Direct Design of Ducts

Abstract

This paper describes a method for calculating the shape of duct that leads to a prescribed pressure distribution on the duct walls. The proposed design method is computationally inexpensive, robust, and a simple extension of existing computational fluid dynamics methods; it permits the duct shape to be directly calculated by including the coordinates that define the shape of the duct wall as dependent variables in the formulation. This “direct design method” is presented by application to two-dimensional ideal flow in ducts. The same method applies to many problems in thermofluids, including the design of boundary shapes for three-dimensional internal and external viscous flows.

A direct design approach using the Euler equations

“…An additional constraint on the location of a boundary point is still needed in a two-dimensional SSD problem. One way of obtaining the required constraint is to force the boundary node to move along a specified direction called the spine [1]. By fixing the spine directions, only one constraint, the spine coordinate R, is needed to specify the location of a grid point in a two-dimensional domain.…”

“…This article presents a direct (fully coupled) SSD method based on the ideas proposed by Ashrafizadeh et al which has only been applied in the context of linear ideal fluid flows before [1][2][3]. The nonlinear set of Euler equations are used here as the flow governing equations and a number of shape design problems are solved to validate the method and to provide shape design examples in subsonic and supersonic internal flows.…”

“…A novel direct shape design method was proposed by Ashrafizadeh et al [1][2][3]. They basically showed that a fully coupled formulation of the SSD problem could be solved in the physical domain using a simple extension of commonly used CFD algorithms.…”

Computational optimization of the thermal performance of internally finned ducts

“…Ashrafizadeh et al (2003) have proposed a method to optimize the shape of nozzles, diffusers, and elbows. In their method, an optimal shape is achieved by iterative1y adjusting the coefficients in the discretized equations of a finite volume method (in which the coefficients depend on the dependent variable) during the overall solution process, based on the latest available distribution of the dependent variable, solving the direct fluid flow problem, and repeating the process until convergence.…”

Alternative Methods for Generating Elliptic Grids in Finite Volume Applications

“…Therefore, the source terms P and Q can be used as interpolants in an elliptic grid generation problem. The source values in these examples, which are Laplacians of the logical coordinates, have been calculated using the finite volume method as described in (Ashrafizadeh et al, 2002;Ashrafizadeh et al, 2003).…”