18.08.2015   NUCLEAR POWER PLANTS

Variables affecting tube natural frequencies

The tube natural frequencies are affected by tube-to-baffle hole clearance, axial stress, fins, span length, span shape (straight, U-tube), support type, temperature and tube vibration (Chenoweth, 1976, Elliot & Park, 1973, Pettigrew et al., 1986, Simpson et al., 1974, Tanaka & Takahara, 1981, TEMA Standards, 8th edition). At about one tenth of TEMA allowable clearance, the frequency is about 7% higher than that predicted for simple supports. For most exchangers, tube-to-hole clearance is not a significant parameter for controlling natural frequencies, but it may be important in damping and tube wear (Chenoweth, 1993). Due to manufacturing procedures, the tubes may be under a tension or compression axial loading. (Kissel, 1972) found a variation in natural frequency due to axial loading in a typical exchanger as much as ± 40%. The natural frequency varies as reciprocal of the span length squared (unsupported span). For finned tubes, effective diameter for the outside diameter should be used to find the area moment of inertia for natural frequency calculation (Chenoweth, 1993). Currently, software by TEMA (FIV) (TEMA Standards, 8th edition) is capable of predicting the natural frequencies.

Formula/ Procedure

Conditions

f-( Ш (f Г(Jones, 1970)

Straight beams /single span

n is the mode number and *n is a frequency factor which depends upon the end conditions

j—Ш E f <Ard’er, 1960)

Curved beams/ single span *n is a frequency factor

R is the radius of curvature and a is the subtended angle

f — ^1 (й J

(TEMA, 6th Edition, 1978)

U-tube curved

Cu is the first mode U-tube constant

Experimental/ computer program

f — {P-l)2 Eg

Jn 2;L2 V W (Lowery & Moretti, 1975)

Straight/multiple, free-free spans (1-5 span tests); idealized support conditions, (flnL)2 is eigen value

FEM in-plane and out of plane Experimental/ analytical (Elliott & Pick, 1973)

Straight/curved

Beams immersed in liquids, air, kerosene, and oil (Jones, 1970)

Straight/simply supported/clamped

Out of plane:

f 3 13 * Iе * -(-2 -1)

Jn 3 13 R2.l, *n I————————————- —

R УА V1 + kn2 (Ojalvo & Newman, 1964)

Clamped ring segments n is mode number; k is bending stiffness у is specific weight; C is the torsional stiffness. А is cross-sectional area

Graphical in-plane and out of plane (Chen & Wambsganss, 1974)

Straight/curved, single span /multiple span

Formula/ Procedure

Conditions

Analytical/experimental (Khushnood et al., 2000)

Straight tubes single/multiple spans with damped/ fixed boundaries, Experimentation on refinery research exchanger (in-service)

Plucking and transient decay (Simpson & Hartlen, 1974)

Tubes were not fully straightened.

(Slight residual wiggleness)

Wind tunnel determination of fluid-elastic thresholds

Tubes were found sensitive to temperature

Table 5. Tube natural frequencies (MacDuff et al., 1957, Kissel, 1977)