Dynamic modeling and simulation of an Organic Rankine Cycle (ORC) system for waste heat recovery

This paper presents an advanced switched modeling approach for vapor compression cycle (VCC) systems used in Air Conditioning and Refrigeration. Building upon recent work ( McKinley and Alleyne, 2008 ), a complete dynamic VCC model is presented that is able to describe the severe transient behaviors in heat exchangers (condenser/evaporator), while maintaining the moving-boundary framework, under compressor shut-down and start-up operations. The heat exchanger models retain a constant structure, but accommodate different model representations. Novel switching schemes between different representations and pseudo-state variables are introduced to accommodate the transitions of dynamic states in heat exchangers while keeping track of the vapor and liquid refrigerant zones during the stop–start transients. Two model validation studies on an experimental system show that the complete dynamic model developed in Matlab/Simulink can well predict the system dynamics in shut-down and start-up transients.

A dynamic model of a vapor compression cycle with shut-down and start-up operations

This paper presents a methodology for developing a low order dynamic model of a transcritical air-conditioning system, specifically suited for multivariable controller design. An 11th-order nonlinear dynamic model of the system is derived using first principles. Analysis indicates that the system exhibits multiple time scale behavior, and that model reduction is appropriate. Model reduction using singular perturbation techniques yields physical insight as to which physical phenomena are relatively fast/slow, and a 5th-order dynamic model appropriate for multivariable controller design. Although all results shown are for a transcritical cycle, the methodology presented can easily be extended to subcritical cycles.

https://www.ideals.illinois.edu/bitstream/handle/2142/12122/TR204.pdf?sequence=2

Control-Oriented Modeling of Transcritical Vapor Compression Systems

Simulation is commonly used to develop control and diagnostic algorithms. Because vapor compression cycles are essentially heat management devices, transient and steady-state heat exchanger performance must be predicted accurately. However, for hardware- and software-in-the-loop purposes, the simulation must run in real-time. To reconcile these competing needs, a new lumped parameter or moving-boundary heat exchanger model was created. Accuracy concerns are addressed by including finned surfaces, nonlinear air temperature distributions, and non-circular passages. In its current form, the model is applicable to single pass, cross-flow heat exchangers. The mathematical basis of the model is given and shown to be consistent with integral forms of the energy and continuity equations. Although known to be more computationally efficient than finite volume models, moving-boundary models become singular and fail under certain conditions. To address this shortcoming, particular attention was focused on algorithms for switching between different representations and rezoning wall temperatures. Robustness to changing flow regimes is demonstrated through simulation test cases, and model application to a chiller system is shown. As such, the model provides improved accuracy, robustness, and operating range while maintaining real-time capability.

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

A mathematical model describing the transient phenomena of two-phase flow heat exchangers is presented. Based on the one-dimensional partial-differential equations representing mass and energy conservation (leaving out momentum equations assuming pressure drops to be negligible) and a tube-wall energy equation, a simpler set of ordinary-differential equations is formulated by integrating separately over the three zones (liquid, two-phase, and vapor) generally present in a heat exchanger. Special attention is given to the study of large transients induced by on/off control of vapor-compression cooling systems.

A general dynamic simulation model for evaporators and condensers in refrigeration. Part I: moving-boundary formulation of two-phase flows with heat exchange

A mathematical model of an evaporator based on one-dimensional partial differential equations representing mass conservation, and tube wall energy has been formulated. These equations are then restructured and linked to a program data base of all major refrigerants and refrigerant mixtures. The result is a simulation model of an evaporator that is general and flexible. The model is tested over a wide range of operating conditions and a simple controller is implemented to demonstrate the effectiveness of the model for controller and systems design.

L. Ploug-Sørensen

Papers

A general dynamic simulation model for evaporators and condensers in refrigeration. Part I: moving-boundary formulation of two-phase flows with heat exchange

A general dynamic simulation model for evaporators and condensers in refrigeration. Part II: simulation and control of an evaporator