A Thermodynamic Theory of Circulation in Water-Tube Boilers

Abstract

A thermodynamic evaluation is made of the work available for, and the resistance to circulation by, natural convection in a water-tube boiler. This leads to a theory of circulation which is independent of the usual type of hydraulic theory expressed in terms of density difference. The theoretical circulation equation is first used for the direct estimation of examples of particular circuits. Estimates made by means of this are in good agreement with estimates made on existing hydraulic theories. It is then shown that the present theory lends itself to a more general formulation, and the treatment is developed to elucidate the general physics of natural convection in water-tube boilers. The fundamental variables are certain characteristic non-dimensional groups. The system is shown to possess critical limits of stability and of circulating quantity. Expressions for these are derived, and the general type of performance is given in charts. The relation of operating pressure and rate of heating to these critical limits is discussed. In the course of the development a definition of an ideal standard boiler is proposed which is suggested to be a useful conception. By means of the present theory an adequate account of qualitative characteristics of boiler operation can be given. Its possible quantitative accuracy is then discussed. Some comparison with experimental results is given. Appendix I shows that the theory is generally applicable to the convection of non-evaporating fluids in tubes as well as to the boiler circuit. Appendix II indicates the relevance of the theory to the question of forced circulation. In Appendix III the problem is treated by dimensional methods and the characteristic non-dimensional groups are confirmed. Another characteristic group is shown to apply when capillarity is included. This permits some discussion of the effects of discontinuity and of the requirements of scale models.