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High-pass acoustic filters for hydraulic loops
J. Sound Vib. (1971) 14 (4), 433-437
HIGH-PASS
ACOUSTIC
FILTERS
FOR
HYDRAULIC
LOOPS
M. P. PAIDOUSSIS Department
of Mechanical Engineering, McGill University, Montreal,
Canada
(Received 9 April 1970)
This paper presents a novel design of acoustic filters which may be used for the suppression of low-frequency pressure disturbances in hydraulic loops. The filters, designed by the simplest theory, are experimentally shown to be quite effective in one particular hydraulic loop in the range O-100 Hz, where the pressure disturbances were predominantly at the rotational speed of the pump, i.e. at approximately 30 or 60 Hz.
1. INTRODUCTION The problem of reducing the amplitude of pressure waves in a closed-loop, pump-driven, water-circulating facility arose in connection with some experiments conducted on the flow-induced vibration of flexible cylinders in axial flow [ 1,2]. It was particularly important to avoid large disturbances with frequency components in the range of the first-mode resonant frequencies of the test cylinders used, i.e. 2-100 Hz. The largest component of the pressure depending waves was found to be at the pump rotational speed, at 30 or 60 Hz approximately, on the pump used-two pumps having been used at different times. However, there were numerous other frequency components. It was decided to try using high-pass acoustic filters to reduce or eliminate the low-frequency components of pressure disturbances.
2. DESIGN
OF THE ACOUSTIC
FILTERS
The normal configuration for high-pass acoustic filters for an air-filled pipe without flow in it involves a number of regularly spaced, lateral, tubular openings (“constrictions”), open to atmosphere, which have low acoustic impedance at low frequencies as compared to the impedance of the pipe itself [3]. Obviously, in a closed-loop circulating system, such an arrangement is inadmissible; the alternative of having the pipe immersed in a large waterfilled tank is equally impractical. Accordingly, as the static pressure in the loop near the testsection was small (typically l-10 lb/in*), it was decided to have the constrictions communicating with air-filled spheres, the acoustic impedance of which, it was hoped, would approximate that of open atmosphere. (It is noted that, as the loop was continuously deaerated, the problem of dissolved air was not of consequence.) The arrangement is shown in Figure 1. In this particular case the pipe diameter, D, was 4.03 in. The spheres were commercially available for use in large float valves; they were made of fairly thin copper sheet and were of 12 in. diameter. Taps were installed for filling the spheres with air, as well as a simple level gauge. The filters were designed using the simplest theory [3, 41, according to which the cut-off frequency of high-pass filters is given by 1 Itc =z
c2s “2 z, V ’ c-1 433
434
M. P. PAIDOUSSIS
where c is the velocity of sound in the pipe, S is the cross-sectional area of each lateral constriction, Vis the volume of fluid in the pipe between constrictions, and 1, is the effective length of each constriction, 1, z I + O*8S1/2,where I is the actual length of each constriction (Figure 1). This result is obtained by a lumped-impedance theory assuming an infinite network; space limitations, however, only allowed for three-stage filters on either side of the test section, as shown in Figure 1. The dimensions selected were d = 1 in., L = 13 in. and I = 1.25 in., giving a theoretical cut-off frequency of approximately 225 Hz.
Figme 1. Schematic diagram of the high-pass filters on either side of the test section.
The infinite network theory predicts zero transmission at frequencies less than v, and perfect transmission at higher frequencies. This is not true for finite filters. In Figure 2(a) we consider the equivalent electrical network of our three-stage filter [4]. We assume a resistive load impedance, R, corresponding to the acoustic resistance of a long pipe (no reflected waves) [51, such that R = PC/S,, where p is the density, c the velocity of sound and S, is the crosssectional area of the pipe. Analysing the network by standard circuit analysis, we obtain the ratio leo/ei] which is compared to the infinite network case in Figure 2(b). We can see that for v/v, > 1 we encounter resonance phenomena; only for very high frequencies le,/eiJ -+ 1. It is obvious that this is not an ideal high-pass filter, the reason being that it was designed rather crudely using infinite network theory and not considering such important criteria as matching of filter with load impedance. Nevertheless, we can see that for V/V,< 0.8, the filter is quite efficient in suppressing low-frequency waves, which in practical terms was its aim.
(a)
(b)
Figure 2. (a) Electrical analogue of the three-stage low-pass acoustic filter used; (b) transmission characteristics --infinite network; three-stage.
According to the design, under operating conditions water should have been allowed to rise just above the 1 in. constrictions, and the remainder of the spheres should be air filled. In practice, however, it, was found necessary to let the water rise up to 1 in. into the spheres, to avoid entraining air by the water flow.
435
HIGH-PASS ACOUSTIC FILTERS
3.
THE EFFECTIVENESS OF THE FILTERS
The effectiveness of the filters may be assessed from Figures 3-5, obtained when a 3540 rev/min pump was used. The sensor was a pressure transducer installed at a static pressure tapping on the test-section; the signal was amplified and analysed by a spectrum-analyser.
40
50
Frequency
--,
60 (Hz)
Figure 3. The effectiveness of the acoustic filters at zero flow velocity. Amplitude Without filters; ---, with spheres full of water; ****. ., with air in spheres.
I
.?
scale = 2.75 lb/ir?/V.
I
I
I
I
I
I
I
I
20
30
40
50
60
70
80
90
006-
32 ; 0
06 -
.!z % 2
004-
3 02
C
0
IO
I’
Frequency (Hz)
Figure 4. The effectiveness of the acoustic filters at a flow velocity in 10.9 ft/sec. Amplitude Ib/in2/V. Legend as in Figure 3.
scale 2.75
436
M. P. PAIDOUSSIS
In Figure 3 the flow velocity is zero, indicating that the pump was running, but the valve which was upstream of the test section was fully shut. Figures 4 and 5 are for flow velocities of 10.9 and 23.6 ft/sec, respectively. Tests were conducted with the spheres removed, the spheres full of water, and (mostly) full of air. It is seen that in the latter case the filters were quite effective, particularly for frequencies less than 100 Hz. The filters were also reasonably effective when completely water-filled. In this case, however, fairly large amplitude frequency components were generated that were previously absent within the region of interest, i.e. v < 100 Hz.
Frequency
(Hz)
Figure 5. The effectiveness of the acoustic filters at a flow velocity of 23.6 ft/sec. Amplitude scale 0.92 lb/inz/V. Legend as in Figure 3.
Similar experiments conducted when a 1760 rev/min pump was used, showed the filters to be equally effective in this case also. In this case it was noted that there were some frequency components in the region of 200-250 Hz which were actually amplified when the filters were inserted [6]; this presumably corresponds to the resonance phenomena shown in Figure 2(b). To assess the acoustic filters further, their efficacy was compared to that of straightforward air accumulators. Two such accumulators were placed, one on each side of the test-section, of capacity equal to that of the spheres combined. It was found that the acoustic filters were much superior in suppressing disturbances, particularly in the low frequency range. In conclusion, it may be stated that with this simple and inexpensive design of acoustic filters, it was possible to achieve fairly good suppression of low frequency components of pressure disturbances. Its usefulness, in preference to accumulators, in liquid metal loops and where fluid inventory costs are high (e.g. mercury loops) is obvious.
ACKNOWLEDGMENTS
The author acknowledges the assistance given him with the experiments by Mr F. L. Sharp. These experiments were conducted at the Chalk River Nuclear Laboratories of Atomic Energy of Canada, where the author was then employed.
REFERENCES 1. M. P. PAIDOUSSIS 1966 J. ~7uid Me&. 26,737. Dynamics Part 2. Experiments.
of flexible slender cylinders
in axial flow ;
HIGH-PASSACOUSTIC FILTERS
437
2. M. P. PAIDOUSSIS1969 Nucl. Sci. Engng 35, 127. An experimental study of vibration of flexible cylinders induced by nominally axial flow. 3. G. W. STEWART1922 Phys. Rev. 20,528. Acoustic wave filters. 4. H. F. OLSON1958 Dynamical Analogies Princeton, N.J. : D. Van Nostrand Co., Inc. 2nd edition. 5. G. W. STEWARTand R. B. LINDSAY1930 Acoustics. New York: D. Van Nostrand Co., Inc. 6. M. P. PAIDOUSSISand F. L. SHARP 1967 Rep. CRNL-76, Atomic Energy of Canada, Chalk River, Ontario, Canada. An experimental study of the vibration of flexible cylinders induced by nominally axial flow.
29
HIGH-PASS
ACOUSTIC
FILTERS
FOR
HYDRAULIC
LOOPS
M. P. PAIDOUSSIS Department
of Mechanical Engineering, McGill University, Montreal,
Canada
(Received 9 April 1970)
This paper presents a novel design of acoustic filters which may be used for the suppression of low-frequency pressure disturbances in hydraulic loops. The filters, designed by the simplest theory, are experimentally shown to be quite effective in one particular hydraulic loop in the range O-100 Hz, where the pressure disturbances were predominantly at the rotational speed of the pump, i.e. at approximately 30 or 60 Hz.
1. INTRODUCTION The problem of reducing the amplitude of pressure waves in a closed-loop, pump-driven, water-circulating facility arose in connection with some experiments conducted on the flow-induced vibration of flexible cylinders in axial flow [ 1,2]. It was particularly important to avoid large disturbances with frequency components in the range of the first-mode resonant frequencies of the test cylinders used, i.e. 2-100 Hz. The largest component of the pressure depending waves was found to be at the pump rotational speed, at 30 or 60 Hz approximately, on the pump used-two pumps having been used at different times. However, there were numerous other frequency components. It was decided to try using high-pass acoustic filters to reduce or eliminate the low-frequency components of pressure disturbances.
2. DESIGN
OF THE ACOUSTIC
FILTERS
The normal configuration for high-pass acoustic filters for an air-filled pipe without flow in it involves a number of regularly spaced, lateral, tubular openings (“constrictions”), open to atmosphere, which have low acoustic impedance at low frequencies as compared to the impedance of the pipe itself [3]. Obviously, in a closed-loop circulating system, such an arrangement is inadmissible; the alternative of having the pipe immersed in a large waterfilled tank is equally impractical. Accordingly, as the static pressure in the loop near the testsection was small (typically l-10 lb/in*), it was decided to have the constrictions communicating with air-filled spheres, the acoustic impedance of which, it was hoped, would approximate that of open atmosphere. (It is noted that, as the loop was continuously deaerated, the problem of dissolved air was not of consequence.) The arrangement is shown in Figure 1. In this particular case the pipe diameter, D, was 4.03 in. The spheres were commercially available for use in large float valves; they were made of fairly thin copper sheet and were of 12 in. diameter. Taps were installed for filling the spheres with air, as well as a simple level gauge. The filters were designed using the simplest theory [3, 41, according to which the cut-off frequency of high-pass filters is given by 1 Itc =z
c2s “2 z, V ’ c-1 433
434
M. P. PAIDOUSSIS
where c is the velocity of sound in the pipe, S is the cross-sectional area of each lateral constriction, Vis the volume of fluid in the pipe between constrictions, and 1, is the effective length of each constriction, 1, z I + O*8S1/2,where I is the actual length of each constriction (Figure 1). This result is obtained by a lumped-impedance theory assuming an infinite network; space limitations, however, only allowed for three-stage filters on either side of the test section, as shown in Figure 1. The dimensions selected were d = 1 in., L = 13 in. and I = 1.25 in., giving a theoretical cut-off frequency of approximately 225 Hz.
Figme 1. Schematic diagram of the high-pass filters on either side of the test section.
The infinite network theory predicts zero transmission at frequencies less than v, and perfect transmission at higher frequencies. This is not true for finite filters. In Figure 2(a) we consider the equivalent electrical network of our three-stage filter [4]. We assume a resistive load impedance, R, corresponding to the acoustic resistance of a long pipe (no reflected waves) [51, such that R = PC/S,, where p is the density, c the velocity of sound and S, is the crosssectional area of the pipe. Analysing the network by standard circuit analysis, we obtain the ratio leo/ei] which is compared to the infinite network case in Figure 2(b). We can see that for v/v, > 1 we encounter resonance phenomena; only for very high frequencies le,/eiJ -+ 1. It is obvious that this is not an ideal high-pass filter, the reason being that it was designed rather crudely using infinite network theory and not considering such important criteria as matching of filter with load impedance. Nevertheless, we can see that for V/V,< 0.8, the filter is quite efficient in suppressing low-frequency waves, which in practical terms was its aim.
(a)
(b)
Figure 2. (a) Electrical analogue of the three-stage low-pass acoustic filter used; (b) transmission characteristics --infinite network; three-stage.
According to the design, under operating conditions water should have been allowed to rise just above the 1 in. constrictions, and the remainder of the spheres should be air filled. In practice, however, it, was found necessary to let the water rise up to 1 in. into the spheres, to avoid entraining air by the water flow.
435
HIGH-PASS ACOUSTIC FILTERS
3.
THE EFFECTIVENESS OF THE FILTERS
The effectiveness of the filters may be assessed from Figures 3-5, obtained when a 3540 rev/min pump was used. The sensor was a pressure transducer installed at a static pressure tapping on the test-section; the signal was amplified and analysed by a spectrum-analyser.
40
50
Frequency
--,
60 (Hz)
Figure 3. The effectiveness of the acoustic filters at zero flow velocity. Amplitude Without filters; ---, with spheres full of water; ****. ., with air in spheres.
I
.?
scale = 2.75 lb/ir?/V.
I
I
I
I
I
I
I
I
20
30
40
50
60
70
80
90
006-
32 ; 0
06 -
.!z % 2
004-
3 02
C
0
IO
I’
Frequency (Hz)
Figure 4. The effectiveness of the acoustic filters at a flow velocity in 10.9 ft/sec. Amplitude Ib/in2/V. Legend as in Figure 3.
scale 2.75
436
M. P. PAIDOUSSIS
In Figure 3 the flow velocity is zero, indicating that the pump was running, but the valve which was upstream of the test section was fully shut. Figures 4 and 5 are for flow velocities of 10.9 and 23.6 ft/sec, respectively. Tests were conducted with the spheres removed, the spheres full of water, and (mostly) full of air. It is seen that in the latter case the filters were quite effective, particularly for frequencies less than 100 Hz. The filters were also reasonably effective when completely water-filled. In this case, however, fairly large amplitude frequency components were generated that were previously absent within the region of interest, i.e. v < 100 Hz.
Frequency
(Hz)
Figure 5. The effectiveness of the acoustic filters at a flow velocity of 23.6 ft/sec. Amplitude scale 0.92 lb/inz/V. Legend as in Figure 3.
Similar experiments conducted when a 1760 rev/min pump was used, showed the filters to be equally effective in this case also. In this case it was noted that there were some frequency components in the region of 200-250 Hz which were actually amplified when the filters were inserted [6]; this presumably corresponds to the resonance phenomena shown in Figure 2(b). To assess the acoustic filters further, their efficacy was compared to that of straightforward air accumulators. Two such accumulators were placed, one on each side of the test-section, of capacity equal to that of the spheres combined. It was found that the acoustic filters were much superior in suppressing disturbances, particularly in the low frequency range. In conclusion, it may be stated that with this simple and inexpensive design of acoustic filters, it was possible to achieve fairly good suppression of low frequency components of pressure disturbances. Its usefulness, in preference to accumulators, in liquid metal loops and where fluid inventory costs are high (e.g. mercury loops) is obvious.
ACKNOWLEDGMENTS
The author acknowledges the assistance given him with the experiments by Mr F. L. Sharp. These experiments were conducted at the Chalk River Nuclear Laboratories of Atomic Energy of Canada, where the author was then employed.
REFERENCES 1. M. P. PAIDOUSSIS 1966 J. ~7uid Me&. 26,737. Dynamics Part 2. Experiments.
of flexible slender cylinders
in axial flow ;
HIGH-PASSACOUSTIC FILTERS
437
2. M. P. PAIDOUSSIS1969 Nucl. Sci. Engng 35, 127. An experimental study of vibration of flexible cylinders induced by nominally axial flow. 3. G. W. STEWART1922 Phys. Rev. 20,528. Acoustic wave filters. 4. H. F. OLSON1958 Dynamical Analogies Princeton, N.J. : D. Van Nostrand Co., Inc. 2nd edition. 5. G. W. STEWARTand R. B. LINDSAY1930 Acoustics. New York: D. Van Nostrand Co., Inc. 6. M. P. PAIDOUSSISand F. L. SHARP 1967 Rep. CRNL-76, Atomic Energy of Canada, Chalk River, Ontario, Canada. An experimental study of the vibration of flexible cylinders induced by nominally axial flow.
29