1、2010 ASHRAE 323ABSTRACTExisting methods for fan performance model are mostlybased on fan static pressure and fan airflow. However, for typi-cal packaged HVAC units, a non-ideal airflow pattern arisesdue to the compact arrangement of the interior components,resulting in both the fluctuation of the fi
2、eld fan static pressureand the difficulties of installing the pressure sensors. Thispaper describes the development of the fan performance grey-box model, which relates fan power consumption to fan speedand airflow, both of which are much easier to measure. Severalpractical field measuring or predic
3、tion methods of blowerspeed for the model implement and validation are proposed.Finally, the model is evaluated in terms of interpolation andextrapolation using the manufacturers data and validatedwith laboratory data. This model can be used to predict thepower consumption and fan static pressure, f
4、or comparativeanalysis of fan types, wheel diameters widths and air density,and for fault detection and diagnosing of fan operation.INTRODUCTIONFan performance characteristics, especially fan powerconsumption, is critical for the investigation of the HVACsystem operations optimization and energy sav
5、ing strategies.Simulation software, such as DOE-2, HAP, eQUEST, assumethat: (1) each fan operates on a single system curve thatuniquely maps airflow to static pressure; (2) fan system effi-ciency is a direct function of airflow; (3) and a second-orderequation sufficiently models both of these effect
6、s. A black-box regression model is used, producing the fan system powerdraw as a function of the percent design airflow using asecond-order equation as follows:(1)While in Energy Plus, the fan performance modeldescribes the fan through the values for the design pressureincrease across the fan, the d
7、esign volumetric flow rate, the fantotal efficiency and the fan motor efficiency. The followingequations define the model for the single speed fan.(2)(3)For the variable speed fan, it adopts the coefficients of a4th order polynomial that relates the fan mass flow rate to thefan power consumption. Th
8、e dependent variable is the massflow fraction, and the independent variable is the fan powerpart load ratio.(4)(5)(6)Jeff Stein (2004) developed a characteristic curve fanmodel, a gray-box model, which produces fan efficiency as afunction of the airflow and static pressure.HHdesign- ab+QQdesign- c+Q
9、Qdesign-2=HtotmPetotair-=HshaftemotorHtot=fflowmmdesign-=fplc1c2fflowc2fflow2c3fflow3c4fflow4+=HtotfplmPetotair-=Development and Validation of a Fan Performance Model for Typical Packaged HVAC SystemsKeke Zheng Haorong Li, PhDStudent Member ASHRAE Member ASHRAEK. Zheng and H. Li are from the Univers
10、ity of Nebraska-Lincoln, Omaha, NE.OR-10-035 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print
11、or digital form is not permitted without ASHRAEs prior written permission. 324 ASHRAE Transactions(7) = ln(SCC)(8)(9)(10)In Equations (9) and (10), third-order polynominals areused to represent the efficiency of gamma, with separate equa-tions in the “surge” and “normal” regions. Where S0 S2andN0 N2
12、are regression coefficients developed from tuningdata on the left side and right side of the peak efficiency point.In sum, existing research on the fan characteristics isbased on the large-scale air handling unit (AHU) systems,while there is a lack of research concerning the packagedHVAC systems. Ty
13、pical packaged HVAC systems are mainlyemployed in light commercial use including hotels, supermar-ket or retail stores, the compact arrangement of interiorcomponents introduces a non-ideal airflow pattern, resultingin both the fluctuation of the field fan static pressure and thedifficulties installi
14、ng the pressure sensors. Therefore, thosemodels introduced above that are dependent on the pressureparameter would be improper to be adopted for packagedsystems.Additionally, most of the current methods for modelingthe fan power consumption are to fit the manufacturers datausing a black-box model fo
15、rmat. One limitation of thisapproach is that the model can only be trusted within the rangeof conditions to which it was fit. In addition, these black-boxmodels are not useful for investigating the design retrofitsassociated with the fan, such as changes in the fan speed, airdensity, or limited map
16、data.The goal of this paper is to develop an empirical fanperformance model for typical packaged HVAC units, basedon the grey-box model of the fan power consumption and themanufacturers data. This model was tested using both inter-polation and extrapolation, and then implemented in a labora-tory roo
17、ftop system. Comparing with measured values in thelaboratory, it can give an accurate prediction of the fan powerconsumption.MODELFigure 1 shows a cross section of the impeller of an ideal-ized two-dimensional centrifugal fan with a typical backward-curved design. The radius of the fan inlet hub and
18、 fan wheel areseparately r1and r2. The installation angle of each impellerblade is 1for the inlet side and 2for the outlet side. Theimpeller rotates with an angular velocity , having a tip speedequal to u1in the inlet side and u2in the outlet side. Airflowenters the wheel through the inlet hub with
19、an absolute speedv1and a relative speed w1, and exits the wheel at an absolutespeed v2and a relative speed w2. The velocities tangential andnormal to the wheel are denoted as vrand vufor both the inletand outlet sides.According to the Impulse-Momentum Principle, alongwith the continuity and energy b
20、alance principle (Vennard andStreet 1988), we can obtain:H = Qu2v2cos2(11)Usually, the inlet air characteristics are defined as thestandard fan characteristics (ASHRAE STD51 1999), andbased on the mass conservation equation:Q = 1Q1= 2Q2(12)givingH = 2Q2u2v2cos2(13)Equation (13) is developed under th
21、e assumption thatthere are infinite fan blades and an ideal flow pattern inside thefan impeller, in reality, however, only limited blades areinstalled. As a result, the turbulent flow correction factor k isintroduced for the correction, usually less than one with typi-cally values 0.7 to 0.9 (Zhou 1
22、993).ThenH = k2Q2u2v2cos2(14)Based on the velocity vector diagram in the Figure 1, weget vcos = vu = u vrctg (15)So that,u2v2cos2= u22 u2vr2ctg2(16)H = k2Q2(u22 u2vr2ctg2)(17)And,u = r = DN/60 (18)Q = vrF = vr(Db)(9)SCC P Q2=fanLeftPeakEfficiencyS0S1+ S2+ 2 Sa+ 2=fanRightPeakEfficiencyN0N1+ N2+ 2 Na
23、+ 2=Figure 1 Schematic of airflow in fan space and the velocityvector diagram. 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution
24、, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 325Substituting these equations into Equation (14), gives(20)(21)Moreover, as seen from the Equation (21), this modelshows the effects of using different types of fans wit
25、h differentwheel diameter, width and the air density.In the fan power model, the airflow rate and fan speed areindependent variables, with the fan power consumption is adependent variable. The other unknown parameters to deter-mine include the turbulent flow correction factor k, the fanwheel outlet
26、side diameter D, the fan blade installation angle2, the fan blade width b and the fan blade displacement thick-ness correction factor .Traditionally, in order to implement this model, all theunknown parameters must be known in advance, the fan wheeloutlet side diameter D, the fan blade installation
27、angle 2, thefan blade width b can be acquired from the fan design docu-ments, while the turbulent flow correction factor k and the fanblade displacement thickness correction factor are empiricalvalues, both of which are related to different dimensional andmodel fans.To simplify the unknown parameter
28、s estimation process,a convenient approach using the fan manufacturers data isproposed.According to the ANSI/ASHRAE Standard 51-1999, themanufacturers fan performance data is standardized using thestandard fan inlet condition, and we should also convert theairflow in the model from the outlet to the
29、 inlet variable.Substitute the mass conservation Equation (12) intoEquation (21) to get:(22)Equation (22) could be further simplified by combiningall the unknown parameters into C1and C2,(23)(24)The theoretical power input for the fan is:H = C1Q1N2 C2Q12N (25)Further, the fan static pressure (Ps) or
30、 total pressure can beconveniently obtained from the map data. It is based on themeasured airflow Q and the H calculated from the model.Hhence the fan efficiency could be calculated according to thefollowing:(26)VALIDATIONTwo methods have been implemented to validate the fanpower model. The first ap
31、proach is to compare the modelresults with the manufacturer map data. Results from thepredicted power consumption results in the model are directlycompared with the values from the manufacturer map data.The interpolation and the extrapolation of the model was alsotested using the manufacturers data.
32、 Secondly, compare themodel predictions with the measured power consumptionusing the power meter installed in the laboratory setup.A 7.5 ton (26.37 kW) rooftop unit, equipped with a cen-trifugal supply blower with backward curved blades wastested in a laboratory environment.Model Correlation Testing
33、 Using Manufacturers DataThe unknown parameters of the model are determined byminimizing the sum of squares of the differences between themanufacturers and the models fan power consumption, andthen the predicted power consumption results are comparedwith the manufacturer map data.The manufacturers b
34、lower performance data of the7.5 ton (26.37 kW) rooftop unit was used in this case. All dataavailable were used to identify the model parameters.Then, all the fan power consumption data in the manufac-turer table were compared to the corresponding predictedmodel results under the same rated fan airf
35、low and fan speeddata.As shown in Figure 2, the empirical model correlates wellwith the manufacturers data, which is comparable to black-box model correlation.Table 1 summarizes all the predicted results of sevenblower models. Overall, fan power consumption comparisonsresults show little error, whic
36、h indicates that the model formatcorrelates very well with the data.Where,Bias error: bias = sum (Hi Hi, i = 1, N)/N;Sum of square errors: sigma = sum (Hi-Hi)2, i = 1, N;Root mean squared error: RMSE = sqrt sum (errorsquare i, i = 1, N)/N.Hk2Q2DN60-2DN60-Q2Db-ctg2=Hk2D60-2Q2N2ctg260b-Q22N=Hk1D60-2Q1
37、N2ctg260b-12-Q12N=C1k1D60-2=C2k12-ctg260b-=sHoH-QPsC1Q1N2C2Q12N-= 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmis
38、sion in either print or digital form is not permitted without ASHRAEs prior written permission. 326 ASHRAE TransactionsModel Interpolation and Extrapolation Testing Using the Manufacturers DataInterpolation and extrapolation performances of themodel were tested. The manufacturers fan performance dat
39、afrom the 7.5 ton (26.37 kW) rooftop unit was used in this test.As shown in Table 2, the manufacturers data is dividedinto multiple sets:Set #1: the set marked with dark-grey color means no dataavailable;Set #2: the set marked with “*” symbols used for modeltraining for interpolation testing;Set #3:
40、 the complementary data set of data Set #2 used fortesting the interpolation performance of the model trained bydata Set #2;Set #4: the set marked with “#” symbols used for modeltraining for extrapolation testing.Set #5: the complementary data set of data Set #4 used fortesting the extrapolation per
41、formance of the model trained bydata Set #4.Table 3 summarizes the parameters and correlation per-formance of both interpolation and extrapolation tests for themodel.Figures 3 and 4 show separately the accuracy in thecomparison between the model prediction results and themanufacturers map data throu
42、gh interpolation and extrapola-tion. Both figures show a good approximation.Model Validation Using Laboratory Experimental DataThe laboratory experiment was also conducted using thesame 7.5 ton (23.67 kW) rooftop unit. Different scenarioswere tested by adjusting the supply airflow rate from around14
43、55 cfm (0.687 m3/s) to 3300 cfm (1.557m3/s).In the validation experiment, we should directly measurethe fan speed, airflow values and power consumption of themotor. The predicted fan power consumption of the model iscompared with the measured power consumption. Figure 5 isa schematic of the test set
44、up.The airflow rate was measured using a air flow stationwith 2% accuracy within the actual airflow range, which isinstalled in end side of the supply air duct. The airflow stationis actually a differential air pressure device designed tomeasure the velocity, and the probe includes multiple sensingp
45、oints to measure the total and static pressure, incorporates aunique design to amplify the differential pressure by approx-imately 2.5 times for accurate measurement of lower velocitydown to 200 fpm (1.016 m/s), the value is much lower than thetypical velocity of the airflow in the tested rooftop sy
46、stem.Figure 2 Comparison of the fan power of the model with the manufacturer data.Table 1. Model Prediction ResultsModel Data Number C1C2RMSE Sigma Bias1 65 2.828E-06 2.011E-07 0.03906 0.0912 0.0059772 108 1.739E-06 3.449E-07 0.015 0.0243 0.0027223 24 2.407E-06 1.000E-14 0.04167 0.0416 0.017354 20 1
47、.686E-06 1.333E-07 0.02733 0.01494 0.011665 16 1.94E-06 1.000E-14 0.02438 0.009512 0.009446 32 2.923E-06 3.422E-07 0.02736 0.02395 0.0075287 28 3.368E-06 2.931E-07 0.03137 0.02755 0.0097 2010, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published
48、 in ASHRAE Transactions 2010, Vol. 116, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAEs prior written permission. ASHRAE Transactions 327Figure 3 Comparison of the fan power of the model with the manufacturer data.Figure 4 Comparison of the fan power of the model with the manufacturer d
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