A Comparison of Transient Heat-Pump Cycle Simulations with Homogeneous and Heterogeneous Flow Models

This paper compares the effects of two different refrigerant flow modeling assumptions on the transient performance of vapor-compression heat pump cycles. These simulations are developed in the next-generation modeling language Modelica, which uses an acausal, equation-oriented approach to describe physical systems. The effect of the flow assumptions and specific slip ratio correlations on both the equilibrium operating point and the transient behavior of the cycle are demonstrated through these simulations. It is shown that equivalent simulations with different slip ratio correlations each have different equilibrium mass inventories, and that some aspects of the transient system behavior exhibits minor differences between the representative simulations. The effect of the software implementation on the model performance is also discussed

Numerical Modeling of Fin-and-Tube Condenser with Wet-wall Desuperheating

Current heat exchanger simulation models typically divide the condenser into three regimes (desuperheating, two-phase and subcooled) and assume that condensation does not start until the bulk refrigerant flow reaches a state of saturated vapor. However, plenty of experiments have verified that condensation can occur much earlier than that when the tube wall surface temperature drops below the dew point of refrigerant even though the bulk flow is still superheated. This phenomenon is called wet-wall desuperheating (also referred to as wet-desuperheating, or condensation from desuperheated vapor in some publications). Wet-wall desuperheating is rarely modelled in the extant heat exchanger simulations due to lack of understanding in its physical process. However, neglecting this important phenomenon may lead to substantial performance prediction errors. This paper proposes a new fin-and-tube condenser heat exchanger model to bridge the research gap. In the proposed model, the heat exchanger is divided into four regimes: dry-wall desuperheating, wet-wall desuperheating, two-phase condensation and subcooled. The existence of dry-wall desuperheating and the onset point of wet-wall desuperheating are determined by rigorous algorithms. Boundaries between different flow regimes are captured to eliminate numerical discontinuities. A tube-by-tube analysis is adopted to allow for the simulation of complex tube circuitries. Simulation studies are performed to demonstrate the capabilities of the proposed model. The results show that wet-wall desuperheating always exists in the condenser with refrigerant vapor entering at the inlet, and neglecting the phenomenon can lead to significant under prediction for heat exchanger performance

Modeling and Analysis of Pressure Drop Oscillations in Horizontal Boiling Flow

In general, two-phase flow phenomena can be described based on the one-dimensional conservation laws. Models with different formulations can be obtained with different assumptions. This paper presents three models with different complexity to simulate pressure drop oscillations. The direct comparison indicates that there are substantial differences between these models. The mechanism of pressure drop oscillations is discussed and the effect of operating parameters on system instability is explored. It is shown that two bifurcation points can exist when varying heat input and inlet subcooling. Root locus analysis corroborates the simulation results

Patch-based Thermodynamic Property Models for the Subcritical Region

Model-based design approaches for vapor-compression cycles depend heavily upon refrigerant property representations that are fast, accurate, and consistent. We describe an approach based upon B-spline interpolants that describes properties such as density, temperature, and specific entropy as the intersection of multiple surfaces, which are referred to as ”patches.” When combined with a transformation of thermodynamic coordinates, this approach can calculate the density over a domain with a maximum absolute percentage error less than ×1P− and a speedup over REFPROP of greater than 100x

Modeling of Finned-Tube Heat Exchangers: A Novel Approach to the Analysis of Heat and Mass Transfer under Cooling and Dehumidifying Conditions

The construction of physics-based models of the simultaneous heat and mass transfer on the air-side surface of air-cooled fin-and-tube heat exchangers during dehumidification can present distinct challenges. Because only part of the external surface of a finite length finned tube may be wetted in the radial and/or axial directions, the determination of the wet/dry boundary for this partially wet tube surface must parsimoniously describe the nonlinear variations in both the refrigerant temperature and air temperature profiles. A literature review indicates that extant heat exchanger models tend not to consider the partially wet conditions due to modeling complexity; moreover, many standard dehumidification models in the literature also exhibit significant deficiencies. For instance, the Lewis number is often incorrectly assumed to be unity, and the air saturation enthalpy at the surface interface is also assumed to be a linear function of temperature in both the Effectiveness model and the LMED (Logarithmic-Mean Enthalpy Difference) model. These simplifying assumptions can often introduce appreciable deviations between simulation outputs and measured data. This paper proposes a new heat exchanger model that aims to address these challenges through new modeling approaches. After reviewing extant heat exchanger models that include the effects of dehumidification, a novel approach based upon the underlying physics is presented to analyze the air-side simultaneous heat and mass transfer. This new approach has a number of distinct advantages, including the fact that it allows scenarios with non-unity values of the Lewis number to be modeled, as well as the fact that the model accuracy is also significantly improved over extant models because of the assumption of the air saturation humidity ratio as a cubic function of temperature. In addition, these models allow the dry-wet boundary for partially wet surfaces to be readily determined from both air flow and refrigerant flow directions. A tube-by-tube analysis (which can be easily extended to a segment-by-segment analysis) including multiple refrigerant phases is adopted to allow for the simulation of complex tube circuitries. Results from this new approach are validated with experimental data reported in literature, and demonstrate good agreement

Fault detection methods for vapor-compression air conditioners using electrical measurements

Includes bibliographical references (p. 409-424).Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Architecture, 2008.(cont.) This method was experimentally tested and validated on a commercially available air handler and duct system. In the second class of faults studied, liquid refrigerant, rather than vapor, enters the cylinder of a reciprocating compressor during operation. Since the higher cylinder pressures that result can cause substantial damage and are difficult to measure directly, a method for detecting this fault is proposed that only uses observations of the compressor voltage and current. The performance of this fault detection method was also experimentally validated with electrical and mechanical measurements on a semi-hermetic compressor. The final diagnostic method detects refrigerant leakage in a residential air conditioning system by identifying changes in the system's cycling behavior. This method also uses measurements of the compressor's electrical power, as well as a small set of temperature measurements, to determine the presence of the fault. This fault detection method was developed and tested on an occupied residence.This thesis proposes novel methods that use measurements of electrical terminal variables to identify common mechanical faults in vapor-compression air-conditioners. The importance of air-conditioning in many applications and the current cost of energy both provide powerful incentives for developing fault detection methods, as faults can have a significant impact on the system's functionality and efficiency. While many extant fault detection and diagnostic (FDD) methods depend upon arrays of mechanical sensors, concerns about sensor reliability and the overall complexity of these methods motivated this research into electrically-based FDD methods, which typically incorporate smaller numbers of more reliable sensors. These electrically-based methods use models of the electromechanical energy conversion process to correlate observed changes in the electrical variables to changes caused by faults in the mechanical load. Such an approach allows both electrical and mechanical faults to be identified via the same sensor apparatus, and makes it possible to identify faults that manifest themselves on a wide range of timescales.FDD methods for three different classes of common faults are studied in this research. The first diagnostic method identifies blockage or leakage in a duct via electrical measurements made at the fan motor terminals. The estimates of the motor's speed and torque developed at the operating point are used in tandem with a fan curve to directly estimate the airflow through a duct system without any additional mechanical measurements.by Christopher Reed Laughman.Ph.D

Proportional-Integral Extremum Seeking for Optimizing Power of Vapor Compression Systems

Conventionally, online methods for minimizing power consumption of vapor compression systems rely on the use of physical models. These model-based approaches attempt to describe the influence of commanded inputs, disturbances and setpoints on the thermodynamic behavior of the system and the resultant consumed electrical power. These models are then used online to predict the combination of inputs for a measured set of thermodynamic conditions that both meets the heat load and minimizes power consumption. However, these models of vapor compression systems must contain nonlinear terms of sufficient complexity in order to accurately describe the region near the optimum operating point(s), but also must rely on simplifying assumptions in order to produce a mathematically tractable representation. For these reasons, model-based online optimization of vapor compression machines have not gained traction in application, and have created an opportunity for model-free techniques such as extremum seeking control, which is gradient descent optimization implemented as a feedback controller. While traditional perturbation-based extremum seeking controllers for vapor compression systems have proven effective at minimizing power without requiring a process model, the algorithm\u27s requirement for multiple distinct timescales has limited the applicability of this method to laboratory tests where boundary conditions can be carefully controlled, or simulation studies with unrealistic convergence times. Perturbation-based extremum seeking requires that the control input be manipulated with a time constant approximately two orders of magnitude slower than the slowest vapor compression system dynamics, otherwise instabilities in the closed loop system occur. As a result, convergence to the optimum for slow processes such as thermal systems is restrictive due to inefficient estimation of the gradient, and slow (integral-action dominated) adaptation in the extremum seeking control law. In order to address this timescale separation issue, we have previously developed an algorithm called ``time-varying extremum seeking that more efficiently estimates the gradient of the performance metric and applied this algorithm to the problem of setpoint optimization for compressor temperatures. That algorithm improved the convergence rate to one timescale slower than the vapor compression machine dynamics. In this paper, we optimize power consumption through the application of a newly-developed proportional--integral extremum seeking controller (PI-ESC) that converges at the same timescale as the process. This method uses the improved gradient estimation routines of time-varying extremum seeking but also modifies the control law to include terms proportional to the estimated gradient. This modification of the control law, in turn, requires a revision to the gradient estimator in order to avoid bias. PI-ESC is applied to the problem of compressor discharge temperature selection for a vapor compression system so that power consumption is minimized. Because of the improved convergence properties of PI-ESC, we show that optimum values of discharge temperature can be tracked in the presence of realistic disturbances such as variation in the outdoor air temperature---enabling application of extremum seeking control to vapor compression systems in environments where previous methods have failed. The method is demonstrated experimentally on a 2.8 kW split ductless room air conditioner and in simulation using a custom-developed Modelica model