27 January 2021 Report 22W33E

|1253.1.55|30,100|33.286,500 57,000 ,312320.68 45.6 53.2||2014 26270.36 0.6457,100] 87,20045.6: 53.22516 18950.ho 0.8783,300] 53,700]85.2 48.4 29,600,33.8}1110|1.9226,70037.4

7.7 | 2955 1.37 5,000 60.8 ° 3125 1.21 |122,000; 60.8 2998 0.48 116,700; 60.0 55.4 | 3228 0.71 148,000 66.2 3437 0.58 157,000) 66.2 3402 0.30 155,000 63.2

62.1 FRACTURE FRACTURE FRACTURE se FrreRSEl. ImeenMeetBScee)pe se———

;

2 S =~

bad

MATERIAL 304

Temperature--Dry Ice & Acetone (-77°C)

Tungsten Carbide Dies

Lubricant--Molykote Z

Head Speed 7.0 ins/min 1.12 ins/min 0.28 ins/min Red Area

in | Average Force

Draw | Average Deviation|Draw

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Stress Force

Draw | Deviation Draw

Stress Force

Draw Deviation

Stress

Draw AverageAverageAverage|AverageAverageAverageAverage

(%) | (ws) (%) (psi) (1s) (%) (psi) (1bs) (%) (psi)

15.3 28.1 a——— San -— -

i 1809 2881

. 1.47 3.61|

81,600 2925 0.64 82,900 143,50016891.2940,700

W7.7 38.5 eo3519 FRACTURE 1.71 | 116,500 ————— 3721 _——

FRACTURE 0.83|FRACTURE

ee 123,20037601.06124,500

Temperature--Liquid Nitrogen (-189°C)

Tungsten Carbide Dies

Lubricant--Molykote Z

1.12 ins/min

Red Ps? van {Average in | Draw |Deviation! Draw Area'ForceStress (4) (ms) (®) (pst) |

15.3 1 2110 3.37 50,700

28.1 | 3765 4.02 107,000

38.5 4888 1.50 162,000

bey 7 FRACTURE

MATERIAL 301

Room Temperature

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Tungsten Carbide Dies

Lubricent—-Melykote Z

Head Speed 7.0 ins/min 1.12 ins/min 0.28 ins/min

Redin Average! Draw fvermae IDeviation|Average Draw eeDetor- Average Draw Average Deviation| ier Draw (mation rere Draw |Devistion Average Draw |{mation Defor—

+ Area}|ForceStressEffi-:ForcefirensRosie|ForceStress|Effi- | etorey ieiency eiency

(#) | (1bs) (%) (psi) ~ (vs) «+ (%) (psi) | fo {11a} pei; 4

15.3 1478 4.06 | 35,500 KT 1256 1.87 30,200 ¢ 4" 35,~ © °C

28e1l | meee ==cc somewosmes J =e 2372 1.49 68,100 , 45.5 ¢ ? . 81.20 5

38,5 307% 0.89 02,000 . " 2906 1.05 96,400 = 53.9 g Hod 94,000 . * .,3

55.4 3739 C.8C 071,000 | 62.5 3664 0.19 [167,300 * 63.2 -— —— | m————

62.1

| FRACTURE

roti

FRACTURE FRACTURE

Ent

fee LD1

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Temperature--Liquid Nitrogen (-189°C) Temperature--Dry Ice & Acetone (-77.C)

Tungsten Carbide Dies Tungsten Carbide Dies

Lubricant--Molykote Z Lubricant--Molykote Z

Head Speed 1.12 ins/min HeadSpeed 1.12 ins/min

[Red verage Average Average Red Average Average oo Average

in Draw . Deviation Draw in Draw Deviation Draw | (%, Area (1os) Force (%) Stress (psi) Area («1

(ibs) (%) (psi) ForceStress

115.3 | 2506 1.45 60,300 15.3|21483.0051,700

‘28.1 138.5|4167 31893.45 3.1290,600 138,00028.1 38.5|3105 37182.28 0.8388,000 123,000 ¥7.7. |FRACTURE hor FRACTURE

MATERIAL 70-30 BRASS

Room Temperature

Tungsten Carbide Dies

Lubricant--Molykote Z

Head Speed 1.12 ins/min

Red verage: Average Average + Deformation

in Draw : Deviation Draw : Efficiency

-Area (¢:|(Los) Force(%)Stress (psi)(%) 15.31 72 0.42 17,800 bh .9 28.1 38.5{|1498 11730.57 1.5049,600 33,200||64.5 54.2 W7.7|16770.5065,30073.5 WEN 2 FRACTURE

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VALUES USED IN CALCULATIONS OF DRAW STRESSES AND DEFORMATION EFFICIENCIES

Red | Aree. Naturel (Energy/Vol. in "Homogeneous" Deformation (in.—-1bs/cu. in.)

Aree

in After

Draw

Strain i

304

=51 | Brass

(%) (sg. ins) + (in/in)

15.3 | 04.6 0.166 10,000 12,000 8,000

28.1 {| .0353 0.329 26,000 31,000 18,000

38.5 | .0302 0.485 46,000 52,000 22,000

47.7 +0257 0.647 70,000 78,000 48,000

55,4 .0219 0.806 98,000 107,000 66,000

¥Initiel Ares = .0491 sg. ins.

Table 1 Coefficients Cos 12

Teble 2 Performence of an evaporator 35

Table 3 Coordinetes for Figure 2 49

Table 4 : 50

Table 5 50

Table 6 52

Table 7 53

Table 8 54

Table 9 54

Table 10 55

Figure 1 Cross-sectional diagram of a standard verticaltube evaporator with natural-circulation.

Figure 2 Work function ¥ to calculate the rate of heat 11

transfer from the condensing steam.

Figure 3 Work function @ to calculate the rate of heat 14

transfer due to nucleate boiling, for water.

Figure 4 Work function £ to calculate the rate of heat 15

transfer due to convection, for water.

Figure 5 Volume fraction of water vs. weight percent of 20

vapor at any point.

Figure 6 Volume fraction of liquid water in the tube vs. 2a

welght percent of vapor at the exit of the tube.

Figure 7 Ratio of the local two-phase frictional pressure 23

gradient to the local frictional pressure

gradient for the flow of liquid water alone vs.

quality at any point.

Figure 8 Ratio of frictional pressure drop for two-phase 24

flow to frictionel pressure drop if liquid

water flowed alome vs. weight percent of vapor

at the exit of the tube.

Figure 9 Constant AR vs. weight percent of vapor at the 26

exit of the tubes.

Figure 10 Heat transfer coefficients, predicted and 36

experimental.

Figure 11 Rates of total heat flow, predicted and

experimental.

List of Tables and Figures (cont.)

page

Figure 12 Predicted velocity of the liquid entering the 38

tubes.

Figure 13 Weight percent of vepor leaving the tubes. 39

Figure 14 Individual rates of heat flow. 40

Figure 15 Pressure drops in the vertical tubes, 41

In this paper an attempt was made to compile and apply basic

principles and some recently developed methods and theories for the

determination of the performance of a vertical-tube natural-circulation

evaporator.

Although the method developed in this work is not absolute in

scope, it is hoped that the system used may serve in the future as a

model for computing and investigating performance characteristics, like

rate of heat transfer and overall heat transfer coefficients, for any

commercial natural-circulation evaporator.

A "calandria" vertical-tube type evaporator was chosen for

investigation because of its simplicity in geometry.

In order to determine the steady state rate of heat transfer to

the liquid boiling inside the vertical tubes of a standard evaporator,

previously it has been necessary to know the overall coefficient of heat

transfer in the tubes.

A method is suggested in this paper to predict simultaneously

the steady rate of heat transfer and the corresponding velocity of the

liquid entering the tubes without requiring the use of an experimentally

obtained overall heat transfer coefficient.

The method consists of assuming a temperature drop in the film

of condensate and then calculating the rate of heat transfer and the

velocity of the liquid entering the tubes from an expression that results

upon equating the heat transfer rate from the condensate to the heat

transfer rate predicted by Rohsenow's relation (1) and Colburn's equation

(11). The results obtained are correct if, upon calculating, it is found

that the pressure head that produces the circulation of liquid is

approximately equal to the sum of pressure drops suffered by the mixture

of vapor and liquid in the vertical tubes. These pressure drops are

calculated by a modification of the method of Martinelli and Nelson {2}.

Themethod was fully developed for the case of water being evaporated in

a standard evaporator.

A particular evaporator wae investigated in order to show the

possibilities of the method. The calculated results conformed, as to

general trend, with the experimental data of other investigators.

III Introduction

For years natural-circulation evaporators, as well as other

heat exchangers, have been designed and operated without the exact

knowledge of the physical phenomenons that govern their functioning.

The complete understanding of these phenomenons was hindered by:

1. Partial ignorance of the complex mechanism of heat flow into

a boiling liquid and, therefore, absence of a satisfactory

analysis on the basis of dimensionless equations.

2. Lack of a satisfactory method to predict the behavior of the

two-phase flow of liquid and vapor which exists in the boiling

section of the evaporator.

The existence of evaporation and the necessity of the

transmission of heat to a boiling liquid had been known to man as far

back as history records, but this phenomenon was taken for granted and

no real scientific study of it was done until the very beginning of

this century.

The formation of vapor bubbles on the heating surface in

contact with a boiling liquid and the existence of a slight superheat of

the liquid near a bubble had been observed; Bosnyzkovie (3) offered the

first novel theory on this field of scientific endeavor when he suggested

that the slight superheating provided the impulse to heat transmission

needed for evaporation. He understood how, due to this difference in

temperature between liquid and vapor,heat flows from the liquid to the

surface of the vapor bubble and how, on this surface the liquid evaporates

into the bubble. Jakob (3) suggested, as a consequence of this theory,

the possibility that the heat transmitted directly from the heating

surface to the vapor bubble might be insignificant.

Only in very recent years Rohsenow and Clark (4) measured the

heat quantity required to form a vapor bubble in a liquid and they were

able to prove experimentally that the bubbles are not important "carriers"

for the heat transfer process in pool boiling but act as agitators of the

fluid thus increasing the heat transfer from the heating surface to the

liquid.

With the mechanism of heat transfer from a solid surface to a

boiling liquid more clearly understood, Kohsenow (1) introduced the

concept of a bubble Reynolds number to account for the effect of the

agitation produced by the bubbles, and using with this the concept of

bubble Nusselt number introduced by Jakob (3), he was able to find a

dimensionless correlation that yielded very closely to experimental data

for surface boiling of liquids. It was later found (5) experimentally,

that when the total heat flux to a liquid in forced convection boiling

was measured it resulted equal, on the average, to the heat flux predicted

by the correlation for surface boiling plus the heat flux that could be

attributed to the forced convection.

In trying to calculate the pressure drop during the forcedcirculation boiling of a liquid, a difficulty arises in the estimation of

the friction factor since a Reynolds number for the liquid vapor mixture

is difficult to define, In a series of papers (2, 6) Martinelli and his

co-workers have proposed a method for the repid calculation of the pressure

drop during forced circulation boiling of water. They proposed that the

pressure drop during a simultaneous flow of vapor and liquid be related

to the pressure drop occurring if a single phase flowed alone in the pipe.

The method was originally proposed for horizontal tubes but Cheshire znd

Stirling (7) proved that the method was applicable with certain

reliability to the calculations of pressure drops in a vertical-tube

evaporator.

Those recently developed correlations and methods above

mentioned have been combined in this paper with other accepted correlations and with some basic principles in an effort to develop a method

for calculating the performance of a vertical-tube natural-circuleation

evaporator.

The resulting method then, is subjected to a number of

limitations imposed by the assumptions made in the development of the

methods and correlations which were used as tools.

A standard evaporator was chosen as the subject for this

investigation because it is the simplest in geometry and the most widely

used of all evaporators. A typical standard evaporator is shown

disgramaticelly in Fig. 1. It consists of a short vertical-tube bundle

known as the “calandria". The tubes are set between two fixed tube

sheets which are bolted to the shell flanges. The steam flows outside

the tubes in the steam chest. Liquid circulation is upward through the

tubes due to the pumping action of water vapor formed in the tubes.

There is a large circular space for downtake in the center of the bundle

whereby the cooler liquid circulates back to the bottom of the tubes.

The flow area of the downteke is from one half the flow area of the

tubes to zn area equal to it. The tubes are from 1/4 in. to 3 in. in

diameter and from 30 in. to 6 ft. long.

The liquid level is usually maintained the lowest consistent

with efficient operation in order to reduce the effect of the hydrostatic

head.

Presumably the steam is baffled so that there is a relatively

uniform tube coverage, and adequate bleed points are provided so that no

pockets of non-condensable gases develop.

These evaporators are usually operated with relatively low

temperature differences between the condensation temperature of the steam

and the boiling point of the liquid, temperature differences from 10 to

50 F are common. The velocity of the liquid entering the tubes has been

measured in the range of 1 to 5

In the standard evaporator, heat is transferred from steam

condensing on the outside of the vertical tubes through the walls of the

tubes to the liquid boiling inside the tubes. Thus the total resistance

to heat transfer is the sum of the individual resistances of the film of

condensate, the wall and the surface in contact with the boiling liquid.

For the steady state trensfer of heat

‘ ‘

Fora =F na

and as explained in the introduction of this paper

= 9wll = % ool + (1)

A. Heat Transfer from the condensing steam.

In 1916, Nusselt (3) derived theoretical relations for

predicting the coefficient of heat transfer between a pure saturated

vapor and a colder surface when the condensation is of the film type.

The following assumptions were made:

2. The force of gravity alone causes the flow of condensate thus

neglecting the possible effect of steam velocity upon the thickness of the condensate film.

The total thermal resistance lies in the film of condensate, i.e.,

the latent heat of condensation is transmitted by conduction

neglecting the cooling of the condensate.

The temperature difference between vapor and wall is constant

at all points.

The theoreticsl Nusselt relation is

he = 0.943 (zen)’ (2) ™ L Me At

After correlating the data of various investigators, McAdams (9)

found that the hm reported was on the average 28 percent above that

predicted by equation (9 and recommended the following correlation

hus? (Ke2292) (3) L Me At,

For short tubes this correlation has yielded satisfactorily to experimental

data. By using hm from equation (3), qond can be readily calculated

Fond = hem Ac At, (4)

Substituting hm from equation (3)

a I

and = 1.13 Ao (£822) py, LA, At, (5)

Rewriting equation (5)

3/4,

od = Ao Y = (6)

where

¥ 21.13 flvAlg (7)

Theoretically ¥ should depend upon the temperature of

saturation of the condensing steam and upon the temperature of the film

of condensate. For standard evaporators where the temperature drops are

relatively small the temperature of the film of condensate is rarely 20 F

below the saturation temperature of the steam, under those conditions the

physical properties of the condensate at the temperature of the condensate

are essentially equal to the physical properties at the temperature of

saturation. Thus the work function ¥ could be considered & function of

the temperature of saturation of the steam. In Fig. 2 a plot of 7)

versus temperature of saturation of the steam is given. To decrease, on

the average, the small error that is introduced by the assumptions given

above, the physical properties of water were teken at a temperature 5 F,

below the saturation temperature of the steam.

B. Heat Transfer through the well of the tubes,

The steady rate of heat transfer through the wall of the tube

is given by the basic Fourier's law for thermal conduction

Fall = 22 Am (two -tux) &)

For thin tubes no substantial discrepancy occurs if A or Ay is used

instead of A

C. Heat Transfer to the boiling liquid.

When liquid boils in contact with a heating surface, various

regimes of boiling (10) can occur depending on the difference between the

temperature of the liquid. For the range of temperature differences at

which a stenderd evaporator is operated, nucleate boiling (bubble form)

usually occurs.

Rohsenow (1) suggested the following relation from which the

heat transfer to a nucleate boiling liquid for the case of pool boiling

can be calculated,h¢q CAM'

The magnitude of Cor is

determined by the particular surface-fluid combination. By correlating

the data of other investigators, Rohsenow calculated values of Cop which

are given below.

Table 1 = Loefficients Cop

Fluid-heating surface of

Water-platinum 0,013

Benzene-chromium 0,010

Ethyl alcoho-chromium 0.0027

N-pentane-chromium 0.015

Water-brass 0.0060

The exponent 0.33 appeared to be adequate for most of the data correlated

whether the heating surface was clean or not, but the 1.7 exponent appeared

to be valid only for clean surfaces. With dirty surfaces the value of

this exponent was quite erratic varying between 0.8 and 2.0.

Equation (9) can be rewritten

= Ia [oe 7he (fw: te) (9a) Css|hsq\CupeVit Vi

‘

ail = 2 Al (kwi-tev)? (10)

where

Ds oe EL Siahy i. hg\copEy ST

Vi.

The work function @ is a function of the temperature of saturation

corresponding to the local pressure of evaporation. In Fig. 3 a plot of

@ versus temperature of saturation for boiling water is given.

For the case of forced convection of water inside tubes

Colburn (11) suggested the following correlation

(heen) (s& S————— ¥ = 0.023LR. 5)

co K (O&/n) (12)

which can be written as

0.023 0.8 oa 2

heonv = (SEY Cy uM Xe (12a)

0.8 heonv= tND (13)

where sl P 0.023 C,Gilde2

$ 7 CAV i Gs (14)

so that

Goon = Nom Ai Ata 8)

; vO& . J “Cov Qeonv = 5 o** A (tu ) (16)

The work function < is a function of the temperature of the liquid. In

Fig. 4 2 plot of t versus temperature is given for water.

It has been found experimentally (5) that in forced convection

boiling the totel heat transferred to the boiling liquid can be calculated.

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27 January 2021 Report 22W33E

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