Finite Difference Methods for Computation of Flow into Local Exhaust Hoods

Abstract

Local exhaust hoods play an important role in controlling exposures. Airflow into these hoods may be approximated by Laplace's equation. Previous experimental work by other authors along with other data tend to support this assumption. Currently, theoretical models are available for computing the flow into plain and flanged slots and flanged rectangles and circles. These models are analytical solutions of Laplace's equation and are possible because the velocity potentials at a given point in space can be calculated. As the geometry of configurations under study becomes more complex, closed-form solutions to Laplace's equation become more difficult to find. In such situations numerical methods of solution are called for. A finite difference method for computing the airflow is presented and was developed using the plain and flanged slot configurations. The method generally is useful for solving problems in which the location and shape of the flow boundary and the values of the velocity potential or its normal derivative are known. The analytical models for the slot were used to determine the accuracy of the numerical methods by comparison of the equal velocity contours generated by the various models. Good general agreement between the numerical solutions and analytical models was observed.