1、NA-04-6-5 Validating and Improving the Delta-Q Duct Leakage Test Darryl Dickerhoff lain Walker, Ph.D. Member ASHRAE Max Sherman, Ph.D. Member ASHRAE ABSTRACT The Delta-Q duct leakage test has been developedover the past several years as an improvement to existing ductpressur- ization tests. It focus
2、es on measuring the air leakage flows to outside at operating conditions that are required for energy loss calculations forductsystems, and infiltration impacts. The Delta-Q test builds on the standard envelope tightness measurement technique of a blower door by repeating the tests with the system a
3、ir handler ofand on. This study uses detailed laboratory measurements to validate the Delta-Q testproce- dure and calculations. The laboratory measurements used a purpose-built test chamber coupled to a duct system typical of forced-air systems in US. homes. Special duct leab with controlled and mon
4、itored airflow were designed and installed in the duct system. This testsystem enabled us to systematically vary the duct and envelope leakage and to accurately measure the duct leakageflows for comparison to Delta-Q test results. The laboratory testing has also led to enhancements to the Delta-Q ca
5、lculations that increase the accuracy of the leakage measurement. INTRODUCTION Distribution system leakage is a key factor in determining energy losses from forced-air heating and cooling systems. (Cummings et al. 1990). Several studies (Francisco and Palm- iter 1997, 1999; Andrews et al. 1998) have
6、 shown that the air distribution system efficiency cannot be reliably determined without good estimates of duct air leakage. Specifically, energy calculations require the air leakage flow to outside conditioned space at operating conditions to be known. The test methods currently used in ASHRAE Stan
7、dard 152 (ASHRAE 2004) and many utility and weatherization programs either precisely measure the size of leaks (but not the flow through them at operating conditions) or measure these flows with insufficient accuracy. This and other methods to measure thermal distribution system leakage are discusse
8、d in Walker et al. (1998a, 1998b, 2001), Francisco et al. (2002), Andrews (1998), and ASHRAE (2003). The Delta-Q test uses a simplified physical model of the distribution system leakage that uses prior knowledge regard- ing how distribution systems function in residential buildings. The test procedu
9、re builds on existing envelope leakage measurement techniques to infer thermal distribution system leakage at normal operating conditions. This study builds onprevious studies (Walker et al. 1998a, 1998b, 2001 , 2002) by performing a systematic laboratory evaluation of test accuracy and by making im
10、provements to the analytical methods used to derive the air leakage flows from the measured airflow and pressure data. This study eval- uates the Delta-Q test against a truth standard approaching the accuracy of the known leakage values for the test chamber. BUILDING ENVELOPE LEAKAGE Building envelo
11、pe leakage has been thoroughly studied over many years because it relates to the envelope that encloses the building and acts as a pressure boundary. Empir- ically, the flow of individual building leaks has been shown to have the non-Darcy functional form in Equation 1. Q = C(P)“ (1) where . See, fo
12、r example, the Air Infiltration and Ventilation Centre, http:/ /www.aivc.org, for resources on infiltration and air leakage. Darryl Dickerhoff is a principal research associate, lain Walker is a staff scientist, and Max Sherman is a senior scientist with the Energy Performance of Buildings Group of
13、the Indoor Environment Department, Environmental Energy Technologies Division of the Lawrence Berke- ley National Laboratos: University of California, Berkeley, Calif. 02004 ASHRAE. 741 Q = volumetricairflow C = leakagecoefficient P = pressure across the leak n = pressureexponent Physically, the exp
14、onent must be between half and unity, corresponding to inertial flow and fully developed laminar flow. Sherman (1992) and Walker et al. (1998) have shown that power-law behavior with an intermediate exponent is to be expected from short path-length leaks and is physically described by developing lam
15、inar flow. Sherman and Dicker- hoff (1 998) have shown that the exponents are clustered near 2/3 (0.65k0.08). The standard technique for measuring building envelope leakage is fan pressurization (ASTM 1999), during which a set of steady-state pressures is built up by use of a fan and the airflow ver
16、sus pressure data is fit to Equation 1. The device used to pressurize the building is colloquially known as a “blower door,” and its use and history are described by Sher- man (1995). DISTRIBUTION SYSTEM LEAKAGE In many parts of the U.S., distribution system leakage is a more important problem than
17、envelope leakage in terms of energy, indoor air quality, and peak power usage. Understand- ing the process, being able to quantifi the effect, and being able to predict benefits of leakage reduction require a robust model of the process. Most distribution systems, especially in the climates that req
18、uire cooling, can be characterized by Figure 1. In most smaller buildings, at least some part of the air distribution system extends outside of the pressure boundary formed by the envelope so that leakage from those parts of the system represent a loss of conditioned air from the building. The physi
19、cally important quantities to determine are the supply and return airflows through the leaks (to outside condi- tioned space) under normal operating conditions, Because there is an air handler inducing airflow through the distribution system, the pressures in the distribution system will be quite di
20、fferent from those across the enclosure. In particular, the return side of the system will generally be under negative pressure, and air leakage enters the duct system. Conversely, the supply side is at a positive pressure, and supply air leakage leaves the duct system. DEVELOPMENT OF DELTA-Q The de
21、velopment of the Delta-Q model comes from split- ting the total leakage into three parts: the envelope, the supply ducts, and the return ducts. When the air-handler fan is on, these leaks all see different pressures. The full development of the Delta-Q equation can be found in Walker et al. (2001),
22、and is given in Equation 2. AQ(P) = Q, ( I -t- ps P)l - (P)” ps - -e,.( - pr p”+ (:)“I (2) where AQ is the difference in airflow through the blower door required to keep the enclosure at a fixed pressure relative to outside when the air handler is switched on, and the subscripts “s” and “r” refer to
23、 the supply side and return side, respec- tively. Thus, Q, is the supply leakage flow and P, is the char- acteristic pressure for the supply ducts. All pressures are expressed relative to outside the house, and P, and P, are expressed as positive values. In most cases, the normal oper- ating supply
24、and return leakage flows are not equal, resulting in a net pressurization or depressurization of the house. This usually small pressure is often ignored, but later we will discuss a correction for this effect on the Delta-Q analysis. It is also assumed that all measurements are taken at the same air
25、 density. Note that to maintain the proper sign conventions, we have used the notation that Equation 2 is linear in the two most important parame- ters-namely, the supply and return leakage airflows-but it does have, in principle, four other unknown parameters: the operating pressures and exponents
26、of the supply and return leakage. In most systems, there is more than one leak site and one operating pressure. P, and P,. are then the two pressures that best characterize the individual pressures across all supply and return leaks. ANALYSIS OF THE DELTA-Q MODEL A robust inverse model must be able
27、to accurately deter- mine the parameters of interest within the likely range of application. For a nonlinear model, it is quite likely that there will be ranges of the parameters in which the model will not work well, so there is some value in examining the limits of Air Handier Figure 1 Illustratio
28、n of a typical residential air distribution system. 742 ASHRAE Transactions: Symposia Equation 2 with respect to the pressure and exponent param- eters. Consider the limit in which the applied presswe is much larger than the induced supply or return pressures: in the measurements of pressure and flo
29、w, the wider the range of pressures for which we will be able to extract useful infor- mation. However, it is clear that if the range of applied pres- sures is far away from the characteristic supply and return pressures, we will not get good information from Equation 2. If we have prior knowledge a
30、bout the supply and return pres- sures and the exponent, we are not limited in this regard. AQ(P)Psr) % Qs.s(g)“- -Qr,r(pp?nr- (3) Equation 3 shows that for any exponent less than unity, the Delta-Q value will go asymptotically to zero when the applied pressure is much larger than the characteristic
31、 supply and return leakage pressures. In circumstances where the leak- age is very large (on the order of 50% of fan flow or more), the true Delta-Q relationship is more complex and its limits are less well defined. However, precision diagnostics are not required to detect duct failures of this magn
32、itude. We also consider the opposite limit in which the applied pressure is much smaller than either of the characteristic leak- age pressures: We can explore the nature of operational range by plotting Equation 2 for some intermediate conditions. Figure 2 contains a plot of the kinds of Delta-Q cur
33、ves we might expect for a distribution system that had leakage in the supply only, and the leak is at three different leak pressures: 0.060, 0.141, and 0.281 in. water (1 5,35, and 70 Pa). The inflection point in the Delta-Q curve corresponds to these leak pressures. For a supply leak, the inflectio
34、n point is found during envelope depressurization as the sign of the pressure difference across the leak changes from positive to negative. The flow direction through the leak goes from outflow, through zero (at the inflec- tion point), and then becomes inflow because the whole system is depressuriz
35、ed more than the positive pressure exist- ing in the supply ducts during normal operation. Similarly, for return leaks, there will be an inflection point at a positive enve- lope pressure difference. In Figure 2, we show three curves that represent the iden- tical airflows at operating conditions bu
36、t are for three different characteristic pressures (Le., P,). The shape of the curve in the region of interest is quite different (Andrews 2002), suggest- ing that we canuse experimental data to determine this param- AQ(p ( P,) = g“ .(:) %- - 4?,.“.() %- (4) In this limit, the Delta-Q equation does
37、not provide any information except for the imbalance flow, Q, - Q, If all of the data are in this regime, the De1ta-Q procedure will fail, but some data in this regime can be helpful. The exact limits of when the Delta-Q equation breaks down are going to depend on data quality. The more precision En
38、velope Pressure Difference (Fa) -50 -2 5 O 25 50 - _ _ . - - -a 300 E r o Y 250 200 150 1 O0 125 1 O0 50 - ._ _ _ -li - . . _ 25 50;- - I O O -0.2 -0.15 -0 1 -0 05 O O 05 o1 O 15 02 Envelope Pressure Difference (in. of water) Figure 2 Supply leakage Delta-Q curves with diferent supply leakage pressu
39、res. ASHRAE Transactions: Symposia 743 eter. The positive and negative pressure asymptotes go to zero for all physical combinations of parameters. The exception occurs if the leakage exponent is unity. If the pressure flow leakage relationship is linear, the Delta-Q curve becomes a horizontal line,
40、and the only quanti that can be determined from the data is the difference between supply and return leak- age. Leak Pressures The standard Delta-Q model assumes that there is a single supply or return leakage pressure and, thus, there is one equiv- alent leak on each side; this is sometimes assumed
41、 to be the plenum pressure. A single leak pressure leads to the charac- teristic inflection point and shape of Figure 2. In reality, there are going to be many leaks in the duct system. Even if all of the leaks were in the plenum, the plenum pressure might not be the appropriate pressure because of
42、inertial effects. In a real duct system, the leaks will be distributed at multi- ple pressures. A measured Delta-Q curve for such leaks would have multiple inflection points and have a more stair-step pattern rather than a single maximum and minimum. If we knew in advance the size and locations of a
43、ll of the leaks, we could devise an exact Delta-Q expression to match it, but we are interested in the reverse modeling problem of trying to infer properties from measurements. Thus, we will continue to assume that there is a single leak on each side with the understanding that we are finding an equ
44、ivalent leak with the same performance as the actual system. By doing so, we are finding the effective leakage properties of the system, which may or may not represent the conditions of an actual leak. Use of Prior Knowledge The Delta-Q equation (Equation 2) ostensibly has six unknown parameters tha
45、t need to be resolved. The typical experiment, however, generates around ten to twenty indepen- dent data points, each at a different envelope pressure differ- ence, leaving only a few degrees of freedom and decreasing the statistical power of the model. One way to improve this situation would be to
46、 take data over a wide range of envelope pressures. Another is to use prior knowledge about the parameters of interest to either remove them from the analysis or to restrict their values. Let us review what is known about these quantities. . . 744 We know both physically and by definition that the l
47、eakage flows must be non-negative. They also have a physical maximum equal to the flow through the air handler, but, since typical leakage rates are around 10% of air-handler flow, this maximum does not often play an important role. Ps,l: The supply and return leakage pressures must be positive (as
48、defined here). Their maximum value would be the pressure just on either side of the fan, which is normally represented by their respective plenum pres- sures. Because of the opportunity for leakage and larger impact of the leaks at higher pressure, we would nor- mally expect the leak pressure to be
49、in the upper-half of its range. Experience to date has borne out this assump- tion. ns,: Physically, the exponents must be between half and unity, but, as mentioned earlier, existing pressurization data have shown that the exponent tends to be close to 0.6 for air distribution systems. The only notable excep- tion to this generalization is when there is a large hole caused either by a disconnection or, as in our experi- ments, with added plenum leaks. In such a case, the exponent is much closer to 0.5. Prior information provides several alt
