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6.11 Abaqus/Aqua analysis

• “Abaqus/Aqua analysis,” Section 6.11.1

6.11.1 Abaqus/AQUA ANALYSIS

Product: Abaqus/Aqua

References

• “UWAVE,” Section 1.1.59 of the Abaqus User Subroutines Reference Guide
• “Defining an analysis,” Section 6.1.2
• *AQUA
• *CLOAD
• *C ADDED MASS
• *DLOAD
• *D ADDED MASS
• *SURFACE SECTION
• *WAVE
• *WIND

Overview

An Abaqus/Aqua analysis:

• is used to apply steady current, wave, and wind loading to submerged or partially submerged structures in problems such as the modeling of offshore piping installations or the analysis of marine risers;
• can be performed using the static (“Static stress analysis,” Section 6.2.2), direct-integration dynamic (“Implicit dynamic analysis using direct integration,” Section 6.3.2), explicit dynamics (“Explicit dynamic analysis,” Section 6.3.3), or eigenfrequency extraction (“Natural frequency extraction,” Section 6.3.5) procedures;
• will calculate drag, buoyancy, and inertia loading only for beam, pipe, elbow, truss, and certain rigid elements;
• can include elements that model spud cans for jack-up foundation analysis in Abaqus/Standard; and
• can be linear or nonlinear.

Procedures available for Aqua analysis

Aqua loading can be applied in static steps (“Static stress analysis,” Section 6.2.2), direct-integration dynamic steps (“Implicit dynamic analysis using direct integration,” Section 6.3.2), and explicit dynamic steps (“Explicit dynamic analysis,” Section 6.3.3). During these steps fluid particle velocity is assumed to consist of two superposed effects: steady currents, which can vary with elevation and location, and gravity waves. Fluid particle accelerations are associated with gravity waves only.

The fluid particle velocities and accelerations are used to calculate drag and inertia loading on the immersed body. Abaqus/Aqua also computes the fluid surface elevation and allows for partial immersion; drag and buoyancy loadings are omitted for those parts of the structure that are above the fluid surface or below the seabed level.

An eigenfrequency extraction step (“Natural frequency extraction,” Section 6.3.5) can be used to extract the natural frequencies of a structure prestressed by the Aqua loading in a static or direct-integration dynamic step (if that step included the effects of nonlinear geometry). The added-mass effect due to fluid inertia loads can be included in an eigenfrequency extraction step.

Defining an Abaqus/Aqua problem

Aqua loads are applied in the following manner:

1. The fluid properties and steady current velocity are defined for the model.
2. Gravity waves and wind velocity are defined for the model.
3. Drag, buoyancy, and fluid inertia loads are applied to elements and nodes of the structure using distributed or concentrated load definitions within the static or direct-integration dynamic step definition. The magnitudes of the loads applied are determined by the fluid properties, steady current, wave, and wind definitions.
4. In an eigenfrequency extraction step concentrated and distributed added mass definitions are used (instead of concentrated and distributed loads) to include the effects of fluid inertia.

The load-stiffness terms from Abaqus/Aqua loads, which are important in geometrically nonlinear analysis, are fundamentally unsymmetric. Therefore, the unsymmetric matrix solution and storage scheme should be used for the step when nonlinear geometric effects are included (“Defining an analysis,” Section 6.1.2). It is essential to use the unsymmetric solver when the structure being analyzed is flexible (see, for example, “Slender pipe subject to drag: the “reed in the wind”,” Section 1.13.3 of the Abaqus Benchmarks Guide).

On the other hand, if a relatively stiff structure is subject to Aqua loads or if a dynamic step uses small time increments, the unsymmetric load-stiffness terms may not be dominant and you may be able to obtain a convergent solution with the symmetric solver (see, for example, “Riser dynamics,” Section 12.1.2 of the Abaqus Example Problems Guide).

Coordinate system

The z-coordinate axis must point vertically for three-dimensional cases, and the y-coordinate axis must point vertically for two-dimensional cases. For the three-dimensional case the still fluid surface (when there is no wave motion) lies in a plane that is parallel to the x–y plane. For the two-dimensional case it lies parallel to the x-axis. The position of the still fluid surface is specified as part of the fluid property data.

Defining the fluid properties

Aqua loadings require the definition of fluid density, seabed and free surface elevation, and the gravitational constant.

Input File Usage: *AQUA

seabed elevation, free surface elevation, gravitational constant, fluid density

The *AQUA option must be included in the model data portion of the input file.

Defining a steady current

Steady currents are defined by giving steady fluid velocity as a function of elevation and location. Elevation is defined in the positive z-direction for three-dimensional models and in the positive y-direction for two-dimensional models. For two-dimensional cases the z-component of the steady current velocity is ignored. See “Input syntax rules,” Section 1.2.1, for an explanation of how to define one property (in this case steady current velocity) as a function of multiple independent variables.

If the fluid velocity is not a function of elevation or location (for example, when modeling a problem in a coordinate system that moves uniformly through the still fluid, such as a tow-out analysis), only one fluid velocity need be specified.

The steady current velocities can be scaled by referring to an amplitude curve (“Amplitude curves,” Section 34.1.2) from the concentrated or distributed load definitions used to apply drag loads, as described later.

Input File Usage: *AQUA

fluid properties on first data line (described above)

X-velocityfluid , Y-velocityfluid , Z-velocityfluid , elevation, X-coord, Y-coord

Defining gravity waves

Gravity waves are defined by specifying a wave theory. The wave theory determines fluid acceleration, velocity, and pressure field fluctuations. The fluid acceleration and velocity field fluctuations contribute to the drag loads. The fluid pressure field fluctuations contribute to the buoyancy loads.

Choosing the type of wave theory to be used

Using Abaqus/Aqua in an Abaqus/Standard analysis, you can choose Airy linear wave theory, Stokes fifth-order wave theory, wave data read from a gridded mesh, or fluid kinematics defined in user subroutine UWAVE. For Airy and Stokes waves the fluid surface elevation and the fluid particle velocities and accelerations will be calculated as functions of time and location based on the wave definition. If wave data are provided in the form of a gridded mesh, you must specify these quantities. If user subroutine UWAVE is used, the fluid kinematics must be defined in that routine.

Similarly, using Abaqus/Aqua in an Abaqus/Explicit analysis, you can choose Airy linear wave theory, Stokes fifth-order wave theory, or fluid kinematics defined in user subroutine VWAVE.

All of the built-in wave theories assume a series of waves in the horizontal plane (the plane of the fluid surface) that are unaffected by any fluid-structural interaction. The Airy and Stokes theories are based on irrotational flow of an inviscid, incompressible fluid, where the wave height H is small compared to the still water depth d. The bottom of the fluid is assumed to be flat (the still water depth is constant).

The Ursell parameter,

\frac {H}{\lambda} \left(\frac {\lambda}{d}\right) ^ {3},

where is the wavelength, should be much less than 1.0 for Airy wave theory to be applicable and should be less than 10.0 for Stokes theory to be applicable. For ratios of H/ greater than 0.142, the crest of the wave is predicted to break. The assumed boundary conditions on the free surface are then no longer valid in either theory, which limits the maximum wave amplitude for either theory.

Airy wave theory

Linear Airy wave theory is generally used when the ratio of wave height to water depth, H / d , is less than 0.03, provided that the water is deep (ratio of water depth to wavelength, d / \lambda _ { : } , is greater than 20). Convective acceleration terms are neglected in the Airy theory as part of the linearization. The Airy wave theory is described in detail in “Airy wave theory,” Section 6.2.2 of the Abaqus Theory Guide.

Since the Airy wave theory is linear, any number of wave trains traveling in different directions across the water can be defined; the fluid particle velocities and accelerations sum by linear superposition. The direction of each wave component is given by specifying the direction cosines of a vector, d _ { N } , lying in the plane defined by the still fluid surface.

By default, Airy waves are defined in terms of wavelength, \lambda _ { N } . Alternatively, you can define the waves in terms of wave period, \tau _ { N } . For Airy wave theory the wavelength and period of each component are related by

\frac {2 \pi}{\tau_ {N} ^ {2}} = g \frac {1}{\lambda_ {N}} \tanh \frac {2 \pi h}{\lambda_ {N}},

where

\tau _ { N } is the period of this component,

g is the gravitational acceleration,

\lambda _ { N } is the wavelength, and

h is the undisturbed (still) water depth.

Input File Usage: Use the following option to define an Airy wave in terms of wavelength:

*WAVE, TYPE=AIRY

amplitude, wavelength, phase angle, x-direction cosine, y-direction cosine

Use the following option to define an Airy wave in terms of wave period:

*WAVE, TYPE=AIRY, WAVE PERIOD

amplitude, wave period, phase angle, x-direction cosine, y-direction cosine

In either case repeat the data line to define multiple wave trains.

Stokes fifth-order wave theory

The Stokes fifth-order wave theory is a deep-water wave theory that is valid for relatively large wavelengths. Convective terms are included in the fluid particle acceleration calculations for Stokes fifth-order theory and can be significant for larger ratios. The Stokes wave theory is described in detail in “Stokes wave theory,” Section 6.2.3 of the Abaqus Theory Guide.

Because the Stokes fifth-order wave theory is nonlinear, only one wave train is allowed in an analysis. The relationship between wavelength and period of the waves in Stokes fifth-order theory is not as simple as that for the Airy theory, although the formula given above is a first-order approximation. Stokes waves can be defined only in terms of the wave period, .

Input File Usage: *WAVE, TYPE=STOKES

wave height, wave period, phase angle, direction of travel cosines

Gridded wave data

You can choose to provide wave surface elevations, particle velocities and accelerations, and the dynamic pressure at points in a user-defined grid through a binary data file. The binary file contains information about the wave definition, the location of the grid points where wave information is specified, and the wave kinematics at user-defined times. At spatial locations within the user-defined grid, Abaqus/Aqua will interpolate the wave kinematics from the nearest grid points, using either linear or quadratic interpolation. When a point on the structure is above the user-defined grid, Abaqus/Aqua assumes that the point is above the free surface elevation. Hence, no fluid loads are applied. If a point on the structure falls outside the user-defined spatial grid without being above the grid, Abaqus/Aqua finds the wave kinematics at the nearest point within the grid and uses those values at the point on the structure.

Input File Usage: *WAVE, TYPE=GRIDDED, DATA FILE=file_name

Binary data file requirements for gridded wave data

The data file must contain the following unformatted (binary) records (see “Aqua load cases,” Section 3.11.1 of the Abaqus Verification Guide). The data for the FORTRAN WRITE statement are given for each record:

First record:

NCOMP, DTG, NWGX, NWGY, NWGZ, IPDYN

where

NCOMP is the number of wave components to be read in the data file;

DTG is the time increment at which wave data are given on the grid;

NWGX is the number of grid points in the grid’s x-direction;

NWGY is the number of grid points in the grid’s y-direction—if this number is one, Abaqus/Aqua assumes that the wave data are constant with respect to the local y-direction;

NWGZ is the number of grid points in the grid’s z-direction—if this number is zero or one, the analysis is two-dimensional and the y-direction is vertical; and

IPDYN is an integer flag indicating whether dynamic pressure information is stored (IPDYN=1) or not stored (IPDYN=0) in the gridded wave file.

Second record:

(AMP(K1), WXL(K1), PHI(K1), K1=1, NCOMP) 

where

NCOMP is read on the first record, above;

AMP contains the wave component amplitude, ;

WXL contains the wavelength of this component, ; and

PHI contains the phase angle of this component, (in degrees).

The second record of this file contains the wave component data used to generate the gridded wave data; it is not used by Abaqus/Aqua. This record is provided only for information in user subroutine UEL by using the GETWAVE interface (see “Obtaining wave kinematic data in an Abaqus/Aqua analysis,” Section 2.1.13 of the Abaqus User Subroutines Reference Guide). The meaning of the arrays AMP and WXL is left to you; however, PHI is converted to radians.

Third record:

(WGX(K1), K1=1, NWGX), (WGY(K1), K1=1, NWGY), (WGZ(K1), K1=1, NWGZ) 

NWGi are read on the first record, above;

WGX contains the local x-coordinates of the grid points;

WGY contains the local y-coordinates of the grid points; and

WGZ contains the local z-coordinates of the grid points (not included in the gridded wave file for two-dimensional analyses).

Remaining records if IPDYN=0:

For three dimensions:

((WGVX(K1,K2,K3), WGVY(K1,K2,K3), WGVZ(K1,K2,K3), WGAX(K1,K2,K3), WGAY(K1,K2,K3), WGAZ(K1,K2,K3), K3=1,NWGZ), WZCRST(K1,K2), NCRST(K1,K2), K1=1,NWGX), K2=1,NWGY) 

For two dimensions:

((WGVX(K1,K2), WGVY(K1,K2), WGAX(K1,K2), WGAY(K1,K2), K2=1,NWGY), WZCRST(K1), NCRST(K1), K1=1,NWGX) 

Remaining records if IPDYN=1:

For three dimensions:

((WGVX(K1,K2,K3), WGVY(K1,K2,K3), WGVZ(K1,K2,K3), 

WGAX(K1,K2,K3), WGAY(K1,K2,K3), WGAZ(K1,K2,K3), P(K1,K2,K3), DPDZ(K1,K2,K3), K3=1,NWGZ), WZCRST(K1,K2), NCRST(K1,K2), K1=1,NWGX), K2=1,NWGY) 

For two dimensions:

((WGVX(K1,K2), WGVY(K1,K2), WGAX(K1,K2), WGAY(K1,K2), P(K1,K2), DPDZ(K1,K2), K2=1,NWGY), WZCRST(K1), NCRST(K1), K1=1,NWGX) 

where

WGVX contains the local x-components of the wave particle velocity,
WGVY contains the local y-components of the wave particle velocity,
WGVZ contains the local z-components of the wave particle velocity,
WGAX contains the local x-components of the wave particle acceleration,
WGAY contains the local y-components of the wave particle acceleration,
WGAZ contains the local z-components of the wave particle acceleration,
WZCRST contains the wave surface elevation,
NCRST contains the index for the vertical grid level just above the instantaneous water surface,
P contains the dynamic pressure, and
DPDZ contains the gradient of the dynamic pressure in the vertical direction. 

User-defined wave theory in Abaqus/Standard

A user-defined wave theory can be coded in user subroutine UWAVE in an Abaqus/Aqua analysis in Abaqus/Standard. You can define the fluid particle velocity, acceleration, free surface elevation, and fluid pressure field in the user subroutine.

For stochastic analysis, you can specify a random number seed, r, and define frequency/amplitude pairs that define the wave spectrum. During the analysis Abaqus/Aqua stores an intermediate configuration that can be used in the user subroutine to compute the stochastic description of the waves. The intermediate configuration is initialized as the reference configuration and is replaced by the current configuration only when requested by the user subroutine. In this way the stochastic description of the wave field can be stored in an external database and recalculated only when necessary.

Input File Usage:

Use the following option to specify the wave kinematics in user subroutine UWAVE:

*WAVE, TYPE=USER

Use the following option for stochastic analysis to make the intermediate configuration available in user subroutine UWAVE:

*WAVE, TYPE=USER, STOCHASTIC=r frequency, amplitude

User-defined wave theory in Abaqus/Explicit

A user-defined wave theory can be coded in user subroutine VWAVE in an Abaqus/Aqua analysis in Abaqus/Explicit. You can define the fluid particle velocity, acceleration, free surface elevation, and fluid pressure field in the user subroutine.

The quantities required to define the wave kinematics can be specified as properties and passed into the user subroutine. For example, in the case of stochastic wave kinematics, any required seed variable and/or frequency-amplitude data pairs can be specified as properties.

You can also declare and use state variables for user-defined wave calculations, which will be provided at the nodes and initialized to zero at the beginning of the step. You have to update the state variables within the user subroutine. For example, the state variables can be used to store any intermediate configuration of the structure that is used to describe a stochastic wave field.

Input File Usage:

Use the following option to specify the wave kinematics in user subroutine VWAVE:

*WAVE, TYPE=USER

Use the following option to specify properties available as a real-array argument PROPS of size NPROPS in user subroutine VWAVE:

*WAVE, TYPE=USER, PROPERTIES=nprops prop_1, prop_2, ..., prop_8 ..., prop_nprops

Use the following option to specify state variables available as a real-array argument STATEVAR of size NSTATEVAR in user subroutine VWAVE:

*WAVE, TYPE=USER, DEPVAR=nstatevar

Wave position as a function of time

For Airy and Stokes waves the position of the wave at time can be chosen by specifying the phase angle of the wave (or wave components for Airy waves). By default, the waves are chosen such that they have a trough (vertical displacement of the fluid surface is a minimum) at the origin of the horizontal axes at time . You can change this trough by introducing a phase angle for the waves. A positive phase angle shifts the waves backward in their travel direction (see Figure 6.11.1–1).

The time t used in the wave theory is the total time in the analysis. Therefore, if the direct-integration dynamic steps in which Airy or Stokes waves are applied are preceded by any steps other than directintegration dynamic steps (such as static steps), it is usually convenient to make the time period in these steps very small compared to the period of the wave.

Because total time is used, the phase of the wave will be continuous from the end of one dynamic step to the beginning of the next dynamic step.

Defining a minimum wave trough elevation

For computational efficiency Abaqus/Aqua uses a minimum wave trough elevation below which the structure is assumed to be immersed. Below this elevation no calculation of the fluid surface need be done