An FEA-Based Acoustic Fatigue Analysis Methodology

Timothy C. Allison, Ph.D.

Lawrence J. Goland, P.E.

Southwest Research Institute

San Antonio, TX

ANSYS Regional Conference: Engineering the System

August 31 - September 1, 2011

Houston, TX

Outline

• Introduction and Theory

• Existing Acoustic Fatigue/AIV Screening Methods

– Carucci-Mueller, Eisinger

– Energy Institute

• SwRI Method

• AIV Solutions

• Conclusions

Introduction

• Acoustically Induced Vibration (AIV) refers to high-frequency vibration (typically 500-1500+ Hz) in piping downstream of a pressure-reducing device – E.g. a control valve or pressure relief valve

• Can result in high cycle fatigue failures, particularly at branch connections

• First identified in 1983 by Carucci and Mueller

• Often a concern in flare/blowdown piping with thin walls and large diameters.

Image Courtesy Tyco Valves & Controls

Theory Overview

• AIV is caused by the following four physical phenomena: – Excitation from a pressure-reducing valve causes high-

frequency pressure fluctuations in downstream piping.

– These fluctuations excite higher order acoustic modes in the pipe with circumferentially varying pressure mode shapes.

– The acoustic pulsations couple to shell modes of the main piping.

– Branch connections or other welded discontinuities in the main line serve as stress risers.

Theory: Acoustic Cross Modes

Theory: Pipe Shell Modes

Existing AIV Screening Methods

• Carruci-Mueller paper (1983) introduced design limits based on failure/non-failure experience. – PWL and Pipe Diameter

• Eisinger (1997) modified the Carruci-Mueller limits to include different excitation parameter and wall thickness. – M*∆P and Pipe D/t Ratio

• Eisinger later (1999) used FEA to extend the design curve to lower D/t ratios.

Existing AIV Screening Methods (2)

Carruci-Mueller Design Curve Eisinger Design Curve

Existing AIV Screening Methods (3)

• The Energy Institute (2005) introduced a screening methodology for AIV: – Simple source PWL computation – PWL decay to branch connection and addition of PWL

from multiple sources at each branch – Estimate of fatigue life from curve-fit data (data from FE

models calibrated to historical failure/non-failure data) – Fatigue life estimation including reduction due to

weldolet fittings and small branch diameter to main line diameter ratios

– Likelihood of Failure (LOF) computed from estimated fatigue life

SwRI Method Overview

• Valve excitation analysis, acoustic analysis and finite element analysis performed to determine coincidence of acoustic and pipe shell modes

• Forced response analysis of FE model at coincident modes performed with shell models to determine stresses at fillet weld and resulting fatigue life. – Excitation from valve amplified by acoustic amplification

factor to account for acoustic resonance – Stresses evaluated using mesh-insensitive procedure for

welded joints in accordance with Section 5.5.5 of the ASME Boiler and Pressure Vessel Code, Section VIII, Division 2

SwRI Method – Valve Excitation • Valve excitation analysis performed

using control valve noise prediction standard IEC 60534-8-3 – Detailed source PWL prediction – Peak noise frequency from vena

contracta velocity and jet diameter

• Model PWL decay to branch and summation of sources at branch in same manner as Energy Institute method

• Convert PWL to SPL and dynamic pressure

Image Courtesy Floyd Jury, Fisher Controls

SwRI Method – Acoustic Modes

• Closed form solution used to model higher-order acoustic modes

• Resulting acoustic frequencies and mode shapes validated with ANSYS Acoustic 3D FEA models

• Multiply valve excitation by amplification factor to account for acoustic resonance

p1p2

p3

p4

p5

p6

q1

SwRI Method – Pipe Shell Modes

• ANSYS APDL scripts constructed to efficiently construct shell element models of piping at branch connections

• Modal analysis performed for each connection over excitation frequency range

• Results postprocessed externally via spatial FFT to determine dominant nodal diameter patterns in each mode

SwRI Method – Pipe Shell Modes (2)

SwRI Method – Pipe Shell Modes (3)

Circumferential Mode

Shape (n) FFT performed in order to

identify ‘n’

SwRI Method – Coincidence

SwRI Method – Forced Response

SwRI Method – Forced Response (2)

1150 1170 1190 1210 1230 1250 1270 1290

Me

sh-S

en

siti

ve P

eak

Str

ess

Frequency, Hz

Coincident

Mode

SwRI Method – Forced Response (3)

Note: Stresses shown are mesh-sensitive and are not accurate

absolute values. Mesh-insensitive stresses are calculated with

ASME B&PV Code Sec VIII Div 2 procedure

SwRI Method – Forced Response (4)

At Fillet

Weld

Toe

Note: Stresses shown are mesh-sensitive and are not accurate

absolute values. Mesh-insensitive stresses are calculated with

ASME B&PV Code Sec VIII Div 2 procedure

SwRI Method – Fatigue Life

• Use relative stress distribution from mesh-sensitive results to find location of maximum stress

• Use nodal forces and moments to calculate bending and membrane stresses and assess fatigue life

Images Courtesy ASME Boiler & Pressure Vessel Code, Section VIII, Division 2

SwRI Method – Fatigue Life • ASME Div 2 master S-N developed based on a large

amount of welded pipe and plate joint fatigue test data

• Fatigue life assessed on -3σ S-N curve for <1% probability of failure

Image Courtesy Dong 2009

Conclusions • New AIV analysis methodology developed based

on physical principles

• Method uses automated implementation of valve noise prediction standard and exact acoustic solution for efficient excitation solution

• Automated scripting tools applied for efficient FEA solution of coincident stress at connection and mesh-independent fatigue life results

• FEA-based approach allows for modeling of various countermeasures

Method Comparison Carruci-Mueller

Eisinger Energy Institute

SwRI Method

Calculates PWL X X X X

Includes Pipe Diameter X X X X

Uses historical data X X X See (1)

Includes pipe wall thickness X X X

Includes multiple sources & decay X X X

Includes connection type X X

Includes branch diameter X X

Includes acoustic/structural coincidence X

Includes excitation frequency X

Allows detailed analysis of design alternatives

X

Fatigue Life Calculation See (2) X

1Future work includes validation of method with test and historical data

2Calculated fatigue life is part of calibrated screening procedure, not end result

QUESTIONS?