Rainfall

The tropics extend for 23°28′ either side of the equator, stretching from the Tropic of Cancer in the north to the Tropic of Capricorn in the south, and represent the tilt of the earth’s axis relative to the path around the sun. The sun will pass overhead twice in a year, passing the equator on June 21 on its travel north and September 23 on its travel south. The sun’s rays will pass perpendicular to the earth’s atmosphere and so will have the least amount of filtration, giving high levels of ultraviolet rays.

The area has little seasonal variation; however, the main characteristic of the area is the pronounced periods of rainfall. Typhoons and cyclones are common to certain parts of this area.

It is not surprising that the records for the highest rainfall ever recorded are all within the tropics. Intense rainfall is difficult to measure since its maximum intensity only lasts for a few minutes. Rainfall can be expressed in many ways, either as the precipitation that has fallen within 1 hour (in millimeters per) or over shorter or longer periods but all relating back to that same unit of measurement. Since gas turbines experience problems due to rainfall within a few minutes, it is important to take account of the values of “instantaneous rainfall” that can occur.

The most intense rainfall ever recorded was in Barst, Guadeloupe (latitude 16°N), on November 26, 1970, when 38.1 mm fell in just 1 min.

Another important feature regarding rainfall is the effect of wind speed. “Horizontal rain” is often described, but in practice is unlikely to occur. However, wind speeds can give rain droplets significant horizontal components. The impact of this can be very important, particularly with small droplet sizes. Even droplets 5 mm in diameter will cause a vertical surface to be almost four times wetter in wind speeds of 37 m/s than on the horizontal surface (to which the rainfall rates relate).

The effect of rainfall in tropical environments on the operation of gas turbines has been very much underrated.

The humid environment also ensures that relative humidities are generally high, with the lowest humidities being experienced during the hottest part of the day and the highest occurring at night. During the rainy season, the humidity tends to remain constant throughout the day. The effect of humidity is important where airborne salt is concerned since salt can become dry if the humidity is below 70%.

Dust

Dust levels in tropical environments in Southeast Asia are generally low.

There are, of course, always specific exceptions to this, for example, near new construction sites or by unpaved roads. But, in general, dust is not a significant problem. Mother nature ensures this by casting her seeds on the fertile soil and quickly turning any unused open space into a mass of overgrown vegetation very quickly, thereby suppressing the dust in the most natural way.

Insects and Moths

In the tropics, the hot, humid environment is a natural encouragement to growth of all kinds. It is often said that if a walking stick is stuck into the rich fertile soil of the area and left for 3 months, it will sprout leaves and grow. Certainly the insect population reflects this both in size and quantity. Large moths are common to the area and tend to occur in quantity during specific breeding periods. These can quickly cover intake grills, obstructing airflow and even causing large gas turbines to trip. Some of the largest moths are found in the tropics. A common moth in India and Southeast Asia is the Swift moth (Hepralidae), which can have a wing span of some 15 cm and is said to lay up to 1200 eggs in one night. Another moth is the Homoprera shown in Figure 6–1, which has a similar wing span. Moths are attracted by the lights that often surround the turbine installations, as well as the airflow, which acts as a great vacuum cleaner.

On one installation in Sumatra, large gas turbines have been known to trip out after only 8 hours of operation due to blockage of the air filters with moths.

Fortunately, moths tend to confine themselves to within a few miles of land and so offshore installations do not tend to suffer these problems.

Design Problems Experienced

Many feel that standardization is the key to reducing costs and boosting profits. It is not surprising, therefore, that gas turbine air-filter systems were designed with this in mind.

Dust was important to system designers, and so filter systems may be chosen to be able to deal with prodigious amounts of it, whereas, in practice, dust is only normally a problem next to unpaved roads or construction sites.

Despite this, most gas turbines were fitted with elaborate and expensive solutions to overcome a problem that hardly existed, or at least only in a relatively small percentage of installations. Many of these systems employ bleed fans that need additional electrical energy and a constant maintenance requirement. A typical system is shown in Figure 6–2. This system employs spin tubes that swirl dust to the outside of the tube where a bleed slot extracts the dust while allowing the cleaner air to pass through the main core of the tube. Since the air is rotated, the peripheral speeds need to be high, which, in turn, results in a relatively high pressure-loss coefficient. The efficiency of the system is very reliant on the bleed air, which is provided by auxiliary fans.

Another bleed extract system uses a series of convergent vanes that funnel the air toward a central slot through which bleed air is extracted. The heavier dust particles are guided toward the bleed extract, while the main air passes between the vanes at almost 180° to the general direction of airflow. Again, the efficiency of the system is reliant on the provision of bleed air.

Protection against rain was elementary. On many systems that had dust-extract systems, no further provision was made. On others a coarse weather louver, often of plastic, was provided. Sometimes a partial weatherhood was provided, sometimes not.

The emphasis on the designer was to provide a “three-stage” filter system, without worrying too much about the suitability of those stages.

There was recognition of the high humidities that exist, and so most systems incorporated a coalescer, whose function was to coalesce small aerosol droplets into larger ones, which could then be drained away. These coalescer panels varied between pieces of knitted mesh wound between bars within the filter housing to separate panels with their own framing. Loose glass fiber pads were used as an inexpensive solution and also served as a prefilter pad.

The final stage in almost all of these systems was the high-efficiency filter element, either as a cartridge or as a bag. The high-efficiency cartridge was typically a deep-pleated glass-fiber paper sealed in its own frame and with a seal on its rear face. Other high-efficiency filters employed glass-fiber pockets that fitted into permanent wire baskets within the filter house.

Almost all of the filter systems were enclosed in housings constructed in carbon steel, finished with a variety of paint finishes. Other materials, such as stainless steel, were not common since their initial cost was thought to be excessive.

Protection against complete filter blockage was often provided by means of a bypass door. This normally was a counterbalanced door in which a weight held the door closed. When the pressure drop across the filter was high, this overcame the force exerted by the balance weight and the door opened, thereby bypassing the filter system with unfiltered air.

Offshore Application Design Problems Encountered

In general, problems were slow to appear, typically taking three to five years after start-up, but since a lot of equipment had been installed at about the same time, the problems manifested themselves like an epidemic.

These problems could be categorized as follows:

By far the most serious of these problems was the erosion of compressor blading that was experienced almost simultaneously on many platforms. This occurred about three to five years after start-up, as this was the time that repainting programs were initiated. Grit blast found its way into the turbine intakes either through leaking intakes, bypass doors, or through the media itself (see Figure 6–6). Since the airborne levels were high, the air filters quickly blocked up, allowing the bypass doors to open. As filter maintenance is not a high priority on production platforms, considerable periods were spent with grit passing straight into the turbine through open bypass doors. Even where maintenance standards were more attentive, there were usually enough leaks in the intake housing and ducting to ensure delivery of the grit to the turbine.

It often seemed contradictory that the system designers would spend a lot of time specifying the filter system, but would pay little attention to ensuring the airtightness of the ducting downstream.

Since the grit was sharp, it sometimes damaged the filter media itself, reducing the system efficiency dramatically.

Bypass doors were a major problem. Early designs failed to take account of the environment or the movement in the large structures of the filter housings. Very few of those initial designs were airtight when shut, and it was not uncommon for them to be blown open by the wind.

Turbine corrosion could almost always be traced to leaky ducting or operation with open bypass doors. Very few systems gave turbine corrosion problems if the ducting was airtight. The few installations that did give problems were usually the result of low-velocity systems operating with poor aerodynamics, so that local high velocities reentrained salt water droplets into the airstream and onward to the engine.

Rapid compressor fouling was usually the prelude to more serious problems later, since it was usually caused by the combined problems of filter bypass.

Compressor cleaning almost once a week was fairly standard for systems with those problems.

As time progressed the marine environment took its toll on the carbon steel and severe corrosion was experienced on the intake housing and ducting. In some cases, corrosion debris was ingested into the turbine causing turbine failure. This again was accelerated by poor design, which allowed dissimilar metals to be put into contact, leading to galvanic corrosion.

How Good does your Filter Need to be for the above Applications

The end-user is the best judge of this. Clearly, in the clean air of northern Canada, the gas turbine engine might not be expected to ingest oil fumes (as in offshore applications) or insects (as in the tropics), but icing (ice ingestion) may be a factor. In the heavily industrialized areas of Europe however, dirty particulates are prevalent. The GT system may allow for online washing but some of these particulates bake onto the airfoil surfaces and destroy aerodynamic performance. Additional filtration capacity may be in order, but at what point does the additional capital cost justify itself? What is the GT power that has to be sacrificed for more efficienct filtration and can the end-user tolerate it? These are, once again, end-user questions.

The case study that follows does present some perspective on the testing and financial analysis on three = phase filtration systems. Again, the end-user ought to pay attention to the model numbers of GT involved in this case study and their respective power ratings. Sometimes accessories that work well with one power size bracket of gas turbine may not “scale up” well with larger power brackets due to system geometries, other accessory systems on the gas turbine and various other factors. The study does present the key parameters to be potentially studied were a similar study to be undertaken elsewhere.

Sound Intensity Meters

A sound intensity meter comprises a probe and an analyzer. The analyzer may be of the analog, digital, or FFT (fast Fourier transform) type. The analog type has many practical disadvantages that make it suitable only for surveys and not precision work.

Digital analyzers normally display the results in octave or ⅓ octave frequency bands. They are well suited to detailed investigations of noise sources in the laboratory or on site. Early models tended to be large and heavy and require electrical main supplies, but the latest models are much more suited to site investigations.

FFT analyzers generate spectral lines on a screen. This can make the display very difficult to interpret during survey sweeps because of the amount of detail presented. Another disadvantage of FFT-based systems is that their resolution is generally inadequate for the synthesis of ⅓ octave band spectra.

Sound Intensity Probes

There are several probe designs that employ either a number of pressure microphones in various configurations or a combination of a pressure microphone and a particle velocity detector. The first type of probe uses nominally identical pressure transducers that are placed close together. Various arrangements have been used with the microphones either side by side, face to face, or back to back. Each configuration has its own advantages and disadvantages.

If the output signals of two microphones are given by P_a and P_b, then the average pressure, P, between the two microphones is

$P=\frac{1}{2}(P_a+P_b)$ (6.2)

(6.2)

The particle velocity, u, is derived from the pressure gradient between the two microphones by the relationship

$\begin{array}{l}u=-\int \frac{1}{\text{ρ}}·\frac{\partial p}{\partial r}·dt\\ u=-\frac{1}{\text{ρ}}\int \frac{(P_{\text{b}}-P_{\text{a}})}{\mathrm{\Delta }r}·dt\end{array}$ (6.3)

(6.3)

Since sound intensity, I, is the product of the pressure and particle velocity, combining equations (6.2) and (6.3) gives the intensity as

$I=\left(\frac{P_a+P_b}{2\rho \mathrm{\Delta }r}\right)\int (P_a-P_b)·dt$ (6.4)

(6.4)

Figure 6–30 shows a two-microphone probe, with a face-to-face arrangement, aligned parallel to a sound field. In this orientation the pressure difference is maximized, and so is the intensity. If the probe is aligned so that the axis of the two microphones is normal to the direction of propagation of the sound wave, then the outputs of the two microphones would be identical in magnitude and phase. Since the particle velocity is related to the difference between the two pressures, P_a and P_b, then the intensity would be zero.

The second type of probe combines a microphone, to measure the pressure, and an ultrasonic particle velocity transducer. Two parallel ultrasonic beams are sent in opposite directions as shown in Figure 6–31. The oscillatory motion of the air caused by audio-frequency sound waves produces a phase difference between the two ultrasonic waves at their respective detectors. This phase difference is related to the particle velocity component in the direction of the beams. This measure of particle velocity is multiplied directly by the pressure to give the sound intensity.

Guidelines and Standards

Work began in 1983 on the development of an international standard on the use of sound intensity and the final document is about to be issued. Further standards are expected dealing specifically with instrumentation.

In the absence of a full standard the only guidance available was the draft ISO standard (ISO/DP 9614) and a proposed Scandinavian standard (DS F88/146).

The ISO document ISO/DP 9614 gives specific methods for determining the sound power levels of noise sources within specific ranges of uncertainty.

The proposed test conditions are less restrictive than those required by the International Standards series ISO 3740–3747, which are based on sound pressure measurements. The proposed standard is based on the sampling of the intensity normal to a measurement surface at discrete points on this surface. The method can be applied to most noise sources that emit noise that is stationary in time and it does not require special purpose test environments.

The draft document defines three grades of accuracy with specified levels of uncertainty for each grade. Since the level of uncertainty in the measurements is related to the source noise field, the background noise field, and the sampling and measurement procedures, initial procedures are proposed that determine the accuracy of the measurements. These procedures evaluate the “field indicators” that indicate the quality of the sound power measurements. These field indicators consider, among other things:

The three grades of measurement accuracy specified in ISO/DP 9614, and the associated levels of uncertainty, are given in Table 6–7.

The Scandinavian proposed standard DSF 88/146 was developed for the determination of the sound power of a sound source under its normal operating conditions and in situ. The method uses the scanning technique whereby the intensity probe is moved slowly over a defined surface while the signal analyzer time-averages the measured quantity during the scanning period.

The results of a series of field trials by several Scandinavian organizations suggested that the accuracy of this proposed standard is compatible with the “Engineering Grade,” as defined in the ISO 3740 series.

The equipment under test is divided into a convenient number of subareas that are selected to enable a well-controlled probe sweep over the subarea. Guidance is given on the sweep rate and the line density. Measurement accuracy is graded according to the global pressure-intensity index, LK. This is the numerical difference between the sound intensity level and the sound pressure level. If this field indicator is less than or equal to 10 dB then the results are considered to meet the engineering grade of measurement accuracy. As this field indicator increases in value, the level of uncertainty in the intensity measurement increases. When the LK value lies between 10 and 15 dB the measurement accuracy meets the “Survey” grade.

Measurement Techniques

The precise measurement technique adopted in a particular situation depends on the objectives of the investigation and the level of measurement uncertainty that is required.

Background Noise

One of the main advantages of the sound intensity method of measurement is that accurate assessments of sound power can be made even in relatively high levels of background noise. But this is only true if the background noise is steady (i.e., not time varying). Using conventional sound pressure level methods the background noise level should be 10 dB below the signal level of interest.

Using sound intensity techniques the sound power of a source can be measured to an accuracy of 1 dB even when the background noise is 10 dB higher than the source noise of interest. Figure 6–32(a) shows a noisy machine enclosed by a measurement surface. If the background noise is steady, and there is no sound absorption within the measurement surface, then the total sound power emitted by the machine will pass through the measurement surface, as shown.

If, however, the noisy machine is outside the measurement surface, as shown in Figure 6–32(b), then the sound energy flowing into the surface on the left hand side will be emitted from the right hand side of the measurement surface. When the sound intensity is assessed over the whole measurement surface the net sound power radiated from the total surface will be zero.

Effects of the Environment

When the sound power of a noise source is evaluated in the field using sound pressure level techniques, it is necessary to apply a correction to the measured levels to account for the effects of the environment. This environmental correction accounts for the influence of undesired sound reflections from room boundaries and nearby objects.

Since a sound intensity survey sums the energy over a closed measurement surface centered on the source of interest, the effects of the environment are cancelled out in the summation process in the same way that background noise is eliminated. This means that, within reasonable limits, sound power measurements can be made in the normal operating environment even when the machine under investigation is surrounded by similar machines that are also operating.

Sound Source Location

Since a sound intensity probe has strong directional characteristics there is a plane at 90° to the axis of the probe in which the probe is very insensitive. A sound source just forward of this plane will indicate positive intensity, whereas if it is just behind this plane the intensity will be negative (Figure 6–33).

This property of the probe can be used to identify noise sources in many practical situations. The normal procedure is to perform an initial survey of the noise source to determine its total sound power. The probe is pointed toward the source system to identify areas of high sound intensity. Then the probe is reoriented to lie parallel to the measurement surface and the scan is repeated. As the probe moves across a dominant source the intensity vector will flip to the opposite direction.

Testing of Panels

The traditional procedure for measuring the transmission loss, or sound reduction index, of building components is described in the series of standards ISO 140. The test method requires the panel under investigation to be placed in an opening between two independent, structurally isolated reverberation rooms, as shown in Figure 6–34.

Sound is generated in the left hand room and the sound pressure levels in the two rooms are measured. Assuming that the sound energy in the right hand room comes through the panel then the sound reduction index (SRI) of the panel is given by

$\text{SRI}=L_1-L_2+10\ast {\log }_{10}\left(S/A\right)\text{dB}$ (6.5)

(6.5)

For this method to give accurate results, flanking transmission (sound bypassing the test panel) must be minimal and both rooms must be highly reverberant.

If the measurements in the right hand room are carried out using sound intensity, then it is necessary to reduce the amount of reverberation in this room. Since the probe can measure the sound intensity coming through the panel then flanking transmission is no longer a limitation.

For these reasons one can dispense with the second reverberation room altogether. The sound reduction index is then given by

$\text{SRI}=L_1-LI-6\text{dB}$ (6.6)

(6.6)

If the panel contains a weak area, such as a window, the sound reduction index of the window can be assessed separately. But this will only work if the panel is a greater sound insulator than the window.

Gas Turbine Package Witness Testing

Gas turbine packages are normally assembled in large factory buildings or in the open air between factory buildings. In either case, the environment is totally unsuitable for reliable acoustic tests to be carried out using sound level meters alone. Sound intensity techniques are especially relevant in these situations because of the location in which the tests are to be carried out and because some components, such as the compressor test loop, may not be contract items. By surveying each component with a sound intensity meter the sound power for each component can be determined separately.

Figure 6–35 shows a typical gas turbine driving a compressor. The figures on the drawing indicate the sound pressure and sound intensity levels that were measured during a particular witness test on an RB211 gas turbine package. The sound pressure levels in close proximity to the package were between 89 and 103 dB(A), with the higher levels dominating. Even so, reliable values of the intensity levels were obtained from which the sound power levels were determined. These values are given in Table 6–8. Since the sound intensity level is numerically equal to the sound pressure level in free field, the average sound intensity over a given surface area of a gas turbine package provides a direct indication of the average sound pressure level from that surface in free field conditions.

Referring again to Figure 6–35, the sound intensity level measured by the casing of the ventilation fan was 94 dB(A). It would not normally be possible to measure the output from this fan accurately, using a sound level meter, in this situation because of the relatively high sound pressure level in this area due to other sources.

During the testing of another package, the sound power levels from the ventilation fan casing and the fan motor were measured separately. The fan motor was found to be noisier than the manufacturer’s stated levels. Discussions with the motor manufacturer revealed that the wrong cooling fans had been fitted to the motors, which accounted for this increase in noise level. The correct cooling fans were subsequently fitted.

This example clearly illustrates the benefits of sound intensity measurements to check compliance with noise specifications when the test items are very large and are cited in acoustically undesirable areas.

Acoustical Properties of Flexible Connectors

Heavy-duty flexible connectors are used to join separate components of a gas turbine package. When high-performance acoustic hardware is used it is imperative that these flexible connectors do not compromise the total acoustic performance of the package. This is particularly so in the gas turbine exhaust system where multilayered flexible connectors are exposed to high temperatures and severe buffeting from exhaust gases. In some exhaust systems overlapping metal plates are inserted inside the flexible connectors to reduce the buffeting of the flexible material. If additional sound attenuation is required, a heavy, fibrous mat, or “bolster,” is inserted between the plates and the flexible connector.

For the acoustics engineer, these flexible connectors are a problem because there are very few data on their acoustical performance, and the designs do not lend themselves to simple theoretical prediction. A brief laboratory investigation was carried out to compare the performances of seven types of flexible connectors with and without plates and bolsters. The tests were carried out in Altair’s acoustical laboratory, which was designed to test materials using sound intensity techniques. The samples were physically quite small so the low-frequency performances were probably distorted by the small size of the samples. Nevertheless, the exercise yielded much valuable information and led to a simple engineering method of predicting a flexible connector’s acoustic performance from knowledge of its basic parameters.

Figure 6–36 compares the sound reduction indices of a typical, multilayered flexible connector tested alone, with plates and with bolster and plates. All of the test results showed a sharp increase in performance at 250 Hz due to the plates. No satisfactory explanation can be offered at this stage for this effect, which may be related to the small size of the samples. But in the middle and high frequencies the results were generally as expected with the plate giving an additional attenuation of about 5 dB compared to the compensator alone. The combination of the plate and bolster gave an additional attenuation of between 10 and 15 dB compared to the flexible connector alone.

Sound Source Location

During two noise surveys the sound power levels from two different designs of lube oil console were measured using the sound intensity meter. The overall sound power levels were 93 dB(A) and 109 dB(A). The two consoles had electrically driven pumps and both emitted strong tonal noise. In the first case the tonal noise was centered on 8 kHz; using the sound intensity probe it was possible to “home in” on the pump section pipe as a major noise source. This was confirmed by vibration measurements.

In the second survey the pump outlet pipe gave the highest sound intensity reading. Since this was a relatively long pipe, which was rigidly attached to the frame of the console, it was a dominant source both in its own right and because it was “exciting” the framework. In these cases the sound intensity meter was a useful tool in identifying dominant sources among a number of small, closely packed noise radiators.

This section has discussed the concepts of sound intensity, sound power, and sound pressure. It has shown how sound intensity meters have given the acoustic engineer a very powerful diagnostic tool. Noise specifications for large, complex machinery can now be checked without the need for special acoustics rooms.

The advantages, and limitations, of sound intensity have been discussed in some detail and several applications have been illustrated by case histories taken from surveys carried out in the process and gas turbine industries.

The superiority of sound intensity meters over sound level meters is clearly apparent. Certain types of laboratory studies can also be carried out more cost effectively using intensity techniques.

Although there are some limitations in the use of sound intensity instrumentation, when used intelligently, it can yield valuable information on dominant noise sources, which, in turn, should provide more cost-effective solutions to noise control in the oil and power industries.

The superiority of sound intensity meters over sound level meters is clearly apparent. Certain types of laboratory studies can also be carried out more cost effectively using intensity techniques.

Although there are some limitations in the use of sound intensity instrumentation, when used intelligently, it can yield valuable information on dominant noise sources, which, in turn, should provide more cost-effective solutions to noise control in the oil and power industries.

Sound Transmission through Unlined Flat Panels

When a sound wave is incident on a wall or partition, some of the sound energy is transmitted through the wall. The fraction of incident energy that is transmitted is called the transmission coefficient. The accepted index of sound transmission is the sound reduction index, which is sometimes called the transmission loss. This is related to the transmission coefficient by the equation

$R=10{\text{log}}_{10}(1/\tau ),\text{dB}$ (6.7)

(6.7)

The behavior of flat panels has been described extensively in the literature, so only the outline of their theoretical performance is given here. The general behavior of a single skin, isotropic panel is shown in Figure 6–37. This characteristic behavior is valid for a wide range of materials, including steel and aluminum.

The propagation of audio-frequency waves through panels and walls is primarily due to the excitation of bending waves, which are a combination of shear and compressional waves. When a panel is of finite extent then a number of resonances are set up in the panel that are dependent on the bending stiffness of the panel. The frequency of the first panel resonance, f1, is given by

$f1=(\pi /2)\sqrt{(B/m)(L/a^2+1/b^2),}\text{Hz}$ (6.8)

(6.8)

The second resonance occurs at the “coincidence” frequency, fc, when the projected wavelength of the incident sound coincides with the wavelength of the bending wave in the panel. The coincidence frequency is given by

$f=(c^2/2\pi )\sqrt{(m/B),}\text{Hz}$ (6.9)

(6.9)

The amount of sound transmitted by a panel is dependent on the surface weight, the damping of the panel, and the frequency of the sound. For a finite panel exposed to a random noise field, the acoustic behavior is specified mathematically as follows:

$R=20{\log }_{10}\text{S}-20{\log }_{10}f-20{\log }_{10}(4\text{πρ},c),dB,f<f1$ (6.10)

(6.10)

$R=20{\log }_{10}\left(mf\right)-47,\text{dB},f1<f<f_c$ (6.10a)

(6.10a)

$R=20{\log }_{10}(\pi fm/{\text{ρ}}_0\text{c})+10{\log }_{10}(2\text{η}f/\text{π}{f}_c),\text{dB},f>f_c$ (6.10b)

(6.10b)

In most practical situations the lowest resonance frequency is below the audio range. Above this frequency a broad frequency range occurs in which the transmission loss is controlled by the surface weight and increases with frequency at the rate of 6 dB per octave. In the coincidence region the transmission loss is limited by the damping of the panel. Above the coincidence frequency the transmission loss increases by 9 dB per octave and is determined by the surface weight and the damping.

Clearly for a high value of sound reduction index over the majority of the audio-frequency range (the mass-controlled region) it is better to have a high surface weight, a low bending stiffness, and a high internal damping.

The acoustic performances of some materials have been predicted and are compared to measured values in Table 6–10. The data for 3-mm steel and 6-mm aluminum are shown in Figures 6–38 and 6–39. Each of the examples shown has the characteristic shape described above and the agreement between the measured and predicted values of transmission loss is good.

Sound Transmission through Unlined Corrugated Panels

In corrugated panels the characteristics of the panel are not the same in all directions. The moment of inertia across the corrugations differs from that parallel to the corrugations; thus the bending stiffness varies with direction. This affects both the first panel resonance and the coincidence frequency so that the sound transmission characteristics for these panels differ from flat panels with the same thickness. The first panel resonance is now given by

$f1=(\pi /2m^{0.5})\times \sqrt{(Bx/a^1(1-{\upsilon }^2)+By/b^4(1-{\upsilon }^2)+Bxy/a^2{b}^2),}\text{Hz}$ (6.11)

(6.11)

where Bx and By are the bending stiffnesses in the two principal planes of the panel and Bxy accounts for the torsional rigidity of the plate.

For real panels, measuring several meters in length and height, the frequency of this first resonance may still be in the subaudio range but can be several octaves higher than the first resonance of a flat panel of the same dimensions.

Since the coincidence frequency is determined by the bending stiffness, the presence of two bending stiffnesses gives rise to two critical frequencies, f_cx and f_cy, where

$f_{cx}=(c^2/2\text{π})\sqrt{(m/Bx),}{f}_{cy}=(c^2/2\pi )\sqrt{(m/By)}$

If the ratio of the bending stiffnesses, Bx and By, is less than 1.4, then the effects on the transmission loss of the panel will be small, but in typical panels the ratio of the bending stiffnesses is usually much greater than 1.4. This gives rise to a plateau in the transmission loss curve, which is illustrated in Figure 6–40. The plateau may extend over several decades for common corrugated or ribbed panels.

The sound transmission through orthotropic (corrugated) panels has been investigated by Heckl, who derived the following relationships for the diffuse field sound transmission:

$\tau =({\text{ρ}}_{0}c{f}_{cx}/\text{πω}mf){\left[\text{In}(4f/f_{cx})\right]}^2,f_{cx}<f<f_{cy}$ (6.12)

(6.12)

$\tau =({\text{πρ}}_{0}c/\text{ω}mf){(f_{cx}{f}_{cy})}^{0.5},f>f_{cy}$ (6.13)

(6.13)

where f_cx and f_cy are the two coincidence frequencies and where f_cx is the lower of the two values.

The performances of two designs of corrugated panels have been predicted for panels made of 2.5-mm-thick steel with the designs shown in Figure 6–41. The predicted transmission losses are given in Table 6–11 and Figure 6–42.

The predicted panel bending stiffnesses and resonant frequencies for the two panels are tabulated in Table 6–12 for a simply supported panel 4 m wide by 2.5 m high. The values for a flat panel of the same overall dimensions have also been included. The bending stiffness of panel B, in the direction parallel to the corrugations, is slightly less than that for panel A. This causes a shift in the lower critical frequency of about half an octave, which gives rise to a slightly higher transmission loss at lower frequencies.

Transmission loss measurements have been carried out on a partition with the design of panel A. The test was carried out in accordance with the standard ISO 140 (1978). Table 6–13 and Figure 6–43 compare the predicted and measured performances. Both sets of curves show a plateau effect, which is more evident in the measured values. The predicted and measured values are within 4 dB of each other up to 4 kHz, above which the curves differ by about 7 dB. Although the agreement is not as close as for flat panels, it is encouraging. Of more interest is the comparison between the transmission losses of unlined, flat, and corrugated panels with the same thickness. Figure 6–44 and Table 6–14 show that the corrugated panel is substantially less effective in reducing sound transmission in the mid-frequencies compared to the flat panel equivalent.

Clearly, if noise control is a primary consideration then unlined corrugated panels are not recommended, unless other engineering considerations dictate their use. Corrugated panels offer a considerable increase in bending stiffness, compared to flat panels, which reduces the amount of additional stiffening that would be required for a flat panel. But the volume of material required to produce a corrugated panel is significantly greater than that for a flat panel. For the two corrugated panel designs considered above, panel A contains 23% more material than the flat panel, and panel B contains 13% more material. Depending on the structural requirements, the additional stiffening required for a flat panel may result in a material savings when a corrugated design is chosen, especially if the flat panel is much thicker to compensate for its inherent low bending stiffness.

Attenuation of Sound by Absorptive Linings

Sound-absorbent linings are frequently fitted in acoustic enclosures to reduce the buildup of reverberant noise inside the enclosure. Typical reductions in the reverberant noise level may be between 3 and 10 dB depending on the application. An additional benefit is the increase in transmission loss of the enclosure panel, which further reduces the noise level outside the enclosure.

The increase in panel transmission loss arises because of several mechanisms. First, if the absorbent lining is sufficiently heavy and the panel is relatively thin, then the added layer may give sufficient additional weight to affect the “mass-law” performance and increase the damping of the panel. At high frequencies the absorbent may be relatively thick in comparison to the wavelength of the sound. The high-frequency sound may be attenuated not only because of the impedance mismatch between the air and the absorbent, but as the sound wave passes through the added layer a significant amount of acoustic energy is converted into heat by viscous losses in the interstices. In practice, the amount of heat generated is minute.

It is possible to distinguish between three frequency regions in which different attenuating mechanisms are predominant. For convenience these are described as regions A, C, and B, where A is the low-frequency region, C is the high-frequency region, and B is the transition region. The boundaries between these three regions are defined by the physical characteristics of the absorptive material in terms of the flow resistivity and the material thickness.

The flow resistivity of fibrous absorptive materials is dependent upon the bulk density and fiber diameter by the approximate relationship.

The frequency limits of the three regions, A, B, and C, are defined by

$R1=(3.18\times {10}^2)({\text{ρ}}_{\text{α}}^{15}/d^2)$

Region A: 101 < λ_m

Region B: 101 > λ_m, αl < 9 dB

Region C: αl > 9 dB

The values of λ_m, the wavelength of the sound inside the absorptive layer, and α, the attenuation constant for the material, can be measured or predicted for semirigid materials:

$\text{α}=(\text{ω}/c)\left[0.189{({\text{ρ}}_{\text{α}}f/RI)}^{0.280}\right]$ (6.14)

(6.14)

${\lambda }_m=(c/f){[1+0.0978{({\text{ρ}}_{\text{α}}f/R1)}^{-0.7}]}^{-1}$ (6.15)

(6.15)

For an absorptive layer of known thickness and flow resistivity, the attenuation predicted from the equations given above is additive to that produced by the unlined panel.

The predicted and measured acoustic performances of two flat panels and one corrugated panel, each with an absorptive lining, are shown in Table 6–15 and Figures 6–45 to 6–47.

The predicted performances of the two flat panels are in good agreement with the measured performances over the majority of the frequency range. The largest discrepancies occur at 63 Hz and 8 kHz.

The agreement between the theoretical and measured performances of the corrugated panel is not as good as for the flat panel. The largest discrepancies occur at the lower frequencies with better agreement occurring at high frequencies. This follows the low-frequency trend shown in Figure 6–44 where the corrugated panel was unlined and the predicted performance was less than the measured performance by 5 dB. Nevertheless, the agreement is sufficiently close to support the theoretical model.

Experience Thus Far

It has been shown that the acoustic performance of lined and unlined panels can be predicted with reasonable accuracy for flat and corrugated panels. It has also been shown that, where noise control is important, unlined corrugated panels are not recommended unless other engineering considerations dictate their use, because corrugated panels are intrinsically less effective as sound insulators than flat panels of the same thickness.

A lining of sound absorptive material can substantially increase the sound reduction index of panels and the additional attenuation depends on the density, fiber diameter, and thickness of the lining. By careful selection of these parameters, the acoustic disadvantages of corrugated panels can be considerably reduced so that corrugated panels can be used confidently in situations where noise control is a primary requirement. The additional bending stiffness of corrugated panels permits a thinner outer skin to be employed and reduces the amount of additional bracing required to provide the structural integrity necessary in the demanding environment offshore. This reduction in overall weight compensates for the additional material used in forming the corrugations.

By careful design of the panel, a corrugation profile can be selected, which provides the most cost-effective solution when structural integrity, weight cost, ease of manufacture, and acoustic performance are considered. When expensive materials, such as stainless steel and aluminum, are employed, the reduction in cost by using a thinner-walled corrugated panel can be considerable.

A further consideration is the fire rating of lined corrugated panels. The normal requirement for bulkheads and decks offshore is the “A-60” class division. Corrugated panel designs of the type described here have been submitted to, and approved by, the appropriate authorities.

In some situations where a particularly high acoustic performance is called for, the corrugated design lends itself well to a multilayer construction employing an additional inner layer of heavy impervious material. Cheaper materials are used for the additional septum rather than for the outer skin. The acoustic attenuation of these multilayer designs is comparable to the performance of flat panels employing outer skins of twice the thickness of the corrugated outer skin. Figure 6–48 compares the measured performances of a traditional 5-mm-thick flat panel design with a 100-mm-thick absorptive lining and a multilayered panel based on a 2.5-mm-thick corrugated panel lined with a 50-mm absorptive layer.

The nominal surface weights of the two designs are 50 kg/m² and 40 kg/m² for the flat and corrugated panels, respectively. Except at 63 and 125 Hz, the performance of the two panels is very similar.