Singular system theory applied to the evaporator dynamics of a once - through subcritical steam generator: The differential discrete mathematical modeling based approach

A dynamic thermal-hydraulic mathematical model of the evaporator dynamics of a once - through sub critical steam generator was derived and presented. This model allows the investigation of evaporator dynamics including its transient responses. The evaporator was considered as part of a three-section (economizer, evaporator and super-heater) model with time varying phase boundaries and was described by a set of linearized discrete - difference equations which, with some other algebraic equations, constituted a closed system of equations possible for exact computer solution. This model was derived using the fundamental equations of mass, energy and momentum balance. For the first time, a discrete differential approach was applied in order to investigate such complex, two phase processes. Namely, this approach allows one to escape from the model of this process usually described by a set of partial differential equations and enables one, using this method, to simulate evaporator dynamics in an extraordinarily simple way. In the current literature this approach is sometimes called physical discretization.

High Order Subharmonic Response of High Speed Rotors in Bearing Clearance

Subharmonic vibration refers to the response of a dynamic system to excitation at a whole-number multiple (n) of its natural frequency by vibrating asynchronously at its natural frequency, that is, at (1/n) of the excitation. The phenomenon is generally associated with asymmetry in the stiffness vs. deflection characteristic of the system. It may be characterized as the “bouncing” of the rotor on the surface of the stiff support, energized by every nth unbalance impulse prior to contact. Second, third and fourth order subharmonic vibration responses have previously been observed in high speed rotating machinery with such an asymmetry in the bearing supports. An incident is reported where 8th and 9th order subharmonic vibration responses have been observed in a high speed rotor. A simple but exact computer model of the phenomenon has been evolved based on the numerical integration of a finite difference formulation. Response curves and wave forms of rotor deflection at individual speeds are computed. It is shown that the response is a series of pseudo-critical peaks at whole-number multiples of the rotational speed. Very high orders of subharmonic vibration are found to be possible for systems with low damping and extreme nonlinearity.

Dispersion by random velocity fields

A simple approximation is proposed for the problem of the dispersion of marked particles in an incompressible fluid in random motion when the probability distribution of the velocity field is taken as Gaussian, homogeneous, isotropic, stationary and of zero mean. Approximations for the Lagrangian velocity correlation function and the dispersion are given and compared with exact computer calculations of Kraichnan. Agreement is found to be good except for time-independent velocity fields and singular wavenumber spectral functions.

Stiffening of Shear Walls

In interacting shear wall and flat slab-column construction it is desirable to be able to evaluate the contribution of the columns to the stiffness of the lateral load resisting system. This paper presents a relatively simple method whereby this contribution can be determined, both in terms of the reduction in lateral displacement and the reduction in overturning moment in the shear walls. For the case of a continuous flat slab connection, the bending of the slab induces axial forces into the exterior columns, which therefore causes a portion of the moment to be carried by the columns. Axial forces can also be induced into the exterior columns by means of a very stiff top beam extending from the shear wall to the exterior columns. Design curves are presented for both types of stiffening so that the method can be applied easily by the designer. Comparisons of specific examples with results obtained by a more exact computer-oriented method show that the method gives reliable results.