A recirculating thermoelectric generator based on

0 downloads 0 Views 737KB Size Report
resistance and radiation coefficients for thermal losses, while it is also shown that the ... electrode is observed as a function of internal source tem- .... If the efficiency of internal thermal transfer from the heater ... Q",=K,,"[21Tr,(r2 -r,)ILo](T2 -To), .... RO = 0.01 ohm .... total resistance in the circuit should be kept below 0.02 n or.
A recirculating thermoelectric generator based on sodium ~" alumina M. Sayer, M. F. Be/l,a) B. A. Judd, and S. Sherrit Department of Physics, Queen's University. Kingston, Ontario K7L 3N6, Canada

K. EI-Assal and B. Kindl A/max Industries Ltd., 61 Needham Street, Lindsay. Ontario K9V 4Z7, Canada

(Received 28 December 1988; accepted for publication 15 September 1989) A convectively cooled, recirculating thermoelectric generator based on f3" alumina has been designed and operated over the temperature range of 400-600 0c. The design employs a stainless-steel wick and flame sprayed molybdenum electrodes and the unit can be assembled and operated with ease. A full treatment of all thermal and electrical flows is given and theoretical efficiencies of 10%-15% are predicted. Critical parameters are the internal resistance and radiation coefficients for thermal losses, while it is also shown that the flow of sodium within the electrode and the geometry of the evaporating and condensing surfaces is of importance in limiting the measured efficiency to 1%-3%. Units have been operated for up to 3000 h.

I. INTRODUCTION

Thermoelectric generation using sodium ion flow through an ionic ally conducting membrane is predicted to achieve conversion efficiencies as high as 40%.1-5 Such devices have been variously termed thermoelectric generators (TEG), alkali metal thermoelectric converters (AMTEC),4 or sodium heat engines. n The highest measured efficiency has been 19% 7 All employ heat to create a sodium vapor pressure difference across a ceramic electrolyte of sodiump " alumina. This generates an open circuit voltage between inner and outer electrodes according to the Nernst equation, V"C = (R T I F) In (P I P' ),

(I)

where R is the gas constant, F the Faraday, T the temperature in K and P and P' are the sodium vapor pressures in the inner (high pressure) and outer (low pressure) compartments, respectively. Experimental devices which have been constructed to date:' 7 generally consist of a sodiump" alumina tube which is partly filled with liquid sodium. Porous metal of the area of the order of 1 cm:' is fabricated on the outside of the tube. The tube is suspended in a vacuum chamber such that a pressure difference ('ij.n be maintained between the inner and outer compartments, and the passage of sodium to the outer electrode is observed as a function of internal source temperature Tand outside (wall) temperature 7;). The system is run either until all the sodium has been transferred between the compartments, or an electromagnetic pump is employed to recirculate the liquid metal for continuous operation. Such devices are calculated to have electrode conversion efficiencies (neglecting parasitic heat losses to the structure) of from 10% to 30% at source temperatures from 400 to 1000 °C and may operate close to the Carnot efficiency. The operating voltage is from 0.3 to 1.2 V with specific output powers from 0.1 to 1.1 W Icm:' depending on load current and source temperature. Since this implies electrode current

.• , Pre'ent addres" Department of Chemistry. Concordia University, Montreal. P.Q. Canada. 832

J. Appl. Phys. 67 (2), 15 January 1990

densities of several AIcm 2 , the operation of this low voltage, high current device is critically dependent on the magnitude of electrode and electrolyte resistances and on any electrochemical potentials which develop at the interfaces. In this paper we consider the design of a simple single cell, recirculating TEG for continuous low temperature ( 600 ·C) operation. The unit is intended to be free standing and convectively cooled and is the first such TEO to be recirculated by a wick. The objective has been to fully understand the factors which must be taken into account in practical TEO design rather than to achieve the maximum possible power density and efficiency. We have also sought a reliable cell suitable for commercial development for low temperature operation from natural gas or propane heaters. Such cells would find application in cathodic protection of isolated structures, or as remote power supplies for electronic equipment. The following matters are considered: (1) Heat flow and thermal losses, (2) wick design for sodium recirculation, (3) electrode systems and dissipative losses, and (4) operating performance and temperature limits. Deviations between the predicted and observed behavior are suggested to be related to the flow of sodium within the porous metal electrode. II. CELL DESIGN

The thermoelectric generator (TEG) is shown schematically in Fig. 1. It consists ofa stainless-steel core into which heat can be introduced. A stainless-steel wick is fitted over this core to raise sodium from the liquid pool at the bottom of the device to the heated region. Sodium diffuses through an inverted sodium p " alumina tube which fits over the wickl heater and stands in the liquid sodium pool, thus separating the inner and outer compartments. A porous molybdenum electrode is fabricated by flame spraying or magnetron sputtering on the outer surface of the alumina, with the electrode being isolated from the sodium pool by 2-5 cm of uncoated alumina. The condensing wall and outer vacuum chamber is made from standard stainless-steel tubing with fingers and copper O-rings. The unit is evacuated via a valve fitted with a

0021-8979/90/020832-10$03.00

© 1990 American Institute of Physics

832

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 137.78.3.36 On: Tue, 28 Jan 2014 23:38:45

~---------------

Outer wall

f I..,.-------POSITIVE ELECTRODE

[

iB

~ t

h

nI

~lL----.,

-----l

~

,

=

~

r1

I

I I

I I

I

MESH CURRENT COLLECTOR

I

Mo ELECTRODE

I I ,I

I I

I I

__ ro_

i

r1

I

ra

I

PUMPING LINE FREEZE SEAL

~ '----,--v.:::::--,-=LGOLD O-RING

~

r

ALUMINA TUBE

MESH WICK

I,

THERMAL SHIELD

I

I I

---

"c:

1--/

Na & wick SODIUM POOL

FIG. I. Thermoelectric generator based on a recirculating wick design. The casing is stainless steel. The heat source is a cartridge heater inserted into the central core.

freeze seal and electrical connection to the porous molybdenum electrode is made through a feedthrough at the top of the device. Appropriate shields have to be fitted to prevent short circuiting of this electrode by condensed sodium metal. The dimensions, temperatures, and pressures of the various elements of the unit are defined in Fig. 2. In the initial loading, part of the sodium metal is inserted at the top of the wick inside the alumina tube to ensure full wetting of the stainless-steel mesh. Heat (at temperature T, ) is provided by a cartridge heater inserted into the central core. The outer surface cools by convection, and its temperature ( T7 ) is set by the equilibrium between heat losses to the surroundings and heat transfer across the working volume of the device. The bottom of the unit is maintained at a temperature> 100 DC to keep the sodium pool molten. III. OUTPUT VOLTAGE AND CONVERSION EFFICIENCY

The equations which determine the current-voltage relations and their dependence on pressure and temperature have been summarized by Cole4 and Hunt et al. 6 A glossary of parameters used throughout this paper is given in Table I. In the outer compartment, sodium must diffuse from the /3 " alumina through a porous metal electrode, and evaporate 833

....................•.....

J. Appl. Phys., Vol. 67, No.2, 15 January 1990

FIG. 2. Cross section of the thermoelectric generator including heat shields. The dimensions, temperature, and pressure at each surface are defined by the same subscript. The dimensions are in cm. r, = 1.18, r, = 1.20, r, = 1.30, r4 = 1.55, r, is variable, rh = 3.02, r? = 3.16.

from the outer surface. Two modifications of the Cole equations are necessary. First, a pressure drop flp across the electrode thickness is introduced. 2 •8 This term is due to the Knudsen flow of sodium atoms within the e1ectrode. 7 •9 Second, the evaporation and condensation processes at the electrode surface and the condenser wall are taking place within a cylindrical geometry and a term (Ab!A4) to account for the respective areas must be included. 10 The effective pressure P4 at the electrolyte electrode interface under load is 6

P4

=P6[(~)(~)1/2] +_I_(21TMRT

)1/2+flp, (2) 4 A4 T6 FA4 where M is the gram molecular weight of sodium and P6 is the pressure at the cold wall. Under load conditions, a reduction of output voltage 1R6 occurs due to ohmic loss in the resistance Ro of the electrolyte, electrode, and leads. Combining this with Eqs. (1) and (2), the operating voltage is given by

(3) Sayer 6tal.

833

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 137.78.3.36 On: Tue, 28 Jan 2014 23:38:45

1'0{

I A

B RI>

71,

QD Qs

Q, QU" Q, QNa Qrad

QSI'

Q'H Q

Thick SS - Multiple wick Sheath 5 x 325 mesh

W

Efficiency

Increaa!l

due to Structural

4

o

Heat Loss Reduction

~-----~------~------~----~~----~

400

500

Core

Temperature

600

(DC)

FIG. 4. The computed efficiency for various device configurations as a funct ion of the central core temperature. The racJiation and convection con,rants and the internal resistance are kept constant. The upper two graphs illustrate the df.-:ct of a change from a fivc-Iayer stainlc5s-steel wick of 325 in. 1 mesh to a single layer. The lowest curve shows the effect of thermal conduction along a central stainless-sted tube. The wall thickness of f3" alumina is 2.2 mm.

The performance of the TEG was simulated using a program which incorporated the above heat flows and operating equations. For a given core temperature, the program assigns a wall temperature and calculates the heat flows. From this total heat flow, the program then recalculates the wall temperature required to transfer the heat to the surroundings. This new wall temperature is then used to calculate new heat flows and so on until the wall temperature converges. From the final temperature distribution, the voltage and efficiency are calculated. The relative magnitudes of these transfer terms are illustrated in Figs. 5 and 6 as a function of core temperature and current, respectively. The radiative term becomes increasingly important at high temperatures making it the single most important factor affecting the efficiency of the device at all power outputs. Although minor changes in this term can be achieved by the device geometry, the dominant parameter is the radiative loss coefficient Z. In the development ofTEG devices, experiments to define, measure, and increase Z are essential. The latent heat term Q LH is important at high power outputs, Figure 7 shows the efficiency as a function of current and core temperature. A striking feature is that a temperature for maximum efficiency is observed in the range 500600 0c. This maximum arises from a more rapid increase in the outer wall temperature as the core temperature increases. In the simulation shown, the conversion efficiency is of the order of 10% at 10 A. As noted above, this is strongly affected by the structural heat loss (Fig. 4) and the radiation term (Fig. 5), while Fig. 8 shows that electrode resistance plays an important role. In the simulations shown, the internal resistance was 0.0 I n. As shown by other investigators, 4 higher efficiencies are

between the electrode and the external circuit. This lead resistance R L is part of the total circuit resistance Ro. For the evaluation of heat flow, the effective length of the copper lead resistance is d such that Q!""j = Kcu A

dT

dx

(T4 - To) = KCuA~· d .

(17)

z = 13 Ro=O.Olohm I = IDA

30

Applying the Weidemann-Franz law to the conductor K nJu = LT, where L is the Lorenz number and T = (T4 + T6)/2, then T6/2, (18 ) 10 r-~~

C. Outer condenz!n~ wall

The heat transfer through the outer chamber is regulated by conduction through the condensing wall and convection from a vertical cylinder. It may be assumed that the heat flow through the wall is rapid and the limiting flow is that due to convection in air at atmospheric pressure such that Q." =HA(T7 -293),

J. Appl. Phys., Vol. 67, No.2, 15 January 1990

Os ~_ .. _ ___

-·.C·:--:""===;:~=::t::=~~=:::c===~

400

500

Teare (,C)

800

700

(19)

where H = 5 W1m K, I.l and A is the surface area of the cylinder. 836

o

____________________~02IhL-______~

FIG. 5. Thermal transfer terms as a function of the core temperature at a fixed current of 10 A. The terms associated with mass transport (involving latent heat Q 1 " and specific heat QSI' ) change little. The major change occurs in the radiation term. Sayer et a/.

836

[This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to ] IP: 137.78.3.36 On: Tue, 28 Jan 2014 23:38:45

I

Z = 13

Orad

T,= 550 C 10

15.----

Z

~--_ _~O~s_ _

I = 10A

8 -

= 13

RO = 0.01 ohm Teore= 525C

..

-

at

QI

or.

5

-

2

I

0.001

0.1

0.01

Ro(ohms)

FIG. 6. Thermal transfer terms as a function of current for a fixed core temperature. These act to vary the temperature of the outer wall and therefore modify radiation Q"," and structural Qs terms. The major effect is on the heat transfer due to the latent heat of the working gas.

theoretically possible, particularly in multiple units. The present single cell design is the worst case for structural heat loss. V. WICK DESIGN FOR SODIUM RECIRCULATION

The TEG involves the isothermal expansion of sodium from partial pressure P2 at temperature T2 to partial pressure P6 at temperature T 6 • In the present design this pressure difference must be maintained by the wick at a distance of h = 0.15 m above the liquid sodium pool closing the end of the inverted /3 " alumina tube. At 600 ·C, P2 = 3090 Pa. The capillary pressure that is developed by a wick of capillary radius rc for a liquid of surface tension as is 14

Pc = 2aJrc N/m

2

(20)



FIG. 8. Efficiency as a function of internal resistance for a core temperature of 550"C. All other parameters are as noted in Fig. 7.

For sodium at 250 ·C, a, = 0.19 N/m, and for a stainlesssteel mesh of mesh number M" = 325 in. - I = 1.28 X 104 m - I, the capillary radius rc = ~M" = 3.91 X 10 - 5 m, leading to Pc = 9760 Pa = 73.2 Torr. The hydrostatic pressure in the column pgh = 1140 Pa = 8.52 Torr. The effective pumping pressure in the wick at 6OO·C is therefore about 5530 Pa. This is sufficient to provide the required pumping of sodium at 600 ·C, but it limits the operating temperature of a device using wick recirculation to about 670·C using a wick of this pore size. The flow of liquid sodium in a vertical wick can be described by Darcy's Law l4

KAu,(dP ), (21) 1]5 dL where q is the volumetric flow rate, K and A are the permeability and cross-sectional area of the wick, 1], andp are the viscosity and density of sodium, both of which are a function of temperature. P is the pressure difference across a wick of length L. The permeability of the wick is determined by its structure and is related to the mesh number, wire diameter, and crimping factor. This calculation is summarized in Table II. The overall result is that the flow rate for a single layer of 325 in. - I mesh of 15 cm length is 3.5 X 10- 8 m 3 /s. This corresponds to a total current of 120 A and a current density of 1.2 A/cm 2 for a 100 cm 2 electrode. This meets the design parameters. q=~--pg

Ii'

10

!38 ,.,

"

c 8

II

'u :

w

4

700 600 500