AC-2332 -- Laboratory Fan Test: Error Analysis PDF

In the process of writing ASHRAE STANDARD 51-74, "Laboratory Methods of Testing Fans forRating Purposes", the Standards Committee decided that an error analysis would be needed forguidance on instrumentation requirements and for evaluating the overall accuracy to beexpected using the STANDARD. Concurrently with the other work, the analysis was completedand did prove useful for its intended purposes. Systematic instrument errors were minimizedin the STANDARD through the use of calibration procedures. The remaining errors were consideredto be random and independent and thus, susceptible to statistical analysis.

To simplify the analysis, the flow processes are considered to be incompressible, andgeneralized equations covering the basic determinations of all set-ups are used. The testresults are considered to be curves of fan static pressure versus fan flow rate (fan characteristiccurve) and fan static efficiency versus fan flow rate (fan efficiency curve).An analysis based on fan total pressure would be more complicated mathematically while providingsimilar results.

The purpose of a laboratory fan test is to determine the fan characteristic curve, sothat the operational performance of the fan, when used with various system resistances, canbe predicted. The characteristic curve is a graphical presentation of a series of calculatedvalues for separate points on the curve, and each involving a complex combination of measuredquantities. Each measured quantity contains an uncertainty of measurement, and thus there isan uncertainty in the value of the characteristic curve itself. This can be visualized asa displacement of the test characteristic curve from its true or most probable position(Fig. 1).

When the test fan characteristic is used to predict the air flow in a given system, therewill be an error in the predicted air flow due to the displacement of the intersection ofthe system resistance curve from the true fan characteristic. This error, which will becalled the characteristic error (deltaQ_K) is the net result of all testing errors and isillustrated graphically in Fig. 1. The system resistance curve is presumed to be a parabolawith its vertex at the origin and is as~umed to be without error. This system resistancecurve is also the locus of the fan "fan point of operation" for various fan speeds and isthus the curve along which the fan laws apply.