Thermal Design of a Radiant Gas Heater for ... - ASME Proceedings [PDF]

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Thermal Design of a Radiant Gas Heater for Brayton Cycle Power System D. M. EVANS Analytical Group Engineer, Solar Division, International Harvester Co., San Diego, Calif. Mem. ASME

P. F. PUCCI Professor of Mechanical Engineering, U.S. Naval Postgraduate School, Monterey, Calif. Mem. ASME

The thermal design of a ground test gas heater for the NASA Brayton cycle power system is reviewed. The heater consists of a U-tube heat exchanger flowing a helium-xenon gas mixture, irradiated by a low-density pattern of tungsten filament quartz lamp heater modules, arranged to produce an exponential flux distribution along the tube axis. Choice of the correlating equation for gas-mixture forced-convection heat transfer, methods for selecting the most critical design cases with respect to flow friction and heat transfer, and the method of calculating radiant flux distribution for a particular heater module arrangement are discussed.

Contributed by the Gas Turbine Division of The American Society of Mechanical Engineers for presentation at the ASME Gas Turbine Conference & Products Show, Brussels, Belgium, May 24-28, 1970. Manuscript received at ASME Headquarters, January 19, 1970. Copies will be available until March 1, 1971.

THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS, UNITED ENGINEERING CENTER, 345 EAST 47th STREET, NEW YORK, N.Y. 10017

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Thermal Design of a Radiant Gas Heater for Brayton Cycle Power System D. M. EVANS

P. F. PUCCI

INTRODUCTION The gas heater is to be utilized in a ground test of a Brayton cycle space power system (1). 1 Functionally, the electrically powered gas heater acts as the heat source for a closed Brayton cycle gas turbine, with the working fluid a mixture of helium and xenon. The heater simulates a heat exchanger combined with either a radioactive isotope or solar energy heat source, which has been proposed for use in space. The electrically powered gas heating system is required to operate in a pressure environment range from one atmosphere to 10 8 torr. These requirements must all be achieved consistent with an allowable maximum heat exchanger surface temperature of 1700 F. Several key features characterize the gas heating system. A bundle of Utubes was chosen for the heat exchanger core geometry with a vertical plane of symmetry, allowing a maximum tube temperature consistent with structural requirements. The radiant heat source consists of a low-density pattern of water-cooled -

1

Underlined numbers in parentheses designate References at end of paper.

rectangular modules, in which an array of tungsten filament quartz lamps is mounted. Heat sources are mounted in two facing plane walls, parallel and external to the U-tube bundle plane of symmetry, on flow inlet and outlet sides. A separation wall is mounted in the U-tube bundle plane of symmetry, to provide a more uniform circumferential temperature around the tubes. The system enclosure is heavily insulated throughout, as are the feed and discharge ducts. Fig.l presents a view of the gas heating system with one of the heat source walls opened to illustrate the internal system components. SELECTION OF DESIGN CONDITIONS The various design operating cases, specified by NASA, differing in respect to gas flows, pressures and temperatures, and performance demands, were examined to determine which case dictated the final design of the heater. Pressure drop and heat-transfer requirements were considered separately. In determining the most critical flow-pres-

NOMENCLATURE A = area, sq ft C = specific heat, constant pressure, Btu/ lb - deg F M D = diameter, ft F = radiation view factor f = fanning friction factor h = coefficient of heat transfer, Btu/hrsq ft-deg F k = thermal conductivity, Btu/hr-ft-deg F L = length, ft LMTD = log mean temperature difference, deg F N = Nusselt number Nu N = Prandtl number Pr NRe = Reynolds number n = number of tubes P = pressure; area per unit length - lb F/ sq in., sq ft/ft Q = heat flow rate, Btu/hr

q(x) T t W x

= = = = =

heat flux, length basis, Btu/hr-ft temperature, deg R temperature, deg F mass flow rate, lb hr distance from entrance, ft E = gray plane emissivity temperature difference, deg F = dynamic viscosity, lb m/hr-ft

Subscripts D = g = I = i = m = o = w = x = 1 =

elemental area gas ideal inlet mean at x=0 wall flow length "x" source no. 1

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sure loss condition, the tube friction pressure drop was assumed to dominate other pressure losses associated with inlet, outlet, and tube bends. Assuming fully developed turbulent flow in circular smooth bore tubes, the friction factor, f, is (2) f= 0. 046 N

Re

- 0. 2

(1)

Assuming that the kinetic theory of gases applies, the gas viscosity is proportional to the square root of the absolute temperature. Thus, for a given gas and fixed surface geometry

AP oc W

1. 8

T

Fig.l Radiant gas heater (artist's conception)

1. 1

2

(2)

Hence, the most critical flow pressure loss case occurs when

= T - T (x) and w g

dx

+130 = 0



P

-

hP WC

hence

we obtain

0= C l e -

13x

1. 8 1. 1

W T P2

r AP 1

is a maximum.

P allowable

Applying the boundary condition that T g = Tgi at (3) x = 0, or G = G o = T w - Tgi ; then C must equal 1 G o and the temperature distribution becomes: T

-

T

(x)

w g - e -)18x (6) The most critical case, from the viewpoint T -T 0 of heat transfer, is defined as that particular w o gi combination of flow conditions and demand (duty) which dictates the largest heat exchanger. Es- From equations (5) and (6), the ideal heat flux tablishment of a figure of merit for this particu- distribution, q(x) , becomes lar set of conditions is accomplished by writing the basic energy balance and solving for the (7) q(x) 1= hP0 = hP 0 e -flx area requirement: o WC

A-

P

At

h • LMTD

(4)

Feed and discharge duct heat losses were evaluated and duty and LMTD modified to reflect the related gas temperature drops. Maximizing the log mean temperature difference, LMTD, minimizes the surface area required. A maximum LMTD is obtained by a constant wall temperature fixed at its maximum permissible value. An energy balance for an incremental length of tube, dx, yields:

dQ =q (x) 1 dx=hPdx

rr

vi

dT -T 001 =WC dxg dx (5) g p

where q(x) is the ideal heat flux per unit length, I h the convective heat-transfer coefficient, P the tube internal area per unit length, W the gas flow rate, and C. the gas specific heat. Letting:

Thus, for a constant heat-transfer coefficient, h, the ideal energy input flux is required to vary exponentially along the tube axis. The magnitude of the heat-transfer coefficient, h, also influences the surface area required by its dependence upon the operating design conditions. The choice of the correlating equation for internal forced convection was not apparent. The problem results from the fact that the gas mixture Prandtl number (0.27) is substantially less than that for normal "gas range" < 1.0) and is additionally subfluids, (0.7 < N Pr stantially greater than that required to qualify < 0.1). A as a "low Prandtl number fluid" (N Pr quote from a recent, authoritative, heat-transfer book (3) tends to illustrate the point: "Most liquid metals have Prandtl numbers in the range of 0.003 to 0.03, with no known fluids between 0.05 and 0.5." Kays (4) presents a tabulation of recommended correlations for fully developed turbulent flow in 3

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Table 1 Heater Design Summary

COMPARISON OF POSSIBLE FORCED — CONVECTION CORRELATIONS

Geometry 40; 3/4 - 0.042 inch; Inconel 600: 8.5 ft flow length

Tubes:

—

Inlet header:

4.5 inches - 0.065 wall tube: 63 inches long

Outlet header:

5.0 inches - 0.250 wall tube; 63 inches long

Inlet duct:

4.5 inches - 0.065 wall: 116 inches long; two 90 degree elbows

Outlet duct:

5.0 inches - 0.250 wall: 82 inches long: one 75 degree elbow, one 90 degree elbow and a transition

Distance of heat source plane from tube plane:

Number of heater modules:

NR. .021 NR. • 21„ • 6

inlet outlet

-

11„ 4.8 + .003

9.6 inches 14.0 inches

inlet outlet

NR. .023 N.. •" N,

15 6

R.. 11 „)--.4.-

(N

Pressure Loss

2

Core



Inlet duct

0.914 psi

Outlet duct

Design N,

0.080 psi

Inlet header

0.086 psi

0.021 psi

Outlet header



0.024 psi

/AP ducts and headers /AP heat exchanger Allowable A P NOTE: FULLY DEVELOPED TURBULENT FLOW IN CIRCULAR TUBE; CONSTANT

I

4

1

1

6



1 1.

1

8 10 -1

2

I

I

1

4

1

(Demand) (Achieve)

1 1

1

6

8 1 0

N, - PBANDTL NUMBER

Radiation losses to modules

Fig.2 Comparison of possible forced convection correlations

circular tubes, separated by the appropriate applicable range of Prandtl number for which they are valid. Apart from the range 0.1 < N < 0.5, Pr the recommended correlations are continuous in Prandtl number. A review of available literature failed to produce a recommended correlation in this range. The most logical solution to this problem is to extrapolate the bounding recommended correlations into the Prandtl number range of interest, and select the most conservative of the two at the particular point of interest. The recommended (4) bounding correlations for fully developed turbulent flow in circular tubes for the constant wall temperature case are: N Pr < O. 1 : N 0. 5 < N

Pr

Nu

= 4. 8 + O. 003 (N

< 1. 0 : N

Nu

= 0. 021 N

Pr

•N

Re

)

(8)

0 8 N 0. 6 Re

Pr

(9)

The 0.6 power exponent on Prandtl number, equation (9), is somewhat greater than normally utilized in "traditional" gas range correlations: N

Nu

= 0. 023 N

0.211 psi 1.125 psi 1.200 psi

Output:

WALL TEMPERATURE

I



Heat Balance

2—

I



0. 8 N Pr1 /3 Re

(1 0)

Equation (10) is quoted as being valid for 0.7 < N < 120, when suitably modified for temperature Pr

122,879 Btu/hr 125,600 Btu/hr 38,600 Btu/hr

Conduction losses through walls 53,200 Btu/hr Input

217,400 Btu/hr

variation in the radial direction ( t). The three correlating equations for forced convection are plotted as functions of Prandtl number in Fig.2, for two levels of Reynolds number: 10 4 and 10 5 . (Reynolds number in the final design 4 varied from about 1.0 to 2.2 x 10 for the full range of flow conditions.) Examination of Fig.2 reveals that the Kays correlation matches the "low N " correlation better than does the "traPr ditional " correlation in the range 0.1 < N 0.5. Further, since a discontinuity cannot occur at the bounding Prandtl numbers (0.1 and 0.5), the Kays correlation is the only reasonable choice. A number of possible secondary effects, which might have some influence upon the forced convection heat-transfer behavior, were examined. A modifying flow development (L/D) term was added to the correlation to account for the entry region behavior W. The effect of bends was neglected; therefore, heat transfer will actually be greater than predicted. The effect of tube roughness was found to be negligible for the tube diameters considered. A modification of the basic correlation was made to account for the radial variation of thermal and transport properties with temperature, based on the recommendations of Kays and London (2)• The final correlation for internal forced convection heat transfer was

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..



1

125



1 12.375

I

I

11.5

0

124.625

I

136.875

116.875

132.375

49,02

49.02 46.02

149.125

DISTANCE FROM MODULE PLANE TO TUBE PLANE- 14,0 IN, MODULE DIMENSIONS 12 IN, x 3. IN,

36.0

147.75

8

4 4

C

110.5

149.25

124.625

149.25

I

I

24.5 1i1

124.625

2

138.75

I

29

I

2 4

O

1 0.

I

DISTANCE FROM MODULE PLANE TO TUBE PLANE. 9.6 I.Y. 001111.1, DIMENSIONS 12 IN. x 3 111.

132.375

16.875

147.75

I I

1 I

1

6.02

61.25

Fig.3 Heater module arrangement: inlet source plane

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5 Downloaded From: https://proceedings.asmedigitalcollection.asme.org on 01/12/2019 Terms of Use: http://www.asme.org/about-asme/terms-of-use



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tAl , w

.2

n AA&

^nnn , B6A

,

7

7

14r

Fig.6 Contour map of relative radiation flux impinging upon outlet sink plane

0. 5 N

Nu

= [0. 021 N

0. 8 N 0. 6

Re Pr

_ 1. 4] 1+ L/D T

w

The espresSion for the heat-transfer coefficient, h, reduces to the following proportionality: 0.4 0.6 k C

hoc P µ 0.2

I470. 8

(12)

tions. Therefore, no compromise was required between cases, and the design was based on a single operating condition. Combining pressure drop and heat-transfer correlations, the number and length of U-tubes required was examined for a range of tube diameters, assuming a constant tube wall temperature of 1700 F. The final surface geometry was selected after an allowance for an overload margin was made. RADIATION CONSIDERATIONS

Combining this proportionality with the expression for surface area requirement, equation (4), allows selection of the most critical heat-transfer case. This calculation established that the most critical design case for heat transfer was identical to that for pressure loss in regard to flow condi-

The heater units are rectangular modules, each mounting 16 tungsten-filament, quartz tube lamps of 750-watt capacity in two rows of 8 on 1 1 /2-in. centers. The basic module was produced in sand-cast aluminum. Reflector basins were ma-

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1600

1

HEAT FLOW RATES - BTU/IIR

1200

INTEGRATED INLET SIDE INTEGRATED OUTLET SIDE INTEGRATED TOTAL DEMAND 80

92,600 33,000 125,600 122,875

- IDEAL FLUX DISTRIBUTION FLUX ABSORBED BY ANY TUBE

90 0 -

INLET SIDE N. OUTLET SIDE 20

80

100

Fig.7 Flux distribution along tube flow length

Fig.8 Gas and wall temperature distribution as function of flow length

chined, and passages were cored in the module to accommodate water cooling. The heater modules tal area A D, then the rate of energy intercepted were assumed to behave as strip (finite rectangu- by the area AD : lar plant) sources due to the close spacing of F • Q Q individual lamps, as well as the composition and (1 3) D 1D 1 wide angle of the reflectors. Selection of the U-tube bundle configuration, By the reciprocity theorem on the basis of structural requirements and the desired exponential flux distribution, produces a (14) F =F •A • 1D 1 D1 D much greater flux level requirement on the inlet side of the bundle than at the outlet. A sepathus, A rating sheet was inserted in the plane of symmetry (15) Q F • — • Q of the tube bundle to minimize flux maldistribu1 D D1 A l tion around the tube circumference. The separating sheet reduces the system to two tube banks with a The appropriate view factor, F for the speciD1 common wall. If heat transfer across the sheet is fied system is consistent with that for an eleneglected, the wall may be assumed to be a refrac- mental plane area parallel and directly below one tory (no-flux) backing surface. The radiation de- corner of a rectangular surface. sign method and data for this geometry was devel- Dividing the gray plane into elemental plane oped by Hottel W. Although reduction of the areas (points), and computing the view factors of tube pitch reduces the heat exchanger size and the total finite plane sources to the points by increases the fraction of radiant flux impinging superposition, yields the flux distribution indirectly on the tubes, manufacturing considerations pinging upon the gray plane (based on any particurestricted the minimum pitch to two diameters. lar choice of source and sink geometry, as well as The arrangement of a comparatively small number and arrangement of sources). number of heater modules to produce an acceptable A computer program was prepared to further approximation of an exponential axial and relative- develop and examine the implications derived from ly uniform longitudinal flux distribution was a these basic calculations. To obtain the clearest major problem. An equivalent gray plane was subpossible interpretation of relative flux distribustituted for the combined tube bank and backing tion in the gray plane, readouts were obtained refractory wall, in the fashion of Hottel both as a contour map and numerically, with F D, locating the gray plane in the plane of the tube the output of the computer. row. For this system of geometry (finite plane The energy absorption rates can be obtained sources parallel to a plane), radiation view facby multiplying the incident rate by the equivalent tors may be computed as a function of source geomgray plane emissivity specified by Hottel etry (strip source size, location, and orientaLetting E equal the equivalent gray plane emistion,) sink geometry (gray plane size), and sivity, we obtain for the external (radiation) source-sink plane separating distance. axial flux distribution expression: If Q is the energy rate emitted by a source 1 Q of area A and F1 is is the fraction of the energy 1 l' q (x) = 1 r (16) emitted by A l which is intercepted by the elemenA Ed a p

Q

1

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where Q1/A1 is the rate of emitted heat energy divided by the area of the module, A . Integra1 tion of the external flux distribution along a tube axis results in the energy rate absorbed by the tube, and a summation of all tubes in the bundle yields the total heat energy flow rate to the gas. In this simplified analysis, only the absorbed portion of direct radiation from the sources has been considered. The introduction of factors resulting from the effects of reflections within the enclosure tends to modify the differences in net flux along the tubes. This design may be considered conservative, in that the gray plane emissivity is high (0.85), and source-totube radiation is the dominant factor. A comparison of the heat flux distribution, q(x), was made with the ideal exponential heat flux distribution, q(x) I , required for a constant wall temperature at the maximum permissible 1700 F. Because of the excess surface area incorporated in the design, the ideal flux distribution yields an integrated heat energy rate greater than the required duty. The ideal flux distribution does, however, provide an approximate tube temperature limit line for guidance during the course of the design. Once a satisfactory external flux distribution had been established, which provided an integrate: heat flow rate equal to, or in excess of, the demand, and the distribution did not exceed the temperature limit line (ideal flux distribution), an exact axial gas and wall temperature profile was calculated from fundamental energy balance considerations. This assured compliance with the maximum wall temperature constraint. In this instance, the axial tube temperature profile is necessarily an integrated average value around the circumference. A circumferential temperature distribution analysis was made by utilizing a relative circumferential external flux distribution about the tube presented by Hottel and Sarofim (6), for a similar irradiated tube bank. This analysis revealed that apart from the "entrance region" (up to perhaps 30 percent flow length), the maximum temperature differential along the circumference is not significant, due to substantial convective resistance, which is increasing in the flow direction. In the "entrance region," the maximum circumferential temperature differential was greatly attenuated due to relatively low average tube wall temperature. FINAL DESIGN A final configuration containing 21 heater modules mounted on the inlet and outlet source

planes was obtained after an intense study of many arrangements. A summary of all pertinent design geometry and predicted performance is given in Table 1. The geometric arrangement of the modules is shown in Figs.3 and 4. The contour maps of Figs.5 and 6 display the relative intensity of flux distribution impinging upon the sink plane. In these figures, the relative level of impinging flux is identified by letter so that A > B > C, with 0 as a minimum and Z as a maximum. The incremental difference between letters is constant and continuous from 0 to Z. The average heat flux distribution along the tube axis is shown in Fig.7, which also displays the maximum flux value seen by any tube. The ideal exponential flux distribution, which implicitly represents the approximate maximum allowable tube wall temperature of 1700 F, is also seen in this figure. Fig.8 presents the axial average tube wall temperature and axial gas temperature distributions, computed from fundamental energy balance considerations, as well as the peak temperature of the tube wall facing the modules, as computed during the circumferential distribution analysis. ACKNOWLEDGMENTS The material used in this paper is based on work performed under NASA Contract NAS3-10945, with technical direction provided by Mr. W. T. Wintucky and Mr. L. W. Gertsma of NASA-Lewis Research Center. Permission to publish this paper by NASA and Solar Division of International Harvester Company is greatly appreciated. The assistance of Mr. A. Renton and Mr. P. J. Knowles of Solar, in accomplishing the thermal design of this heat exchanger, is gratefully acknowledged. REFERENCES 1 Klann, J. L., "2 to 10 Kilowatt Solar or Radioisotope Brayton Power Systems," Intersociety Energy Conversion Conference 1968 Record, IEEE document 68 C 21 - Energy, Vol. 1 of 2, pp. 407415. 2 Kays, W. M. and London, A. L., Compact Heat Exchangers, 2nd edition, McGraw-Hill, 1964, pp. 107, 88. 3 Rohsenow, W. M. and Choi, H. Y., Heat, Mass, and Momentum Transfer, PrenticeHal I, Inc., 1961, p. 191. 4 Kays, W. M., Convective Heat and Mass Transfer, McGraw-Hill, 1966, p. 173. 5 McAdams, W. H., Heat Transmission, 3rd edition, McGraw-Hill, 1954, pp. 225-226, 63-82. 6 Hottell, H. C. and Sarofim, A. F., Radiative Transfer, McGraw-Hill, 1967, p. 38.

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