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

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

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

Integrated Control of Multi-Zone Buildings with Ventilation and VRF systems in Cooling Mode

The accelerating decarbonization of energy systems to address climate change and the increasing recognition of the role that buildings play in occupants\u27 health have served to further emphasize two long-standing trends in the buildings and HVAC industries: the pursuit of ever-higher energy efficiency for buildings, and the proper management of the overall indoor environment. These two objectives, which are often at odds, are becoming ever more linked due to the emergence of new practices in the buildings industry that require both reductions in energy intensity and the improved management of temperature, humidity, and ventilation. In seeking to improve thermal comfort while reducing power consumption, the dynamics due to interactions between coupled subsystems, such as ventilation systems and VRF systems, become increasingly important, and must be properly designed and managed to achieve the desired system-level performance. We explore one approach to address these challenges by using a model-based process to design an HVAC system for a building including both a multi-zone variable refrigerant flow (VRF) system and a ventilation system. Such an approach is essential because the dynamics of both the VRF system and the ventilation system affect the thermal conditions of each zone; as each system acts as a disturbance to the other, the overall dynamical system can either develop limit cycles or can evolve toward an operating point which consumes more power than is necessary while satisfying specified setpoints. We use the equation-oriented language Modelica to construct detailed multiphysics models of the individual VRF, ventilation, and building systems, and then couple these models together to analyze the overall system properties. We then design a method for coordinating the control of these systems to maintain system performance while minimizing the energy consumption, and demonstrate the efficacy of these methods using realistic dynamic building inputs, such as time-varying occupancy and weather data. While these models have significant advantages in their use for control design, their modularity also provides a promising path for the rapid evaluation of alternate system architectures. This is particularly useful for the system under study, as multiple ventilation systems with different costs and energy performance can be used to provide fresh air to the occupied space. We thus study the performance of the building with the VRF system with three alternate ventilation approaches: a simple fan, an energy recovery ventilator (ERV), and a dedicated outdoor air system (DOAS). Such an methodology illuminates the potential energy impact of each ventilation approach on the overall HVAC system; because the use of the DOAS significantly reduces the load on the VRF system, the total system energy consumption can be reduced by over 50% by using the DOAS as opposed to a simple fan. The final paper will describe and elaborate on such results, providing a concrete demonstration of the benefits of model-based system and control design for HVAC systems in buildings

Dynamic Charge Management for Vapor Compression Cycles

Because vapor compression air-conditioners and heat pumps consume significant amounts of electrical power in today\u27s residential and commercial buildings, energy optimization of these systems is becoming increasingly important from the perspectives of both environmental conservation and economic value. Corresponding efforts to improve the energy efficiency of these machines require attention to all stages of system design, installation, and operation, due to the myriad factors influencing power consumption. Among the many variables that must be optimized, one particularly salient variable is the mass of refrigerant contained within the cycle, or the refrigerant charge; this variable is strongly coupled to many other variables in the system, including the electrical power consumption, the system pressures, and the degree of subcooling and superheat in the heat exchangers. As such, the mass of refrigerant in the system must be carefully tuned for a given set of operational conditions to maximize the system\u27s energy efficiency. In practice, field-installed vapor compression systems are often not charged with the mass of refrigerant that optimizes energy efficiency for the conditions in which systems actually operate. In accordance with the conventional view of the refrigerant charge as a static system parameter, the mass of refrigerant is often specified to maximize the average energy efficiency over a set of multiple conditions. This approach results in suboptimal energy efficiency at any one of the conditions within the rating set, and furthermore often results in lower energy efficiency at non-rated conditions. Such an impact is especially evident in reversible heat pump cycles because the optimal refrigerant mass for a cycle over a range of conditions in cooling mode is often very different than the optimal refrigerant mass in heating mode. As today\u27s system manufacturers sell equipment across large geographic ranges with a wide range of ambient conditions and operational requirements, the cumulative impact of operating these systems with suboptimal refrigerant charge is generally a much higher rate of energy consumption than would be observed with cycles that incorporate an optimally specified refrigerant charge. In this paper, we describe a system architecture for a vapor compression system that enables the circulating refrigerant charge to be modulated as a function of time, effectively allowing the refrigerant charge to be optimized for a predicted or observed set of operational conditions. This is accomplished by dynamically controlling the amount of refrigerant sequestered in a storage vessel (referred to as a dynamic receiver) that is continuously coupled to the other components of the system. We first explore alternate system architectures that have been previously proposed for similar purposes, and elaborate on the opportunities that are afforded by this particular candidate architecture. A set of first-principles physics-based dynamic models are then developed using the Modelica language, and a candidate controller architecture is discussed that directly optimizes the electrical power consumption by using this new dynamic receiver. Finally, we will compare energy performance of this proposed system with that of conventional system architectures to evaluate its benefits over a range of operational conditions

Model Predictive Control of Variable Refrigerant Flow Systems

Model Predictive Control (MPC) of vapor compression systems (VCSs) offers several advantages over conventional control methods (such as multivariable process control with selector logic) in terms of 1) the resulting closed-loop performance and 2) the control engineering design process. VCSs are multivariable systems and feature constraints on system variables and actuators that must be enforced during steady-state and transient operation. We present the design and validation of an MPC for a split ductless VCS. The design regulates room temperature with zero steady state error for unknown changes in the thermal load and enforces constraints on system variables such as compressor discharge temperature and actuator ranges and rates. We show how the MPC design can evolve during the engineering process by adding and modifying constraints and process variables. The design methodology provides guarantees in terms of closed loop stability and convergence. Importantly, in contrast to other published results on MPC for VCSs, our design makes use of only available temperature measurements and does not require pressure or mass flow measurements which are typically not available in production VCSs

The Deep Propagating Gravity Wave Experiment (DEEPWAVE): An airborne and ground-based exploration of gravity wave propagation and effects from their sources throughout the lower and middle atmosphere

The Deep Propagating Gravity Wave Experiment (DEEPWAVE) was designed to quantify gravity wave (GW) dynamics and effects from orographic and other sources to regions of dissipation at high altitudes. The core DEEPWAVE field phase took place from May through July 2014 using a comprehensive suite of airborne and ground-based instruments providing measurements from Earth’s surface to ∼100 km. Austral winter was chosen to observe deep GW propagation to high altitudes. DEEPWAVE was based on South Island, New Zealand, to provide access to the New Zealand and Tasmanian “hotspots” of GW activity and additional GW sources over the Southern Ocean and Tasman Sea. To observe GWs up to ∼100 km, DEEPWAVE utilized three new instruments built specifically for the National Science Foundation (NSF)/National Center for Atmospheric Research (NCAR) Gulfstream V (GV): a Rayleigh lidar, a sodium resonance lidar, and an advanced mesosphere temperature mapper. These measurements were supplemented by in situ probes, dropsondes, and a microwave temperature profiler on the GV and by in situ probes and a Doppler lidar aboard the German DLR Falcon. Extensive ground-based instrumentation and radiosondes were deployed on South Island, Tasmania, and Southern Ocean islands. Deep orographic GWs were a primary target but multiple flights also observed deep GWs arising from deep convection, jet streams, and frontal systems. Highlights include the following: 1) strong orographic GW forcing accompanying strong cross-mountain flows, 2) strong high-altitude responses even when orographic forcing was weak, 3) large-scale GWs at high altitudes arising from jet stream sources, and 4) significant flight-level energy fluxes and often very large momentum fluxes at high altitudes

The Detection of Liquid Slugging Phenomena in Reciprocating Compressors via Power Measurements

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