Temperature and pressure discontinuity stresses in compact heat exchangers

Abstract

N an era of increased material strengths and supersonic aircraft, the weight of an aircraft heat exchanger is coming under close scrutiny. Many aircraft parts are being optimized using a performance criteria of minimizing the strength to weight ratio. Gardner1 is the first published work which calculates the stress in a heat exchanger tube sheet by treating the tubes as an elastic foundation on which the tube plate rests. His analysis does not consider the following: 1) thermal stresses may arise due to the temperature differential between tube sheet forces; 2) discontinuity stresses may be significant between the tube sheet and the outer shell. K. A. G. Miller2 extends the work of Gardner by accounting for the weakening effect of the holes in the plate by introducing expressions for the deflection and ligament efficiencies defined by Gardner. These efficiencies are shown to lie within the range specified by Gardner and this leads to definite design equations. Figure 1 shows free body diagrams of the heat exchanger tube sheet and the shell. Consider the shell and tube sheet with an applied shear Fo and an applied moment MQ with positive directions as shown. MQ has the dimensions of in.-lbf/in. of circumference and Fo has the dimensions of Ibf/ in. of circumference . Roark 3 has compiled an extensive table of deformations and stresses for pressure vessels, shells, and plates. These formulae can be used with the theories of superposition and discontinuity stresses to predict the stress level at the change of shape (shell and tube sheet connection).