Six-Degree-of-Freedom Sensor Fish Design: Governing Equations and Motion Modeling

Abstract

The Sensor Fish device is being used at Northwest hydropower projects to better understand the conditions fish experience during passage through hydroturbines and other dam bypass alternatives. Since its initial development in 1997, the Sensor Fish has undergone numerous design changes to improve its function and extend the range of its use. The most recent Sensor Fish design, the three degree of freedom (3DOF) device, has been used successfully to characterize the environment fish experience when passing through turbines, in spill, or in engineered fish bypass facilities at dams. Pacific Northwest National Laboratory (PNNL) is in the process of redesigning the current 3DOF Sensor Fish device package to improve its field performance. Rate gyros will be added to the new six degree of freedom (6DOF) device so that it will be possible to observe the six linear and angular accelerations of the Sensor Fish as it passes the dam. Before the 6DOF Sensor Fish device can be developed and deployed, governing equations of motion must be developed in order to understand the design implications of instrument selection and placement within the body of the device. In this report, we describe a fairly general formulation for the coordinate systems, equations of motion, force and moment relationships necessary to simulate the 6DOF movement of an underwater body. Some simplifications are made by considering the Sensor Fish device to be a rigid, axisymmetric body. The equations of motion are written in the body-fixed frame of reference. Transformations between the body-fixed and interial reference frames are performed using a formulation based on quaternions. Force and moment relationships specific to the Sensor Fish body are currently not available. However, examples of the trajectory simulations using the 6DOF equations are presented using existing low and high-Reynolds number force and moment correlations. Animation files for the test cases are provided in an attached CD. The next phase of the work will focus on the refinement and application of the 6DOF simulator developed in this project. Experimental and computational studies are planned to develop a set of force and moment relationships that are specific to the Sensor Fish body over the range of Reynolds numbers that it experiences. Lab testing of prototype 6DOF Sensor Fish will also allow for refinement of the trajectory simulations through comparison with observations in test flumes. The 6DOF simulator will also be an essential component in tools to analyze field data measured using the next generation Sensor Fish. The 6DOF simulator will be embedded in a moving-machinery computational fluid dynamics (CFD) model for hydroturbines to numerically simulate the 6DOF Sensor Fish.