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Characterisation of valves as sound sources: Fluid-borne sound
Applied Acoustics 72 (2011) 428–436
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Characterisation of valves as sound sources: Fluid-borne sound T.H. Alber a,⇑, B.M. Gibbs b, H.M. Fischer a a b
University of Applied Sciences Stuttgart, Department of Civil Engineering, Building Physics and Economy, Schellingstrasse 24, D-70174 Stuttgart, Germany Acoustics Research Unit, School of Architecture, University of Liverpool, L69 3BX, UK
a r t i c l e
i n f o
Article history: Received 24 February 2009 Received in revised form 12 March 2010 Accepted 13 January 2011
Keywords: Fluid-borne sound Structure-borne sound Valves Prediction model
a b s t r a c t The sound pressure level in receiving rooms, caused by taps at the ends of pipe systems, is considered. The structure-borne sound power, from the pipes to the supporting wall, was obtained from intensity measurement of the fluid-borne sound power of the tap. The fluid-borne sound power is combined with a ratio of structure-borne sound power to fluid-borne sound power, obtained from laboratory measurements of similar pipe assemblies. Alternatively, a reception plate method is proposed, which avoids the necessity for intensity measurements. The structure-borne power into walls, to which the pipe work is attached, provides input to the standard building propagation model, which yields the predicted sound pressure level in the adjacent room. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In a companion paper [1] the role of structure-borne transmission in the sound emission of water appliances in buildings has been discussed. Methods are proposed for the characterisation of valves and taps as sources of structure-borne sound. The case considered is that of taps on basins, where the running tap generates reactive forces, which energise the basin into vibration. The basin then transmits structure-borne sound into the supporting wall, which radiates sound into the adjacent room. The focus of this paper is on the fluid-borne emission that forms another component of sound emission from water taps; airborne emission is not considered. Fig. 1 (taken from [1] for completeness) indicates that noise in buildings, resulting from fluid-borne sources, is the result of the following processes: fluid-borne sound emission into the fluid column; fluid–structure interaction, i.e. energy flow from the fluid into the pipe wall; structure-borne transmission from the pipe wall through connectors to building elements; propagation through the building and radiation into the room of interest. These four processes were considered in developing the source characterisation adopted and are described in this paper in the same order.
to obtain an independent source characterisation, on a power basis, the effect of pipe material, thickness and diameter, and of pipe length and junction boundary conditions, must be considered. If pipe material, thickness and diameter are fixed, then a source characterisation may be obtained for that particular pipe work, if the effect of resonances in the fluid column and due to the pipe length and junction boundary conditions can be removed or circumvented. Two approaches were considered. The first involved the design of a non-reflective end condition in order to simulate a semi-infinite fluid column. The second involved signal post-processing to eliminate reflection effects. Both approaches were applied to a sound intensity measurement technique. Sound intensity has been widely used, particularly for airbornesound sources [2] and has also been applied successfully for fluidborne sound sources [3] even to the extent of becoming a standardized method [4]. Constant or controllable operating conditions are required. This, in turn requires a specified test environment and the knowledge of possible sources of error within the measurement system. These are now discussed, followed by a description of the implementation of sound intensity for water appliances, along with measurement results.
2.1. Operating conditions 2. Fluid-borne sound emission The fluid-borne sound emission, from a tap into a water-filled pipe, is influenced by the impedance of the water column. In order ⇑ Corresponding author. E-mail address: [email protected] (T.H. Alber). 0003-682X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2011.01.007
Operating conditions, such as flow rate, water pressure and temperature, influence the acoustic emission of taps and valves. In general, it is necessary to control these parameters and keep them at steady levels during acoustical measurements. A water supply system was constructed, shown in Fig. 2, with several operating modes possible: at a constant pressure, volume flow, or
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Fig. 1. Sound transmission from water appliances: Structure-borne sound transmission shown in red; fluid-borne sound transmission shown in green. Secondary structureborne sound shown as dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3 1 2
rect measure of the particle velocity [7]. The intensity is obtained in terms of the cross-spectrum between two closely spaced pressure transducers, which are mounted flush and at a right angle to the water flow direction. The intensity is given by:
I¼
4
5
6 8
7
Fig. 2. Measurement rig for fluid-borne sound power: 1 valve/tap under test; 2 copper pipe; 3 pressure transducers; 4 flexible pipe; 5 pressure gauge; 6 flow meter; 7 high-pressure inline pump; 8 water tank.
pump speed. A high-pressure inline pump generated pressures up to 0.6 MPa. The temperature in the water tank was monitored and controlled, so that 25 °C was not exceeded, according to the standard requirement [5]. The flow rate was recorded with a magnetic-inductive flow meter which did not introduce further excitations in the water. The water was pumped from a water tank through a short steel-piping system with flow meter and pressure pick-off, before it is passed into a 5 m flexible rubber pipe. The rubber pipe served to reduce the structure-borne and fluid-borne sound transmission from the pump and the hydraulic measurement devices, to allow the unrestricted measurement of the fluid-borne sound emission of the tested appliance. The appliance under test was attached to a copper pipe with inner diameter 10 mm and 1 mm wall thickness. This allowed measurement under typical installation conditions.
2.2. Sound intensity The technique of sound intensity measurement can be used for the characterisation of fluid-borne sources, provided that only plane waves propagate in the receiving system [6]. The measurement involves a finite difference approximation to obtain an indi-
1
qf xDr
Im½GAB ðpA ; pB ; f Þ
ð1Þ
where Im[GAB(pA, pB, f)] is the imaginary part of the cross spectral density between the pressure transducers A and B with a separation distance Dr. The sound power of the valve is the product of the intensity and the inner cross-sectional area of the pipe. 2.3. Measurements errors Associated with this technique are systematic and random errors. The systematic errors are due to the finite difference approximation and to phase mismatch between transducers. Random errors result from inherent deficiencies in the instrumentation or from limitations in signal processing. The error due to the finite difference approximation sets an upper frequency limit and the normalised error can be estimated according to [2]: 4
eðIÞ ¼ ð2=3Þ ðkDr=2Þ2 þ ð2=15Þ ðkDr=2Þ
ð2Þ
For a maximum error of 0.5 dB, and for an upper frequency of 5 kHz, the required separation distance was 30 mm. The phase mismatch error is, again, according to [2]:
edB ðIÞ ¼ 10 logð1 þ eðIÞÞ ¼ 10 log ð1 þ /s =kDrÞ
ð3Þ
us is the transducer phase mismatch, which was 0.15°, giving an error less than 1 dB for the frequency range of interest. The random error for the power measurement is:
~sfPðf Þg ¼
S
q f x Dr
~sðIm½GAB Þ
ð4Þ
The error for one measurement, with N = 5000 samples, was 2%. Other errors were due to irregularities in the fluid, such as bubbles, which can cause changes in the speed of sound and lead to damping effects in the transmission path [8]. These were reduced by the use of a closed water circuit with venting. The temperature dependent error was of the order of 0.3% increase per 1 °C increase, over the normal operating range.
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2.4. Semi-infinite end condition Reflections in a receiving pipe are a hindrance to the use of intensity methods and compensating steps are required. The reflections are a result of impedance changes in the contained fluid, primarily due to those in the containing pipe wall. The relation between the speed of sound in an unbounded fluid c0 and that in a nonrigid pipe c0 is given by Korteweg [9] as:
c’ 1 ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 c0 2Ef 1 þ Es ðrðr=ro =rÞi2Þ1 o
ð5Þ
i
Ef and Es is the Young’s Modulus of the fluid and the pipe wall, respectively. A decrease in wall stiffness results in a reduction of the velocity of sound in the fluid. At 20 °C, the calculated velocity in the copper pipe is 1422 m/s. In the flexible rubber pipe, the calculated velocity is 690 m/s. Abrupt changes in wall stiffness cause abrupt changes in fluid impedance and thus reflections. If a gradual transition can be affected between the impedance of the copper and that of the rubber pipe, then a sufficiently long following rubber pipe (in this case, 5 m) will attenuate the transmitted pressure to the noise level, with no returning wave. A gradual transition was attempted by reinforcing the rubber tube with metal ring clips. The clips were closely spaced, in the region close to the join with the copper pipe, and increasingly spaced with increased distance from the join. The effectiveness of the transition piece in controlling fluid-borne reflections was assessed by generating impulses into the fluid column with a shaker-driven piston and recording pressure transducer signal time histories, with and without the transition piece. In Fig. 3 are shown the reflected time signals for the unchanged copper-rubber junction and that with a gradual decrease in flexible wall stiffness. With the latter, the reflected wave was reduced by 2–4 dB. Results were little improved by changes in clip spacing and clamping pressure and therefore this approach was not pursued further. A more convenient method is to use a commercially available anechoic liquid termination (ALT) to the design of CETIM [10,11]. It consists of a perforated pipe of the same inner diameter as the piping system under test. This inner pipe is surrounded by a flexible hose of slightly greater diameter. The device allows a gradual impedance matching between a rigid test pipe on the one side of the ALT and a flexible hose on the other side by steadily increasing the distance between perforations. The device also is not capable to reducing reflections completely and is expensive. Despite various attempts to construct nonreflecting connections and terminations, it was not possible to adequately simulate a semi-infinite pipe system.
Fig. 4. Fluid-borne sound power of tap with and without correction for reflections; also shown is background level.
2.5. Correction for fluid-borne sound reflection Signal conditioning was considered, which has been implemented successfully for small heating pumps [4]. Consider the reflection coefficient r, which is the complex ratio of reflected (pr) and incident wave pressure (pi). Two transducers, at fixed positions in a pipe, record the superposition of the incident and reflected wave. The reflection coefficient is expressed in terms of the transfer function between pressure transducers HAB(x) as follows:
r¼
eikzB HAB ðxÞ eikzA eikDr HAB ðxÞ ei2kzA ¼ HAB ðxÞ eikzA eikzB HAB ðxÞ eikDz
ð6Þ
where zA and zB are the distances of the pressure transducers from the join between the copper and rubber pipes and Dz is the transducer spacing. For an ideal single-input/single-output system, the transfer function can be expressed by auto- and cross-power spectra and the square of the reflection coefficient is given in the form:
jrj2 ¼ kDz kDz GAA þ GBB 2 ½Re½GAB cos c þ Im½GAB sin c GAA þ GBB 2 ½Re½GAB cos
kDz cf f
Im½GAB sin
kDz cf
ð7Þ
f
The fluid-borne power Pc into a semi-infinite is obtained by correcting the power measured I S in the presence of the reflection,
Pc ¼
IS ð1 jrj2 Þ
ð8Þ
In Fig. 4 is shown the fluid-borne sound power of a single-lever mixer, corrected according to Eq. (8). The background level was recorded with a flexible pipe as a substitute for the tap, with the water supply system operating at the same speed as for the test. In addition to the reflections in the fluid-column, pipe-wall resonances also were considered. Pipe-wall resonances are functions of wall material, radius, thickness, length and end conditions. For a 2.45 m copper pipe measured, longitudinal resonances were observed at 600 Hz and 1.2 kHz; the same frequencies where dips in the reflection coefficient and power spectrum were observed. However, the wall resonances generally were above the frequency range of interest and could be neglected. 3. Single-lever mixer taps
Fig. 3. Time history of reflected wave for the unmodified and modified copper/ rubber transition.
The fluid-borne sound power of four single-lever taps were recorded. The taps were designed for mounting on wash basins. The influence of water pressure and lever position, on the power, was considered. The fluid-borne sound powers are shown in Fig. 5 as
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flow rates. Again, the spectral behaviour is similar to earlier results, with most of the power below 300 Hz. Most power is emitted with the valve fully open. 4. Fluid–structure interaction
Fig. 5. Fluid-borne sound powers of four different single-lever taps, also shown are A-weighted values.
one-third octave values, along with the A-weighted values. The spectral behaviour is similar for all taps, with a significant rolloff in level above 400 Hz. Tap 2, which was considered to be of the highest quality, emitted the least power although it operated at a greater flow rate than Tap 1. The two other taps, which were sold by a supermarket chain, emitted the greatest powers. The influence of water pressure is indicated for the single-lever mixer (Tap 1) in Fig. 6. The power reduces with decrease in water pressure, but the spectral shape does not change with most of the power below 300 Hz. In Fig. 7 are shown results for operation at constant pressure while the lever position of the tap was varied from fully open to almost closed. This variation also yields different
Fluid-borne sound itself does not result in noise perceived by residents, but rather through fluid–structure interaction along the piping. The resultant pipe wall vibration transmits to the supporting building structure, through the connectors, and thence propagates through the building and radiates into the rooms. Fuller and Fahy [12] and Pavic [13] consider fluid–structure interaction in detail. The considerations are based on thin-wall theory with ratio of wall thickness to pipe radius h/R 1. When discussing the different possible wave types, reference is made to the non-dimenf sional frequency X ¼ fring ¼ xcLiR, where cLI is the longitudinal wave speed in the pipe wall and fring ¼ 2cpLIR is the ring frequency. The copper pipe used in this study had a ring frequency at approximately 100 kHz. For fluid-filled pipes three axially symmetric modes, of order n = 0, start at zero frequency. The s = 1 wave, the Korteweg wave [9], is a fluid plane wave. The s = 2 wave is a quasi-longitudinal wave in the pipe wall with associated radial wall motion due to Poisson contractions. Another branch of the n = 0 order is formed by a torsional wave (s = 3), which is largely unaffected by the presence of the contained fluid. A wave, of mode order 1, is a bending wave. Leissa [14] and Fuller and Fahy [12] show that the bending wave corresponds to the bending wave in a beam for X 6 0:2. This was assumed for the domestic pipe systems considered. 4.1. Energy distribution in fluid-filled pipes The compressional waves carry energy in the fluid as a plane wave (s = 1) and in the pipe wall as a quasi-longitudinal wave (s = 2). The degree to which the energy is concentrated in the fluid or the pipe wall will depend upon the type of excitation and the physical parameters of the pipe wall and the contained liquid. Fuller and Fahy [12], derive the ratio of powers in the fluid Pfb and in the shell Psb:
Er ðn ¼ 0Þ ¼
Fig. 6. Influence of water pressure on fluid-borne sound power of Tap 1.
qf Pf Ff 1 ¼ X2 ðkns RÞ Ps qs ½krs RJ0n ðkrs RÞ2 Sf
ð9Þ
where Ff is the fluid factor and Sf is the shell factor; both values are described in [12]. At low frequencies (X 1), for the n = 0 mode, most of the energy is contained in the pipe wall, for structural excitation. For excitation of the fluid, most energy remains in the fluid. Pavic [13] has demonstrated that the fluid contribution to the energy flow due to the bending motion is usually negligible in comparison with the structural contribution. The ratio of the two is given as:
Xw Er ðn ¼ 1Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffi 8 2þw
ð10Þ
where wis the non-dimensional constant: w = (qf/qs) (ri/h). For a copper pipe, in the frequency range 0–5 kHz, Er ðn ¼ 1Þ 6 1:7 103 . 5. Wave conversion in pipe systems
Fig. 7. Influence of lever position on fluid-borne sound power of Tap 1.
So far, straight pipes have been considered. In pipe systems with changes in direction at junctions, wave mode conversion takes place, such as between quasi-longitudinal and bending waves [15]. In related work on structure-borne transmission from vibrating sources into connected plate structures, it was concluded that the dominant component of excitation is through forces perpendicular to the plate [1,16]. Therefore, for a pipe parallel to
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and connected to a supporting wall, it is assumed that the component of bending motion perpendicular to the surface forms the dominant transmission. This was assumed for both rigid and flexible connectors. A three-dimensional pipe system was assembled in order to measure the structure-borne sound power caused by fluid flow in the piping. The objective was to establish if there was a relationship between the number of bends in a system and the ratio between the fluid-borne power from a tap, to the resultant structure-borne power into a supporting wall. The pipe system consisted of four segments with lengths between 1.8 m and 2.4 m. The pipes were of copper with an inner diameter of 10 mm and 1 mm wall thickness. A straight pipe was first considered and then 90° bends were added to eventually produce a pipe system in three planes with a total of three bends. The pipe assembly was mounted on two of the plates of a test rig composed of three mutually perpendicular 100 mm concrete plates, which were isolated from each other (Fig. 8). The pipes were fixed by commercially available plastic clips, which were screwed to 2 mm aluminium indenters and super-glued to the reception plates. An installation noise standard (INS) was used to generate strong excitation of the fluid. It was connected via a short flexible tube to prevent direct structure-borne sound excitation of the copper pipe. The repeatability of the source power was within ±1.5 dB. The number of pipe connections to the reception plates also was varied. The complete measurement program is shown schematically in Fig. 9. The fluid-borne sound power was recorded at a pressure transducer pair 1 m from the source. The structure-borne sound power was recorded for the concrete reception plate connected to the furthest pipe segment from the source. This was the vertical plate for cases I–III and the horizontal plate for cases IV–X, in Fig. 9. The reception plate method of obtaining the structure-borne power of a vibrating source is described in [1,17]. It is based on an energetic balance of the power emitted by the source into the receiving plate and the energy loss of the plate. It is assumed that the plate is energised into bending vibration so that the structure-borne sound power P of the mounted pipe can be calculated where:
Vertical plate
I
II
III
Horizontal plate
Cases:
IV-VI
VII-IX
IV connected to III V only on horizontal plate VIconnected toII
Cases: VII connected to II (represents maximum number of connections) VIII connected to III IX as in picture
Flexible tube for connection to pump
X
Valve (INS) as source
Fig. 9. Pipe configurations examined for the fluid–structure interaction.
The reception plate powers, for the 10 configurations, are shown in Fig. 10. The general trend is a decrease in power at about 4 dB/octave. While the trends are similar, there are shifts in the peaks due to differences in pipe length. They may also be due to the clamps being connected at nodal positions on the reception plate. In Fig. 11 the corresponding fluid-borne sound powers are shown. Most of the energy is below 300 Hz, above which the power decreases at 30 dB/octave. Again, there are dips in the spectra which are due to resonances in the bending field of the pipe system. 5.1. Fluid–structure power ratio
averaged squared velocity of the excited plate. In this case, where each reception plate was structurally isolated, the total loss factor is composed of the internal (material) loss factor and the radiation loss factor. In the case of plates rigidly connected to other plates, coupling loss factors assume importance at low frequency [18].
A power ratio cs=f ¼ PPs was calculated from the fluid-borne and f associated structure-borne sound powers for each connected pipe configuration. In Fig. 12 are shown values for the 10 configurations investigated. There is a rising trend, up to 1 kHz, above which the value is at a plateau of 103 (30 dB). In Fig. 13 are shown the mean and standard deviation. The mean value of the ratio provides a transformation of the fluid-borne emission of a tap or valve into the reception plate power for the specific case: copper piping, plastic connectors and 100 mm concrete plate. For other cases, where another connection system and/or pipe-type are used, another power ratio is required.
Fig. 8. Pipe system with three sections mounted on two plates of a three-plate reception rig. The source was located at the upper right end of the pipe.
Fig. 10. Structure-borne sound powers for 10 pipe configurations.
P ¼ gxmv~ 2
ð11Þ
g is the total loss factor, m is the mass of the plate and v~ 2 the spatial
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6. Vibration activity and mobility of pipe system with flow
Fig. 11. Fluid-borne sound power for 10 pipe configurations with mean value.
It has been demonstrated elsewhere that structure-borne sound sources can be characterised in terms of free velocity and mobility [1,17]. Also, it can be assumed that the force perpendicular to the surface dominates the structure-borne power, while the roles of moments and in-plane forces can be neglected [1,16]. Therefore, only the velocity perpendicular to the proposed receiving plate need be considered, along with the associated mobility. A pipe system was assembled from three segments connected by two 90° bends as shown in Fig. 14. Again, the pipe was to be connected with seven plastic clamps that were screwed to aluminium indenters and super-glued on the wall, with a minimum of two clamps per pipe segment. The free velocities, at seven connection positions of the freely suspended pipe, i.e. prior to connecting to a wall, are shown in Fig. 15. The range of values is of the order of 10 dB. The phase differences, between six connection points and the connection point nearest the source, are shown in Fig. 16. The phase differences are small up to 200 Hz. Above 200 Hz, the phase differences increase and the contacts can be assumed to be independent. The source mobility at the seven connections on the freely suspended pipe also was recorded, using an instrumented impulse hammer, and the average value is shown in Fig. 17. The receiver mobility of a wall was recorded at the corresponding seven
Fig. 12. Ratio of structure- to fluid-borne sound power for 10 pipe configurations, with mean value. Fig. 14. Arrangement for the in situ measurement of the sound pressure level with three pipe segments (I–III).
Fig. 13. Mean and standard deviation of ratio of structure- to fluid-borne sound power for 10 pipe configurations.
Fig. 15. Free velocity at seven connection points on pipe, with mean value.
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tal power from multiple connections is shown in Fig. 19, normalised with respect to the expected increase in power relative to that through one connection. It would be expected that, for independent connections, the power would increase by 3 dB on increasing the number of connections from one to two, and by 6 dB on increasing from one to four, and so on. Below 200 Hz, the measured level differences are less than the expected and differ by 8 dB in some cases. In general, the dips in the summed powers
I
IV
II
III
V
VI
Fig. 16. Phase difference of free velocity at seven connection points.
Source (INS)
VII
Connection Flexible tube for connection to pump
Fig. 18. Schematic of the connection configurations for same pipe geometry.
Fig. 17. Average point mobility of pipes and supporting wall.
connection points. The wall was of 175 mm aerated concrete (density 700 kg/m3) with two free edges and two forming junctions with other walls. The average receiver mobility is also shown in Fig. 17. The pipe mobility is three decades above that of the wall. The source-receiver mobility mismatch condition is not likely to be changed significantly, on the introduction of other rigid or flexible connectors.
Fig. 19. Structure-borne power from multiple connection points normalised with respect to the expected power relative to that of a single contact.
6.1. Conversion of reception plate power to installed power From consideration of the pipe mobility and that of a typical wall, the pipe system can be assumed to be a high mobility source for typical installations in heavyweight buildings. This means that the structure-borne power Prec, obtained by the reception plate method, can be used to predict the structure-borne power Pinstalled into a wall, of different material and thickness, from the ratio of the real parts of the two mobilities, where
Pinstalled ¼
ReðY build Þ ReðY rec Þ
Prec
ð12Þ
6.2. Influence of the number of connections Several connection configurations were examined, while the total pipe length and geometry were kept the same (Fig. 18). The to-
Fig. 20. Measured and predicted sound pressure level in receiving room.
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Free velocity (z-direction)
Mobility (z-direction)
Structure-borne emission
TAP Fluid-borne emission
Intensimetry Free velocity (z-direction; x-axis)
Mobility (z-direction; x-axis)
Structure-borne emission
BASIN Reception plate Intensimetry Transmission coefficient
PIPE
Structure-borne emission
Reception plate Fig. 21. Schematic of data requirements for fluid-borne and structure-borne sources.
correspond to a contact spacing of one half the governing wavelength. Above 200 Hz, the measured level difference fluctuates about the expected value, again indicating interference effects. Therefore, although the contacts may be assumed independent, in terms of free velocity, above 200 Hz, the resultant power into a wall is influenced by the ratio of spacing to governing wavelength and +/6 dB fluctuations can be expected. 7. Sound pressure level in situ The remaining step in the sound power transmission chain is the structure-borne propagation through the building and radiation into the room of interest. The sound pressure level in a receiving room was calculated for transmission between horizontally adjacent rooms; the source room contained the pipe work connected to the separating wall. The prediction model was that detailed in EN 12354-5 [19]. The piping and connections were as previously described and consisted of three segments. The sound pressure level in the receiving chamber was measured according to ISO 140 part 4 [20] and ISO 10052 [21]. The background noise level was recorded in the receiving room with the water supply pump in operation but without water flow through the piping, and also with the water supply system switched off. The sound pressure level was dominated by background noise at frequencies below 100 Hz, irrespective of pump operation. The background noise is controlled by the water supply system above 160 Hz, but is well below the sound pressure level with the pipe system in operation. The prediction procedure requires the installed structure-borne power into the building structure, in this case, the 175 mm wall. The installed power was obtained from the reception plate power, as in Eq. (12). The reception plate power can be obtained directly, as in Eq. (11), or indirectly from the fluid-borne power and the power ratio, described earlier, where
Prec ¼ cs=f :P f
ð13Þ
The power ratio cs/f was that for Case II, of a pipe system with two pipe segments and a 90° bend. The fluid-borne sound power of the tap under test was obtained previously. Once the installed power was known, the sound pressure level was calculated according to [19]. The measured and predicted sound pressure levels, in the receiving room, are shown in Fig. 20, along with A-weighted values for the frequency range 125 Hz–1 kHz. In general the agreement is within 3 dB but with
significant differences due to resonant effects of the finite pipe system.
8. Proposed test procedure Fig. 21 encapsulates the whole process of structure-borne and fluid-borne transmission from taps and valves into building elements. It therefore includes the findings of the companion paper on structure-borne sound into support walls as a result of reacting forces and moments from taps under flow [1]. For the case of taps as fluid-borne sources, the secondary structure-borne transmission, due to fluid–structure interaction, can be obtained by two means. Either a small scale test rig can be constructed that allows the fluid-borne sound power emission in a short pipe of about 2–3 m length to be obtained. The secondary structure-borne emission could then be calculated from a database of power ratios for different configurations of that pipe type and connecter type. Alternatively, a reception plate method can be employed, circumventing fluid-borne sound intensimetry. A database of transmission coefficients would not be necessary, but rather the reception plate power of different valves under set operating conditions, could be recorded for the specified pipe material, geometry and connectors.
9. Concluding remarks A ratio of structure-borne power to fluid-borne power is proposed that allows the structure-borne sound power from pipe work into a wall or floor to be obtained from knowledge of the fluid-borne sound power of a valve or tap which excites the pipe work into vibration. The structure-borne power can be modified to yield the installed power from the same pipe system, now connected to the wall or floor of interest, to provide input data for prediction of sound propagation through a building. The fluid-borne power is obtained from intensity measurement where a correction is included for reflections due to pipe discontinuities. The structure-borne power can be obtained by a reception plate method, thereby avoiding the need for fluid-borne sound intensity measurements. This has the additional advantage in that the efficacy of alternative pipe material and connectors can be assessed
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in terms of the change in the fluid–structure power ratio. A lower ratio corresponds to a reduction in potential noise. The approach offers the possibility of assembling a data set of power ratios for the most popular pipe systems and connectors as a prerequisite for prediction. The approach also allows assessment of the acoustical improvement of connectors or special pipes, where a low value of power ratio will reflect a reduction in potential noise. References [1] Alber TH, Gibbs BM, Fischer H-M. Characterisation of valves as sound sources: structure-borne sound. Appl Acoust 2009;70:661–73. [2] Fahy FJ. Sound intensity. 2nd ed. Elsevier Applied Science; 1995. [3] Qi N, Gibbs BM. Circulation pumps as structure-borne sound sources: emission to semi-infinite pipe systems. J Sound Vib 2003;264:157–76. [4] prEN 1151-2. Pumps – rotodynamic pumps – circulation pumps having an electrical effect not exceeding 200 W for heating installations and domestic hot water installations – part 2: noise test code (vibro-acoustics) for measuring structure- and fluid-borne noise; 2003. [5] ISO 3822-1. Acoustics – Laboratory tests on noise emission from appliances and equipment used in water supply installations – part 1: method of measurement; 1999. [6] Pavic G. Measurement of sound intensity. J Sound Vib 1977;51:533–45. [7] Thomson JK, Tree DR. Finite difference approximation errors in acoustic intensity measurements. J Sound Vib 1981;75:229–38. [8] Troshin AG, Popkov VI, Popov AV. The measurement of vibration power flux in rod structures. In: 3rd International congress on intensity techniques, Senlis, France; 1990. p. 265–72.
[9] Korteweg DJ. Ueber die Fortpflanzungsgeschwindigkeit des Schalles in elastischen Röhren (On the speed of sound in elastic pipes). Annalen der Physik – Band; 1878. p. 241 [in German]. [10] Anechoic Liquid Termination. Product information, CETIM, France; 1991. [11] Bernard G et al. Industrial procedure for determination of the hydroacoustics power of centrifugal pumps by using anechoic liquid terminator. Proc Internoise 1980;88:663–6. [12] Fuller CR, Fahy FJ. Characteristics of wave propagation and energy distributions in cylindrical elastic shell filled with fluid. J Sound Vib 1982;81(4):501–18. [13] Pavic G. Vibrational energy flow in elastic circular cylindrical shells. J Sound Vib 1990;142(2):293–310. [14] Leissa AW. Vibration of shells. Acoustical Society of America; 1993. [15] Gibbs BM, Qi N. Circulation pumps as structure-borne sound sources: emission to finite pipe systems. J Sound Vib 2005;284:1099–118. [16] Yap SH, Gibbs BM. Structure-borne sound transmission from machines in buildings – part 2: indirect measurement of force and moment at the machine–receiver interface of a single point connected system by a reciprocal method. J Sound Vib 1999;222(1):99–113. [17] Cremer L, Heckl M. Structure-borne sound. 2nd ed. Springer-Verlag; 1996. [18] Craik RJM. Sound transmission through buildings using statistical energy analysis. London: Gower Publishing Limited; 1996. [19] prEN 12354-5. Building acoustics – estimation of acoustic performance of building elements from the performance of elements – part 5: sound levels due to service equipment; 2004. [20] ISO 140-4. Acoustics – measurement of sound insulation in buildings and of building elements – part 4: field measurements of airborne sound insulation between rooms; 1998. [21] ISO 10052. Acoustics – field measurements of airborne and impact sound insulation and of service equipment sound – survey method; 2004.
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Applied Acoustics journal homepage: www.elsevier.com/locate/apacoust
Characterisation of valves as sound sources: Fluid-borne sound T.H. Alber a,⇑, B.M. Gibbs b, H.M. Fischer a a b
University of Applied Sciences Stuttgart, Department of Civil Engineering, Building Physics and Economy, Schellingstrasse 24, D-70174 Stuttgart, Germany Acoustics Research Unit, School of Architecture, University of Liverpool, L69 3BX, UK
a r t i c l e
i n f o
Article history: Received 24 February 2009 Received in revised form 12 March 2010 Accepted 13 January 2011
Keywords: Fluid-borne sound Structure-borne sound Valves Prediction model
a b s t r a c t The sound pressure level in receiving rooms, caused by taps at the ends of pipe systems, is considered. The structure-borne sound power, from the pipes to the supporting wall, was obtained from intensity measurement of the fluid-borne sound power of the tap. The fluid-borne sound power is combined with a ratio of structure-borne sound power to fluid-borne sound power, obtained from laboratory measurements of similar pipe assemblies. Alternatively, a reception plate method is proposed, which avoids the necessity for intensity measurements. The structure-borne power into walls, to which the pipe work is attached, provides input to the standard building propagation model, which yields the predicted sound pressure level in the adjacent room. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction In a companion paper [1] the role of structure-borne transmission in the sound emission of water appliances in buildings has been discussed. Methods are proposed for the characterisation of valves and taps as sources of structure-borne sound. The case considered is that of taps on basins, where the running tap generates reactive forces, which energise the basin into vibration. The basin then transmits structure-borne sound into the supporting wall, which radiates sound into the adjacent room. The focus of this paper is on the fluid-borne emission that forms another component of sound emission from water taps; airborne emission is not considered. Fig. 1 (taken from [1] for completeness) indicates that noise in buildings, resulting from fluid-borne sources, is the result of the following processes: fluid-borne sound emission into the fluid column; fluid–structure interaction, i.e. energy flow from the fluid into the pipe wall; structure-borne transmission from the pipe wall through connectors to building elements; propagation through the building and radiation into the room of interest. These four processes were considered in developing the source characterisation adopted and are described in this paper in the same order.
to obtain an independent source characterisation, on a power basis, the effect of pipe material, thickness and diameter, and of pipe length and junction boundary conditions, must be considered. If pipe material, thickness and diameter are fixed, then a source characterisation may be obtained for that particular pipe work, if the effect of resonances in the fluid column and due to the pipe length and junction boundary conditions can be removed or circumvented. Two approaches were considered. The first involved the design of a non-reflective end condition in order to simulate a semi-infinite fluid column. The second involved signal post-processing to eliminate reflection effects. Both approaches were applied to a sound intensity measurement technique. Sound intensity has been widely used, particularly for airbornesound sources [2] and has also been applied successfully for fluidborne sound sources [3] even to the extent of becoming a standardized method [4]. Constant or controllable operating conditions are required. This, in turn requires a specified test environment and the knowledge of possible sources of error within the measurement system. These are now discussed, followed by a description of the implementation of sound intensity for water appliances, along with measurement results.
2.1. Operating conditions 2. Fluid-borne sound emission The fluid-borne sound emission, from a tap into a water-filled pipe, is influenced by the impedance of the water column. In order ⇑ Corresponding author. E-mail address: [email protected] (T.H. Alber). 0003-682X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.apacoust.2011.01.007
Operating conditions, such as flow rate, water pressure and temperature, influence the acoustic emission of taps and valves. In general, it is necessary to control these parameters and keep them at steady levels during acoustical measurements. A water supply system was constructed, shown in Fig. 2, with several operating modes possible: at a constant pressure, volume flow, or
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Fig. 1. Sound transmission from water appliances: Structure-borne sound transmission shown in red; fluid-borne sound transmission shown in green. Secondary structureborne sound shown as dashed lines. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
3 1 2
rect measure of the particle velocity [7]. The intensity is obtained in terms of the cross-spectrum between two closely spaced pressure transducers, which are mounted flush and at a right angle to the water flow direction. The intensity is given by:
I¼
4
5
6 8
7
Fig. 2. Measurement rig for fluid-borne sound power: 1 valve/tap under test; 2 copper pipe; 3 pressure transducers; 4 flexible pipe; 5 pressure gauge; 6 flow meter; 7 high-pressure inline pump; 8 water tank.
pump speed. A high-pressure inline pump generated pressures up to 0.6 MPa. The temperature in the water tank was monitored and controlled, so that 25 °C was not exceeded, according to the standard requirement [5]. The flow rate was recorded with a magnetic-inductive flow meter which did not introduce further excitations in the water. The water was pumped from a water tank through a short steel-piping system with flow meter and pressure pick-off, before it is passed into a 5 m flexible rubber pipe. The rubber pipe served to reduce the structure-borne and fluid-borne sound transmission from the pump and the hydraulic measurement devices, to allow the unrestricted measurement of the fluid-borne sound emission of the tested appliance. The appliance under test was attached to a copper pipe with inner diameter 10 mm and 1 mm wall thickness. This allowed measurement under typical installation conditions.
2.2. Sound intensity The technique of sound intensity measurement can be used for the characterisation of fluid-borne sources, provided that only plane waves propagate in the receiving system [6]. The measurement involves a finite difference approximation to obtain an indi-
1
qf xDr
Im½GAB ðpA ; pB ; f Þ
ð1Þ
where Im[GAB(pA, pB, f)] is the imaginary part of the cross spectral density between the pressure transducers A and B with a separation distance Dr. The sound power of the valve is the product of the intensity and the inner cross-sectional area of the pipe. 2.3. Measurements errors Associated with this technique are systematic and random errors. The systematic errors are due to the finite difference approximation and to phase mismatch between transducers. Random errors result from inherent deficiencies in the instrumentation or from limitations in signal processing. The error due to the finite difference approximation sets an upper frequency limit and the normalised error can be estimated according to [2]: 4
eðIÞ ¼ ð2=3Þ ðkDr=2Þ2 þ ð2=15Þ ðkDr=2Þ
ð2Þ
For a maximum error of 0.5 dB, and for an upper frequency of 5 kHz, the required separation distance was 30 mm. The phase mismatch error is, again, according to [2]:
edB ðIÞ ¼ 10 logð1 þ eðIÞÞ ¼ 10 log ð1 þ /s =kDrÞ
ð3Þ
us is the transducer phase mismatch, which was 0.15°, giving an error less than 1 dB for the frequency range of interest. The random error for the power measurement is:
~sfPðf Þg ¼
S
q f x Dr
~sðIm½GAB Þ
ð4Þ
The error for one measurement, with N = 5000 samples, was 2%. Other errors were due to irregularities in the fluid, such as bubbles, which can cause changes in the speed of sound and lead to damping effects in the transmission path [8]. These were reduced by the use of a closed water circuit with venting. The temperature dependent error was of the order of 0.3% increase per 1 °C increase, over the normal operating range.
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2.4. Semi-infinite end condition Reflections in a receiving pipe are a hindrance to the use of intensity methods and compensating steps are required. The reflections are a result of impedance changes in the contained fluid, primarily due to those in the containing pipe wall. The relation between the speed of sound in an unbounded fluid c0 and that in a nonrigid pipe c0 is given by Korteweg [9] as:
c’ 1 ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 c0 2Ef 1 þ Es ðrðr=ro =rÞi2Þ1 o
ð5Þ
i
Ef and Es is the Young’s Modulus of the fluid and the pipe wall, respectively. A decrease in wall stiffness results in a reduction of the velocity of sound in the fluid. At 20 °C, the calculated velocity in the copper pipe is 1422 m/s. In the flexible rubber pipe, the calculated velocity is 690 m/s. Abrupt changes in wall stiffness cause abrupt changes in fluid impedance and thus reflections. If a gradual transition can be affected between the impedance of the copper and that of the rubber pipe, then a sufficiently long following rubber pipe (in this case, 5 m) will attenuate the transmitted pressure to the noise level, with no returning wave. A gradual transition was attempted by reinforcing the rubber tube with metal ring clips. The clips were closely spaced, in the region close to the join with the copper pipe, and increasingly spaced with increased distance from the join. The effectiveness of the transition piece in controlling fluid-borne reflections was assessed by generating impulses into the fluid column with a shaker-driven piston and recording pressure transducer signal time histories, with and without the transition piece. In Fig. 3 are shown the reflected time signals for the unchanged copper-rubber junction and that with a gradual decrease in flexible wall stiffness. With the latter, the reflected wave was reduced by 2–4 dB. Results were little improved by changes in clip spacing and clamping pressure and therefore this approach was not pursued further. A more convenient method is to use a commercially available anechoic liquid termination (ALT) to the design of CETIM [10,11]. It consists of a perforated pipe of the same inner diameter as the piping system under test. This inner pipe is surrounded by a flexible hose of slightly greater diameter. The device allows a gradual impedance matching between a rigid test pipe on the one side of the ALT and a flexible hose on the other side by steadily increasing the distance between perforations. The device also is not capable to reducing reflections completely and is expensive. Despite various attempts to construct nonreflecting connections and terminations, it was not possible to adequately simulate a semi-infinite pipe system.
Fig. 4. Fluid-borne sound power of tap with and without correction for reflections; also shown is background level.
2.5. Correction for fluid-borne sound reflection Signal conditioning was considered, which has been implemented successfully for small heating pumps [4]. Consider the reflection coefficient r, which is the complex ratio of reflected (pr) and incident wave pressure (pi). Two transducers, at fixed positions in a pipe, record the superposition of the incident and reflected wave. The reflection coefficient is expressed in terms of the transfer function between pressure transducers HAB(x) as follows:
r¼
eikzB HAB ðxÞ eikzA eikDr HAB ðxÞ ei2kzA ¼ HAB ðxÞ eikzA eikzB HAB ðxÞ eikDz
ð6Þ
where zA and zB are the distances of the pressure transducers from the join between the copper and rubber pipes and Dz is the transducer spacing. For an ideal single-input/single-output system, the transfer function can be expressed by auto- and cross-power spectra and the square of the reflection coefficient is given in the form:
jrj2 ¼ kDz kDz GAA þ GBB 2 ½Re½GAB cos c þ Im½GAB sin c GAA þ GBB 2 ½Re½GAB cos
kDz cf f
Im½GAB sin
kDz cf
ð7Þ
f
The fluid-borne power Pc into a semi-infinite is obtained by correcting the power measured I S in the presence of the reflection,
Pc ¼
IS ð1 jrj2 Þ
ð8Þ
In Fig. 4 is shown the fluid-borne sound power of a single-lever mixer, corrected according to Eq. (8). The background level was recorded with a flexible pipe as a substitute for the tap, with the water supply system operating at the same speed as for the test. In addition to the reflections in the fluid-column, pipe-wall resonances also were considered. Pipe-wall resonances are functions of wall material, radius, thickness, length and end conditions. For a 2.45 m copper pipe measured, longitudinal resonances were observed at 600 Hz and 1.2 kHz; the same frequencies where dips in the reflection coefficient and power spectrum were observed. However, the wall resonances generally were above the frequency range of interest and could be neglected. 3. Single-lever mixer taps
Fig. 3. Time history of reflected wave for the unmodified and modified copper/ rubber transition.
The fluid-borne sound power of four single-lever taps were recorded. The taps were designed for mounting on wash basins. The influence of water pressure and lever position, on the power, was considered. The fluid-borne sound powers are shown in Fig. 5 as
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flow rates. Again, the spectral behaviour is similar to earlier results, with most of the power below 300 Hz. Most power is emitted with the valve fully open. 4. Fluid–structure interaction
Fig. 5. Fluid-borne sound powers of four different single-lever taps, also shown are A-weighted values.
one-third octave values, along with the A-weighted values. The spectral behaviour is similar for all taps, with a significant rolloff in level above 400 Hz. Tap 2, which was considered to be of the highest quality, emitted the least power although it operated at a greater flow rate than Tap 1. The two other taps, which were sold by a supermarket chain, emitted the greatest powers. The influence of water pressure is indicated for the single-lever mixer (Tap 1) in Fig. 6. The power reduces with decrease in water pressure, but the spectral shape does not change with most of the power below 300 Hz. In Fig. 7 are shown results for operation at constant pressure while the lever position of the tap was varied from fully open to almost closed. This variation also yields different
Fluid-borne sound itself does not result in noise perceived by residents, but rather through fluid–structure interaction along the piping. The resultant pipe wall vibration transmits to the supporting building structure, through the connectors, and thence propagates through the building and radiates into the rooms. Fuller and Fahy [12] and Pavic [13] consider fluid–structure interaction in detail. The considerations are based on thin-wall theory with ratio of wall thickness to pipe radius h/R 1. When discussing the different possible wave types, reference is made to the non-dimenf sional frequency X ¼ fring ¼ xcLiR, where cLI is the longitudinal wave speed in the pipe wall and fring ¼ 2cpLIR is the ring frequency. The copper pipe used in this study had a ring frequency at approximately 100 kHz. For fluid-filled pipes three axially symmetric modes, of order n = 0, start at zero frequency. The s = 1 wave, the Korteweg wave [9], is a fluid plane wave. The s = 2 wave is a quasi-longitudinal wave in the pipe wall with associated radial wall motion due to Poisson contractions. Another branch of the n = 0 order is formed by a torsional wave (s = 3), which is largely unaffected by the presence of the contained fluid. A wave, of mode order 1, is a bending wave. Leissa [14] and Fuller and Fahy [12] show that the bending wave corresponds to the bending wave in a beam for X 6 0:2. This was assumed for the domestic pipe systems considered. 4.1. Energy distribution in fluid-filled pipes The compressional waves carry energy in the fluid as a plane wave (s = 1) and in the pipe wall as a quasi-longitudinal wave (s = 2). The degree to which the energy is concentrated in the fluid or the pipe wall will depend upon the type of excitation and the physical parameters of the pipe wall and the contained liquid. Fuller and Fahy [12], derive the ratio of powers in the fluid Pfb and in the shell Psb:
Er ðn ¼ 0Þ ¼
Fig. 6. Influence of water pressure on fluid-borne sound power of Tap 1.
qf Pf Ff 1 ¼ X2 ðkns RÞ Ps qs ½krs RJ0n ðkrs RÞ2 Sf
ð9Þ
where Ff is the fluid factor and Sf is the shell factor; both values are described in [12]. At low frequencies (X 1), for the n = 0 mode, most of the energy is contained in the pipe wall, for structural excitation. For excitation of the fluid, most energy remains in the fluid. Pavic [13] has demonstrated that the fluid contribution to the energy flow due to the bending motion is usually negligible in comparison with the structural contribution. The ratio of the two is given as:
Xw Er ðn ¼ 1Þ ¼ pffiffiffiffiffiffiffiffiffiffiffiffi 8 2þw
ð10Þ
where wis the non-dimensional constant: w = (qf/qs) (ri/h). For a copper pipe, in the frequency range 0–5 kHz, Er ðn ¼ 1Þ 6 1:7 103 . 5. Wave conversion in pipe systems
Fig. 7. Influence of lever position on fluid-borne sound power of Tap 1.
So far, straight pipes have been considered. In pipe systems with changes in direction at junctions, wave mode conversion takes place, such as between quasi-longitudinal and bending waves [15]. In related work on structure-borne transmission from vibrating sources into connected plate structures, it was concluded that the dominant component of excitation is through forces perpendicular to the plate [1,16]. Therefore, for a pipe parallel to
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and connected to a supporting wall, it is assumed that the component of bending motion perpendicular to the surface forms the dominant transmission. This was assumed for both rigid and flexible connectors. A three-dimensional pipe system was assembled in order to measure the structure-borne sound power caused by fluid flow in the piping. The objective was to establish if there was a relationship between the number of bends in a system and the ratio between the fluid-borne power from a tap, to the resultant structure-borne power into a supporting wall. The pipe system consisted of four segments with lengths between 1.8 m and 2.4 m. The pipes were of copper with an inner diameter of 10 mm and 1 mm wall thickness. A straight pipe was first considered and then 90° bends were added to eventually produce a pipe system in three planes with a total of three bends. The pipe assembly was mounted on two of the plates of a test rig composed of three mutually perpendicular 100 mm concrete plates, which were isolated from each other (Fig. 8). The pipes were fixed by commercially available plastic clips, which were screwed to 2 mm aluminium indenters and super-glued to the reception plates. An installation noise standard (INS) was used to generate strong excitation of the fluid. It was connected via a short flexible tube to prevent direct structure-borne sound excitation of the copper pipe. The repeatability of the source power was within ±1.5 dB. The number of pipe connections to the reception plates also was varied. The complete measurement program is shown schematically in Fig. 9. The fluid-borne sound power was recorded at a pressure transducer pair 1 m from the source. The structure-borne sound power was recorded for the concrete reception plate connected to the furthest pipe segment from the source. This was the vertical plate for cases I–III and the horizontal plate for cases IV–X, in Fig. 9. The reception plate method of obtaining the structure-borne power of a vibrating source is described in [1,17]. It is based on an energetic balance of the power emitted by the source into the receiving plate and the energy loss of the plate. It is assumed that the plate is energised into bending vibration so that the structure-borne sound power P of the mounted pipe can be calculated where:
Vertical plate
I
II
III
Horizontal plate
Cases:
IV-VI
VII-IX
IV connected to III V only on horizontal plate VIconnected toII
Cases: VII connected to II (represents maximum number of connections) VIII connected to III IX as in picture
Flexible tube for connection to pump
X
Valve (INS) as source
Fig. 9. Pipe configurations examined for the fluid–structure interaction.
The reception plate powers, for the 10 configurations, are shown in Fig. 10. The general trend is a decrease in power at about 4 dB/octave. While the trends are similar, there are shifts in the peaks due to differences in pipe length. They may also be due to the clamps being connected at nodal positions on the reception plate. In Fig. 11 the corresponding fluid-borne sound powers are shown. Most of the energy is below 300 Hz, above which the power decreases at 30 dB/octave. Again, there are dips in the spectra which are due to resonances in the bending field of the pipe system. 5.1. Fluid–structure power ratio
averaged squared velocity of the excited plate. In this case, where each reception plate was structurally isolated, the total loss factor is composed of the internal (material) loss factor and the radiation loss factor. In the case of plates rigidly connected to other plates, coupling loss factors assume importance at low frequency [18].
A power ratio cs=f ¼ PPs was calculated from the fluid-borne and f associated structure-borne sound powers for each connected pipe configuration. In Fig. 12 are shown values for the 10 configurations investigated. There is a rising trend, up to 1 kHz, above which the value is at a plateau of 103 (30 dB). In Fig. 13 are shown the mean and standard deviation. The mean value of the ratio provides a transformation of the fluid-borne emission of a tap or valve into the reception plate power for the specific case: copper piping, plastic connectors and 100 mm concrete plate. For other cases, where another connection system and/or pipe-type are used, another power ratio is required.
Fig. 8. Pipe system with three sections mounted on two plates of a three-plate reception rig. The source was located at the upper right end of the pipe.
Fig. 10. Structure-borne sound powers for 10 pipe configurations.
P ¼ gxmv~ 2
ð11Þ
g is the total loss factor, m is the mass of the plate and v~ 2 the spatial
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6. Vibration activity and mobility of pipe system with flow
Fig. 11. Fluid-borne sound power for 10 pipe configurations with mean value.
It has been demonstrated elsewhere that structure-borne sound sources can be characterised in terms of free velocity and mobility [1,17]. Also, it can be assumed that the force perpendicular to the surface dominates the structure-borne power, while the roles of moments and in-plane forces can be neglected [1,16]. Therefore, only the velocity perpendicular to the proposed receiving plate need be considered, along with the associated mobility. A pipe system was assembled from three segments connected by two 90° bends as shown in Fig. 14. Again, the pipe was to be connected with seven plastic clamps that were screwed to aluminium indenters and super-glued on the wall, with a minimum of two clamps per pipe segment. The free velocities, at seven connection positions of the freely suspended pipe, i.e. prior to connecting to a wall, are shown in Fig. 15. The range of values is of the order of 10 dB. The phase differences, between six connection points and the connection point nearest the source, are shown in Fig. 16. The phase differences are small up to 200 Hz. Above 200 Hz, the phase differences increase and the contacts can be assumed to be independent. The source mobility at the seven connections on the freely suspended pipe also was recorded, using an instrumented impulse hammer, and the average value is shown in Fig. 17. The receiver mobility of a wall was recorded at the corresponding seven
Fig. 12. Ratio of structure- to fluid-borne sound power for 10 pipe configurations, with mean value. Fig. 14. Arrangement for the in situ measurement of the sound pressure level with three pipe segments (I–III).
Fig. 13. Mean and standard deviation of ratio of structure- to fluid-borne sound power for 10 pipe configurations.
Fig. 15. Free velocity at seven connection points on pipe, with mean value.
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tal power from multiple connections is shown in Fig. 19, normalised with respect to the expected increase in power relative to that through one connection. It would be expected that, for independent connections, the power would increase by 3 dB on increasing the number of connections from one to two, and by 6 dB on increasing from one to four, and so on. Below 200 Hz, the measured level differences are less than the expected and differ by 8 dB in some cases. In general, the dips in the summed powers
I
IV
II
III
V
VI
Fig. 16. Phase difference of free velocity at seven connection points.
Source (INS)
VII
Connection Flexible tube for connection to pump
Fig. 18. Schematic of the connection configurations for same pipe geometry.
Fig. 17. Average point mobility of pipes and supporting wall.
connection points. The wall was of 175 mm aerated concrete (density 700 kg/m3) with two free edges and two forming junctions with other walls. The average receiver mobility is also shown in Fig. 17. The pipe mobility is three decades above that of the wall. The source-receiver mobility mismatch condition is not likely to be changed significantly, on the introduction of other rigid or flexible connectors.
Fig. 19. Structure-borne power from multiple connection points normalised with respect to the expected power relative to that of a single contact.
6.1. Conversion of reception plate power to installed power From consideration of the pipe mobility and that of a typical wall, the pipe system can be assumed to be a high mobility source for typical installations in heavyweight buildings. This means that the structure-borne power Prec, obtained by the reception plate method, can be used to predict the structure-borne power Pinstalled into a wall, of different material and thickness, from the ratio of the real parts of the two mobilities, where
Pinstalled ¼
ReðY build Þ ReðY rec Þ
Prec
ð12Þ
6.2. Influence of the number of connections Several connection configurations were examined, while the total pipe length and geometry were kept the same (Fig. 18). The to-
Fig. 20. Measured and predicted sound pressure level in receiving room.
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Free velocity (z-direction)
Mobility (z-direction)
Structure-borne emission
TAP Fluid-borne emission
Intensimetry Free velocity (z-direction; x-axis)
Mobility (z-direction; x-axis)
Structure-borne emission
BASIN Reception plate Intensimetry Transmission coefficient
PIPE
Structure-borne emission
Reception plate Fig. 21. Schematic of data requirements for fluid-borne and structure-borne sources.
correspond to a contact spacing of one half the governing wavelength. Above 200 Hz, the measured level difference fluctuates about the expected value, again indicating interference effects. Therefore, although the contacts may be assumed independent, in terms of free velocity, above 200 Hz, the resultant power into a wall is influenced by the ratio of spacing to governing wavelength and +/6 dB fluctuations can be expected. 7. Sound pressure level in situ The remaining step in the sound power transmission chain is the structure-borne propagation through the building and radiation into the room of interest. The sound pressure level in a receiving room was calculated for transmission between horizontally adjacent rooms; the source room contained the pipe work connected to the separating wall. The prediction model was that detailed in EN 12354-5 [19]. The piping and connections were as previously described and consisted of three segments. The sound pressure level in the receiving chamber was measured according to ISO 140 part 4 [20] and ISO 10052 [21]. The background noise level was recorded in the receiving room with the water supply pump in operation but without water flow through the piping, and also with the water supply system switched off. The sound pressure level was dominated by background noise at frequencies below 100 Hz, irrespective of pump operation. The background noise is controlled by the water supply system above 160 Hz, but is well below the sound pressure level with the pipe system in operation. The prediction procedure requires the installed structure-borne power into the building structure, in this case, the 175 mm wall. The installed power was obtained from the reception plate power, as in Eq. (12). The reception plate power can be obtained directly, as in Eq. (11), or indirectly from the fluid-borne power and the power ratio, described earlier, where
Prec ¼ cs=f :P f
ð13Þ
The power ratio cs/f was that for Case II, of a pipe system with two pipe segments and a 90° bend. The fluid-borne sound power of the tap under test was obtained previously. Once the installed power was known, the sound pressure level was calculated according to [19]. The measured and predicted sound pressure levels, in the receiving room, are shown in Fig. 20, along with A-weighted values for the frequency range 125 Hz–1 kHz. In general the agreement is within 3 dB but with
significant differences due to resonant effects of the finite pipe system.
8. Proposed test procedure Fig. 21 encapsulates the whole process of structure-borne and fluid-borne transmission from taps and valves into building elements. It therefore includes the findings of the companion paper on structure-borne sound into support walls as a result of reacting forces and moments from taps under flow [1]. For the case of taps as fluid-borne sources, the secondary structure-borne transmission, due to fluid–structure interaction, can be obtained by two means. Either a small scale test rig can be constructed that allows the fluid-borne sound power emission in a short pipe of about 2–3 m length to be obtained. The secondary structure-borne emission could then be calculated from a database of power ratios for different configurations of that pipe type and connecter type. Alternatively, a reception plate method can be employed, circumventing fluid-borne sound intensimetry. A database of transmission coefficients would not be necessary, but rather the reception plate power of different valves under set operating conditions, could be recorded for the specified pipe material, geometry and connectors.
9. Concluding remarks A ratio of structure-borne power to fluid-borne power is proposed that allows the structure-borne sound power from pipe work into a wall or floor to be obtained from knowledge of the fluid-borne sound power of a valve or tap which excites the pipe work into vibration. The structure-borne power can be modified to yield the installed power from the same pipe system, now connected to the wall or floor of interest, to provide input data for prediction of sound propagation through a building. The fluid-borne power is obtained from intensity measurement where a correction is included for reflections due to pipe discontinuities. The structure-borne power can be obtained by a reception plate method, thereby avoiding the need for fluid-borne sound intensity measurements. This has the additional advantage in that the efficacy of alternative pipe material and connectors can be assessed
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in terms of the change in the fluid–structure power ratio. A lower ratio corresponds to a reduction in potential noise. The approach offers the possibility of assembling a data set of power ratios for the most popular pipe systems and connectors as a prerequisite for prediction. The approach also allows assessment of the acoustical improvement of connectors or special pipes, where a low value of power ratio will reflect a reduction in potential noise. References [1] Alber TH, Gibbs BM, Fischer H-M. Characterisation of valves as sound sources: structure-borne sound. Appl Acoust 2009;70:661–73. [2] Fahy FJ. Sound intensity. 2nd ed. Elsevier Applied Science; 1995. [3] Qi N, Gibbs BM. Circulation pumps as structure-borne sound sources: emission to semi-infinite pipe systems. J Sound Vib 2003;264:157–76. [4] prEN 1151-2. Pumps – rotodynamic pumps – circulation pumps having an electrical effect not exceeding 200 W for heating installations and domestic hot water installations – part 2: noise test code (vibro-acoustics) for measuring structure- and fluid-borne noise; 2003. [5] ISO 3822-1. Acoustics – Laboratory tests on noise emission from appliances and equipment used in water supply installations – part 1: method of measurement; 1999. [6] Pavic G. Measurement of sound intensity. J Sound Vib 1977;51:533–45. [7] Thomson JK, Tree DR. Finite difference approximation errors in acoustic intensity measurements. J Sound Vib 1981;75:229–38. [8] Troshin AG, Popkov VI, Popov AV. The measurement of vibration power flux in rod structures. In: 3rd International congress on intensity techniques, Senlis, France; 1990. p. 265–72.
[9] Korteweg DJ. Ueber die Fortpflanzungsgeschwindigkeit des Schalles in elastischen Röhren (On the speed of sound in elastic pipes). Annalen der Physik – Band; 1878. p. 241 [in German]. [10] Anechoic Liquid Termination. Product information, CETIM, France; 1991. [11] Bernard G et al. Industrial procedure for determination of the hydroacoustics power of centrifugal pumps by using anechoic liquid terminator. Proc Internoise 1980;88:663–6. [12] Fuller CR, Fahy FJ. Characteristics of wave propagation and energy distributions in cylindrical elastic shell filled with fluid. J Sound Vib 1982;81(4):501–18. [13] Pavic G. Vibrational energy flow in elastic circular cylindrical shells. J Sound Vib 1990;142(2):293–310. [14] Leissa AW. Vibration of shells. Acoustical Society of America; 1993. [15] Gibbs BM, Qi N. Circulation pumps as structure-borne sound sources: emission to finite pipe systems. J Sound Vib 2005;284:1099–118. [16] Yap SH, Gibbs BM. Structure-borne sound transmission from machines in buildings – part 2: indirect measurement of force and moment at the machine–receiver interface of a single point connected system by a reciprocal method. J Sound Vib 1999;222(1):99–113. [17] Cremer L, Heckl M. Structure-borne sound. 2nd ed. Springer-Verlag; 1996. [18] Craik RJM. Sound transmission through buildings using statistical energy analysis. London: Gower Publishing Limited; 1996. [19] prEN 12354-5. Building acoustics – estimation of acoustic performance of building elements from the performance of elements – part 5: sound levels due to service equipment; 2004. [20] ISO 140-4. Acoustics – measurement of sound insulation in buildings and of building elements – part 4: field measurements of airborne sound insulation between rooms; 1998. [21] ISO 10052. Acoustics – field measurements of airborne and impact sound insulation and of service equipment sound – survey method; 2004.