Free PDF Ebooks Files @AcrobatPlanet.Com

Variational integrators are a class of discretizations for mechanical systems which are derived by discretizing Hamilton's principle of stationary action. They are applicable to both ordinary and partial differential equations, and to both conservative and forced problems. In the absence of forcing they conserve (multi-)symplectic structures, momenta arising from symmetries, and energy up to a bounded error.

Experimental measurements of the particle pressure were obtained for a liquid fluidized bed and for a vertical gravity driven liquid-solid flow. The particle, or granular, pressure is defined as the extra pressure generated by the action of particles in a particulate multi-phase flow. Using a high-frequency-response pressure transducer, individual collisions of particles were collected and measured to obtain a time-averaged particle pressure. Results were obtained for a number of different particles and for two different test section diameters. Results show that the particle pressure experiences a maximum at intermediate concentrations, and that its magnitude is scaled with the particle density and the square of the terminal velocity of the particles. The particle pressure was found to be composed of two main contributions: one from pressure pulses generated by direct collisions of particles against the containing walls (direct component), and a second one from pressure pulses due to collisions between individual particles that are transmitted through the liquid (radiated component).

Granular materials flowing down an inclined chute were studied experimentally and analytically. Characteristics of convective heat transfer to granular flows were also investigated experimentally and numerically. Experiments on continuous, steady flows of granular materials in an inclined chute were conducted with the objectives of understanding the characteristics of chute flows and of acquiring information on the rheological behavior of granular material flow. Two neighboring fibre optic displacement probes were employed to measure mean velocity, one component of velocity fluctuations, and linear concentration at the wall and free surface boundaries. A shear gauge was also developed to make direct measurement of shear stress at the chute base. Measurements of solid fraction, velocity, shear rate, and velocity fluctuations were analyzed to understand the chute flow characteristics, and the rheological behavior of granular materials was studied with the present experimental data. The vertical profiles of mean velocity, velocity fluctuation, and solid fraction were also obtained at the sidewalls.

An experimental and theoretical investigation on a series of three centrifugal pump impellers has been made in order to determine the usefulness and validity of tyro-dimensional potential theory for the description of the flow.