The standard towed and self-propelled simulations in Orca3D Marine CFD provide a wealth of information about the steady state resistance and powering characteristics of a given vessel design. Naval architects have been able to successfully apply steady state performance information, whether it be from scale model tests, high fidelity CFD simulation, or other semi-empirical prediction methods to the design of ships and boats by making appropriate modifications to accommodate real-world effects such as the impacts of environmental effects of wind and waves. In many cases this approach is sufficient. However, for certain flow phenomena, the unsteady effects of the flow can have a large enough impact on the vessel's performance that cannot be neglected. Cavitation and ventilation are two examples of flow phenomena that often come about as a result of unsteady changes in the flow field. In such cases it may be important for the naval architect to examine the transient behavior through different simulation techniques.
Prescribed Dynamics
The first example shows a way to create an unsteady simulation by prescribing the pitch motions of the vessel. In this example, a standard self-propelled simulation has been created with Orca3D Marine CFD for the Eastport 32 with a propeller rpm of 1700. The steady state results of the simulation are shown below.
In order to generate an unsteady behavior, the pitch motions are prescribed to oscillate in a sinusoidal manner with a specified amplitude and frequency. This oscillation starts as a continuation of the steady run shown above. To apply the oscillatory pitch behavior, first open the Expression Editor and define the PrescribedPitch variable as a function of amplitude and period as shown below. In this example, the steady state pitch value was -3.31 degrees (note the sign), the amplitude of pitch oscillation is 0.5 degrees, the pitch period is 2 seconds, and the start time at the end of the steady run is 8 seconds.
After closing the editor, select the "Rotation (1 DOF) marinePitch" dynamics module in the Model panel. In the Properties panel set the Motion Type to Prescribed and set the Angle Displacement to PrescribedPitch as shown below.
Because this continuation simulation will be focused on unsteady phenomena, we must adjust the time step and other factors to reflect a transient analysis. To do this, select the "Marine" module in the Model panel, and in the Properties panel change the Numerical Option to Medium (Transient) as shown below.
Finally, make sure you've loaded the results from the steady simulation into the model and that the Continuation Run radio button is selected in the Simulation panel as below. Note that it is good practices to save this continuation simulation with a new name to differentiate it from the initial simulation. Click the Start button to continue from the prior simulation with the new settings.
The resulting unsteady pitch behavior starting after 8 seconds can be seen below.
External Force/Moment
Another example of perturbing the steady state solution involves applying an external force and/or moment to a simulation for a fixed period of time. In this example we will apply a momentary pitching moment to a steady state resistance run to evaluate the dynamic pitch stability (i.e., porpoising stability) of a planing hull. Below we see the result of a resistance run at a speed of 25 kt, noting how the heave and pitch motion of the vessel has converged to steady state values.
To evaluate the pitch stability of the vessel in this condition, we will "bump" the model by applying a specified pitch moment for a specific amount of time. Before describing this process, we first disable the numerical heave and pitch damping in the simulation so that they don't affect the dynamic behavior of the design. To do this, in the Model panel select the "marineHeave" module and then in the Properties panel set the Damping Coefficient. Then do the same for "marinePitch" as shown below.
Next we define an expression for the pitching moment as a function of time in the Expression Editor. Open the Expression Editor and enter a formula like that shown below, where the startTime is the simulation time at which the moment should start and the endTime is that when the moment should return to zero. The start and end times, as well as the magnitude of the pitching moment, depend on the simulation and model you are running. The pitching moment should be large enough and be applied long enough to induce a reasonable pitch perturbation from the steady state so that you can check whether the vessel returns back to the steady solution, but not so large as to cause an unrealistic behavior. Generally a pitch angle perturbation of a few degrees might be representative of the boat passing over another boat's wake. This may take some trial and error to determine.
To apply this external pitching moment to the simulation, close the Expression Editor and select the "Marine" module in the Model panel. In the Property panel change the "Setup Options" to Extended Mode which reveals additional inputs for External Force and External Moment. As shown below, enter the expression, "externalPitchMoment" as the Y component of the External Torque.
The last thing to consider for this example is that whenever we are analyzing a dynamic behavior of the vessel, such as the vessel response to a perturbation from a steady state solution, it is a good idea to decrease the simulation time step. An easy way to do this is to change the "Numerical Option" of the Marine module to something more conservative than the default for steady state solutions (which is "Medium (Steady)"). In this example we've changed the setting to "Conservative (Steady)" which has the effect here of halving the time step and doubling the number of iterations.
All that is left to do now is to continue the simulation and observe the results. Make sure the results from the steady simulation are loaded and click the Start button to continue the simulation. As shown in the pitch time history below, the external pitch moment resulted in a perturbation of about 1 degree from the steady state solution. After the external moment was removed, the vessel returns to the steady state pitch angle very quickly indicating that the vessel is dynamically stable in pitch for this speed and load condition.
