Development of Measurement Methods for Testing of Hydrokinetic Devices to Evaluate the Environmental Effect on Local Substrate

Modifications and upgrades to the hydraulic flume facility in the Environmental Fluid Mechanics and Hydraulics Laboratory (EFM&H) at Bucknell University are described. These changes enable small-scale testing of model marine hydrokinetic(MHK) devices. The design of the experimental platform provides a controlled environment for testing of model MHK devices to determine their effect on localsubstrate. Specifically, the effects being studied are scour and erosion around a cylindrical support structure and deposition of sediment downstream from the device.

Energy harvesting through arterial wall deformation: A FEM approach to fluid–structure interactions and magneto-hydrodynamics

Engineers are confronted with the energy demand of active medical implants in patients with increasing life expectancy. Scavenging energy from the patient’s body is envisioned as an alternative to conventional power sources. Joining in this effort towards human-powered implants, we propose an innovative concept that combines the deformation of an artery resulting from the arterial pressure pulse with a transduction mechanism based on magneto-hydrodynamics. To overcome certain limitations of a preliminary analytical study on this topic, we demonstrate here a more accurate model of our generator by implementing a three-dimensional multiphysics finite element method (FEM) simulation combining solid mechanics, fluid mechanics, electric and magnetic fields as well as the corresponding couplings. This simulation is used to optimize the generator with respect to several design parameters. A first validation is obtained by comparing the results of the FEM simulation with those of the analytical approach adopted in our previous study. With an expected overall conversion efficiency of 20% and an average output power of 30 μW, our generator outperforms previous devices based on arterial wall deformation by more than two orders of magnitude. Most importantly, our generator provides sufficient power to supply a cardiac pacemaker.

Performance analysis of a miniature turbine generator for intracorporeal energy harvesting

Replacement intervals of implantable medical devices are commonly dictated by battery life. Therefore, intracorporeal energy harvesting has the potential to reduce the number of surgical interventions by extending the life cycle of active devices. Given the accumulated experience with intravascular devices such as stents, heart valves, and cardiac assist devices, the idea to harvest a small fraction of the hydraulic energy available in the cardiovascular circulation is revisited. The aim of this article is to explore the technical feasibility of harvesting 1 mW electric power using a miniature hydrodynamic turbine powered by about 1% of the cardiac output flow in a peripheral artery. To this end, numerical modelling of the fluid mechanics and experimental verification of the overall performance of a 1:1 scale friction turbine are performed in vitro. The numerical flow model is validated for a range of turbine configurations and flow conditions (up to 250 mL/min) in terms of hydromechanic efficiency; up to 15% could be achieved with the nonoptimized configurations of the study. Although this article does not entail the clinical feasibility of intravascular turbines in terms of hemocompatibility and impact on the circulatory system, the numerical model does provide first estimates of the mechanical shear forces relevant to blood trauma and platelet activation. It is concluded that the time-integrated shear stress exposure is significantly lower than in cardiac assist devices due to lower flow velocities and predominantly laminar flow.

Primary Oil Migration Through Buoyancy-Driven Multiple Fracture Propagation: Oil Velocity and Flux

We present a fracture-mechanics-based formulation to investigate primary oil migration through the propagation of an array of periodic, parallel fractures in a sedimentary rock with elevated pore fluid pressure. The rock is assumed to be a linearly elastic medium. The fracture propagation and hence oil migration velocity are determined using a fracture mechanics criterion together with the lubrication theory of fluid mechanics. We find that fracture interactions have profound effects on the primary oil migration behavior. For a given fracture length, the mass flux of oil migration decreases dramatically with an increase in fracture density. The reduced oil flux is due to the decreased fracture propagation velocity as well as the narrowed fracture opening that result from the fracture interactions.

Steady streaming in a two-dimensional box model of a passive cochlea

Acoustic stimulation of the cochlea leads to a travelling wave in the cochlear fluids and on the basilar membrane (BM). It has long been suspected that this travelling wave leads to a steady streaming flow in the cochlea. Theoretical investigations suggested that the steady streaming might be of physiological relevance. Here, we present a quantitative study of the steady streaming in a computational model of a passive cochlea. The structure of the streaming flow is illustrated and the sources of streaming are closely investigated. We describe a source of streaming which has not been considered in the cochlea by previous authors. This source is also related to a steady axial displacement of the BM which leads to a local stretching of this compliant structure. We present theoretical predictions for the streaming intensity which account for these new phenomena. It is shown that these predictions compare well with our numerical results and that there may be steady streaming velocities of the order of millimetres per second. Our results indicate that steady streaming should be more relevant to low-frequency hearing because the strength of the streaming flow rapidly decreases for higher frequencies.

Electric current of an electrified jet issuing from a long metallic tube.

This paper presents an analysis of the transport of electric current in a jet of an electrically conducting liquid discharging from a metallic tube into a gas or a vacuum, and subject to an electric field due to a high voltage applied between the tube and a far electrode. The flow, the surface charge and the electric field are computed in the current transfer region of the jet, where conduction current in the liquid becomes surface current due to the convection of electric charge accumulated at its surface. The electric current computed as a function of the flow rate of the liquid injected through the tube increases first as the square root of this flow rate, levels to a nearly constant value when the flow rate is increased and finally sets to a linear increase when the flow rate is further increased. The current increases linearly with the applied voltage at small and moderate values of this variable, and faster than linearly at high voltages. The characteristic length and structure of the current transfer region are determined. Order-of-magnitude estimates for jets which are only weakly stretched by the electric stresses are worked out that qualitatively account for some of the numerical results.

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.

The scenario of two-dimensional instabilities of the cylinder wake under EHD forcing: A linear stability analysis

We propose to study the stability properties of an air flow wake forced by a dielectric barrier discharge (DBD) actuator, which is a type of electrohydrodynamic (EHD) actuator. These actuators add momentum to the flow around a cylinder in regions close to the wall and, in our case, are symmetrically disposed near the boundary layer separation point. Since the forcing frequencies, typical of DBD, are much higher than the natural shedding frequency of the flow, we will be considering the forcing actuation as stationary. In the first part, the flow around a circular cylinder modified by EHD actuators will be experimentally studied by means of particle image velocimetry (PIV). In the second part, the EHD actuators have been numerically implemented as a boundary condition on the cylinder surface. Using this boundary condition, the computationally obtained base flow is then compared with the experimental one in order to relate the control parameters from both methodologies. After validating the obtained agreement, we study the Hopf bifurcation that appears once the flow starts the vortex shedding through experimental and computational approaches. For the base flow derived from experimentally obtained snapshots, we monitor the evolution of the velocity amplitude oscillations. As to the computationally obtained base flow, its stability is analyzed by solving a global eigenvalue problem obtained from the linearized Navier–Stokes equations. Finally, the critical parameters obtained from both approaches are compared.

Towards the foundation of a global modes concept

A contribution is presented, intended to provide theoretical foundations for the ongoing efforts to employ global instability theory for the analysis of the classic boundary-layer flow, and address the associated issue of appropriate inflow/outflow boundary conditions to close the PDE-based global eigenvalue problem in open flows. Starting from a theoretically clean and numerically simple application, in which results are also known analytically and thus serve as a guidance for the assessment of the performance of the numerical methods employed herein, a sequence of issues is systematically built into the target application, until we arrive at one representative of open systems whose instability is presently addressed by global linear theory applied to open flows, the latter application being neither tractable theoretically nor straightforward to solve by numerical means. Experience gained along the way is documented. It regards quantification of the depar- ture of the numerical solution from the analytical one in the simple problem, the generation of numerical boundary layers at artificially truncated boundaries, no matter how far the latter are placed from the region of highest flow gradients and, ultimately the impracti- cally large number of (direct and adjoint) modes necessary to project an arbitrary initial perturbation and follow its temporal evolution by a global analysis approach, a finding which may question the purported robustness reported in the literature of the recovery of optimal perturbations as part of global analyses yielding under-resolved eigenspectra.

Effect of Aspect Ratio on the Three-Dimensional Global Instability Analysis of Incompressible Open Cavity Flows

The stability analysis of open cavity flows is a problem of great interest in the aeronautical industry. This type of flow can appear, for example, in landing gears or auxiliary power unit configurations. Open cavity flows is very sensitive to any change in the configuration, either physical (incoming boundary layer, Reynolds or Mach numbers) or geometrical (length to depth and length to width ratio). In this work, we have focused on the effect of geometry and of the Reynolds number on the stability properties of a threedimensional spanwise periodic cavity flow in the incompressible limit. To that end, BiGlobal analysis is used to investigate the instabilities in this configuration. The basic flow is obtained by the numerical integration of the Navier-Stokes equations with laminar boundary layers imposed upstream. The 3D perturbation, assumed to be periodic in the spanwise direction, is obtained as the solution of the global eigenvalue problem. A parametric study has been performed, analyzing the stability of the flow under variation of the Reynolds number, the L/D ratio of the cavity, and the spanwise wavenumber β. For consistency, multidomain high order numerical schemes have been used in all the computations, either basic flow or eigenvalue problems. The results allow to define the neutral curves in the range of L/D = 1 to L/D = 3. A scaling relating the frequency of the eigenmodes and the length to depth ratio is provided, based on the analysis results.

Linear instability of orthogonal compressible leading-edge boundary layer flow

Instability analysis of compressible orthogonal swept leading-edge boundary layer flow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to efficiently analyze the effect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this flow as a function of the Mach number in the range 0 ≤ Ma ≤ 1. The present numerical results fully confirmed the asymptotic theory results of Theofilis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.

The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension

The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order finitedifference-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of efficiency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity offered by the finite-difference scheme and, as expected, is shown to perform substantially more efficiently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the flow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic flow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional flow composed of a counter-rotating pair of nonparallel Batchelor vortices.

Coupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometries

The development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and finite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantified. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base flow do not have affect significantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on finite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshes

Wave-like Disturbances on the Downstream Wall of an Open Cavity

This contribution presents results of an incompressible two-dimensional flow over an open cavity of fixed aspect ratio (length/depth) L/D = 2 and the coupling between the three dimensional low frequency oscillation mode confined in the cavity and the wave-like disturbances evolving on the downstream wall of the cavity in the form of Tollmien-Schlichting waves. BiGlobal instability analysis is conducted to search the global disturbances superimposed upon a two-dimensional steady basic flow. The base solution is computed by the integration of the laminar Navier-Stokes equations in primitive variable formulation, while the eigenvalue problem (EVP) derived from the discretization of the linearized equations of motion in the BiGlobal framework is solved using an iterative procedure. The formulation of the BiGlobal EVP for the unbounded flow in the open cavity problem introduces additional difficulties regarding the flow-through boundaries. Local analysis has been utilized for the determination of the proper boundary conditions in the upper limit of the downstream region

A regular perturbation approach to surface tension driven flows

Surface tension induced convection in a liquid bridge held between two parallel, coaxial, solid disks is considered. The surface tension gradient is produced by a small temperature gradient parallel Co the undisturbed surface. The study is performed by using a mathematical regular perturbation approach based on a small parameter, e, which measures the deviation of the imposed temperature field from its mean value. The first order velocity field is given by a Stokes-type problem (viscous terms are dominant) with relatively simple boundary conditions. The first order temperature field is that imposed from the end disks on a liquid bridge immersed in a non-conductive fluid. Radiative effects are supposed to be negligible. The second order temperature field, which accounts for convective effects, is split into three components, one due to the bulk motion, and the other two to the distortion of the free surface. The relative importance of these components in terms of the heat transfer to or from the end disks is assessed