## Clarification of Sound Power Level Evaluation for Acoustically Induced Vibration Fatigue

There are multiple sources of vibration in piping that can lead to failures, usually occurring at welds, penetrations, or other ‘discontinuities’. The EI Guidelines for the Avoidance of Vibration Induced Fatigue Failure in Process Pipework^{1} indicates the following common causes of piping vibration:

- Flow induced turbulence
- Mechanical excitation
- Pulsation
- Surge/momentum changes due to valve operation
- Cavitation
- Flashing
- High frequency acoustic excitation

Pressure-relieving and related systems often operate at choked-flow conditions, which generate the high frequency acoustic energy associated with high dynamic stress levels that can cause “circumferential discontinuities on the pipe wall, such as small bore connections, fabricated tees or welded pipe supports” to fail quickly.^{1, §2.3.4, p. 13} Given the applicability of this potential failure mode to pressure-relieving systems, API Standard 521 §5.5.12.2^{2} also discusses this acoustical fatigue.

The EI Guidelines (Flowchart T2-5, High frequency acoustic fatigue assessment) and API Standard 521 (Equation 43) provide a calculation for the estimation of the acoustical energy that can be generated based on the work of Carucci and Mueller^{3}; however, there are some confusing aspects that are worthy of clarification.

**Acoustic excitation occurs at locations of sonic flow**. The generation of the high frequency acoustical energy is associated specifically with compressible fluid flow achieving sonic conditions. The ‘choking’ that occurs at these conditions results in a significant amount of useful mechanical energy being ‘lost’, some of which is converted to internal thermal energy and some of which is converted into the high frequency acoustical energy of interest here.

Sustained flow rates at very high (but not sonic) velocities can cause flow induced turbulence, which can generate a wide spectrum of frequencies; however, “the majority of the excitation is concentrate at low frequency (typically below 100 Hz); the lower the frequency, the higher the level of excitation from turbulence.”^{1, §2.3.1, p. 7}

As a result, we will only calculate an estimate for the generation of high frequency acoustical energy as cited above for locations where sonic flow is predicted (‘sources’ of the high frequency acoustic energy). Specifically, we would look at any place where sudden expansion of compressible fluid flow takes place: pressure relief valves, depressuring or control valves, restriction orifices, pipe expanders, and expanding tees. The evaluation for a given piping segment starts at the first instance of choking.

**Attenuation occurs downstream of the source**. As the sound energy travels down the pipe wall, some reduction in the power (attenuation) occurs. The guidelines are pretty clear about the attenuation due to lengths of constant area piping (6dB for every 100 pipe diameters of length). Attenuation also occurs at expansions that have subsonic flow in accordance with A_{Exp}=2(D_{2} ⁄ D_{1} -1), where D_{2} is the downstream inner diameter and D_{1} is the upstream inner diameter^{4}. Attenuation is also expected to occur at tees that have subsonic flow, although we are not aware of any publicly available information on the magnitude of this attenuation.

With the interest in circumferential discontinuities in the pipe, we specifically look at locations of small bore branch connections (for example, bleeder valves) and tees (for example, where a bypass branch ties into the discharge line, and where the discharge line ties into the flare header). The attenuation of the sound power level from the source to the location of interest is calculated, and then compared to the screening criterion (155 dB).

**Choking in series uses logarithmic addition of sound power levels**. The relatively straightforward calculation process just described gets complicated whenever sonic flow is encountered en route to the location of interest. In this case, the acoustical energy generated by the sonic flow conditions needs to be added to the acoustical energy coming from the upstream source(s). Both the EI Guidelines and API Standard 521 provide the logarithmic addition needed to combine the acoustic energies at a point. To give an order of magnitude of the effect of this logarithmic addition, if two equal sound power levels are added together, the outgoing sound power level is 3 dB (10·log_{10} (2)=3.01) greater than the incoming sound power levels.

It is useful to note that this logarithmic addition is also employed when the location of interest is a tee having a sound generating source upstream of both legs of the tee.

**Sonic flow factor is specifically for branched tees with choked flow**. Based on a number of instances of acoustically induced failures reported, one common location of failure is at a branch connection into a tee, and specifically for cases where the branch connection is smaller in diameter than the tee body and choked flow occurs at this point. There is likely additional vibration caused by the turbulent flow and impingement on the tee opposite of where the branch ties in, as well as the oft-cited “intensified dynamic strain response” at the tee.

If one were to use the process outlined above for the simple, common setup of a single sound-generating source (pressure relief valve) that discharges into a larger flare header with sonic flow predicted at the tee, one would perform the following:

- Estimate the sound power level at the pressure relief valve
- Attenuate the sound power level through the discharge piping to the tee branch
- Estimate the sound power level at the tee due to sonic flow
- Logarithmically add the sound power levels (2) and (3) and compare to the screening criterion, perhaps with an additional safety factor given industry experience with failures at this location

Given that the logarithmic addition is inconvenient, it would be nice to have a simple rule of thumb to work with, especially for this common configuration. Also, since we seem to have more failures for this specific configuration (branch tee with sonic flow), an additional safety factor on the screening criterion would be justified. Rather than adjust the screening criterion, we can ‘kill two birds with one stone’ by specifying a factor to add for this specific configuration that encompasses both elements. This is the basis for the “Sonic Flow Factor” of 6dB, which is ill-defined in the EI Guidelines and perhaps a bit ambiguous in API Standard 521.

**A complicated example for clarification**. To illustrate each of these clarifications, we provide an example below derived from an actual installation we have evaluated.

AIV example illustrating points above

[1] Energy Institute. “Guidelines for the Avoidance of Vibration Induced Fatigue Failure in Process Pipework”. 2nd Edition, 2008 Jan.

[2] American Petroleum Institute. “API Standard 521: Pressure-relieving and Depressuring Systems”. 6th Edition, 2014 Jan.

[3] Carucci VA, Mueller RT. “Acoustically induced piping vibration in high capacity pressure reducing systems”. In 92-/WAPVP-8, pp. 1-13. American Society of Mechanical Engineers. 1982.

[4] Melhem GA. “Estimate Vibration Risk for Relief and Process Piping”. In American Institute of Chemical Engineers 2013 Spring Meeting,

*9th Global Congress on Process Safety*. April 2013.

## 17 Comments

For the pressures used, would you use static pressure or stagnation pressure?

We normally use the stagnation pressure, but would agree the EI guidelines and other documentation do not specify. We’ve used stagnation pressure as the basis for the acoustic energy is from the shock wave and irreversible expansion, which are related to the stagnation conditions. Looking back at the source data, it isn’t clear what pressure the calculations were based on and it is possible they are based on static pressures as they are more easily measured in the field.

I talked to Rob Swindell of the Wood Group, and he said the pressure used out of the PSV should be static pressure, and not stagnation pressure. I asked him about choked enlargements, but I have not heard back yet.

Rob Swindell said to use static pressure for the pressure upstream and downstream of sonic pipe expansions. Note that I have problems with equation 43 in API 521 6th edition when the sonic pressure increases out out the expansion as the negative result makes the equation crash. Therefore, I would use the K1, K2, K3, K4 and K5 method and just set the K1 to zero for cases where the static pressure increases across the sonic expansion. I ran some checks, and equation 43 gives nearly identical results to the K1, K2, K3, K4 and K5 method.

Note the ‘K’ approach is just the expansion of the logarithmic expression {log(A

^{x}*B^{y}) = x*log(A) + y*log(B)}, so they are mathematically the same {as context for other readers, there is an alternative expression for the Carucci/Mueller sound power level correlation involving the expansion of the logarithmic expression into K values that represent each of the correlation groups used, that is flow (W), pressure drop ratio (P1-P2)/P1, and temperature to molecular weight ratio (T/M)}. That being said, it does not make sense to just set K1=0, as at least the K1 through K3 factors are all part of the empirical correlation between the conditions at that location and the sound power level estimated.Actually, the K1 gets more negative the smaller the pressure drop with the K1, K2, K3, K4 and K5 method. At really small pressure drops, the decibels go negative. I suppose I can just ignore sound generation at choked enlargements where the static pressure increases across the enlargement.

Trey

Would it be proper to calculate an AIV Sound Power Level on the final PSV discharge outlet piping fitting which is sonic when it is discharging to atmosphere?

The AIV evaluation is specifically focused on the potential for loss of containment in piping. If the piping in question discharges to atmosphere, the designer has already deemed the atmosphere to be a safe discharge location, so there is no objective of the AIV evaluation at that point. The designer would still need to provide support for momentum forces and consider the impact of noise on personnel nearby, but I do not see the point of evaluating a sound power level in the context of AIV at the final outlet piping fitting having sonic flow to atmosphere.

For the “Sonic Flow Factor” at branched tees with choked flow, is that 6 dB a local penalty at that fitting, or should that 6 dB that was added be sent down to pipe to the subsequent fittings?

Recall that the 6 dB of the sonic flow factor for branched tees is an attempt to encompass both the logarithmic addition and provide a ‘local penalty’ as you say (good description!). 3 dB is from the estimate of logarithm addition, and 3 dB is for the local penalty. I would agree that since the intent of the local penalty is to help us screen for problematic cases, that does not need to be incorporated into the propagation of the sound power level downstream. So, perhaps a better way to do the evaluation is to perform the normal calculations, and at these branched tees with choked flow subtract 3 dB from the allowable SPL at that specific point to represent the local penalty.

The way I have heard is the choked leg coming into the tee gets 6 dB added onto it, and then the two SPL are log-summed. The resulting SPL is what is sent down to subsequent fittings. This method results in about a 3 dB drop compared to the method of log-suming the two legs and then adding 6 dB to that result.

Could you share where you got the equation for expansion attenuation?

Reference [4] has the equation for the attenuation of non-choked expansions.

For a PSV followed by a choked expander, could you explain why the SPL from the PSV and the SPL from the expander are logarithmically added for the SLP to pass down the pipeline? I’ve seen examples where 6 dB is added directly and passed down the pipe line and I have seen cases where the SPL generated by the expander is set as the new SPL and the SPL from the PSV is ignored since the sound would not pass through the choked enlargement.

The API and EI guidelines discuss the need to add power levels from different sources without qualifying where those sources are in relation to each other. The EI guidelines state the acoustic energy is manifested as vibration in the piping, so it makes sense to me that the effect of adding energy to the piping would be cumulative. In addition, while it is true that the effects of sound propagation in a fluid do not ‘flow upstream’ through a shock wave, the acoustic energy is being transferred to the piping, not simply contained within the fluid (and only a fraction of that energy is being transferred from the fluid to the piping, which is implicitly contained within the empirical SPL equation). While I don’t know of specific empirical evidence for the case of a PSV followed downstream by a choked expander, I would add the SPL generated by both together based on the EI guidelines. I could be persuaded that an expander that is close coupled to the PSV outlet would be a different case, and would lean towards treating that expander as an extension of the PSV body / outlet flange.

In your example, the choked expander is 1 foot away from the PSV. Would you say that is enough distance to treat is as separate from the PSV body/outlet flange?

That is a judgment call – I usually use the hydrodynamic entrance length as a suitable criterion for cases where I want to define what is ‘close-coupled’.

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