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Effects of cavitation and plate thickness on small diameter ratio orifice meters
Flow Meas. Instrum., Vol. 8, No. 2, pp. 85–92, 1997 1998. Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0955–5986/97 $17.00 + 0.00
PII: S0955-5986(97)00034-4
Effects of cavitation and plate thickness on small diameter ratio orifice meters B.-C. Kim,* B.-C. Pak,† N.-H. Cho,‡ D.-S. Chi,‡ H.-M. Choi,§ Y.-M. Choi§ and K.-A. Park§ *Tong Yang Machinery and Engineering Co. Ltd. R & D Center, Kyonggido, Korea †Chonbuk University, Chonbuk, Korea ‡Hitrol R & D Institute, Kyonggido, Republic of Korea §Korea Research Institute of Standards and Science, Taejon, Korea
(Received 14 January 1997; in revised form 21 November 1997) High differential pressure drop is frequently required in the process line of electric power plants. However, cavitation produced by a high pressure drop could damage the pipe and pump blades. In these experiments, the effects of cavitation and plate thickness for small-bore diameter (d) to pipe diameter (D) ratio ( = d/D) orifice plates were evaluated in a 100 mm diameter test section of a water flow calibration facility. Three size orifice meters were tested with  = 0.10, 0.15, and 0.33 and no bevel on the throat. The cavitation number at inception was measured to be 1.0 to 1.2 for all experiments. Although cavitation occurred in all experiments, the discharge coefficient was affected by cavitation only for the smallest bore ( = 0.10) and thickest plate tested, 7.0 mm or t/d = 0.70 where t is the plate thickness. Thickness seemed to influence the discharge coefficient only for the  = 0.10 plate. But the trends in the results for thickness were not conclusive and could be attributed to edge sharpness. 1998. Published by Elsevier Science Ltd.
Visual observation of cavitation was performed for small throat orifices by Oba, et al. [3] Throat diameters of less than 1 mm were tested. The thickness of the orifice plates was t/d ⬍ 2.5. The discharge coefficients, Cd, of the orifice plate (d = 0.2 mm,  = 0.33) were 0.9 to 1.1. The discharge coefficients were higher than ISO 5167 predictions [4]. Adachi, et al. [5] measured the cavitation noise in high-speed water jets by hydrophone. The power spectra of the cavitation noise were analyzed with a variation of the injection pressure and nozzle geometry. However, such methods have not been previously applied to orifice meters in conjunction with discharge coefficient measurements. Cavitation and discharge coefficient information is not available for the design of thick orifice plates in electric power plant applications. The specifications for conventional orifice plates are described in ISO 5167 and A. G. A. Report Number 3 [4,6]. The differential pressure between upstream and downstream of the orifice plate is usually less than 1 bar. The plates should be designed for small differential pressure according to standard specifications. The minimum throat diameters recommended by ISO 5167 and A. G. A. Report 3 are 12.5 and 11.4 mm, respectively. Normally, a 45° bevel is specified for the downstream face of the plate with a throat edge thickness and plate thickness. In ISO 5167, the throat edge thickness, e, is 0.02 ⱖ e/D ⱖ 0.005 while the plate thickness, E, is e ⬍ E ⬍ 0.05 D. In A. G. A. 3, the maximum throat edge thickness is e/D
1. Introduction Orifice meters with a small diameter ratio ( = d/D where d is the orifice meter diameter and D is the pipe diameter) are used to generate high pressure drop and to control the flow rate of the process line in electric power plants for the water coolant. The high pressure drop is also required in the by pass line of the pump or the heat exchanger. The small throat orifice plates can control the flow rate in the main pipeline but induce strong cavitation. Double orifice plates or conical orifice plates have been adopted to reduce cavitation due to the high pressure drop. The cavitation phenomenon, including bubble nucleation, growth, and collapse process, produces noise and vibration in the pipeline. Cavitation can cause damage and erosion. Cavitation was observed in the multiple orifices installed in the inlet of the heat exchanger in a ship by Simpson [1]. The high pressure of sea water should be reduced for safe operation of a heat exchanger. The multiple orifice plates were a combination of orifice plates with different  and installed at an optimum distance to minimize cavitation damage. Cavitation level could be reduced by 1/3 to 1/4 of the level for a single orifice plate. Kamiyama and Yamasaki [2] tested small and long throated orifices with various fluids. The tested ratios of orifice plate thickness, t, to throat diameter were higher than 15 (t/d ⬎ 15). The predicted cavitation number was in agreement with experimental data for high velocity at the throat. 85
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⬍ 0.02 or e/d ⬍ E ⬍ 0.05 D. In A. G. A. 3, the maximum throat edge thickness is e/D ⬍ 0.02 or e/d ⬍ 0.125 while plate thickness is dependent on the differential pressure and is specified in Table 2-4 of A. G. A. 3.
2. Experimental facilities and instrumentation These experiments were performed in the water flow calibration facility in Figure 1. The facility is a primary flow measurement standard with two weighing tanks (8 and 1 m3) and a diversion device. The tanks are weighed by three load cells each. The uncertainty in the flow rate measurement is estimated to be ± 0.2% at the 95% confidence level. The water flow is circulated with 3 pumps (40, 10, and 10 hp). Three pumps in parallel were selected to eliminate the possibility of bubbles from pump cavitation. A surge tank was also included to reduce pressure fluctuations from the pumps. A schematic of the test section is presented in Figure 2. The test section pipe diameter was 100 mm with a total upstream length of 65 D. The orifice meter pressure differential was measured at flange taps with two pressure transducers with maximum ranges of 1 and 7 bar. A calibrated thermometer, a 100 ⍀ industrial platinum resistance thermometer, was installed downstream of the orifice meter. The line pressure was measured by a pressure gage with a maximum range of 10 bar. The noise generated by cavitation was measured with a sound level meter and a hydrophone. The sound level meter was placed at a distance of 0.9 m from the orifice plate in a sealed chamber (2.4 × 1.2 × 1.2 m) shown in Figure 2. The hydrophone was placed at a distance of 125 mm (1.25 D) downstream from the orifice plate. The signal of the hydrophone was monitored and measured with a spectrum analyzer.
3. Orifice plate design Three orifice meter sizes with throat diameters of 33, 15, and 10 mm ( = 0.33, 0.15, and 0.10) and without bevels were tested. The plate thickness was 4.0, 5.5, and 7.0 mm. The combinations of throat diameter and plate thickness for the experiments are summarized in Table 1. Only the plate with a bore diameter of 33 mm is within the minimum diameter requirements of ISO 5167 and A. G. A. 3. Additionally, this plate does meet the plate thickness specifications for ISO 5167 but not A. G. A. 3. According to ISO 5167, the  = 0.33 orifice plate should have maximum plate thickness of 5 mm with a throat edge thickness between 0.5 and 0.20 mm and a downstream bevel while the recommended plate thickness per A. G. A. 3 is 3 mm.
4. Experimental results The orifice meter discharge coefficients as defined in ISO 5167 were calculated from the pressure differential across the flange taps and the mass flow rate as measured by the weighing system in Figure 1. The results are presented in Figures 3–5 for  = 0.33, 0.15, and 0.10, respectively, as a function of pipe Reynolds.
Although throat-edge thickness is not within ISO 5167, the results for  = 0.33 are in good agreement with the Stoltz equation in ISO 5167. The uncertainty in Cd from the ISO 5167 equation is ± 0.6%. Although cavitation was observed for Re ⬎ 100 000, no effect on Cd was detected from cavitation for  = 0.33. The effect of plate thickness for  = 0.15 is shown in Figure 4. In this case no discernible difference is observed on Cd between 2 plates with different thickness. The Cd is 3.3% higher than the ISO 5167 equation; however, A. G. A. 3 states that the uncertainty for this size orifice plate can be as high as 3% and that most of the large uncertainty is attributed to edge sharpness. Again no effect of cavitation was observed on Cd. In this case, cavitation was observed for Re ⬎ 43 000. For  = 0.10, systematic differences do occur for 3 plates with different thickness as indicated in Figure 5. The lowest values of Cd were obtained for the thinnest plate (4 mm) while the largest values occurred for the intermediate size plate (5.5 mm). Over most of the Reynolds number range, the thinnest plate (4 mm) was 3.3% higher than the ISO 5167 equation. Again this difference may be mostly due to edge sharpness. Also, the Cd for the 4 and 7 mm plates tended to have a minimum near a Reynolds number of 12 000. That is, over the Reynolds number range of the data, the discharge coefficients were higher at the lowest and highest Reynolds numbers. Cavitation occurred for the  = 0.10 orifice meter at Re ⬎ 14 000. The Cd results for the 4.0 and 5.5 mm were not affected by cavitation. However, the Cd dramatically increases at Re = 14 000 for the 7 mm plate apparently due to cavitation. Above Re = 14 000, the Cd for the 7.0 and 5.5 mm plates are nearly the same. As a reference, the noise inside the pipe was measured at 900 mm (9 D) upstream of the orifice meter. The noise spectrum for the measurement is shown in Figure 6. As the figure indicates, the noise was essentially white, and no harmonics were present. The noise spectrum from the pump and other flow sources occurs at frequencies below 100 Hz. The remainder of the spectrum is instrument noise. In Figure 7, the noise spectrum was essentially the same downstream of the orifice meter for  = 0.10, plate thickness of 4 mm, and Re = 14 000 when no cavitation occurs. The spectrum at the inception of cavitation is presented in Figure 8 for  = 0.10, plate thickness of 4 mm, and Re = 10 000. The highest intensity occurred at low frequency with a magnitude of 25 dB Vrms. The cutoff frequency for the noise from cavitation occurs at about 30 kHz. The two primary peaks in the spectrum are at about 10 and 12 kHz. The spectrum for strong cavitation is shown in Figure 9 for the same orifice plate. The cutoff frequency in this case is slightly lower at 25 kHz. The largest signal was 50 dB Vrms at 5.6 kHz. Typical results for the external sound level meter are presented in Figure 10 for a  = 0.10 plate with a thickness of 4 mm as a function of pipe Reynolds number. The sound level increases almost linearly up to a Reynolds number of 14 000 then it dramatically increases. This increase is consistent with the inception
Effects of cavitation and plate thickness on small diameter ratio orifice meters
Figure 1 Schematic of water flow facility
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Figure 2 Schematic of test section
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Effects of cavitation and plate thickness on small diameter ratio orifice meters
89
Table 1 Summary of orifice plate dimensions for 100 mm diameter pipe d (mm)

t (mm)
t/d
t/D
10
0.10
15
0.15
33
0.33
4.0 5.5 7.0 4.0 5.5 4.0
0.40 0.55 0.70 0.27 0.37 0.21
0.040 0.050 0.070 0.040 0.055 0.040
Figure 5 Thickness effect of orifice plate for  = 0.1
Figure 3 Experimental results for  = 0.33
5. Conclusions Orifice plates with small diameter ratios were tested to determine the effect of plate thickness and cavitation on orifice meter discharge coefficient. The inception of cavitation as measured by the following three methods was in agreement: 1. An increase in the spectrum from a hydrophone downstream of the orifice meter 2. An increase in noise from a sound level meter external to the orifice meter 3. A cavitation number between 1.0 and 1.2.
Figure 4 Thickness effects of orifice plates for  = 0.15
of cavitation as observed with the spectrum analyzer measurements of the hydrophone in Figure 8. The inception of cavitation was also determined on the basis of cavitation number defined as follows:
= 2g(pf⫺pv)/(V2)
(1)
where is the cavitation, pf is the fluid static pressure, pv is fluid vapor pressure, V is the velocity, and is the fluid density. For these calculations, the fluid static pressure was measured at the downstream flange tap, and the velocity is the nozzle throat velocity computed from the measured mass flow rate. The cavitation number for these experiments was between 1.0 and 1.2 for all three orifice meters,  = 0.10, 0.15, and 0.33, in agreement with previously published results for  ⬎ 0.4 [7].
Cavitation affected the Cd results of only one meter with a  = 0.10 and a plate thickness of 7.0 mm. In that case, the Cd dramatically increased at Re = 14 000. The same meter was unaffected by cavitation for thinner plates with a thickness of 4.0 and 5.5 mm. Otherwise, the effect of plate thickness on meter discharge coefficient was not conclusive. For the  = 0.33 plate, the plate was thicker than allowed by A. G. A. 3 but was within ISO 5167 thickness specifications, and it did not have a downstream bevel as required by the standards. However, the Cd results were in agreement with the ISO 5167 equation and its uncertainty. In the case of the  = 0.15 plate, the results for plate of 2 different thickness were in agreement but were higher than the ISO 5167 equation by 3.3%. Results did differ systematically for 3 plates of different thickness for  = 0.10; however, the results for the thickest plate were between the other two with the Cd being largest for the intermediate plate (5.5 mm). According to A. G. A. Report No. 3, the uncertainty in Cd for small bore plates can be as high as
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Figure 6 Hydrophone spectrum of flow facility at 900 mm (9 D) upstream of orifice meter
Figure 7 Hydrophone spectrum with no cavitation at orifice meter with  = 0.10, plate thickness of 4 mm and Re = 6 000
Effects of cavitation and plate thickness on small diameter ratio orifice meters
91
Figure 8 Hydrophone spectrum with inception of cavitation at orifice meter with  = 0.10, plate thickness of 4 mm and Re = 14 000
Figure 9 Hydrophone spectrum with strong cavitation at orifice meter with  = 0.10, plate thickness of 4 mm and Re = 16 000
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= 0.10, 0.15, and 0.33 and plate thickness of 0.55 ⱖ t/d and over the Reynolds number range reported here.
References
Figure 10 Typical noise level of cavitation for  = 0.1
3%. Most of the uncertainty is attributed to edge sharpness. In the future, several plates (at least three) should be tested with the same bore size and plate thickness to determine the accuracy and reproducibility of the machining on the results. Those results should then be compared to plates of different thickness. In any case, these experiments do demonstrate that Cd is unaffected by cavitation for plates with a 
1 Simpson, H. R., Cavitation in shipboard sea water cooling systems. Cavitation and Multiphase Flow Forum, FEDVol. 36. American Society of Mechanical Engineers, New York, 1986, pp. 54–57. 2 Kamiyama, S. and Yamasaki, T., Critical condition of cavitation occurrence in various liquids. Journal of Fluids Engineering, 1986, 108, 428–432. 3 Oba, R., Ikohagi, T. and Kim, K. T., Cavitation in an extremely limited flow through very small orifices. Journal of Fluids Engineering, 1982, 104, 94–98. 4 ISO 5167, Measurement of fluid flow by means of pressure differential devices - Part 1, Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. International Standards Organization, Geneva, 1991. 5 Adachi, Y., Soyama, H., Yamacichi, Y., Sato, K., Ikohagi, T. and Oba, R., Cavitation noise characteristics around high-speed submerged water jets. Transaction of JSME (B), 1994, 60(579), 730–735. 6 A. G. A. Report Number 3, Orifice metering of natural gas and other related hydrocarbon fluids, Part 1 and 2. American Gas Association, Arlington, Virginia, 1991. 7 Miller, R. W., Flow measurement engineering handbook. McGraw-Hill Publishing Company, 2ed, 1989.
PII: S0955-5986(97)00034-4
Effects of cavitation and plate thickness on small diameter ratio orifice meters B.-C. Kim,* B.-C. Pak,† N.-H. Cho,‡ D.-S. Chi,‡ H.-M. Choi,§ Y.-M. Choi§ and K.-A. Park§ *Tong Yang Machinery and Engineering Co. Ltd. R & D Center, Kyonggido, Korea †Chonbuk University, Chonbuk, Korea ‡Hitrol R & D Institute, Kyonggido, Republic of Korea §Korea Research Institute of Standards and Science, Taejon, Korea
(Received 14 January 1997; in revised form 21 November 1997) High differential pressure drop is frequently required in the process line of electric power plants. However, cavitation produced by a high pressure drop could damage the pipe and pump blades. In these experiments, the effects of cavitation and plate thickness for small-bore diameter (d) to pipe diameter (D) ratio ( = d/D) orifice plates were evaluated in a 100 mm diameter test section of a water flow calibration facility. Three size orifice meters were tested with  = 0.10, 0.15, and 0.33 and no bevel on the throat. The cavitation number at inception was measured to be 1.0 to 1.2 for all experiments. Although cavitation occurred in all experiments, the discharge coefficient was affected by cavitation only for the smallest bore ( = 0.10) and thickest plate tested, 7.0 mm or t/d = 0.70 where t is the plate thickness. Thickness seemed to influence the discharge coefficient only for the  = 0.10 plate. But the trends in the results for thickness were not conclusive and could be attributed to edge sharpness. 1998. Published by Elsevier Science Ltd.
Visual observation of cavitation was performed for small throat orifices by Oba, et al. [3] Throat diameters of less than 1 mm were tested. The thickness of the orifice plates was t/d ⬍ 2.5. The discharge coefficients, Cd, of the orifice plate (d = 0.2 mm,  = 0.33) were 0.9 to 1.1. The discharge coefficients were higher than ISO 5167 predictions [4]. Adachi, et al. [5] measured the cavitation noise in high-speed water jets by hydrophone. The power spectra of the cavitation noise were analyzed with a variation of the injection pressure and nozzle geometry. However, such methods have not been previously applied to orifice meters in conjunction with discharge coefficient measurements. Cavitation and discharge coefficient information is not available for the design of thick orifice plates in electric power plant applications. The specifications for conventional orifice plates are described in ISO 5167 and A. G. A. Report Number 3 [4,6]. The differential pressure between upstream and downstream of the orifice plate is usually less than 1 bar. The plates should be designed for small differential pressure according to standard specifications. The minimum throat diameters recommended by ISO 5167 and A. G. A. Report 3 are 12.5 and 11.4 mm, respectively. Normally, a 45° bevel is specified for the downstream face of the plate with a throat edge thickness and plate thickness. In ISO 5167, the throat edge thickness, e, is 0.02 ⱖ e/D ⱖ 0.005 while the plate thickness, E, is e ⬍ E ⬍ 0.05 D. In A. G. A. 3, the maximum throat edge thickness is e/D
1. Introduction Orifice meters with a small diameter ratio ( = d/D where d is the orifice meter diameter and D is the pipe diameter) are used to generate high pressure drop and to control the flow rate of the process line in electric power plants for the water coolant. The high pressure drop is also required in the by pass line of the pump or the heat exchanger. The small throat orifice plates can control the flow rate in the main pipeline but induce strong cavitation. Double orifice plates or conical orifice plates have been adopted to reduce cavitation due to the high pressure drop. The cavitation phenomenon, including bubble nucleation, growth, and collapse process, produces noise and vibration in the pipeline. Cavitation can cause damage and erosion. Cavitation was observed in the multiple orifices installed in the inlet of the heat exchanger in a ship by Simpson [1]. The high pressure of sea water should be reduced for safe operation of a heat exchanger. The multiple orifice plates were a combination of orifice plates with different  and installed at an optimum distance to minimize cavitation damage. Cavitation level could be reduced by 1/3 to 1/4 of the level for a single orifice plate. Kamiyama and Yamasaki [2] tested small and long throated orifices with various fluids. The tested ratios of orifice plate thickness, t, to throat diameter were higher than 15 (t/d ⬎ 15). The predicted cavitation number was in agreement with experimental data for high velocity at the throat. 85
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B.-C. Kim et al.
⬍ 0.02 or e/d ⬍ E ⬍ 0.05 D. In A. G. A. 3, the maximum throat edge thickness is e/D ⬍ 0.02 or e/d ⬍ 0.125 while plate thickness is dependent on the differential pressure and is specified in Table 2-4 of A. G. A. 3.
2. Experimental facilities and instrumentation These experiments were performed in the water flow calibration facility in Figure 1. The facility is a primary flow measurement standard with two weighing tanks (8 and 1 m3) and a diversion device. The tanks are weighed by three load cells each. The uncertainty in the flow rate measurement is estimated to be ± 0.2% at the 95% confidence level. The water flow is circulated with 3 pumps (40, 10, and 10 hp). Three pumps in parallel were selected to eliminate the possibility of bubbles from pump cavitation. A surge tank was also included to reduce pressure fluctuations from the pumps. A schematic of the test section is presented in Figure 2. The test section pipe diameter was 100 mm with a total upstream length of 65 D. The orifice meter pressure differential was measured at flange taps with two pressure transducers with maximum ranges of 1 and 7 bar. A calibrated thermometer, a 100 ⍀ industrial platinum resistance thermometer, was installed downstream of the orifice meter. The line pressure was measured by a pressure gage with a maximum range of 10 bar. The noise generated by cavitation was measured with a sound level meter and a hydrophone. The sound level meter was placed at a distance of 0.9 m from the orifice plate in a sealed chamber (2.4 × 1.2 × 1.2 m) shown in Figure 2. The hydrophone was placed at a distance of 125 mm (1.25 D) downstream from the orifice plate. The signal of the hydrophone was monitored and measured with a spectrum analyzer.
3. Orifice plate design Three orifice meter sizes with throat diameters of 33, 15, and 10 mm ( = 0.33, 0.15, and 0.10) and without bevels were tested. The plate thickness was 4.0, 5.5, and 7.0 mm. The combinations of throat diameter and plate thickness for the experiments are summarized in Table 1. Only the plate with a bore diameter of 33 mm is within the minimum diameter requirements of ISO 5167 and A. G. A. 3. Additionally, this plate does meet the plate thickness specifications for ISO 5167 but not A. G. A. 3. According to ISO 5167, the  = 0.33 orifice plate should have maximum plate thickness of 5 mm with a throat edge thickness between 0.5 and 0.20 mm and a downstream bevel while the recommended plate thickness per A. G. A. 3 is 3 mm.
4. Experimental results The orifice meter discharge coefficients as defined in ISO 5167 were calculated from the pressure differential across the flange taps and the mass flow rate as measured by the weighing system in Figure 1. The results are presented in Figures 3–5 for  = 0.33, 0.15, and 0.10, respectively, as a function of pipe Reynolds.
Although throat-edge thickness is not within ISO 5167, the results for  = 0.33 are in good agreement with the Stoltz equation in ISO 5167. The uncertainty in Cd from the ISO 5167 equation is ± 0.6%. Although cavitation was observed for Re ⬎ 100 000, no effect on Cd was detected from cavitation for  = 0.33. The effect of plate thickness for  = 0.15 is shown in Figure 4. In this case no discernible difference is observed on Cd between 2 plates with different thickness. The Cd is 3.3% higher than the ISO 5167 equation; however, A. G. A. 3 states that the uncertainty for this size orifice plate can be as high as 3% and that most of the large uncertainty is attributed to edge sharpness. Again no effect of cavitation was observed on Cd. In this case, cavitation was observed for Re ⬎ 43 000. For  = 0.10, systematic differences do occur for 3 plates with different thickness as indicated in Figure 5. The lowest values of Cd were obtained for the thinnest plate (4 mm) while the largest values occurred for the intermediate size plate (5.5 mm). Over most of the Reynolds number range, the thinnest plate (4 mm) was 3.3% higher than the ISO 5167 equation. Again this difference may be mostly due to edge sharpness. Also, the Cd for the 4 and 7 mm plates tended to have a minimum near a Reynolds number of 12 000. That is, over the Reynolds number range of the data, the discharge coefficients were higher at the lowest and highest Reynolds numbers. Cavitation occurred for the  = 0.10 orifice meter at Re ⬎ 14 000. The Cd results for the 4.0 and 5.5 mm were not affected by cavitation. However, the Cd dramatically increases at Re = 14 000 for the 7 mm plate apparently due to cavitation. Above Re = 14 000, the Cd for the 7.0 and 5.5 mm plates are nearly the same. As a reference, the noise inside the pipe was measured at 900 mm (9 D) upstream of the orifice meter. The noise spectrum for the measurement is shown in Figure 6. As the figure indicates, the noise was essentially white, and no harmonics were present. The noise spectrum from the pump and other flow sources occurs at frequencies below 100 Hz. The remainder of the spectrum is instrument noise. In Figure 7, the noise spectrum was essentially the same downstream of the orifice meter for  = 0.10, plate thickness of 4 mm, and Re = 14 000 when no cavitation occurs. The spectrum at the inception of cavitation is presented in Figure 8 for  = 0.10, plate thickness of 4 mm, and Re = 10 000. The highest intensity occurred at low frequency with a magnitude of 25 dB Vrms. The cutoff frequency for the noise from cavitation occurs at about 30 kHz. The two primary peaks in the spectrum are at about 10 and 12 kHz. The spectrum for strong cavitation is shown in Figure 9 for the same orifice plate. The cutoff frequency in this case is slightly lower at 25 kHz. The largest signal was 50 dB Vrms at 5.6 kHz. Typical results for the external sound level meter are presented in Figure 10 for a  = 0.10 plate with a thickness of 4 mm as a function of pipe Reynolds number. The sound level increases almost linearly up to a Reynolds number of 14 000 then it dramatically increases. This increase is consistent with the inception
Effects of cavitation and plate thickness on small diameter ratio orifice meters
Figure 1 Schematic of water flow facility
87
Figure 2 Schematic of test section
88
B.-C. Kim et al.
Effects of cavitation and plate thickness on small diameter ratio orifice meters
89
Table 1 Summary of orifice plate dimensions for 100 mm diameter pipe d (mm)

t (mm)
t/d
t/D
10
0.10
15
0.15
33
0.33
4.0 5.5 7.0 4.0 5.5 4.0
0.40 0.55 0.70 0.27 0.37 0.21
0.040 0.050 0.070 0.040 0.055 0.040
Figure 5 Thickness effect of orifice plate for  = 0.1
Figure 3 Experimental results for  = 0.33
5. Conclusions Orifice plates with small diameter ratios were tested to determine the effect of plate thickness and cavitation on orifice meter discharge coefficient. The inception of cavitation as measured by the following three methods was in agreement: 1. An increase in the spectrum from a hydrophone downstream of the orifice meter 2. An increase in noise from a sound level meter external to the orifice meter 3. A cavitation number between 1.0 and 1.2.
Figure 4 Thickness effects of orifice plates for  = 0.15
of cavitation as observed with the spectrum analyzer measurements of the hydrophone in Figure 8. The inception of cavitation was also determined on the basis of cavitation number defined as follows:
= 2g(pf⫺pv)/(V2)
(1)
where is the cavitation, pf is the fluid static pressure, pv is fluid vapor pressure, V is the velocity, and is the fluid density. For these calculations, the fluid static pressure was measured at the downstream flange tap, and the velocity is the nozzle throat velocity computed from the measured mass flow rate. The cavitation number for these experiments was between 1.0 and 1.2 for all three orifice meters,  = 0.10, 0.15, and 0.33, in agreement with previously published results for  ⬎ 0.4 [7].
Cavitation affected the Cd results of only one meter with a  = 0.10 and a plate thickness of 7.0 mm. In that case, the Cd dramatically increased at Re = 14 000. The same meter was unaffected by cavitation for thinner plates with a thickness of 4.0 and 5.5 mm. Otherwise, the effect of plate thickness on meter discharge coefficient was not conclusive. For the  = 0.33 plate, the plate was thicker than allowed by A. G. A. 3 but was within ISO 5167 thickness specifications, and it did not have a downstream bevel as required by the standards. However, the Cd results were in agreement with the ISO 5167 equation and its uncertainty. In the case of the  = 0.15 plate, the results for plate of 2 different thickness were in agreement but were higher than the ISO 5167 equation by 3.3%. Results did differ systematically for 3 plates of different thickness for  = 0.10; however, the results for the thickest plate were between the other two with the Cd being largest for the intermediate plate (5.5 mm). According to A. G. A. Report No. 3, the uncertainty in Cd for small bore plates can be as high as
90
B.-C. Kim et al.
Figure 6 Hydrophone spectrum of flow facility at 900 mm (9 D) upstream of orifice meter
Figure 7 Hydrophone spectrum with no cavitation at orifice meter with  = 0.10, plate thickness of 4 mm and Re = 6 000
Effects of cavitation and plate thickness on small diameter ratio orifice meters
91
Figure 8 Hydrophone spectrum with inception of cavitation at orifice meter with  = 0.10, plate thickness of 4 mm and Re = 14 000
Figure 9 Hydrophone spectrum with strong cavitation at orifice meter with  = 0.10, plate thickness of 4 mm and Re = 16 000
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= 0.10, 0.15, and 0.33 and plate thickness of 0.55 ⱖ t/d and over the Reynolds number range reported here.
References
Figure 10 Typical noise level of cavitation for  = 0.1
3%. Most of the uncertainty is attributed to edge sharpness. In the future, several plates (at least three) should be tested with the same bore size and plate thickness to determine the accuracy and reproducibility of the machining on the results. Those results should then be compared to plates of different thickness. In any case, these experiments do demonstrate that Cd is unaffected by cavitation for plates with a 
1 Simpson, H. R., Cavitation in shipboard sea water cooling systems. Cavitation and Multiphase Flow Forum, FEDVol. 36. American Society of Mechanical Engineers, New York, 1986, pp. 54–57. 2 Kamiyama, S. and Yamasaki, T., Critical condition of cavitation occurrence in various liquids. Journal of Fluids Engineering, 1986, 108, 428–432. 3 Oba, R., Ikohagi, T. and Kim, K. T., Cavitation in an extremely limited flow through very small orifices. Journal of Fluids Engineering, 1982, 104, 94–98. 4 ISO 5167, Measurement of fluid flow by means of pressure differential devices - Part 1, Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. International Standards Organization, Geneva, 1991. 5 Adachi, Y., Soyama, H., Yamacichi, Y., Sato, K., Ikohagi, T. and Oba, R., Cavitation noise characteristics around high-speed submerged water jets. Transaction of JSME (B), 1994, 60(579), 730–735. 6 A. G. A. Report Number 3, Orifice metering of natural gas and other related hydrocarbon fluids, Part 1 and 2. American Gas Association, Arlington, Virginia, 1991. 7 Miller, R. W., Flow measurement engineering handbook. McGraw-Hill Publishing Company, 2ed, 1989.