Optimal Velocity Distribution Research Articles

Optimization Design of Velocity Distribution in the Airways of the Fluidized Bed Based on CFD and Taguchi Algorithm

A vital component that is frequently employed in the industrial powder conveying sector is the fluidized bed. In the light of powder unloading with a fluidized bed as the research object, an orthogonal experiment with two factors and four levels was established for the structural parameters of the fluidized bed. In the case of different noise factors, 16 schemes are designed and all schemes via computational fluid dynamics numerical simulation. The Taguchi method and regression analysis are used to analyze the response. Finally, the accuracy of the optimization results is tested. The results show that gas velocity decreases sharply at the airway’s entrance and, then, gas flows to the second half of the airway and velocity decreases steadily and uniformly. Airway arc length L exerts a greater effect on the signal-to-noise ratio (SNR) than airway height H. The parameter combination of 180 mm L and 17 mm H for obtaining the optimal velocity distribution uniformity is determined. The test results indicate that the overall fluidization effect of the fluidized bed with the optimal parameters is better. The linked research findings can be used as a guide when designing a fluidized bed system for transporting comparable powder.

Numerical investigation on the recovery process of the flow field in a rotating duct

Turbulent flow inside a rotating duct widely exists in revolving hydromachines. The Coriolis force and the centrifugal force generated in the rotation greatly modify the development of the flow field and consequently affect the efficiency of these hydromachines. A deviation of the mainstream to the pressure sidewall of the duct, which occurs as soon as the fluid flows to the rotating duct, is commonly observed and previously thought to remain throughout the flow field. However, this study discovers a recovery process of the modified flow field and numerically investigates that process for the first time. The recovery process begins very close to the entrance of the duct and ends when the same fully developed flow field as that without rotation is obtained. The results indicate that the recovery process can be divided into four phases: the linear recovery phase, stationary mixing phase, nonlinear recovery phase, and finish of the recovery process. The characteristic details of the four phases and the evolving mechanisms of the recovery process are discussed. The algebraic relationships between the characteristic parameters of the recovery process and the inflow conditions (the rotation velocity, rotation numbers, mean inflow velocity, and height of the duct) are obtained. It is found that the characteristic deviation distance of the velocity peak in the linear recovery phase linearly moves toward the centerline of the duct with a slope of k=−0.0023ω+0.0748. The recovery distance linearly increases with the product of the mean streamwise velocity U and the rotation velocity ω as follows: (XsH)0.2=0.025U·ω+b. It also denotes that the recovery process can be accelerated by reducing the height H of the duct. Accelerating the recovery process and reaching the ideal optimal velocity distribution as soon as possible can effectively improve the efficiency of the flow field.

COMPUTER-AIDED OPTIMIZATION OF EXTRUSION DIES

When designing a complex profile extrusion die, an iterative process has to be performed to optimize the flow channel. This procedure is time-consuming and cost-intensive. By means of FEA it is possible to pre-design the flow channel and hence to reduce the number of experimental iteration steps in order to optimize the flow channel. But this procedure only shifts the first iteration steps from practice into the computer. Up to now no procedure has been found to predict the die geometry in order to gain an even velocity profile at the outlet. In the two procedures mentioned above, optimization of the geometry is done by trial and error. In this paper a program is presented that works with a new method to optimize complex extrusion dies. It uses a combination of FEA and network theory. By means of this method it is possible to speed up the iterative optimization process. Furthermore, the user can be given a hint from the program where and how to change the geometry of the flow channel to approach the optimum velocity distribution at the outlet.

Correlation between plasma dynamics and thin film properties in pulsed laser deposition

The pressure–distance scaling law for pulsed laser deposition is examined for several thin film systems. This scaling law is due to the plasma dynamics occurring within the laser plasma plume near the location of the substrate. Time-of-flight studies of both ions and neutrals confirm the existence of an optimal velocity distribution for optimal film deposition. Fast ions play a major role in determining the quality of the films deposited. They may provide surface activation of the film or induce damage to the film depending on their kinetic energies.

Time-optimal control of multiple cooperating manipulators with trajectory and motion program constraints

Two types of problems associated with time-optimal control of multiple manipulators moving a commonly held object along specified trajectories are studied. The first problem involves finding the minimum traveling time and the optimal control torques for any desired motion programs of the given trajectory. The second problem involves finding the optimal velocity distribution along the trajectory such that the motion can be completed in the minimum time. To solve these problems, a parametric form of the generalized dynamic equation is derived. An iterative search procedure is developed for solving the first problem. During the search, the lower bound of the traveling time at any point of the given trajectory is determined by using the linear programming technique. The second problem is solved by integrating the parametric dynamic equation along the given trajectory based on the phase-plane switching curve approach. The maximum acceleration and the upper bound of the operation speed at each integration instance are determined from two linear programs. The proposed methods are applicable to various complex multi-robot systems and can handle nonlinear torque-speed characteristics of the joint actuators. © 1996 John Wiley & Sons, Inc.

Results of acoustic optimization of a point‐driven, thin‐shelled cube using the boundary element method

The sound power radiated by a thin‐shelled cube is calculated from simulated acoustic velocities (equal to the normal shell velocity) using the boundary element method (BEM) [K. A. Cunefare and G. H. Koopmann, J. Vib. Acoust. 113, 387–394 (1991)]. Optimization techniques are then used to predict velocity distributions that result in the minimum output sound power. In future work, recommendations for the addition of passive noise control materials will be defined on the basis of achieving the calculated optimal velocity distribution that will result in the minimum radiated sound power. These criteria are tested on a point‐driven, thin‐shelled cube in an anechoic chamber. The normal shell velocity is measured using a laser velocimeter. Again, sound power is calculated and the optimal velocity distribution is determined using the BEM. Accuracy of power predictions, based on experimental power measurements and computational examples, as a function of frequency and vibration pattern are studied.

The minimum multimodal radiation efficiency of baffled finite beams

A technique for deriving the optimal surface velocity distribution on the surface of a finite baffled beam has been developed. The optimal velocity distribution minimizes the radiation efficiency of the beam for a specified maximum permissible mode and frequency. A modal expansion of the surface velocity in terms of unknown modal amplitude coefficients, the Rayleigh integral, and a far-field intensity integration are employed to obtain a quadratic expression for the radiation efficiency of the beam. Application of a suitable constraint to avoid trivial solutions leads to an eigenvalue problem identical in form to the Rayleigh quotient employed in dynamic mechanical systems. The eigenvector of modal amplitude coefficients corresponding to the lowest eigenvalue yields the minimum radiation efficiency, while the eigenvalue itself is the actual value of the minimum radiation efficiency. Near and below coincidence, the optimal eigenvector of modal amplitude coefficients yields a radiation efficiency significantly less than the radiation efficiency of any single modal component acting alone. Simply supported and clamped–clamped boundary conditions are considered, and numerical examples are presented for each.

Three-Dimensional Analysis of Closed-Die Forging Processes: Part 1: Formulation

In this series of papers, a theoretical model based on the upper bound elemental technique is presented for prediction of forging load and metal flow in three-dimensional closed-die forging processes. Three basic elements are introduced in order to partition a forging into simple elementary regions. An optimum velocity distribution within the forging is obtained by minimizing the total rate of energy dissipation using a simplex optimizing procedure. Applications of the proposed model are discussed in Part 2.

A Method for Transonic Inverse Cascade Design With a Stream Function Equation

A new profile design method is developed on the basis of [1–3] for transonic flow. The rotational dynamic stream function equation, which is expressed in functional form using calculated coordinates, is deduced. This method can be used for the calculation of cascade and S1 stream surface of a transonic flow with a local shock wave on the blade suction surface. This method consists of two parts: an inverse method with a given velocity distribution along the suction surface and a given thickness distribution; and an inverse method with given velocity distributions on suction and pressure surfaces. Using this method it is easy to obtain a blade profile with prescribed velocity and thickness distributions. The design of optimal profile may then be done with the calculated optimal velocity distribution on the blade surface. The rotational condition is satisfied when the stream function equation is adopted with the entropy term. If the compatibility condition can be fulfilled between the S1 and S2 equations, the iterative calculations of two kinds of stream surfaces in three-dimensional flow will be convergent. In this paper a unique value of density can be determined from the known stream function value. The computational program is written with this method and several transonic examples have been calculated. These results are quite good.

On the Elliptic Path of an End-Effector for an Anthropomorphic Manipulator

This paper deals with the problem of an anthropomorphic manipulator with an end-effector traveling along a path whose projection on the rz-plane of a cylindrical coordinate system is an ellipse. The elliptic motion, coupled with an angular movement in the ϕ-direction, provides a smooth transition for motion reversal at both terminal points. To im prove the smoothness of reversal, one may vary the elliptic eccentricity to alter the shape of the path. The analysis reveals that the coordinates along the path may be expressed in terms of ( πt/τ + ζ), where ζ( t) is an unknown function of time to be determinedfor an optimal velocity distribution along the path by minimizing the total energy used by the manipu lation system. The computational technique employed in this paper is to express ζ as a finite series, satisfying the bound ary conditions at two terminal points, with the optimal coeffi cients λn, fn, and kn to be evaluated. For numerical illustra tion, two different values of eccentricity are chosen: one is the smallest value for the problem under investigation, and the other is 0.995 (close to the largest value). The results indicate that the energy optimization is essentially due to λ1 and f 1, which ensures a rapid convergence. The contributions due to kn are usually quite small, while the contributions due to iteration are relatively insignificant.

Compressor Cascade Optimization based on Inverse Boundary Layer Method and Inverse Cascade Method : 1st Report, An Inverse Cascade Method for Incompressible Two-dimensional Potential Flow

An aerodynamic approach to an optimum compressor cascade in a two-dimensional incompressible flow is described on the basis of two inverse problems; namely, inverse boundary layer problem to produce the optimum velocity distribution and inverse cascade problem to obtain a blade section which realizes a prescribed velocity distribution. A new method for the latter problem is developed in this report. In this method a cascade is transformed into a row of circular cylinders and the blade section is calculated for prescribed velocity distribution, velocity triangle and solidity by solving simultaneous equations about the mapping function. The mapping distortion is exceedingly small in this transformation, and so the inverse problem about the potential flow through a cascade whose solidity, stagger angle and load per blade are high can be solved accurately even near the leading- and trailing-edge.

A Method for Optimal Synthesis of Manipulation Robot Trajectories

Manipulation robots belong to a class of complex, nonlinear dynamic systems. In addition, they are subjected to the constraints resulting from work-space obstacles, kinematical and physical characteristics of the mechanism itself and the actuators. Therefore, the application of optimal control theory (in energy or time optimization) leads to substantial practical difficulties, so that significant simplifications are usually performed, either in model complexity or by neglecting the existing constraints. In this paper the problem of obtaining such an optimization method, which would take into account the complete system dynamics and all the constraints is considered. The only method found to be suitable for such a complex optimization should be based on dynamic programming. In this paper an algorithm for determining optimal velocity distribution for a given manipulator tip trajectory is elaborated in detail. Practical application of the developed procedure is in off-line calculation of nominal input generalized forces (programmed control) of a nonredundant manipulator, by which the minimum of consumed energy is ensured. This is specially important for high speed motions as well as handling of heavy loads.

Two-Dimensional Compressor Cascades With Optimum Velocity Distribution Over the Blade

Results are presented of a research on an optimum cascade problem in two-dimensional subsonic flow at SVUSS (National Research Institute for Machine Design, Bechovice). The optimisation is based on a determination of the optimum velocity distribution (OVD) and on the solution of the inverse cascade problem. The OVD has been ascertained from a variational problem formulated by Sˇpacˇek as follows: to find such a velocity distribution on the suction surface for which the momentum thickness at the trailing edge has a minimum value. The problem was solved by Ru˚zˇicˇka using a simplified boundary layer method. Inverse cascade problem due to Pola´sˇek was employed to calculate the cascade geometry for a given optimum velocity distribution and the given stagger angle and the space chord ratio. Series of compressor cascades having the optimum velocity distributions has been designed by means of a digital computer. Some cascades of the series were tested in the low-speed windtunnel as well as at the high subsonic speeds. Reasonable agreement between the predicted and the experimental pressure distributions, flow deflection and loss coefficient has been achieved.

Stack exit velocity distribution for higher effective stack height

The effective height of a smoke stack can be increased by better preserving the temperature and velocity of the flue gases, which in turn, can be achieved by minimizing the entrainment of the cold ambient air into the plume. Based on the entrainment hypothesis, the optimal velocity distribution at the stack exit and the optimal size of the stack exit for minimum ambient entrainment are derived. Laboratory experiments were performed to compare the ability of rising across an inversion by a plume from a conventional stack and by a plume from a stack designed according to the new theory. The qualitative experiments showed that under identical atmospheric conditions, while the plume from the conventional stack would be trapped by the inversion, the plume from the new stack penetrated across the inversion. Based on the theory, devices may be built and installed on the top of industrial chimneys to eject the effluents to a higher altitude. The present study is for a neutral and calm atmosphere only. Parallel studies on two-dimensional plumes are also made.