For this orientation, heating current affected sensitivity as shown in Figure 4. T h e free and forced convection forces act in mutually perpendicular directions; hence, a change in current causes a chang: in the resultant wake angle. Since the thermistor is not symmetrical in the cross section about which the wake is shifting, It is not surprising that the calibration curves a t different currents are not alike. The calibrations also would vary strongly ivith current if the anemometer were used with the air stream floliing counter to the force of gravity. A maximum in temperature would be expected for this case, since the inertial and buoyant forces act in opposite directions on the heated fluid. Calibration in Water. A preliminary determination was made of the sensitivity of the thermistor in water. T h e thermistor used was a l~enwalbead-type glass probe thermistor (GB32P38) having both the bead and the leads encapsulated in glass (Figure 5). The thermistor was sealed inside a Swagelok 300-R-6 brass fitting with silicone RTV adhesive sealant. Calibration was carrietl out a t the center line of the parabolic velocity developed in a 0.934-inch i.d. Plexiglas tube, which was inclined a t a 15” angle u i t h the horizontal to keep the tube filled Lvith water for at least 7 inches beyond the thermistor. IVater was fed a t a known flow rate by gravity from a constant head tank. The average value of R,/log(R,/R,) was 2784 + 5 ohms. The value of R/log(R,,/R) -R,/log(R,/R,) is plotted against in Figure 6 for a thermistor current of 3 ma. The squareroot relationship is valid down to u = 0.1 cm. per second, and the instrument is capable of measuring to 0.02 cm. per second.
4;
ture. Temperature compensation is accomplished by switching the anemometer to a temperature-sensing mode. Calibration shows the anemometer to be sensitive down to 0.1 cm. per second in air, and preliminary results indicate a sensitivity in water down to 0.02 cm. per second. The anemometer response is proportional to the square root of velocity at all but the lowest velocities, as expected from reports in the literature. The sensitivity of anemometer response is a function of heating current when free and forced convection do not act in the same direction. literature Cited
Bowman, C. I$’., IYard, D. M., Johnson, A . I., Trass, O., Can. J . Chem. Eng. 39, 9 (1961). Broer, L. J. F., Hoogendoorn, C. J., Kortleven, A., Appl. Sci. Res. A7. 1 (1957). Clayton, B . R., Farmer, E. G., J . Sei. Instr. 40, 579 (1963). Bruijsten, J., AB$. Sei. Res. A2,439 (1951). Kronig, R., Kumazawa, S., “Investigation of Hot-Element Anemometry at Very Low Velocity,” M. S. thesis, Chemical Engineering Science Group, Case Institute of Technology, Cleveland, Ohio, 1965. Mc.\dams, L$’. H., “Heat Transmission,” 3rd ed., p. 266, McGrawHill, New York, 1954. Murphy, D. E., ‘‘A Study of Low Speed Momentum Transfer in Packed Beds,” Ph.D. dissertation, Chemical Engineering Science Group, Case Institute of Technology, Cleveland, Ohio, 1967. Ram, \$‘. E., Marshall, I+‘. R., Chem. Eng. Progr. 48 (3), 141; (4), 173 (1952). Simmons, T. F. F., J . Sei. Instr. 26, 407 (1949). Tsubouchi, T., Sato, S., Chem. E n g . Progr. Symp. Ser. 56 (30), 285 (1960).
Veprek,’J. .4., J . Sei. Instr. 40, 66 (1963). Yuge, T., Rept. Inst. H i g h Sjeed Mechanics, Tohaku Univ. 6 , 143 (1956). RECEIVED for review May 15, 1967 ACCEPTED July 1, 1968
Summary
A lowspeed, self-heated thermistor anemometer has been developed which does not require constant bulk fluid tempera-
Investigation supported by the U.S. Atomic Energy Commission through Contract AT(11-1)-1605.
MEASUR,EMENT OF ENTHALPY DIFFERENCES WITH A FLOW CALORIMETER J . P. DOLAN, B. E. E A K I N , AND Institute of Gas Technology, Chicago, Ill.
R . F. B U K A C E K
60676
A flow calorimeter has been developed for determining enthalpy differences of natural gases in the range 100” F. for pressures up to 2000 p.s.i.a. Provisions for measurement of integral isothermal, of - 320” to
+
integral isobaric, and total enthalpy differences are included. Measurements are made by heat transfer between a reference fluid and/or heaters and the test material stream. Operating capability and an accuracy characteristic as a function of test stream energy throughput were established from runs on nitrogen.
u
or overdesign of chemical processing plants is costly. One factor contributing to design errors is the uncertainty in the values of the physical properties of the many different materials Processed. The experimental d a t a available are insufficient to produce correlations of general application or to evaluate the accuracy of correlations. Many investigations, both experimental and analytical, are being made to reduce this deficiency. The calorimeter described in this paper is part of an experimental investigation of the physical properties of natural gases. NDER-
Three major goals were stressed in the design of the calorimeter: T o define the enthalpy-pressure-temperature field of a fluid of known composition writhout reference to the measurements of other investigators. T o provide for cross checks on the data by alternative measuring techniques. T o measure enthalpy differences with an uncertainty of not than lyo,
A design satisfying these goals is described. Trial runs on VOL. 7
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Figure 1.
Schematic of the calorimeter system
nitrogen demonstrate the actual uncertainty of the measurements. Calorimeter
One of the principal advantages of a flow calorimeter is the possibility of observing the cumulative heat effects on a large quantity of material undergoing a change of state. Further, a t steady conditions the heat capacity of the container does not enter into the heat balance in a flow system as it does in a static system. These were the major reasons for choosing aflow system in the present unit. The calorimeter described includes provisions for measuring both the integral isobaric and integral isothermal enthalpy differences and the sum of these two integrals. The values of the enthalpy differences between two states are crosschecked by summing the results of the first two measure646
l&EC FUNDAMENTALS
ments and comparing them with the third. Cross checks of the isobaric enthalpy differences can be made by conducting the runs with the stream heating and cooling. Some limitations exist on the temperature differences between which the isobaric checks can be made. The precision with which the heat added to or removed from the fluid can be determined is the controlling factor in defining the uncertainty of a measured enthalpy difference. I n this calorimeter this quantity is determined from the product of the mass flow rate of a refrigerant and the enthalpy of vaporization of the refrigerant. I n certain cases the heat rate is the difference between the product and a known electrical heat input. In this calorimeter these quantities could be determined with a high degree of precision. Use of a reference fluid imposes a reference temperature on the enthalpy system. The reference fluid employed in
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Calibration of wet-test meters
this calorimeter was Freon 11, which has a boiling temperature of 74.5' F. a t the ambient pressures normally encountered. Therefore the enthalpy zero point was taken a t 1 standard atm. and 74.5" F. T h e choice of this reference state for the light natural gases eliminates consideration of the enthalpy of mixing because behavior is close to ideal. T h e principle of operation is straightforward. T h e isobaric technique is that of 9e:ison and Holcomb (1953) and Jenkins and Berwaldt (1963). The isothermal and total enthalpy measurements employ the technique of Wiener (1966). I n isobaric operation the test stream is previously conditioned to a temperature either higher or lower than the reference temperature. If the inlet temperature is higher than the reference, the heat given u p by the test stream in cooling to the reference temperature boils off a quantity of reference fluid. When the inlet. temperature of the test stream is below that of the reference, electrical heating is used to overcome the refrigerating effect. Sufficient heat is added to maintain a small steady boil-off of reference fluid. Isothermal and total enthalpy runs are conducted similarly, except that a restriction is included in the flow stream to create a high pressure drop in isothermal runs. Electrical heating is again empl'oyed to overcome cooling effects. Figure 1 shows the arrangement of the mechanical components of the calorimeter system. T h e fluid is not recirculated in the present operation. A complete description of the components is found in Dolan's thesis (1967). The major components are the calorimeter, A , the preconditioning bath, B, a! post-conditioning bath, C, the test fluid source, D ,the wet-test meters, S and T , the rotameter, R, inlet, E, and outlets, P and Q , pressure controls, the flow control valve, 2.44, and the pressure measuring system, V , and valves 14 through 17. Auxiliary :systems are the preconditioning bath temperature control, F, G, H, vacuum system, I , J , K , the postconditioning bath temperature control, 0, the reference fluid system, L , M , A', for automatically maintaining the level ', Y , Z , A A , and valves, in the calorimeter, and a system, PIT, A for calibration of the wet-test meters. Selection of the mode of operation is made with valves 4B and 5B. With valve 4B open, operation is isobaric; with valve 5B open, operation is isothermal (valve 4B i!; closed). The reference fluid boil-off stream is carried in the jacketed lines designated by the zigzag crosshatching. A positive vent system, U , removes the expended fluid from the laboratory. Temperatures throughout the system are measured with copper-constantan thermocouples that were calibrated against a platinum resistance thrx-mometer over the range -320" to +200° F. With the calibration corrections the temperatures can be determined within 0.1' F. Locations of thermo-
l i
I
I
Figure 3.
Cross section of the calorimeter
couples in Figure 1 are shown by a heavy black dot with the designation T C followed by a number giving the potentiometer position. The wet-test meters were calibrated by comparison with volumes of nitrogen expanded from a cylinder of known volume. Over the useful range of flow ranges (2 to 20 standard cu. feet per hour) no deviations of the meter factor from 1.000 =t 0,0015 were observed, as shown for both meters in Figure 2. Thermocouple e.m.f.'s and heater voltages are measured with a certified Leeds & Northrup K 3 potentiometer. Thermocouple e.m.f.'s are measured directly in the usual manner with an ice-point reference. A dividing bridge of calibrated resistors is used to obtain the heater voltage. A voltage measurement across a calibrated resistor determines the current supplied to the heater. A detailed cross section of the calorimeter is shown in Figure 3. The calorimeter is bounded by the upper tray, 5. the base, 11, and the side wall, 14. The main calorimeter parts are the isobaric coil and associated heater, 6, and the isothermal-total enthalpy coil and capillary, 7, with heaters, 8. The vaporized reference fluid leaves the calorimeter via tube 9. The liquid container, 12, surrounds the calorimeter and seals against an upper plate. The test fluid enters the calorimeter through the vacuum-jacketed tube, 2 and 4, past a small heater, 3, from the preconditioning bath, 1. This design surrounds the calorimeter as much as possible with material the same temperature as the reference, if the fluid in the upper tray and surrounding the calorimeter is boiling. Heaters 5 and 15 ensure boiling of the fluid external to the calorimeter proper. All exit tubes for the fluid stream pass through the bottom of the calorimeter and are submerged in the exterior boiling fluid. Because they are thus long paths subject to small temperature gradients, they do not contribute to heat leakage into the Calorimeter. Except during isothermal runs, a temperature gradient will exist on the inlet tube within the vacuum jacket, 4. The resulting heat leak was reduced to negligible proportions. A plastic tube, which is a poor conductor, was included to increase thermal resistance. Since the temperatures a t the VOL. 7
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top and bottom are known and the geometry is fixed, the heat leak may be calculated according to
where T iis the temperature of the test fluid a t the top of the section and T , is the temperature of the boiling fluid-the effective temperature-at the bottom. A correction for this quantity is included in the energy balance for the calorimeter. Calorimeter Energy Balance and Measurement Precision
The heat balance equation gives the relationship between the enthalpy change of the test fluid and the measured quantities. A heat balance on the calorimeter accounting for the effects of a flowing stream results in the following: Ah, =
[
{-x415
[El
(y (g)) - ]+ (“ 830 - Ti)
O n the right-hand side the terms (in order) account for electrical heat input, inlet tube heat conduction, test fluid kinetic energy change, test fluid potential energy change, energy of the reference fluid boil-off stream, and the test fluid mass for the run duration. Since the first four terms have dimensions of rates, their sum is multiplied by the run duration, 8. All of the quantities on the right of Equation 2 are either measured in the course of a run or determined by previous calibrations. Each has associated with it some measure of uncertainty representing the limits of the measuring technique or the precision of the literature values for the properties of the streams. The effect of these uncertainties will be reflected in the uncertainty of the final value for the enthalpy difference. The following statistical method was used to determine the effect of the measurements on the final values. Numerical values of the standard deviation, a measure of uncertainty, were established as follows : Where calibration procedures determined values before assembly or quantities were measured during a run, multiple readings were made. The mean and the standard deviation from the mean were computed directly. Where values were obtained from the literature-Le.: specific volumes of fluid streams-the authors’ estimate of precision was interpreted as the standard deviation. Compensation was made for errors introduced by interpolation of tabulated literature values. The variance of the dependent quantity, the enthalpy difference, is related to the variance of the measured quantities by (3) where f ( x t ) is given by Equation 2. The pressures and temperatures between which the fluid changes occur do not appear explicitly in Equation 2. The uncertainty in fixing the pressures and temperatures must be introduced by numerical evaluation of the quantities [3(Ah)/dpplT and [ d ( A h ) / b T ] , and addition in proper form to Equation 3. For the trial runs on this apparatus these quantities could be evaluated from literature information. I n practice they will be evaluated from the experimental enthalpy data after sufficient data have been obtained to fix the behavior in a given region. The standard deviation is obtained by calculating the square root of UA?. 648
I&EC FUNDAMENTALS
lest Runs
Trial runs were made with nitrogen as the test fluid. Nitrogen was chosen because of the high quality experimental and calculated information available in the literature (Bloomer, 1952; Mage et al., 1963). Freon 11 (trichloromonofluoromethane) was used as the reference material. Its properties are tabulated in the literature (Air-conditioning and Refrigeration Institute, 1957). For the trial runs, steady state was assumed when pressures were constant within 1 0 . 5 p s i . , temperatures within 1 0 . 2 ” F., and flow rates within 1 0 . 5 % for ‘/2 hour preceding a ‘/2-hour run. Only isobaric and isothermal runs were made. These were sufficient to demonstrate operating capability, establish a pattern of precision, and evaluate any residual heat leaks. The results of the trials are presented in tabular form for isobaric runs in Table I and for isothermal runs in Table 11. Inlet and outlet states within the definition of steady state above are specified. The value of each term in Equation 2 is recorded, as is the standard deviation resulting from Equation 3 and a mass flow rate characteristic of the run. The final column lists the enthalpy differences corrected to the nominal temperatures in the table headings. The value denoted by “literature” a t the bottom of the last column is the enthalpy difference for the nominal conditions derived from the literature. The agreement among all of these values is sufficient to demonstrate operating capability for this apparatus. Residual Heat leaks
I n a previous discussion some attention was devoted to the insulation of the calorimeter against heat leaks. I t is of interest to determine whether all of the leaks were found and compensated for. I n a brief form, on a rate basis, the energy balance for the calorimeter is mAh = -qe
- 41 f
qb
(4)
If any heat leaks not compensated by qe exist, the deviation will appear in qb. Treating q b as having two components, qb,l,the true boil-off corresponding to the electrical input and the test fluid throughput, and q b , $ , the effect of residual heat leaks, the enthalpy difference can be evaluated from (5) The first term on the right side is constant because it represents the true value of Ah. For a fixed geometry and steadystate conditions, q b , 1 is constant. Thus,
Using Equation 6 as a model, a “least squares” procedure was used to fit the isobaric data of Table I. The isothermal data could not be used because only one mass flow rate can be obtained for a given pressure drop. Employing a matrix inversion technique permitted determining values for kl and kz and estimating the standard deviation of these coefficients. The result for the data of Table I, runs 1 through 7, was
Since the standard deviation of coefficient kz is four times greater than the coefficient itself, k~ cannot be distinguished from zerothat is, the data will not support the hypothesis that the un-
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accounted-for heat leak is different from zero. The same observation follows from the data for runs 8 through 1 5 and runs 16 through 23 of Table I. Therefore, the unaccounted-for heat leak is too small for experimental determination, and use of the weighted mean was justified in comparing the data obtained with that in the literature.
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000
999 000
Nomenclature
E
=
voltage, volts
= function of specified variables h = specific enthalpy, B.t.u./lb., k = constant KE = kinetic energy, B.t.u./hr. m = mass rate, lb.m,'hr. q = energy rates, B.t.u./hr.
f
999 000
Q = volume displaced a t meter, cu. ft. P = absolute pressure, p.s.i.a. PE = potential energy, B.t.u./hr.
R T u
Y?? ddd
r-r-r-
?tN.
ddd
r-r-b
000
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electrical resistance, ohms temperature, OF. = specific volume, cu. ft./lb., = =
GREEKLETTERS A = difference e = time, hr. u = standard deviation SUBSCRIPTS b = boil-off stream conditions c = observed value e = electric heat inputs = test stream condition, calorimeter inlet i 1 = heat leak m = condition at the pertinent meter = test stream condition leaving calorimeter o = reference fluid stream conditions r = test fluid conditions in general t v = vaporization literature Cited
Air-conditioning and Refrigeration Institute, Washington, D. C., "Properties of Commonly Used Refrigerants," 1957. Bloomer, 0. T., Rao, K. N., Institute of Gas Technology, Res. Bull. 18 (1952). 650
I&EC FUNDAMENTALS
Dolan, J. P., Ph.D. dissertation, Illinois Institute of Technology, Chicago, 1967. Jenkins,-A. C., Berwaldt, 0. E., Ind. Eng. Chem. Process Design Deoelop. 2, 193 (1963). Mage, D. T., Jones, M. L., Jr., Katz, D. L., Roebuck, J. R., Chern. Eng. Progr. Symp. Ser. 59, No. 44,61-5 (1963). Nelson, J. M., Holcomb, D. E., Chem. Eng. Progr. Symp. Ser. 44 (7), 93-106 (1953).
rYiener, L. D., 58th National A.1.Ch.E. Meeting, Symposium on Thermodynamic Properties, Dallas, Tex., Feb. 6-9, 1966. RECEIVED for review November 16, 1967 ACCEPTEDJune 24, 1968 Research carried out as a Basic Research Project of the Institute of Gas Technology, supported by contributors and members of the institute.
FLOWMETER CALIBRATED FOR ANY GAS IN T H E RANGE OF I T O 5 0 0 LITERS PER HOUR S T U A R T B. REED AND M I C H A E L P. SPRANGE Watson House, The Gas Council, London, S. W.6, England
The prediction of flowmeter performance, commonplace in industrial practice, is difficult at the low gas flow rates frequently met in small scale laboratory experiments. However, if a flowmeter employing a conical-entrance orifice is used, the flow rate of any gas or gas mixture may b e predicted, from an experimentally determined calibration on a single gas, b y means of a simple density correction only. New experimental data are measurements of discharge characteristics of conical-entrance orifices, ranging from 0.018 to 0.076 cm. in diameter, determined using hydrogen, helium, methane, nitrogen, ethylene, argon, and propane a t pressure differentials from 1 to 120-cm. water gage.
-
research and development, an instana number of pure gases or gas mixtures in the flow rate range from 1 to 500 liters per hour is frequently required. If, in such cases, a meter calibration curve for any gas or gas mixture may be calculated from a Calibration curve determined experimentally for a single gas, there is a considerable saving of time and tedious experimental effort. Such a prediction procedure is also useful where the supply of a gas is limited or the temperature or pressure a t the meter is different from the calibration conditions. Although calibration predictions of this sort are commonplace in industrial practice, where flow rates and Reynolds numbers are high, the problem is much more difficult at the low flow rates frequently met in small-scale laboratory experiments and in pilot plant investigations. This paper discusses the applicability of the types of flowmeter which are suitable for general laboratory use. Experimental results show that the flow characteristics of small conical-entrance orifices are such that the flow rate of any gas or gas mixture, through a meter utilizing this type of orifice, may be predicted, simply and precisely, from the original calibration curve of the meter. N
EXPERIMESTAL
I taneous indication of the flow rate of
Suitability of Various Types of Flowmeter
Several types of flowmeter for general laboratory use may reasonably be considered in the context of the interchangeability of calibration-for example, capillary, variable-area, critical-orifice, and subcritical-orifice meters. The flow rate in capillary-type flowmeters is directly dependent upon the viscosity of the gas used and, a t the low flow rates considered here, this is also true of variable-area flowmeters. Since in many cases experimentally obtained viscosity data, even for pure gases, show variations of the order of =k3yObetween experimenters, and values for gas
mixtures may be calculated (British Standards Institution, 1964; Chakraborti and Gray, 1965) probably only to within iloro, this limits the possible accuracy of any interchangeability procedure for meters in which viscous drag forces are controlling. So far as the critical orifice is concerned, the steps that are prone to error when predicting a calibration curve for one gas or gas mixture from a n actual calibration on another gas are the use of the function involving the ratio of specific heats and the assumption that the discharge coefficient of the orifice 1)]1/2(2/y remains constant. The y function [2y, (y l ) l / y - l changes by 15y0\\.hen y changes from 1.13 (propane) to 1.67 (argon) and the function itself may be calculated within approximately =k10% for gas mixtures (British Standards Institution, 1964), so that errors from this source are likely to be acceptable in many cases. Errors arising from variation of the discharge coefficient may be appreciable with gases with more than two atoms to the molecule, because of departures from ideality. The critical-orifice type of flowmeter has certain drawbacks-for example, to give even a small range of flow rates the supply pressure required is frequently higher than is conveniently available, and measurement of the supply pressure generally necessitates the use of a cumbersome mercury manometer if high accuracy is required. If the type of flowmeter which utilizes a subcritical orifice has a constant coefficient of discharge, the calculation of the calibration curve for a gas or gas mixture from an experimentally determined calibration, obtained using a different gas, involves only the densities of the two gases concerned. This procedure is particularly convenient when gas mixtures are involved, because the density of the mixture may be computed easily, compared with the relatively complex procedures for the precise calculation of, say, the viscosity of the mixture. However, most standard designs of orifice achieve a reasonably
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