Hayatoshi Sayama

Natural convection in an inclined rectangular channel at various aspect ratios and angles—experimental measurements

Abstract Rates of heat transfer were measured for laminar natural convection in silicone oil and air in a long rectangular channel. The aspect ratio (width/height) of the cross-section of the channel was varied over 1, 2, 3, 4·2, 8·4 and 15·5, and the Rayleigh number from 3 × 103 to 105. The channel was heated from below and cooled from above while the other two sides were insulated. The channel was then rotated about the long axis in steps through 180 degrees. The effect of inclination and of the aspect ratio on the rate of heat transfer was measured experimentally. A minimum and a maximum rate of heat transfer occurred as the angle of inclination was increased from 0 to 180 degrees. The angle of inclination at these critical conditions was found to be a strong function of the aspect ratio and a weak function of the Rayleigh number. A transition in the mode of circulation occurred at the angle corresponding to the minimum rate of heat transfer.

NATURAL CONVECTION PATTERNS IN A LONG INCLINED RECTANGULAR BOX HEATED FROM BELOW PART I. THREE-DIRECTIONAL PHOTOGRAPHY

Abstract The transient and steady flow patterns in glycerol in a slightly inclined, long box with a cross-sectional width-to-height ratio of 2.0 were photographed by the method of Krishnamurti. The box was rotated about the long dimension as an axis. The stable mode for very small angles of inclination was found to be a series of roll-cells with their axes running in the upslope. As the angle of inclination was increased to five or six degrees the circulation pattern changed to a series of oblique cells. Above seven degrees a single quasi-two-dimensional cell was observed with flow up the inclined heated plate and down the cooled plate. The rate of heat transfer was also measured. The average Nusselt number at first increased with angle of inclination, then decreased as the oblique cells appeared, and finally increased again as the quasi-two-dimensional cell was formed. Significant hysteresis was not observed in either the circulation pattern or the Nusselt number as the angle of inclination was decreased. The studies were carried out for a Rayleigh number of about 12000.

A generalized Lagrangian function and multiplier method

As is well known, a saddle point for the Lagrangian function, if it exists, provides a solution to a convex programming problem; then, the values of the optimal primal and dual objective functions are equal. However, these results are not valid for nonconvex problems.In this paper, several results are presented on the theory of the generalized Lagrangian function, extended from the classical Lagrangian and the generalized duality program. Theoretical results for convex problems also hold for nonconvex problems by extension of the Lagrangian function. The concept of supporting hypersurfaces is useful to add a geometric interpretation to computational algorithms. This provides a basis to develop a new algorithm.

Computer-aided operability study

Abstract Operability study is a systematic technique for identifying hazards or operability problems throughout an entire facility. In this paper, we have proposed an approach using knowledge engineering techniques to the automated operability study. The computer-aided operability study system consists of the plant-specific knowledge-base, the generic knowledge-base and the inference engine. Causal relationships between input and output variable deviations for components are modeled using decision tables. Decision tables for components are developed by the user and stored in a generic knowledge-base in computers. The plant structure (piping and instrumentation diagram) and reaction types are inputted to the plant-specific knowledge-base in computers. Each process variable of equipment is examined in sequence by searching the generic knowledge-base, and operability study is generated resulting from the search. We demonstrate via the Solvey process how the computer-aided operability study can identify hazards, and substantiate the usefulness of the method.

Fuzzy fault diagnostic system based on fault tree analysis

A method is presented for process fault diagnosis using information from fault tree analysis and uncertainty/imprecision of data. Fault tree analysis, which has been used as a method of system reliability/safety analysis, provides a procedure for identifying failures within a process. A fuzzy fault diagnostic system is constructed which uses the fuzzy fault tree analysis to represent a knowledge of the causal relationships in process operation and control system. The proposed method is applied successfully to a nitric acid cooler process plant.<<ETX>>

Computational schemes of the Davidon-Fletcher-Powell method in infinite-dimensional space

The disadvantage of the extension of the Davidon-Fletcher-Powell method to infinite-dimensional space is that the information to be stored in the computer increases with the number of iterations. In this paper, a computational scheme is proposed to remove this disadvantage and make the extension method more practicable. The linear operator which determines the direction of one-dimensional search in the method is formulated by integral kernels to derive the scheme. Furthermore, polynomial interpolation methods are proposed to save computer storage. The computational scheme which is presented here and the polynomial interpolation method are successfully applied to an optimal control problem.

Multiplier method and optimal control problems with terminal state constraints

The multiplier method for constrained optimization problems is considered geometrically with the concept of supporting hypersurfaces. This geometric interpretation simplifies the comparison of the multiplier method with other existing methods and provides a basis from which to develop new algorithms. Moreover, though it is proved that the algorithm of the multiplier method can be derived from different viewpoints, the convergence of the multiplier method as a successive approximation algorithm is verified in this paper. Finally, the multiplier method is applied to optimal control problems with terminal state constraints, and some numerical experiments are presented.

Multimodality analysis of a class of multistage allocation problems

Multiple optimum solutions of a multistage allocation problem, well-known to chemical engineers, are analyzed. The number of local optima becomes greater with a decrease in the initial-condition value of the first stage or with an increase in the total stage number. The fact that this behavior is closely related to the flat portion of the profile of a curvef(x), which determines the objective function, is revealed. A construction method by Aris is used to give an excellent insight into this behavior. Moreover, the construction curves ensure that all stationary points are found. Finally, a theorem to discriminate local optima from stationary points, without evaluating second-order derivatives, is presented.

On Lagrange multipliers and constraints I. Lagrangian approach

This paper establishes the relations between the changes in tho values of the Lagrange multipliers and the changes in the values of tho constraint and objoetivo functions for a non-linear, convex programme based on the classical Lagrangian. Using somo Lagrange multipliers which are larger (smaller) than the optimal ones, it is possible that a point minimizing the Lagrangian is inside the feasible (infeasible) region. Illus-strativo examples are presented for quadratic programming problems.

On Lagrange multipliers and constraints II. Augmented Lagrangian approach

This paper establishes the relations between the changes in the values of the augmented multipliers and the changes in the values of the constraint and objective functions for a non-linear, non-convex programme based on the augmented Lagrangian which was introduced by one of the present authors. If the penalty parameters are sufficiently large, the monotonic relations hold between the augmented multipliers and the constraint functions near the optimal solution. Illustrative examples show that the classical Lagrangian fails to give rise to the relations for a. non-convex programme.