Cross Flow of Water through a Tube Bank at Reynolds Numbers up to

Cross Flow of Water through a Tube Bank at Reynolds Numbers up to a Million. O. E. Dwyer, T. V. Sheehan, Joel Weisman, F. L. Horn, R. T. Schomer. Ind...
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Heat Transfer Rates 0. E. DWYER, T. V. SHEEHAN, JOEL WEISMAN’, F. L. HORN Brookhaven National Laboratory, Upton, Long Island, N. Y.

R. T. SCHOMER2 Gibbs and Cox Co., New York, N. Y.

Cross Flow of Water through a Tube Bank at Reynolds Numbers up to a Million T H E heat transfer research described here should be of interest to design and research engineers for two reasonsthe experimental conditions were new and the size of the heat transfer facility was unusually large for one designed purely for experimental purposes. The research program was carried out in order to obtain dependable design data for a heat exchanger system in a nuclear power plant. The scale of operation is indicated by the fact that the entire facility cost in the neighborhood of $150,000; required a minimum of three men to operate it; and circulated hot high pressure water at rates up to 6000 gallons/minute. 1

Present address, Westinghouse Electric

Gorp., Pittsburgh, Pa. 2

Present address, Babcock and Wilcox

Co., New York, N. Y .

I

The main purpose of this report is to present results on the measurement of average film coefficients and forced convection boiling coefficients for heat transfer from individual tubes in a staggered tube bank to cross-flowing water a t high Reynolds numbers. The primary object of the “boiling” work was to determine the amount of superheat ( t , ~- t,) required for inception of nucleate boiling at representative flow rates and water temperatures for the full scale model tube bank. Equipment limitations prevented the taking of data very far into the full surface boiling region. Pressure drop results are also reported. Most of the data were obtained in the Reynolds number range 200,000 to 1,200,000, but a few were taken below this for the purpose of “tying-in” with previously published results and correlations. Prior to this study, the upper explored limit of the Reynolds number

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was about 50,000 for flow normal to tube banks. Moreover, this is the first study of its kind where water was used as the heat transfer medium, all previous work having been done with gases or oils. The scope and conditions of the present investigation are given in Table I. I n examining this work, the reader probably will feel that there are certain gaps in the study and that there are possibly too few data in certain instances where a particular variable is under study. The authors, in recognition of this, would like to point out that the purpose of the work was to obtain performance characteristics of a prototype heat exchanger when operating under certain specified conditions rather than to make a n extensive heat transfer study. Another reason for the scarcity of the data in some instances is that the time available for the experiments was very limited because of the expiration of the

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DENOTES

POSITION OF SIX COPPER CURRENT-RETURN

PRESSURE TAPS IN TOP TUBE SHEET PRESSURE

(0

TAP IN

LOCATION OF TEST

Figure 1.

1 836

RODS

I

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MIDDLE OF LENGTH OF ROD ELEMENTS

Plan view of tube bank-numbered

INDUSTRIAL AND ENGINEERING CHEMISTRY

elements indicate the heated nickel tubes

LIQUID LEVEL CONTROLL

6"

HEATER-COOLER MEASURING SHUNTS TUBE BANK OR CAGE CURRENT RETURN CABLES

Figure 2.

Equipment flow sheet 200 H P 2 5 0 0 GPM PUMPS 75*/;' DIFFERENTIAL HEAD

~~

contractual arrangements under which the work was done. It is believed, however, that the results, obtained under very careful experimental conditions, should be of considerable interest to heat transfer engineers, particularly those concerned with the design of nuclear reactors for power purposes.

Table 1. Experimental Conditions and Scope of Investigation Tube size, o.d., inch 0.810 12 Length of tubes (vertical), inches Tube spacing Equilateral Tube pitch, inches 18/a2 (1.281) Tube pitch/diameter 1.58 Lattice size 10 tubes wide; 20 tubes deep Total No. positions tested 29 Bulk water temperature, F. 360 Static pressure, lb./sq. inch 380-410 3 Max. No. tubes heated simultaneously 0.4 Max. temperature rise of water passing through tube bank, O F. PrandtI No. V2Q/uf/h/) 0.93-0.97 30,000 to 1,200,000 Reynolds No. range 0.8 to 31 Linear velocity range, V,., ft./sec. 6000 Max.flow rate of water, gal./min.

Equipment and Expefrimental Method

The tube bank consisted of 200 elements, either tubes or dummy rods, 10

rn

SIX SOLID COPPER CURRENT RETURN RODS. SEE #FIG.2

---t

1-

DIRECTION OF CURRENT FLOW

OTENTIAL LEADS

COPPER BASE

Figure 3. Tubular test element and probe assembly

BOTTOM '

VOL. 48, NO. 10

OCTOBER 1956

1837

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Symbol

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A

: 16 1 21 24 29 I

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various fixed angles around the circumference of the tube by a revolving pin-point thermocouple probe. A drawing of the test element and probe assembly is shown in Figure 3. This procedure gave local heat transfer coefficients around the circumference of a tube. Coefficient versus angle curves are not presented here, how-ever, because it appears that the method of measuring t , ~may have resulted in some averaging of the temperatures, thereby smoothing the profile curves. All thermocouples were frequently calibrated, and temperature readings were taken every IO", 20",or 30". depending on the circumferential variation for a particular run. All the nickel tubes were accurately measured for straightness, roundness, and wall thickness. The thickness was measured within 0.0002 inch, and circumferential variation in this quantity, for a given tube, was taken into account when calculating local coefficients. Nonboiling Heat Transfer

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Calculation Procedure. In this treatment, the average heat transfer coefficient on a tube basis, h , is defined by q

Heat transfer coefficients for tubes in middle longitudinal row of tube

rows wide and 20 deep. The geometry of the tube bank, or lattice as it is often called, is described fully in Table I. Figure 1 is a plan view of the lattice. The numbered elements lvere the active ones and were made of nickel tubes having a 0.063-inch wall, while the others were carbon steel rods. The clearance between the outer tubes and the side walls was half that between the tubes or 0.236 inch. The nickel tubes were heated electrically by their own resistance with high amperage, low voltage direct current. The maximum capacity of the two power generators was 15,000 amp. at 4 volts which was enough to heat three elements simultaneously. There were no screens or straightening vanes to even out the flow pattern in the 13-inch i.d. pipeline leading to the tube bank; the top and bottom sides of the enlargement section had 4' and 16" angles with the horizontal, respectively; the straight run of pipe upstream from the tube bank was about 10 feet long, in accordance with test specifications. The experimental facility was a closed circuit comprising, in addition to the tube bank, two 3000 gallon/minute centrifugal pumps connected in parallel, a heater cooler, a 3000-gallon pumping drum, and a flowmeter. The equipment flow sheet is shown in Figure 2. The flow rate was manually controlled and measured with a sharp-edged stainless steel orifice. This orifice meter was accurately machined and installed to

1 838

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h=1.85 Position

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-

= ZA(Zw2

(1 1

tB)

where i,2 the average outside wall temperature of the tube is defined by

ASME (7) specifications. The flow rates were so high-up to 6000 gallons: minute-that it was impractical to calibrate the meter; the ASME recommendations were, however. considered quite reliable. The static pressure on the tube bank was maintained at 400 poundsjsquare inch gage to suppress any tendency for nucleate boiling which was later found to be unnecessary. This pressure was produced by a steam pressurizer located on top of the pumping drum and was automatically controlled. The liquid level in the pumping drum was also automatically controlled. The heater-cooler heat exchanger was used to bring the temperature of the water up to operating temperature during startup and then to maintain that temperature. It used steam for heating and cold water for cooling. During operation, the three heated elements supplied about 45 kw. to the water and the pumps 300. The radial heat flux from a given tube was determined by measuring the current through the tube and the voltage drop across the middle 4-inch section. The latter measurement was made with a two-point probe. As indicated by equation 18, the heat transfer coefficient was determined by measuring the total temperature difference between the inside wall temperature of the tube and the bulk water temperature ( t , ~- tis). This difference was obtained by "bucking" the two particular Chromel-Alumel thermocouples and was measured at

INDUSTRIAL A N D ENGINEERING CHEMISTRY

so""

iu2

twz

de

= -~

(2)

2T

But 2202

-

where

t B = (?=I Zwl

-

tB)

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(tu1

-

tu2)

(3)

is defined by

so""

t,l

=

L 1

dB

2T

(4)

Combining Equations 1 and 3, and then rearranging

I n the experimental study, the three heated tubes in the lattice were heated by passing direct electrical current through them; the temperature gradients through the tube ~valls were small enough to assume safely that the heatgeneration rate, under a given set of conditions and for a given tube, was uniform throughout the tube. The rate of heat generation per unit volume of tube wall, W, is given by 3.413 IE 3.142 (r2' 7i2)L

-

(6)

q = 3.413 IE

(7)

A = 6.283 rzL

(8)

W =

Moreover and The differential equation expressing

the tempexature in the tube wall as a function of radius and angle is

g the t h d conductivity of nickel to be independent of temperature and no axial vakiation of temperature. The boundary conditions to be

d

imposedare 1. No heat flow a t the inner surface,

or

2. The known temperature variation around the inside circumfessnce of th> tube, which can be e x p r e e d by a series of the form

Combining Equations 4 and 11,

The solution of Equation 9 for these boindary conditions is

IO

REYNOLDS

NUMBER

IO' ~

(13)

which for the outside wall temperature, becomes

which can be rewritten as

&here

(15) Now, combining Equations 2 and 14

pnd subtracting thisquation fromFquation 12

(17)

I n evaluating from the expuimentA data and m l a t i o g the nsults, care was takco to me what were considered the most accurate physical properties available. The thermal conductivity of the nickel waa specially measured a t the National Bureau of Standards from the same A-nickel bar stock fromwhich the tubes were made. The thenual conductivity of water was baeed on the data of b t h and Vergaftik (22)and the viscosity on the data of Sigwart (70) and Timroth (27); the density w a s obt a h c d from Keenan and Kcyes' "Thermodynamic Roperties of Steam" (72) and the bpecitic heats from the American Society of Heating and Ventilating EnginGuide, 1937. Method of Corrdation. Comlation of heat transfer data for fluids flowing normal to staggered tube banks in turbulent motion is usually done with the follbwing two equationa: iD =

%.

CPJPf

(7 (F) ) (19)

The first of thee is due to N u d t (77) while the second, obtained by dividing both sides of the first by the Reynolds number, was first w d hy Colhurn (6). For the Reynolds number range 3000 to 40,OCO, Equation 20, with a = 0.33, m = 0.6, and n = I/,, is commooly rcfemd to as the Colburn equation. In this stu+y, a single tube diameter was used, and, in addition, thm was no appreciable change in fluid properties. The data were therehre comlated by a modification of Equation 19:

Results

Langitndid Variaiion of Coefficient along Iattice. Data on six tubes in the central wrtion of the lattice are shown in Fnee tubes were all in the 6fth longitudinal row from the left-hand wall facing downsmam and in the 3 4 5th, 9th, llth, 13th, and 19th Parows. The best straight line through the p i n t s is repnaentcd by

k.

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SYMBOLS TUBE 14-0 TUBE 1 5 - n TUBE 17-A TUBE 18-0

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As the Reynolds number is increased above 75,000, the coefficients begin to deviate markedly from the line for the extrapolated Colburn (20) equation. O n the other hand, the three points below 80,000 suggest agreement with the Colburn equation. At a Reynolds number of a million, the average film coefficient was 11,500 B.t.u./(hr.) (sq ft.) ( " F.), which is more than 60% greater than that predicted by extrapolation of the Colburn equation. Within the precision of the data, it is concluded that each of the six tubes tested in the fifth longitudinal row gave the same results. Transverse Variation of Coefficient across Lattice. In moving from the central longitudinal row of tubes toward the side walls, the average coefficients, on a tube basis, were found to increase appreciably. T o study the transverse variation of the coefficient across the lattice, heat transfer measurements were made on tubes in the 5th, 9th, and 13th transverse rows, counting from the front end of the lattice. The results are shown in Figures 5, 6, and 7. In Figure 5 , where tubes 9, IO, and 11 were the Ist, 3rd, and 5th, respectively, from the left-hand wall in the third row, there is a decided increase in the coefficient in moving from the 5th or central tube to the 1st or wall tube, the increase being approximately 12y0. I n Figure 6, data are shown for four tubes in the 9th

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109

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NUMBER

Figure 6. Variation of heat transfer coefficient across tube bank at ninth transverse row

1 840

101 '

Figure 7. Heat transfer coefficients in thirteenth transverse row showing wall effect

row, where tubes 14, 15, 17, and 18 were the Ist, 3rd, 7th, and 9th tubes from the left-hand wall. Here again, a similar trend is observed-the tubes nearer the walls giving the higher coefficients. In Figure 7, tubes 22 and 24 were the first and fifth tubes in the 13th row. The points are few for tube No. 24; nevertheless, a n appreciable difference in the heat transfer capacities of the two tubes is clearly indicated. The line for the extrapolated Colburn equation is given in Figure 7 to show that, here again, the data points below R e = 80,000 indicate a line closer to 0.6 slope than one of 0.8. Figure 8 is a smoothed cross plot of the foregoing results, showing that the tubes at the side walls give coefficients that are about 15% greater than those in the central longitudinal row. The tendency for the tubes at the side walls to give higher coefficients was also observed by Snyder (20) for flow of air across a staggered tube bank a t a Reynolds number of 20,000, but the effect was not nearly as pronounced as that found in this study, where the Reynolds numbers were 5- to 50-fold greater. The higher coefficients near the wall are presumably due to the greater turbulence existing there as a result of more free space in the vicinity of the wall tubes. In the first transverse row, there was no significant difference in the heat transfer characteristics of the individual

INDUSTRIAL AND ENGINEERING CHEMISTRY

tubes across the lattice; at least any differences were within the precision of the data. These results are shown in Figure 9, where tubes 1, 2, and 3 were the Ist, 3rd; and 5th, respectively, from the left-hand side. One would not expect as great a difference in the heat transfer capacities between the wall and central tubes in the first row as in the later rows: because the flow pattern is such that the tubes behave more like single cylinders. Entrance Effect. The tubes in the first transverse row were found to behave differently in another respect. Not only did all the tubes tested in this row show the same heat transfer rates, but these rates were considerably below those for the lattice as a whole. Figure 9 shows the experimental results for the first row of tubes compared with the average curve for the whole lattice. The interesting thing about the line for the first row is that it has a slope of 0.65 compared to 0.8 for the other line; furthermore, it is well below the other line. At R e = 105, the coefficient for the first row is about 30y0 below the lattice average, while a t R e = 106, it is about 40y0 below. The data for the first row were best represented by h = 0.76 (Re)O.oj

(23)

Unfortunately, no data were taken in the second transverse row. The third row, from the limited data obtained,

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7,000 6,OOOk 5,000 4,000 I

TUBE BANK

300,000,

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2 3 4 5 6 7 8 NUMBER OF TUBES ACROSS LATTICE

IO

9

Position

Figure 8. Variation of heat transfer coefficients across tube bank in ninth transverse row (smoothed curves from cross plot of smoothed data)

t

Fiaure 9. Heat transfer rates for front row of tubes comp i r e d to those for tube bank as a whole

behaved similarly to the fifth and succeeding rows. No tubes in the fourth row were tested either. I t is presumed that the second row would give coefficients between those of the first and third rows. This is essentially what Snyder (20) found for air flowing normal to a staggered tube bank, with isoscelestriangular spacing, in the Reynolds number range 8000 to 25,000. Specifically, Snyder found that in proceeding from the first transverse row of tubes back through the lattice, the coefficient increased sharply up to the third row, then began to drop slightly in the fourth and fifth rows, finally rising slightly to a constant value from the sixth row on. This general situation also was observed previously in some data cited by Boelter and coworkers (3). Snyder found that for a given Reynolds number the coefficient for the first row was approximately 35y0 below the average for his IO-row lattice, about the same as that found in this study.

A comparison of the over-all results obtained in the present study with published results and correlations is shown in Figure 10, where the heat transfer j-factor is plotted against Reynolds number. Since most of the published results were already in the form of j factors, it was more convenient to prepare a j-factor versus Re plot rather than one of versus Reynolds number. I n Figure 10, the results of this investigation indicate that above Re = 75,000, the mechanism of heat transfer is different from that at lower Reynolds numbers. I n the range 2000 to 40,000, j always has been represented as varying as the 0.4 power of the Reynolds number. O n the other hand, above Re = 75,000, according to our results, j varied only as the 0.2 power of the Reynolds number. The over-all decrease in slope

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bank. All three curves either coincide or overlap to give a single curve from Reynolds number 10 to 40,000. The McAdams and Colburn curves are general ones for application to staggered tube banks of any geometrical arrangement. Curve A - B obtained by Bergelin is for an equilateral arrangement where P / D = 1.50. These latter experimenters, as did Pierson ( 7 8 ) and Huge ( g ) , found that the coefficient depended to a small extent on tube arrangement. The solid line is one obtained by Grimison (8) from Pierson's (78) data for an equilateral arrangement where the P / D ratio was also 1.50. This line lies just slightly above the general curve of Colburn and the specific curve of Bergelin. The long dashed curve in Figure 10 is based on the average heat transfer coefficient for the tube bank used in this work. This curve connects very well with the other curves and parallels the F F curve for single cylinders as

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105 106 REYNOLDS NUMBER

of the curve as the Reynolds number is increased is in qualitative agreement with experimental results on heat transfer for air flowing normal to a single cylinder aqd mass transfer in packed beds. With reference to the last case, the analogy between heat and mass transfer is inferred. Referring still to Figure 10, curve F F is the one obtained several years ago by McAdams (74) from experimental data of several investigators for flow of air normal to a single tube. This curve is one of continuously decreasing slope all the way up to a Reynolds number of 250,000 which was the limit of the data. Curve A - C, also recommended by McAdams (75), is for flow of fluids normal to staggered tube banks having ten or more transverse rows; curve D E was the one proposed by Colburn (6) for similar heat transfer conditions; B is one obtained by and curve A Bergelin and coworkers (7, 2) for flow of oil normal to a ten-row, staggered tube

Discussion

Symbol

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A-B CORRELATION

McADAMS FOR AIR

FLOWING NORMAL $10-2zTO SINGLE TUBES

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AVERAGE CURVE FOR

-

10.31

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Figure 10. Heat transfer factor j for cross flow of fluids through staggered tube banks (in Bergelin correlation, fluid properties were evaluated at the bulk temperature) VOL. 48, NO. 10

OCTOBER 1956

184 1

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/ ,

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LOW VELWITY.G,/

('ve-b' Figure 1 1. Plot showing qualitative off& of velocity and pressure on inception of boiling under forced conveaion do the other curves a t the lower Reynolds numbers. I n #e correlation work, the physical properties of the water were evaluated a t the averfilm temperature. As already stated, the bulk water temperature remained easentully constant in passing through the tube bank, but the tube surface temperature newssarily varied, depending on %hq beat flux and the Bow rate. Thus, for all the a m shown on the various plots, the Randtl number actually vaned slightly. The absence of tbia modulus from most of the plots would imply that this modulus was constant. It did vary, but only Slightly-hm 0.93 to 0.97. Assuming the heat t r a d e r d c i e n t varies approximately as the one third p e r of the Prandtl number, the foregoing maximum variation would account for leas than 2% change in the coefficient. Since the temperature measumnents were made in the middle of each rod where the axial temperature gradients were zero or near ZM, axial flow of heat was also zero or negligibly low. Thus, in calculating the coefficients, it was correct to assume that all the heat generated in the vicinity of the themocouples flowed radially through the tube wall. This was proved experimentally by taking readings a t short distanm above the middle of a tube which showed no decrease in the temperature drop a c m the tube wall. There was no noticeable vibration of the tube bank. I t is estimated that the heat transfer &dents presented herein are accurate within 15% and'the water flow rates W i t h i n 5%.

1842

Forced Convection Boiling H m Tmnrtn

*

Thrnretie.l COnsidera(i0as. A common lnethod of representing heat t r a d e r graphically for the nonboiling, transition. and boiling regions is to plot the'heat flu venus the t e m p e r a m drop from Nbe wall to water on logaridunic wordinates. For this study, however, the type of plot shown in Figure 11 where coefficient h is represented as the chief dependent variable, is more useful. The codficient (h) defined by dq = h t b

- re) dA

(24)

is a sensitive indication of the inception and also the d e g w of nudeate boiling. F i m 11 shows qualitatively the effects of changes in masd velocity heat flux, and static pressure on the rate of heat transfer and the phenomenon of f o m d wnvection boiling. A family of curves is shown for each of two different m888 velocities where Gr is greater than GI, ,the parameter of each family being prrsrure. The velocity lines, in this illustration, are shown merging a t very high values of h. Constant heat-flux curves also are shown. Curve ab$ is the isobar for pressure PI a t docity GL. section Pbc represents the nonboiling +on, with c representing the p i n t of boiling inception. Likewise, is the isobar for Gr a t Ps, and ijk that for GIa t P8. Since the bulk temperature is constant, the isoban in the boiling region are a h wnstant submoling lines. One way to induce boiling in forced wnvection systems h to reduce the static pressure gradually, while the heat

INWS'IUIAL AND E N O I N W CHEMISTRY

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flux, flow rate, and hulk temmraN are hcld conslant, until a prcsuk eventually is reached at which boiling CMUCS. This p i n t is indicated by an obeervablc decrease in the tube temperature conwmitant with an increase in h. Further reductions in p r r s r m would rcsult in further decreases in the tube temperature, which would indicate a funher advance into the state of boiling. For example, referring to Figure 11, if the prcmre w m in excess of PI, with a heat flux corresponding to the (q/A)z line and a m888 velocity of GI,the heat t r a d e r would be reprcwnted by point e, which would bc nonboiling. If the prrsrure were then reduced to PI, the heat t r a d e r still would be represented by point e, hut it would be on the thrrshold of boiling, for if the prrsrure were reduced any further, we would move up on the (q/A)r line into the boiling region with a corresponding higher h. Another method of inducing boiling is IO increase the heat flux while the pressure, bulk temperature, and velocity are held constant. Thus, for GI and Pa thh is shown by following the isobar from a to 8 at constant h. At p i n t u, boiling begins a t a heat flux of (q/A):. As the heat flux is increased funher, we move up along the isobar toward k with incrcadngly vigorous boiling. Both of these methods were used in tbip invcstigation. Still a third way of inducing boiling is to dcveaae the vclodty as the static pressure, bulk tcmpaature, and heat flux arc held constant. For example, in Figure 11 it is &own that at P: and ¶ / A , , b o i i g enma when the velocity is dccrcaxd h m G, to GI,or as we move along the q/A, line from point b to j. Results of Previoui Inve.tint;ona. The expeximental rraults of MEAdam and coworkers (7G)Boelterandcoworken (4, and Kreith and Summerfield (73) indicate that the heat flux for surface boiling of water under forced convection in tubes and annuli a t wnstant p r r s r w can be expressed aatisfaaorily by the empirical equation

5 = (a wnstant) (cr-

I.Y

(25)

where the exponent bhasavalueofabout 4. It is logical that the temperature potential should be the diffmnce a m the "h" separating the tube wall from the vaporization zone. This temperature difference is commonly ref e m d to as "superheat." Prcaently available data indicate h t the heat flu is not significantly affected by the hulk temperature of the flowing s e a m . For a 6xed value of (t., t.), the heat flux incwith prcsw, but the available data are not in complete agreement. McAdams and coworkers (76) found that preenwe had nnlf a small effect on heat transfa from the smaller tube in an annulus. Jena and

-

Loties ( 7 0 , using the.data of Boelter (4, showed that the heat flux varied with pressure in accordance with

5

= (a C O M t m t ) dpI'ul

(26)

for water flowing i ~ d ea 0.226-inch i.d. No. 347 stainless steel tube at constant values of 0.2 - 1.). This equation says that the heat flux a t 100 pounds/ square inch abs. is about 25% greater than'that a t 50 pounds/square inch a b . In comparison with thii, Krcith and Summefield, using a 0.587-inch i.d. stainlevl steel tube, found a 60% increax for the same p m u r e s . As far as linear velocity is concerned, ita effect on heat transfer rate in forced convection nucleate boiling had not been established definitely. At the point of incipient boiling, one would expect that the effect of velocity would be about the same as that for nonboiling, but at very vigorous boiling one would expect the Reynolds number effect to be overahadowed, if not washed out, by the strong, ebullient agitation. That is why the two velocity curves, at the same pressure, were made to converge with increase in (f,s - fa) in Figure 11. The superheat (tm2 - t,) required to initiate boiling increases with velocity. Clark and Rohvnow (5) have postulated that, under conditions of forced convection boiling heat t r a d e r , the total heat flux consists nf a contribution from the convection effect and one from the boiling effect, or that

.

They suggest evaluating (q/A)-" by the usual relationships for forced convection nonboiling flow, recognizing that it m a y not be quite proper to do w becauee the normal flow pattern is upset by the ebullition. The quantity, (q/A)btt, from the foregoing equation was successlully correlatedwith the pertinent variables by

mately all Reynolds numbera, which was genaaUy true for all tubes tested. This means that the surface temperahre of the tube a t this angle would be the bighest, and therefore it was believed that boiling would occur first a t this point on the tube circumference. Although local low presure in the neighborhood of 90°, due to increased velocity at that angle, would tend to move the point where boiling first occurred nearer the stagnation point, it was estimated that this pnssure &ect should be minor. Consequently, much of the boiling data were taken at the 155' angle. However, wme data also were taken a t various other angles around the tube circumference to determine heat t r a d e r characteristics for the tube as a whole. Although Equatinn 24 strictly pertains to the nonboiling range, it was uscd in this study for the transition and boiling reginns as well, for RWM mentioned earlier. I t already haa been stated that the hcginning of boilLtg was detected hy a fall in tu,. From Equation

where C,/isaconstantwhichischaracteristic of the surface-fluid system. From this equation (q/A)b,t varies as the cube of the superheat. The equation indicaten that, keeping the superheat constant, increasing the preaaure from 50 to 100 pounds/square inch a b . for water would increase the flux by about loyo. This treamsent does not aUnw for the paasibility that the (q/A)-, contribution to the total heat flux decreases as the degrcz of boiling increases, although it obviously contributes la9 to (q/A)-l as (q/A/A)boltincreases. Smpe of E.perimentd Work. The tube a t lattice position 16, which wan in the c e n w of the lattice, wan c h m n for m t of the boiling runs. The location of this tube is shown in Figure 4. The minimum local h for this tube occurred in the neighborhood of 155O for approxi-

24, it is dear that this was accompanied hy z'dmultanmus inmasc in h, since q/A and r, were held constant. Result. a t 155' An&. Three runs, IWA, 119A, and 120& were made to determine the incept& of boiling. The experimental d t s for run 118A are shown in Fgurt 12. In this run, boiling wan i n d u d by increasing the heat flux gradually, while p m , velocity, and bulk t e m p e r a m were held constant. The p m was held a t 160 2 pounds/squarc inch gage, the Reynolds n w n k was 935,000, and the bulk water temperature was 360° F. At 160 pounds/squarc inch gage, the nonboilkig h was 9550 B.t.u./hr.-aq. ft.-O F. Boiling began in the vicinity of a flux of 300,000, and further increme8 in heat flux pmdnced mom vigorous boiling as indicated by the steady in-

(q/A),ot", = ( q / A ) w

+( q / A L

(27)

(tw2-t*)

Figure 12. Wad of heat Aux on inception d boiling a t canstant prersurelattice position 16

*

crease in h. At a flux of 500,000, h had risen to 11,200. At the inception of boiling, the outside wall temperature was 392' F. and, since the saturation temperature was 370° F., this gave a superheat of 22' F. In run 119A, boiling was induced by lowering the static p m u r e and maintaining the heat flux a t 230,000 5000 B.t.u./hr.-sq. ft., the Reynolds number a t 240,000, and the bulk water temperatum at 340' F. The pressurt was decreased from 300 to 117 pounds/square inch and, as indicated by the plot in F i p 13, boiling began at a b u t 160 pounds/square inch gqge. At 160 pounds/~uareinch gage, the saturation temperature is 370° F. This means that, at inception of boiling, since total t e m p e a r n drop (tux t,) was 61' F., the supxheat ( t , ~- t.) was 31' F. or somewhat bighex than for run 118A. The m l t s of run 120A a b are shown graphically in F@#C 13. I n this run, boiling was again induced hy lowering of the prrraurc. The heat flux was held a t 496,000 f H)o B.t.u./hr.-sq. ft., the Reynolds n u m b a t 960,000, and the bulk temperature a t 36Q0 F. The preasum was decreasd from 280 to 153 pounds/square inch gage and the inception nf boiling occurred a t or very doae to 185 pounds/squarc inch gage. The constant-pruunur lines, shown dashed, were estimated &the data paints. A+ the inception of boiling, h was 10,200, and it had increapd to 11,600 by the time the prnrnve reached 153 pounds/ square inch gage. For,this run, boiling began when the superheat rcachcd 26' F. For the 350,000 and 410,000 flm, it is estimated that the critical superheats for the initiation of boiling were 24' and 25' F., respectively. The nonboiling (constant h) linea in F w s 12 and 13 were located from several sets of nonboiling data taken for each run. In order to consider the effectsof some of the Operating variables on the super-

+

-

VUk.U.NO.

WO

.

OCmSn I956

1843

I

I

I

I

I

as Equation 28 shows. Of course, the experimental conditions of this work and those of Clark and Rohsenow were quite different. Since the boiling results described were obtained on a single tube with the rest of the tubes in the lattice as dummies, it was thought possible that, if all the tubes in the lattice were transferring heat at approximately the same rate, the rate of heat transfer capacity from a 6,000 given tube under boiling conditions (A) Re=240,000 RUN NO 119A would be influenced by the tubes ahead 5,000 Tg'34O0F of it. To see whether or not this was 4,000 the case, boiling data were taken on ----three tubes-16, 21, and 24-aligned 3,000 in the direction of flow in the center of ANGLE = 155" the lattice. (For location of tubes, . ' 2,000 see Figure 1.) Within experimental error, it was concluded from the experi1,000 mental results that there was no signifi0 cant effect on the boiling heat transfer 10 20 30 40 50 60 70 80 90 characteristics. In other words, the OVERALL TEMPERATURE DIFFERENCE itW,-t g ) , - F boiling at tube 16 had no effect on tube Figure 13. Graphs showing effect of static pressure on inception of boiling at 21. and the boiling at these two tubes did constant heat flux-lattice position 16 not affect tube 24. The assumption is that, a t these heat fluxes, the vapor which heat required to initiate boiling, an is formed a t the circumference of a ( q / A L v . = (~/A)b~,i analysis is made similar to that made tube during forced convection boiling and the combination of Equations 25 and previousIy by McAdams and coworkers is immediately condensed in the sur29 gives (76) for flow in annuli: In Figure 14, rounding subcooled water. The ava n isobar passing through the nonboiling, (twz - t , ) 4 = (a constant) (Re)0.8(twz - t ~ ) erage coefficient h under nonboiling transition, and full boiling regions is conditions for these tubes was 3750, (30) shown. For the nonboiling region whereas for the boiling runs it was 5400, which can be rewritten as an increase greater than 407,. I t is (q/A)conv. = (aconstant) (Re)0.8 ( t w 2 - t ~ ) evident that the lower the mass velocity ( t W p - t,) = (a constant) (Re)0.2 (t,z - t ~ ) 0 . * 5 (29) the easier it is to achieve boiling condican be written for a particular liquid. (30a) tions and to realize a given increase in And in the boiling region, the heat transthe coefficient. as indicated by Figure 11. This equation indicates that the superfer can be represented by Equation 25. Dissolved Gas. Undoubtedly, disheat required to precipitate boiling This assumes that the effect of velocity solved gas has an effect on the inception should vary as the 0.2 power of the Reynin the boiling region is negligibly small of boiling and also on the rate of heat olds number and the 0.25 power of the compared to that in the nonboiling transfer under full boiling conditions for total simultaneous temperature drop. region. The nonboiling and boiling forced convection of subcooled water, For the experiments under consideration, straight portions of the isobar can be but the currently available data are not the temperatures were close enough to extended to meet a t the transition conclusive. Boelter and his colvorkers neglect the effect of the Prandtl modulus point, c. At this point ( 4 ) found little effect of dissolved nitroin the foregoing treatment. In the exgen a t a concentration of 750 cc. (standperiment of Figure 14, boiling actually ard temperature and pressure) per begins a t point b and not point c: which liter of water on either the inception of means that, for a given pressure and boiling or on the heat transfer at full bulk temperature, (tmz - t,) by Equation boiling. This was for flow of water 30a is slightly larger than the actual inside a 0.226-inch i.d. stainless steel value of ( t , ~- t,) required to initiate tube. O n the other hand, McAdams boiling. I t is believed, however, that and his co-workers a t M I T (76) obthis is not enough to change the general tained limited data to show that for qualitative conclusions which indicate forced flow7 of water in an annulus. 69 that the superheat necessary to initiate LOG % cc. of dissolved air per liter had a proboiling is not a sensitive function of the nounced effect on the initiation of boiloperating variables and therefore should ing-i.e., it lowered the required surface not be expected to vary appreciably for temperature but had a minor influence considerable changes of Reynolds numon heat transfer in the full boiling region. ber and total temperature drop. Thus I n this work the concentration of disit is not surprising that, for the runs solved air was low because the heat just discussed, the superheats a t the intransfer circulation system was kept well ception of boiling were, in general, not above the normal boiling point of widely different. water and was continuously vented at The amount of data obtained in this the top of the circulation drum to release investigation was not sufficient to test LOG itW2-tg) noncondensables from the vapor space. adequately the applicability of Equation Hence, it is believed that the boiling Figure 14. Typical heat transfer curve 28. The limited results indicated that data obtained should not have been covering nonboiling, transition, and (q/A)boil was proportional to (tu full boiling regions for single pressure appreciably affected by dissolved gas. t,)* where b was much higher than 3 l2.000~

I

I

i

1

1844

INDUSTRIAL AND ENGINEERING CHEMISTRY

"4

4.0 I

Pressure Drop Determination

Pressure taps were located in the top tube sheet immediately in front of, immediately in back of, and at seven points along the middle of the tube bank. Thus, it was possible to determine the pressure drop across certain sections as well as the whole of the tube bank. I n the interior of the lattice, the taps were placed exactly between the fifth and sixth tubes in each row, or at points of minimum cross section and maximum velocity. I n addition to these taps, the fourth tube (from the left-hand side of the lattice) in the sixth and sixteenth transverse rows was punctured at the 90' point to serve also as pressure taps. The locations of all these pressure taps are shown in Figure 1. For cross flow of fluids through tube banks, pressure drop has been correlated successfully by

where f is a function of geometry and Reynolds number. For staggered tube banks, Jakob (70) has proposed the relation

I

+ (X,-

I

I

SYMBOLS

El a

*3t

PRESSURE DROP OBTAINED FROM HOLLOW TUBES PRESSURE DROP OBTAtNED FROM TAPS IN TOP TUBE SHEET OBTAINED FROM PRESSURE DROP ACROSS ENTIRE LATTICE

I1111

1

1

B

a

0 CK

n

.02 *031 I

I

I

I l l l d

those of Bergelin and coworkers (7) obtained a t lower Reynolds numbers with oil. In the Reynolds number range 106 to 106, the friction factor (33)

l)L.O*]

The pressure drop results are shown graphically in Figures 15 and 16 Figure 15 shows that the pressure drop results agree very well with the extrapolation of Equation 33. Both the plate taps and the punctured tubes gave the same results. I t was decided to omit pressure versus row or pressure drop versus row curves because such profiles would be difficult to interpret at the lattice entrance and exit sections, owing to pressure changes resulting from velocity changes. When such calculated pressure changes are taken into account, the frictional pressure drop across the first three and one half rows is about the same as for any three and one half rows in the remainder of the lattice. The frictional pressure drop for the last two and one half rows appears to be somewhat more per row than for the rest of the lattice. I n general, the observed pressure drop through the lattice was essentially linear. Unfortunately, there were no taps a t the second and third transverse rows. As shown in Figure 16, the over-all pressure drop results are consistent with

I

/ /

0.11

*fi = [ 0 . 2 3

I

2.0

I

which is based on pressure drop data for flow of air normal to staggered tube banks for Reynolds numbers ranging between 200 and 40,000. Combining Equations 31 and 32, and rearranging, gives

I 1 1 1 1 1 1

I

varied inversely as the 0.15 power of the Reynolds number, which appears to be a lower limit for the high Reynolds numbers. The pressure drop measurements are believed accurate to less than 0.5 pound/square inch.

IO',

I

I

I

I

I

I1l111

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Conclusions

Based on the results and analyses presented here, the following conclusions are drawn :

1. In Equation 21 exponent m varies with the Reynolds number. I n the Reynolds number range 106 to 106 an average value for m for the particular tube bank studied is 0.8. Exponent m is presumably also a function of tube arrangement, but this parameter was not studied. The average coefficient for the tube bank as a whole is expressed by

I

I

DATA FROM P R E S

' \

BERGELIN ET A L ( I 1 FOR OIL P/D=1.5

VOL. 48, NO. 10

OCTOBER 1956

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1845

= 0.19

(Re)O8

At a Reynolds number of lo6, the average coefficient for the tube bank was more than 60y0greater than that obtained by extrapolation of the Colburn equation. 2. The heat transfer coefficients for the tubes in the front row are, depending on the Reynolds number, considerably below those for the tube bank as a whole. At Reynolds numbers of IO5 and IO6, they are approximately 30 and 40% below, respectively. There appeared to be no variation in the coefficients across the first row of tubes, where the results may be expressed by

2 [(:)”

v2m,x

.

The study would not have been possible without the efforts of many on the technical staff of the Nuclear Engineering Department a t Brookhaven who helped build and operate the equipment. However, special thanks are due W. H. Regan, Jr., for assisting in the supervision of the experimental work. Melvin Silberberg for many calculations, and W. J. Johnson and Gloria Atkinson for drawing the plots. Finally, the authors take pleasure in acknowledging the assistance of several members of the Walter Kidde Nuclear Laboratories of Garden City, N. Y., by whom the experimental results were required in connection with a nuclear reactor feasibility study for the Atomic Energy Commission. The assistance of W. I. Thompson of Kidde was ’particularly helpful during the equipment design phase of the project.

DGrnax, Reynolds number, ___ Pf tube radius, ft. inner radius of tube, ft. outer radius of tube, ft. temperature of tube wall at radiusr, “ F . bulk temperature of water, F. saturation temperature corresponding to static pressure, F. inside wall temperature of tube,

F.

average inside wall temperature, defined by Equation 4, O F . outside wall temperature of tube, O

1 84.4

constant heat transfer area, sq. ft. INDUSTRIAL AND ENGINEERING CHEMISTRY

F.

average outside wall temperature, defined by Equation 2, F. velocity of water based on minimum flow area, ft./sec. rate of heat generation in tube per unit volume, B.t.u./hr.cu. ft. transverse tube pitch/tube diamO

F,tP.t.

-I--

surface tension of liquid-vapor interface, lb./ft. = angle from forward stagnation point, degree = viscosity of water at average film temperature, lb./hr.-ft.

=

= =

)

thermal conductivity of water at average film temperature, B.t.u./hr.-ft.-” F. thermal conductivity of saturated liquid, B.t.u./hr. ft.-” F. average thermal conductivity of nickel tube, B.t.u./hr.-ft.-” F. distance between voltage probes, ft exponent on Reynolds number constant number of transverse rows in lattice tube pitch, distance between centers. ft. pressure, lb./sq. inch pressure drop, lh./sq. inch heat flow rate, B.t.u./hr.

Acknowledgment

Nomen cloture

,

gravitational constant conversion factor, 4.17 X 10s (1b.-mass)(ft. ) (Ih. force)(hr.)2 mass velocity of water based on minimum flow area, lb./hr.sq. ft. local heat transfer coefficient, B.t.u./hr.-sq. ft.-” F. average heat transfer coefficient for a single tube, B.t.u./hr.sq. ft.-” F. average heat transfer coefficient for entire tube hank, B.t.u./hr.sq. ft.-” F. latent heat of evaporation, B.t.u./ lb. current through tube, amp.

No data were taken a t the second transverse row. A few taken a t the third row and appreciable data a t the 5th, 9th, 11th. 13th, and 19th rows showed the same heat transfer rates from the third row on back through the bank. 3. There was transverse variation in heat transfer capacity across the tube bank, with the tubes at the side walls giving coefficients about 15% greater than the average for the tube bank. This is attributed, in part a t least, to the greater free space a t the wall tubes, promoting increased turbulence. 4. Within the range of variables studied, the superheat required to initiate boiling did not vary greatly with Reynolds number or total temperature and was in the neighborhood of 25’ F. 5. Pressure drop results for the Reynolds number range IO5to 1O6 showed excellent agreement with the relation of Jakob, which was based on data obtained o n air a t much lower Reynolds numbers. T h e results also tie in well with those obtained by Bergelin and coworkers on oil, also a t considerably lower Reynolds numbers.

‘4

(:)-“I

I

h = 0.76 (Re)0.65

U

+

A‘,, = = constant A, AO = constant C I = specific heat of saturated liauid. B.t.u./lb. F. sDecific heat of water evaluated at average film temperature, B.t.u./lb. O F. coefficient of Equation 28 which depends on nature of heating surface fluid combination outside diameter of tube, ft. e.m.f. drop between test probes in tube, volts friction factor [72go(A))]/(.Vp~-

viscosity of saturated liquid, lb./hr.-ft. = viscosity of oil at wall temperature, lb./hr.-ft. = density of water at bulk temprrature, lb./cu. ft. = density of saturated liquid, Ib./cu. ft. = density of saturated vapor, Ib /cu. ft. =

pl

PB pi pu

Literature Cited (1) Bergelin, 0. P., BTown, G. .A. Doberstein, S. C., Trans. Am. ,%IC. Mech. Engrs. 74, 953 (1952). ( 2 ) Bergelin, 0. P., Brown, G. A., Hull, H. L., Sullivan, F. W., Ibid., 72, 881 (1950). (3) Boelter, L. M. K., Cherrey, V. H., Johnson, H. A., htartinelli, K. C., “Heat Transfer Notes,” University of California Press, Berkeley, Cali!’,, 1946. (4) Boelter, L. M. K., others, “Boiling Studies” Progr. Rept. 1 on A E C Contract No, AT-1 1-I-Gen. 9, front the University of California, Rrrkeley, Calif., August 1949. ( 5 ) Clark, J. A., Rohsenow, W. M.. “Local Boiling Heat Transfer to Water at Low Reynolds Numbers and High Pressure,” Tech. R e p . 4 to Office of Naval Research from MIT, Cambridge, Mass., J u l y 1 , 1952. (6) Colburn, A . P., Truns. Am. Init. Chem. Engrs. 29, 174 (1933). (7) “Fluid Meters, Their Theory and -4pplication,” Am. SOC. Mecli. Engrs., 1937. 18) Grimison, E. D., Trans. w n . SOL..Vluch. Engrs. 59, 583(1937).‘ ( 9 ) Huge, E. C.,Zbid., 59, 573 (1937). (10) Jakoh, M., Zbid., 60, 385 (1938). (11) Jens, W. H., Lottes, P. &4.,“Analysis of Heat Transfer, Burnout, Pressure Drop, and Density Data for High Pressure Water,” Argonne National Laboratory Rept. ANL-4627, May 1, 1951. (12) Keenan, J. H., Keyes, F. G., “Theymodynamic Properties of Stcam,” Wiley, New York, 1937. (13) Kreith, F., Surnmerfield, M., 7’ruti.r. Am. SOC.Mech. Engrs. 71, 805 (1949). (14) McAdams, W. H., “Heat Transmission,” p. 221, McGraw-Hill, Nebv York, 1942. (15) Ibid.,p. 230. (16) McAdams, W. H., Kennel, W. E., hfinden, C. S., Carl, R., Picornall, P. M., Dew, J. E., INU. ENC. CHEM.41, 1945 (1949). (17) Nusselt, W., %. Veer. dezct. Zng. 53, 1750 (1909). (18) Pierson, 0. L., Truns. Am. Soc. M e r i i . Engrs. 59, 563 (1937). (19) Sigwart, K., Forsch. Grbiele Ingenirurw. 7 , 128 (1936). (20) Snyder, N. W., “Heat Transfrr Symposium,” American Institutr of Chemical Engineers, Symp. Ser. 16, December 1951. (21) Timroth, D. L., J . Phys. (U.S.S.R.) 2, 419 (1940). (22) Timroth, D. L., Vergaftik, J . 7Zc.h. Phys. (U.S.S.R.) 10,1063 (1940). \

,

RECEIVED for review June 11 1955 ACCEPTED February 23, 1956 This paper is, in part, a condensation of two papers presented at the Milwaukee meeting of the ASME, September 8-10, 1954. It i3 based on work done under the auspices of the U . S. Atomic Energy Commission.