A mathematical model for the doubly-fed wound rotor generator, part 2

A mathematical analysis of a doubly-fed wound rotor generator is presented. The constraints of constant stator voltage and frequency to the circuit equations were applied and expressions for the currents and voltages in the machine obtained. The derived variables are redefined as direct and quadrature components. In addition, the apparent (complex) power for both the rotor and the stator are derived in terms of these redefined components

Description and test results of a variable speed, constant frequency generating system

The variable-speed, constant frequency generating system developed for the Mod-0 wind turbine is presented. This report describes the system as it existed at the conclusion of the project. The cycloconverter control circuit is described including the addition of field-oriented control. The laboratory test and actual wind turbine test results are included

The spatial stability of a class of similarity solutions

The spatial stability of a class of exact similarity solutions of the Navier–Stokes equations whose longitudinal velocity is of the form xf′(y), where x is the streamwise coordinate and f′(y) is a function of the transverse, cross‐streamwise, coordinate y only, is determined. These similarity solutions correspond to the flow in an infinitely long channel or tube whose surface is either uniformly porous or moves with a velocity linear in x. Small perturbations to the streamwise velocity of the form x^λg′(y) are assumed, resulting in an eigenvalue problem for λ which is solved numerically. For the porous wall problem, it is shown that similarity solutions in which f′(y) is a monotonic function of y are spatially stable, while those that are not monotonic are spatially unstable. For the accelerating‐wall problem, the interpretation of the stability results is not unambiguous and two interpretations are offered. In one interpretation the conclusions are the same as for the porous problem—monotonic solutions are stable; the second interpretation is more restrictive in that some of the monotonic as well as the nonmonotonic solutions are unstable

Analysis of the Brinkman equation as a model for flow in porous media

The fundamental solution or Green's function for flow in porous media is determined using Stokesian dynamics, a molecular-dynamics-like simulation method capable of describing the motions and forces of hydrodynamically interacting particles in Stokes flow. By evaluating the velocity disturbance caused by a source particle on field particles located throughout a monodisperse porous medium at a given value of volume fraction of solids ø, and by considering many such realizations of the (random) porous medium, the fundamental solution is determined. Comparison of this fundamental solution with the Green's function of the Brinkman equation shows that the Brinkman equation accurately describes the flow in porous media for volume fractions below 0.05. For larger volume fractions significant differences between the two exist, indicating that the Brinkman equation has lost detailed predictive value, although it still describes qualitatively the behavior in moderately concentrated porous media. At low ø where the Brinkman equation is known to be valid, the agreement between the simulation results and the Brinkman equation demonstrates that the Stokesian dynamics method correctly captures the screening characteristic of porous media. The simulation results for ø ≥ 0.05 may be useful as a basis of comparison for future theoretical work

The pressure moments for two rigid spheres in low-Reynolds-number flow

The pressure moment of a rigid particle is defined to be the trace of the first moment of the surface stress acting on the particle. A Faxén law for the pressure moment of one spherical particle in a general low-Reynolds-number flow is found in terms of the ambient pressure, and the pressure moments of two rigid spheres immersed in a linear ambient flow are calculated using multipole expansions and lubrication theory. The results are expressed in terms of resistance functions, following the practice established in other interaction studies. The osmotic pressure in a dilute colloidal suspension at small Péclet number is then calculated, to second order in particle volume fraction, using these resistance functions. In a second application of the pressure moment, the suspension or particle-phase pressure, used in two-phase flow modeling, is calculated using Stokesian dynamics and results for the suspension pressure for a sheared cubic lattice are reported

Dynamic simulation of an electrorheological fluid

A molecular-dynamics-like method is presented for the simulation of a suspension of dielectric particles in a nonconductive solvent forming an electrorheological fluid. The method accurately accounts for both hydrodynamic and electrostatic interparticle interactions from dilute volume fractions to closest packing for simultaneous shear and electric fields. The hydrodynamic interactions and rheology are determined with the Stokesian dynamics methodology, while the electrostatic interactions, in particular, the conservative electrostatic interparticle forces, are determined from the electrostatic energy of the suspension. The energy of the suspension is computed from the induced particle dipoles by a method previously developed [R. T. Bonnecaze and J. F. Brady, Proc. R. Soc. London, Ser. A 430, 285 (1990)]. Using the simulation, the dynamics can be directly correlated to the observed macroscopic rheology of the suspension for a range of the so-called Mason number, Ma, the ratio of viscous to electrostatic forces. The simulation is specifically applied to a monolayer of spherical particles of areal fraction 0.4 with a particle-to-fluid dielectric constant ratio of 4 for Ma=10^−4 to [infinity]. The effective viscosity of the suspension increases as Ma^−1 or with the square of the electric field for small Ma and has a plateau value at large Ma, as is observed experimentally. This rheological behavior can be interpreted as Bingham plastic-like with a dynamic yield stress. The first normal stress difference is negative, and its magnitude increases as Ma^−1 at small Ma with a large Ma plateau value of zero. In addition to the time averages of the rheology, the time traces of the viscosities are presented along with selected "snapshots" of the suspension microstructure. In particular, at small Ma, the suspension dynamics exhibit two distinct motions: a slow elastic-body-like deformation where electrostatic energy is stored, followed by a rapid microstructural rearrangement where energy is viscously dissipated. It is suggested that the observed dynamic yield stress is associated with these dynamics

The non-Newtonian rheology of dilute colloidal suspensions

The non-Newtonian rheology is calculated numerically to second order in the volume fraction in steady simple shear flows for Brownian hard spheres in the presence of hydrodynamic and excluded volume interactions. Previous analytical and numerical results for the low-shear structure and rheology are confirmed, demonstrating that the viscosity shear thins proportional to Pe2, where Pe is the dimensionless shear rate or Péclet number, owing to the decreasing contribution of Brownian forces to the viscosity. In the large Pe limit, remnants of Brownian diffusion balance convection in a boundary-layer in the compressive region of the flow. In consequence, the viscosity shear thickens when this boundary-layer coincides with the near-contact lubrication regime of the hydrodynamic interaction. Wakes are formed at large Pe in the extensional zone downstream from the reference particle, leading to broken symmetry in the pair correlation function. As a result of this asymmetry and that in the boundary-layer, finite normal stress differences are obtained as well as positive departures in the generalized osmotic pressure from its equilibrium value. The first normal stress difference changes from positive to negative values as Pe is increased when the hard-sphere limit is approached. This unusual effect is caused by the hydrodynamic lubrication forces that maintain particles in close proximity well into the extensional quadrant of the flow. The study demonstrates that many of the non-Newtonian effects observed in concentrated suspensions by experiments and by Stokesian dynamics simulations are present also in dilute suspensions

Force on a sphere via the generalized reciprocal theorem

An approach based on the generalized reciprocal theorem is presented to derive the well-known result for the drag force exerted on a rigid sphere translating in a viscous fluid in an arbitrary manner. The use of generalized reciprocal theorem allows one to bypass the calculation of stress distribution over the particle surface in order to compute the force

Sterilizable liquid propulsion system Quarterly progress report, Oct. 1 - Dec. 31, 1967

Exposure of assembled and fueled bipropellant liquid rocket propulsion system to ethylene oxide and heat sterilization environment