Dynamic analysis of a 1-1 shell and tube heat exchanger by superposition of simultaneous flow rate disturbances

Abstract

Extensive research on the dynamics of heat exchange between two fluids has been carried out in the past with orientation mainly towards the industrially important situation of a single variable process operating in the high turbulent flow region. The need for a more general understanding of the phenomenon and the wider requirements of more recent processes justified the investigation of heat exchange under multivariable conditions and at lower Reynolds numbers, particularly in the transition and laminar regions. Based upon the experience and results reported for the turbulent regime the techniques of analysis were extended to investigate the region of present interest. This meant treating the system as a linear one with combination of the simultaneous disturbances by superposition as required by linear system theory. Two mathematical models were developed for the purpose, based on the description of the process by a set of four partial differential equations. The first model, representing the system in the time domain, is an explicit numerical algorithm applicable to countercurrent and parallel flow schemes under single or simultaneous flow disturbances. The effect of these disturbances on the heat transfer coefficients can be chosen as the exact ones given by the current’ correlations or as the corresponding linearised ones. This model also includes the dynamics of the control valves regulating the flow rates. The second method representing the system in the frequency domain is a linearised version of the same set of same set of differential equations, expressed as a transfer function, and also applicable to the case of countercurrent and parallel flow schemes, under single or double variable operation. Both models were evaluated by computer for relevant operating conditions. To test the models, a liquid-liquid 1-1 shell-and-tube heat exchanger was operated under several sets of conditions, and the experimental results indicated that: (i) The superposition of two flow disturbances in the heat exchanger can be simulated adequately by use of linear system principles in both the time domain and the frequency domain. (ii) Although in general the data collection at low Reynolds numbers has a larger degree of uncertainty, the process dynamics in this region of the time domain can be described satisfactorily by the model proposed, for both single and double variable operation. (iii) The quality of representation in the frequency domain was less satisfactory for the tube-side outlet temperature and had severe limitations for the shell-side outlet temperature. The fact that this representation was based on a fully linearised set of convective equations, as required for application of the Laplace transformation, makes it less useful in a region where thermal diffusion assumes greater significance.