VELOCITY OF SOUND MEASUREMENTS
IN WET STEAM R . E . C O L L I N G H A M A N D J . C. F l R E Y Department o j Mechanical Engineering, University of Washington, Seattle, I t h s h .
The velocity of sound in wet steam was measured b y determining the time taken by a single rarefaction wave to travel a known distance through a sample of wet steam. Results were obtained over a range of quality vapor a i 1 and 3.05 atm. The velocity of sound was found to be independent of from 5 to 100 weighi the quality of the wet steam and approximately equal to the velocity in dry, saturated steam. The liquid and vapor portions of wet steam do not remain in thermodynamic equilibrium during the passage of a pressure wave. These results explain, in large part, the difference between measured and calculated flow rates of wet steam under so-called critical or choking conditions-Le., where flow rate i s independent of downstream pressure. A possible interpretation assumes the liquid and vapor portions of the wet steam to respond independently to the action of the pressure wave.
70
WHEN the flow rate through a pipe or orifice is no longer affected by further reduction in discharge pressure, critical flow is presumed to exist. According to Reynolds ( 7 ) , fluid velocity a t some section equals the propagation velocity of rarefaction waves when critical flow exists and a wave of further decrease of back pressure can no longer travel upstream to affect the flow rate. Measured critical flow rates of gases agree very closely with values calculated by Reynolds’ explanation. when rarefaction wave velocity is that resulting from isentropic expansion within the wave. When this method of calculation is used for wet steam, the calculated results are severalfold smaller than the measured values a t low qualities ( 7 , 2, 3 ) . The investigation reported was undertaken in an effort to ascertain whether Reynolds’ explanation was invalid for wet steam or whTther the expansion of \vet steam in a rarefaction wave was not isentropic. For this purpose the
velocity of propagation of rarefaction waves in wet steam was measured. Critical flow rates calculated by using Reynolds’ explanation and these measured wave velocities were then compared usith measured critical flow rates. Experimental Setup
T h e experimental apparatus included a steam-water mixer, a test section, a rarefaction wave generator, and electronic apparatus to measure wave velocity. Figure 1 is a schematic piping diagram of the steam-water mixer. Hot water a t high pressure was delivered to the calibrated water spray nozzle. A metered quantity of steam was added to the mixer to create wet steam. The steam quality leaving the mixer was calculated from the measured steam and bvater f l o ~rates . and enthalpies. T h e schematic diagram of the test section is shown in Figure 2. \Yet steam from the mixer entered a t the top. passed ver-
WATER SPRAY N O Z Z L E 7 \\\\\\\\\\\\\\~,\\\\\\
/
WAVE GENERATOR-
6HOT p \WATER 1 ! , & 2 yq-
TO TEST SE C T I ON
(+
t
FROM MIXER
UPPER PRESSURE GAGE
*7
CORE CALORIMETER PROBE
CONTROL VALVE
n
+LPI:
?+ I
THROTTLING CALORIMETER
HIGH ?RESSUR€ STEAM
Figure 1.
f
Schematic diagram of steam-water mixer
TO WASTE
Figure 2. tion
Schematic diagram of test sec-
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TO VACUUM)
PLASTIC DISC
TlON
Figure 3. Schematic diagram of rarefaction wave generator
TEST SECTION
\fl-q
w 1
/I
tically downward through a straight portion, and left from the lower end of the test section. The straight portion of the test section consisted largely of rubber steam hose 2 inches in inside diameter. T h e rarefaction wave generator is sketched in Figure 3. Plastic disks of various strengths were clamped in the union, R. Vacuum was applied to the chamber, Q, until the disk burst. The resulting rarefaction wave traveled downward through the wet steam contained in the straight portion of the test section. An isolation gasket of foam rubber was inserted between the rarefaction wave generator and the test section to minimize wave transmission via the pipe walls. The time taken by the rarefaction wave front to travel from the upper to the lower pressure gage in the test section was measured in order to calculate the wave velocity. Quartz crystal, piezoelectric pressure gages were used. The amplified pressure gage signals were applied to the vertical input of a cathode ray oscilloscope through a “chopper” circuit which applied the upper pressure gage signal and the lower pressure gage signal alternately to the vertical deflection plates a t a frequency of 100,000 cycles per second. The oscilloscope trace was moved horizontally a t a uniform, calibrated speed by the sweep generator within the oscilloscope. .4 single sweep occurred, triggered by the signal from the upper pressure gage. With these arrangements both pressure gage signals appeared upon the oscilloscope screen to a common time scale just after the bursting of the plastic disk. The time interval taken by the wave front to travel between the pressure gages was measured from a photograph of the oscilloscope trace, Wave velocity was calculated as the ratio of test section length between gages (7.416 feet) to this time interval. T h e barrel calorimeter sketched In Figure 4 was used to measure local steam quality within the rest section. These measurements were made separately from the wave velocity experiments. since the presence of the steam sample probe in the test section might disturb the uave. Identical flow conditions were used for both experiments. A small sample of test section steam was condensed into a measured amount of cold water and the temperature rise and weight increase of the water were noted. The specific enthalpy and quality of the steam sample were calculated by a n energy balance. The steam sampling nozzle for this calorimeter had a single inlet hole at right angles to the sampling tube and the sampling tube was rotatable, so that samples could be taken from different angular positions in the test section. With this sample nozzle only local quality was measured, which was of interest as a n indicator of the extent of phase separation occurring in the test section.
WATER BUCKET
Errors and Corrections INSULATED CONTAINER
Figure 4. Schematic diagram of calorimeter
Figure 5. gram
barrel
Typical oscilloscope trace of pressure-time dia-
Upper. Lower pressure gage with rarefaction causing downward deflections lower. Upper pressure gage with rarefaction causing upward deflections Horizontal time scale, 0.001 second per major interval. Tesi section at 45 p.5.i.a. and gross quality 0.791
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I&EC PROCESS DESIGN A N D DEVELOPMENT
Of the several sources of error in the experimental arrangement used, the following are considered most significant : Flow velocity of the wet steam in the test section Method of triggering the sweep. Wave distortion. Heat loss.
The measured wave velocity was corrected for the flow velocity of the wet steam in the test section by assuming both the liquid and vapor portions to be moving a t the same velocity. The maximum velocity of the wet steam was below 30 feet per second The oscilloscope sweep could not start until the required triggering voltage v a s developed by the upper pressure gage. Hence. the front of the rarefaction wave is already slightly past the upper pressure gage when the sweep commences. This error was estimated to be less than 1% of the measured wave velocity, by a n extrapolation of the nearly straight-line rarefaction wave front forward to the known zero signal-biased position of the oscilloscope trace, The time interval was measured between the starting points or fronts of the rarefaction wave, since subsequent portions of the wave were distorted. This distortion is probably due to the effect of rarefaction on wave velocity, the effect of friction. and the effect of transverSe waves in the test section.
When steam of 99% quality or drier was flowing through the test section, the steam enthalpy measured by the barrel calorimeter in the test section agreed with the value measured by the throttling calorimeter ahead of the steam meter within =k1%. This indicates heat loss through the walls ia small. Periodically during the experiments, the test section was filled with air a t atmospheric pressure and 70' F. and the velocity of a rarefaction wave measured. These measured wave velocities agreed within =t3Oj, with the known velocity of sound in air, indicating the apparatus was capable of giving results accurate to within this limit. These air measurements include the errors due to triggering and wave distortion. Experimental Results
Rarefaction wave velocity was measured in wet steam a t 1atm. (14.7 p.s.i.a.) and 3-atm. (45 p.s.i.a.) pressure with qualities between 5 and 100 weight % vapor. Duplicate runs were made a t each test condition. An example of the oscilloscope trace obtained is shown in Figure 5. Since the rise time of the pressure gage is less than about 20 microseconds, the wave forms shown are very close to the true form of the experimental rarefaction wave. This is seen to be a simple rarefaction wave a t the wave front. Within a rarefaction wave the wave front moves fastest and a t the velocity of sound-see, for example, Shapiro ( 9 ) or Sabersky (8). Hence, these rarefaction wave velocities are also the velocity of sound. The maximum cumulative error of measurement is estimated to be =t4'%, The velocity of sound in wet steam was found to be independent of the quality and approximately equal to the velocity of sound in dry steam. as shown in Figures 6 and 7 . Calculated values of the isentropic velocity of sound in wet steam are also shown in Figures 6 and 7 for comparison. These isentropic velocity of sound values are a combination of those of Faletti
( 3 )in the low quality region and Steltz (70) in the high quality region. These recent calculated values agree closely with earlier calculated values of Isbin, Moy, and Cruz (4). Evidently the actual wave process is not isentropic. T h e quality of steam-water mixture in the core of the test section was higher (drier) than the gross quality of the fluid flowing through the test section, as shown in Figure 8. These results suggest that annular flow conditions existed in the test section with a large portion of the liquid flowing down the walls. Nevertheless, low quality steam (circa 0.266) existed in the core for several of the test runs. These core quality data are necessarily only very approximate because of the nature of the sampling probe used. This is shown by the core quality measurements obtained when the probe was rotated to point across the direction of flow and then downstream. as listed in Table I. Table I.
Effect of Calorimeter Sample Probe Orientotion on Measured Core Quality (Fixed gross quality of 0.051)
Sample Probe Orientation
Facing upstream Facing across Facing downstream
Measured Core Quality 0.266 0.476
0.150
An accurate measurement of the core quality apppars difficult to obtain. Visual observations of the wet steam in the test section were made a t 1-atm. pressure by removing the lower end of the test section and examining the leaving wet steam. These examinations confirmed that some phase separation had occurred as liquid was running off the wall surfaces and the core mixture was a fog of minute liquid droplets suspended in the steam. These visual observations are in qualitative accord with the core quality data. 1600
I400
1200
v)
k
s
1000
t 0
2>
800
0
t;
$
600
4
400
;
200
0 ,
o
1
!
o
2
0 0
0.2 0.4 0.6 0.8 1.0 GROSS QUALITY, X G , OF STEAM-WATER MIXTURE
Figure 7. Acoustic velocity in wet steam of various gross qualities a t pressure of 15 p.s.i.a. VOL. 2
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Discussion of Results
When a rarefaction wave enters a saturated liquid-vapor mixture, the fluid may respond to the wave by four different actions.
1. The wave pressure gradient causes the fluid to move and acquire a velocity. 2. The pressure drop causes the liquid portions to evaporate partially. 3. The pressure drop causes the vapor portions to condense partially. 4. The pressure drop causes the vapor portions to expand. These responses in turn determine the propagation velocity of the wave through the mixture, Hence, we will attempt to explain, in terms of these four actions, the large difference between observed and isentropic velocities of sound in wet steam. T o be isentropic, the fluid motion must be friction-free and the liquid and vapor portions have the same velocity. Hence, in a n isentropic rarefaction wave the liquid and vapor portions are equally accelerated by the wave pressure gradient. In wet steam this is impossible, since the liquid portions, being of much higher density, will be less accelerated than the vapor portions. Only in the region of the critical state, where vapor and liquid densities are equal, could this isentropic requirement be met. In our experiments the quantity of liquid was varied over a wide range without any effect on the wave velocity. Hence, we may suggest that under these experimental conditions the motion response of the liquid regions was negligible. I n an isentropic rarefaction wave the vapor and liquid regions remain in thermodynamic equilibrium. Hence, evaporation of the liquid portions and condensation of the vapor portions required for equilibrium are expected to occur. The net equilibrium effect will vary with the quality of the mixture, I n mixtures rich in liquid, evaporation will predominate and a net partial volume increase will result. In mixtures low in liquid. condensation will predominate and a net partial volume decrease will result. These partial volume changes will affect the wave propagation velocity. The experimental wave velocity was unaffected by a large change in the liquid portion, indicating that only negligible evaporation took place from the liquid regions under experimental conditions. S o conclusion can be drawn as to whether condensation occurred in the vapor regions in our experiments, since the vapor quantity varied only slightly over the range of qualities tested, the added liquid being of such low specific volume. We may summarize by suggesting that a rarefaction wave in wet steam travels through the continuous vapor portion as if no liquid were present. Hence, the wave velocity is independent of steam quality and equal to the velocity of sound in dry steam as observed in these experiments. This proposed mechanism may not be applicable: Near the critical state. At extremely low quality when the continuous phase is liquid. When liquid droplet size becomes very small.
GROSS QUALITY, XG, OF STEAM-WATER MIXTURE
IN THE TEST SECTION
Figure 8. Comparison of gross quality of wet steam to measured core quality at center of test section Sample hole of probe located at center of test section and facing directly upstream
are obliged thereby to make a proper motion response. The vapor bubbles, being of lower density, may also make a proper motion response. Under these conditions the wave velocity would be expected to be more nearly equal to the isentropic value, as observed by Karplus (5). As liquid droplet size is reduced, the drdg force of the vapor per unit mass of liquid increases. Hence, the difference between the liquid and vapor velocities becomes less and the morion response of the liquid portions may more nearly approximate the isentropic. Whether such a drag-induced motion response of the liquid portions would affect the wave propagation velocity is not known. If it does, the data reported herein suggest that droplet size must be very small before the effect becomes significant. Although marked phase separation took place in our tests, the core steam was very wet in some experiments (circa 26% quality) and consisted of a fog of liquid droplets suspended in the vapor. The liquid droplet size within the fog was so small that fog segments drifted in room air without visible settling.
Application to Critical Flow of Wet Steam
At pressures near the critical state, where vapor and liquid densities are nearly equal, the motion responre of the liquid regions may approximate the isentropic and the wave propagation velocity may correspondingly be affected. At extremely low quality the continuous phase may become the liquid. When the continuous phase is liquid, the wave is constrained to pass through this phase and the liquid regions 200
I&EC PROCESS D E S I G N A N D DEVELOPMENT
W h m we seek to calculate the critical flow rate of wet steam the following problems are encountered: The vapor velocity is not clearly known. Slip flow probably occurs3 wherein the liquid and vapor phases are not moving a t the same velocity and the ratio of these velocities is unknown. The wet steam may not be in thermodynamic equilibrium
1.6
Isentropic model critical mass velocity Gth -observed critical mass velocity GO
I
i
Second model critical mass velocity _ -G, observed critical mass velocity Go The values of Go, the experimentally observed critical mass velocity, are those reported by Faletti (3) in pipes of constant cross-sectional area. Faletti found the ratio of isentropic critical m a s velocity to observed critical mass velocity, Glh/Go, to be largely independent of pressure within the range of pressure (26 to 106 p.s.i.a.) and gross quality (0.1 to 0.975) of his measurements. Since a value of unity for the mass velocity ratio would indicate perfect correlation between calculated and observed valurs, Figure 9 shows the second flow model to be a closer approximation than the isentropic flow model. Although significant differences remain, the approximate agreement between G , and Go shown in Figure 9 indicates Reynolds' description of the critical flow phenomenon to be correct for wet steam. Only a part of the remaining difference can be explained as an effect of slip flow. It has been shown ( 6 ) that the ratio G,/G, follow the relation :
d W 0
8 a
"quo vi
2 l-
a a
0
0
0.2
0.4
0.6
ae
1.0
EOUlLlBRlUM GROSS QUALITY, X G q AT CRITICAL SECTION
Figure 9. Comparison of measured critical mass velocity, G,, of wet steam to critical mass velocity calculated by two methods G o volues from doto of Faletti (31 in pipes of constant cross section
and thus its density is unknown-e.g., a temperature difference may exist between the liquid and vapor regions. T o calculate critical flow rates, assumptions must be made for each of these three problems. Two sets of assumptions are examined here: For the isentropic flow model: T h e flow velocity equals the isentropic velocity of sound. the velocities of both phases are the same, and the two phases are in equilibrium. For the second flow model: T h e vapor velocity equals the velocity of sound in dry steam as observed herein, the velocities of both phases are the same, and the specific volume a t the critical section equals that required for thermodynamic equilibrium. These two sets of assumptions were chosen to show that the real critical vapor velocity is probably the velocity of sound in dry steam as measured in our experiments. \Yii h this assumption. a large part of the discrepancy between observed and calculated critical flow rates disappears. The remaining discrepancies can be explained as resulting from the occurrence of slip flow and the lack of thermodynamic equilibrium between phases. Consequently, we may suggest for the real flow model that the vapor velocity equals the velocity of sound in dry steam, the liquid velocity is less than the vapor velocity, and the specific volume a t the critical section is not equal to that required for thermodynamic equilibrium. T h e results of critical floiv rate calculations carried out according to the above two flow models are presented in Figure 9, where the following two ratios are plotted against equilibrium gross quality:
Slip ratio, K , is defined here as the ratio of steam velocity to water velocity. If we accept Reynolds' description of the critical flow process, a, and ugoare identical and their ratio is unity. It would appear, therefore, that we can calculate slip ratio under observed conditions, K O from , the foregoing relation. When this is attempted, the resulting values of KO are greater than unity a t qualities below about 507, and less than unity a t higher qualities. This result appears unreasonable, since a slip ratio less than unity means that the water velocity is greater than the steam velocity. Under the action of a pressure gradient the more dense water will be less accelerated than the steam and K is expected to be always greater than unity. Hence, the occurrence of slip flow can, at best, explain only those differences between G , and Gooccurring in the low quality region. One method of resolving the foregoing difficulty is to propose that the fluid passing through the critical section has a greater density than would be calculated from the steam tables. This situation might prevail if the expansion of wet steam through a pressure gradient in a pipe were nonisentropic. Yellott ( 7 7 ) , Bottomley (7), and others have shown that such is the case in nonuniform passages. The acoustic velocity results reported herein demonstrate that the expansion of wet steam through the pressure gradient of a rarefaction wave is nonisentropic. \\'e may reasonably assume therefore, that the wet steam passing through a critical flow section is not in equilibrium and its properties, including density. are not those found in the steam tables (the thermodynamic equilibrium properties). A quantitative evaluation of the foregoing proposals is not possible, since neither the slip ratio, K. nor the properties of nonequilibrium n e t steam are known. Nomenclature a
= velocity of sound, feet per second
G = mass velocity, pounds mass (lb. m.) per sq. foot per second u x
= specific volume, cu. feet per lb. m. = steam quality = ratio of Ib. m . vapor to lb. m. liquid plus
vapor u = linear flow velocity, feet per yecond VOL. 2
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K
= slip ratio = ratio of vapor velocity to liquid velocity
agement and assistance provided by R. W. Moulton of the Chemical Engineering Department. The assistance rendered by W. W. Piispanen, W. Slattery, W. Schoenfeld, and Y . B. Safdari is also gratefully acknowledged.
SUBSCRIPTS
f
= liquid phase g = vapor phase c = critical flow conditions o = experimentally observed conditions th = isentropic conditions rn = nonisentropic conditions G = gross properties a t a section
literature Cited
Conclusions
Within th? range of these experiments (pressure between 14.7 and 45 p.s.i.a. and groas quality between 5 and 100%) whose continuous phase is the vapor: The acoustic velocity in wet steam has a constant value, independent of mixture quality, which is approximately equal to the acoustic velocity in dry steam. Reynolds’ description of the critical flow phenomenon appears valid for wet steam. Acknowledgment
The authors thank the Department of iMechanical Engineering and the Engineering Experiment Station, University of Washington, for the generous financial assistance which made this work posible. They express appreciation for the encour-
(1) Bottomley, W. T., Trans. ’Vorth East Coast Inst. Engrs. & Shipbudders 53, 65-100 (1937). (2) Cruz, A. J. F., “Critical Discharges of Steam-Water Mixtures,” M.S. thesis, University of Minnesota, 1953. (3) Faletti, D. W., “Two-Phase Critical Flow of Steam-iVater Mixtures,” Ph.D. thesis, University of LYashington, 1959. (4) Isbin, H. S., Moy, J. E., Cruz, .4. J. R., A.I.Ch.E. J. 3, 361-5 (1957). (5) Karplus, H. B., “Propagation of Pressure Waves in a Mixture of Water and Steam,” Armour Research Foundation of Illinois Institute of Technology, Rept. ARF 4132-12 (January 1961). (6) Moulton, R. LV., Firey, J. C., “Pressure Drop and Critical Flow for Steam-Water Mixtures,” General Electric Co., Hanford Atomic Products Operation, Richland, Wash.. HW-47681 (1957). (7) Reynolds, Osborne, “Papers on Mechanical and Physical Subjects,” Vol. 2, University Press, Cambridge, 1901. (8) Sabersky, R. H., “Elements of Engineering Thermodynamics,” McGraw-Hill, New York, 1957. (\9 ,) Shauiro. A. H.. “Dvnamics and Thermodvnamics of Compressible Fluid Flow,” Vol. 1, Ronald Press, dew York, 1953, (10) Steltz, W.B., J . Eng. Power 83, 145-54 (1961). (11) Yellott, J. J., Trans. A S M E 56, 411-30 (1934). RECEIVED for review July 30, 1962 ACCEPTEDMarch 22, 1963
THE KINETICS OF NICKEL CARBONYL FOR MAT ION W. M. GOLDBERGER’ AND D. F. OTHMER Polytechnic Institute of Brooklyn, Brooklyn, .V. Y
Extraction of nickel b y formation of the volatile carbonyl is a well known metallurgical operation, but little information is available concerning the rate. Kinetic data for the formation of nickel carbonyl were obtained by passing purified carbon monoxide through a fixed bed of freshly reduced nickel powder at temperatures from 25” to 150” C. and pressures from 1 to 4 atm. Powders of reproducible reactivity were obtained by hydrogen decomposition of nickel oxalate dispersed in finely divided fused silica to prevent sintering of the nickel. The rate of the surface chemical reaction appeared to control the over-all reaction rate, which reached a maximum at about 75” C. a t all pressures, The reactivityof the nickel was influenced by both pressure and temperature. A modified first-order rate equation was found to correlate the data when an empirical term was introduced to account for changes in the reactivity of the nickel with temperature and pressure.
receiving renewed attention in the field of extractive metallurgy is the formation of nickel carbonyl from metallic nickel and carbon monoxide. Since the turn of the century, this reaction has served as a means of extracting nickel from Canadian ores by the Mond process. Because of its unusual physical and chemical properties, nickel carbonyl has been the subject of many investigations and hundreds of articles and patents have been published relating to its preparation, properties, and applications (70). Mittasch made extensive studies of the thermodynamic properties of nickel carbonyl and also reported on the rate
A
REACTIOS
Present address, Extractive Metallurgy Division, Battelle Memorial Institute. Columbus 1 Ohio. ~
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l&EC PROCESS DESIGN A N D DEVELOPMENT
of formation at subatmospheric pressure in a closed system (7). Workers have not been in agreement on the actual mechanism of the reaction and several complex surface intermediates have been suggested ( 7 , 7, 9, 75) ; gas phase intermediates, however, were not detected by Srinivasan and Krishnaswami (72). Sykes and Townshend (73) presented very limited data indicating the effect of temperature on the formation of nickel carbonyl at atmospheric pressure. The patent literature also contains some information regarding the formation of the carbonyl, but this refers mainly to batch reactions at pressures high enough that the carbonyl forms as a liquid. The only detailed kinetic data that have been published on the volatilization reaction remain those reported by Mittasch in 1902;
