipe, but high manufacturing costs are needed. As a preliminary design, the wire screen mesh wick which belongs to the homogenous structures is chosen, and stainless steel is selected as the wick material, which is commercially available and compatible with the potassium working fluid. There is no need to develop any advanced wick materials, because the wick only provides thermal features and does not need to bear any structural loads. An integral copper fin is applied in the TOPAZ-II system, but in the advanced space radiator designs, graphite-carbon composite (i.e., carbon-carbon (C-C)) technology has been developed and tested(Juhasz, 2008, 2002), and it was utilized in the SP-100 power system design. Heat pipes with carbon-carbon fins and armor are the preferred choice for these radiators for the high thermal conductivity, efficient spreading and inherent redundancy. It would further reduce the area density of spacecraft radiators (Tournier and El-Genk, 2005). As a result, the integral C-C fin is applied to improve the TOPAZ-II system radiator in this paper. 2.2. Operation limits of heat pipes Although the heat pipe has an excellent performance of heat transfer, there are a series of limitations to heat transport. The operation limits of a heat pipe, in the order of increasing power throughput and temperature, are the viscous, sonic wicking or capillary, entrainment, boiling etc. These limits are affected by the size and shape of heat pipe, working fluid, temperature and other related parameters, and they are important criteria for the design and verification of the heat pipe (Ivanovskii et al., 1982). These limits are illustrated in Fig. 3. It is necessary for the operating point to be chosen in the area lying below these curves. The actual shape of this area depends on the working fluid and wick material and varies appreciably for different heat pipes. 2.2.1. Sonic limit The heat pipe has a constant diameter and the steam accelerates due to the adding steam in the evaporation section, and decelerates for the vapor condensation in the condensation section. At a
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
211
The friction coefficient of liquid can be expressed as follows:
Fl ¼
ll
ð7Þ
KAW ql hfg
The friction coefficient of vapor has different forms of expressions under different flow conditions, as shown in Table 2. During the process of calculation, the Fv will be selected based on the Reynolds number and Maher number.
Fig. 3. Limitations to heat transport in the heat pipe.
somewhat higher temperature choking at the evaporator exit may limit the total power handling capability of the pipe. When the steam reaches the sonic velocity in the evaporation section, critical flow will occur. Changes in the condenser heat rejection rate cannot be transmitted upstream to the evaporator section. It means the further reduction in the condenser temperature and pressure will not increase the vapor flow rate, but will cause the vapor velocity to become supersonic in the condenser section. The sonic limit, is always dominant at low temperatures, should be avoided. The heat pipe sonic limit can be expressed as:
Q s;max ¼
dv ¼
Av qo hfg M v
1=2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi cv Rv T o 1 þ cv21 M2v 1 þ cv M 2v
20Q s;max pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
pqo hfg cv Rv T o
ð2Þ
ð3Þ
where, Av is the cross sectional area of vapor region, hfg is the latent heat of potassium, Mv is the molecular weight of the vapor, cv is the vapor specific heat ratio, Rv is the ideal gas constant, T o is potassium heat pipe operating temperature. 2.2.2. Capillary limit The capillary operation limit is encountered when the maximum capillary capability of the porous wick cannot overcome the combined liquid and vapor pressure losses along the heat pipe. The capillary pressure head for circulating the heat pipes working fluid will be higher if increases the liquid surface tension and decreases the radius of the liquid-vapor meniscus in the surface pores of the wick. When the capillary limits occurs, liquid cannot be pumped to the surface. Dry out will occur and the heat pipe may overheat. In order for the heat pipe to operate normally, Eq. (4) must be satisfied, namely
Dpc;max P Dpl þ Dpv þ Dpg
ð4Þ
When the capillary heat transfer limit occurs, the maximum theoretical capillary pressure can be expressed as:
Dpc;max ¼ Q c;max ðF l þ F v Þ þ Dpg
ð5Þ
where, F l is the friction coefficient of liquid, F v is the friction coefficient of vapor, DPg is the gravitational pressure drop, which is determined by the deploying planet or zero in the weightless space condition. Combing the capillary pressure and the other three pressure drops, the capillary limit can be derived. The equation is written as follow:
Q c;max ¼
2r=r c ql gdv cos h ql gl sin h ðF l þ F v Þleff
ð6Þ
2.2.3. Entrainment limit In the heat pipe, the vapor flows from the evaporator to the condenser and the condensed liquid returns through the wick structure. At the interface of the wick and vapor, the vapor exerts a shear force on the liquid in the wick. The magnitude of the shear force depends on the vapor properties and velocity. The force drives the droplets into the steam flow and transport them to the condensation section. This tendency of droplets to entrain the steam is resisted by the surface tension of the liquid. When the vapor flow at the evaporator section is chocked, the entrainment limit will encountered. Entrainment will prevent the heat pipe operating normally. The following equation gives the entrainment limiting flux as:
Q e;max ¼ Av hfg
qv r
1=2
2r w
ð8Þ
where, r is the surface tension of the liquid potassium, r w is the hydraulic radius of the capillary wick. 2.2.4. Boiling limit Boiling in wicks is a topic of considerable interest. Burnout will occur at the evaporator at high radial fluxes. A similar limit on peak radial flux will also occur at the condenser. The boiling limit will become effective only when the bubbles generated within the wick become trapped there, forming a vapor blanket. The growing bubbles block the flow of the liquid in the wick and it would cause the heat pipe to burn up. The following equation gives the boiling limiting flux:
Q b;max ¼
2ple keff T v 2r Dpc hfg qv lnðri =rv Þ r b
ð9Þ
where, le is the length of the evaporator, r b is the vaporization center radius of bubbles, DPc is the maximum capillary pressure, ri =r v is the ratio between the heat pipe diameter and the vapor cavity diameter, keff is the effective thermal conductivity and it can be expressed as:
keff ¼
kl ½ðkl þ ks Þ ð1 eÞðkl ks Þ ½ðkl þ ks Þ þ ð1 eÞðkl ks Þ
ð10Þ
2.3. Design parameters and materials of the radiator The nominal thermal power of TOPAZ-II reactor is 115 kW and the electric power is 5 kW, so about 110 kW waste heat should be rejected by the radiator. With reference to the similar radiator design, five design schemes are chosen and analyzed. The number of the heat pipes is 140, 160, 180, 200 and 220, respectively. Fig. 4 shows the design flow chart. According to the operation requirements, the working fluid and structure materials are selected firstly. Then the geometric parameters are determined by the heat transfer limits. The lower limit of vapor region is determined by the sonic limit and the thickness of the wick is determined by the capillary limit. Because the friction coefficient of vapor has different expressions under varies conditions, as shown in Table 2 previously, so the Reynolds number should be checked whether it is suitable for the equation chosen to calculate the capillary limit.
212
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220 Table 3 Design parameters and materials of radiator components. Parameter
Value design A design B design C design D design E
Number of heat pipes Average heat pipe power/W Pipe wall material Porous wick material/type Working fluid Heat pipe total length/mm Evaporator length/mm Condenser length/mm Radius of vapor space/mm Wick average porosity/mm Wick thickness/mm Pipe wall thickness/mm Heat pipe total mass/kg Fin material Fin width(average)/mm Fin thickness/mm Effective surface emissivity Fin total mass/kg Transport duct wall material Length of cross section/mm Width of cross section/mm Transport duct total mass/kg
140 160 180 786 688 611 Inconel Stainless Steel/mesh Potassium 780 720 660 130 120 110 650 600 550 8.97 8.39 7.90 0.6 0.6 0.6 0.57 0.55 0.52 1.0 1.0 1.0 73.06 71.75 68.92 Carbon-Carbon 20 20 20 0.4 0.4 0.4 0.9 0.9 0.9 3.34 3.48 3.55 Stainless steel 140 130 120 46.2 43.8 41.7 41.33 44.09 46.16
200 550
220 500
600 100 500 7.50 0.6 0.5 1.0 65.70
540 90 450 7.15 0.6 0.47 1.0 61.25
20 0.4 0.9 3.56
20 0.4 0.9 3.49
110 40.0 47.58
100 38.5 48.32
Fig. 4. The heat pipe radiator design flow chart.
Table 2 The expressions of Fv under different flow conditions. Flow condition
F v expressions
Rev 6 2300; Mv 6 0:2
Fv ¼ A
8lv 2 v rv qv hfg
Fv ¼ A
8lv 2 v rv qv hfg
Rev 6 2300; Mv > 0:2 Rev > 2300; M v 6 0:2 Rev > 2300; M v > 0:2
1=2 c 1 1 þ v2 M 2v 3=4
0:038lv 2 v rv qv hfg
F v ¼ 2A Fv ¼
0:038lv Av r2v qv hfg
2r hv Q Av hfg lv
2r v Q Av hfg lv
3=4 3=4 c 1 1 þ v2 M 2v Fig. 5. Mass and operation limit redundancy changes with the number of heat pipes.
If the Reynolds number is not in the required range, the thickness of the wick will be adjusted. The design values of the parameters is shown in Table3. As shown in Table 3, the design parameters of the five schemes are summarized. The average heat pipe power is used as the nominal design power. The C-C fins of the five radiators have the same width and thickness. The masses of heat pipe, fin and transport duct are also calculated and shown in Table 3. Fig. 5 presents the radiator mass and heat pipe operation limit redundancies of the five designs. The radiator mass here is the sum of heat pipe, fin and transport duct, not including the support frame and radiator armor. As we can see, the mass of the radiator using 160 heat pipes is maximum and declines when the heat pipe number increases. As shown in Table 3, although the mass of transport duct increases with the increasing number of heat pipes, he mass of heat pipes decreasing at the same time. The operation limit redundancy is defined as (QlimitQhp)/Qhp. The radiator average temperature is used as the reference temperature to calculated the limits. As shown in Fig. 5, both the capillary limit and the sonic limit increases with the number of heat pipes and the entrainment limit is almost stable. Based on the radiator mass and the operation
limit, it is better to choose the bigger heat pipe number. But if choose the 220 heat pipes design scheme, the diameter of the transport duct becomes too large and cannot match with the other components of the system, so the 200 heat pipes design scheme is selected. 3. Steady state analysis model of the heat pipe radiator 3.1. Mathematical models of the heat pipe radiator steady analysis Based on the design of the radiator of SPACE-R reactor power system, combined with the original TOPAZ-II radiator features, a truncated cone radiator using heat pipe is designed, as shown in Fig. 6. An annular transport duct which has a rectangular cross section is employed. The heat pipes can simply be attached to the surface of the duct or actually penetrate the duct wall. Here, we take the latter design choice for the better heat transfer capability. In this situation the pipes are coupled by forced convection with the duct fluid. The heat pipes actually penetrate the duct wall from
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
213
action causes pressure and density to decrease. As a result, the compressibility should be considered. The vapor pressure drop due to friction cannot be recovered completely in the condenser section. Therefore, the temperature distribution along the length of the heat pipe are not isothermal. Studies of the distributions of temperature, pressure, and velocity in the vapor passage are essential to predict correct heat pipe performance. Thus, compressible, one-dimensional laminar flow in the vapor passage is considered. For the purpose of formulating the mass, momentum, and energy equations in one-dimensional form, the average velocity is taken. In addition, friction at the liquid-vapor interface, and momentum and energy factors are similarly calculated. Mass, momentum and energy conservation equations are given as follows:
D
d _0 ðqVÞ ¼ m dZ
dp d F qV 2 þ ðM f qV 2 Þ ¼ dZ dZ 8D " !# ! E V2 d V2 _ 0 h0 þ 0 qV h þ f ¼m D dZ 2 2
ð12Þ ð13Þ
ð14Þ
A friction factor for the surface is written as
F¼
8sv qV 2
ð15Þ
Momentum and energy factors are expressed as
Mf ¼ Fig. 6. Structure of the designed heat pipe radiator.
Ef ¼
both the top and bottom sides with a staggered arrangement. The transport duct carries the fluid heated by the reactor core to the evaporator section of heat pipes. 3.1.1. Heat pipe container and capillary wick structure The liquid potassium in the wick structure flows very slow for the much larger density of the liquid potassium than that of vapor. In addition, the thermal conductivity of liquid sodium is large and the thickness of the wick is very thin. It is then assumed that influence of the liquid flow in the wick is negligible and the pure conduction model is applied in the wick. Therefore, heat transfer through the wick structure can be analyzed using heat conduction model. The governing equations for the container and wick heat conduction is expressed as follows:
1 @ @T i @ @T i þ ¼ 0 i ¼ 1; 2 Rki ki R @R @Z @R @Z
ð11Þ
Z
1 DV
2
1 DV 3
D
U 2 dy
ð16Þ
0
Z
D
U 3 dy
ð17Þ
0
Bankston and Smith (1972) ever did a research on the vapor flow in the heat pipe, and obtained the value of the coefficients in the above equations. Shear stress at the interface, ant the momentum and energy factors are shown in Fig. 7. During the heat pipe operation, the potassium droplet would be entrained into the vapor space. As a result, two-phase flow occurs in the vapor region and the quality of vapor is taken into account. The specific volume and the enthalpy are expressed as
t ¼ tl þ Xðtg tl Þ
ð18Þ
h ¼ hl þ X hfg
ð19Þ
The specific volume of the saturated potassium vapor can be approximately expressed as
tg ¼
Ru T PM
ð20Þ
where, the subscriptsi ¼ 1 and i ¼ 2 denote the pipe container and the capillary structure, respectively.
The Clausius-Clapyron equation is applied to obtain the relationship between temperature and pressure, which is shown as follows:
3.1.2. Vapor region During the operation of the heat pipe, the vapor zone may be free molecular, choked, and continuum flow at various times. The present work just calculates and analyzes the steady state of the heat pipe after startup, so only the continuum stage was modeled. Even though the Reynolds number depends on the geometry of the heat pipe and the actual heat transfer rate, the results cited from the reference (Bowman, 1987) show that the vapor flow in heat pipe can be assumed laminar. The vapor with small density has a very low pressure. Even for relatively small heat flux, the vapor will flow very fast, accelerating towards sonic velocity because viscous
dP hfg M dT ¼ P Ru T 2
ð21Þ
Based on Eqs. (12)–(17), Eqs. (18)–(21), the gas state equation and other constitutive equations, the following equations can be derived. These equations are solved to obtained the vapor flow characteristics in the code. The axial gradient for vapor density:
dq 1 dX q tg X q Ru T dp ¼ 2 ðtg tl Þ þ 1 hfg M dZ dZ t dZ p
ð22Þ
214
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
Fig. 7. Variations of friction, momentum and energy factors.
The axial gradient for vapor quality:
dX q t2 ¼ dZ ðtg tl ÞV 2
ðtg
("
1 V 2Xq þ Mf p
tg Rv T 1 hfg M t2
#
dp FV 2 dy 8DtMf
)
Q i4 ¼ f pw epw r
_0 2m tl Þ DV
t2
ð23Þ The axial gradient for vapor velocity:
_ 0 Vðtg tl Þ dX q VX q dV tm ¼ þ þ dZ D t dy p
tg Ru T dp 1 dZ t hfg M
ð24Þ
The axial gradient for vapor pressure: Mf m _0 VD
dp Ef ¼ dZ
h
2hfg þ
ðtg tl Þ
t
þ E1 f
i E V2 h V2 ðt t Þ F h0 h þ f2 þ 20 E1 tfg 8D gt2 l f 2 M h X t M ðt t Þ c R T E f gt2 l hp Mv Tp E f fgp q t2g 1 hRv M
ðtg tl Þ
t hfg V2
f
fg
f
FV 2 8D
li ðT 4wci T 4s Þ
phðD þ dfin Þ 360
ð360 hÞpD li ðT 4pwi T 4s Þ 360
ð27Þ
ð28Þ
where, f wc and f pw are the geometric view factors of the welded strip and the naked pipe, respectively; T wci and T pwi are the temperature of the welded strip and the naked pipe wall associated to the control volume i of the pipe. The T wci is obtained by one-dimension conduction calculation of the welded strip with a radiation boundary of the outer surface. Since the fin is very thin, the temperature distribution is assumed to be two-dimensional. In order to simplify the calculation, a quasi steady-state thermal model is developed to analyze the heat transfer of the fin. The energy balance equation of the flat strip is given as:
fg
ð25Þ
2
d T fin 2
dx
The axial gradient for vapor temperature:
dT Rv T 2 dp ¼ dZ hfg Mp dZ
Q i1 ¼ f wc ewc r
ð26Þ
3.1.3. Numerical method For the container and capillary wick of the heat pipe, the FEM (finite element method) is adopted to calculated the conduction. The one-dimensional vapor flow model is used to analyze the central vapor passage and a series of first-order differential nonlinear equations are obtained. The Runge–Kutta method is employed to solve these equations. The equations of container, wick and vapor region are solved separately. In the interface between the wickliquid and vapor, coupling is implemented. Fig. 8 shows the twodimension mesh of the heat pipe.
¼
ðf sout esout þ f sin esin ÞrðT 4fin T 4s Þ Q i2 þ Q i3 ¼ dx k dfin li kdfin
ð29Þ
Considering the symmetry of the fin between the adjacent pipes, just half of it is modeled. The finite difference method (FDM) is used to discretize the Eq. (29) and the discrete equations obtained are calculated by Newton iterative method. The schematic of fin solution is presented in Fig. 9. The number of axial control volumes equals to that of the heat pipe. The root temperature of fin is assumed to equal to the temperature of pipe wall. A nonuniform factor is defined here to present the temperature nonuniform of the integrated fin, which can be written as follows:
P¼
T max T min T av e
ð30Þ
where, T max and T min are the maximum temperature and the minimum temperature of the integrated fin, respectively; T av e is the average temperature of the fin.
3.2. Mathematical model of the carbon-carbon fin 3.3. Mathematical model of the transport duct The basic mechanism of heat transfer in the space radiator is conduction combined with radiation. A radiating element consists of a heat pipe, the carbon-carbon strip welded to it and two half part of the flat fin. For each radiating element, the radiation can also be divided into four parts: heat dissipated from the welded strip, naked part of the heat pipe wall and two surfaces of the flat carbon-carbon fin. The radiation of the welded fin and naked part of the heat wall can be estimated by
The transport duct in the middle of the radiator is designed with two entrances and two exits. It carries the fluid heated by the heat source to the evaporative section of the heat pipe. Just a quarter of the radiator is taken to be analyzed for its symmetry. One-dimensional flow and heat transfer model is established. The control volume division is shown in Fig. 10. To simplified the calculation, each five adjacent heat pipes are considered to have the same flow and heat transfer performance and only
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
215
Fig. 8. Two-dimensional mesh used to represent the heat pipe.
3.4. Mathematical model of the pumped loop radiator The TOPAZ-II radiator consists of the following elements: upper header, lower header, radiating elements and supporting frame. This radiator is shaped as a truncated cone, whose bases are formed by upper and lower headers. The headers, 24 mm outer diameter and a 1 mm thick, stainless steel wall, are connected by the radiation elements. Different from the heat pipe radiator, the radiating element of the pumped loop radiator consists of a stainless steel coolant pipe and a copper strip welded to the pipe. Considering the symmetry of this tube-fin radiator, only a quarter is analyzed, as shown in Fig. 11. To simplify the calculation, four radi-
Fig. 9. Two-dimensional mesh of the carbon-carbon fin.
one is calculated for each pipe group. Therefore, ten heat pipes are modeled, and each one represents five adjacent heat pipes of the actual radiator. The coolant temperature and the convective heat transfer coefficient are obtained by the transport duct calculation, and they are used as the evaporator convection boundary of the heat pipe. The heat pipe and fin calculation will return dissipation heat to the transport duct model as its inner heat source. The heat transfer coefficient to determine the temperature drop from the transport duct fluid to a heat pipe immersed in the fluid is determined by standard empirical relationships. The following equation is used to obtain the heat transfer coefficient of which the liquid metal flows across a heat pipe evaporator is described below (Hainley, 1991):
h ¼ ðl=lw Þ0:14 Dout ½5:0 þ 0:025ðRePrÞ0:8
ð31Þ Fig. 11. Calculating schematic of the pumped loop radiator.
Fig. 10. Control volume division of the transport duct.
216
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
ating elements are modeled, and each one represents the actual five adjacent elements. One-dimensional analysis model is established for the coolant tube and heat transfer in the copper fin is modeled by the same way in Section 3.2.
4. Radiator performance analysis 4.1. Analysis of the radiator under nominal condition Select the first heat pipe near the coolant inlet (heat pipe1) in the calculation model to analyze in detail. From the temperature contour of heat pipe shell and wick in Fig. 11, we can see that the temperature in the outer part is higher than that of inner in the evaporator and the temperature difference between the out surface of the shell and inner surface of the wick is about 5 K. In the condensing section, the temperature of the inner surface is higher than that of the outer part and the temperature difference is about 0.7 K. This difference is caused by the length difference between the condenser and evaporator. Meanwhile, as shown in Fig. 12, the condensing section has a good isothermal performance. Fig. 13 shows the variation of the vapor parameters in the pipe length direction. It can be seen that the vapor pressure, temperature and density all reduce from evaporator to condenser. The vapor pressure drop along the whole length is 25 Pa, the temperature difference is 0.6 K and the density decreases by 0.2 g/m3. Meanwhile, these variables drops fast in the evaporator section and slow in the condenser section. This is because the vapor accelerates to the maximum velocity in the evaporator section with
mass adding and slows down with mass removal in the condenser section, as shown in Fig. 17. Fig. 14 compares the temperature distributions of the heat pipe radiator fin and the pumped loop radiator fin. The left one is the former and the right one is the latter. Both are the hottest fins in the calculation models. As we can see, the temperature of heat pipe radiator fin reduces in the direction vertical to the heat pipe and has a good isothermal performance in the pipe length direction which is related to the almost constant temperature of the vapor. Meanwhile, the temperature difference between the hottest point and the coldest point is also small. The maximum temperature is 792 K while the minimum is 764 K in this fin and the temperature difference is just 28 K. But from the temperature contour of the pumped loop radiator fin, we can see that it has a much larger temperature difference. The maximum temperature is 833 K while the minimum is 735 K and the temperature difference is 98 K. The reason is that the copper fin of the pumped loop radiator is in connection with the coolant tube which has a large temperature difference between the coolant inlet and outlet. Therefore, for a single fin, the heat pipe radiator has a better isothermal performance and smaller thermal stress. Figs. 15–17 show the calculating results of a quarter of the radiator. Fig. 15 shows the variation of average temperature of the coolant, evaporator and condenser along the coolant flow direction. After extension, the coolant temperature decreases from 839 K to 740 K which coincides with the TOPAZ-II design values. So the heat pipe radiator has the same heat dissipation capability as the pumped loop radiator under the nominal condition. It also can be seen that the main heat resistance locates between the cool-
Fig. 12. Temperature distribution of the heat pipe wall and wick.
Fig. 13. Axial variation of vapor temperature, pressure and density.
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
217
Fig. 14. Temperature distribution of the fins.
Fig. 15. Average temperature variations of the coolant, evaporator and condenser in the coolant flow direction.
ant in the transport duct and outer surface of evaporator. The maximum temperature difference between them is 20 K (the coolant inlet side) and the minimum temperature difference is 13 K (the coolant outlet side). The temperature difference between the evaporator and condenser is just about 3 K. Hence, the convectional heat transfer enhancement between the coolant and the heat pipe is meaningful to improve the heat dissipation capability of radiator. Fig. 16 presents the variations of average temperature, pressure, density and velocity of the vapor along the transport duct. As we can see, the average temperatures of the working fluid in different heat pipes decrease from 809 K to 731 K. The pressures and densities also decrease following the temperature drop. But the velocities of the heat pipes increase along the transport duct. Although the powers of heat pipes reduce gradually along the coolant flow direction, the lower temperature causes reducing of the vapor density so that the vapor velocity becomes larger. Fig. 17 shows the axial distributions of vapor velocity of the selected five heat pipes. As we can see, the vapor velocity of the heat pipe near the coolant outlet is larger than that of the heat pipe
Fig. 16. Average temperature, pressure, density and velocity variations of vapor in the coolant flow direction.
218
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
Fig. 20. The comparison of the radiation powers and coolant outlet temperatures of the two radiators. Fig. 17. Axial variations of vapor velocity of different heat pipes.
Fig. 21. Fin temperature distribution. Fig. 18. The heat pipe power variation along the transport duct.
Fig. 19. Heat transfer limitation changes with the coolant inlet temperature.
Fig. 22. The maximum temperature and minimum temperature of the radiator fins.
near the inlet. In each heat pipe, the vapor velocity increases from zero to the maximum value and then decreases to zero. In the evaporator section, the vapor accelerates due to the mass adding
while in the condenser section the vapor slows down with the vapor condensing. Meanwhile, the maximum velocity of the first heat pipe reaches 42 m/s, and the maximum Mach number is about
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
Fig. 23. Temperature nonuniform factor of the integrated fins.
0.1. As a result, the power throughput of the heat pipe is still much lower than its sonic limit.
4.2. Analysis of the radiator with different coolant inlet temperatures Selecting five coolant inlet temperatures, 750 K, 800 K, 843 K, 900 K and 950 K, the heat pipe radiator was calculated to predict its heat rejection performance. Fig. 18 shows the heat throughput variation along the transport duct. As we can see, the power of the first heat pipe near coolant inlet decreases from 1030 W to 455 W while that of the last heat pipe near the outlet decreases from 629 W to 331 W. It can be seen that the magnitudes of thermal power of all the heat pipes drop to nearly half. Consequently, the coolant temperature has a great effect on the radiator heat rejection power. The sonic, capillary and entrainment limits of the potassium heat pipe near the transport duct inlet are calculated at different coolant inlet temperature, as shown in Fig. 19. As we can see, the sonic limit is the smallest at 750 K, but it rises very fast with the increasing of coolant temperature and becomes much larger than heat pipe power. As a result, at high working temperature, the sonic limit has the minimal threat to the heat pipe operation. The capillary limit keeps at a low level in different coolant temperatures. Therefore, when the heat pipe works at a high temperature, the capillary limit would be encountered first. Fig. 20 compares the radiating power and coolant outlet temperatures of pumped loop radiator and heat pipe radiator. As we can see, there is little difference between the heat rejection capabilities of the two radiators. They have almost the same heat rejection power under the nominal condition which is one of the design criteria. Because the fin of pumped loop radiator is directly connected to the coolant tube, the thermal resistance of the pumped loop radiator is smaller than that of the heat pipe radiator. As a result, when the coolant inlet temperature increases, the radiating power of the former becomes larger than that of the latter. When the radiator works at a low temperature, however, the radiating power of the heat pipe radiator becomes larger than that of the pumped loop radiator for its isothermal character. Fig. 21 shows the average fin temperature distribution of the selected heat pipes along the direction vertical to the heat pipe at different coolant inlet temperatures. As we can see, the total temperature difference of the same fin increases following the coolant temperature. For instance, the temperature difference of the heat pipe fin near the coolant entrance increases from 18 K
219
to 38 K. For each fin, the temperature gradient is larger near the root than that of the outer part. Fig. 22 compares the maximum temperature and minimum temperature of the radiator fins. As we can see, the highest temperature of pumped loop radiator fin is obviously higher than that of heat pipe radiator fin and the lowest temperature of pumped loop radiator is also slightly larger than that of heat pipe radiator. With the increasing of coolant inlet temperature, the difference becomes larger and larger. This phenomenon is also related to the thermal resistances of radiators and the heat pipe radiator has a larger thermal resistance for its complicated heat rejection process. Fig. 23 compares the temperature nonuniform factors of the two integrated fins. As we can see, the nonuniform factor of the heat pipe radiator fin is much smaller than that of the pumped loop radiator fin. And with the increasing of the coolant inlet temperature, the difference also becomes larger and larger. Therefore, it is proved that the heat pipe radiator has a better isothermal performance than the pumped loop radiator and it leads to a smaller integral thermal stress of the heat pipe radiator. 5. Conclusions In this paper, a new concept heat removal system using heat pipe radiator was proposed for the TOPAZ-II reactor power system to overcome the single point failure problem of the original pumped loop radiator. Steady-state numerical calculations were conducted to analyze the heat transfer performances of two types of radiators. Several conclusions are summarized as follows: (1) The radiator design scheme using 200 heat pipes are selected from the candidates, because of the lower mass, higher operational limit redundancies and suitable size. This heat pipe radiator has a good isothermal performance that the maximum temperature difference of a single fin is just 30 K while that of the pumped loop radiator is about 100 K. As a result, the heat pipe radiator will have a smaller thermal stress. (2) The sonic limit of the heat pipe rises fast with the temperature increase, while the capillary limit changes a little with the temperature and keeps at a low level under 2000 W. Capillary limit has a greater harm to heat pipe than sonic limit, especially at high working temperature. (3) The heat pipe radiator has a more complex heat transfer process than the pumped loop radiator. There are several thermal resistances in the heat transfer process. The thermal resistance between the coolant of duct and outer surface of evaporator is the largest.
Acknowledgements The present study is support by the National Natural Science Foundation of China (no. 11505134) and by the China Postdoctoral Science Foundation (no. 2015M572568). References Bankston, C.A., Smith, H.J., 1972. Incompressible Laminar Vapor Flow in cylindrical Heat Pipes[R]. Los Alamos Scientific Lab, N. Mex.. Bennett, G.L., Hemler, R.J., Schock, A., 1996. Space nuclear power – An overview[J]. J. Propul. Power 12 (5), 901–910. Bowman, W.J., 1987. Simulated Heat Pipe Vapor Dynamics (Ph. D. Dissertation). Air Force Institute of Technology. Dunn, P.D., Reay, D., 2012. Heat Pipes[M]. Elsevier. El-Genk, M.S., Seo, J.T., 1990. Study of the SP-100 radiator heat pipes response to external thermal exposure[J]. J. Propul. Power 6 (1), 69–77.
220
W. Zhang et al. / Annals of Nuclear Energy 97 (2016) 208–220
El-Genk, M.S., Tournier, J.M.P., 2004a. ‘‘SAIRS”-Scalable AMTEC integrated reactor space power system[J]. Prog. Nucl. Energy 45 (1), 25–69. El-Genk, M.S., Tournier, J.M., 2004b. Performance analysis of potassium heat pipes radiator for HP-STMCs space reactor power system[C]. In: AIP Conference Proceedings. IOP Institute of Physics Publishing Ltd, pp. 793–805. El-Genk, M., Tournier, J.M., 2011. Uses of Liquid-metal and water heat pipes in space reactor power systems[J]. Front. Heat Pipes (FHP) 2 (1). Faghri, A., 2014. Heat pipes: review, opportunities and challenges[J]. Front. Heat Pipes (FHP) 5 (1). Hainley, D.C., 1991. User’s manual for the heat pipe space radiator design and analysis code (HEPSPARC)[J]. Ivanovskii, M.N., Sorokin, V.P., Vagodkin, I.V., 1982. The Physical Principles of Heat Pipes[J]. Oxford University Press. Juhasz A J. Design Considerations for Lightweight Space Radiators Based on Fabrication and Test Experience With a Carbon-Carbon Composite Prototype Heat Pipe. Revised[J]. 2002. Juhasz, A.J., 2008. High conductivity carbon-carbon heat pipes for light weight space power system radiators[J]. Merrigan, M.A., 1984. Heat Pipe Technology Issues[R]. Los Alamos National Lab, NM (USA). Paramonov, D.V., El-Genk, M.S., 1995. A detailed thermal-hydraulic model of the TOPAZ-II radiator[C]. Proceedings of the 12th symposium on space nuclear power and propulsion: conference on alternative power from space; conference
on accelerator-driven transmutation technologies and applications, vol. 324(1). AIP Publishing, pp. 485–493. Tournier, J.M., El-Genk, M.S., 1992. ‘‘HPTAM” heat-pipe transient analysis model: an analysis of water heat pipes[C]. Proceedings of the ninth symposium on space nuclear power systems, vol. 246(1). AIP Publishing, pp. 1023–1037. Tournier, J.M., El-Genk, M.S., 1995. HPTAM for modeling heat and mass transfers in a heat pipe wick, during startup from a frozen state[C]. Proceedings of the 12th symposium on space nuclear power and propulsion: conference on alternative power from space; conference on accelerator-driven transmutation technologies and applications, vol. 324(1). AIP Publishing, pp. 123–134. Tournier, J.M., El-Genk, M.S., 2002. Current capabilities of ‘‘HPTAM: for modeling high temperature heat pipes’ startup from a frozen state[C]. In: AIP Conference Proceedings. IOP Institute of Physics Publishing Ltd, pp. 139–147. Tournier, J.M., El-Genk, M., 2005. Radiator heat pipes with carbon-carbon fins and armor for space nuclear reactor power systems[C]. Space Technology and Applications Int, vol. 746(1). AIP Publishing, p. 935–945. Tournier, J.M.P., El-Genk, M.S., 2006. Liquid metal loop and heat pipe radiator for space reactor power systems[J]. J. Propul. Power 22 (5), 1117–1134. Tower, L.K., Baker, K.W., Marks, T.S., 1992. NASA Lewis steady-state heat pipe code users’ manual[J]. Von, Arx, Alan, Vincent, 1999. System simulation of a multicell thermionic space power reactor[M].