Generalized convection and power-law models to represent the residence time distribution for non-ideal laminar flow in a double-pipe heat exchanger

摘要

The residence time distribution (RTD) is essential for the design and analysis of continuous thermal processing equipment. For the processing of liquid foods, flow is usually laminar and the classic RTD models often can not characterize non-ideal laminar flow. Such deviations are associated with coils, curves or tube roughness/corrugation. Generalized forms of the theoretical convective and power-law models were proposed in order to characterize non-ideal laminar flow in tubes. Introduced parameters were the breakthrough time and the flow index, respectively. The combined PFR+CSTR model was also considered. To test the models, experimental data was obtained from a sanitary double-pipe heat exchanger using an ionic tracer and a conductivity flow cell. Tube diameter was 4.5 mm with a total length of 19.5 m and internal volume of 311 mL. Tested flow rates were between 12 and 20 L/h of distilled water (960 < Reynolds number < 1620). The model E-curve was fitted to experimental data after numerical convolution with the E-curve of detection unit to correct the signal distortion. Adjusted parameters were correlated with flow-rate. The best fit was obtained with the combined model, followed by the generalized convection and generalized power-law models. The adjusted flow index was under 1.0, suggesting that the velocity profile was flatter than the theoretical parabola. This can be explained by the high roughness to diameter ratio of the tube. The higher breakthrough time obtained from the convection model also indicates a flatter velocity profile. The combined model was useful to determine the contribution of dead space and stagnation zones in the equipment, which are due to the curves and thermocouple connections. The proposed models proved to be useful to represent RTD of non-ideal laminar flow in a tubular system.