Simulation and control of a stepping motor

Open-loop operatlon of the stepping motor exploits the inherent advantages of the machine. For near optimum operation: in this mode, however, an accurate system model is required to facilitate controller design. Such a model must be comprehensive and take account of the non-linearities inherent in the system. The result is a complex formulation which can be made manageable with a computational aid. A digital simulation of a hybrid type stepping motor and its associated drive circuit is proposed. The simulation is based upon a block diagram model which includes reasonable approximations to the major non-linearities. The simulation is shown to yield accurate performance predictions. The determination of the transfer functions is based upon the consideration of the physical processes involved rather than upon direct input-outout measurements. The effects of eddy currents, saturation, hysteresis, drive circuit characteristics and non-linear torque displacement characteristics are considered and methods of determining transfer functions, which take account of these effects, are offered. The static torque displacement characteristic is considered in detail and a model is proposed which predicts static torque for any combination of phase currents and shaft position. Methods of predicting the characteristic directly from machine geometry are investigated. Drive circuit design for high efficiency operation is considered and a model of a bipolar, bilevel circuit is proposed. The transfers between stator voltage and stator current and between stator current and air gap flux are complicated by the effects of eddy currents, saturation and hysteresis. Frequency response methods, combined with average inductance measurements, are shown to yield reasonable transfer functions. The modelling procedure and subsequent digital simulation is concluded to be a powerful method of non-linear analysis.

Transition in inclined internally heated fluid layers

Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

Mechanisms of heat and mass transfer to and from single drops freely-suspended in an air stream

A specially-designed vertical wind tunnel was used to freely suspend individual liquid drops of 5 mm initial diameter to investigate drop dynamics, terminal velocity and heat and mass transfer rates. Droplets of distilled, de-ionised water, n-propanol, iso-butanol, monoethanolamine and heptane were studied over a temperature range of 50oC to 82oC. The effects of substances that may provide drop surface rigidity (e.g. surface active agents, binders and polymers) on mass transfer rates were investigated by doping distilled de-ionised water drops with sodium di-octyl sulfo-succinate surfactant. Mass transfer rates decreased with reduced drop oscillation as a result of surfactant addition, confirming the importance of droplet surface instability. Rigid naphthalene spheres and drops which formed a skin were also studied; the results confirmed the reduced transfer rates in the absence of drop fluidity. Following consideration of fundamental drop dynamics in air and experimental results from this study, a novel dimensionless group, the Oteng-Attakora, (OT), number was included in the mass transfer equation to account for droplet surface behaviour and for prediction of heat and mass transfer rates from single drops which exhibit surface instability at Re>=500. The OT number and the modified mass transfer equation are respectively: OT=(ava2/d).de1.5(d/) Sh = 2 + 0.02OT0.15Re0.88Sc0.33 Under all conditions drop terminal velocity increased linearly with the square root of drop diameter and the drag coefficient was 1. The data were correlated with a modified equation by Finlay as follows: CD=0.237.((Re/P0.13)1.55(1/We.P0.13) The relevance of the new model to practical evaporative spray processes is discussed.

Heat and mass transfer in membrane distillation used for desalination with slip flow

A theoretical model for the transport phenomena in an air gap membrane distillation is presented. The model is based on the conservation equations for the mass, momentum, energy and species within the feed water solution as well as on the mass and energy balances on the membrane sides. The slip flow occurs due to the hydrophobic properties of the membrane. The slip boundary condition applied on the feed saline solution-membrane interface is taken into consideration showing its effects on process parameters particularly permeate flow, heat transfer coefficient and thermal efficiency. The theoretical model was validated with available experimental data and was found to be in good agreement especially when the slip condition is introduced. Increasing slip length from zero to 200 μm was found to increase the permeate flux and the thermal efficiency by 33% and 1.7% respectively.