Correction of Log Mean Temperature Difference Method and Effectiveness-NTU Relations for Two-phase Heat Transfer with Pressure Drop and Temperature Glide

The Logarithmic Mean Temperature Difference (LMTD) method and the effectiveness-NTU method are the two important methods for design and analysis of heat exchangers. The derivation of these two methods relies on a critical assumption, i.e., the fluid specific heats are constant. Under special operating conditions where one fluid experiences condensation or evaporation at constant temperature, these two methods are still valid. In practice, however, the fluid temperature in heat exchangers will never remain constant during phase change because of pressure drop. Meanwhile, zeotropic refrigerant mixtures exhibit temperature variations even during a constant pressure phase change process. Therefore, both LMTD and effectiveness-NTU methods can introduce appreciable errors when applying to the cases in which refrigerant temperature change is not caused by heat transfer, rather than by pressure drop and temperature glide. This paper proposes modified LMTD method and effectiveness-NTU relations to remove the restriction of constant temperature phase change in the original approaches. The new methods account for the effects of pressure drop and temperature glide on the two-phase heat transfer process and make corresponding corrections based on simplifying assumptions. The new methods are applicable for both parallel-flow and counter-flow configurations, with phase change on one side. Rigorous error analyses indicate that the new approaches can substantially improve the thermal performance prediction for heat exchangers with large pressure drop and temperature glide

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

TRANSIENT MODELING OF TWO-STAGE AND VARIABLE REFRIGERANT FLOW VAPOR COMPRESSION SYSTEMS WITH FROSTING AND DEFROSTING

This thesis presents the development of an advanced modeling framework for the transient simulation of vapor compression systems. This framework contains a wide range of components and its modular nature enables an arbitrary cycle configuration to be analyzed. One of the highlights of this framework is the first-principles heat exchanger models with many salient simulation capabilities. Specifically, a high-order discretized model employing finite volume analysis is developed based on a decoupled approach to modeling the heat transfer and pressure drop performance of the heat exchanger. The frosting and defrosting models developed in the thesis are integrated into this heat exchanger model, allowing more accurate performance assessment of heat pumps. Meanwhile, an advanced low-order moving boundary heat exchanger model is developed with switched model representations to accommodate the changing numbers of fluid zones under large disturbances. Compared to the existing moving boundary models in the literature, this new model accounts for refrigerant pressure drop and possesses a more accurate evaluation for the air side heat transfer. Based on this modeling framework, the transient characteristics of a flash tank vapor injection (FTVI) heat pump system undergoing cycling, frosting and reverse-cycle defrosting operations are thoroughly explored. The dynamic system response when subjected to a step change in the opening of the upper-stage electronic expansion valve is also investigated. Comparison between the predictions and experimental data shows that the simulation can adequately capture the transient heat transfer and fluid flow phenomena of the system and thus demonstrating the fidelity of the models. Furthermore, a pull-down simulation for a multi-split variable refrigerant flow (VRF) air-conditioning system with six indoor units has been carried out. Control strategy that aims to maintain the indoor air temperatures at set values is proposed. The simulation test for controllability shows that the proposed control strategy is feasible to achieve the temperature control of individual zones

A New Dynamic Heat Exchanger Model with Frosting and Defrosting

In this paper, a dynamic heat exchanger model that unifies the frosting and defrosting analyses is presented. A novel scheme is proposed to solve the air flow redistribution due to non-uniform frost blockage. Unlike the existing defrost models which separate analysis for tubes and fins, the proposed defrost model unifies the analysis to maintain model consistency. The first-principles based frost and defrost models developed in this research allow for a more realistic assessment of the heat pump systems and greatly facilitate the design of controls. Utilizing the developed models, the transient behavior of a flash tank vapor injection heat pump under frosting and defrosting conditions is investigated and validated against experimental data

An Improved Moving Boundary Heat Exchanger Model with Pressure Drop

A literature review indicates that almost all moving boundary heat exchanger models used in dynamic simulations of heat pumps rely on the common hypothesis that the refrigerant pressure drop is negligible. In fact, it is important to include the momentum balance in some applications, such as electronics cooling where microchannels are commonly used and significant pressure drop is observed and large-scale heat exchangers in solar thermal plants where tube length can be longer than several hundred meters. In addition, a comprehensive and robust switching approach is needed to handle transitions between different model states due to phase change. It is found that the current switching methods in the literature exhibit several shortcomings which may cause serious errors and stability issues when simulating cycling transients of vapor compression systems. The objective of this paper is to propose an improved moving boundary formulation that aims to fill in the above research gaps. Specifically, two different approaches are presented to account for the refrigerant pressure drop across the heat exchanger. A novel and comprehensive switching scheme is introduced to ensure smooth transition between different model representations under large disturbances. The proposed model is validated using measured data. The validation shows that the proposed heat exchanger model along with other supporting component models can reasonably capture the start-up transients of a flash tank vapor injection heat pump system