Development and Testing of the Characteristic Curve Fan Model

Transcription

1 AN Development and Testing of the Characteristic Curve Fan Model Jeff Stein, P.E. Member ASHRAE Mark M. Hydeman, P.E. Member ASHRAE ABSTRACT This paper describes the development and testing of the characteristic curve fan model a gray-box model. This model produces fan efficiency as a function of airflow and fan static pressure. It is accurate, relatively easy to calibrate, and could be easily incorporated into commercial simulation programs. Also presented is an application of an existing model to predict fan speed from airflow and fan static pressure. These models were developed as a part of a larger research project to develop design guidelines for built-up variable air volume fan systems. The models have been successfully employed in comparative analysis of fan types, wheel diameters, fan staging, and analysis of supply pressure reset. INTRODUCTION The authors were part of a publicly funded energy efficiency research team developing design guidelines for builtup fan systems in commercial buildings. According to previous research, fan energy in new construction for commercial buildings in California accounts for 1 terawatt-hour of electric energy usage per year, representing approximately half of all HVAC energy usage (CALMAC 2003). The authors research demonstrates that up to half of that fan energy is avoidable through cost-effective design practices, including fan selection (size and type), fan sizing, fan staging, and static pressure control (Hydeman and Stein 2003). Five monitoring sites provided field data on which to test the alternative fan system designs and design techniques. These sites were selected to represent a range of climates, occupancies, and fan system configurations (Kolderup et al. 2002). As part of this work, a simulation model of a fan system was sought that had all of the following characteristics: Accurate at predicting fan system energy over the full range of actual or anticipated operating conditions. Applicable for the full range of fan types and sizes. Easy to calibrate from manufacturer s or field-monitored data. Ability to identify operation in the surge region. Relatively simple to integrate into existing simulation tools. Ability to independently model the performance of the fan system components, including the motor, the mechanical drive components, the unloading mechanism (e.g., VSD), and the fan. The purpose of this model is to evaluate design alternatives for fan selection and control through simulation. Optimally, simulation tools would directly utilize the manufacturers fan curves to evaluate fan system operation at each discrete step of evaluation. Since this is not currently available, the authors sought models that simulation tools could easily incorporate that replicated fan performance. MAIN BODY Literature 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 (Brandemuehl et al. 1993; Clark, 1985). We also looked briefly at the models embedded in commercial simulation software, such as Trace and HAP, but found these suffered from the same problems as the model in DOE-2. DOE-2 uses a black-box regression model that produces the fan system power draw as a function of percent design airflow using a second-order equation as follows: Jeff Stein is a senior engineer and Mark Hydeman is a principal at Taylor Engineering, LLC, Alameda, Calif ASHRAE. 347

2 P a + b CFM CFM = + c P design CFM design CFM design 2 This model is implicitly built on several assumptions: 1. Each fan operates on a single system curve that uniquely maps airflow to static pressure. 2. Fan system efficiency is directly a function of airflow. 3. A second-order equation sufficiently models both of these effects. The DOE fan model implicitly combines the operating system curve with the models for each of the fan system components. Power is directly produced as a function of airflow only, and there is no opportunity to have different conditions of fan static pressure at a given airflow. Real VAV systems do not remain on a fixed system curve. System pressure as a function of airflow behaves differently depending on the location of the boxes that are modulating, the location of the static pressure sensor(s), and the static pressure control algorithm. Although this model is simple to use, it does not allow the user to independently model and evaluate each of the fansystem components. Thus, if designers wanted to evaluate the impact of motor oversizing, they would have to independently assemble fan and motor models to develop the DOE-2 performance curve that represented the combination of the two together. This model also does not directly account for the variation in fan system component efficiencies as the fan unloads, nor does it allow for evaluation of a multiple fan system, where fan staging will change both the operating efficiency and potentially the individual fan static as they are staged on and off. The model in the ASHRAE Secondary Toolkit is a graybox fan component model that uses the perfect fan laws through application of dimensionless flow (φ) and pressure (ψ) coefficients. This model uses a fourth-order equation to predict fan efficiency from the dimensionless flow parameter. where CFM N D ρ P C 1 and C 2 = airflow = fan speed = fan diameter CFM φ = c N D 3 P ψ = c ρ N 2 D 2 η fan = a + b φ + c φ 2 + d φ 3 + e φ 4 = average air density = fan static pressure and = constants that make the coefficients dimensionless (1) (2) (3) (4) This model allows the user to calibrate an entire family of fan curves with data from a single model. Unfortunately, this model does not permit the direct calculation of fan efficiency from airflow and pressure; rather, it correlates efficiency to the dimensionless flow term (φ), which requires both airflow and fan speed as inputs. As elaborated below, a designer (and most simulation tools) will use airflow and fan pressure as inputs to the fan system model in order to calculate fan speed and efficiency. A second problem is that this model assumes a fixed peak efficiency for fans of all sizes. This simplification reduces the applicability of the fan model for comparative analysis of fan options as peak efficiency tends to increase with fan diameter. As a result of these shortcomings, the authors set out to develop a new component model that could directly be driven by airflow and pressure. Based on the fan laws (ASHRAE 2000), the core assumption of this new characteristic curve fan model is that the efficiency of a fan is constant as the fan rides up and down on a particular characteristic system curve. Extensive testing with manufacturers fan selection software demonstrates that the manufacturers also use this simplifying assumption for developing fan performance data in both the surge and non-surge regions. ANSI/ASHRAE Standard (ANSI/AMCA Standard ) (ASHRAE 1999) explicitly permits this. For this model, a characteristic system curve is defined as a second-order equation, equating fan static pressure to airflow (cfm) with a zero constant and no first-order coefficient. For example, a VAV supply fan with a fixed duct static pressure setpoint of 1.5 in. w.c. will ride up and down on a system curve that runs through the design point and through 1.5 in. at 0 CFM. A characteristic system curve is a particular type of system curve in that it must run through the origin (0 in. at 0 CFM). A characteristic system curve is characterized by a single coefficient, SCC (system curve coefficient). The equation for any characteristic system curve is P SCC = (5) CFM 2. Using this assumption, it is only necessary to find fan performance at a single point on a characteristic system curve to define its performance along that curve at all speeds. As depicted in Figure 1, there are three characteristic system curves of particular importance: the curves at the minimum and maximum ends of the tuning data set and the curve that represents the highest efficiency for the fan. As described below and depicted in Figure 3, fans behave very differently on either side of this peak efficiency. The minimum and maximum curves represent the boundaries of the model tuning data. The triangles in Figure 1 depict points of data that were sampled from the manufacturer s fan selection software. Each point represents the fan efficiency for all points on a characteristic system curve. The fan efficiency is calculated from the fan brake horsepower (BHP), airflow (CFM), and fan static pressure ( P) reported by the software through the following equation: 348 ASHRAE Transactions: Symposia

3 CFM P η fan = BHP The model can be used to predict the fan power for any point whose system curve is between the two extreme system curves. Figure 1 is overlaid on top of an output screen from a manufacturer s selection program. Notice that the peak efficiency line is also the boundary of the manufacturer s Do Not Select or surge region. This is typical for plenum, backward inclined, and vane-axial fans. For airfoil, mixed flow, and propeller fans, the peak efficiency is well to the right (i.e., outside) of the surge region (see Figure 5). Figure 1 (6) Tuning data for 66 in. plenum fan shown on a manufacturer s fan curve. When a fan enters the surge region, not only does the efficiency drop, but also the fan begins to vibrate, which can create audible noise and damage the fan, bearings, drive, and attached ductwork. The further the fan moves into the surge region, the greater the vibration. Catastrophic failure can occur if the fan moves well into the surge region at high power (high static). Some manufacturers appear to be more conservative than others in terms of what amount of vibration is acceptable. Moving into the surge region at low power (low static) is not likely to cause catastrophic failure or unacceptable vibration, but it will reduce fan life. From our experience, fans with variable-speed drives commonly operate for extended periods of time in the surge region, but it is usually at low power. Figure 2 shows fan efficiency plotted against system curve coefficient (SCC) for the data from this 66 in. plenum fan. The efficiency data naturally divide into two regions left and right of the peak efficiency. It is interesting to note that the surge region in Figure 2 is to the right of peak efficiency, whereas it is to the left in the manufacturer s fan curve (Figure 1). The representation in Figure 2 is also somewhat hard to read, as it condenses the normal region to a small space. The efficiency curve is easier to visualize and to fit a regression equation if plotted as a function of the negative of the log of the system curve coefficient (see Figure 3). The log causes the efficiency curves to become nearly linear, and the negative flips the surge and normal regions so that it matches manufacturer s curves (i.e., surge to the left, normal operation to the right). The base of the log does not seem to make much difference. Natural log is used here. Gamma is defined as the negative of the natural log of the system curve coefficient. Figure 2 Fan efficiency vs. system curve coefficient. ASHRAE Transactions: Symposia 349

4 Figure 3 Fan efficiency as a function of gamma. γ ln( SCC) Fan efficiency can be accurately predicted as a function of gamma. The recommended procedure is to break the function into two parts: an equation for gammas in the surge region and another for gammas in the normal region. For this reason, it is important to get an accurate indication of the critical gamma, which is the gamma that corresponds to the system curve of highest fan efficiency. This can be done with the manufacturer s software by iterating on the airflow conditions in the vicinity of the critical gamma. Figure 3 shows the R-square regression statistic for various orders of polynomials to the example 66 in. plenum fan. As demonstrated in Figure 3, a first-order polynomial (i.e., straight line) is reasonably accurate. Higher order polynomials provide a better fit, but they require more data to calibrate and can produce undesirable results between calibration data points. A third-order regression appears to provide a good balance between calibration accuracy to the tuning data set and rational function behavior between calibrating data points. These equations are of the form: η fan_left_of_peak_efficiency = S 0 + S 1 γ + S 2 γ 2 + S 3 γ 3 η fan_right_of_peak_efficiency = N 0 + N 1 γ + N 2 γ 2 + N 3 γ 3 (7) (8) (9) where S 0 S 3 and N 0 N 3 are regression coefficients developed from tuning data on the left (surge) side and right (normal) side of the peak efficiency point. Regardless of the equation order, care must be taken to provide a continuous function through the critical gamma point. Figure 4 shows the accuracy of the characteristic curve fan model across 224 points, representing a wide range of fan speeds, pressures, and airflows. This tuning data came from a manufacturer s selection program, and the results are presented against this tuning data set. We used third-order polynomials to represent efficiency of gamma, with separate equations in the surge and normal regions (Equations 8 and 9). The characteristic curve model has been found to be accurate for at least six types of fans: plenum, backward inclined, airfoil, mixed flow, propeller, and vane-axial with fixed blades. This model does not apply to fans with variable pitch blades or inlet vanes. Figure 5 shows sample gamma curves for four types of fans. The curves are divided into the surge and non-surge regions in order to illustrate the relationship between peak efficiency and the surge region. Table 1 presents the characteristic curve fan model fit results across a range of manufacturers and fan types (plenum and housed, airfoil, and flat blade) and wheel diameters. This table presents the coefficient of variation root mean square error (CVRMSE) across the 57 fans in the database. Again, this represents third-order polynomial fits against tuning data from manufacturer s selection programs. Typically a fit of 1% to 3% CVRMSE is excellent; a 5% fit is acceptable. Table ASHRAE Transactions: Symposia

5 Figure 4 Accuracy of the characteristic curve fan model against tuning data. Figure 5 Sample gamma curves for six fan types. ASHRAE Transactions: Symposia 351

6 Table 1. CVRMSE for 57 Fans Left Region Right Region Count Min Max Average Min Max Average % 5.74% 0.37% +/- 0.76% 0.17% 3.66% 1.79% +/- 0.83% Figure 6 Manufacturer A 66 in. plenum fan efficiency map using the characteristic curve fan model. Figure 7 Phi as a function of efficiency. shows that the average CVRMSE is well within the excellent region. Figure 6 depicts the predicted fan efficiency from the characteristic curve fan model for the example 66 in. plenum fan. The predicted efficiency is plotted on the Z-axis as a function of the airflow (cfm, X-axis) and fan static pressure (H 2 O, Y-axis). The efficiency is computed between the minimum and maximum characteristic system curves. When viewed from the top, this curve presents the same XY plane as the manufacturer s fan curve (Figure 1). The Z-axis goes from white at the highest efficiency to purple at the lowest efficiency. It is interesting to note that fan efficiency falls more rapidly with a change in airflow in the normal region than in the surge region. In addition to the characteristic curve fan model, which predicts fan efficiency, a second model was developed for predicting fan speed from airflow and fan static pressure. This model, referred to as the Phi model, is used to simulate the performance of fans when they are riding the fan curve (e.g., at fixed speed). With variable-speed driven fans, this occurs when the fan reaches its minimum speed for motor cooling. The Phi model is derived from the Transys program, as reported in the ASHRAE Secondary Toolkit (Clark 1985; Brandemuehl et al. 1993). This model produces the dimensionless flow coefficient, φ (Equation 2), from fan efficiency, as predicted by the characteristic curve fan model. φ left_of_peak_efficiency = PS 0 + PS 1 η + PS 2 η 2 + PS 3 η 3 (10) φ right_of_peak_efficiency = PN 0 + PN 1 η + PN 2 η 2 + PN 3 η 3 (11) where PS 0 PS 3 and PN 0 PN 3 are regression coefficients developed from tuning data on the left (surge) side and right (normal) side of the peak efficiency point. Figure 7 shows the model parameters and r-square statistic for the example 66 in. plenum fan. Once φ is determined from Equations 10 and 11, Equation 2 can be used to calculate fan speed (N, rpm) from φ, airflow (CFM), and fan diameter (D, in.). DISCUSSION As displayed in Table 1 and Figure 4, the characteristic curve fan model is quite accurate at predicting fan efficiency from manufacturer s data. The model presented in the ASHRAE Secondary System Toolkit provides similar results. As stated in the objective, the real issue is how to take these models and apply them to design and analysis. This includes a number of subtopics: 1. The need to model the other components in the fan system. This includes the motor, physical drive (belts, coupling, or gears), and variable-speed drive (if applicable). 2. The accuracy of the fan system model compared to fieldmeasured data. 3. A methodology to apply the model to new construction, where the airflow and pressure demand need to be estimated. 352 ASHRAE Transactions: Symposia

7 Both the characteristic curve fan model and the ASHRAE Secondary Toolkit fan model produce fan efficiency as a function of operating parameters. However, total fan energy is typically more important for design studies. Fan energy cannot be determined without component models for motors, belts, and variable-speed drives. The researchers have developed these component models and have assembled them into a fan system model. This is documented in the project reports and will be the subject of another ASHRAE paper. Resources for existing component models include the following: 1. The research project web site, at < click on link for Large HVAC Integration. 2. The Department of Energy s Motor Challenge market transformation program (< and MotorMaster+ Program (< mm3.energy.wsu.edu/mmplus/default.stm>) for models and performance data of poly phase motors. 3. Data on variable-speed drive efficiencies are reported in Gao et al. (2001). 4. AMCA Publication (AMCA 1990) for belt drives. Figure 8 presents the accuracy of an assembled fan system model against field-measured data from one of the five monitored research sites. As can be seen in this figure, the fan system model underpredicts measured fan system energy by approximately 36%. There are a number of potential reasons for this, including, but not limited to, the following: measurement error model error (for the fan and other components) variation of the fan performance in the field inaccuracy in the tuning data reported by the manufacturers The fan measurements used in this field test include fan airflow, differential pressure across the fan, and fan power. A true RMS power meter with high sampling rate was used for measurement of power; it was the most accurate of the measurements. Airflow and air pressure measurements are inherently inaccurate, particularly when the fan is operating in surge, causing the airflow and pressure to fluctuate (analysis indicated that this fan was in surge over 60% of the time [Hydeman and Stein 2003]). The fan airflow was measured with a calibrated pressure grid located in the inlet of the fan. At this site, each fan had an inlet barometric backdraft damper that was used to isolate fans for staging. The fan pressure was measured across the fan and backdraft dampers and included the pressure drop of the inlet dampers. The inlet dampers, inlet configuration, and proximity of another plenum fan at the discharge most likely also created system effects that reduced potential fan output. This is a general issue with prediction of fan performance in the field. Not only is it inherently difficult to measure fan airflow and pressure accurately, seldom, if ever, will the field conditions approximate the ANSI/ASHRAE Standard (ANSI/AMCA Standard ) test conditions used for development of manufacturers data. Field conditions will always impart inlet and discharge system effects that cause actual fan performance to deviate from test stand conditions. It is likely that these field effects will always lead to lower fan performance (higher energy and lower flow) than the manufacturer s data predicts. This is further complicated by the fact that large parts of the manufacturers reported fan data are extrapolated from actual factory test data. Data are extrapolated through speed using the assumption of fixed efficiency along a fan characteristic system curve. Data are also extrapolated between fan Figure 8 Accuracy of the fan system model on field-measured data. ASHRAE Transactions: Symposia 353

8 Figure 9 Fan efficiency vs. gamma for several of Manufacturer A s fans. Figure 10 Housed airfoil fans: peak efficiency vs. diameter. sizes within a model line using other perfect fan laws. Under ANSI/ASHRAE Standard (ANSI/AMCA Standard ), manufacturers are not required to test all fan sizes. According to the standard, test information on a single fan may be used to extrapolate the performance of larger fans that are geometrically similar using the fan laws (ASHRAE 2000). Figure 9 shows curves for several fans, including five sizes of Manufacturer A s plenum airfoil fans. The 54 to 73 in. diameter plenum airfoil fans have virtually identical curve shapes, just shifted along the x-axis (gamma). The 49 in. version has a different peak efficiency and curve shape. This suggests that Manufacturer A tested the 54 in. fan and extrapolated the performance to the 60 to 73 in. sizes. Using the fan laws, one can exactly duplicate the curves from 60 in. through 73 in. using the 54 in. fan data. Figure 9 also shows one airfoil fan and a forward curve fan. These fans have different curve shapes than the plenum fans. Figure 10 shows the highest efficiency (efficiency at critical gamma) for a number of housed airfoil fans from two manufacturers as a function of wheel diameter. By reviewing the step changes in the peak efficiency data as a function of fan 354 ASHRAE Transactions: Symposia

9 diameter, it is clear from this figure which fans the manufacturers tested and which they extrapolated. For example, both Manufacturer A and Manufacturer B tested their 30 in. fans. Manufacturer A then extrapolated the 30 in. data all the way up to 73 in. (the variability in the peak efficiency of the Manufacturer A 30 in. to 73 in. fans is due to rounding and sampling error). Manufacturer B only extrapolated the 30 in. up to 36 in., then they tested the 40 in.and extrapolated that all the way to 73 in. Manufacturer A s 30 in. is more efficient than Manufacturer B s 30 in. but not more efficient than the Manufacturer B s 40 in. Had Manufacturer A tested a 40 in. (or larger) fan, they might have found that it had higher efficiency than equally sized Manufacturer B s fans. To use the characteristic curve fan model in a design context, we suggest the following process: 1. Develop a simulation model of the facility. 2. Export the hourly demand for fan airflow cfm. 3. Bin the data by hours spent at increments of airflow (10 to 20 bins should suffice). 4. Develop a system curve that represents the coincident pressure at each fan airflow. Note: this may actually be a family of curves representing issues such as supply pressure reset control and the fixed pressure overhead for individual fans run alone or in parallel. 5. Evaluate the performance of alternate fans across the bin data using the system curves to develop a coincident pressure. This, of course, is moot if software developers incorporate the characteristic curve fan model in their programs directly for a parametric analysis. CONCLUSIONS As shown in this paper, it is possible to accurately predict manufacturers fan performance using the characteristic curve fan model. However, it is a challenge to predict field performance due primarily to inaccuracies in instrumentation, system effects due to field conditions, and inaccuracies in the manufacturers reported performance data (due mostly from their extrapolation of test data). From a design perspective, some of these issues are moot, as biases in instrumentation, measurement, and data reporting will tend to cancel out in a comparative analysis of design alternatives. To serve as a design tool, a predictive fan model should be developed to predict brake horsepower from airflow and fan static pressure. These are the inputs that are typically provided in a simulation tool. The model should also have discrete submodels for the separate fan system components so that analysis can be done on the impact of design alternates for each of those components. Overall, the characteristic curve fan model meets all of these requirements. It is accurate at predicting manufacturers data, relatively easy to tune, and could easily be incorporated into existing simulation tools. The authors have successfully employed it in Visual Basic code. There are limitations; this model works for systems with fixed-speed fans and fans with variable-speed drives, but it will not work for fans with inlet vanes or variable-pitch blades. Those challenges are left up to future researchers. Also left to future researchers is the development of generalized fan models based on the characteristic curve fan model. The techniques described thus far require tuning data specific to each fan to be evaluated. However, there are clear patterns between gamma curves for fans of the same type (see Figure 9) A single gamma curve could be used to represent all fans of a certain type (housed airfoil, plenum airfoil, plenum flat blade, etc.). This curve could then be translated along the gamma axis using the perfect fan laws and along the efficiency axis as a function of diameter. Figure 10 shows such a function for housed airfoil fans. ACKNOWLEDGMENTS The authors would like to acknowledge the input and work of other members of our research team, including Cathy Higgins of the New Buildings Institute, Steve Taylor of Taylor Engineering, Erik Kolderup and Tianzhen Hong of Eley Associates, Lynn Qualman from SBW Consulting, Inc., and Roger Lippman from New Horizon Technologies. They would also like to recognize the contributions of our technical advisory team members. Finally, special thanks to the numerous building engineers and property managers at these sites for putting up with our intrusions at their buildings and for their significant assistance in our work. REFERENCES AMCA AMCA Publication , Field performance measurement of fan systems, 0203X90A-S. Arlington Heights, Ill.: The Air Movement and Control Association International, Inc. ASHRAE ANSI/ASHRAE Standard (ANSI/ AMCA Standard ), Laboratory Methods of Testing Fans for Aerodynamic Performance Rating. Atlanta: American Society of Heating, Refrigerating and Air- Conditioning Engineers, Inc. ASHRAE ASHRAE Handbook HVAC Systems and Equipment, Chapter 18, Fans. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Brandemuehl, M.J., S. Gabel, and I. Andresen HVAC 2 Toolkit: Algorithms and Subroutines for Secondary HVAC System Energy Calculations. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. CALMAC Data from the non-residential new-construction database available from the California Measurement Advisory Council s web site, < Clark, D.R HVACSIM+ building systems and equipment simulation program: Reference Manual. NBSIR ASHRAE Transactions: Symposia 355

10 , U.S. Department of Commerce, Washington D.C. DOE (Department of Energy) DOE 2 Reference Manual, Part 1, Version 2.1. Lawrence Berkeley National Laboratories, Berkeley Calif., May. Gao, X., S.A. McInerny, and S.P. Kavanaugh Efficiencies of an 11.2 kw variable speed motor and drive. ASHRAE Transactions 107(2). Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Hydeman, M., J. Stein A fresh look at fan selection and control. HPAC Magazine, May. Kolderup, E., M. Hydeman, M. Baker, and R.L. Qualmann Measured performance and design guidelines for large commercial HVAC systems. ACEEE Conference on Energy Efficiency, August. DISCUSSION David Yuill, Principal, Building Solutions Inc., Omaha, Neb.: We have done some similar work in which we developed a model to predict airflow through a fan using the design fan curve, fan head, and fan speed as inputs. We set up an experiment to test this model, but we found that the manufacturer s fan curves were not accurate. Have you found this, and are you aware of any data on fan curve accuracy? Jeff Stein: As noted in the paper we did not find a good correlation between measured fan energy and predicted energy (based on manufacturer's data). There are many possible reasons including: (1) The pressure and air flow sensors used in the field tests may be inaccurate. (2) Even if the sensors are accurate, field tests of fan operating static cannot match the AMCA test conditions of "fan static" in the lab: it is impossible to measure "fan static" (the Y axis on a fan curve) in the field since the installation conditions are completely different. System effects play havoc with fan performance in the field. (3) Manufacturer's do not test all sizes. The AMCA rating standard for fans allows them to test a fan and extrapolate the results to all larger fans of the same type. (4) Accuracy of the manufacturer's tests. We noticed that performance data for some fan types got worse and then better as you move to larger sizes. This suggests that there may be variability in the manufacturing or testing processes. We are not aware of any data on fan curve accuracy. 356 ASHRAE Transactions: Symposia