Modeling ventilated double skin façade—A zonal approach
Introduction
Double skin façades (DSF) are building envelopes, which are comprised of two glass façades, a ventilated air cavity and solar control (shading) devices placed within the cavity. The ventilated cavity functions as a thermal buffer, which reduces problems such as undesired heat gain during the cooling season, heat loss during the heating season and thermal discomfort due to asymmetric thermal radiation. DSF can be classified according to ventilation and construction type. The ventilation of the DSF cavity can be either mechanical or natural. Mechanically ventilated façades, shown in Fig. 1a, are usually part of Heating Ventilation and Air Conditioning (HVAC) system of the building. The driving force for natural ventilation is either thermal buoyancy or wind pressure. The airflow is therefore not easy to control nor is it continuous since it depends on the weather condition. Naturally ventilated façade, depicted in Fig. 1b, can be used as a supply window for natural ventilation of room (when the window on the internal façade is open) or as an insulation envelope for a conditioned room (when the window on the inner façade is closed), which increases the thermal resistance. The type of opening on the inner façade can be like a window for naturally ventilated façade or simply a slot for a mechanically ventilated façade. Naturally ventilated DSF can further be subdivided based on the way the façade is constructed: box windows, shaft-box windows, corridor façades, and multi-story or continuous façades [1].
Experimental and numerical models have been used for studying the performance and optimization of DSF. Models that have been used for the prediction and analysis of the performance of DSF include analytical and lumped models, dimensional analysis, network models, control-volume models and Computational Fluid Dynamics (CFD). The lumped approach represents each façade and cavity by a single temperature. Lumped model was used for naturally ventilated DSF [2], [3], [4], [5], [6]. Dimensional analysis was used to describe the energy performance of different DSF designs [7]. Analytical models for ventilated DSF were also developed, which assume a linear vertical temperature gradient [8]. The airflow network model was applied for DSF equipped with venetian blinds [9]. Airflow network models coupled with energy simulation have also been used to evaluate the natural ventilation of office buildings with DSF [10], [11], and to evaluate the energy performance of office buildings with DSF [12], [13]. In the control-volume approach, only one-dimensional flow in the vertical direction is assumed. The temperature stratification in a ventilated façade is evaluated by dividing the façade into control volumes in the vertical direction and setting the mass flow rate for each control-volume equal to the inlet mass flow rate [14], [15], [16]. The control-volume models are thermal models similar to the empirical zonal models, which are calibrated and used to predict temperature stratification in a room [21]. Detailed studies have also been conducted using CFD and experiment for mechanically ventilated façades [17], for naturally ventilated façades [18], [19] and for naturally ventilated façades equipped with venetian blinds [20].
The most important problem associated with the CFD approach is the requirement of computer resources such as speed and memory. On the other hand the limitation of the control-volume models is that the airflow has to be known a priori and it is an input to the numerical solution. Moreover, the extension of the control-volume models to other shading devices such as venetian blinds is not straight forward, as it requires pressure distribution in the cavity for the evaluation of the airflow in the inner and the outer cavities [14]. Therefore, in order to enhance the prediction capability of the control-volume models for a DSF with venetian blinds, without significant additional requirement of computational resource, the zonal approach was applied in this study.
Zonal models are intermediate approach between the extremes of lumped model and CFD. In the zonal approach, the DSF can be divided into a number of control volumes, using two or three-dimensional cells, which are usually larger than the cells normally used in CFD applications. The advantage of using the zonal approach is that the resulting systems of algebraic equations are smaller and much easier to solve than the CFD approach. The zonal models can therefore provide information on airflow and temperature distribution in a ventilated space faster than CFD, but with more accuracy and detail than lumped and control-volume models. In the zonal method, conservation equations are formulated for each cell. The mass and energy conservation equations for each cell can be given as:where mj is the mass flow rate; SM is the mass source; Qj is the heat flow; Sq is the heat source. The mass flow rate, mj is computed using the Power Law Model (PLM):where K is the flow coefficient; A is area of cell; ρ is density of air; ΔP is the pressure difference between neighboring cells (zones).
The zonal models have been applied to predict moisture distribution [22], thermal comfort [23], contaminant distribution [24] and personal exposure [25]. They have also been integrated with airflow network models such as COMIS [26]. Nevertheless, the zonal approach has not been applied to predict the performance of DSF [27]. The power law relation was employed for calculating the airflow through the blinds using the network approach [9]. The main difference between the present study and [9] is that in the latter the total airflow in the outer and inner cavity is calculated using the power law equation but the airflow through each blind is approximated as a fraction of the total airflow rate. In this study, the airflow rate through the blinds and in the air cavities was modeled using the Power Law Model (PLM), Eq. (3). The pressure drop for banks of tubes in cross and parallel flow is calculated using an equation similar to the PLM. Therefore, the application of the PLM assumes each slat of the venetian blind as long horizontal cylinder in the ambient fluid except when the venetian blinds are completely closed.
Section snippets
Case description
The case used for the development and verification of the DSF models is an experimental test cell at the Dipartimento di Energetica, Politecnico di Torino, Italy. The test cell was 2.5 m high, 1.6 m wide and, 3.6 m long. The south facing side of the cell, which was 1.6 m wide and 2.5 m high, had a mechanically ventilated DSF with an outer double-pane façade, and an inner façade as shown in Fig. 2. The outer double-pane façade, L1 and L2, was divided into three parts: upper, middle and lower. L1 and
Thermal modeling methodology
The energy balance equation for DSF includes the absorbed solar radiation, long wave radiation exchange between layers, convective heat transfer between the cavity air and the layers, and conduction in the DSF layers (glass and shading device). Hence, the zonal energy equation (Eq. (2)) for any cell in layer of the DSF system can be given as:where mLi,j is the mass of the glass cell j in layer i; cp,Li specific heat capacity of
Numerical solution of airflow and energy equations
The numerical procedure used to solve the non-linear system of equations of pressure is based on the balance of mass flow for each cell, Eq. (1). The Newton–Raphson method was used to solve the non-linear problem by an iterative mass balance approach in which cell pressures are adjusted until the mass residual of each zone is minimized. In this method, a new estimate of the vector of all cell pressures is computed from the previous estimate of pressures as:where and are
Model verification, discussion and application
In order to avoid overheating of the DSF cavity and the venetian blinds, and to monitor the energy exchanged as the ventilating air flows through the cavity, temperature distributions in the outer cavity (Ca1), inner cavity (Ca2), venetian blinds (L3), and the exhaust temperature should be predicted. Moreover, the temperature distribution in the inner glass (L4) should be known in order to evaluate the thermal comfort in the room. Thus the comparisons of the measured and predicted temperature
Conclusion
In this paper, the methodologies and applications of zonal modeling of DSF with venetian blinds were discussed. The results show that the zonal models can be used to assess the performance of the DSF system with venetian blinds. The zonal models provided more detailed information, which is not possible for the lumped and the control-volume models. Parametric study was also conducted to assess the influence of cavity height, H; inlet mass flow rate, M0; and presence of venetian blinds on the
Acknowledgement
We would like to extend our sincere appreciation to faculty and staff of the Dipartimento di Energetica, Politecnico di Torino, Torino, Italy for allowing us to use their experimental facilities and providing all the necessary information and help during and after the experimental program.
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