The lift, drag, and inertia coefficients have been determined experimentally for two cylinders at various positions subjected to harmonically oscillating flow. The cylinders were placed at 0, 30°, 60°, and 90° to the flow direction in separate series of tests. The spacing between the cylinder centers was varied from 1.5 diameters to 3.5 diameters. The results are presented in terms of the relative spacing, Keulegan Carpenter number, and the flow direction.
A body's resistance to flow is strongly affected by what surrounds it. When two bodies are in close proximity, not only the flow about the downstream body but also that about the upstream body may be influenced. Examples include condenser tubes in heat transfer; columns in pressure suppression pools of nuclear reactors; members of the jacket type drilling platforms, semisubmersibles, floating tubular structures, risers, and other tubular structures in offshore engineering; turbine and compressor blades in mechanical and aerospace engineering; and high-rise buildings, cooling towers, and transmission lines in civil engineering.
The quantification of the interference effects in terms of the pressure distribution, lift and drag on individual members, vortex shedding frequency, and the dynamic response of members of the array in terms of the governing flow and structural parameters constitute the essence of the problem.
There are infinite numbers of possible arrangements of two or more bodies positioned at right or oblique angles to the approaching flow direction. In wavy or time-dependent flows one needs the lift, drag, and inertia coefficients for all members of the array. Evidently, the members of the array may not be all parallel and normal to the flow. The quantification of the flow interference on lift, Strouhal frequency, and the in-line force for cylinders with relative inclinations and spacings in a design-wave environment is an exceedingly complex problem. In the absence of data on the interaction between drag and inertia coefficients in wavy and harmonic flows for cylinder groups one is tempted to use steady-flow results for the drag coefficient and the unseparated potential flow results for the inertia coefficient.
The inertia coefficient for a group of cylinders in inviscid unseparated flow may be obtained through the use of the method of images1,2 or through the use of the linear potential theory including wave diffraction. 3,4, These analyses do not deal with the effects of separation and vortex shedding. Consequently, the results are more appropriate to the determination of earthquake forces and wave forces on large bodies rather than to the evaluation of the inertial components of the force in the drag/inertia dominated regime.
It is evident from the foregoing that experiments must be conducted with carefully selected tube bundles and cylinder combinations in order to develop some understanding of the flow interference and to provide data for body combinations of practical importance.
The dependence of the lift, drag, and inertia coefficients .for a single circular cylinder in wavy and harmonic flows on the Reynolds number, Keulegan Carpenter number, and the relative roughness ratio has been clearly established. 5–7
