LOW ORDER DYNAMIC MODEL of A VAPOR COMPRESSION CYCLE FOR PROCESS CONTROL DESIGN

Abstract

Control of food processes involving vapor compression cycles as actuators is often a difficult task: indeed this particular device is itself a complex process including coupled unit operations as evaporation, compression, condensation and expansion. Nevertheless, an accurate control of heat transfer rate is often essential for global quality of product and stability of flow in exchangers. Moreover a number of vapor compression systems are already equipped with variable speed‐compressors and fans. However, due to lack of knowledge about the dynamic behavior of these systems, the industry has not taken full advantage of these variable devices to get substantial control performance improvement. This paper presents a lumped‐parameter model for describing the dynamics of vapor compression cycles. Based on moving‐boundary approach for the description of two‐phase/single phase interface inside the heat exchangers, this low‐order model composed of only ordinary differential equations can be highly useful for design of control strategies. This model has been validated on an experimental device and a good agreement between measurements and computed data has been found. Use of this model in food process control design is discussed.

An advanced nonlinear switched heat exchanger model for vapor compression cycles using the moving-boundary method

“…refrigerant and structure masses, specific heats, latent heats) are also adequately represented, the model will give accurate transient predictions. In fact, moving-boundary techniques have already been shown to provide reasonably accurate transient predictions (Grald and MacArthur, 1992;Rasmussen, 2006;Leducq et al, 2003;Bendapudi, 2004;Alleyne et al, 2007). Nevertheless, further experimental validation against both steady-state and transient data is planned.…”

“…Although attractive for controls' applications (Rasmussen, 2006;Willatzen et al, 1998;He et al, 1995;Leducq et al, 2003;Cheng and Asada, 2006;Jensen and Tummescheit, 2002) there are still critical areas for improvement of existing movingboundary model formulations. Most importantly, many models assume a fixed number of zones.…”

“…While finite volume or finite difference models are fully capable of predicting system transients (Cullimore and Hendricks, 2001;MacArthur and Grald, 1989;Eborn et al, 2005;Limperich et al, 2005), Grald and MacArthur (1992) showed that the ''lumped parameter'' or ''moving-boundary'' method is much faster. Even though real-time capability using a finite volume technique has been demonstrated by Rossi and Braun (1999), the faster speed of the moving-boundary method has caused it to become the method of choice for controls' purposes (Rasmussen, 2006;Willatzen et al, 1998;He et al, 1995;Leducq et al, 2003;Cheng and Asada, 2006;Jensen and Tummescheit, 2002) The primary reason for the speed difference is that the moving-boundary method divides the heat exchanger into a minimum number of zones (at most three), representing regions where refrigerant is in the superheated vapor, saturated mixture, and sub-cooled liquid phases. Because refrigerant-side heat transfer coefficient and refrigerant density vary substantially between these regions, zone lengths must be resolved to accurately predict total heat transfer rate, refrigerant mass, and refrigerant pressure.…”

“…Interface boundaries between zones vary over time and are tracked by the model -hence, the term moving-boundary method. As described in the literature (Grald and MacArthur, 1992;Rasmussen, 2006;Willatzen et al, 1998;He et al, 1995;Leducq et al, 2003;Cheng and Asada, 2006;Jensen and Tummescheit, 2002;Bendapudi, 2004), the governing equations are derived by considering conservation of mass and energy in each control volume. Simplifying assumptions are as follows:…”

Non-linear predictive control of a vapour compression cycle

“…Based on this principle, Leducq and et al [9] have proposed a low order model by reduction of a fully distributed model of a vapor compression cycle composed of seven ordinary differential equations. This model as used to simulate the behaviour of a refrigerating plant for the development and tests of the non-linear predictive controller as presented in this paper.…”