Baracu- Theoretical Evaluations of the Natural Infiltration of the Air in Buildings, 2013, CIEM_S2_3

8/13/2019 Baracu- Theoretical Evaluations of the Natural Infiltration of the Air in Buildings, 2013, CIEM_S2_3

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CIEM 2013

THEORETICAL EVALUATIONS OF THE NATURAL

INFILTRATION OF THE AIR IN BUILDINGS

TudorBARACU1, CatalinTEODOSIU2,

Marius-Victor BIRSAN3, AdrianBADEA4

Heat loss throughairinfiltrationcan reach50% of totalin a buildingfrom the

interactionwith the external environment. Tolimitor

controlairinfiltrationinbuildingsrequires acorrect estimate of them based onseveral

models. From thetechnicalliteratureare foundvariousevaluation algorithmsstartingfromtheusual"rule of practice" to rigorous analyticalalgorithms. This studyaims

atpresentingvariousexistingmodelsfor estimatingair leakage, and also it is builta new

algorithmto evaluate thenatural infiltrationof the air through the envelope, taking inconsideration the cyclicvariation of theatmospheric pressure.

Keywords: Natural Infiltration of the Air, Air Leakage, Air Infiltration

1. Introduction

Naturalairinfiltrationproblemappearedafterthe

buildingenergyconcernsbecame moreintenseas a result ofthe 1973 oilcrisis. In

order to evaluatescientificallythe aeraulicbehaviorof a building, it was inventedin1977 initially in Sweden the Blower Window as a research tool, then in USA

was found that using the equipment"Blower Door" is more practical for

meteringair exchangeinterms ofa given pressure difference.

In 1977 Esbensen and Korsgaard concluded that buildings were not so

tight as they were assumed, finding that the number of air changes per hour after

measurements was 5 times higher [1].

In the same year, GautamDutt make calculations for estimating heat loss in

buildings from New Jersey, and in 1979 published in the "New York Times" that

at measurements on some buildings the heat loss is 3 ... 7 times more than

estimation calculations [2].

The problem of estimating air leakage in natural conditions based oninformation obtained from pressure tests resulted in an interest to researchers, but

so far are mainly empirical formulas due to nonlinearity of the phenomenon and

the diversity of ways and surfaces of interacting between the and outdoor. There

1PhDc, University POLITEHNICA of Bucharest, Romania, e-mail: [email protected]

2Prof. Dr., Technical University of Civil Engineering, e-mail: [email protected]

3PhD., National Meteorological Administration, Romania, e-mail:[email protected]

4Prof. Dr., University POLITEHNICA of Bucharest, Romania, e-mail: [email protected]


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Tudor Baracu, CatalinTeodosiu, Marius-Victor Birsan, Adrian Badea

are also analytical approaches having as example the evaluations of Mattson

(2007) considering the simplified case of initial pressure difference that is

equilibratedin time by interaction building- environment [3].

Lee et al. (2001) [4] prepared an installation to study airtightness

measurement with transient methods and succeeded to obtained also the

differential equation of the process, finally obtaining close results in comparisons.

This study aims to present theoretical approaches that describe the air

change between building and exterior. It prepares the ground of more detailed

analysis that will follow after the issues of some special defined pressure tests at

the Passive House POLITEHNICA from Bucharest. At that location are already

done measurements [5] according to standard EN13829 [6] and it is also in the

view a new approach that will consider also the time between successive pressurepoints in the process of free equilibration of the pressure difference house-

environment.In [7] was published also pressure tests for a building with detailed

information of empirical procedures.

2.Estimations of the natural infiltration of the air

In this section it is underlined the state of the researches involving the

evaluation of natural air leakage and later is described a new algorithm that is

using to the power law of the air leakage in buildings.

Sherman (1987) [8] considers a relation ofthe natural infiltration of the airas air changes per hour

(1)

where is a correlation factor for which Sherman [8] formula:

(2)

where is an climatic factor function of temperature and wind,

factor of height (given in tables) and is a factor

of shading to the wind. In this way can be obtained the range of the values that

can be taken by correlation factor.

(3)

From various measurements data was found that the most frequent value

of is centered around 20.


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Theoretical evaluations of the natural infiltration of the air in buildings

Those empirical formulas have to be taken in consideration only as a

simple reference because it is not published explicitly the methods that drived to

them.

An ASHRAE Addendum [9] present also a method of determination of the

air leakage normalized for a year.

(4)

where NL is normalized leakage, a factor of weather and shielding and

floors area. It is also interesting that the addendum offer a balanced approach,

such that the necessary ventilation rate takes in consideration the average

infiltration:

(5)

Awbi (2003) [9] indicates formula

(6)

Also it is cited the result of Building Research Establishment [10] obtained

by gas tracing test and statistical processing of data available for non-domestic

buildings

(7)

Another approach is to estimate the natural air leakage based on climatic

data containing atmospheric pressure. In [11] is described a method that

considered power law of the air leakage and atmospheric pressure having a simple

sinusoidal cyclic variation. There was obtained finally that

(8)

where is a coefficient that can be calibrated according to the measurements.

That algorithm is more complete if it is considered a normalized value by

RMS method

(9)


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where is the daily amplitude of pressure along of a day with

.

In this way is obtained a slightly different expression

(10)

wherefmis also a coefficient that have to be calibrated by measurements.

It can be considered a RMS normalization where mechanical power is

analogical to the electric power in alternating current along of a period of

variation.

(11)

(12)

a) b)Fig. 1 Atmospheric pressure along of the year 2012:a) natural variation (Source: National

Meteorological Administration, Romania); b) parametric variation

If it is analyzed the atmospheric pressure along of a year (fig. 1a) it is

found that can be used a parametric form (fig. 2b) that approximate and reproduce

it with a good accuracy. This parametric form is more suitable for mathematical


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analysis and also gives in a simplistic manner the trends of atmospheric pressure

variation. Fig. 2b is the representation of the equation:

(13)

In this way, the variation of the pressure along of a year has mainly 3

cyclic components with their initial phases , , and periods , and

. However, in the equations solved in this study it is used an simplified

parametric form

(14)

The most quantifiable situations of air leakage are: pressure difference

between two faces of a building (example: one face being upwind and the other

downwind) such that in steady regime the flow rate that goes in is equal to the

flow rate that goes out; an initial pressure difference indoor-outdoor that

diminishes progressively after the building is put in interaction with the

environment; pressure difference due created by the cyclic outdoor pressure

variation.

Mattson (2007) [3] proposed a differential equation of the air leakageconsidering an initial known pressure difference outdoor-indoor.

(15)

or, in a simple form

(16)

Resolving the equation he found the solution

(17)

In this study is proposed a generalization of Mattsons approach

considering not only a pressure equilibration after an initial disequilibrium but an

active and cyclic action (in simplified sinusoidal form) of the daily outdoor

pressure.


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Equation (13) had shown earlier three main cyclic components of

atmosphere pressure along of the year, and in order to simplify the problem will

be considered only the daily variation. Because of the slow variation along of the

day with relatively small amplitude (about 500 Pa) the regime of air flow in the

infiltration process it is laminar.

The equation will have the general form

(18)

Exponent aof the power law of air leakage has values in the range of

0.5-1.0 and the value a=2/3 is the most common. The problem is that for non-

integer values of a, like 1/2 or 2/3, the differential equation is non-resolvable byquadrature methods. The only way to find a parametric solution for the equation

(18) is to consider value a=1, the upper limit of the exponent.

(19)

where it is considered that initially the indoor and outdoor pressure are the same

(pi=pe=pm), so

(20)

Firstly it is solved the linear differential equation

(21)

obtainingthe integrating factor

(22)

is obtained the general solution

(23)

and applying initial condition gives


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(24)

For a given exponent a, the pressure difference will be considered as the

pressure difference for a=1 corrected by a factor fa that can be calibrated by

experimental measurements.

(25)

This article, by its approaches prepares the theoretical background of the

practical tests that will be issued later. It is aimed in the end to be done

comparative analysis, calibrations of the theoretical results from the

measurements.

6. Conclusions

In this study was presented empirical formula that evaluate the air leakage

of the buildings normalized for long periods (usually one year) published by

several authors. Additionally, it is remarked an analytic approach of Mattson for

simplified physical conditions of air leakage.

The empirical data of atmospheric pressure was parameterized in order toobtain a sinusoidal expression of it and to be able to use it in the differential

equation of air leakage.

Atmospheric pressure have relatively slow variation along of the time of a

day and this fact conducted to the assumption that the regime of air leakage

through envelope of the building is laminar, a thing that is different from the

standard Pa, pressure tests where the regime is turbulent especially for pressure

differences like 50 Pa, 75 Pa.

In this paper was adapted and completed the approach of Mattson for more

realistic outdoor conditions like the cyclic variation of the atmospheric pressure. It

was assumed a value a=1 of the exponent of power low in order to obtain a

solvable differential equation. The solution of the differential equation will becorrected by a factor that will take in consideration empirical measurements.

There are prepared the analytical instruments of evaluation of the air

leakage of a building and additionally are planned some pressure tests to the

Passive House POLITEHNICA where will be added new algorithms of

measurements. It will be consideredexplicitly the time in the transient process of

air exchange building-environment while are passed through different pressure

points by the indoor air in the process of free equalization with the outdoor

conditions.


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R E F E R E N C E S

[1]. T. V. Esbensen, V. Korsgaard, Performance of Zero Energy House in Denmark, 1st GermanSolar Energy Forum 26.-28. September 1977, Hamburg, 1977

[2]. http://www.greenbuildingadvisor.com/blogs/dept/musings/blower-door-basics[3]. B. Mattsson, J. A. Claesson, Transient Pressurisation Method for Air Infiltration

Measurements of Building Envelope Components, Journal of Building Physics July 200731: 35-53, 2007

[4]. M. J. Lee, Air tightness measurement with transient methods using sudden, 2011[5]. C. Teodosiu, Determination of air permeability, Report of UTCB, 2010[6]. EN13829:2002, Thermal Performance of Buildings - Determination of air permeability of

buildings - Fan pressurisation method, Brussels, 2002

[7]. A. Damian, V. Iordache, V. Nastase, System of measurement of the permeability of thebuildings, The 15th Conference of Comfort, Efficiency, Energy Conservation and

Protection of environment, 26-28 November, Bucharest, 2008.

[8]. The Energy Conservatory, Minneapolis Blower Door- Operation Manual for Model 3 andModel 4 Systems, 2010

[9]. ASHRAE Addendum 62.2 2010, Ventilation and Acceptable Indoor Air Quality in Low-Rise Residential Buildings, Atlanta, 2012

[10]. H. B. Awbi, Ventilation of buildings, 2 Ed., Spon Press, Taylor & Francis, London, 2003[11]. T.Baracu, V.Tanasiev, T.Mamut, C.Streche, A.Badea, A transient thermal analysis by

thermal networks of the Passive House POLITEHNICA from Bucharest, International

Journal of Sustainable Building Technology and Urban Development, Taylor & Francis,

London - Seoul, 2013.

Documents

Baracu- Theoretical Evaluations of the Natural Infiltration of the Air in Buildings, 2013, CIEM_S2_3