Investigation of the Relation Between Tube Spacing and Tube Sheet Deformation in Heat Exchangers due to the Mechanical Rolling Process: A Numerical Study

The focus of this paper is a numerical investigation of tubesheet deformation in tube-tubesheet joints used in tube bank heat exchangers. To increase the thermal performance of a cooler the tubes can be moved closer together to increase turbulence and the heat transfer coefficient. Reducing the tube spacing is an alternative to using finned tubes to increase thermal performance. Finned tubes is more susceptible to fouling and therefore the small tube spacing can be an attractive alternative in some cases. From a manufacturing point of view, there are some problems with small tube spacing. When the tube spacing is reduced the deformation of the tube sheet increases. The relation between the tube spacing and tubesheet deformation is of great interest to the thermal designers of heat exchangers since it sets a limit for the tube spacing. The limit depends on how much tube sheet deformation is acceptable in the design. In most cases, the tubes are joined to the tube sheet by an expansive cold forming process. The expansion process that is investigated in this paper is the mechanical rolling expansion process. The tube is plastically deformed by a series of hardened steel rollers that roll across the inner tube surface while being pushed outwards. This results in a residual contact pressure between the tube and tube sheet after relaxation/springback. The expansion process is modeled using finite elements, the model used is a 2D plane-strain model that is capable of capturing the effect of adjacent holes. This approach is new compared to previous research done in the field of mechanical roll expansion where the most commonly used model is an axisymmetric model. It is however not possible to investigate tube sheet deformation versus tube spacing with the axisymmetric model since it doesn’t include the effect of adjacent holes. The material used in the analysis is a typical stainless steel, the material is modeled using a bilinear isotropic hardening model. At some point, the deformation of the tube sheet will exponentially increase with reduced tube spacing. This effect can only be investigated using numerical tools. Too much tube sheet deformation is not desirable since it will cause the tube sheet to permanently change shape and in some cases, adjacent tube-tubesheet joints will be compromised due to the nearby expansion. The results of this paper is the relation between the tube spacing and the amount of tubesheet deformation for a given amount of apparent tube wall reduction. This relation is used to set up limits for the amount of expansion and the minimum tube spacing for the given material combination.