Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userScaling Laws for the Propulsive Performance of Three-Dimensional Pitching Propulsors
74
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn (2018) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor, and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a range of reduced frequencies, Strouhal numbers and aspect ratios relevant to bio-inspired propulsion. The scaling laws elucidate the dominant flow physics behind the thrust production and energetics of pitching bio-propulsors, and they provide guidance for the design of bio-inspired propulsive systems.
rate research
Read More
Scaling laws for the thrust production and power consumption of a purely pitching hydrofoil in ground effect are presented. For the first time, ground effect scaling laws based on physical insights capture the propulsive performance over a wide range of biologically-relevant Strouhal numbers, dimensionless amplitudes, and dimensionless ground distances. This is achieved by advancing previous scaling laws (Moored & Quinn 2018) with physics-driven modifications to the added mass and circulatory forces to account for ground distance variations. The key physics introduced are the increase in the added mass of a foil near the ground and the reduction in the influence of a wake vortex system due to the influence of its image system. The scaling laws are found to be in good agreement with new inviscid simulations and viscous experiments, and can be used to accelerate the design of bio-inspired hydrofoils that oscillate near a ground plane or two out-of-phase foils in a side-by-side arrangement.
Inviscid computational results are presented on a self-propelled virtual body combined with an airfoil undergoing pitch oscillations about its leading-edge. The scaling trends of the time-averaged thrust forces are shown to be predicted accurately by Garricks theory. However, the scaling of the time-averaged power for finite amplitude motions is shown to deviate from the theory. Novel time-averaged power scalings are presented that account for a contribution from added-mass forces, from the large-amplitude separating shear layer at the trailing-edge, and from the proximity of the trailing-edge vortex. Scaling laws for the self-propelled speed, efficiency and cost of transport ($CoT$) are subsequently derived. Using these scaling relations the self-propelled metrics can be predicted to within 5% of their full-scale values by using parameters known a priori. The relations may be used to drastically speed-up the design phase of bio-inspired propulsion systems by offering a direct link between design parameters and the expected $CoT$. The scaling relations also offer one of the first mechanistic rationales for the scaling of the energetics of self-propelled swimming. Specifically, the cost of transport is shown to scale predominately with the added mass power. This suggests that the $CoT$ of organisms or vehicles using unsteady propulsion will scale with their mass as $CoT propto m^{-1/3}$, which is indeed shown to be consistent with existing biological data.
We formulate multifractal models for velocity differences and gradients which describe the full range of length scales in turbulent flow, namely: laminar, dissipation, inertial, and stirring ranges. The models subsume existing models of inertial range turbulence. In the localized ranges of length scales in which the turbulence is only partially developed, we propose multifractal scaling laws with scaling exponents modified from their inertial range values. In local regions, even within a fully developed turbulent flow, the turbulence is not isotropic nor scale invariant due to the influence of larger turbulent structures (or their absence). For this reason, turbulence that is not fully developed is an important issue which inertial range study can not address. In the ranges of partially developed turbulence, the flow can be far from universal, so that standard inertial range turbulence scaling models become inapplicable. The model proposed here serves as a replacement.Details of the fitting of the parameters for the $tau_p$ and $zeta_p$ models in the dissipation range are discussed. Some of the behavior of $zeta_p$ for larger $p$ is unexplained. The theories are verified by comparing to high resolution simulation data.
An unsupervised machine learning strategy is developed to automatically cluster the vortex wakes of bio-inspired propulsors into groups of similar propulsive thrust and efficiency metrics. A pitching and heaving foil is simulated via computational fluid dynamics with $121$ unique kinematics by varying the frequency, heaving amplitude, and pitching amplitude. A Reynolds averaged Navier-Stokes (RANS) model is employed to simulate the flow over the oscillating foils at $Re=10^6$, computing the propulsive efficiency, thrust coefficient and the unsteady vorticity wake signature. Using a pairwise Pearson correlation it is found that the Strouhal number most strongly influences the thrust coefficient, whereas the relative angle of attack, defined by both the mid-stroke and maximum have the most significant impact on propulsive efficiency. Next, the various kinematics are automatically clustered into distinct groups exclusively using the vorticity footprint in the wake. A convolutional autoencoder is developed to reduce vortex wake images to their most significant features, and a k-means++ algorithm performs the clustering. The results are assessed by comparing clusters to a thrust versus propulsive efficiency map, which confirms that wakes of similar performance metrics are successfully clustered together. This automated clustering has the potential to identify complex vorticity patterns in the wake and modes of propulsion not easily discerned from traditional classification methods.
Following the idea that dissipation in turbulence at high Reynolds number is by events singular in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows scaling laws should depend only on quantities appearing in the Euler equations. This excludes viscosity or a turbulent length as scaling parameters and constrains drastically possible analytical pictures of this limit. We focus on the law of drag by Newton for a projectile moving quickly in a fluid at rest. Inspired by the Newtons drag force law (proportional to the square of the speed of the moving object in the limit of large Reynolds numbers), which is well verified in experiments when the location of the detachment of the boundary layer is defined, we propose an explicit relationship between Reynoldss stress in the turbulent wake and quantities depending on the velocity field (averaged in time but depending on space), in the form of an integro-differential equation for the velocity which is solved for a Poiseuille flow in a circular pipe.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
