PIPE59 Input Summary

PIPE59 Water Motion Information

The data listed in Table 59.2: PIPE59 Water Motion Table is entered in the data table with the TB commands. If the table is not input, no water is assumed to surround the pipe. Constants not input are assumed to be zero. If the table is input, ACELZ must also have a positive value and remain constant for all load steps. The constant table is started by using the TB command (with Lab = WATER). Up to 196 constants may be defined with the TBDATA commands. The constants (C1-C196) entered on the TBDATA commands (6 per command) are:

where:

KWAVE = Wave selection key (see next section)

KCRC = Wave/current interaction key (see next section)

DEPTH = Depth of water to mud line (DEPTH > 0.0) (Length)

DENSW = Water density, ρw, (DENSW > 0.0) (Mass/Length3)

θw = Wave direction (see Figure 59.2: PIPE59 Geometry)

Z(j) = Z coordinate of location j of drift current measurement (see Figure 59.2: PIPE59 Geometry) (location must be input starting at the ocean floor (Z(1) = -DEPTH) and ending at the water surface (Z(MAX) = 0.0). If the current does not change with height, only W(1) must be defined.)

W(j) = Velocity of drift current at location j (Length/Time)

θd(j) = Direction of drift current at location j (Degrees) (see Figure 59.2: PIPE59 Geometry)

Re(k) = Twelve Reynolds number values (if used, all 12 must be input in ascending order)

CD(k) = Twelve corresponding normal drag coefficients (if used, all 12 must be input)

CT(k) = Twelve corresponding tangential drag coefficients (if used, all 12 must be input)

T(j) = Temperature at Z(j) water depth (Degrees)

A(i) = Wave peak-to-trough height (0.0   A(i) < DEPTH) (Length) (if KWAVE = 2, A(1) is entire wave height and A(2) through A(5) are not used)

τ(i) = Wave period (τ(i) > 0.0) (Time/Cycle)

ϕ(i) = Adjustment for phase shift (Degrees)

WL(i) = Wave length (0.0   WL(i) < 1000.0*DEPTH) (Length)

(default )

Use 0.0 with Stokes theory (KWAVE = 2).

The distributed load applied to the pipe by the hydrodynamic effects is computed from a generalized Morison's equation. This equation includes the coefficient of normal drag (C_D) (perpendicular to the element axis) and the coefficient of tangential drag (C_T), both of which are a functions of Reynolds numbers (Re). These values are input as shown in Table 59.1: PIPE59 Real Constants and Table 59.2: PIPE59 Water Motion Table.

The Reynolds numbers are determined from the normal and tangential relative particle velocities, the pipe geometry, the water density, and the viscosity  µ (input as VISC). The relative particle velocities include the effects of water motion due to waves and current, as well as motion of the pipe itself. If both Re(1) and CD(1) are positive, the value of C_D from the real constant table (Table 59.1: PIPE59 Real Constants) is ignored and a log-log table based on Constants 31 through 54 of the water motion table (Table 59.2: PIPE59 Water Motion Table) is used to determine C_D. If this capability is to be used, the viscosity, Re, and C_D constants must be input and none may be less than or equal to zero.

Similarly, if both Re(1) and CT(1) are positive, the value of C_T from the real constant table (Table 59.1: PIPE59 Real Constants) is ignored, and a log-log table based on Constants 31 through 42 and 55 through 66 of the water motion table (Table 59.2: PIPE59 Water Motion Table) is used to determine C_T. If this capability is to be used, the viscosity, Re, and C_T constants must be input and none may be less than or equal to zero.

Various wave theories may be selected with the KWAVE constant of the water motion table (Table 59.2: PIPE59 Water Motion Table). These are:

The wave loadings can be altered (KEYOPT(5)) so that horizontal position has no effect on the wave-induced forces.

Wave loading depends on the acceleration due to gravity (ACELZ), and it may not change between substeps or load steps. Therefore, when performing an analysis using load steps with multiple substeps, the gravity may only be "stepped on" (KBC,1) and not ramped.

With the stream function wave theory (KWAVE = 3), the wave is described by alternate Constants 79 through 193 as shown in Table 59.2: PIPE59 Water Motion Table. The definitions of the constants correspond exactly to those given in the tables in Dean for the forty cases of ratio of wave height and water depth to the deep water wave length. The other wave-related constants that the user inputs directly are the water density (DENSW), water depth (DEPTH), wave direction (Φ), and acceleration due to gravity (ACELZ). The wave height, length, and period are inferred from the tables. The user should verify the input by comparing the interpreted results (the columns headed DIMENSIONLESS under the STREAM FUNCTION INPUT VALUES printout) with the data presented in the Dean tables. Note that this wave theory uses the current value defined for time (TIME) (which defaults to 1.0 for the first load step).

Several adjustments to the current profile are available with the KCRC constant of the water motion table as shown in Figure 59.3: PIPE59 Velocity Profiles for Wave-current Interactions. The adjustments are usually used only when the wave amplitude is large relative to the water depth, such that there is significant wave/current interaction. Options include

Figure 59.3: PIPE59 Velocity Profiles for Wave-current Interactions

Element loads are described in Element Loading. Pressures may be input as surface loads on the element faces as shown by the circled numbers on Figure 59.1: PIPE59 Geometry. Internal pressure (PINT) and external pressure (POUT) are input as positive values. These pressures are in addition to the linearly varying pressure of the fluids on the inside and outside of the pipe. In handling the pressures, each element is assumed to be capped (that is, have closed ends). The internal and external pressure loads are designed for closed-loop static pressure environments and therefore include pressure loads on fictitious "end caps" so that the pressure loads induce an axial stress and/or reaction in the pipe system. If a dynamic situation needs to be represented, such as a pipe venting to a lower pressure area or the internal flow is past a constriction in the pipe, these end cap loads may need to be modified by applying a nodal force normal to the cross-section of the pipe with the magnitude representing the change in pressure. Alternatively, the precomputed end cap loads can be removed using KEYOPT(8) = 1 and the appropriate end cap loads added by the user. The transverse pressures (PX, PY, and PZ) may represent wind or drag loads (per unit length of the pipe) and are defined in the global Cartesian directions. Positive transverse pressures act in the positive coordinate directions. The normal component or the projected full pressure may be used (KEYOPT(9)). See the Mechanical APDL Theory Reference for more details.

Temperatures may be input as element body loads at the nodes. Temperatures may have wall gradients or diametral gradients (KEYOPT(3)). Diametral gradients are not valid for the cable option. The average wall temperature at θ = 0° is computed as 2 * TAVG - T(180) and the average wall temperature at θ = -90° is computed as 2 * TAVG - T(90). The element temperatures are assumed to be linear along the length. The first temperature at node I (TOUT(I) or TAVG(I)) defaults to TUNIF. If all temperatures after the first are unspecified, they default to the first. If all temperatures at node I are input, and all temperatures at node J are unspecified, the node J temperatures default to the corresponding node I temperatures. For any other pattern of input temperatures, unspecified temperatures default to TUNIF.

Eight temperatures (T(j)) are read as Constants 67-74 corresponding to the eight water depths (Z(j)) input as Constants 7-30. These temperatures override any other temperature input (except TREF) unless the element is entirely out of the water or if all eight temperatures are input as zero. The thermal load vector from these temperatures may not be scaled in a superelement use pass if an expansion pass is to follow. Constants 31 through 66 may have zero values if desired. The temperatures input as Constants 67-74 are used to compute a temperature-dependent viscosity based on linear interpolation (if previous constants are not all zero). In the case of a solid cross section (inside diameter = 0.0), they are also used to compute the material properties of the element.

For the mass matrix, the mass per unit length used for axial motion is the mass of the pipe wall (DENS), the external insulation (DENSIN), and the internal fluid together with the added mass of any additional hardware (CENMPL). The mass per unit length used for motion normal to the pipe is all of the above plus the added mass of the external fluid (DENSW).

CI should be 1.0 for a circular cross section. Values for other cross sections may be found in McCormick. The user should remember, however, that other properties of PIPE59 are based on a circular cross section.