Very little reliable hydrodynamic data exists for bare and straked pipes subject to oscillatory flows which describes drag and added mass behavior as a function of Keulegan-Carpenter (KC) and reduced parameter Beta (B) numbers, namely for KC below 4 and B above 6000. The ability to accurately predict the global motions response and fatigue life of an SCR riser operating at such low KC/high B numbers to a large degree depends on the appropriate selection of hydrodynamic coefficients for such an analysis. This paper presents the experimental procedure used in obtaining the drag and added mass coefficients at low KC numbers, consequent results and their use in a design analysis of an SCR operating at extremely low KC numbers.
The question of appropriate drag and added mass coefficients for risers operating at low KC numbers was raised early in the design of a steel catenary gas export riser connected to the Typhoon TLP (Figure 1). The Typhoon SCR is 18" in diameter, and the TLP is located in approximately 2100 feet of water. Drag and added mass coefficients were needed for the straked riser region, which extends several hundered feet below the riser attachment to the TLP, and the bare pipe region, which extends below the strakes to the riser touch down point. The Typhoon 18" SCR is particularly critical in terms of fatigue life at the touch down point due to the low water depth / diameter ratio, which is in fact the lowest of any SCR installed to date (Figure 2).
1Formerly with Advanced Marine Technology Inc.
For the most damaging fatigue seastates, motions of this riser are small, typically less than half a diameter. Figure 3 shows KC values for a typical fatigue seastate plotted along the riser length. From the figure it can be seen that most KC values are below 4.0.
The Typhoon TLP operating conditions relevant to the SCR fatigue life analyses are those of surge and sway in random seas, with underwater current effects considered negligible. Greatest fatigue life sensitivity was found to occur under conditions where significant wave heights varied from 10 feet to 1 foot, and the corresponding wave periods varied from 8 seconds to 2 seconds. In terms of SCR geometry and motions, the above conditions correspond to KC numbers between 4 " 1, and (reduced parameter) Beta numbers of between 20000 - 10000. The KC and Beta numbers are defined as:
KC = Vm*T/D
Beta = D2/(T*nu)
Vm is the SCR maximum oscillation velocity; T is oscillation period; D is riser diameter; and nu is the kinematic viscosity of water. The maximum value of SCR velocity is used, since both the sea-state and the vessel motions (hence the SCR forcing) are specified as random processes.
Hydrodynamic data, compiled in Bearman (1988), Sarpkaya (1986), Triantafyllou (1980), for bare and straked pipes in oscillatory flows does not provide pipe CD values (as a function of KC & Beta numbers) below KC ~ 4 and Beta ~ 6000.