Flow-Induced Vibration of Solitary Wire-Wrapped Cylinders in Axial Flow

Figures & data

Fig. 1. Free-body diagram of a pinned-pinned cylinder.

Fig. 2. Wire-wrapped pin and bundle geometry.

Fig. 3. Elliptical cross-sectional area of a helically wrapped wire spacer.

Fig. 4. Wire added cross-sectional area as a function of P/D and H/D.

Fig. 5. Wire added area moment of inertia as a function of P/D and H/D.

Fig. 6. Square channel cross-section geometry.

Fig. 7. Wire added friction factor as a function of P/D and H/D.

TABLE I Beam Dimensionless Frequency and Mode Shape Parameters*

Boundary Condition	Mode, i	λi	σi
Pinned-pinned	1	π	N/A^a
	2	2π
	3	3π
	4	4π
	5	5π
Fixed-fixed	1	4.730	0.983
	2	7.853	1.001
	3	10.996	1.000
	4	14.137	1.000
	5	17.279	1.000
Fixed-free	1	1.875	0.734
	2	4.694	1.018
	3	7.855	0.999
	4	10.996	1.000
	5	14.137	1.000

*Reference 14.

^aN/A = not applicable.

Fig. 8. Argand diagram for a bare pinned-pinned cylinder.

TABLE II Galerkin Approximation Convergence of Critical Dimensionless Velocities

NGalerkin	1	2	3	4	5
ucd	3.1416	3.1412	3.1412	3.1412	3.1412
ucf	N/A^a	6.2867	6.2851	6.2851	6.2851

^aN/A = not applicable.

Fig. 9. Argand diagram for bare (a) fixed-fixed, (b) fixed-free, and (c) pinned-pinned cylinders.

Fig. 10. Single-pin flow test schematic.

Fig. 11. Single-pin flow test experimental setup.

TABLE III Test Pin Dimensionless Parameters

Test Pin	P/D	H/D	Wire-Wrap Revolutions	Type
1	N/A^a	N/A	N/A	Bare
2	1.100	25.853	6	Reference
3	1.100	19.390	8	Decreased H/D (~25%)
4	1.204	25.853	6	Increased P/D (~10%)
5	1.324	25.853	6	Increased P/D (~20%)

^aN/A = not applicable.

Fig. 12. Test pins 1 through 5 (from left to right) on a pin rail.

TABLE IV Test Pin Geometric Specifications

Test Pin	Cylinder Diameter (mm)	Cylinder Length (mm)	Wire Diameter (mm)	Pitch (mm)	Wire Span Length (mm)	Axial Pitch (mm)
1	6.350	1000	N/A^a	N/A	N/A	N/A
2	6.350	1000	0.635	6.985	985.0	164.2
3	6.350	1000	0.635	6.985	985.0	123.1
4	6.350	1000	1.295	7.645	985.0	164.2
5	6.350	1000	2.057	8.407	985.0	164.2

^aN/A = not applicable.

TABLE V Test Pin Material Specifications

Test Pin	Cylinder Material	Cylinder Elastic Modulus (GPa)	Wire Material	Wire Elastic Modulus (GPa)	Pin Linear Mass Density (kg/m)
1	PEEK	3.6	N/A^a	N/A	0.0419
2	PEEK	3.6	304SS	180	0.0446
3	PEEK	3.6	304SS	180	0.0448
4	PEEK	3.6	1100Al	69	0.0455
5	PEEK	3.6	1100Al	69	0.0510

^aN/A = not applicable.

TABLE VI Effect of Wire on Test Pin Parameters

Test Pin	Area (%)	Linear Mass Density (%)	Area Moment of Inertia (%)	Rigidity (%)	Friction Factor Constant (%)
1	0	0	0	0	0
2	1.01	6.44	0.005	0.25	3.56
3	1.02	6.92	0.005	0.25	7.33
4	4.20	8.59	0.089	1.71	5.65
5	10.63	21.72	0.572	10.96	15.90

Fig. 13. Argand diagram of TP-1 (bare cylinder).

Fig. 14. Argand diagram comparison of bare and wire-wrapped cylinders.

Fig. 15. Experimental flow test schematic.

Fig. 16. (a) Reynolds number and (b) pressure drop as a function of flow rate into the test section.

Fig. 17. Test pin RMS vibration amplitudes in (a) x-direction and (b) y-direction.

Fig. 18. Optical micrometer frequency results for (a) TP-1 and (b) TP-2; modal frequencies for (c) TP-1 and (d) TP-2.

Fig. 19. Optical micrometer frequency results for (a) TP-3, (b) TP-4, and (c) TP-5; DSS frequency results for (d) TP-3, (e) TP-4, and (f) TP-5; modal frequencies for (g) TP-3, (h) TP-4, and (i) TP-5.

Fig. 20. Theoretical model comparison to (a) TP-1 (bare test pin), (b) TP-2, (c) TP-3, (d) TP-4, and (e) TP-5 results.

Fig. 21. Test Pin 5 with varying boundary conditions.

Fig. 22. Theoretical comparison to (a) TP-1, (b) TP-2, (c) TP-3, and (d) TP-4 with fixed-fixed boundary conditions.

R. D. BLEVINS, Formulas for Dynamics, Acoustics and Vibration, John Wiley & Sons, Chichester, United Kingdom (2016).

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