©2004 ASHRAE. 347ABSTRACTThis paper describes the development and testing of thecharacteristic curve fan model—a gray-box model. This modelproduces fan efficiency as a function of airflow and fan staticpressure. It is accurate, relatively easy to calibrate, and couldbe easily incorporated into commercial simulation programs.Also presented is an application of an existing model to predictfan speed from airflow and fan static pressure. These modelswere developed as a part of a larger research project to developdesign guidelines for built-up variable air volume fan systems.The models have been successfully employed in comparativeanalysis of fan types, wheel diameters, fan staging, and anal-ysis of supply pressure reset.INTRODUCTIONThe authors were part of a publicly funded energy effi-ciency research team developing design guidelines for built-up fan systems in commercial buildings. According to previ-ous research, fan energy in new construction for commercialbuildings in California accounts for 1 terawatt-hour of electricenergy usage per year, representing approximately half of allHVAC energy usage (CALMAC 2003). The authors’ researchdemonstrates that up to half of that fan energy is avoidablethrough cost-effective design practices, including fan selec-tion (size and type), fan sizing, fan staging, and static pressurecontrol (Hydeman and Stein 2003). Five monitoring sitesprovided field data on which to test the alternative fan systemdesigns and design techniques. These sites were selected torepresent a range of climates, occupancies, and fan systemconfigurations (Kolderup et al. 2002). As part of this work, asimulation model of a fan system was sought that had all of thefollowing characteristics:• Accurate at predicting fan system energy over the fullrange of actual or anticipated operating conditions.• Applicable for the full range of fan types and sizes.• Easy to calibrate from manufacturer’s or field-moni-tored data.• Ability to identify operation in the “surge” region.• Relatively simple to integrate into existing simulationtools.• Ability to independently model the performance of thefan system components, including the motor, themechanical drive components, the unloading mecha-nism (e.g., VSD), and the fan.The purpose of this model is to evaluate design alterna-tives for fan selection and control through simulation. Opti-mally, simulation tools would directly utilize themanufacturers’ fan curves to evaluate fan system operation ateach discrete step of evaluation. Since this is not currentlyavailable, the authors sought models that simulation toolscould easily incorporate that replicated fan performance.MAIN BODYLiterature on component models for fans was reviewed,including the models used in the DOE-2 simulation program(DOE 1980) and in the ASHRAE Secondary Toolkit (Bran-demuehl et al. 1993; Clark, 1985). We also looked briefly atthe models embedded in commercial simulation software,such as Trace and HAP, but found these suffered from the sameproblems as the model in DOE-2. DOE-2 uses a black-box regression model that producesthe fan system power draw as a function of percent designairflow using a second-order equation as follows: Development and Testing of theCharacteristic Curve Fan ModelJeff Stein, P.E. Mark M. Hydeman, P.E.Member ASHRAE Member ASHRAEJeff Stein is a senior engineer and Mark Hydeman is a principal at Taylor Engineering, LLC, Alameda, Calif.AN-04-3-1348 ASHRAE Transactions: Symposia(1)This model is implicitly built on several assumptions: 1. Each fan operates on a single system curve that uniquelymaps airflow to static pressure.2. Fan system efficiency is directly a function of airflow. 3. A second-order equation sufficiently models both of theseeffects.The DOE fan model implicitly combines the operatingsystem curve with the models for each of the fan systemcomponents. Power is directly produced as a function ofairflow only, and there is no opportunity to have differentconditions of fan static pressure at a given airflow. Real VAVsystems do not remain on a fixed system curve. System pres-sure as a function of airflow behaves differently depending onthe location of the boxes that are modulating, the location ofthe static pressure sensor(s), and the static pressure controlalgorithm. Although this model is simple to use, it does not allow theuser to independently model and evaluate each of the fan-system components. Thus, if designers wanted to evaluate theimpact of motor oversizing, they would have to independentlyassemble fan and motor models to develop the DOE-2 perfor-mance curve that represented the combination of the twotogether. This model also does not directly account for thevariation in fan system component efficiencies as the fanunloads, nor does it allow for evaluation of a multiple fansystem, where fan staging will change both the operating effi-ciency and potentially the individual fan static as they arestaged on and off. The model in the ASHRAE Secondary Toolkit is a gray-box fan component model that uses the perfect fan lawsthrough application of dimensionless flow (φ) and pressure(ψ) coefficients. This model uses a fourth-order equation topredict fan efficiency from the dimensionless flow parameter. (2)(3)(4)whereCFM =airflowN = fan speedD = fan diameterρ = average air density∆P = fan static pressure andC1 and C2= constants that make the coefficients dimensionlessThis model allows the user to calibrate an entire family offan curves with data from a single model. Unfortunately, thismodel does not permit the direct calculation of fan efficiencyfrom airflow and pressure; rather, it correlates efficiency to thedimensionless flow term (φ), which requires both airflow andfan speed as inputs. As elaborated below, a designer (and mostsimulation tools) will use airflow and fan pressure as inputs tothe fan system model in order to calculate fan speed and effi-ciency. A second problem is that this model assumes a fixedpeak efficiency for fans of all sizes. This simplificationreduces the applicability of the fan model for comparativeanalysis of fan options as peak efficiency tends to increasewith fan diameter.As a result of these shortcomings, the authors set out todevelop a new component model that could directly be drivenby airflow and pressure. Based on the “fan laws” (ASHRAE2000), the core assumption of this new “characteristic curve”fan model is that the efficiency of a fan is constant as the fanrides up and
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