Methodology for measuring infiltration heat recovery for concentrated air leakage

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1 Methodology for measuring infiltration heat recovery for concentrated air leakage A. Janssens Ghent University, Department of architecture and urban planning, Gent, Belgium ABSTRACT: This paper presents design calculations for a hot box experiment to define the heat recovery effect for air infiltration through a crack in an insulated wall. The design calculations are performed using a two-dimensional calculation model for combined heat and mass transfer. In the proposed measuring methodology, the temperature difference between the hot and cold climate chamber will be used to create an air exchange through two cracks at different heights in the test wall enclosed between the two chambers. The steady state transmission and infiltration heat loss through the wall will be measured at various temperature differences between hot and cold chamber. A tracer gas technique is developed to measure the infiltration flow rate. The measured transmission and infiltration losses will be compared to the additionally measured steady state transmission loss through the wall with sealed cracks (no infiltration) to determine the infiltration heat recovery effectiveness. This paper reports on numerical simulations of the proposed method, to derive the proper test conditions for a reliable measurement of the infiltration heat recovery effect. 1 INTRODUCTION Current calculation methods for building energy consumption generally predict the heat loss associated with air infiltration by multiplying the mass flow rate of the air change by the sensible enthalpy difference between the inside and outside air. Furthermore the transmission heat loss through the building envelope is calculated by assuming that the thermal interaction of air leakage and heat conduction in building components may be ignored. Many researchers have indicated that these assumptions may lead to an overestimation of building heat loss, particularly in buildings where ventilation is the result of unintentional air leakage through the envelope, as is the case in most houses in Western Europe. On average, the overestimation of infiltration heat loss is projected at 40%. (Anderlind 1985, Claridge & Bhattacharyya 1990, Buchanan & Sherman 2000). The thermal interaction of air leakage and the building envelope reduces the actual building heat loss compared to the conventional addition of transmission and infiltration heat losses. This effect is known as infiltration heat recovery. The magnitude of the effect is characterized by means of the socalled infiltration heat recovery effectiveness or IHRE (Arquis & Langlais 1986, Claridge & Bhattacharyya 1990, Buchanan & Sherman 2000). As Equation 1 shows this is a dimensionless correction factor applied to the conventional infiltration heat loss, much in the same way as heat exchange units in mechanical ventilation systems are accounted for: Φ l = UA + (1 ε ) Mc ) ( θ θ ) (1) ( a i e where Φ l is the actual building heat loss (W), UA the overall heat transmission coefficient of the building envelope (ignoring the interaction with air leakage) (W/K), ε the infiltration heat recovery effectiveness (IHRE), M the mass flow rate of infiltration air (kg/s), c a the specific thermal capacity of air (J/kg/K) and θ i and θ e the interior and exterior air temperatures, resp. The study of infiltration heat recovery is important to reach a better understanding of the heat losses associated with unintentional air leakage through discontinuities in the building envelope. This knowledge would allow a better prediction of the energy conservation potential of air tightness measures and energy-efficient ventilation techniques. In the case of accidental air leakage the air infiltration is usually concentrated near the defect causing the leakage (crack, joint, perforation,..). Ho w- ever, the infiltration heat recovery resulting from such a concentrated air flow pattern is still not very well known. Except for some simple leakage geometries no analytical calculation methods exist to predict infiltration heat recovery (Claesson & Hellström 1995). Therefore a detailed study of the effect requires the use of two- and three-dimensional nu-

2 merical calculation techniques for combined heat and mass transfer supported by full-scale measurements. Still reported results on simulated or measured values of IHRE for concentrated leakage are scarce. The few reported results of numerical calculations contradict and indicate that heat recovery for concentrated infiltration is a more complex phenomenon than described in previous analytical studies (Kohonen et al. 1985, Buchanan & Sherman 2000, Janssens 2001a). Accurate experimental results are reported for the case of diffuse air filtration (Arquis & Langlais 1986), while for concentrated leakage only measurements for a simple 3Dgeometry exist (Claridge & Bhattacharyya 1990). Therefore the experimental determination of the heat recovery effectiveness for concentrated air leakage in typical building components is essential to gain a better understanding of the effect, and to support the numerical analysis of infiltration heat recovery. 2 PHYSICAL BACKGROUND 2.1 Diffuse filtration The combined conductive and convective heat loss through a wall may be calculated with a onedimensional steady-state analytical method for the ideal case when air filtration occurs diffuse and perpendicular to the building envelope surface. This is the so-called diffusion-convection equation (Equation 3, e.g. Arquis & Langlais 1986): θi θe exp(pe ) Φ c = Mca (2a) 1 exp(pe ) and Mca Pe = (2b) UA where Φ c is the combined conductive and convective heat loss (W) and Pe is the system Péclet number or dimensionless flow rate in the diffuse envelope part. In these equations M assumes a negative value when air filtration occurs from inside to outside. In houses where the leakage area is evenly distributed over the building envelope, the Péclet-number is typically of order 1. Anderlind (1985) derived expressions for the IHRE by combining Equations 1 and 2. He found that the IHRE depends on the system Péclet-number and on the ventilation pattern in the building. In the case of double flow ventilation the air both enters and leaves the building by means of air filtration through the envelope (Figure 1). The maximum IHRE is 1 for Pe 0 and decreases exponentially for larger Pe-numbers according to Equation ε = + (3) Pe 1 exppe M A Figure 1: Double flow (left) and single flow (right) ventilation pattern IHRE H/D = Pe A Eq. 3 Eq. 5 Figure 2: IHRE as a function of Péclet-number and wall aspect ratio, in the case of diffuse (upper curve) and concentrated leakage (lower curves). where ε is the infiltration heat recovery effectiveness in the case of double flow ventilation (-). In the case of single flow ventilation the air enters the building through the diffuse envelope and leaves through an exhaust (or vice versa, see Figure 1). In this case infiltration heat recovery is half as efficient as with double flow ventilation. 2.2 Concentrated leakage Claesson & Hellström (1995) presented an analytical solution for the combined conductive and convective heat loss in the case of concentrated leakage through a slit in an insulated wall. The considered geometry concerned a slab of air-permeable insulation material, with one side open to air flow, and the other airtight except for a slit. For this case they found a unique relationship between the IHRE and a modified Péclet-number, defined by Equation 4: M ca Pe H p = 2πλ = (4) 2π D where p is the modified Péclet-number, M the mass flow rate per unit slit length (kg/s/m), λ the thermal conductivity of the insulation material (W/m/K), H the height of the insulated wall (m) and D the thickness of the insulation material. Apart from the constant 2π, this modified number only differs from the previously defined Péclet-number by the aspect ratio between height and thickness of the insulated wall. M

3 For a double flow ventilation pattern the IHRE for concentrated leakage is given by Equation 5. Also here the IHRE decreases from a value of 1 at p 0 to 0 at increasing values of p. As with diffuse leakage, infiltration heat recovery in the case of single flow is half as efficient. ε = 1 2 h( p ) (5) p p h( p ) = ln p π p p 4.2 p < 1.33 p 1.33 Figure 2 compares the IHRE for diffuse filtration (Equation 3) to the IHRE for concentrated leakage (Equation 5). The IHRE is shown as a function of the system Péclet-number and for different values of the aspect ratio of the insulated wall. The difference between both types of leakage is clear: for the same infiltration flow rate and U-value, the infiltration heat recovery effect is much smaller for concentrated leakage than for diffuse filtration. Furthermore, for the same Péclet number, thinner walls have a smaller IHRE. Other configurations of concentrated leakage than the one described here should be solved numerically. Reported results show that apart from Pe-number and wall thickness, also the length of the leakage path and the material properties in the vicinity of the path affect infiltration heat recovery (Janssens 2001a). 3 EXPERIMENTAL DESIGN 3.1 Methodology In order to measure the infiltration heat recovery effectiveness for concentrated leakage, a test method is proposed based on the methodology of the calibrated hot box. During a hot box experiment a test wall is enclosed between a warm and a cold climate chamber (hot and cold box) and the heat transmission coefficient or thermal permeance of the wall is defined. This property is derived from the heating power dissipated in the warm chamber while a steady-state temperature difference is maintained between the warm and cold chamber. Cold Box Test Wall 2.0 m Figure 3: Experimental setup Hot Box 2.4 m Table 1: Material properties of the test wall Layer Thickness mm λ W/m/K k* m² Inner plywood Thermal insulation Outer plywood Wood plates * k: specific permeability Figure 4: Air gap configuration A modified test wall is used to define the thermal interaction between air infiltration and building component. This test wall consists of an insulated airtight wood- frame construction, in which two lo n- gitudinal air gaps are present, one at the bottom and one at the top of the wall. The infiltration heat recovery effectiveness of this configuration is then measured in two stages. First a reference test is performed during which the gaps are sealed such that air leakage through the wall is prevented. From this reference test the heat transmission coefficient UA of the test wall is defined. Afterwards the air gaps at the top and bottom of the wall are left open during the test. Thermal stack will induce air movement in between the hot and cold box, with warm air flowing to the cold box through the upper air gap, and cold air flowing to the hot box through the lower gap (Figure 3). The air infiltration rate is measured. During this second test, the steady-state heating power dissipated in the warm chamber is related to the effective conductive and convective heat loss through the test wall. By comparison with the reference heat loss measured during the first stage of the experiment (without air movement), the IHRE may be derived: Φl UA( θi θe ) ε = 1 (6) Mc ( θ θ ) a a,i a,e where Φ l is the total convective and conductive heat loss measured during the second test stage (W), UA is the reference heat transmission coefficient measured during the first test stage (W/K) and M is the mass flow rate of the air change between hot and cold box (kg/s). A tracer gas technique is used to derive the air flow rate between hot and cold box. During the test a tracer is injected in the hot box to build up the concentration of the gas to a certain level. After the injection of tracer is stopped, the evolution of the gas

4 concentration in the hot and cold box is measured as a function of time. From the time constant of the exponential decay of the concentration in the hot box, the air infiltration rate may be derived. The procedure described above (the second test stage) is repeated for various values of the temperature difference between hot and cold box and the induced air flow rate, in order to determine the relationship between the heat recovery effectiveness and the air infiltration rate. The air gap configuration proposed for the analysis is a gap between two wood plates (Figure 4). This configuration is typical of wood-frame construction, e.g. a crack between the bottom plate of a wall and the floor surface on which it is mounted. Two similar gaps are present in a 2.4 m high and 1.8 m wide wall, one gap at 0.2 m from the bottom, the other at 0.2 m from the top. The wall consists of a sandwich construction with a core of thermal insulation finished at both sides with plywood. Material properties are listed in Table Design calculations As Figure 2 shows, the IHRE for concentrated leakage decreases from a high to a relatively small value in a short interval of Péclet-numbers. Therefore it is important to design the experiment in such a way, that this short Pe-interval is matched by the test conditions. The fact that air infiltration during the test occurs by natural convection and is not controlled, adds to the importance of a proper experimental design. Also the accurate measurement of the air infiltration rate is crucial for the reliability of the results. The dimensions of the air gaps and the test conditions are defined on the basis of numerical calculations with the model 2DHA. This is a twodimensional calculation tool for heat, air and vapour transfer in multi-layered building components, originally developed to assess interstitial condensation due to air leakage (Janssens 2001b). The model describes a building component as a general twodimensional assembly of continuous porous materials and discrete air channels, which are interconnected and saturated by air. Air transfer in the porous domain is physically modelled according to Darcy's law, while in the channels and gaps Poiseuille flow is assumed. The calculations are performed for three gap widths: 2 mm, 3 mm and 5 mm and for three different temperatures in the cold chamber: -10 C, 0 C and 10 C. The temperature in the hot box is in all cases 20 C. The heat transfer coefficients at the inside and outside surface are 8 W/m²/K and 25 W/m²/K respectively. From a first calculation where air movement through the cracks is not considered, the reference mean thermal permeance of the wall is derived: U = 0.29 W/m²/K for all cases, hence UA = 0.69 W/K/m. IHRE 100% 80% 60% 40% 20% 0% Pe 5 mm 3 mm 2 mm Figure 5: Predicted IHRE as a function of Péclet-number for different air gaps widths of the configuration in Figure 4. Table 2: Calculation results (UA = 0.69 W/K/m) θ C Φ l W/m m 3 /h/m 5 mm gap width mm gap width mm gap width The other calculations predict the natural infiltration flow rates through the air gaps and the associated conductive and convective heat loss, with the inside surface as the control surface. From these results the system Péclet-number and the infiltration heat recovery effectiveness is defined according to Equations 2b and 6. Table 2 gives a summary of the calculation results. Figure 5 shows the predicted IHRE as a function of the Péclet-number for each case. It is clear from the figure that the relationship IHRE(Pe) is independent of the actual gap width. Hence the gap width may be considered as a parameter to control the air infiltration rate during the experiment. For the air gap configuration under analysis, the effect of infiltration heat recovery is quickly reduced at increasing air infiltration rates. On the basis of the calculation results it may be concluded that the gap width should be smaller than 3 mm in order to obtain IHRE-values that are significantly larger than the measuring uncertainty. However, accurate results of IHRE may only be obtained if the small infiltration flow rates that develop through these gaps are still detectable by the tracer gas technique described above. Therefore in the remainder of this paper this problem is examined. Pe ε

5 3.3 Tracer gas technique The tracer gas technique proposed to define the air infiltration rate is a modification of the well-known concentration-decay method. After a quantity of tracer gas has been injected in the hot box air, the gas concentration in the hot box decays, while the gas concentration in the cold box builds up. This is the result of the air exchange between the two climate chambers. The evolution of the gas concentration in both chambers as a function of time is then measured. The concentration of the gas in hot and cold box is expected to change exponentially to a constant concentration when the quantity of injected tracer is mixed over the total air volume of both chambers: C C + C 0,HB HB 0,CB CB = (7) HB + CB where C 0,HB and C 0,CB are the gas concentrations (ppm) in hot and cold box at the start of the measuring period (after the injection of tracer gas has stopped), and HB and CB are the volumes of hot and cold box, respectively (m 3 ). The exponential decay of the concentration in the hot box is given by Equation 8. The concentration in the cold box evolves in an analogous way. 1 1 [ ( )t] CHB ( t ) = C ( C C0,HB )exp & HB + (8) HB CB where dotted HB is the volume flow rate in the hot box (m 3 /h) and t is the time (h). Hence the air infiltration flow rate may be found by fitting a curve of the form of Equation 8 to the measured values of the gas concentration. The evolution of tracer gas concentrations will now be studied for the extremes of the air infiltration rates predicted in the numerical calculations (Table 2). This is done for the case of a hot box with dimensions (h/l/w) 2.4m x 2.4m x 2.4m and a cold box with dimensions 2.4m x 3.0m x 1.0m. The air infiltration rates studied are 10.0 m 3 /h and 1.0 m 3 /h (gap length 1.8m). Concentration (ppm) C 10 m 3 /h Time (minutes) 1 m 3 /h Figure 6: Predicted evolution of gas concentrations in hot box (upper curves) and cold box (lower curves). The first value is in the order of the flow rates predicted for the case of 3 mm wide gaps and a temperature difference of 30 C, the second in the order of the predicted flow rates for 2 mm wide gaps and a temperature difference of 10 C.As a tracer the use of carbondioxide is assumed, with starting concentration of 1500 ppm and 350 ppm in hot and cold box. Figure 6 shows the evolution of gas concentrations as a function of time. The time constants for both values of air flow rates are quite different. For an air flow rate of 10 m 3 /h, the time constant of the exponential change is about 30 minutes. In this case a short measuring period is sufficient to register a characteristic part of the concentration-decay and derive reliable values of the air flow rate. For an air flow rate of 1 m 3 /h, the time constant is almost 5 hours, and the gas concentrations should be measured over a period of at least the same length. 4 CONCLUSIONS This paper presented design calculations for a hot box experiment to define the heat recovery effect for air infiltration through a crack in an insulated wall. The temperature difference between the hot and cold climate chamber is used to create an air exchange through two similar cracks at different heights in the test wall enclosed between the two chambers. A tracer gas technique is developed to measure the air exchange rate. The design calculations showed that a proper choice of the crack width is important to obtain reliable measurements of the IHRE. REFERENCES Anderlind, G Energy consumption due to air infiltration, Proceedings of the Third Conference on Thermal performance of the exterior envelope of buildings, ASHRAE Special publications, Atlanta, Ga, Arquis, E. & Langlais, C What scope for 'dynamic insulation?, Building research and practice, ol. 14, Buchanan, C.R. & Sherman, M.H A mathematical model for infiltration heat recovery, Proceedings of the 21st AIC-Conference, AIC, Coventry, UK, paper 45 (14 p.). Claesson, J. & Hellström, G Forced convective-diffusive heat flow in insulations: a new analytical technique applied to air leakage through a slit. J. Thermal insul. and Bldg. envs., ol. 18, Claridge, D.E. & Bhattacharyya, S The measured energy impact of infiltration in a test cell, J. Solar Energy Engineering, ASTM, ol. 112, Janssens, A. 2001a. A comparison between analytical and numerical models to estimate infiltration heat recovery, Proceedings of the International Conference on Building Envelope Systems and Technology ICBEST 2001, Institute for Research in Construction, NRC, Ottawa, Janssens, A. 2001b. Advanced numerical models for hygrothermal research: 2DHA model description. Moisture analysis and condensation control (H.R. Trechsel, editor). ASTM Manual 40. American Society for Testing and Materials, West Conshohocken, PA, USA,

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