Session: 03-02-01 Bio-Inspired and Biomedical Fluid Mechanics

Paper Number: 87219

87219 - Onto Quantifying Unsteady Propulsion Characteristics Using Momentum and Energy Control Volume Assessments 

Propulsion through deforming and oscillating bodies is a highly unsteady process and directly relates to natural propulsion of fish and other marine animals. The quantification of these processes is challenged due to the coupled behavior of both thrust and drag, which drives a need to develop new methods to assess the hydrodynamics. The application of control volumes (CV) are common to assess fluid systems to measure fluid dynamic forces relevant to experimental limitations. That is, they are commonly used to infer difficult or costly measurements. Aside from measuring forces, control volume assessments also pose the capability to examine the transport of momentum and energy within a fluid dynamic system which has value in the context of physically understanding these systems. Unlike the conservation of momentum, which provides insight to reactionary forces, the conservation of energy provides information on body forces as a function of fluid dynamic losses. In this sense, balancing energy provides a less ambiguous description of body forces relative to the conservation of momentum. Although most convention suggests the results should be identical, the authors recently published results indicating that strategic assessments provide the ability to isolate types of forces (such as separate induced drag from profile drag). The use of the energy equation to examine body forces has already been examined for steady fluid systems; however, less is known of the energy equation regarding measuring body forces of unsteady systems. This effort seeks to expand the use of energy-based control volume assessments for measuring time-dependent forces.

There are several challenges associated with developing this novel assessment methodology. Firstly, CV assessments require extensive knowledge of the flow field. Secondly, there needs to be an accurate benchmark to which we can compare our assessment methodology. The first challenge naturally pairs with a numerical framework such as Computational Fluid Dynamics (CFD). It is proposed that utilizing CV analyses with detailed information provided from CFD can provide additional insight into unsteady processes relevant to how fish swim. The second challenge is addressed through two-approaches. The first is drawn from the spirit of the Method of Manufactured Solutions (MMS). We formulate an analytic result by prescribing momentum source terms to model periodic body forces to simplify the dynamic body, its subsequent grid requirements, and enables direct verification of the processes. The second approach involves comparing the energy balance to a conventional momentum balance. By making this comparison, we provide a physical validation for the energy equation to identify body forces.

The proposed paper explores time varying, spatial descriptions of body forces into a CFD model that are assessed through CV assessments. This is proposed as a proxy relevant to more complex scenarios such as the propulsion of a fish. The results from the body force model will be compared to benchmarks to assess the usability of this approach. In the context of an isothermal flow, the paper will also develop detailed comparisons of differences in the momentum and energy equation CV assessments to describe the benefits of assessing energy conservation for these unsteady fluid dynamic systems.

The final paper will present the derivation of our control volume approach along with a description of the simplified benchmark. A grid-refinement study will be used to reduce numerical uncertainty. The derivation of body forces using the energy equation shall be shown followed by results of the application of this methodology. These results will be compared against the benchmark and against the momentum balance. Finally, a discussion on the applicability of the energy equation will be had followed by conclusions.

Presenting Author: George Loubimov University of Central Florida