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EXPERIMENTAL TECHNIQUES
A Fluidic-Electronic Hybrid System for Measuring the Composition of Binary Mixtures Carl Anderson,* Daniel M. Barnett,lWilliam 1. Luyben Departments of Chemical Engineering and Electrical Engineering, Lehigh University, Bethlehem, Pa. 18015
A hybrid fluidic-electronic composition analyzer has been developed to measure the composition of binary gas mixtures. Sample is continuously passed through a fluidic oscillator whose frequency varies inversely with the square root of the average molecular weight of the gas. The difference in frequency between the sample oscillator and a fixed-frequency reference oscillator i s determined by a fluidic beat detector. The resulting low-frequency difference is transduced to an ac signal and electronically converted to a dc voltage proportional to composition. Composition can be monitored with a calibrated voltmeter or the sig nal used as the input to a process controller. Data for the vaporized water-methanol system are presented. The dependence of frequency on weight fraction was found to be nearly linear over the 0-1 0% composition range. The accuracy of the analyzer i s estimated to be within +0.5 wt
70.
Fluidic amplifiers are small, reliable, no-moving-parts devices which operate on small gas flows and utilize such fluid dynamics phenomena as jet interaction, wall attachment, and turbulence amplification to effect a variety of control and logic actions (Humphrey and Tarumoto, 1965). This paper describes the application of an elementary fluidic circuit to measure the composition of water-methanol mixtures. The technique should be readily extendable to many other chemical systems to provide an inexpensive and reliable composition analyzer. The circuit uses a proportional fluidic amplifier to produce an alternating pressure signal whose frequency is proportional t o the composition of the gas passing through the amplifier. The Fluidic Oscillator
A fluidic oscillator utilizes the principle that the speed of a pressure pulse traveling through a gas, the sonic velocity, is proportional to the square root of the gas density. For ideal gas mixtures, density and average molecular weight are directly proportional to composition. The oscillator is basically one type of modified fluidic proportional amplifier. In the amplifier, a power jet issues from a slotted orifice, passes through a free-flow region, and impinges on a flow splitter. I n the absence of any control signal, the power flow is equally distributed to two output ports located on either side of the splitter. When a differential control pressure is applied across two control ports, a control flow is induced which impinges on the power jet in the free-flow region, deflecting it. The deflected jet is unevenly split, causing the control signal to “appear” a t the output ports as a proportionally amplified pressure. If, instead of an externally applied control signal, a portion of each output flow is fed back to its respective control port, the device will oscillate. 1 Present address, Hewlett-Packard, International Division, Palo Alto, Calif.
The period of oscillation is equal to the time required for the two alternating pressure pulses to travel their feedback paths a t sonic velocity and initiate switching to the other output port. For perfect gases, this sonic velocity is related to molecular weight and gas density by eq 1 . Terms are defined in the Nomenclature section.
v = d y ~= l / r~ P/p / ~
(1)
The oscillation period for a given amplifier with feedback legs of equal length will be the sum of the times required for the output pulse to travel the feedback path, tL = L / V , and the switching time between initiation of the control pulse and the appearance of a pressure signal a t the corresponding output, t, = B / V . If B is a constant for the oscillator, the period is described by
T
=
l/f = 2 [ t ,
+
tL] =
S[B/l/?.RT/M
+L / d y R z ]
(2)
At constant temperature and pressure and assuming y does not vary significantly with composition, this reduces to f = C/dM Substituting the definition of average molecular weight and letting A12 = k M 1 ,where w1 w2 = 1,eq 3 predicts a square root dependence of oscillator frequency on weight fraction.
+
(3) For small values of k or wl,an approximately linear relationship is predicted. This square root dependence has been verified for simple, near-perfect, real gases by several workers (Barnett, 1970; Gorland and LeRoy, 1971). Little work on more commercially important complex gases has been reported, and no vaporized liquid mixtures have been considered. Ind. Eng. Chem. Fundam., Vol. 11, No.
3, 1972
407
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analog converter voltmeter
21
I
t 2
I
2,
I
I/n- x
PO
18
18
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10
Figure 3. Verification of frequency dependence on molecular weight square root. Conditions the same as Figure 2
11
air
Figure 1. Schematic drawing of hybrid huidic-electronic composition analyzer
Figure 2. Effect of composition of water-methanol mixtures on oscillator frequency at 400 Hz reference frequency. Reference oscillator, 10 psi; sample oscillator, 12 psi The Fluidic Components and Circuit
T o achieve greater sensitivity of frequency to composition, short feedback lengths are used to obtain high oscillation frequencies. Monitoring these high frequencies requires expensive high-performance transducing and detection equipment. For a practical in-line process analyzer, the cost of transducing such high frequencies is prohibitive. A low frequency, however, can be detected with an inexpensive bellow type of potentiometric transducer. The circuit therefore uses a second, constant-frequency reference oscillator. By varying the feedback length, the reference oscillator can be adjusted arbitrarily close 1o any expected frequency from the sample oscillator. Typically, this would be slightly above the highest or below the lowest expected frequency, so t h a t their difference varies monotonically. The present circuit uses a modular fluidic oscillator in which the output from the proportional amplifier containing the 408 Ind. Eng. Chem. Fundam., Vol. 11, No. 3, 1972
feedback loops is used as the control signal to a digital flip-flop amplifier. This arrangement reduces the device's sensitivity to supply pressure to less than 1% change in frequency per psi (General Electric Co., 1968). The test and reference oscillator outputs are fed t o a fluidic beat detector which determines their frequency difference. The detector is a modular unit containing a summing proportional amplifier and rectifier (General Electric Co., 1968). The two signals of differentfrequency are summed a t the amplifier input. This sum is the control signal to the rectifier. The rectifier is a jet interaction device with a single output collector placed coaxially with the power jet so that the jet impinges directly on the collector when no control signal is applied. The device thus has a maximum pressure output a t zero input. The presence of a control pressure of either sense deflects the jet from the collector, reducing the output pressure. Thus, when the oscillator frequencies are momentarily of the same sense, the instantaneous maximum in the control signal causes a minimum rectifier output. Conversely, when the oscillator signals are of opposite sense they tend to cancel and produce a minimum control signal to the rectifier, which then has a maximum output. I n theory, the output of the beat detector is a series of frequencies comprising powers of the sum and difference of the oscillator frequencies. A fluidic capacitor filters the high-frequency overtones of this heterodyne action, and passes the low-frequency difference of the two oscillators (Kelly, 1967). To be useful in a control circuit, this alternating pressure must be converted to a n analog signal. The available fluidic frequency-analog circuits have a wide frequency range and a high minimum frequency restriction, which results in a low sensitivity in the range of interest for this application. A simple, inexpensive electronic f-a circuit was designed for the frequency range expected from the water-methanol system (Barnett, 1970). A lorn-performance bellows transducer converts the fluidic signals t o a n ac voltage. The Vaporizing System
Liquid mixtures must be vaporized and superheated above their dew point t o prevent condensation. Since from eq 1 the oscillator frequency is also sensitive to pressure, the vaporizer must minimize the pressure fluctuations inherent to a twophase flow process. This is done by maintaining a n adequate
I o
2
4
6
IO
Figure 4. Performance of hybrid fluidic-electronic circuit composition range. Reference oscillator presin 0-1 0 wt sure, 9 psi; test oscillator: solid line, 12 psi; broken line, 10 psi
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pressure drop across the two-phase region and by eliminating restrictions in the boiling zone. As shown in Figure 1, the apparatus is a 1-in. diameter vertical boiling tube followed by a length of tubing enclosed by a section of pipe in which 25 psi steam condenses. The oscillators, beat detector, and capacitor are contained in a heated, vented chamber mounted on the end plate of this heater. The vapor tube enters the chamber through the end plate, where pressure taps are connected to external gauges. Methanol solution is fed to the bottom of the evaporator, and pressure a t the oscillator is controlled by regulating the liquid flow rate. About 5 cm3/min liquid flow is required to maintain 10 psi oscillator supply pressure. A common air supply, also heated in the exchanger, drives the reference oscillator and beat detector. Operation and Results
The fluidic circuit was first tested with individual components. The assembly was evaluated with air and simple gases before testing with water- methanol a t 260’F. Frequency- analog conversion of near-zero frequency signals requires elaborate circuitry. The reference oscillator is therefore tuned to produce a signal 10-20 Hz above the highest frequency expected from the sample oscillator, which occurs a t 100% water. The length of feedback tubing needed to produce a given frequency with 260’F air is estimated from eq 1 and the frequency-tube-length performance curves supplied by the device manufacturer for air a t room temperature.
adjustments were made by trial-and-error with water-methanol. With the reference oscillator tuned to produce 20 Hz above the test oscillator when supplied with pure steam, increasing methanol concentrations further lower the test oscillator frequency below reference, increasing 1 Afl . At a reference frequency about 400 Hz, frequency-composition data for the entire O-lOO% range were collected a t several oscillator pressures. Data from the conditions giving the strongest signals are presented in Figures 2 and 3. The relationship of frequency to d l z is quite linear over the entire composition range, as expected from eq 2 and 3. The plot of frequency against weight fraction for the same data shows the expected curvature. An “overall” sensitivity in this base frequency range of about 1.3 Hz/wt % agrees with that predicted from eq 3. The typical in-line process analyzer, however, will operate within a narrower range of composition. Data were taken in the range 0-10 wt yomethanol a t reference frequencies of 600 and 700 Hz. Frequency- composition and voltage-composition data for a typical case a t the 700 Hz level are presented in Figure 4. Sensitivities of 2.2 Hz/wt %, as predicted by eq 3, and 72 mV/% were obtained. Accuracy within about and repeatability within l/4y0were estimated. The importance of holding a constant oscillator supply pressure can be seen by comparing the solid lines a t a sample oscillator pressure of 12 psi with the broken lines of 10 psi. The frequency difference is seen to change by an average 4 Hz per psi a t 700 HZbase frequency, equivalent to a variation of the sample oscillator frequency of about 0.6%/psi. Nomenclature
B
empirical oscillator constant collection of constants for given oscillator and operating conditions f = frequency, He k = ratio of higher to lower component molecular weights L = length of feedback path, ft M = molecular weight Aq = average molecular weight P = pressure, psi R = universal gas constant T = absolute temperature, OR t = period of oscillation, sec t, = amplifier switching time, sec t~ = signal transport time in feedback path, sec V = sonic velocity, ft/sec Vo = electronic circuit output voltage, V w = weight fraction I Afl = absolute frequency difference between sample and reference oscillators, Hz y = ratio of specific heats, C,/C, p = gas density, lb/ft3 C
= =
SUBSCRIPTS 1 2
=
lighter component
= heavier component
literature Cited
Similarly, the length needed to produce a slightly lower frequency in the test oscillator with 260’F steam can be estimated from eq 4. fatearn fair
- $ateampair
Barnett, D. M., “Development of a Hybrid Fluidic-Electronic System to Measure the Composition of a Water-Methanol Mixture,’’ M.S. Thesis, Lehigh University, 1970. General Electric Co., Catalog Sheets GET 3495 and 3486, Schenectady, N.Y., 1968. Gorland, S. H., LeRoy, M. J., Jr., Instrum. Contr. Syst. 44, 81 (1971) ,-_.-
(4)
YairPsteam
For operation about 400 Hz, the frequency in air was adjusted, using a precision transducer and frequency counter. Final
Hurnphiey, E. F., Tarumoto, D. H., “Fluidics,” Fluid Amplifier Associates, 1965. Kelly, L. R., J . Basic Eng. 89, 341 (1967). RECEIVED for review June 21, 1971 ACCEPTED March 17, 1972 Ind. Eng. Chern. Fundarn., Vol. 1 1 , No. 3, 1972
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