Abstract
This paper studies the root loci of tubular, parallel-flow and counter-flow heat exchangers controlled by a proportional feedback and clarifies the effect of a wall to heat exchanger dynamics. One of features of heat exchangers with a thick wall is that it's transfer function has an essential singular point on the negative real axis and in the vicinity of which infinite number of root loci appear.
In a tubular heat exchanger, the effect of a wall is represented in the neibourhood of the essential singular point by the shape of the root loci which is divided into two types depending on the values of parameters. As the thickness of the wall increases, the root loci relating to the singular point become to cross the imaginary axis at low frequency and low gain, which causes a serious unstable problem. The model for which the distribution of the wall temperature in the radial direction is considered has infinite number of essential singular points on the negative real axis, while a model with uniform wall temperature has a unique one. As the thickness of the wall increases, the distance between the singular points becomes small and difference between the two models becomes large. The latter model estimates too large stable region.
In parallel-flow and counter-flow heat exchangers, the effect of the wall appears as deformation of the root loci of the model with a thin wall rather than as issue of the root loci from the essential singular point: i. e. an appearance of a breakaway point for parallel-flow heat exchanger and a bend of root loci to the imaginary axis for the counter-flow heat exchanger which may cause instability. For thick wall, the model with uniform wall temperature estimates too large stable region and it is serious particularly for the counter-flow heat exchanger.
