Publication: HVAC & R Research
Publication Date: 01-SEP-07
Delivery: Immediate Online Access
Author: Zhou, Xiaotang ; Braun, James E.
Article Excerpt
INTRODUCTION
Dynamic models are often used in the development of advanced feedback controllers, control strategies, and diagnostic methods. In the initial design and validation of these algorithms, the use of computer models is much more cost-effective than running real-time experiments. Bourdouxhe et al. (1996) presented a very detailed review of transient models in the HVAC field. They found a lot of literature on transient modeling of heat exchangers but relatively little work on transient modeling of cooling and dehumidifying coils.
In some situations, quasi-static models may be appropriate for transient simulations if the dynamic variations of the inputs are slower than the response of the cooling coil. The model developed by Braun et al. (1989) is an example of a simplified quasi-static model, which utilizes effectiveness relationships for heat transfer only and heat and mass transfer. This lumped model was validated through comparisons with detailed numerical solutions and manufacturer's catalog data and works very well in predicting air and water outlet states under steady-state conditions.
For heat exchangers without dehumidification, Gartner and Harrison (1963) developed an analytical model for the transient behavior of cross-flow heat exchangers. They derived three partial differential equations, which describe energy storage in the primary fluid (air), heat exchanger material, and secondary fluid (water) with the assumption of steady flow for both flow streams. The solutions were presented in terms of transfer functions that relate outlet air and water temperatures to variations of inlet air and water temperatures under the condition of constant fluid flow rates. The validity of the model was demonstrated through comparisons with transient experimental data. This model has been the basis for many other transient heat exchanger models, including models described by Gartner and Harrison (1965), Gartner and Daane (1969), Tamm (1969), Tamm and Green (1973), Bhargava et al. (1975), and Jawadi (1988). Gartner and Daane (1969) developed a mathematical model for serpentine cross-flow heat exchangers that considers changes in fluid velocities, and Jawadi (1988) simplified this model by neglecting transients associated with air.
Dehumidification adds a significant complication, and only a small number of papers appear in the literature for dynamic modeling of cooling and dehumidifying coils. Based on the level of detail, the models can be categorized into reference, lumped, and filter models as proposed by Bourdouxhe et al. (1996). A reference model is based on a fairly detailed understanding of physical phenomena and usually involves partial differential equations. A lumped model is also based on a physical representation but with certain simplifications so that the mathematical expressions are reduced to a smaller number of ordinary differential and algebraic equations. A filter model is based on the use of a time constant added to the outputs of a steady-state model.
McCullagh et al. (1969) presented a reference model that considers the dynamic behavior of chilled-water cooling and dehumidifying coils. At any position within each row of tubes, temperatures of both the tube and fin materials are assumed to be uniform in the direction normal to the water flow. Between rows of tubes, the air is considered to be completely mixed. Energy balances applied to the air, tube, fin, and water lead to partial differential equations that are solved using a finite-difference numerical solution. Steady-state predictions of the model were compared to experimental results under wet conditions and showed reasonably good agreement for both sensible and latent heat transfer except for two-row coils where the assumption of complete mixing of air between rows was poor. The transient response of the model was not validated using experiments.
Clark (1985) developed a filter model for cooling and dehumidifying coils configured in a counter cross-flow arrangement. The model is based on the steady-state model presented by Elmahdy and Mitalas (1977). In dry conditions, the heat flow rate between moist air and water is calculated on the basis of logarithmic mean temperature difference; in wet cases, logarithmic mean enthalpy difference is used to calculate the heat flow rate. The coil dynamics are modeled very simply by adding a single time constant to the steady-state air outlet temperature and humidity and to water outlet temperature. This time constant is a function of heat capacitance associated with coil material and overall heat transfer coefficient. Use of the model to represent the dynamics of coils with fewer than four rows was not recommended. The dynamics of the coil model were investigated experimentally only for dry conditions with changes in water flow rate and water inlet temperature. The agreement between model and experiment was reasonably good for the conditions considered.
Ding et al. (1990) developed a lumped model for cooling and dehumidifying coils that have counter cross-flow configurations. A single capacitance is used to represent the total energy storage of the coil metal material and water, and the energy transfer rates are determined using effectiveness models similar to those presented by Braun et al. (1989). Air dry-bulb temperatures are used as driving potentials for dry cases, and air wet-bulb temperatures are used for wet conditions. The model was only compared with experimental data for dry coils. The agreement between model prediction and experimental measurement was good for air outlet temperature but poor for water outlet temperature.
Chow (1997) developed a lumped model that arises from energy balances applied to finite control volumes within a chilled-water cooling and dehumidifying coil. The accuracy of the model was demonstrated through comparisons with three other coil models developed by Clark (1985), Holmes (1988), and Stoecker (1975) for both dry and wet coils. The results for air outlet temperatures from the different models were close, while the results for water outlet temperatures had large variations. No experimental validation was performed for this model. Furthermore, the models used as a basis for comparison have not been validated fully using experiments under dry and wet conditions with transient operation.
None of the previous studies explored trade-offs between model accuracy and computational requirements to identify an appropriate model to be used within transient simulations for cooling and dehumidifying coils. Furthermore, experimental validation for transient coil performance has not been performed under both dry and wet conditions. There is a need for an accurate dynamic coil model that executes quickly so that it can be used within system simulations for long time horizons, such as a cooling season or year.
Table 1. Characteristics of Test Coils Coil Physical Parameter Eight-Row Coil Four-Row Coil Fin geometry Wavy Louvered Coil depth, m 0.264 0.132 Number of fins per inch (per 0.0254 m) 8 12 Coil face width, m 0.6096 0.6096 Coil face height, m 0.6096 0.6096 Tube material Copper Copper Tube outer diameter, m 0.0127 0.0127 Tube thickness, m 0.0004 0.0004 Tube longitudinal pitch, m 0.033 0.033 Tube transverse pitch, m 0.0381 0.0381 Fin material Aluminum Aluminum Fin thickness, m 0.0002 0.0002
The current paper develops a simplified dynamic coil model that takes advantage of steady-state performance indices to reduce the number of control volumes needed to accurately characterize a cooling coil. The model is compared with a more detailed reference model and with simplified...
NOTE: All illustrations and photos have been removed from this article.
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