Analysis of Ultrasound Propagation in High- Temperature Nuclear Reactor Feedwater to Investigate a Clamp-on Ultrasonic Pulse Doppler

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1 Journal of Nuclear Science and Technology ISSN: (Print) (Online) Journal homepage: Analysis of Ultrasound Propagation in High- Temperature Nuclear Reactor Feedwater to Investigate a Clamp-on Ultrasonic Pulse Doppler Flowmeter Kenichi TEZUKA, Michitsugu MORI, Sanehiro WADA, Masanori ARITOMI, Hiroshige KIKURA & Yukihiro SAKAI To cite this article: Kenichi TEZUKA, Michitsugu MORI, Sanehiro WADA, Masanori ARITOMI, Hiroshige KIKURA & Yukihiro SAKAI (2008) Analysis of Ultrasound Propagation in High- Temperature Nuclear Reactor Feedwater to Investigate a Clamp-on Ultrasonic Pulse Doppler Flowmeter, Journal of Nuclear Science and Technology, 45:8, To link to this article: Published online: 05 Jan Submit your article to this journal Article views: 503 Citing articles: 7 View citing articles Full Terms & Conditions of access and use can be found at

2 Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 45, No. 8, p (2008) ARTICLE Analysis of Ultrasound Propagation in High-Temperature Nuclear Reactor Feedwater to Investigate a Clamp-on Ultrasonic Pulse Doppler Flowmeter Kenichi TEZUKA 1;, Michitsugu MORI 1, Sanehiro WADA 1, Masanori ARITOMI 2, Hiroshige KIKURA 2 and Yukihiro SAKAI 3 1 Tokyo Electric Power Company, 4-1, Egasaki-cho, Tsurumi-ku, Yokohama , Japan 2 Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology, , Ohokayama, Meguro-ku, Tokyo , Japan 3 ITOCHU Techno-Solutions Corporation, Kasumigaseki Bldg., 3-2-5, Kasumigaseki, Chiyoda-ku, Tokyo , Japan (Received November 2, 2007 and accepted in revised form March 19, 2008) The flow rate of nuclear reactor feedwater is an important factor in the operation of a nuclear power reactor. Venturi nozzles are widely used to measure the flow rate. Other types of flowmeters have been proposed to improve measurement accuracy and permit the flow rate and reactor power to be increased. The ultrasonic pulse Doppler system is expected to be a candidate method because it can measure the flow profile across the pipe cross section, which changes with time. For accurate estimation of the flow velocity, the incidence angle of ultrasound entering the fluid should be estimated using Snell s law. However, evaluation of the ultrasound propagation is not straightforward, especially for a high-temperature pipe with a clamp-on ultrasonic Doppler flowmeter. The ultrasound beam path may differ from what is expected from Snell s law due to the temperature gradient in the wedge and variation in the acoustic impedance between interfaces. Recently, simulation code for ultrasound propagation has come into use in the nuclear field for nondestructive testing. This article analyzes and discusses ultrasound propagation, using 3D-FEM simulation code plus the Kirchhoff method, as it relates to flow profile measurement in nuclear reactor feedwater with the ultrasonic pulse Doppler system. KEYWORDS: ultrasound, Doppler, FEM, flowmeter, high temperature, Kirchhoff I. Introduction Venturi flowmeters are commonly used in power plants because of their reliability and historical performance record. The flow rate of nuclear reactor feedwater is one of the key parameters required to operate and control a nuclear power reactor. This differential-pressure-type flowmeter has been assumed to be accurate based solely on fulfilling standard requirements for design, manufacture and installation, without being subjected to actual flow calibration tests. This is convenient for flowmeter users. Flowmeters, especially those used in nuclear power plants, are usually designed according to ASME (American Society of Mechanical Engineers) standards and have been considered calibrationfree under actual flow conditions. In a boiling water reactor (BWR), the uncertainty of flow rate measurement using a venturi nozzle is estimated to be 1.76% based on the General Electric Company s reactor safety analysis tool GETAB. 1) Reactor safety analyses are performed at 102% of the rated Corresponding author, tezuka.kenichi@tepco.co.jp ÓAtomic Energy Society of Japan power to deal with this uncertainty, and plant process computers monitor the core thermal power to ensure that 100% of the rated thermal power is not exceeded. Plants that have more accurate flow instruments are able to reduce those margins and increase the thermal power. This is called uprating by measurement uncertainty recapture (MUR) and is already in use in the United States. Utilities can get more thermal power without reducing the safety margins, simply by improving the flowmeter accuracy. A Venturi nozzle has an accuracy issue in that the flow profile is not always ideal or uniform over the pipe cross section. Therefore, flow measurement at any point should be corrected by using an appropriate meter factor as determined prior to installation. As power plants age, the readings of flowmeters in reactor feedwater systems drift due to the changing flow profile. Deviations are affected by continuing changes in pipe inner wall roughness, which can change unpredictably from smooth to rough during the life of a power plant. Sometimes an irregularly striped pattern forms on a pipe s inner surface. Therefore, the measurement accuracy of conventional flowmeters cannot be considered reliable. Factory calibration of flowmeters may not be appropriate 752

3 Analysis of Ultrasound Propagation in High-Temperature Nuclear Reactor Feedwater 753 for the large piping in power plants due to the large Reynolds numbers involved. The thermal-hydraulic condition of the fluid is also an issue, because its temperature is over 200 C and the pressure is above 7.5 MPa in a BWR reactor feedwater line. These conditions are too severe to reproduce in a factory test or in the calibration of conventional flowmeters. Flowmeter manufacturers are not able to conduct factory tests at high Reynolds number to determine accurately the flow correction factors required for conventional flowmeters. Clearly, velocity profiles depend heavily on upstream pipe configurations. Therefore, the inaccuracies associated with the velocity profile are major concerns for users and manufacturers of flowmeters. To cope with these problems, other kinds of flowmeters have been proposed and installed in feedwater lines to improve measurement accuracy and allow increases in flow rate that permit uprating the reactor thermal power. Ultrasonic flowmeters manufactured by AMAG Inc. and Caldon Inc. have been used for feedwater in nuclear power plants in the United States. These flowmeters also employ flow profile factors to make corrections to their measurements, using such techniques as measuring the transit time of an ultrasound pulse. Such correction factors also depend strongly on flow profiles. 2 5) To determine the profile factors for actual power plants, the manufacturers of flowmeters usually conduct factory calibration tests under ambient conditions. However, achieving high accuracy in reactor feedwater flow measurement would require them to conduct calibration tests under actual conditions. This makes flow rate measurement errors inevitable in the large piping in power plants. The ultrasonic pulse Doppler method was proposed for measuring the velocity profiles of fluid flows in the 1980s, 6) and Takeda has since developed ultrasonic pulse Doppler flow velocimetry (UVP). 7 9) As mentioned above, conventional time-of-flight ultrasonic flow meters measure ultrasound traveling times between two transducers with small time difference alternately caused by fluid flow in a pipe. They need to employ flow profile factors to correlate this time difference and flow rate in a pipe. Such correction factors strongly depend on flow profiles that will change in time due to the change of pipe roughness, pipe configurations or fluid thermal hydraulic conditions. On the other hand, UVP is capable of directly measuring the flow profile across a pipe and it is not necessary to employ a flow correlation factor to adjust the flow patterns that may change under various conditions. This provides a powerful tool to nonintrusively measure the flow rate in a power plant. Murakawa and Kikura enhanced this technique for application to multiphase flow. 10) In addition, its use requires only a clamp-on device that is noninvasive, making it suitable for measuring the flow rate in actual power plants ) Figure 1 shows a diagram of the ultrasound propagation involved in the ultrasonic pulse Doppler method. Ultrasound with frequency f 0 is emitted into the fluid at some angle f (angle of incidence) by a transducer. The ultrasonic pulses bounce back from particles flowing in the fluid with their frequency shifted f d by the Doppler Effect, in proportion to particle velocity V TDX. By assuming a one-directional flow parallel to the pipe wall, the velocity Fig. 1 Ultrasound propagation in the ultrasonic pulse Doppler method in the axial direction V r can be obtained. By ultrasound echography, the particle position L f is also determined along the ultrasonic path. By measuring the traveling time of the ultrasound pulse t f for the round trip between the transducer and targeting particle in the fluid, the particle position L f can be calculated as a distance between the transducer and a particle with the ultrasound speed C f in fluid. Equations (1) (3) show the relationships used in the pulse Doppler method. V TDX ¼ c f f d ð1þ 2f 0 V r ¼ V TDX sin f ð2þ L f ¼ c f t f ð3þ 2 In order to estimate streamwise velocities V r from velocity vectors in the direction of the ultrasound beam path V TDX obtained by UVP, we need to accurately know the angle of the ultrasound beam path f in the fluid. The angle of incidence of the ultrasound entering the fluid is calculated from the speed of sound in the fluid C f and the wedge C w, and the angle of the wedge w based on Snell s law as shown in Eq. (4). C w ¼ C f ð4þ sin w sin f However, evaluation of the ultrasound propagation path from the ultrasonic transducer to the fluid is not easy, especially in the case of a high-temperature pipe with a clamp-on ultrasonic Doppler flowmeter. The temperature in the wedge is not uniform for the high-temperature case because of the temperature differences between fluid, pipe, wedge and surrounding air, and this produces sound speed variation within the wedge due to the temperature dependence of the speed of sound. Therefore, the ultrasound beam path may differ from what is expected from Snell s law due to the temperature gradient in the wedge and the change in acoustic impedance between interfaces. Recently, simulation code for ultrasound propagation has come into use in the nuclear field for nondestructive testing to improve defect sizing. Komura et al. used this method to simulate nondestructive testing using ultrasonic inspection for defect sizing in a weld between austenitic steel and carbon steel. 16) Koketsu et al. discussed seismic ground motion using a voxel finite element method (FEM). 17) Another approach to evaluating elastic wave prop- VOL. 45, NO. 8, AUGUST 2008

4 754 K. TEZUKA et al. agation in steel is the Kirchhoff theory, or generalized point source synthesis. Ogilvy et al. utilized this method to simulate elastic modeling for the ultrasonic detection of defects in steel. 18) Walte et al. investigated generalized point source synthesis for the evaluation of elastic wave propagation in austenitic steel and compared the calculations with the experimental results. 19) However, no research has been done to investigate the propagation of ultrasound for use in ultrasonic flowmeters in nuclear applications. The objective of this paper is to evaluate ultrasound propagation, using the FEM simulation code and the Kirchhoff method, as it relates to high-temperature and high-pressure flow profile measurement by the clamp-on ultrasonic pulse Doppler method. II. Analysis Model The propagation of ultrasound from the transducer element to the fluid was analyzed using an FEM model that simulates a clamp-on flowmeter device. The FEM model consisted of wedge, pipe and fluid. The pipe was modeled on the pipe geometry of a typical 550 mm (inner diameter) nuclear feedwater line made of 31 mm thick carbon steel. A sufficient length of the pipe was modeled to evaluate the propagation of the main ultrasound lobe, with ultrasound assumed to originate in the transducer element mounted on the wedge. Wedge configuration is described in the following section. The FEM code ComWAVE Ò was used for this analysis. By using FEM outputs, the Kirchhoff method was applied to determine the pressure distribution in the fluid across a pipe cross section. Analyses were conducted both for room temperature of 30 C and nuclear reactor feedwater temperature of 216 C. 1. FEM Model Figure 2 shows the FEM models used in the analyses. Voxel elements were used in this analysis. The Voxel is a term used in the field of computer graphics to indicate a volume pixel, which geometrically is the shape of a cubic. The use of voxel elements leads to a significant reduction in the memory requirements and calculation times. The mesh size was 0: m, which was determined to be onetwentieth of the wavelength of the lowest-velocity (1 MHz) ultrasound in the model. The time step was 8: s for time series analysis and the Courant number was 0.8. Fig. 2 FEM model of fluid, pipe and wedge with incidence angle of 15 ; total mesh number, 9: (left: curved bottom; right: flat bottom with silicone grease) Fig. 3 Schematic diagram of FEM analysis and Kirchhoff method Multiple wedge angles were examined to investigate the effect of ultrasound mode conversions at the interface between wedge and pipe. The critical angle of longitudinal waves in the pipe steel is around 23.8 at 30 C and 22 at 216 C. Three wedge angles were selected (15,26,45 ) to produce both longitudinal and shear waves, or shear waves only, in the steel of the pipe. Wedge bottoms were either flat or curved to investigate the effect of coupling between the wedge and pipe. The couplant was silicone grease suitable for use in high temperatures. The transducer element was defined as a 0.5-inch-diameter circle on the surface of the wedge where the ultrasound originated. The fluid was modeled by the FEM only as far as 14 mm beneath the pipe wall to calculate the pressure distribution on the Kirchhoff integral plane for later use. A nonreflective boundary condition was specified at the air/wedge surface. Figure 3 shows a schematic diagram of the FEM analysis and the Kirchhoff method. A wavelet pulse was used as the ultrasound waveform emitted into the wedge, with a central frequency of 1 MHz and an amplitude of m. The beam diameter was 12: m and the wave was longitudinal. Figure 4 shows the waveform used in this analysis and its fast Fourier transform (FFT). 2. Materials Feedwater pipes in BWRs are usually made of carbon steel. The speed of longitudinal sound waves in carbon steel at ambient temperature is estimated to be 5900 m/s, and the speed of the shear waves is 3150 m/s, which was estimated by a Poisson ratio of 0.3. The pipe density is estimated to be 7800 kg/m 3. 20) Those feed water pipes are usually covered by a thick insulating material and a metal plate. The insulating material is typically made of silicate calcium with the thickness of more than 50 mm in order to thermally isolate the surrounding equipment from the feed water pipes. Therefore, the temperature in the steel pipe can be regarded as uniform and the same as the fluid temperature. Even if the sound speed of the steel pipe may change differently in every material composition as temperature increases, the most important parameter to determine the incident angle of the fluid is the wedge angle that is dependent on its sound speed. As the sound speed is uniform in the steel pipe, the incident angle into the fluid is theoretically determined only by the wedge angle, the sound speed of the wedge and the sound speed of the fluid based on Snell s law. The change of the sound speed in the steel may only have a slight effect JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

5 Analysis of Ultrasound Propagation in High-Temperature Nuclear Reactor Feedwater 755 Fig. 4 Ricker wavelet and its FFT as ultrasound input with a central frequency of 1 MHz Fig. 6 Test specimens and instrumentation placed in the chamber Fig. 5 Test specimens and instrumentation on the evaluation of the ultrasound pressure in different incident angles. Therefore, all of these values are assumed to be temperature-independent in this analysis. The wedge material is a key component determining the transmission of sufficient ultrasonic energy through the wedge-pipe interface for successful flow rate measurement. The material should have excellent thermal tolerance, as well as provide excellent impedance matching between the wedge and the pipe wall. Polyimide and graphite are considered to be superior engineering materials for practical use. Polyimide is a high-performance engineering plastic that is expected to have adequate heat tolerance for continuous use above 250 C. However, these materials may also present problems in having a temperature-dependent speed of sound. Therefore, heat transfer analysis is necessary in order to evaluate the temperature distribution and sound speed distribution in the wedge. Prior to FEM analysis, experiments were conducted to determine the temperature dependence of the speed of sound in polyimide and graphite. Figure 5 shows the test specimens and setups used in this experiment. Specimens were placed in a chamber and heated electrically. An elastometer was used to determine the longitudinal sound velocity. Figure 6 shows the experimental setup to measure the speed of sound in the material at high temperature. Figure 7 shows the result of speed-of-sound measurement versus specimen temperature. Specimens were chosen from thirteen different commercial products. The sound speed decreased as the temperature increased in both materials. Fig. 7 Sound speed measurement versus specimen temperature The temperature dependence varies greatly, subject to influences such as a material s composition and the manufacturing process. Therefore, the speed of sound for a longitudinal wave V p was roughly defined, using the average of polyimide and graphite as a function of temperature t in Eq. (5) and in the following analyses. V p ¼ 2410 t ðm=sþ ð5þ The speed of sound for a shear wave V s was calculated from the speed of sound of a longitudinal wave using the Poisson ratio v shown in Eq. (6). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1 2vÞ V s ¼ V p ðm=sþ ð6þ 2ð1 vþ VOL. 45, NO. 8, AUGUST 2008

6 756 K. TEZUKA et al. The Poisson ratio was assumed to be 0.4. The wedge density and thermal conductivity were estimated to be 1400 kg/m 3 and 0.4 W/mK, respectively, from typical polyimide data. 21) These values were assumed to be isotropic and temperature-independent in this analysis. The thermal hydraulic condition of the fluid was the same as that of the nuclear feedwater: pure water at 216 C and 7.8 MPa. The speed of sound in glycerin paste and its density were used for the silicone grease used as couplant. Ultrasound attenuation due to material damping within the wedge, pipe and fluid was not taken into account in this analysis because of the difficulty in estimating its value in the high-temperature region. 3. Kirchhoff Method for Sound Pressure Calculation in Fluid The region of fluid where the pressure distribution is important is very large, and it is not feasible to perform the entire calculation by FEM due to the computational load. To obtain the pressure distribution in the fluid and at the pipe bottom on the far side, where they should be isotropic and geometrically simple, the Kirchhoff method can be applied in combination with FEM in this analysis. 22) A schematic diagram of the Kirchhoff method is shown in Fig. 8. Given a waveform at time t, the waveform at time t þ dt can be obtained from Huygens principle as an envelope of spherical waves emitted from all points on the surface of the original waveform at time t. Kirchhoff s integral formula is a mathematical expression of Huygens principle and is described in the following equation. Z U! ðrþ ¼ ik G! ðr; r 0 ÞU! ðr 0 Þds ð7þ s Here, G! ðr; r 0 Þ is the Green function describing the sound pressure observed at an arbitrary point r when a spherical wave with unit strength is emitted at point r 0 given in the following equation. Ultrasound attenuates as it passes through fluid. However, attenuation constants are usually dependent on ultrasound frequencies, and accurate values are not available for high-temperate and high-pressure water conditions due to measurement difficulties. In order to investigate the effect of incident angles on the ultrasound pressure field, we can assume no ultrasound attenuation and it is sufficient just to focus on geometric attenuation in the fluid in order to obtain relative changes in ultrasound strength between those angles in this analysis. G! ðr; r 0 Þ¼ expðikrþ ð8þ 4R Here, R: distance between r and r 0 (¼jr r 0 j) k: wave number (¼!=c f ) U! ðr 0 Þ is the Fourier transform of the time domain sound pressure with frequency! on the integral surface defined in the model obtained as output from FEM analysis, as shown in the following equation. Z U! ðr 0 Þ¼p 1 ffiffiffiffiffi Uðr 0 ; tþexpði!tþdt ð9þ 2 As mentioned above, waveforms at point r in the frequency domain can be obtained once sound pressures at Kirchhoff s integral surface are given. Waveforms at point r in the time domain can also be obtained using the inverse Fourier transform, as in the following equation. Z Uðr; tþ ¼p 1 ffiffiffiffiffi U! ðr 0 Þexpð i!tþd! ð10þ 2 In this analysis, Eq. (7) is discretized as the following equation, in which n is the number of voxels and s is an area of the voxel mesh on the Kirchhoff plane. U! ðrþ ¼ Xn G! ðr; r i ÞU! ðr i Þs ð11þ III. Results i¼1 1. Heat Transfer Analysis for High-Temperature Wedge By assuming that the wedge is cooled by forced-convection heat transfer with the surrounding air, the average heat transfer coefficient between the wedge and air is calculated using the Nusselt number for a tetragonal prism placed parallel to the air flow, as shown in Eq. (12) (14). 20) Re ¼ u 0l ð12þ v Nu m ¼ 0:14Re 0:66 ð13þ h ¼ l Nu x ð14þ Fig. 8 Schematic diagram of Kirchhoff method combined with FEM analysis for the calculation of ultrasound pressure distribution in fluid Here, Re: Reynolds number Nu m : average Nusselt number h: average heat transfer coefficient u 0 : air velocity l: characteristic length v: kinetic viscosity : thermal conductivity Air at 30 C is assumed to flow around the wedge at a JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

7 Analysis of Ultrasound Propagation in High-Temperature Nuclear Reactor Feedwater 757 Fig. 9 Temperature distribution in a 15 flat-bottom wedge on a 216 C pipe velocity of 1 m/s. The characteristic length is 0.04 m, from taking the average wedge length of 0.05 m and wedge width of 0.03 m. The kinetic viscosity of air is set to be 1: m 2 /s for 30 C and atmospheric pressure. The bottom of the wedge is heated by thermal conduction from the 216 C pipe wall. Figure 9 shows the temperature distribution in a 15 flat-bottom wedge on a steel pipe as calculated by heat transfer analysis code FINAS Ò. The temperature gradient in the wedge is clearly not simple. Isothermal planes are not parallel to the wedge surfaces. The temperature adjacent to the wedge bottom is high (close to 216 C); however, the transducer element seems to be well isolated thermally and air-cooled to around 55 C, which is low enough to allow the use of composite-type transducers. By using the results of heat transfer analysis, the sound speed distribution within the wedges was calculated using Eq. (5). Figure 10 shows the sound speed distribution for longitudinal waves obtained from temperature distributions along the center of the wedge (in xz and xy planes). Due to the temperature nonuniformity in the wedge, the velocity distributions are also complicated, which may cause ultrasound beam deflection within the wedge. 2. Ultrasound Pressure Field in Fluid (1) Effect of Incidence Angle Determined by Wedge By using the results of FEM analysis, the sound field distribution in the fluid was calculated by the Kirchhoff method. Figure 11 shows the maximum pressure distribution of an Fig. 10 Sound speed distribution for longitudinal waves in central planes in a 15 flat-bottom wedge on a 216 C pipe (left: xz plane, right: xy plane) ultrasound wave passing through room-temperature fluid from different angles of incidence. Three different wedge angles (wedges with flat bottoms) produce different beam angles in the fluid, with characteristic pressure distributions and beam divergence. We observed maximum pressure and minimum beam divergence with a 26 wedge, which was true both at room and elevated temperature. This was due to the mode conversion of longitudinal waves into shear waves at the interface between wedge and pipe. As the incident angle approaches the critical angle for a longitudinal wave, the shear wave gains in strength, producing a high-pressure field in the fluid. Too shallow an angle, such as 45, produces beam divergence, resulting in lower spatial resolution for measurements. Figure 12 shows time series images of ultrasound wave propagation as isobaric surfaces after emission from the transducer and passage through a 15 wedge and into the pipe wall at room temperature. A shear wave following the longitudinal wave in the pipe wall was generated by a mode conversion at the interface. The longitudinal wave is still dominant at this incidence angle and follows a different path than the shear wave. Fig. 11 Sound pressure distributions from ultrasound entering room temperature fluid from wedges with different angles (wedge angles: left: 15, center: 26, right: 45 ) VOL. 45, NO. 8, AUGUST 2008

8 758 K. TEZUKA et al. Fig. 12 Time series images of ultrasound waves represented as isobaric surfaces from an incident angle of 15 Fig. 13 Time series images of ultrasound waves represented by isobaric surfaces from an incident angle of 26 Figure 13 shows ultrasound wave propagation as isobaric surfaces after emission from the transducer, passage through a 26 wedge, and through the pipe wall. Similarly to the 15 case, a shear wave following the longitudinal wave was also generated in the pipe wall by mode conversion at the interface. However, the longitudinal wave became very weak and the shear wave became dominant in this case. For an ultrasonic pulse Doppler flowmeter, it is preferable for the ultrasound beam to have only one sharp and strong main lobe. Otherwise, echoes from different particles in the flow may be superimposed and cause measurement errors. Especially, Fig. 12 expressly indicates a strong and distinctive ultrasound pressure beam within the fluid for the wedge angle of 26 compared with the other angles. In principle, the UVP captures ultrasound echo signals that bounce back from flowing particles and identifies the particle positions along its beam path; one beam is ideally necessary in order to obtain strong echo signals and estimate proper particle positions. This strong beam also eliminates noise caused by multiple reflections in the steel and fluid. Therefore, a 26 angle of incidence is best in this analysis. (2) Temperature Effect on Ultrasound Beam Strength Temperature change affects both the ultrasound deflection in the wedge and the acoustic impedance in all materials. As the fluid temperature increases, the temperature in the wedge increases nonuniformly, inducing changes in the ultrasound velocity and direction in the wedge. Variations in ultrasound velocity and material density, especially the density of the fluid, also affect the transmission efficiency of ultrasound due to impedance mismatching at the interface between the pipe and fluid. Figure 14 compares a 26 ultrasound beam path at 30 C and 216 C. As shown in Fig. 14, the ultrasound pressure decreases at high temperature. This is due mainly to the reduced acoustic impedance of the fluid causing an acoustic impedance mismatch between the pipe and fluid. Figure 15 shows the pressure distribution on the wall at the far side of the 500 mm pipe. The ultrasound beam broadens slightly and creates spadelike pressure fields. The maximum pressure at high temperature decreases by two-thirds from that at room temperature. This indicates that highly sensitive ultrasonic sensors are JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

9 Analysis of Ultrasound Propagation in High-Temperature Nuclear Reactor Feedwater 759 Fig. 14 Sound pressure distributions for ultrasound beams passing through fluid at 30 C (left) and 216 C (right) with a 26 wedge necessary to compensate for echo signal deterioration due to loss of sound pressure. In addition to the sound attenuation, the sensor sensitivity may also decline at high temperature, and ultrasonic reflectors such as gas bubbles may well dissolve in the fluid, causing signal failure. Table 1 shows the ultrasound entry angle into the fluid calculated by FEM and by Snell s Law at high temperature. Incident angles in fluid calculated by FEM are defined as a linear least-square method of maximum sound pressures in fluid obtained by the Kirchhoff method. In Table 1, incident angles calculated by Snell s Law are based on both the spatially averaged temperature in the wedge and a constant temperature of 216 C. There is a slight difference observed in the results between those two methods. This is presumably due to the fact that the beam in the wedge is not the infinite plane wave that is assumed in Snell s Law, but spreads in the wedge. The temperature in the wedge should also be carefully determined in order to estimate the speed of sound in the wedge. As the UVP measures the velocity vectors of flowing particles projected to the ultrasound beam path, accuracies of the particle velocity calculations are proportional to accuracies of the incident angle estimations into the fluid. Table 1 summarizes the effects of the temperature estimation on the change of incident angles into the fluid under different wedge sound speeds. Based on the results, a few percent deviations will possibly occur, which affect the estimation of particle velocities if the temperature dependences of sound speed in the wedge are not properly taken into account for the incident angle estimations. Figure 16 shows the snapshot of ultrasonic wave propagation for infinite plane wave with an incident angle of 26 passing through steel into fluid calculated by 2D FEM in order to investigate the effect of beam spread in the wedge. The incidence of the plane wave has been approximated by expanding the diameter of the transducer. Table 2 shows the comparison of incident angles by FEM and by Snell s law. Incident angles show good agreement between those two methods for the plane waves. This result indicates that the diameter of the transducer should be large enough to be assumed as a plane wave in Snell s law. 23,24) (3) Wedge Bottom Shape Different wedge bottom shapes were investigated to optimize the wedge design. Two shapes were considered in the present analysis: flat bottom and curved bottom. For the flat bottom, silicone grease was used to fill the gaps between the wedge and pipe surface, and modeled in FEM analysis. The contact area of a flat wedge bottom with a pipe wall is not Fig. 15 Sound pressure distributions on the bottom of the 0.55 m pipe from a wedge with the angle of 26 at temperatures of 0 C (left) and 216 C (right) Table 1 Incident angles into fluid calculated by FEM and Snell s Law with spatially averaged temperature in wedge and uniform 216 C in wedge Wedge angle ( ) FEM ( ) Snell s Law with constant temperature of 216 Cin wedge ( ) Snell s Law with spatially averaged temperature in wedge ( ) VOL. 45, NO. 8, AUGUST 2008

10 760 K. TEZUKA et al. Fig. 17 Sound pressure distributions for ultrasound passing through fluid for different bottom shapes in room temperature (wedge angle 26, bottom shape; left: flat; right: curved) Fig. 16 Snapshot of ultrasonic wave propagation for infinite plane wave with an incident angle of 26 passing through steel into fluid Table 2 Incident angles into fluid calculated by 2D FEM and Snell s Law under room temperature of uniform 30 C in wedge Wedge angle ( ) FEM ( ) Snell s Law ( ) an ideal line contact, but has a finite width of approximately 6 mm in this FEM model because the pipe diameter of 550 mm is so large compared with the wedge width of 33 mm. The curved bottom had a curvature to fit the outer pipe surface, and no couplant was modeled in the analysis. Figure 17 shows the sound pressure distribution for flatand curved-bottom wedges. There is no noteworthy difference in the pressure pattern, whether the wedge bottom is flat or curved. This shows that adequate ultrasonic transmission can be expected from a flat bottom wedge, which has the advantages of easy manufacture and a universal application that fits any sufficiently large pipe size. 3. Multiple Ultrasound Reflections in Pipe Wall Most of the ultrasound energy entering the pipe wall passes into the fluid. However, some part of the ultrasound energy reflects at the interface between the pipe and fluid. Reflected ultrasound proceeds to reflect again at the interface between the pipe and air. This multiple reflection of ultrasound in the steel may produce multiple ultrasonic beam paths at different positions in the fluid. As mentioned in Fig. 18 FEM model for a 26 curved-bottom wedge with silicone grease couplant on elongated steel pipe (mesh number: 1: ) the previous section, multiple beams may cause trouble because echo signals from different beams may superimpose each other and cause measurement errors. Under certain conditions defined by the combination of wave frequency, wall thickness and incident angle, a Lamb wave is known to arise in the pipe wall ) A Lamb wave is a combination of longitudinal wave and shear wave, indicating complex behavior. In order to investigate these effects in detail, the FEM model was elongated in the axial direction to observe ultrasound behavior within the pipe wall. The total mesh number increased to 1: (Fig. 18). The analysis was conducted for 216 C with a 26 flat-bottom wedge. The outer surface of the pipe wall was assumed to be surrounded by vacuum so that all ultrasound energy reflected back into the pipe wall at the interface. Figure 19 shows a time series of the calculated ultrasound waves represented by isobaric surfaces. Multiple reflection waves are observed within the pipe wall and reflecting completely at the interface between the pipe wall and vacuum. Figure 20 shows the pressure distribution as ultrasound passes through 216 C fluid from a 26 wedge in the elongated FEM model. Some thin beams that are observed alongside the main lobe are considered to be due to the Lamb wave. Those beams are very weak compared with the main JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY

11 Analysis of Ultrasound Propagation in High-Temperature Nuclear Reactor Feedwater 761 Fig. 19 Time series of ultrasound waves represented by isobaric surfaces, from a 26 wedge at 216 C using an elongated FEM model to show multiple reflections Fig. 21 Beam divergence shown as far-field pressure distribution in axial and circumferential directions Fig. 20 Pressure distribution at 216 C as ultrasound passes through fluid from a wedge with the angle of 26 in the elongated FEM model lobe. Figure 21 shows the far-field pressure distribution in both axial and circumferential directions. The main lobe is defined as the 6 db band area. The effect of multiple reflections in this case may be small. IV. Conclusions Analyses of ultrasound propagation in a high-temperature fluid such as nuclear reactor feedwater were conducted to simulate a clamp-on ultrasonic Doppler flowmeter. Ultrasound was emitted from a transducer element on a mounting wedge on the pipe wall and propagated through the pipe wall into high-temperature fluid. Wedge designs were investigatvol. 45, NO. 8, AUGUST 2008 ed by changing the wedge angle, which affected the ultrasound angle of incidence, and the wedge bottom shape, using silicone grease as a couplant. Heat transfer analyses were conducted prior to ultrasound FEM analysis to determine the temperature field that would induce variations in sound velocity in a wedge mounted on a hot pipe. The following are the technical findings obtained from the experiment and by FEM analysis. - The speed of sound is temperature-dependent in polyimide, which affects the ultrasonic beam path. - The wedge bottom shape has a negligible effect on ultrasound propagation for large pipe diameters. - The sound pressure in high-temperature fluid is less than that at ambient temperature due to the larger acoustic impedance mismatch between the wedge and pipe. - The angle of incidence of the ultrasound strongly affects the ultrasound pressure distribution. An incidence angle of 26, which is close to the critical angle for a longitudi-

12 762 K. TEZUKA et al. nal wave in steel, has advantages compared with other angles in terms of beam power and dispersion. - Multiple reflections and a Lamb wave were observed in the pipe wall. Some beams considered to be induced by the Lamb wave were observed alongside the main lobe, but their energy was very small compared with the main lobe. Based on the analyses, wedge designs are well understood and further detailed investigation relevant to the Lamb wave and wall roughness will be conducted. Nomenclature D: pipe radius f 0 : basic frequency of ultrasound f d : Doppler frequency V r : streamwise velocity V TDX : velocity vector in the direction of the ultrasound beam path L f : distance from pipe wall to particle (particle position) t x : time of flight of ultrasound in fluid w : angle of incidence of ultrasound in wedge f : angle of incidence of ultrasound entering fluid C w : speed of sound in wedge C f : speed of sound in fluid Re: Reynolds number Nu m : average Nusselt number h: average heat transfer coefficient u 0 : air velocity l: characteristic length v: kinetic viscosity : thermal conductivity References 1) General Electric BWR Thermal Analysis Basis (GETAB), Data Correlation and Design Application, General Electric, NEDO-10958A (1977). 2) A. Calogirou et al., Effect of wall roughness changes on ultrasonic gas flowmeters, Flow Meas. Instrum., 12, (2001). 3) M. V. Zagarola et al., Mean-flow scaling of turbulent pipe flow, J. Fluid Mech., 373, (1998). 4) T. T. Yeh, G. E. Mattingly, Pipeflow downstream of a reducer and its effects on flowmeters, Flow Meas. Instrum., 5[3], (1994). 5) T. T. Yeh, G. E. Mattingly, Effects of pipe elbows and tube bundles on selected types of flowmeters, Flow Meas. Instrum., 2[1], (1991). 6) W. D. Barber et al., A new time domain technique for velocity measurements using Doppler ultrasound, IEEE Biomed. Eng., 32[3], (1985). 7) Y. Takeda, Development of an ultrasound velocity profile monitor, Nucl. Eng. Des., 126[2], (1991). 8) Y. Takeda, Velocity profile measurement by ultrasound Doppler shift method, Heat Fluid Flow, 7[4], (1986). 9) Y. Takeda et al., Development of a new flow metering system using UVP (Preliminary performance assessments using NIST flow standards), ASME 2000 Fluid Engineering Division Summer Meeting, FEDSM (2000). 10) H. Murakawa et al., Application of ultrasonic Doppler method for bubbly flow measurement using two ultrasonic frequencies, Exp. Therm. Fluid Sci., 29, (2005). 11) S. Wada et al., Development of pulse ultrasonic Doppler method for flow rate measurement in power plant (multi lines flow rate measurement on metal pipe), J. Nucl. Sci. Technol., 41, (2004). 12) M. Mori et al., Development of a novel flow metering system using ultrasonic velocity profile measurements, Experiments in Fluids, 32[2], (2002). 13) M. Mori et al., Industrial application experiences of new type flow-metering system based on ultrasonic-doppler flow velocity-profile measurement, 3rd ISUD (2002). 14) H. Kikura et al., Development of plus ultrasonic Doppler method for flow rate measurement of power plant, Proc. ICONE10 (2002). 15) M. Mori et al., Development of new type flow-metering system by visualizing flow-profile using ultrasonic-doppler profile-velocimetry, WCIPT (2005). 16) K. Komura et al., Development of large scale simulation code ultrasonic testing, Proc. JSNDI (2000), [in Japanese]. 17) K. Koketsu et al., Finite-element simulation of seismic ground motion with a voxel mesh, Pure Appl. Geophysics, 161, (2004). 18) J. A. Ogilvy et al., Elastic model for simulating ultrasonic inspection of smooth and rough defects, Ultrasonics, 29, (1991). 19) F. Walte et al., Elastic wave propagation and scattering in austenitic steel, Proc. 13th Int. Conf. on NDE in the Nuclear Pressure Vessel Industries, (1995). 20) JSME Data Book: Heat Transfer, 4th Edition, 317 (1986), [in Japanese]. 21) Polyamide Resin Handbook: 1st Edition, Nikkan Kogyo Shimbun, Ltd., (1988), [in Japanese]. 22) K. Kamiya, Vibration and Wave, Saiensu-sha Co., Ltd., (1999), [in Japanese]. 23) Nondestructive Testing Ultrasonic, 2nd edition, General Dynamics, (1981). 24) Ultrasonic Material Testing, revised edition, The Nikkan Kogyo Shimbun, (1974), [in Japanese]. 25) Y. Inoue et al., A study of ultrasonic propagation for flow rate measurement using ultrasonic flowmeter, Proc. 5ISUD, (2006). 26) R. Motegi, Wide beam ultrasonic flowmeter, SICE, 29, (1993), [in Japanese]. 27) R. Motegi, On the spatial frequency dependence of the transit path of ultrasonic wave and excitation efficiency of plate mode for the pipe wall in a clamp-on ultrasonic flowmeter, Acoust. Soc. Jpn., 49, (1993), [in Japanese]. JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY