Flow Induced Noise

To design robust process industry systems that are insensitive to flow induced pulsation, one must first understand the aeroacoustic mechanisms involved, which can be come rather heavy on theory.

Perhaps a simpler way is to understand how wind instruments generate sound and then simply avoid replicating these mechanisms in process equipment?

Most people know that blowing across the edge of a bottle produces a tone and many people may have noticed that the masts and wires of a sailboat sing. The phenomena that make up the above observations are referred to as flow acoustics, aeroacoustics or flow induced noise.

Aeroacoustic noise is a difficult topic and its theory is still under development. We will provide here a brief introduction to the most basic concepts in aerocoustics – the Lighthill analogy and scaling laws.

To analyse both flow and sound, one should solve the Navier Stokes Equation (Link). The Navier Stokes Equation can unfortunately only be solved in some specific situations. Even with current numerical simulation tools, solving the Navier Stokes Equation for sound and flow is difficult (2014).

Note that by now we assume that the reader is able to distinguish between Pulsation (sound) and Kinetic Pressure (KP). If not, look at the Technical Shortlist (Link) and some of the other Problem Types/Examples for more information. (Link)

Figure 1 shows a thought experiment where the Lighthill analogy is demonstrated for the case of fluctuating wind load onto a rigid pillar. The average wind speed is referred to as U and the fluctuating wind speed is denoted as u. Average flow U produces a static KP load on the pillar, but no sound – the flow is silent.

When a time-fluctuating part, u, is added to the average flow velocity, U, we can see that there will be a time-varying pressure fluctuation on the rigid pillar. The Lighthill analogy replaces the time-fluctuating part, u, of the flow with a set of sound sources, e.g. loudspeakers, that are placed on the surface of the pillar. The amplitude and phase of these sources is adjusted to produce a pressure patter that emits the same emitted sound power as the time-fluctuating part, u, of the flow. This is the mechanism that causes a mast and wire to emit the above-mentioned aeolian tones (wind generated tones).

The neat trick of the Lighthill analogy is that this switch is impossible when examined close to the pillar. A loudspeaker combination that can produce the exact pressure pattern on the pillar as well as in the volume situated close to the pillar when exposed also to an average flow U simply does not exist. However, a set of loudspeakers does exist that can produce the same emitted sound power when that sound is evaluated far away from the pillar and where the average flow U is negligible. The latter is referred to as the quiescent zone.

Figure 1. The Lighthill analogy. The oscillating pressure can be emulated by a set of acoustic sources placed on the pillar. This source mechanism switch only holds formally true when sound is evaluated far away from the pillar in a place without wind. (Click figure to expand)

Using the above analogy, Lighthill was able to show that the Navier Stokes equation can be recast into an equivalent set of acoustic source terms (shown in Figure 2). He was also able to derive scaling laws for these equivalent acoustic source types. (Link)

The core component of these equivalent source components is the monopole, which is a volume breathing sphere, i.e. a sphere with a radius that uniformly expands and contracts. It can be intuitively understood that the monopole produces sound – just like a boxed loudspeaker produces sound when the cone oscillates back forth and changes the box volume. The monopole source strength is expressed as m³/s in Figure 2

The combination of two monopoles, where one monopole contracts while the other expands, produces a so-called dipole, as seen in Figure 2. Similarly, the combination of two dipoles (or four monooples) produces a quadrupole, which can be also seen in Figure 2.

Figure 2. Equivalent source and their scaling laws. (Click figure to expand)

The monopole, dipole and quadrupole are well understood in linear acoustics. It has been established that monopoles dominate sound at a low frequency, while dipoles typically dominate the mid-frequency range and quadrupoles dominate at a high frequency.

Figure 2 shows also how the poles’ source strength scales with the average flow velocity, U_m.

It can be shown that the Lighthill analogy does not apply for flow in pipes. The quiescent flow situation in pipes, the situation analogous to having only the average U flow in Figure 1, is known as Bernoulli flow, i.e. flow without viscosity or friction. The sound-generating part of the flow is the difference between the viscous- and the Bernoulli- flows. However, this is much too complicated for most situations, and we revert to the Lighthill analogy instead.

Some practical examples of the previously mentioned source types that have both principal and industrial relevance include:

• Monopole type sound. This is produced when we modulate flow, i.e. when we modify the average flow through a pipe. This actually is how the common flute works. You insert air using your mouth at one end and let it flow against a sharp edge. The edge is aligned such that it can split flow just as easily for passage through the pipe as out through the hole in front of the edge. This flow switching modulates the volumetric flow inside the pipe, which starts to drive the acoustic mode that produces the flute sound. Once generated, the acoustic modes will modulate pressure in front of the edge and start synchronising the flow, as seen in Figure 3. Examples of similar mechanisms can be found in process type systems and include systems with parallel flow paths and butterfly valves that flap and modulate flow. The scaling law tells us that reducing flow velocity modulation by a factor of 2 reduces sound power by 2^4, i.e. 16 times.
• Dipole type sound is produced by blowing across a sharp edge. A key difference between this edge and the flute edge is that flow (mass) is not diverted elsewhere for the dipole source type. This phenomenon is easy to illustrate. First, blow air out of your mouth. This flow is silent. Next, hold up a sharp edge (use a knife, a business card or similar) in front of your mouth and let the flow cross this edge. You are now producing wide frequency random noise, as seen in Figure 4. Examples in process type systems include flow across edges at Tee sections, manifolds and gate valves that are partly closed. The scaling law tells us that reducing flow velocity across a dipole type source by a factor of 2 reduces sound power by 2^6, i.e. 64 times.
• Quadrupole type sound. This is produced when there is flow into still, standing gas, e.g. air from a pneumatic mouthpiece into still (or at least much lower velocity) air. Gas does not take up much shear, and the airstream that is injected will therefore shear the still air and produce turbulence as a result. Turbulence produces sound of the quadrupole type and the process can be quite noisy, as is shown in Figure 5. It is predominantly high frequency. Examples in process type systems include wall turbulence and inlets into knockout bottles and separators. Early jet engines in the 1950s used a small diameter tube and high flow velocity. Newer jet engines in the 1970s had tubes with a larger diameter to lower the flow velocity while maintaining thrust. Modern jet engines in the 1990s and today use a front fan section to blow air into and around the jet engine section to reduce relative velocities between still, intermediate and outer airstreams. The scaling law tells us that reducing flow velocity across a quadrupole type source by a factor of 2 reduces sound power by 2^8, i.e. 256 times.

 

Figure 3. Monopole type sound. Example of the simple flute where flow across a sharp edge guides flow out of or through the pipe and thereby modulates the flow through the pipe. (Click figure to expand)

Figure 4. Dipole type sound. Flow across a sharp edge produces wide band noise. (Click figure to expand)

Figure 5. Quadrupole type sound. Flow into still standing or low velocity air cause turbulence.The vortices in this turbulence produces quadrupole type sound. (Click figure to expand)