This effect is related to the complex mechanism of coke formation which involves adsorption as well as condensation and hydrogen elimination reactions. Literature Cited
(1) Appleby, IV. G., Gibson, J. W., Good, G. M., IND. END. CHEM.PROC.DESIGN DEVELOP. 1,102 (1962). (2) Eberly, P. E., Kimberlin, C. N., Trans. Faraday SOC. 57, 1169 (1961). ( 3 ) Gladrow, E. M., Kimberlin, C. N., Division of Petroleum Chemistry, Symposium on Catalysts and Catalytic Cracking, 138th Meeting, ACS, New York, September 1960.
(4) Good, M., VO e, H. Greensfelder, B. s.9 h i . Eng. Chem. 39, 1032 (19475 ( 5 ) Greensfelder,B. s., Gage, H. H., zbid.,37, 982 (1945). (6) Haldeman, R. G., Botty, M. C., J . Phys. Chem. 63, 489 (1 959). (7) Thomas, C. L., J . Am. Chem. SOC. 66,1586 (1944). (8) Voge, H. H., Good, G. M., Greensfelder, B. S., Third World Petroleum Congress, Sect. IV, The Hague, 1951, E. J. Brite, Leiden, 1951. (9) Voorhies, A., Jr., Znd. Eng. Chem. 37, 318 (1945).
RECEIVED for review August 23, 1965 ACCEPTEDNovember 26, 1965
ADDITIONAL VELOCITY OF SOUND MEASUREMENTS IN WET STEAM W.
G. ENGLAND, J . C. F I R E Y , AND 0 . E. TRAPP
Department of Mechanical Engineering, L'niversity of Washington, Seattle, Wash. The velocity of sound in wet steam decreases slightly with decreasing quality under conditions of "fog flow" of the steam. Analysis indicates the decrease of velocity to depend upon the extent of liquid area in contact with the vapor and suggests that the liquid evaporation, expected for an isentropic expansion of wet steam, does not occur. Therefore the density of rapidly expanding wet steam may be greater than the density expected from an isentropic calculation. For calculations of the critical flow rate of wet steam, these results supply tentative values of the velocity of the vapor phase and the maximum density of the wet steam.
values of the velocity of sound in wet steam were and their relation to the critical flow of wet steam was discussed. These earlier measurements showed the velocity of sound in wet steam to be essentially independent of quality, markedly greater than the isentropic sound velocity except a t very high quality, and approximately equal to the velocity in dry saturated steam. These results indicated that, a t critical flow, the vapor portions of wet steam were probably traveling a t the velocity of sound, in agreement with Reynolds' interpretation of the critical flow phenomenon (3). These results suffered from two primary shortcomings. T h e experimental error of velocity measurement was of the order of +4% and the wet steam was partly separated, with a portion of the liquid flowing down the walls of the test section. Further measurements of the velocity of sound in wet steam have now been made wherein the experimental error was reduced to about .tlyo, the wet steam was only slightly separated, and the measurements were extended into the superheated steam region. EASURED
M reported earlier ( 7 )
Apparatus and Procedure
T h e experimental apparatus included a steam-water mixer, a test section, a rarefaction wave generator, and electronic apparatus to measure wave velocity. This apparatus was essentially similar to that described by Collingham ( I ) , except that major changes were made in the steam-water mixer and in the electronic apparatus, and minor changes were made in the test section and the rarefaction wave generator. A schematic diagram of the steam-water mixer is shown in Figure 1. Hot water a t high pressure was delivered to the calibrated water spray nozzle. High pressure steam, of about 198
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0.99 to 1.00 quality, was supplied to the calibrated steam nozzle. T h e high velocity steam leaving the nozzle was directed countercurrent to the water spray in order to atomize the liquid to very small droplets. The mixing chamber was a 6-inch pipe tee of large volume, so that the larger water droplets would separate and drop to the bottom of the chamber where they could be drained off via the excess water drain. T h e exit pipe from the mixer to the test section extended about 2 inches inside the mixing chamber, so that only water droplets suspended in the steam would be carried into the test section. The mixing chamber was fitted with a sight glass, so that the excess water drain valve could be adjusted to keep a very low water level in the chamber. Variation of steam quality to the test section was obtained by varying water nozzle pressure, steam nozzle pressure, or water nozzle size. This mixer provided wet steam of quality between 0.20 and 1.00 and with the liquid almost entirely suspended as minute droplets within the vapor ("fog flow"). An electric heater, with variable transformer control, was installed in the high pressure steam supply so that superheated steam could also be supplied to the test section. The schematic diagram of the test section is shown in Figure 2. Steam from the mixer entered a t the top, passed vertically downward through the straight test portion, and left through the test section pressure control valve. The straight portion of the test section consisted largely of rubber steam hose 2 inches in inside diameter. The arrangement of the rarefaction wave generator is sketched in Figure 3. Sheet plastic disks of various thicknesses and materials were clamped in the union. Vacuum was applied to the upper chamber until the disk burst. Bursting of the disk generated a rarefaction wave traveling downward through the test section and a compression wave traveling upward into the upper chamber. The upper chamber was fitted with a wave reflector and glass wool-packed wave trap to disperse and dissipate the compression wave. A thick
rubber gasket was mounted between the rarefaction wave generator and the test section to minimize transmission of the pressure pulse through the meta! pipe. As the rarefaction wave passed the upper pressure pickup in the test section, the resulting amplified electrical signal started a n electronic time interval meter. T h e electrical signal generated by subsequent passage of the rarefaction wave over the lower pressure pickup was used to stop the electronic time interval meter. I n this manner the time taken by the rarefaction wave to traverse the 6.4 feet between pressure pickups was measured and the wave velocity was calculated from this measurement. Quartz crystal piezoelectric pressure pickups were used with charge amplifiers. T h e time interval meter was set to read directly in microseconds and was calibrated periodically during the experiments. T h e pressure rise required to trip the electronic time interval meter was not accurately determinable but was very low. T h e trip level on the meter was set as low as possible (circa 0.20 volt). T h e gain of the charge amplifiers, interposed between the pressure pickups and the time interval meter, was set as high as possible, From these settings it is estimated that a pressure change of somewhat less than 0.5 p.s.i. caused tripping of the time interval meter. This corresponds to about one tenth of a major vertical division of the oscilloscope trace of Figure 4. Hence the time interval meter was tripped a t the start of the pressure wave. As a check on the operation of the time interval meter, several measurements of wave travel time were made with a n
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oscilloscope having a uniform, calibrated horizontal sweep velocity. The amplified signals of the upper pressure pickup and the lower pressure pickup were placed alternately on the vertical input to the oscilloscope a t a frequency of 100,000 cycles per second. The oscilloscope sweep was started by the electrical signal generated by passage of the rarefaction wave over the trigger pressure pickup, located about 1 foot upstream of the upper pressure pickup. A typical oscilloscope trace obtained in this manner is shown in Figure 4. This oscilloscope procedure is essentially similar to that used for the earlier measurements (7). Wave travel time as measured with the oscilloscope agreed with the value obtained with the time interval meter to Ivithin the accuracy that the oscilloscope trace could be read. T o check on the over-all operation of the electronic apparatus, the velocity of sound in air was measured a t frequent intervals during the experiments by filling the test section with air a t room temperature. These measured values agreed with the calculated, isentropic values within less than +0.5%. The quality of the steam in the test section was measured by a material and energy balance on the steam-water mixer and by barrel calorimeter measurements of steam samples drawn from the test section. For the material and energy balance the floiv rates and enthalpies of the steam and water entering the mixer and the excess water drained from the mixer were measured. From these data the quality of steam supplied to the test section and the average flow velocity of steam in the test section were calculated. The floiv velocity of steam in the test section was needed to correct the calculated wave velocity to the velocity of sound. The arrangement of the barrel calorimeter and sample probe is shown in Figure 5. A small sample of test section steam flowed through the sample probe and was condensed into a measured quantity of cold water. From the temperature rise and weight increase of the calorimeter water, the sample steam enthalpy and quality were calculated. The sample probe was arranged so that it could be traversed across the test section and rotated within the test section. The sample line between the probe and the calorimeter was preheated, prior to measurements, by bleeding a sample through the probe and exhausting to atmosphere via the two-way cock. The calorimeter measurements were made on runs separate from the wave travel time runs but under identical flow conditions.
Results and Comparisons EXCESS WATER DRAIN VALVE
Figure 1.
Schematic diagram of steam-water mixer
WAVE GENERATOR FROM MIXER
TRIGGER PRESSURE PICKUP UPPER PRESSURE PICKUP
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Visual examination of the test section steam. Comparisons of steam quality values as calculated by a n energy balance on the steam-water mixer and as measured by the barrel calorimeter. Measurements of the effect of sample probe orientation on the value of quality measured by the barrel calorimeter.
CORE CALORIMETER PROBE-
LOWER PRESSURE PICKUP
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* WASTE To
Velocity of sound was measured in slightly superheated and wet steam, down to a quality of about 0.20 weight fraction vapor a t 17 p.s.i.a. and to a quality of about 0.50 a t 45 p.s.i.a. These data are plotted in Figures 6 and 7 against the quality of the steam in the test section. T h e steam quality values are those measured by the calorimeter, and the velocity of sound values are those measured with the time interval meter corrected for steam flow velocity. The wet steam in the test section was in a fag flow condition, wherein the liquid portions are largely suspended as small droplets within the vapor portion. This assessment of the condition of the test steam is based on three independent observations :
I
e
Figure 2. Schematic diagram of test section
The test section steam was examined visually by removing the exit section and allowing the steam to flow into the room air. Very little liquid ran off the pipe walls, the bulk being sufficiently finely divided to remain in suspension after exit. Steam quality calculated by a n energy balance on the steam-water mixer agreed with the quality as measured by the barrel calorimeter to within 4’3& At qualities in excess of about 0.50 the results were virtually identical. Only a t the VOL. 5
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lowest test section qualities of about 0.20 were the results apart by more than-2%. The calorimeter probe has a single and hence local, not average, quality is sampling ured. T h e energy - . balance calculation, on the other hand, gave an average value of quality. Since local and average nearly alike, the liquid be uniformly qualities are dispersed within the vapor. Rotation of the sample Probe altered the measured value of quality only slightly, the greatest differences occurring a t the lowest qualities, as shown in Table I. H a d the liquid portions been present as large droplets or filaments, probe orientation changes would have appreciably altered the measured quality, since large droplets could not readily enter the sample hole when it faced downstream. Since sample probe orientation affected the measured value of quality only slightly, the liquid droplets would appear to be very small. T h e foregoing three independent observations clearly indicate that the wet steam in the test section was in a fog flow condition. The maximum cumulative error of the wave velocity measurement is estimated to be i1%; of the quality measurements, f4%. When the velocity of sound data reported herein are compared with both the earlier data (7) and the theoretical calculated values, the following observations emerge. For superheated steam, measured and theoretical calculated values of the velocity of sound are very nearly identical. For wet steam the velocity of sound decreases slightly as quality is reduced. The decrease of velocity over the range
Table 1. Effect of Sample Probe Orientation on Steam Quality Measured by Calorimeter at an Average Quality Of 0.22 Weight Fraction Vapor Measured Sample Probe Orientation Quality .
Facing upstream Facing across Facing downstream
0.210 0.278 0,242
-WAVE REFLECTOR
of qualities tested is about equal to the experimental error of the data Of (7). Experimental values of the velocity of sound in wet steam are markedly greater than the corresponding theoretical calculated values. For dry, saturated steam the theoretical calculated values shdw a discontinuity of the velocity of sound, in that the velocity for infinitesimally superheated steam is about 8% greater than for infinitesimally wet steam. This theoretical discontinuity is not found in the measured values of the velocity of sound. '
These comparisons are shown on Figures 6 and 7, wherein lines, indicating the range of the data of (7), are plotted together with the results of this investigation and the theoretical calculated values of the velocity of sound. These theoretical calculated values are those of Steltz (4) and are based on the assumptions that the steam is homogeneous, the wave process is isentropic, and thermodynamic equilibrium exists within and between phases. Discussion
The measurements reported herein, together with those of (7), clearly show that the velocity of sound in wet steam for a wide variety of flow conditions is much greater than the theoretical, isentropic value, and is nearly constant and equal to the value for dry saturated steam. The velocity of sound data reported herein are essentially identical to those reported in (7), despite the fact that the flow was partially separaied in ( 7 ) but was fog flow in this investigation. The principal engineering use of velocity of sound data is in the calculation of critical flow rates. For many critical flow calculations in wet steam a velocity of sound value roughly halfway between the theoretical values for slightly superheated steam and for slightly wet steam can probably be used with adequate accuracy a t all qualitites. Although the measurements reported herein clearly show the velocity of sound to decrease as liquid surface area increases, this effect is not large and will, in any event, be difficult to estimate in most flow systems. Where fog flow conditions are known to prevail, a curve of velocity of sound us. quality such as Figures 6 and 7 can perhaps be used for more refined calculations. As discussed below, the important variable appears to be liquid surface area, which will not, in general, bear a fixed relation to quality. The velocity of sound measurements reported herein also demonstrate certain of the rapid expansion characteristics of wet steam. The wet steam in the test section expands as the rarefaction wave passes through it and the characteristics of
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Figure 4. vs. time
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Figure 3. Schematic diagram faction wave generator 200
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Typical oscilloscope trace showing pressure variation a t both pickups
Upper. Lower pressure pickup with polarity direct Lower. Upper pressure pickup with polarity reversed Horizontal time scale, 0.001 second per maior interval; test section a t 17 p.5.i.a.;
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quality 0.21
this expansion determine what the velocity of the wave shall be. I n turn, from measurements of the velocity of the wave, certain rapid expansion characteristics may be inferred. Rapid expansion of wet steam occurs not only in a rarefaction wave but also in some conditions of critical flow. For example, when critical flow occurs a t exit from a pipe of uniform area, Falletti ( 2 ) has shown that the greater portion of the pressure drop and fluid acceleration takes place within a very short distance a t the end of the pipe. Since fluid velocity is high, the expansion of the wet steam through this steep pressure gradient occurs very rapidly. Of the several changes which rapidly expanding wet steam should undergo to maintain equilibrium, only condensation of vapor actually appears to occur, and this incompletely. T h e extent of condensation depends upon the amount of liquid
Figure 5. Arrangement calorimeter
of
area present to function as an acceptor of condensate. This hypothesis is based on the observation that the maximum reduction in velocity of sound with decreasing quality is seen in Figures 6 and 7 to be almost exactly equal to the theoretical discontinuity of the velocity of sound value between infinitesimally superheated steam and infinitesimally wet steam a t the saturated vapor point. From this observation we are led to believe that those expansion processes responsible for the theoretical discontinuity are likely to be those responsible for the reduction of measured velocity with decreasing quality. When wet steam expands isentropically the following changes occur:
A. The vapor portions expand. B. Some of the vapor molecules condense to a liquid. The latent heat of condensation is "left behind" in the vapor phase, since only low energy molecules will condense. C. T h e liquid portions expand. Except a t very high pressures this effect must be very small, since the liquid is so nearly incompressible. D. Some of the liquid molecules evaporate to a vapor. The latent heat of evaporation is carried into the vapor phase, since only high energy molecules evaporate. E. T h e net effect ofvapor condensation and liquid evaporation will depend upon the relative proportion of the two phases present. Very wet mixtures will show net evaporation and very dry mixtures will show net condensation. For infinitesimally or more highly superheated steam only change A-vapor expansion-occurs, since a liquid phase is not present and condensation is not required. This accords with the fact that measured and theoretically calculated values of the velocity of sound in superheated steam are essentially equal. For infinitesimally wet steam all four changes theoretically occur but only changes A and B can be appreciable, since the liquid portions are infinitesimal. Hence change Bvapor condensation and the consequent energy interchangemust be responsible for the discontinuity in the theoretical
barrel
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TEST SECTION STEAM QUALITY OR DEGREES F. SUPERHEAT Figure 6. Velocity of sound in wet and slightly superheated steam a t 17.0 p.s.i.a. with fog flow conditions
TEST SECTION STEAM QUALITY OR DEGREES F. SUPERHEAT Figure 7. Velocity of sound in wet and slightly superheated steam a t 45.0 p.s.i.a. with fog flow conditions VOL. 5
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value of the velocity of sound a t the saturated vapor point. This same vapor condensation change is thus probably responsible also for the reduction of the measured velocity of sound with decreasing quality. Vapor condensation is a process of the vapor phase alone. Since the extent of such condensation is seen to increase when the amount of liquid present is increased, we are led to infer that condensation occurs only upon existing liquid surface. The greater the extent of liquid area in contact with the vapor the greater the extent of vapor condensation under conditions of rapid expansion. T h e density of rapidly expanding )vet steam is probably greater a t any particular pressure than ivould be expected from an isentropic calculation. Calculations reveal that change Dliquid evaporation and consequent energy interchange-would exert a very large effect in reducing the velocity of sound a t lower qualities if this change actually took place. Since the velocity of sound is only slightly reduced at lower quality, liquid evaporation probably does not occur when \vet steam is rapidly expanded. Since liquid evaporation acts to reduce density, failure of evaporation will leave the fluid a t a higher density. For critical flow calculations, a maximum value of the density of wet steam a t the critical section can be calculated by assuming that neither liquid evaporation nor vapor condensation took place within the steep pressure gradient preceding the critical section. The foregoing analysis of the rapid expansion characteristics of wet steam is necessarily tentative, being based on the assump-
tion that the wave processes responsible for the theoretical discontinuity of the velocity of sound a t the saturation point are the processes actually responsible for the slight reduction of the measured velocity of sound as quality is reduced. I t is possible that the nearly equal magnitude of these two effects is simply a coincidence and that all of the changes theoretically called for in wet steam take place, though only partially.
Acknowledgment
T h e authors thank the Department of Mechanical Engineering and the Office of Engineering Research, University of Washington, for the generous financial assistance Lvhich made this work possible. The encouragement and assistance of M . E. Childs, R . C. Corlett, and C. J. Kippenhan are greatly appreciated. The assistance rendered by E. Norris, W.Piispanen, and \Y. Schoenfeld is gratefully acknowledged.
Literature Cited ( 1 ) Collingham, R. E., Firey, J. C., IND. ENG.CHEM.PROCESS DESIGN DEVELOP. 2 , 197-202 (1963). (2) Falletti, D. LV., “Two-Phase Critical Flow of Steam-LVater Mixtures,” Ph.D. thesis, University of LVashington, 1959.
(3) Reynolds, Osborne, “Papers on Mechanical and Physical Subjects,” Vol. 2, University Press, Cambridge, 1901, (4) Steltz, W. B., J . Eng. Pmer 83, 145-54 (1961). RECEIVED for review September 27, 1965 ACCEPTEDDecember 20, 1965
HIGH ACCURACY VARIABLE AREA METER CALIBRATIONS WITH MULTIPLE GASES Engineering Correlations P. T . E U B A N K Texas A&M University, College Station, Tex.
Calculation of accurate calibration results for a pure gas flowing in a variable area meter a t a given scale reading from the original experimental calibration data supplied by the manufacturer for other gases is examined, A correlation based on the kinetic energy theory of dilute gases predicts viscosity effects in terms of Lennard-Jones force constants. The influence of gas temperature and pressure on calibration data for laminar, transitional, and turbulent flow is considered, Calibration data for a number of gases flowing in the same meter are presented in support of the correlation. Application of the method to gas mixtures and to other metering devices is also discussed.
in gas dynamics often the accurate calibration of a given variable area meter with numerous pure gases. Calibration is generally made against one or two gases by the manufacturer prior to shipment. T h e experimentalist later must interpolate or extrapolate these results to obtain calculated calibration results for a new gas. How this may best be performed is the subject of this paper. Of particular interest are meters of high accuracy-at least 1% of the instantaneous scale reading and exceeding 20 inches in scale length-where calibration correlation between gases RESEST EXPERIMEKTAL RESEARCH
P demands
202
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is most difficult. Such meters were definitely not inters changeable if stated accuracy was maintained ; this eliminates the use of friction factor us. Reynolds number type correlationby the manufacturer for multigas use with a given model of meter. Correlation Development
At a given scale reading, the friction factor, f, is a unique function of Reynolds number,
(E),
for prediction of the
