ENGINEERING, DESIGN, AND EQUIPMENT is always very close to the pressure of gas in the reaction compartments of the autoclave. The temperature within the autoclave is indicated and recorded by a Leeds & Northrup Speedomax multipoint recorder. The measuring element, an iron-constantan thermocouple with a 316 stainless steel protection sheath, is suspended in the reaction compartment of the autoclave. For accurate point measurements a Leeds & Northrup portable precision potentiometer is used. Switching from the recorder to the potentiometer is accomplished by the use of a double-throw, double-pole telephone type switch. The pressure in the reaction compartment of the autoclave is indicated by a Marsh (J. P. Marsh Corp. Skokie, Ill.) Type 100 gage mounted in the unit. A similar gage indicates the pressure in the motor compartment. However, this latter gage serves for a bank of similar units and hence is not an integral part of any single unit. The rate of stirring is indicated by a Simpson alternate current voltmeter with a 0-15 volt range (Simpson Electric Co., Chicago, Ill.). The scale of the voltmeter is calibrated in revolutions per minute of the agitator. Preparation of solids gives homogeneous sample with known surface area
Solid samples for study in the reaction unit are prepared by grinding the solid t o -100 mesh and pressing the powder into a disk by means of a die under pressures of 25 to 100 tons per square inch (depending on the solid under consideration). The disk is then pressed by hand into the sample holder. Samples which cannot be pressed are cut from massive crystals, in the case of minerals or from thin sheet, in the case of metals. The weight of the sample in the disk is adjusted to provide a disk with the same thickness as the sample holder. This method of sample preparation provides a homogeneous sample with a known physical surface area. I n initiating the operation of the reaction unit the autoclave is filled with the appropriate volume of reactant and the sample holder with the sample in place is placed a t the top of the guide. The cutout valve between the motor compartment and the reac-
tant compartment is opened, and the entire apparatus is evacuated, flushed with nitrogen, and re-evacuated. The cutout valve is then closed, and the solution within the autoclave is brought to the temperature required for the reaction. The overpressure of gas is applied simultaneously t o both the motor compartment and the reaction compartment. The agitator is set a t the required speed and the system allowed to come to thermal equilibrium. When equilibrium has been reached the sample is lowered into the solution, and the reaction is started. At definite intervals, depending on the rate of the reaction, liquid samples are withdrawn from the autoclave and analyzed. In removing a sample from the autoclave the capillary tube is first flushed by slightly opening the valve and allowing the solution to flash into a beaker. The bomb is chilled in cold water and screwed into place on the sampling valve. The sampling valve is then opened for a brief period of time, then closed. Care must be used in removing the bomb from the valve since it is still under pressure. A slight turn of the bomb releases the pressure, and the bomb can then be unscrewed from the valve body without flashing the contents. By prechilling the bomb the solution is cooled enough to prevent flashing when the pressure is qemoved. The contents of the bomb are then removed with a hypodermic syringe and prepared for analysis. Acknowledgment
The authors wish to express their appreciation to the Atomic Energy Commission and to the University of Utah Research Fund for the financial support which made the construction of this unit possible. They are also deeply greatful t o the University of Utah Experiment Station and to Roscoe H. Woolley for their assistance in the mechanical aspects and the machine work on the autoclave part of the unit. This project was sponsored by t h e Atomic Energy Commission, Contract No. AT(ll-1)-82. Funds f o r the construction of equipment were provided by the University of Utah Research Fund. This paper comprises part of a thesis to be presented by W. H. Dreaher and T. M. Kaneko in partial f u l fillment of the requirements for the degree of doctor of philosophy, Depaitment of Metallurgy. University of Utah.
Improved Integral for Petroleum Distillation Calculations WAYNE C. EDMISTER California Research Corp., Richmond, Calif.
R
ECEXTLY (1-6)an integral method was proposed for making petroleum distillation calculations. Although the principle of the method is simple, previous applications were made by equations which were either awkward or approximate. Because chemical engineers are more accustomed to numerical and graphical solutions of distillation problems, this type of application of the integral technique has been developed and is presented. The principles of this procedure are illustrated for three calculations on petroleum fractions by examples on: 1. equilibrium flash vaporization; 2. bubble and dew points; and 3. fractional distillation. Integral principle i s defined
ZKz: = 1.0 for finite mixture
Petroleum fractions may be regarded as continua (mixtures) of an indefinite numbers of hydrocarbon components, each appearing in an infinitesimal amount. On the true boiling point September 1955
(TBP) distillation curve for the mixture, each of these components will be a point, as contrasted to the plateaus that represent the finite amounts of components on the true boiling point curves of light hydrocarbon mixtures. I n distillation calculations for finite mixtures, the vapor-liquid distribution and properties of the equilibrium phases are found by the summations of component distributions and properties. For continua (mixtures) of an indefinite number of components, the distillation calculations follow the same basic principles, but the summation becomes an integration. This distinction is illustrated by the following bubble point relationships:
sd
KdmF = 1.0 for continuum
I N D IJ S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y
1685
ENGINEERING, DESIGN, AND EQUIPMENT
VI
s W 4
TBP TEMPERATURE,
OF.
For a mixture of finite components, the values of Kx are summed for all components. When the K values are taken a t the correct bubble point temperature, this sum is unity. For the continuum, an integration is performed by determining the area under a curve of K versus mp. The points for this curve are located by finding the values of K a t the system temperature and pressure for each of several component points on the true boiling point curve. At the bubble point, the area under the K versus mp curve equals unity. Points on the distillation curve of the bubble point vapor can be found in the integral procedure by finding the area under the curve t o the value of mF in question. The ratio of this area to the total area under the K versus mp curve gives the value of m y . The same analogy between summations and integral procedure holds for the dew point and other distillation calculations. Component ratios are more convenient to use
and I1 are used for converting the liquid volume true boiling point curve to a molar true boiling point curve. Instantaneous moles per 100 gallons are given in Chart I as a function of boiling point and gravity or UOP K. Delta per cents for converting volumetric to molar true boiling point curves are given on Chart I1 as a function of true boiling point slope, UOP K, and the per cent off point on the volumetric true boiling point. Vapor-liquid equilibria K values for hypothetical components of the mixture are required for these calculations. These may be from vapor pressures, fugacities, or empirical correlations of observed K values. The values presented in two previous papers ( 4 , 5 ) on this subject may be used. Equilibrium Flash Vaporization. Integral equilibrium flash vaporization (EFV) calculations for a continuum mixture are basically the same as equilibrium flash vaporization calculations for a finite mixture. Both involve assuming an L/V ratio, looking up K values, finding component distribution to vapor and liquid, summing up to get total L and V and finally checking the assumed L/V ratio. The equations used in equilibrium flash vaporization are
v/f = 1/(1
+ L / K V ) and l/f
+ KV/L)
Since these equations give component distribution fractions, they can be applied to the components of finite mixtures or to the infinitesimal components of continua. In the integral equilibrium flash vaporization calculation, values of v/f or l / f ( = 1 - v/f) are found for several points along the molar true boiling point curve and plotted against mF. The area under this curve gives vapor-liquid split for the entire mixture. If this checks the assumed L / V , the required equilibrium is satisfied. The integral method differs from the finite component mixture in that calculations are made for several selected points on the molar-true boiling point curve and the totals are found by integrating under a curve. Example 1. Calculate the amount and composition of vapor
The integral technique can be used in equilibrium flash vaporization calculations or fractional distillation calculations and may be applied to increments or components of any amount. In this way distillation calculations can be made for continua by finding the distribution ratios of several points, or infinitesimal components, and then finding the total by integration. In distillation calculations it is more convenient to use component ratios for designating the distribution of the infinitesimal components to the products. Data Requirements. The petroleum fraction must be defined by a molar true boiling point curve-i.e., temperature in ' F. versus mole fraction of original mixture distilled-in this method. All calculations are based on this molar true boiling point curve and result in products defined by similar curves. I n the usual situation, true boiling point distillation data are expressed as temperature versus volume per cent off. Charts I
1686
= 1/(1
INDUSTRIAL AND ENGINEERING CHEMISTRY
z 4
m
0
Vol. 41, No. 9
ENGINEERING, DESIGN, AND EQUIPMENT
~
600
and liquid from an equilibrium flash vaporization of a 39.6" API petroleum fraction a t 390' F. and 22 pounds per square inch absolute with a true boiling point distillation as follows: %
F.
%
0
200 247 291 334
70 90 100
in
..
30 50
O
CURVES OF F E E D AND PRODUCTS FROM F L A S H I N G
F.
Table Gallons
%
L
I.
t,
F.
F.
450
247 20
30
29 1
20
50 20
387 20
90
490 10
?loo b
Mole Fraction
223
6.15
0.615
0.1215
269
5.70
1.140
0.2254
312
5.33
1.066
0.2107
360
4.96
0.992
0.1961
438
4.38
0.876
0.1732
545
3.70
0.370
0.0731
334
70
Molesb
.
b00
400
350 300
300 250
200
Moles Off 0
10 10
'a
Moles/ 100 Gal.=
200
O
500
200
I .o
0
0. e
0.2
0.6
0.4
Numerical Calculations Av.
t,
600
.
.
c
c
0.1215
>
d
0.3469 0.4
0.6
0.2
0.8
0.5576 0,7537
__
0.9269 1.0000
1.0000
5.059
From Chart I. Gallons X moles/100 gal.
0
Step 1 (Alternate). Table I1 shows the conversion of volumetric true boiling point to molar true boiling point by use of Chart 11. When this alternative is used the temperatures in the second column and the moles off in the fourth column are plotted .as in Figure 1. Table
II.
Temp., F.
off
% l
0 0.122 0.348 0.555 0.7440 0.9180 1.00
2.2 4.8 5.5 4.4 1.8
10 30 50 70 90
0
100
Step 2. Assume V / L ,find K values for each 50" F. component. K values given in Table I11 for this solution are from vapor pressures.
t.
E'.
rnF
Separation Functions a t ( V / L ) A ~ ~ = ~ , 3.0 ,,~~ K,
390° F., 22 Lb./Sq. Inch Abs.
K V/L
l/f
v/r
7.40 4.00 2.20 1.30 0.59 0.30 0.14 0.064 0.027
22.2 12.0 6.6 3.90 1.77 0.90 0.42 0,192 0.081
0 0431 0.0769 0.1316 0.204 0.361 0.526 0.704 0.838 0.925
0.9569 0.9231 0.8684 0.796 0.639 0.474 0.296 0.162 0,075
September 1955
-
1
0.6
0.4
1
1
0.0
WLE FRACTION OFF
Step 3. Plot l / f or v/fversus mF (Figure 2 ) . Step 4. Find area under curve and check assumed V / L . (Table IV). Area gives V / L = 2.95 versus 3.0 assumed. This is a'satisfactory check.
Table IV.
Moles Off
A. o/o 0
0
Table 111.
0.2
Conversion of Volumetric to Molar True Boiling Point TBP mF
Liquid Volume,
5 50
500
387 490 600
Solution. Figures 1 and 2 illustrate the solution of this example. Calculation steps are: Step 1. Convert the true boiling point volume per cent to mole fraction and plot. Enter Chart I with the true boiling point 50% temperature of 334' F. and rise t o 39.6" API. This is about 11.2 UOP K . Values of moles per 100 gallons should be read along this UOP K line for other portions of the feed. This assumes that all portions of the feed have the same UOP K . The UOP K determined from the true boiling point 50% temperature is the same UOP K which would be obtained from the equivalent ASTM 50% temperature. The numerical calculations of Step 1 are given in Table I. The temperatures in the third column versus the moles off are plotted in Figure 1.
Liquid Vol.,
600
Mean Ordinate m.n
0
l/f
v/f
0.054
0.946
Integration Calculations Liquid Areas InoreAct./ ment total 0-
0.1 0.0775
0.9225
0.1025 0 . 3 ~ 0.1275 0.4 0.1510 0.5 0.1810 0 , 6--0.2380 0.7-0.3380 0.8 0,5000 0,90.7625 1.0
0.8975
0.2 0.8725
0.0054
-0.02133---
0.00775 --0.05193 0,01025 ---___ 0.09242 0.01275 0.1428 0.01610 0.2024 0.01810 0.2739 0.02380 0,3679----0.03380 -0.5014--0,05000 0.6988--0.07625 1,0000
Vapor Areas IncreAm/ ment total O0.0946 0,09225
0.8190 0.7620 0.6620 0,6000 0,2375
0.2502
0.08975 0.08725
0.3704 -0.4872
_ . _
_ 0.8490 _ ~ _ _ _ _
0.1267
0.08490 0.6009 0,08190 0.07620 0.06620
0 . 05000 0.02375
-___
__--
0.2532
0.7468
0.7105 0.8126 0.9012 0,9682 1.0000
Step 5 . A t the 0.1 abscissa divisions on Figure 1, locate points on the vapor and liquid product curves relative to the feed curve in the manner shown by the horizontal dashed lines
INDUSTRIAL AND ENGINEERING CHEMISTRY
1687
ENGINEERING. DESIGN. AND EQUIPMENT 600
the bubble point calculations and a t the high boiling end in the dew point calculations. Example 2 . For the same petroleum fraction in Example 1 find the bubble and dew point temperatures and distillations of equilibrium vapor and liquid a t 22 pounds per square inch absolute, using vapor pressure K values, Solution. Figures 3 and 4 illustrate the solution of this example. Calculation steps are: Step 1. Temperature is assumed, K values found for several hypothetical components (as defined by the temperature point on the molar true boiling point curve) and a plot of K (or l / K ) versus mF prepared, the proper value of mp for each point being the value a t component boiling point on the true boiling point curve. Both curves are shown on Figure 4. Step 2. For the bubble point, the area under the K versus m~ curve must equal unity. For the dew point, the area under the E/K versus mF curve mdst equal unity. These areas can be found by means of a planimeter or by counting squares on graph paper, or by tabulation, as in Table V and VI. Step 3. The true boiling point curves of the bubble point vapor and dew point liquid can now be determined by plotting values of mv and mL from Tables V and VI versus temperature (Figure 3).
400 u.
rr w 400 < z
Y
t
300
200
4
3
Table V.
K,
t,
I
F.
Bubble Point Temperature Calculation at 327' F.
rnF
Ams
22 Lb./Sq. I n c h Abs.
Mean
K
Area
,
Values of m v = Aco. Areas for Bubble Point Vapor T B P
0
and arrows, using values of prorated accumulated areas for the liquid and vapor from Step 4. The resulting vapor and liquid true boiling point curves versus mole fraction off are then drawn through these points, as shown in Figure 1 for the flash a t 390' F. and 22 pounds per square inch absolute. Bubble and Dew Point. Bubble and dew point calculation for the integral method are the same, in principle, as bubble and dew point calculations for finite mixtures by the conventional methods. The integral relationship for bubble point calculation is
Table VI.
Dew Point Temperature Calculation at 435" F. Values
of
Values of K a t an assumed temperature for several points on molar true boiling point curves are plotted against mF and the area under the curve found. An area of unity indicates the correct temperature assumption. The integral relationship for the dew point calculation is
Values of 1 / K a t an assumed temperature for several points on the molar true boiling point curve are plotted against mp and the area under the curve found. An area of unity indicates the correct temperature assumption. Bubble point calculations are sensitive to the front end K values, while dew point calculations are sensitive to the high boiling end K values. For these reasons, K values are found and plotted a t more frequent intervals for the low boiling end in
1688
200--
rnL
=
0 . 0 9 3 6 ~ -0 0.1283 0.0180 0.163+----0.0180 0.24 0.2225 0.0534 300--0.38----0.2520--0.0714 0.24 0.3880 0 0931 350--0.62---------0.494------------0.1646 0.17 0 7035 0 1196 ___0.2841 400--0.79-------0.913~ 0.05 1.085 0.0542 0.3383 425--0.84--1,257--0 04 1.508 0.0603 450-0. 8 8 p - p 1.76+-----0.3986 0.03 2.130 0.0639 91----2,500---0.4625 475--0. 0.025 3.024 0,0756 0.5381 500--0,935--3.5480.020 4.302 0.0860 526-0.965---5.057-0.6241 0 018 6.146 0.1106 -0.7347 550--0.973-----------7.2360.017 8.323 0.1415 575-0,9909.410 0.8762 12.38 0.1238 0,010 600-1.000--15.38 -1.0000
0.14
250-0.14----
INDUSTRIAL AND ENGINEERING CHEMISTRY
____
Vol. 47, No. 9
ENGINEERING, DESIGN, AND EQUIPMENT Fractional Distillation. The integral technique can be applied to multistage distillation calculations, as well as to single-stage equilibrium flash vaporization. Component distribution calculations are made for infinitesimal portions of the feed to distillate and bottoms in the same way that such calculations are made for mixtures of finite components. Ratio-type component distribution equations for multiconiponent, multistage fractionation are given in terms of absorption and stripping factors.
++ AzAa.
Enricher: ln/d = AoAIA2A3. . . A v L A1A2A3. . . A n
.An
+
,
..
FIGURE 5
/ I
MOLAR TRUE BOILING P O I N T CURVES OF FEED AND PRODUCTS
400
+ An 300
w'
;200 -
where vf/f and l//f are component distribution ratios for feed flashing and subscripts designate plate location numbering from and toward feed.
A
=
L/KV
=
l/X,A ,
=
Table 'VII. CQ 298
Separation Functions C11 CIZ Cia 360
393
415
0.789 4.34
Plate 1 : t = 365' F., L = 1275, V = 818, V / L = 0 642 K 2.4 0.934 0.667 0.486 s1 = K V / L 1.54 0,5996 0.428 0.312
0.279 0.179
Plate 2 : t = 355' F.,L K Az = L / K V
208, V = 822, L / V = 0 . 2 5 3 2.14 0.816 0.575 0.414 0.1182 0.310 0.440 0.611
0,237
Plate 3 : t = 322' F., L = 212, V = 822, L / V = 0 268 K 1.38 0.442 0.377 0 238 Ax = L / K V 0.187 0.524 0.765 1.083
0.130 1.981
Enriching with reflux from total condenser: R = 0 . 8 4 7 5 Ax(1 R) 0,252 0,706 1.031 1.459 An[l A'(1 R)1 = ln/d 0,148 0.5288 0.8936 1.503
2.669
+
SI(SO-I- 1) = u m / b
Feed plate mesh ln/d unt/b 1 !=-vm/b 1' En/d + v m / b
+
+
September 1955
29.5 45.6 46.75
+
0.975
13.4 8.03 9.56 0.839
10.33 4.43 6.32 0.701
0
-100
0
0.2
I
0.4
0.6
I I
10.8
I
1.0
. c 0
m
=
+
Stripping so 1
I00
CIS 453
Reboiler: t = 435' F., L = 196, V = 1079, V / L = 5 . 5 K 5.18 2.25 1.617 1.316 So = K V / L 28.5 12.4 9.33 7.24
++
!
R (for total condenser)
The above component distribution ratio equations represent one of several ways that such calculations can be made. These equations are not part of the integral technique. The component distribution ratios might be found by a short cut method if desired. After separation functions are evaluated and component distribution ratios found, by these or other equations, the values of d/f or b / f are plotted against mF. The area under this curve gives D / F and B / F . Areas to different values of m F are used to determine points on molar true boiling point of products. An interesting feature of the integral method, as applied t o fractional distillation, is that distribution ratios are estimated for several closely spaced points near the cut point and a t a few widely spaced points on the balance of the curve. Example 3. A gasoline rerun column, consisting of a reboiler and one theoretical plate below the feed and two theoretical plates and a total condenser above, will be used t o illustrate the application of the integral technique in fractional distillation. I n this problem the feed stock is defined by a true boiling point distillation curve, the reflux and boil-up are fixed, and the problem is to calculate the products. The problem is from Thiele-Geddes ( 7 ) , and is the same
Equivalent H-C. Atm. B.P., F.
< K Y
1.066
3.912
8.24 2.57
5.34 0.955
5.07 0.487
5.86 0.163
F
problem (6) used to illustrate the integral method. The present solution is simpler. Solution. This calculation is identical to the flash calculation except in the evaluation of the separation functions. The effects of the number of theoretical stages and the reflux must be included. The separation function must be evaluated for the equivalent hydrocarbons in the vicinity of the cut point, however, because of the sharpness of separation. These separation functions are based on an assumed temperature gradient and assumed liquid and vapor traffics from plate to plate. Thus, the calculations give the products from the assumed operation. Figures 5 and 6 illustrate the solution. Calciilations giving the d/f value for each component are plotted a t the proper value of mF and the area undep the curve
INDUSTRIAL AND ENGINEERING CHEMISTRY
1689
ENGINEERING, DESIGN, AND EQUIPMENT Nomenclature Table
nt,
0.1
Mean ordinate
VIII.
Integration Calculations
Distillat GroIncrerated ment increareas ment
0,9999
0.09999
0.1306
0.999
0.0999
0.1303
0.2 0.998
0.0998
0.1293
0.995
0.0995
0.1290
0.00001 0.0001 0.1306
0.0001
0.0004
0.986
0,0986
0.1282
0.0002
0.0009
0.0005
0.0022
0.4
0.0014
0.0060
0.5193-0.6475--0.960
0.0960
0.1248
0.875
0.0875
0.1138
0.600
0.060
0.0780
0.6
0.0040
0.0173
0.0125
0.0541
0.7
0.0400
0.1730
0.9641 0.240
0.024
0.0312
0.036
0.0036
0.0047
0.0760
0.3290
0.0964
0.4170
-_
-
0.9953 __0.76889
-1.000
1.0000
--
= moles of feed mixture
D B 1
= = =
2,
= = = =
f
0.0036
d b
=
K
moles of vapor mixture moles of distillate mixture moles of bottoms mixture moles of any infinitesimal increment (an indefinite number of these infinitesimal increments (or components) make up each petroleum fraction) of liquid moles of any infinitesimal increment of vapor moles of any infinitesimal increment of feed moles of any infinitesimal increment of distillate moles of any infinitesimal increment of bottoms y/z = vapor-liquid equilibria ratio mole fraction of infinitesimal increment of vapor mole fraction of infinitesimal increment of liquid L/KV = absorption factor on indicated equilibrium stage
0.0810
2
0.2540
A
= = = =
8
= - =
0.0269
0.8861
0.8
F
0.0014
0.0096
0.7723
= moles of liquid mixture
0.0001 0.0005
0.3902
0.5
1.0-
~icumulated prorated
0.2609
0.3-
0.9
BottomsProAccuIncre- rated mulated ment increproareas ment rated
L V
y
7
0.5830
1 000 t
0.23111 1.00
mp =
mL =
found. This equals D / F from which D is found and the desired over-all stock balance checked. Product true boiling point curves are plotted with points obtained from the areas up to various mF values. The ndmerical and graphical parts of this operation are shown. Following is the step-by-step procedure. Step 1. Plot molar true boiling point curve for feed, deriving points for this curve from the volumetric true boiling point and Chart I or I1 if necessary. Figure 5 shows resulting plot. Step 2. Assume number of plates, temperatures, and liquid and vapor quantities given by Thiele-Geddes in this case. Step 3 . Select several component points and evaluate separation functions. This is done in Table VII. Step 4. Plot d/f values from Step 3 against m F in Figure 6. Step 5 . Integrate, finding area under curve in Figure 6. This is equal to D / F giving D = 620, which checks material balance. Step 6. Find areas under curve in Figure 6 to different values of mp and from these estimate molar true boiling point curves of products. (Table VI11 shows calculations and Figure 5 shows curves. ) Acknowledgment
The help of H. D. Eddy in making the calculations, charts, and figures is gratefully acknowledged.
stripping factor on indicated equilibrium stage
~
mv
=
P
=
po
=
R
=
mole fraction off a t indicated temperature in true boiling point analytical distillation of feed mole fraction off a t indicated temperature in true boiling point analytical distillation of liquid product mole fraction off a t indicated temperature in true boiling point analytical distillation of vapor product pressure vapor pressure reflux ratio-i.e., moles of reflux to moles of distillate
SUBSCRIPTS 0 refers to reboiler or condenser 1, 2 , 3 indicate equilibrium stages numbered from condenaer or reboiler toward the feed plate n refers to bottom plate in enriching section m refers to top plate in stripping section F and f refer to feed literature cited
(1) Bowman, J. R.; IND. ENG.CHEM.,41, 2004 (1949). (2) Ibid.,43, 2622 (1951). (3) Bowman, 3 . R., and Edmister, W. C., Ibid.,43, 2628 (1961). (4) Edmister, W. C., and Bowman, J. R., Chem. Eng. Progr. Sym. Series, 48, N o . 2, p. 112 (1952). (5) Ibid.,48, No. 3, p. 46 (1952). (6) Edmister, W. C., and Buchanan, D. H., Ibid., 49, No. 6, p. 69 (1953). (7) Thiele, E. W., and Geddes, R. L., IND.ENQ.CHEM.,25, 289 (1933).
RECEIVED f o r review January
6, 1955.
ACCEPTED April 18, 1955,
Correlation of Experimental Data on the Disintegration of liquid Jets C. C. MIESSE Aerojet-General Corp., Azusa, Calif.
T
HE phenomenon of jet disintegration has been subjected
to theoretical and experimental investigation for the past hundred years. Ever since Lord Rayleigh made his first analyses of jet instability in 1868, engineers and physicists alike have derived theories and devised experiments to correlate the data obtained from jet experiments. As the first phenomena which occur in the combustion chamber of a liquid propellant rocket
1690
are the injection of the liquid and the subsequent disintegration of the jets into droplets, a study of jet disintegration should contribute greatly to the understanding of the phenomena that are observed. The methods by which the theoretical analyses of jet disintegration have been made can all be grouped into three genera1 classes, or into a combination of these classes.
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 41, No. 9
