Page 262 - Pressure Vessel Design Manual

240 Pressure Vessel Design Manual

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4
4
Refractory: IL = -(DL - dL) 0 Circumferential pressure strain, €4.
64
0.85~6
&# = - (9)
Composite: I = I, + IL E,
0 Equivalent modulus of elasticity, E,.
Thermal Expansions
ELIL
E,, = E, +- e Thermal expansion of shell, AL1.
Is
AL1 = CU,(T, - T,)
Temperatures
0 Total circumferential expansion without lining
Heat loss through wall, Q. AL2.
m m AL2 = 84 + ALI
10 - la
-+-+-+-
Q=1 tL t, 1
hi KL Ks ho 0 Mean thermal expansion, AL3.
Outside shell temperature, T,, . AL3 = CUL(TL - T,)

0 Mean shrinkage, AL4.

ALA = 0.5(S~s + STL)
Inside shell temperatures, T,Z.
0 Net man unrestrained expansion, AL5.

AI5 = AL3 - ALA

Inside lining temperature, TLI . 0 Net differential circumferential expansion, AL6.

AL6 = AL2 - AL5

Verijcation of temperature gradient. Stresses

e Mean compressive stress in lining due to restraint of shell,
UL1.
Mean shell temperature, T,.

T, = 0.5(TSi + Ts2)
0 Differential stress from mean at hot fae and cold fae of
Mean lining temperature, TL.
lining due to thermal expansion, am.
TL = o.5(Tsz + TL~)

Stresses and Strain
0 Differential stress from mean at hot and cold faces of lining
0 Circumferential pressure stress, a+. due to shrinkage, au.
PD
a@ = -
2tS