Development of two heat transfer correlations for a scraped surface heat exchanger in an ice-cream machine
Interduction
Heat transfer in presence of a high viscosity fluid may be substantially enhanced using heat exchangers supported by a mechanical agitation system that can also “scrape” the exchange surface (Scraped Surface Heat Exchanger, SSHE). In this case, heat transfer efficiency depends strongly on exchanger and agitator geometries, agitation methods as well as fluid characteristics and heat transfer conditions. Correlations used to represent the phenomenon are closely related to the above parameters and hardly employable out of that peculiar context.
In this work some results of an experimental research on SSHE performances, used as the evaporator of a refrigeration cycle in a commercial soft ice-cream machine, are presented. The liquid ice-cream mixture goes in o this component where it is mixed with a variable amount of air and cooled to obtain soft ice-cream. The mixture has a non-Newtonian fluid behaviour that involves a lot of problems related to its physical representation: some assumptions on ice-cream rheological properties have been accepted. Varying ice-cream mass flow, input/output temperatures of the liquid mixture and the agitator speed, ice-cream production tests were carried out. Two heat transfer coefficient correlations are proposed to describe experimental data: the first one arises from the classical dimensional analysis while the second one is related to the agitator engine power consumption. Finally, the experimental results supply a reliable database to find possible improvements in ice-cream machine efficiency.
Highlights
► We present two heat transfer correlations for a scraped surface heat exchanger.
► A semi-empirical relationship correlates the heat transfer coefficient to the impeller rotation speed.
► A useful tool for the design of evaporators installed in soft ice-cream machines is provided.
► The experimental results offer a reliable database to find improvements in commercial machine efficiency.
Conclusions
We are able to present two heat transfer correlations for the Scraped Surface Heat Exchanger installed in a commercial soft icecream machine. The first one has been developed using the dimensional analysis tool, looking for different dimensionless groups allowing a better representation of SSHE features. In spite of the same computational method, the presented relationship differs from that in Ref. as the process fluids are different: solideliquid mixture instead of liquideliquid mixture. This is in agreement with findings by other authors. The second correlation is a semi-empirical relationship straightly correlating the heat transfer coefficient to the impeller rotation speed and to the ice-cream mix exchanged power as well.
The results obtained allow thinking that the chosen dimensionless groups look appropriate to describe current experimental data. Finally, the good performance of semi-empirical correlation proposed encourages further efforts in new experimental campaigns with different SSHE geometries, heat transfer conditions and ice-cream mix as well.
Reference content
In the current paper, a Scraped Surface Heat Exchanger (SSHE), composed of an encased rotor on which two blades are mounted, is studied. The focus is on the effects of the rotor speed, mass flow rate, and outgoing heat flux applied on the shell on the Convection Heat Transfer Coefficient (CHTC) and the Outlet Temperature (OT). To this end, the Response Surface Methodology (RSM) is utilized to achieve the regression modeling and sensitivity analysis. Then, the Nondominated Sorting Genetic Algorithm II (NSGA-II) algorithm is applied to best balance the two conflicting objectives of maximizing CHTC and minimizing OT. The results show that an increase in either the rotation speed of the rotor or mass flow rate leads to a rise in CHTC. Furthermore, decreasing the outgoing heat flux reduces CHTC and amplifies the temperature at the outlet. The sensitivity analysis indicates that OT is most sensitive to a slight change in the mass flow rate and least sensitive to change in the rotor speed. Moreover, an optimal Pareto front with 35 non-dominated optimal points is obtained.
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They concluded that the rotational speed was found to be the most effective factor. Saraceno et al. [10] experimentally investigated a SSHE used as an evaporator in the refrigeration cycle of a commercial soft ice-cream machine. Two correlations for HTC were established using dimensional analysis.
The work deals with an experimental and numerical analysis on disturbed thermal boundary layer obtained in a heat exchanger by two rotating blades (scrapers). A three-dimensional numerical model of unsteady forced convection in an analyzed device is proposed and taken in o consideration. The model allows for the transient nature of the processes occurring in a very efficient in terms of heat transfer the Scraped Surface Heat Exchanger (SSHE) and the impacts on the body forces such as gravity, centrifugal and Coriolis forces on processes. In order to validate the model, a specially constructed experimental test stand was designed and manufactured. The series of experiments for the Reynolds number equal to 1100 and the Nusselt number in the range of 10–25 were performed and compared with numerical results achieving satisfactory agreement, with the error smaller than 5% for temperature and 9% for the heat flux values. The set of governing equations of conservation of mass, momentum, and energy was solved within the framework of the Finite Volume Method (FVM). The movement of the scrapers was incorporated in o the model with the use of the Sliding Mesh Method (SMM). The distributions of temperature and velocity were elaborated and scrutinized. It was found that in the analyzed flow regime, the gap width between the stator wall and the scraping blade tip highly affects the Nusselt number. Moreover, the numerical results were compared with other mathematical models available in the literature and the discrepancy between the conventionally used model based on penetration theory was found.
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Beyond the opportunity for complementary assessment of model predictions, the availability of a broad dataset is necessary to identify heat transfer correlations in SSHE during crystallization. Recent efforts have been devoted on this difficult subject (e.g. Saraceno et al., 2011; Rainieri et al., 2014). Lastly, the product rheology must be fully characterized, as a way to improve the reliability of model predictions under particular operating conditions (low refrigerant fluid temperature, low mass flow rate).
A computational fluid dynamics model was implemented for studying the production of non-aerated sorbet in a scraped surface heat exchanger under different operating conditions. The coupled problem of fluid flow and heat transfer is solved by taking in o account realistic values for the product physical properties as well as its complex rheology. The mathematical solution of the coupled problem represents a challenging task, among other reasons by the strong influence of temperature on product physical properties and rheology due to phase change. Fluid flow, heat transfer freezing and viscous dissipation phenomena are analyzed locally in the heat exchanger. The modeling approach is consistent, as indicated by comparisons between model predictions of the temperature profile along the heat exchanger and available experimental results.