INDUSTRIAL AND ENGINEERING CHEMISTRY
1168
TABLEV.
EFFECTOF AIR FLOW IKTERRUPTIONS
(Same medium used in both fermentors: the air flow was 5 liters per minute or 1/a volume) Duration of Duration of Air Flow Air Flow Total Stoppage, Total Stoppage, Bcidity' Rlin. Aciditya Jfin. Age, Hr. Fermentor A Fermentor B 17
54 90
50
48 114
..
256 292 326 476 Finished
113 141 191 213 258 hI1. of 1 N KOH per liter.
1
...1.
..
a
..
..
138
20
178
30 15
234 266 308
'i ..
180 184
90
6 days) were obtained with 0.5 liter per minute ('/a0 volume) and this became the standard aeration rate. Increasing the air flow above this figure did not improve the yield or give faster fermentations. It is realized that aeration is affected by agitation. I n most of these experiments the agitation was gentle, with the agitator speed about 100 r.p.m. EFFECTOF INTERRUPTED AERATION. Fermentation often slowed down markedly after addition of alkali or antiform agents such as lard oil or octadecanol. At first this effect was attributed to toxic action of the addendum, but later experiments, summarized in Table V, indicate that it was due to interruption of the air flow. The total acidity listed includes some sulfuric acid; a t 17 hours practically the total titer is sulfuric acid. The interruptions were for varying periods a t the hours listed; thus fermentor B was stopped for 20 minutes a t the end of 54 hours. When the
VOI.
44. No. 5
fermentation is allowed to proceed without interruption of air flow and without adjustment of the pH, the p H goes down to as low as 1.6 and sugar is no longer consumed. Fermentors should have provision for the addition of materials without stoppage of aeration. CORNSTEEPLIQUORCONCENTRATION. I n the shaker cultures the optimum steep liquor content was found to be 0.15% by volume (a). Results obtained with the stainless steel fermentors followed the same pattern. Tank cultures containing only the steep liquor materials carried over in the inoculum (amounting to approximately 6 mg. of steep solids per liter of the fermentation medium) were exceedingly slow and gave reduced yields. On the other hand, higher concentrations, 0.3 to 1.5% by volume, resulted in heavier mycelia (over 10 grams per liter as compared with 5 grams per liter in the best fermentations) and correspondingly decreased acid production. LITERATURE CITED
(1) Friedkin, M., IND.EXG.CHEY.,AXAL.ED.,17, 637 (1945). (2) Lockwood, L. B., a n d Nelson, (2. E. N.,Arch. Biochem., 10, 365 (1946).
(3) Lockwood, L. B., a n d Reeves, &/I. D., Ibid., 6, 455, 482 (1945). (4) Lockwood, L. B., a n d W a r d , G. E., IND.ENG.CHEX, 37, 405 (1945). (5) Moyer, A. J., a n d Coghill, R. D., A m h . Biochem., 7, 167 (1945). (6) Shaffer, P. A, a n d H a r t m a n n , A. F., J . B i d . Chem., 45, 365 (1921). RECEIVED for review August 11, 1951. AccEPrsD November 8 , 1951 Presented in part before the Division of Agricultural and Food Chemistry a t QOCIETY, Atlantic City, N. J., the 116th Meeting of the AMEHICASCHEACICAL September 1949. Taken in part from a thesis submitted by G. E. K.Nelson to the Department of Chemistry in t h e Graduate Division of Bradley University in candidacy for the degree of Master of Science.
E
r
Process JACK W. RIZIKA'
I
AND
WARREN M. ROHSENOW
MASSACHUSSETTS INSTITUTE OF T E C H N O L O G Y , C A M B R I D G E , M A S S .
I
IK
ORDER to reduce the uncertainty of thermocouple readings the problem of estimating thermal error in thermocouples often arises. A thermocouple can measure only the temperature of its measuring junction, and to do this a great deal of care is required (6). Even though an excellent thermocouple circuit is provided to obtain an accurate measurement of the junction temperature, thermal errors may cause the junction temperature to differ greatly from the temperature of the substance being measured. In research work and industrial applications it is often necessary to know more accurately the temperature of the substance or fluid being measured. In most cases in which it is desired to measure the temperature of a fluid, part of the length of the t,hermocouple is exposed to the fluid, the thermocouple passes through a wall, and most of the thermocouple is in the surrounding environment, usually the atmosphere. Many times the effect of conducting heat down the wire and protecting tube, from the hotter to the colder sections, produces serious differences between the junction temperature and the fluid temperature. The followiiig analysis provides a means of estimating the thermal error in order to obtain a closer evaluation of the fluid temperature. 1
Present addreas, Oallatin C-35, Harvard University, Boston 63, Mass.
Assummom The following assumptions will be made in the analysis: 1. Heat flow and temperature distribution are independent of time, Le., steady state. 2. Thermocouple material is homogeneous and isotropic. 3 . There are no energy sources within the thermocouple itself. 4. Thermal conductivity, k , of the thermocouple system is uniform and constant. 5. The film coefficient of heat transfer, h, is uniform and constant over the surface of the thermocouple system. 6. Temperature of the surrounding fluid is uniform and constant. 7 . Thermocouple thickness is so small compared with its length that temperature gradients normal to the surface may be neglected. 8. Heat transferred through the tip of the thermocouple is negligible com ared with that passing through the sides. 9. The waf between the fluid and environment (atmosphere) is of negligible thickness. Therefore there is no heat exchange between the wall and the thermocouple system. ANA LYSI §
For purposes of the analysis consider the thermocouple system of length, L,shown in Figure 1. The thermocouple system, con-
INDUSTRIAL AND ENGINEERING CHEMISTRY
May 1952
Tf
Ta
/qdA
1169
tube, the idealized cylinder becomes identical with the thermocouple wire. The finite depth of immersion in the fluid whose temperature, T t , is to be measured is Lc. Let T be the temperature in the cylinder at any section at a distance, x, from the measuring junction and let Ta be the temperature of the atmosphere. By applying the first law of thermodynamics to an elemental section of the cylinder, dx in length, it c a n be seen that qdA
=
-
qz+dz
(1)
4s
From the Fourier law of conduction
In the atmosphere
i
L Thermocouple System L
Figure 1.
q d A = ho(To - T ) Pdx (SB) If it is assumed that the walls are a t such a temperature, T I ,that radiation cannot be neglected qdA
sisting of the thermocouple wire or wires and surrounding protecting tube, is idealized as a single cylinder, whose cross-sectional area is equivalent to the sum of the cross-sectional areas of the wire and protecting tube and whose outer perimeter is equal to the outer perimeter of the protecting tube. If the thermocouple system consists only of the thermocouple wire, with no protecting
where hr = hf
= hi
(Tt
-
+ h, and h, = u
T ) Pdx
(IC)
--
T 4 )which approximates (Tt . , T) the radiation effect by a linear relation (1). By the substitution of Equations lA, SB, and 1C into Equation 1, the following relations may be obtained: ('I4
I
I n the atmosphere
I n the fluid
W-T-Tf whose solutions are, for the atmosphere 6 =
cyeBoz
+
~ 4 e - ~ o *
1
Assuming the end effects of t h e thermocouple are small, the boundary conditions are:
Substituting the boundary conditions (Equation 4)into Equation 3, in the range 0 < x < Li
INDUSTRIAL A N D E N G I N E E R I N G C H E M I S T R Y
1170
Vol. 44, No. 5
Figure 2 is a plot of Equation G showing T f - Ti hi versus BiLi with - as a parameter. Ti - T , h, Figure 3 is an amplification of Figure 2 in the regions of small error (less than 10%). From knowledge of the nature and geometry of the thermocouple wire and protecting tube and of the heat transfer coefficients a t the surface of the sections of tube immersed in the ambient atmosphere and in the fluid whose temperature is to be measured, Figures 2 or 3 may be used conveniently for estimating the resulting thermocouple thermal error. 'rhe thermal error thus obtained is subject to the previously stated assumptions which are well justified in many applications.
t
T, - Tj Tj - To
EXAMPLE. A thermocouple measures the temperature of flue gases within an insulated sheet metal duct. The mass velocity of the gas is 1000 pounds per hour per square foot. The temperature as measured by the thermocouple is 800" F. The room temperature is 65" F. What is the actual temperature of the flue gases if the temperature-sensing element consists of a thermocouple inside of a stainless steel protecting tube with a closed end, which has a 3/g inch outside diameter and '/rinch inside diameter and extends 2 inches into the duct? The thermocouple hot junction is imbedded in the closed end of the tube. It is assumed that radiation between the thermocouple and the duct wall may be neglected. Then T , = G5" F., T , = 800" F., and I,, = 2 inches.
P
= ~ ( 0 . 3 7 5f ) =
(a)
12 = 0.0981 foot
(0.3752 - 0.252)
+ 144
=
0.000425
square. foot
BiLLFigure 3.
Tf Tg ~
- 3T' a versus B,L, -
and where T is the temperature a t any point along the cylinder that is immersed in the fluid. Thus
which is expected. With thermocouples one is interested only in the point where x = 0, at the junction. Usually the thermocouple extends out into the atmosphere a long enough distance so that the length of the thermocouple system, L, may be considered infinite. In such cases Equation 5 reduces to Equation 6, the equation for the temperature of the thermocouple junction
From Mciidams ( 3 ) (Equation 19), estimate the value of h, for natural convection in the surrounding air with a tube surface average temperature of approximately 250" F.; then h, v 2.4. Estimate h, from Figure 111 ( 3 ) . Assuming the flue gas has the viscosity and thermal conductivity of air a t 800" F., d G / p 400; then from Figure 111 (,9),oh,d/k,,, = 9.8 and h, = 9.4 B.t.u. per hour per square foot per F. From ( 4 ) for t8-8 stainless steel, k 2~ 15 B.t.u. per hour per square foot per F. Then
T / - TI and h,/h, = 9.4/2.4 = 3 9. From Figure 2, ___ - 0.10 and T , - To T I - T , = 74" F., whlch is the difference between the gas temperature and the temperature as read by the thermocouple. Some changes in conditions which would result in larger error than the 74" F. as calculated are smaller gas velocity, higher gas temperature, shorter immersion depth, smaller P I S ratio, higher thermal conductivity of the tube material and larger tube diameter. These are often encountered in problems concerning normal furnace temperatures. NOMENCLATURE
T,
=
Tf = T = I n choosing a thermocouple, one will normally make a choice of a small diameter, low thermal conductivity wire having the greatest possible depth of immersion in the fluid. Usually one will arrive at a choice of the wire size and protecting tube by compromising between the requirements of structural rigidity, temperature level, and low thermal error. When no protecting tube is used and when the fluid to be measured is in motion and a t high temperatures, such as those encountered in furnaces, the requirement of structural rigidity is of far greater importance.
T,
=
w
e
= =
T
=
e
=
z
=
L L, P S
=
= =
=
temperature of the atmosFhere, F. temperature of the fluid, F. temperature of thermocouple a t section 2-distance from the junction, F. temperature of the thermocouple junction, O F. T - T j T - T , 3.14 2.718 distance from measuring junction, feet total length of thermocouple system, feet length of thermocouple immersed in the fluid, feet perimeter of thermocouple system, feet cross-sectional area of the thermocouple system, square feet
May 1952 A
k
= =
G
=
p
=
q
ho
= =
h/
=
h,
=
u
= =
hi
INDUSTRIAL AND ENGINEERING CHEMISTRY
outer surface area, square feet thermal conductivity of :he thermocouple system, B.t.u. per hour per foot per F. fluid mass velocity, pounds per second per square foot absolute fluid viscosity, pounds er second per foot rate of heat transfer, B.t.u. per {our film coefficient of heat transfer between the air and thermocouple system, B.t.u. per hour per square foot per O F. film coefficient of heat transfer between the fluid and thermocouple system, B.t.u. per hour per square foot per F. radiation coefficient when approximated bz a linear relation, B.t.u. per hour per square foot per F. constant in Stefan-Boltzmann law = 0.1723 X 10-8 h, h,
+
1171 Subscripts o = reference to atmosphere i = reference to fluid
LITERATURE CITED
(1) McAdams, W. H., “Heat Transmission,” 2nd ed., p. 63, Yew York, McGraw-Hill, 1942. (2) Ibid., p. 221. (3) Ibid., p. 241. (4) Marks, L. S., “Mechanical Engineers’ Handbook,” 4th ed., p. 392, New York, McGraw-Hill Book Co., 1941. (5) U. S. Bur. Standards, Tech. Paper 170 (1921). RECEIVED for review July 30, 1951.
ACCEPTEDDecember 17, 1951
EngFnTring
Generation and Tyndallmetric Measurement of Dust Clouds
Process development I
w. L. CHEN, R. J. FORESTI, JR.,
AND
H. B. C H A R M B U R Y
PENNSYLVANIA STATE COLLEGE, STATE COLLEGE, PA.
C
were developed from the original work of Rayleigh (14) and Mie ORRECT evaluation of mine dust in the size range of 1 to 3 microns is a problem of great concern to many mine oper(19). In addition, work with larger size particles has been conducted by Tolman et al. (21). An attempt to utilize the light ators. Dust of this size reduces visibility in the mines as well as scattering principle for evaluating relatively large sizes of dust has assists indirectly in creating a physiological and, a t times, an exbeen carried out in this work. plosion hazard. The present method of collecting dust in the mines and then analyzing the samples in the laboratory is timeconsuming, expensive, and has numerous limitations (9)restrictDESCRIPTION OF APPARATUS ing its use and application. This investigation was conducted in an effort to develop an accurate, convenient, and inexpensive A schematic diagram of the assembled apparatus is &own in Figure 1. Compressed air passes through a pressure regulator method of mine dust evaluation. valve which is used t o reduce the pressure and to regulate the flow velocity. The low pressure air is filtered and dried by passing it Prior to the development of a dust analyzer it was necessary to study dust generation so that uniform dust clouds to simulate through a glass tube packed with activated aluminum and glass wool. The rate of air flow is measured by the Pressure drop &Crow mine dusts could be used. As a result, a dust generator capable of producing fairly uniform clouds of coarse sizes has a tubing with a mercury The dry? metered air is then passed through a pipe which extends through also been developed. This paper describes the apparatus and inthe dust generator. vestigations to determine the characteristics of the generator and The pipe contains an open slit exposed t o the interior of the generator which permits the suspended dust in the generator t o enter analyzer. the air stream. The suspension thus formed passes into the phoNumerous methods of generating uniform dust clouds in the toelectric anal zer. A small measured portion of the suspension Size range from colloidal and submicron to relatively Coarse Sizes which tLough the photoelectric analyzer is drawn through have been described in the literature (1, 3-6, 7, 10, 13, 16, 18). a midget impinger by means of an air ejector made from a laboratory as irator. The volume is m m m ~ e dby an Orifice-tYPe meThese methods are based primarily upon an air-jet principle. ter. T i e impinger sample is used t o calibrate the geneyator and utilized an electromagnet to vibrate an iron diaCassel et al, the analyzer. phragm on which the dust sample was placed, thoroughly to disDUSTGENERATOR.The body of the generator is machined from a piece of standard 4-inch pipe, 5 l / 2 inches long. A thin perse the dust particles prior to the application of the air jet. flange is welded $0 the top of the Pipe. A Lucite cover is held in This basic principle of using a vibrating membrane to disperse the place by 3 bolts. The bottom is formed by drawing a piece of # dust has been utilized in this inveatigation. lightweight silk very taut over a thin lywood ring and cementAt the Present time the methods used to analyze relatively ing it t o the frame. Several coats of facquer are applied to the silk to make it impermeable and the whole assembly is bolted to coarse sizes of dust are based upon one of five general principles: filtration (17), impingement (11, FLOW METER 167, sedimentation (8), and electrostatic (6)or thermal (22)precipitation. All of these methods ‘OM require that the dust be collected and then analyzed. A more di4 rect method, which has been used for the evaluation of colloidal PRESSED and submicron sizes of aerosols, AIR is based upon the scattering of a light beam by the solid particles (9,19,20). These methods Figure 1. Schematic Diagram of Assembled Apparatus
