structural response of piping to internal gaseous detonation

6/21/2007 Structural Response of Piping 1

XII. Structural Response of Piping to Internal Gaseous Detonation


Structural Response to Explosions

Structures move in response to forces (Newtons Law) Structure has mass and stiffness

Structure pushes back


Pressure Loading Characterization

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Wload Wunload


Explosions in Piping

Safety analysis of facilities handling hazardous materials

Response of industrial piping systems to accidental internal explosions

Predicting loading on pipe segments and components

Predicting loading on supports and hangers


Generic features


Hamaoka-1 NPP

Brunsbuettel KBB

Recent Accidental Detonations

Both due to generation of H2+1/2O2 by radiolysis and accumulation in

stagnant pipe legs without high-point vents or off-gas systems.


Nuclear Fuel Cycle and Power Plant Safety

Hanford WA Pu-239 from 1945 to 1989

2 x 108 l radioactive waste in leaking

tanks

WTP convert to glass, 36 tonne/day in

2014

Radiolysis and chemical reaction create

H2, N2O, O2. 6/21/2007 Structural Response of Piping 8

Detonations Excite Elastic Waves


Measuring Elastic Vibration


Flexural Waves in Tubes

Coupled response due to hoop oscillations and bending

Traveling load can excite resonance when flexural wave group velocity matches wave speed

Can be treated with analytical and FEM models

Measured strain (hoop)

t (ms)0 2 4 6 8

10-4

Amplification factor

U (m/s)


Fracture

Fracture

External Blast


Strain

Gage

Locations

Strain Response of Fracturing TubesStrain Response of Fracturing Tubes

6/21/2007 Structural Response of Piping 13 6/21/2007 Structural Response of Piping 14

Post-test Al 6061-T6 Specimens (Pcj = 6.2

MPa)

Surface Notch Length = 1.27 cm

Outer diameter: 41.28 mm, Wall thickness: 0.89 mm, Length: 0.914 m

Surface notch dimensions: Width: 0.25 mm, Notch depth: 0.56 mm, Lengths: 1.27 cm, 2.54 cm, 5.08 cm, 7.62 cm

Detonation wave direction




Fracture Behavior is a Strong Function of Initial Flaw Length


Fracture Threshold Model

Flat Plate

Model

analyzed by

Newman and

Raju (1981)

Actual

tube

surface

Fracture Condition:

)'pR/h)Sd)/KIc > Q)/F

where Q, F = functions of flaw length

(2a), flaw depth (d), and wall

thickness (h)

Approximate


Note:

1) Parameters on the axes are

non-dimensional

2) Threshold is a 3-D surface

'P = Pcj - PatmR = Tube mean radiush = Tube wall thicknessd = Surface notch depth2a = Surface notch lengthKIc = Fracture toughness) = Dynamic

Amplification factor

Tube material: Al6061-T6

Wall thickness: 0.089 to 0.12 cm

d/h: 0.5 to 0.8

Pcj: 2 to 6 MPa

Axial Flaw Length: 1.3 to 7.6 cm

O.D.: 4.13 cm

Rupture

No Rupture

Threshold Theory

Fracture Threshold of Flawed Tubes under Detonation Loading


Deflagration-to-detonationtransition


burned unburned

1. A smooth flame with laminar flow ahead

2. First wrinkling of flame and instability of upstream flow

3. Breakdown into turbulent flow and a corrugated flame

4. Production of pressure waves ahead of turbulent flame

5. Local explosion of vortical structure within the flame

6. Transition to detonation


Effect of FA on Pressure


Structural Response to DDTThick walled vessels for elastic response

Thin-walled vessels for plastic response and failure

Use bars or tabs as obstacles to cause flame acceleration


Reflection of near-CJ Detonation

30% H2 in H2-N2O mixture at 1 atm initial pressure


DDT near end flange

15% H2 in H2-N2O at 1 atm initial pressure


Summary of results for H2-O2 Mixtures

Strains and pressures are a strong function of composition, peak occurs when

DDT is close to the end of the tube.


Single Degree of Freedom (SDOF) Model

Maximum dynamic hoop stress

) = dynamic loading factor

'P = Pmax Patm

R = tube radius

t = tube thickness

W = characteristic structural

response time

M

k WSZ 2

t

PRH

)' V

SDOF Model for )

M

F(t)

k

U

SWE

R2


SODF - Square Pulse


Loading Regimes

Sudden) = 2

Impulsive T/W < 1/4) = ZT

Quasi-static ZT >>1 ) = 1

P

tT


DLF versus Loading Time

D

y

n

a

m

i

c

L

o

a

d

F

a

c

t

o

r

0

1

2

ZT

Sudden

Quasi-static

Impulsive

DLF = Peak Strain/Static strain for peak pressure


Effect of load localization

p

w

Infinite thin-walled (R/t>10) cylinder of radius R under uniform radial pressure p over length w.

2R

t


Dynamic Effects of Finite Load

Commercial finite element code: LSDYNA

Assumption: Rotational symmetry of loading

Parametric study (thin and thick tube):

load length w/D: 10, 2.5, 1.2, 0.6, 0.3, 0.15

pulse length : ,100, 50,10,5,1 Pspressure P: 3, 10 MPa

p

w

D

t

time

P


Thick tube, P=10MPa, W=50Ps, w/D=0.15

Hoop strain [Pa]

T

u

b

e

a

x

i

s

Displacement

factor: 2000

L

=

1

.

2

4

m

D=127 mm

t=13 mm

P


Two dimensional elastic simulations

Hmax = Hstatic DLF(W) LLF (w/D)

DLF & LLF are good approximations to 2D dynamic simulations in elastic regime

DLF & LLF are good approximations to 2D dynamic simulations in elastic regime


Estimating Peak Pressures and Strains

Peak pressures occur near DDT threshold region, up to 4-5 PCJ

Peak strains are bounded by DLF = 2 and Reflected CJ pressure


Thermal Stress


Thermal stress Contribution

Heat transfer from hot combustion

products to inner wall of tube

Creates thin, heated layer of metal

Thermal expansion of heated layer

creates strain

Outer layers are stiff and straining

motion of inner layer generates

stress throughout the tube

thickness

Observed as additional hoop strain

on outer surface

ri

ro

h: thickness of thermally

affected region

Cross section of tubeThermal Stresses


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Downstream 0.6 m of tube was insulated on the insidewith 6 mm of neoprene.

End-flange

Neopreneinsulation

6mmIgnition

insulation

S0 S1 S2 S3 S4


Insulation dramatically influences strain measurements!

Downstream part

of tube is

insulated on the

inside with 6mm

neoprene

Peak strain

measurements

including thermal

stresses are up to

a factor of 2.5

higher (O2/C=0.7)


Thermal stress component of strain

Characteristic rise

time of 50 ms

Contribution to hoop

strain is about 125%

of peak value due to

mechanical loading

alone.

Dominates long-time

(> 100-200 ms)

observations


Correlation between pressure and mechanical strain for O2/C=0.75

Mechanical

component of

hoop strain is in

good agreement

with that

inferred from the

pressure

measurements

assuming a

dynamic load

factor of DLF =

1

SDOF model

adequate for

flames


Simplified model for heat transfer

From experimental observation:

characteristic time scale:

tc ~ 50 ms

From 1-D heat equation, the

penetration depth h is given:

d = N tc ~ 0.4 mm

N : thermal diffusivity of steel, 3.5*10-6 m2/s

t

wall thickness

Thot gas

h

Temperature


Square wave approximation for temperature profile

D : Coeff. of thermal expansion,9.6 *10-6 K-1

E: E modulus, 210 GPa

t

'T

h = 0.4mm

Temperature

VTT = 2 D h E 'T

Strain on outer surface:

ri2 ro

2

2 ri

'T from energy balance between hot gas and tube,

assuming cool-down to 500K : 'T ~ 45K

VTT = 4.11 MPa

HT = 16 * 10-6

Good agreement with

experimental observations


Plastic Deformation Study


Considerations about material properties

Simple models: perfectly plastic,

elastic perfectly plastic

More realistic models Strain hardening VY (H)

Strain rate effects, VY(dH/dt)

Temperature effects V

Y(T)

V

H

V

H

dHdW


Thin Tube Facility

S5 S1S2S3S4 P1P2

1.24 m long,

ID 127 mm, 1.6 mm

wall thickness

Obstacles as for thick

tube

Mixtures: CH4-O2, 0.6 < O2/C < 2

1 bar < P0 < 3.5bar

2 pressure transducers (P1,P2) in

ignition flange and end plug

5 Strain gauges attached to outer

tube surface (S1-S5)

tank specimen

Ignition

flange

assembly

Valve

assembly on

ignition

flange

circulation

pump


Thin Tube Facility Four quick clamps

secure the igition

flange assembly to

the tank

Tank is evacuated

prior igition via glow

plug

Strain gauges attached to tube surface

Maximum data sampling rate: 2.5 MHz

Strain

gauges


Elastic RegimeShot 1, O2/C=1, P0=1atm


Plastic RegimeShot 8, O2/C=2, P0=3.5atm

Significantly smaller plastic strain (2.5%) for cases in which transition to detonation occurs shortly after initiation.


Peak deformation at tube endO2/C=1, P0=3.5atm

Repeatable plastic deformation of up to 18% close to the tube end plug.

end plug removed


What happens at the tube end ?

Two possible scenarios:

Case A: Detonation travels into unburned mixture, which is close to initial pressure. CJ-detonation reflects as shock of end-wall into burned mixture

Case B: Fast flame propagates in

the tube, compressing the

unburned gas ahead. Transition

event is taking place close to the

end-wall. Detonation develops in

the pre-compressed mixture

P0UCJunburnedburned

P>>P0burned

U


Detonation Reflection

3-in Schedule 40 316L pipe 1-m long, 38 mm diam, 4.5 mm wall 240 MPa yield stress

Reflected CJ detonation. CJ Velocity 2600 m/s, PCJ/Po = 26

Three initial pressures 3, 6, 9 atm

LS-DYNA simulation with traveling load model of waves

6/21/2007 Structural Response of Piping 503 atm

6/21/2007 Structural Response of Piping 516 atm 6/21/2007 Structural Response of Piping 529 atm


Spatial distribution of Effective Plastic Strain

3 atm

6 atm

9 atm


Bends and Tees

Limited data available Important for plants and facilities Some enhancement of hoop load due to

wave reflections Transverse loads can be quite

significant Creates bending in tubes Supporting structures (hangers) can fail Flange bolts can fail in shear due to

transverse loads


Example: Flow in a 90o Bend

d

dt

Z}~u dV = c~F c

Z}~u~u ndAc

ZPn dA

Momentum equation (general case):

Simplification for uniform, steady flow:

~F = xA1P1 + }1u21

+ yA2

P2 + }2u22

General unsteady case:

~F = xFx(t) + yFy(t)


Detonation Waves in Bends

Deiterding simulations with AMROC

L.T. Yang et al. (Eds.): HPCC 2005, LNCS

3726, pp. 916927, 2005.

Curran and Liang

Experiments 2006

Ethylene-oxygen

detonation 0.8 bar

Initial pressure


Superposition of Modesextrados intrados

end


Detonations and ASME Code Rules

Not covered under current BPVC VIII or Piping Code B31

Proposed code case for impulsively loaded vessels is under development by ASME Task Force on Impulsively Loaded Vessels, SWG/HPV, ASME VIII.

Current impulsive loading code case intended to cover vessels used to contain high explosive detonation. many common elements associated with dynamic loading

Further work needed to treat gas detonation specific issues


Issues for Gaseous Detonation

Loading is more difficult to define for gases than for HE detonation More testing is needed to have generic

results

Mixed loading regime, not purely impulsive.

Plastic deformation will require considering entire loading history.

Traveling load aspects of gaseous detonation


Acknowledgments

Experiments were carried out in the EDL at Caltech by Florian Pintgen

James Karnesky

Rita Liang

Sponsored by ConocoPhillips

DOE

Los Alamos National Laboratory

ASC program at Caltech

structural response of piping to internal gaseous detonation

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