Chun-I Chen

Unsteady unidirectional flow of second grade fluid between the parallel plates with different given volume flow rate conditions

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of second grade fluids between the parallel plates are considered. The flow motion in the plates is induced by a given but arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved, which are a sudden started and a constant acceleration flow, respectively. Then we apply these two results to a practical case that is a trapezoidal piston motion which contains three phases of piston motion, the constant acceleration from the rest to a fixed velocity, then keeping at this velocity, following with the constant deceleration to a stop. In addition, the oscillatory flow is also considered.

Weakly nonlinear stability analysis of thin viscoelastic film flowing down on the outer surface of a rotating vertical cylinder

Abstract The paper presents both of the linear and nonlinear stability theories for characterization of viscoelastic film flows down on the outer surface of a rotating infinite vertical cylinder. After showing the insufficiency of the linear model in characterizing certain flow behaviors, a generalized nonlinear kinematic model is then derived to represent the physical system. The model is solved by the long wave perturbation method in a two-step procedure. In the first step, the normal mode method is used to characterize the linear behaviors. The amplitude growth rates and the threshold conditions are characterized subsequently and summarized as the by-products of the linear solutions. In the second step, an elaborated nonlinear film flow model is solved by using the method of multiple scales to characterize flow behaviors at various states of sub-critical stability, sub-critical instability, supercritical stability, and supercritical explosion. The modeling results indicate that by increasing the rotation speed, Ω , and decreasing the radius of cylinder, R , the film flow will generally make the flow system less stable. In this study, the interaction of the rotation and the radius of cylinder are taken into account. Generally, Reynolds number is divided into three regions, which are Re Re Re , for discussion corresponding to the pre-selected Rossby number ( Ro =0.1) and viscoelastic parameter ( k =0.05).

Analysis of unsteady flow through a microtube with wall slip and given inlet volume flow rate variations

This study examines the effects of rarefaction of an unsteady flow through a microtube for a given but arbitrary inlet volume flow rate. Four cases of inlet volume flow rate proposed by Das and Arakeri (2000, ASME J. Appl. Mech., 67, pp. 274-281) are as follows: (1) trapezoidal piston motion, (2) constant acceleration, (3) impulsively started flow, and (4) impulsively blocked fully developed flow. During the analysis process, the Knudsen number (Kn) is used to represent the degree of rarefaction. The analytical results are presented graphically and compared to the results for a continuum under a no-slip condition. The effect of wall-slip became significant with the increasing degrees of rarefaction. The velocity in the boundary layer increased, whereas the velocity in the potential core of the microtube decreased, under the same condition. The influence of the rarefaction for the pressure gradient varied for the four cases.

Unsteady unidirectional flow of a Voigt fluid between the parallel surfaces with different given volume flow rate conditions

In this paper, the velocity profile and pressure gradient of the unsteady state unidirectional flow of a Voigt fluid between the parallel surfaces are considered. The flow motion between the surfaces is induced by a prescribed arbitrary inlet volume flow rate which varies with time. Based on the flow conditions described, two basic flow situations are solved; these are a suddenly started, and a constant acceleration, flow respectively. These two results are applied to a practical case that is a trapezoidal motion. In addition, oscillatory flow is also considered.

A computer-aided method for solvents and spectral factors of matrix polynomials

A new approach for determining the complete sets of solvents and spectral factors of a monic matrix polynomial is proposed. A systematic method for determining the initial guess for the extended multidimensional Newton-Raphson method is first proposed, such that the eigenspectrum corresponding to each solvent of the matrix polynomial can be determined. With the evaluated eigenspectra, complete sets of solvents and spectral factors of a monic matrix polynomial can be obtained by utilizing the applications and the advantages of the principal-nth-root method, the matrix sign function, and the block-power method. The established algorithms can be applied in the analysis and/or design of systems described by high-degree vector differential equations and/or matrix fractions.

Modelling of multirate feedback systems using uniform-rate models

Abstract A new method is proposed to analyze a multirate feedback system by reducing it to an equivalent uniform- rate feedback system. The solution is essentially based on the developments of state-space model conversions in closed-loop systems with multiple rates. Either a slow-rate controlled system with a fast- rate feedback or a fast-rate controlled system with a slow-rate feedback is modeled by state-space expressions with either a unified slow-rate frame or a unified fast-rate frame. It is shown that the proposed method is suitable for computer programming and convenient for analysis and design of multirate sampled-data control systems.

Digital modelling, ideal state reconstructor, and control for time-delay sampled-data systems

The cascaded discrete-time state-space representation of a cascaded continuous-time system with fractional input delays is established. Based on the time-delay digital modelling, a practically imple-mentable ideal state reconstructor is also established such that system states are exactly reconstructed via the measurement histories of inputs and outputs without a state observer. By utilizing the block-pulse function approximation the digital modelling of cascaded continuous-time systems with fractional input delays can be carried out, and an artificial input design method is proposed to determine the state feedback gain. Thus the practically implementable digital control law can be established for digital control of time-delay sampled-data systems. An illustrative example is shown to demonstrate the effectiveness of the proposed method.