Ventilated Walls and Energy Saving in Summer

Ventilated Walls and Energy Saving in Summer Cooling of Buildings MARIO CIAMPI, Full professor of Fisica Tecnica, Department of Energetica “Lorenzo Poggi”, Faculty of Engineering, University of Pisa, Via Diotisalvi n.2, 56126 Pisa (Italy) – Phone: +39 (0)50 569639; Fax: +39 (0)50 569604; e-mail: [email protected] FRANCESCO LECCESE, Ph.D., Dept. of Energetica “L. Poggi”, Faculty of Engineering, University of Pisa, Via Diotisalvi n.2, 56126 Pisa (Italy) – Phone: +39 (0)50 569611; Fax: +39 (0)50 569604; e-mail: [email protected] GIUSEPPE TUONI, Full professor of Fisica Tecnica Ambientale, Dept. of Energetica “L. Poggi”, Faculty of Engineering, University of Pisa, Via Diotisalvi n.2, 56126 Pisa (Italy) – Phone: +39 (0)50 569642; Fax: +39 (0)50 569604; e-mail: [email protected]

Abstract In this paper a simple analytical method for design applications, able to provide all the useful criteria for choosing the most suitable ventilated wall, is discussed. As an example two peculiar cases of remarkable importance are investigated: the first in which the inner face is given, and the air duct and the outer face have to be optimized; the second in which, on the contrary, the outer face is given, and the inner face and the air duct have to be optimized. The first case can occur in building recovery interventions, while the second case can occur during the design process. Finally the influence of the variation of some quantities necessary for calculation, such as the heat transfer coefficient of the wall’s outer surface and the relative roughness of the slabs delimiting the air duct, on the energy performance of ventilated walls, is investigated.

1.

Introduction

In the last few years ventilated walls, facades and roofs, have been widely investigated both from an architectonical and a physical point of view owing to the possible energy saving achievable by using these building systems [1-8]. In Mediterranean countries, the ever-growing demand for air-conditioning plants and split systems, has been involving a remarkable rise in energy consumption in summer, and in Italy the power required on summer peak is foreseen to distinctly exceed, within a short time, the one required on winter peak. It follows that an accurate building envelope design is necessary in order to reduce summer thermal loads; ventilated walls, if well designed, can help to reduce considerably the summer thermal loads due to direct solar radiation [9-11]. Ventilated facades can be used even in cases of building recovery interventions, for instance, in the absence of rules relating to historic-architectonical preservation. Ventilated structures can prove useful also for the cooling of photovoltaic panels (PV) in order to increase their efficiency; significant, as regards this, result to be ventilated roofs in which a part of the covering is composed of photovoltaic panels [12-13]. A complete thermo-fluid dynamic analysis of a ventilated air duct requires an accurate knowledge of heat transfer coefficients, friction factors and thermophysical properties of the materials; the determination of such quantities is, unfortunately, not so easy and values currently used for them are often quite uncertain. In particular, the uncertain knowledge of heat transfer coefficients and the head loss inside the ventilation duct can result so relevant to frustrate, in many cases, the use of sophisticated and

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Ventilated walls and energy saving in summer cooling of buildings

complex calculation methods, such as the ones based on the Computational Fluid Dynamics (CFD). Note that in most cases the precise value of energy saving, achievable by using a given ventilated wall, doesn’t result to be of so much interest as the criteria, even qualitative, about the positioning of the insulating layer, the air duct dimensions, and about the materials to be used for the realization of the inner and outer walls. In this paper a simple analytical method for design applications is discussed, able to provide all the useful criteria for choosing the most suitable ventilated wall to be used in case of forced ventilation (due to the action of a fan) and natural ventilation (stack effect). As an example of this method two peculiar cases of remarkable importance are investigated: the first in which the inner masonry wall is given, and the air duct and the outer facing have to be optimized; the second in which, on the contrary, the outer facing is given, and the air duct and the inner masonry wall have to be optimized. Finally, the influence of the variation of some quantities necessary for calculation such as the heat transfer coefficients of the outer facing and the relative roughness of the slabs delimiting the air duct, on the energy performance of ventilated walls, is investigated. 2.

Problem statement

In recent papers [9-10] the same authors have proposed a simple analytical method suitable for design applications, in order to estimate the energy performance of ventilated facades and roofs both when the air flow inside the air duct is due to the action of a propulsor (fan) or to differences in temperature (stack effect). In spite of the problem complexity and the large number of physical quantities influencing a ventilated wall’s thermal behaviour, it is possible to resume its energy performance using a unique formula, having as input quantities just five dimensionless parameters [10]. More precisely, energy saving S, due to the air duct ventilation, can be introduced in the following form: S = (Q 0 − Q ) Q 0 where Q is the mean heat flow coming into the room through the ventilated wall, while Q0 is the one coming into the room when the ventilated air duct is closed. The meaning of S is strongly intuitive, particularly when it assumes values from 0 to 1; negative values of S clearly indicate that ventilation is not convenient. Note that, in certain cases (very peculiar ones), S can show values higher than 1: it means that Q is negative, that is to say that the ventilation is able to carry out even a cooling of the room. The analysis proposed in [10] allows to express the percentage energy saving, S, in the following form:    χ  S = 1 − χ + γ z (ϕ − z) 1 − exp  −  γ [H + z (1 − z)]  

(1)

depending on five parameters: ϕ, z, χ, γ and H, defined in the following way.

The environmental parameter ϕ=(Te−T0)/(Te−Ti) with Ti indoor air temperature, T0 outdoor air temperature in the shade and Te sol-air temperature. We have: Te=T0+areI, where a is the outer surface solar radiation absorptance, re is the outer surface thermal resistance, and I (W m-2) is the incident solar radiation intensity.


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The ratio z=Re/Rt with Re thermal resistance between the ventilation air duct and the outdoors and Rt total thermal resistance between the indoor air and the outdoor one.

The ratio χ=Rt0/Rt with Rt0 total thermal resistance between the indoor air and the outdoor one without ventilation inside the air duct and Rt the same thermal resistance in case of ventilation inside the air duct.

The parameter γ=ρ0W0CpRt0d/L, equal to the product of the air heat capacity rate and total thermal resistance of the closed air duct (ρ0 is the outdoor air density, Cp is the specific heat at constant pressure, W0 is the mean air velocity at the ventilation duct inlet opening, L and d, respectively, height and width of the duct).

A radiative correction factor H, for the definition of which we refer to [10], due to the fact that the introduction of the surface thermal resistance heat transfer coefficients (instead of the convective ones) is not sufficient for quantifying entirely the radiative heat transfer inside the air duct.

The influence of the five parameters on S has been studied in [10], where has been also investigated the behaviour of some ventilated facades and roofs, chosen among those of simplest realization. The parameter γ can be considered as an independent variable in case of forced ventilation within the air duct. In case of natural ventilation γ is determined by thermal field and it is strongly influenced by the duct geometry, by fluid dynamic head losses and even by the external atmospheric conditions (in particular by the wind velocity and direction); if we neglect their effect, which is hardly quantifiable [12], the values of the air mass flow rate in ventilated facades, by stack effect, can be estimated as in [10]. Indicating by λ the friction factor of the air duct, by λ′i and λ′u the friction factors of the head losses located on the inlet and outlet sections, by g the acceleration due to gravity, the velocity W0 can be expressed by the following relation: 1  W = gL ⋅ 1 − T0 < T  2 0

  λ ' −1 Lλ < T > λ ' u +1 Tu  > ⋅  i + + ⋅  2DT0 2 T0    2

−1

(2)

In Eq. (2) by T0 and Tu has been indicated the air temperature, respectively, at the inlet and at the outlet openings of the air duct, by and the mean values, respectively, of the air temperature and its inverse function, calculated along the duct full height. The Eq. (2) has to be used iteratively, as the air velocity inside the air duct influences temperature distribution. If ventilated facades are used, two peculiar cases of remarkable importance can occur: the first in which the inner masonry wall is given, and the air duct and the outer facing have to be optimized; the second in which, on the contrary, the outer facing is given, and the air duct and the inner masonry wall have to be optimized. These cases will be studied, in condition of natural ventilation in order to find, for each of them, the most suitable facade scheme to minimize thermal loads in summer cooling of buildings. Calculations have been carried out according to the method proposed in [10]; in particular for the friction factor λ has been used the Haaland relation, for the convective heat transfer coefficients has been used the Gnielinski formula, while radiative heat transfer between the surfaces delimiting the duct has been linearized. The climatic conditions and duct geometry have been assumed to be fixed except for the air duct width; values assumed for calculation are indicated in Tab. I. As references values, for the thermal resistances of the wall’s outer surface, re, of the wall’s inner surface, ri, and of the


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non-ventilated air duct, Rcc, (see Tab. I) have been assumed the ones recommended by EN ISO 6946 standard [14]. Table I. - Reference values for calculation Climatic conditions: Outdoor air temperature T0 Indoor air temperature Ti Solar radiation intensity I Wall’s outer surface: Thermal resistance re Absorptance a Wall’s inner surface: Thermal resistance ri Ventilation air duct: Lenght ℓ Height L Width d Closed cavity thermal resistance Rcc Emissivity of surfaces ε Inlet friction factor λ′i Outlet friction factor λ′u Relative roughness b

3.

28°C 24°C 400 W m-2 0.04 m2 K W-1 0.70 0.13 m2 K W-1 10 m 15 m 0.10 m 0.18 m2 K W-1 0.9 0.5 1 0.02 m

Assigned inner masonry wall.

This case can occur in building recovery interventions in the absence, for instance, of rules relating to historic-architectonical preservation; such interventions represent, in Italy, a remarkable share of building activity. On this topic some recent regional rules allow a volumetric increase in order to achieve an energy behaviour improvement of building, for example by applying layers of outer facing in order to realize a ventilated air duct [15-16]. As an example of such case six ventilated facades have been taken into account, labelled with FBj (j=1, ...6) and characterized by the same bearing wall made of hollow brick in blocks to which are anchored the most common types of outer facings; among them FB2 and FB5 are completely made of brick. In particular, FB1 has an outer facing realized in copper plates; FB2 and FB5 present an outer facing made of brick (slabs or hollow flat blocks); FB3 is made of asbestos cement panels; FB4 is realized in plates of fine porcelain stoneware; FB6 in plastic panels of reinforced polyester. Thermophysical and geometrical properties of the layers composing the six facades described are reported in Table II. All facades present a thermal insulating layer (fibreglass in rigid panels) with thickness 4 cm, located inside the ventilation duct in contact to the bearing wall and are, in practise, characterized by the same total thermal resistance without ventilation Rt0≅2.0 m2 K W-1; the conductive resistance of the inner masonry wall is in any case RB=1.58 m2 K W-1. Fig. 1 shows the energy saving S for each facade FBj as the air duct width d varies by 0.06