Numerical simulation of the temperature evolution in a room with a mur neutralisant. Application to "The City of Refuge" by Le Corbusier

Numerical simulation of the temperature evolution in a room with a mur neutralisant. Application to “The City of Refuge” by Le Corbusier. C. Ram´ırez-Balasa, E. D. Fern´andez-Nietob, G. Narbona-Reinab, J. J. Sendraa, R. Su´areza aInstituto Universitario de Arquitectura y Ciencias de la Construcci´on. Escuela T´ecnica Superior de Arquitectura. Universidad de Sevilla. Av. Reina Mercedes 2. 41012 Sevilla, Espa˜na bDepartamento de Matem´atica Aplicada I. Escuela T´ecnica Superior de Arquitectura. Universidad de Sevilla. Av. Reina Mercedes 2. 41012 Sevilla, Espa˜na Abstract This paper examines a mathematical model of the thermal evolution in a specific room of “The City of Refuge”, built in Paris (1933) by Le Corbusier. Although the architect proposed an environmental conditioning system by combining two technological advances: the mur neutralisant −a double-glazed wall with an air cavity that can be heated or cooled−and the respiration exacte −a purified circulating air maintained at constant temperature−, this was never incorporated. This article aims to acquire knowledge of indoor air distribution in the room under study by considering the combination of the mur neutralisant and the respiration exacte. The problem is resolved through a “coupled code”. The first is a two-dimensional model simulating the temperature evolution in the room, while the second is a one-dimensional model used to represent the problem of the mur neutralisant. The numerical model develops the technical issues associated with the implementation of computational fluid dynamics (CFD). The numerical simulations carried out validate the solution of the system proposed. Control of the fa¸cade temperature using the active chamber ensures that the operative temperatures obtained for summer and winter fall within the comfort range. The City of Refuge is the clearest precursor of modern active fa¸cade systems. Keywords: Mur neutralisant,respiration exacte, Le Corbusier, The City of Refuge, Active fa¸cade system, Double Skin Fa¸cade (DSF), Computational Fluid Dynamics (CFD), Numerical simulation. 1. Introduction The case study analyses the atmosphere of the City of Refuge in Paris (1929-30), an experimental building in which Le Corbusier attempted to implement two of his own discoveries, the Email addresses: [email protected] (C. Ram´ırez-Balas), [email protected] (E. D. Fern´andez-Nieto), [email protected] (G. Narbona-Reina), [email protected] (J. J. Sendra), [email protected] (R. Su´arez) Preprint submitted to Energy and Buildings October 14, 2014 mur neutralisant and the respiration exacte, to support his concept of machine `a habiter and to show the adaptation of new glass architecture to environmental conditions. The combined use of these two elements aimed to maintain indoor comfort temperature and ideal indoor air quality conditions throughout the year, regardless of outdoor environmental conditions. To do so, the large glazed south fa¸cade would be composed of the mur neutralisant, with double sheets of glass and an active air chamber, into which air was to be introduced in order to maintain a constant indoor temperature regardless of the season (Figure 1(a)). Respiration exacte, a ventilation system completely independent from this wall while acting in conjunction with it, would guarantee a suitable indoor air quality in the building, and would contribute to the indoor thermal quality of rooms with a mur neutralisant (Figure 1(b)) [12]. (a) Description of the mur neutralisant. (b) Schematic drawing of the respiration exacte. Figure 1: Sketches by Le Corbusier about The City of Refuge. The City of Refuge, belonging to the Salvation Army, was a building designed for the homeless [25]. It could house up to 600 people, distributed in large dormitories and “roomettes”, small rooms used mainly for single women with children. For the City of Refuge to be more than a mere shelter for the night it required installations on several levels that could operate throughout the day, meeting the needs of its occupants [11]. The building was placed in an urban context, but practically isolated from other buildings. It is composed of a basement floor, for workshops, laundry rooms and machine rooms; the “pilotis” floor, used for workshops, kitchens and conference rooms; and the ground floor, used for access (see Figure 2). The mur neutralisant was meant to be executed between the first and fifth floors, acting as the envelope for the female dormitories −the first floor case study−as well as for the 2 smaller rooms between the second and fifth floors [3]. Respiration exacte was finally installed in the City of Refuge in Paris, but not so the mur neutralisant, which was never incorporated for financial reasons and technical concerns. It was replaced with a pan de verre similar in appearance to the mur neutralisant, but with quite different thermal behaviour, creating the need for a traditional heating system installation, although the building lacked a cooling system. This makes it impossible to establish its behaviour as an environmental conditioning solution in relation to the building fa¸cade, either alone or in combination with the respiration exacte. Although the construction of the mur neutralisant had been ruled out, Le Corbusier reserved the space for its construction and maintained an interest in the results it would have produced had it been executed. This interest led engineers from the Saint Gobain company to resume trials in August 1932, when the pan de verre had already been installed in the City of Refuge. 3 Figure 2: Situation of the case study in the City of Refuge and detail of the first floor. Several tests were carried out on different types of glazing in order to verify the coefficients for heat transmission proposed by G. Lyon, and to check the operation of the air heating system of the active chamber [22]. These trials provided the heat transmission coefficients for different types of glazing: 2 mm, 7 mm and 12 mm double glazing with a 100 mm active chamber. The following conclusions were reached from the result of the trials [19]: - A maximum impulse flow of 60 l/s was to be ensured. - The maximum width of the active chamber should be set at 100 mm, since at greater widths the convection currents would cause a reduction in heat exchange and an increase in thermal loss. - A thermal difference of at least 10◦C should be maintained between the airflow to the exterior from the chamber and the indoor temperature of the heated room, in order to compensate for 4 thermal loss. This research aims to resolve the physical problems resulting from the combination of the mur neutralisant and the respiration exacte and establish what the real system behaviour would have been if both these innovations had been implemented in the City of Refuge as planned by Le Corbusier and calculated by G. Lyon (Figure 1(b)). The mur neutralisant is composed of a 7 mm double glass sheet with an active inner chamber measuring 100 mm, through which hot or cold air was circulated depending on the time of the year in order to provide active thermal isolation (see Figure 1(a)). This system is extremely difficult to model and simulate. In fact, current energy and environmental computer simulation programs, such as DesignBuilder [6], cannot be used for this system, especially not combined with Le Corbusier’s mechanical ventilation system, respiration exacte. Therefore FreeFem++ software (v. -3.20) was chosen [10]. This program uses C++ language to process and calculate all sorts of mathematical codes and solution methods for assessment with Computational Fluid Dynamics (CFD). Specific models and programs were created for this study using algorithms integrating all phenomena and physical characteristics in order to reproduce the combination of both of Le Corbusier’s systems for the City of Refuge. The energy models generated take into account climate conditions in Paris, profiles of usage and operating conditions, and the spatial and material characteristics of the envelope of the City of Refuge. This made it possible to calculate the main parameters of the thermal environments of the room studied and to carry out graphic representations of the evolution of interior climate in relation to variations in exterior climate: differences in temperature, airflows, thermal radiation, etc. In short, simulation using FreeFem++ codes makes it possible to reliably predict what the interior temperature of the spaces designed would be. Given the interest in the progress and development of energy efficiency systems and energy preservation in buildings, double skin fa¸cades (DSF) are currently a major research topic as studies of Joe et al. [18] and Ghadimi et al. [13]. In [24], Shameri et al. analyse different elements relating to the design of DSFs, such as geometrical characteristics, types of glass, natural lighting, wind loads, etc. Ventilation and solar protection systems are the most important systems in the inner chamber of the double skin given the reduction in thermal gain produced through the envelope. Zhou et al. [27] present the main methods for the analysis of the thermal behaviour of DSFs, developed to prevent overheating, mainly for cold climate zones in winter and warm climates 5 in summer. The application of ventilated DSFs with an integrated and controlled solar protection device makes it possible to control the building’s thermal conditions in these sorts of climates. Research by Chen et al. [5] uses a mathematical model for a glass double skin fa¸cade with slats in the inner air chamber to reduce solar gains in climates with warm summers. At present, models and simulation using programmed software are some of the most powerful tools available for research on thermal behaviour and fluid dynamics in ventilated DSFs, known as Active Transparent fa¸cades (ATFs), as one of three different fa¸cade analyzed through 3d Computational Fluid Dynamics (CFD) in the study of Brandl et al. [4]. For example, Ismail et al. present a two-dimensional model with numerical simulation of heat transfer in single glazing [15]. This model is based on an energy equation applying the terms of absorbed, transmitted and reflected solar radiation, as well as exterior and interior convection flows through the glass, depending on the incident solar radiation and outdoor temperature. This initial research serves as an introduction to the problem and was subsequently developed by the same authors [16], paying special attention to the effects of mass flow in the chamber between the double glazing in order to determine the superficial temperature of the inside glass. They establish how the increase in mass flow of the natural ventilation reduces total heat gain in comparison with a single glazed window. Research by Ismail et al. [17] was taken into consideration when establishing the mathematical model for the mur neutralisant case study. These authors describe a transitory two-dimensional model formulated using basic mass and energy conservation equations associated with variations in climate and atmospheric conditions. Thus, the results are obtained for the temperatures along and through the air chamber with mechanical ventilation. This study examines a numerical method different to that proposed by Ismail et al. [17] or Liu et al. [20], discretising the equation into partial differentials which define the model for studying the evolution of temperature in the mur neutralisant. These calculations also take into consideration the coupling of the mur neutralisant and the evolution of indoor temperatures. This article has mainly been prompted by the lack of research focusing jointly on the simulation of the mur neutralisant and respiration exacte. The implementation and subsequent simulation using FreeFem++ entails two main tasks. The first is the coupling of a 1D and 2D model. Physical problems and solution methods are applied to the problem of respiration exacte (2D model), a code for an implicit resolution of the problem of the mur neutralisant (1D model) and finally, a coupled code for the correct operation of the combination of mur neutralisant and respiration exacte. The second task is the definition of the mathematical codes in the 1D model, since an implicit method of finite volumes should be established as a resolution procedure, in order to 6 optimize simulation time for the problems of the mur neutralisant with respect to the problem of respiration exacte (2D model) with minimum margin of error in the solutions. 2. Coupled model for the temperature evolution problem This section defines the mathematical model proposed to solve the temperature evolution problem. The main objective is to assess the influence of the mur neutralisant on the temperature of the room with the respiration exacte system. As mentioned above, the problem is divided into two physical systems: the mur neutralisant is examined using a 1D problem, while a 2D problem is used to evaluate the indoor temperature. Figure 3 shows a diagram of the operation of the coupled problem. Thus, in order to establish a final time tf, it is necessary to first solve the 2D problem and obtain the indoor temperature, Tint. This data is then used to resolve the 1D problem, calculating the temperature of the internal glass, Tig, which is embedded into the 2D problem as a boundary condition.    Figure 3: Diagram of the operation of the coupled 1D - 2D problems. In order to give a complete graphic description of the whole domain we show in Figure 4 the schematic representation of the studied room (2D problem) and a cross section of the mur neutralisant (1D problem). In the following subsections we detail the numerical approximations of the 1D and 2D models. 7 Section AA’ Figure 4: Complete physical domain and detail of physical phenomena in the mur neutralisant. 2.1. Evolution of indoor temperature (2D problem) Temperature evolution is simulated using a convection-diffusion problem. Since the room is affected by a respiration exacte system, it is necessary to first calculate the velocity field to be used by the convection phenomena. This problem is modelled on the Navier-Stokes equations, and the unknowns are the velocity field (solution of the Navier-Stokes problem) and the temperature (solution of the convection-diffusion problem). The density is assumed to be constant and the fluid is incompressible. Here we consider a study domain Ω with boundaries Γi(i= 1, . . . , M). We assume that the initial glass wall is located on the boundary Γ1and the entrance of the respiration exacte is made through the boundary Γ3, the rest of the boundaries are assumed to be internal walls. For the case of the City of Refuge the schedule of the domain Ω is shown in Figure 4, the 8 corresponding boundaries are represented in Figure 7. The system required is written as                              ∂~u ∂t +~u ·∇−∇·(ν∇~u) + ∇q=~g in Ω ∇ · ~u = 0 in Ω ∂T ∂t +~u · ∇T−k∆T=ϕin Ω T=Tig1d(m)on Γ1 T=Textef on Γ3 T=Trad on Γ2∪Γ4∪. . . ∪ΓM (1) with initial condition T(0) = Top in Ω. where: ~u : Velocity field, T: Temperature, t: Time, ν=µ ρ: Kinematic viscosity, q=p ρ: Pressure, ~g =~ f ρ: Density of the heating source due to the radiation, k: Thermal diffusion coefficient. ϕ: Source term due to the occupancy. The different notations for boundary conditions are as follows: Tig1d(m)is the temperature of the internal glass wall, imposed on the boundary Γ1. This value is obtained by averaging the temperature obtained by the 1D problem on the internal glass. Trad is the heating temperature of the walls enclosing the room. These walls are labelled Γ2,Γ4,...,ΓM, with (M−1) being the number of boundaries considered in the internal walls (see Figure 7). Thus, it is possible to impose different heating temperatures in each of them. The boundary Γ3is used to simulate the entrance of the respiration exacte, so Textef is the temperature of this incoming flow. Finally, Top is the initial temperature assumed for the room over the domain Ω. The numerical approximation of this problem was carried out using the mixed P2−P1Finite Element method. FreeFem++ software was used for the computing implementation. 2.2. Simulation of the mur neutralisant (1D problem) 2.2.1. The mur neutralisant The solution proposed, though not incorporated, by Le Corbusier was that of a double plane of glass with air recirculation in the inner chamber heated/cooled by the building’s air conditioning system to provide greater thermal insulation than that provided by openings with single glazing or with double glazing and passive air chambers. Controlling the temperature of the interior air 9 6 8 10 12 14 16 18 20 ï100 0 100 200 300 400 500 600 Time [hours] Total Heat Gain [W/m²] Mass flow= 1.0 eï3 [kg/(m s)] Mass flow= 1.8 eï3 [kg/(m s)] Solar radiation [W/m²] (a) Variation of total heat gain qtotal over time. 6 8 10 12 14 16 18 20 19 21 23 25 27 29 31 33 Time [hours] Temperature [°C] Mass flow= 1.0 eï3 [kg/(m s)] Mass flow= 1.8 eï3 [kg/(m s)] External temperature (b) Effect of air mass flow on the temperature of glass interior surface Tigzmed over time. Figure 6: Testing prescriptive model. in surveys for each of the levels in order to obtain a better understanding of the building and to choose the room for study: the women’s dormitory on the first floor, to the left of the staircases (Figure 2), which had the greatest surface area, 295 m2, the longest length of mur neutralisant, 37.2 m, and highest occupancy, 67 beds. The surrounding conditions imposed in the two-dimensional model (see Section 2.1) correspond to each of the enclosures defined in Figure 7, in a horizontal section carried out at a height of 2.35 m, at a level with the impulse grid for air ventilation. Three types of mur neutralisant were proposed and tested by Saint Gobain in August 1932 [19], with measurements 2+100+2, 7+100+7 and 12+100+12 mm. This allowed a precise and rigorous assessment of the true conditions under which the mur neutralisant system might have operated, had it been incorporated, bearing in mind that Le Corbusier reserved a space for the possible incorporation into the wall of 7+100+7 mm glazing at a later stage. We perform the numerical simulation of this type of glass chosen by Le Corbusier. Figure 4 shows the properties of the physical phenomena for the specific mur neutralisant system simulated, including the percentages of solar radiation transmitted through the mur neutralisant. All the values for emissivity, absorptance, transmission, density, specific heat and thermal resistance of glazing have been taken from the data provided by Saint Gobain [23], Table 2. The value of Tig1d(m), which is the temperature of the glazed enclosure, is imposed on boundary Γ1. This value is obtained from the result of the 1D problem which simulates the evolution of temperatures in the mur neutralisant. The radiant temperature of the interior enclosures of the 16 Properties External glass Channel gap Internal glass Thickness (m)eeg 0.007 ec0.10 eig 0.007 Emissivity ξeg 0.07 ξig 0.07 Absorptance αeg 0.14 αig 0.14 Transmission τeg 0.79 τig 0.79 Density (kg/m3)ρeg 2500 ρf1293 ρig 2500 Specific heat (kg J/K)ceg 750 cf1004 cig 750 Thermal Reg RfRig resistivity (m K/W) 0.17545 0.125 0.17545 Table 2: Properties of simulation hypothesis 7+100+7 mm. room studied is imposed on boundaries Γ2, Γ4, Γ5, Γ6, Γ7y Γ8(see Figure 7). Textef is imposed on boundary Γ3. This corresponds to the point where the flow for the respiration exacte is boosted. Top is the initial operative temperature in the room studied over the space Ω. The source term due to the occupancy, involved in the evolution of the temperature in the room (equation (1)) for the 2D problem, is calculated according to a ratio of 25 person/m2and an energy charge of 46 W/person. This is defined as follows: ϕ=0.25person m2·46 W person ρcfH= 0.00316K s(11) where ρis the air density (kg/m3), cfthe specific heat of the air (kg J/K) and Hthe height of the room (m). Initial radiant temperature conditions obtained from the simulations with the DesignBuilder energy simulation tool have only been used as a starting point for the initial radiant temperature conditions of the room studied. See Appendix A for details. 0 5 10 15 20 25 30 35 40 ï2 0 2 4 6 8 10 12 K6 K5 K7 K1 K8 K4 K2 K3 Figure 7: Labels corresponding to each of the surrounding conditions of the room studied and probes of internal points where the temperature is measured (marked with asterisks). 17 3.2.1. Initial conditions In this subsection we specify the initial conditions for the problem. The numerical simulations are developed for two representative days in winter and summer, namely, August 15 and December 30. The calculations are made referring to solar time. The total time of the numerical simulation is two solar days (48 h) and the initial data specified here refers to the first solar time hour. •Initial climate conditions The climate files for Paris Orly were used, considering exactly the same files used by Design- Builder. See Appendix A. •Initial temperatures and impulse flow in the mur neutralisant (1D problem) As was mentioned above, for the initial temperature conditions a previous calculation was performed using the simulations of DesingBuilder, based on the EnergyPlus simulation tool. The resulting data gives an initial temperature in the interior of the room of 27.58◦C for summer and 7.14◦C for winter. The initial temperatures for the internal glass and the temperature of the room are the same, so Tint =Tigini = 27.58◦C in summer and Tint =Tigini = 7.14◦C in winter. The external glass is supposed to be at the same exterior temperature, so Tegini = 19.7◦C in summer and Tegini =−3.8◦C in winter. In order to establish the impulse temperature of the active chamber, a 10◦C thermal leap was considered in relation to the temperature of the desired indoor temperature of the room: 20◦C in winter and 25◦C in summer. Therefore, the constant impulse temperatures in the active chamber are set to 30◦C in winter and 15◦C in summer. The Saint Gobain technicians had established that high flows (120 l/s and 150 l/s) increased energy losses as a result of the turbulence inside the active chamber, with a decrease in the heat exchange between fluid and glass surfaces. A more appropriate 60 l/s flow was chosen for the air impulse flow into the active chamber. To introduce this data into the FreeFem++ code, it is necessary to relate this flow to the mass flow which is the quantity that is really imposed. Thus, we calculate the mass flow ηto be imposed as follows: η=ρ·v=ρ·q S=1.293 kg m3·60 l s·1m3 1000 l 0.10 m·L= 0.7758 kg s·m·L(12) where ρis the air density (kg/m3), vthe velocity (m/s), qthe impulse flow (m3/s), and Sthe surface area of the passage section where the respiration exacte is implemented (m2). Note that this quantity is normalised with a characteristic length Lassociated to the dimension of the 3D 18 case which is avoided in the 2D calculation (L= 1 in simulations). •Initial temperatures and impulse flow in the room (2D problem) The impulse temperature at the respiration exacte is fixed at 20◦C in winter and 25◦C in summer. These are the desired indoor temperatures stated in the tests carried out by Saint Gobain. The initial temperature conditions in the interior of the room have already been specified, 7.14◦C for winter and 27.58◦C for summer. 3.2.2. 1D model results First, we study the evolution of the temperatures in the mur neutralisant, by considering a constant temperature in the room. The objective is to study the influence of the external temperature, radiation and the temperature of the air impulsed between the glass, on the temperature of the internal glass. Therefore, for the first test it is enough to consider the numerical simulation produced with the 1D code described in Subsection 2.2.2. •Evolution of heat transfer First, we study the relation of the heat transfer (qtotal) in the mur neutralisant to the solar radiation. 0 5 10 15 20 25 30 35 40 45 150 200 250 300 350 400 450 500 550 Solar time [Hours] Total heat gain [W/m2] Solar radiation [W/m2] Mur neutralisant (a) December 30 0 5 10 15 20 25 30 35 40 45 0 500 1000 1500 2000 2500 Solar time [Hours] Total heat gain [W/m2] Solar radiation [W/m2] Mur neutralisant (b) August 15 Figure 8: Total heat gain in the mur neutralisant for the two days under study. Figure 8 represents the evolution over time of the total heat gain together with the solar radiation for both cases. In the case of the summer day (Figure 8(b)), the maximum heat transfer 19 difference occurs at 12:00 h each day when there is 2200 W/m2solar radiation in the exterior. Heat transfer to the interior atmosphere for 7 mm glass manages to transfer 63.3% which does not seem to high to provide reasonable temperature to the interior to achieve comfort conditions. In contrast, this heat gain increases to 79.2% for the winter sample (Figure 8(a)) where the maximum heat transfer to the interior is required. For the day studied, the maximum solar radiation received is 535 W/m2also around midday. The most positive point of this case is that even after 15:00 h the heat gain remains quite high demonstrating the advantages of the mur neutralisant system. •Evolution of the temperature of the internal glass Figure 9 shows the evolution over time of the temperature of the internal glass together with the exterior temperature. 0 5 10 15 20 25 30 35 40 45 −10 −5 0 5 10 15 20 25 Solar time [Hours] Temperature [ºC] Exterior temperature [ºC] Internal glass temperature (a) December 30. 0 5 10 15 20 25 30 35 40 45 5 10 15 20 25 30 35 40 Solar time [Hours] Temperature [ºC] Exterior temperature [ºC] Internal glass temperature (b) August 15. Figure 9: Evolution of the temperature of the internal glass surface for the two days under study. For the winter case (Figure 9(a)), the temperature of the interior glass achieved remains almost constant, at approximately 20.7◦C. With a small increase of temperature, following the increase of the external temperature, it goes up to 21.2◦C. The strong increase in the first 12 hours approximately is due to the initial condition. After this time, the temperature is established and there is no influence from the initial data. In summer (Figure 9(b)), the behaviour of the mur neutralisant manages to reduce the temperature in the interior glass in a range of 21.7◦C - 25.7◦C once established. Observe that the temperature of the internal glass buffers the exterior temperature in the hottest hours, achieving 20 a difference of 4◦C less. 3.2.3. Coupled 1D/2D model results In this section we show the results of the coupled model, taking into account: solar radiation, external temperature, temperature of the impulsed air in the mur neutralisant and the temperature of the impulsed air in the room. We analyse the results obtained for the temperature inside the mur neutralisant and the temperature in the room. We have studied two scenarios, with or without occupancy defined by equation (11) in the room. In the case considered, the schedule of occupancy was fixed between 18:00 h and 8:00 h each day. To be brief, we do not show the graphics corresponding to the 1D results here because the behaviour of the mur neutralisant has already been shown. •Evolution of temperature in the room Before analysing the results for the interior temperatures of the room it is important to note two specific aspects relating to the general behaviour of the area occupied: - In the southwest corner, the accumulation of air that is less cold than in the rest of the room in winter and less hot in summer provides a suitable temperature in the area that is farthest away from the air impulse, also encouraging air convection to the area with greatest occupancy. - In contrast, in the northeast corner in winter there are colder air currents, while in the summer the currents are hotter. Although this is considered one of the least favourable areas in the room, this is not entirely relevant as this corner is actually a small room. Figures 10 and 11 show the isovalues of the temperature obtained for the representative hour 25 (at the middle of the first occupation range) for both cases in winter and summer. We comment on these below: Winter after 25 hours (Figure 10): In this case the temperature of the active chamber is maintained constant at 30 ◦C and the respiration exacte impulse temperature occurs at 20 ◦C. Thus, the temperature of the room with occupancy increases by 3.5 ◦C with respect to the air impulse by respiration exacte, while in the case without occupancy the increase is 2 ◦C. We can see how the increase in temperature when occupied occurs in an almost regular way throughout the room, always with higher temperatures near the mur neutralisant than in the rest of the room. Summer after 25 hours (Figure 11): 21 When the active chamber temperature is maintained constant at 15 ◦C and the respiration exacte occurs at 25 ◦C in neutral air conditions, the temperature in the room for the occupancy case increases by only 1.5 ◦C with respect to the temperature supplied by respiration exacte. While if there is no occupancy, the temperature undergoes a steady increase of 0.5 ◦C. We observe the same behaviour as in the winter case, the temperature increases uniformly in the room when it is occupied.                        (a) With occupancy                        (b) Without occupancy IsoValue 19.5 19.85 20.2 20.55 20.9 21.25 21.6 21.95 22.3 22.65 23 23.35 23.7 24.05 24.4 24.75 25.1 25.45 25.8 26.15 26.5 Temperature (ºC) Figure 10: Simulation at the middle of the pane height for December 30, after 25 hours, (with respiration exacte temperature at 20 ◦C and mur neutralisant temperature at 30 ◦C). To show the results more clearly we have measured the temperature obtained by the simulation in several points located in the room, marked in Figure 7. We then averaged these values to obtain an averaged temperature inside the room for each time. The results are shown for the 48 hours of simulation in Figure 12 and for clarity, we have marked the ranges of hours when occupancy is considered. The temperature is more stable if the occupancy load is not taken into account. For winter and summer cases, the temperatures remain similar even after the first occupancy range, and a clear increase in temperature is observed during the occupancy hours. 22                        (a) With occupancy                        (b) Without occupancy IsoValue 19.5 19.85 20.2 20.55 20.9 21.25 21.6 21.95 22.3 22.65 23 23.35 23.7 24.05 24.4 24.75 25.1 25.45 25.8 26.15 26.5 Temperature (ºC) Figure 11: Simulation at the middle of the pane height for August 15, after 25 hours, (with respiration exacte temperature at 25 ◦C and mur neutralisant temperature at 15 ◦C). 23                           !" #  !" # (a) August 15.                          ! "  ! " (b) December 30. Figure 12: Comparison of the temperature in the room with and without occupancy load. 24 4. Conclusions The FreeFem++ simulations and their subsequent analysis support Le Corbusier’s proposal to combine the mur neutralisant and respiration exacte for the environmental conditioning of the City of Refuge, G. Lyon’s calculations for both systems and the main conclusions reached by J. Le Braz in the St. Gobain tests. This shows the importance of this proposal, more than 50 years ahead of its time in relation to modern active fa¸cade systems, of which Le Corbusier’s project is the clearest precursor. In the results we observe uniform room temperature and suitable climate conditions for both winter and summer cases. There is an exception at the Northeast corner and mainly at the Southwest corner due to the irregular geometry of the room. The thermal activity in the mur neutralisant balances the external temperature to produce a milder temperature of the internal glass and in turn, approach climate comfort conditions within the room. In winter for an air flow supply (respiration exacte) of 20◦C and a chamber temperature of 30◦C (heating), the superficial temperature of the internal glass is uniform with slight variations between 20.7◦C and 21.2◦C. The temperature in the room for the representative solar hour 25 (at the middle of the first occupation range) and an exterior temperature of -4◦C is homogeneous with average values of 23.5◦C if occupied and of 22◦C if not. Similarly for the summer case, for an air flow supply (respiration exacte) of 25◦C (neutral primary air) and an air flow supply of 15◦C (into the active chamber), climate comfort is maintained. The highest exterior thermal oscillation leads to a range of internal glass temperature between 21.7◦C and 25.7◦C. In addition, the temperature of the room for the solar hour 25 −the most unfavourable case because of night occupancy−is 25.5◦C with the room empty and presents a small increase to 26.5◦C when occupied. The innovative technologies developed by Le Corbusier based on the mur neutralisant and the respiration exacte, provide a new conditioning system through the building envelope ahead of the first air conditioning systems then appearing in the United States. Unlike these, Le Corbusier proposed to provide the fa¸cade with heating and air-conditioning of the interior spaces and a ventilation mechanism through the respiration exacte. He was clearly the precursor of the later active system fa¸cades. Thus, comfort conditions and thermal uniformity are achieved by simply heating or cooling the air volume inside the mur neutralisant, by at most 10◦C−for the most unfavourable conditions−in relation to the desired temperature into the room. In theory this system seems more economical 25 Appendix B. Nomenclature ρDensity of glass [ kg m3] cSpecific heat [ J kgK ]=[W s kgK ] VArea [m2] ηMass flow in the channel per unit depth [ kg sm ] σStephan-Boltzman constant 5.5710−8 εeg Emissivity of external glass εig Emissivity of internal glass αeg Absorbency of external glass αig Absorbency of internal glass τeg Energy transmission of external glass τig Energy transmission of internal glass Qig Net radiant heat transfer in the internal glass Qeg Net radiant heat transfer in the external glass UTransmittance coefficient [ W m2K] Uext Transmittance coefficient of external glass [ W m2K] Uext =1 Rse +Reg +Rsi Uint Transmittance coefficient of internal glass [ W m2K] Uint =1 Rse +Rig +Rsi Rse Film exterior coefficient [m2K W] RcThermal resistance of channel [m2K W] Rsi Film interior coefficient [m2K W] Reg Thermal resistance of external glass [m2K W] Reg =eeg λeg Rig Thermal resistance of internal glass [m2K W] Rig =eig λig eeg Depth of external glass [m] eig Depth of internal glass r [m] λeg Thermal conductivity of external glass [ W mK ] λig Thermal conductivity of internal glass [ W mK ] 32 [1] Balacco, C., Colombar, M. Thermal behaviour of interactive mechanically ventilated double glazed fa¸cade: bib-dimensional analysis. Energy and Buildings 38 (2006) 1-7. [2] Balocco, C. A non-dimensional analysis of a ventilated double fa¸cade energy performance. Energy and Buildings 36 (2004) 35-40. [3] Boesiger, W. Le Corbusier et Pierre Jeanneret: oeuvre complete. Vol 2, 1929-1934(1999). Basel, Switzerland: Birkhauser. [4] Brandl, D., Mach, T., Grobbauer, M., Hochenauer, C. Analysis of ventilation effects and the thermal behaviour of multifunctional fa¸cade elements with 3D CFD models. Energy and Buildings (2014), http://dx.doi.org/10.1016/j.enbuild.2014.09.036. [5] Chen, YH., Sa, Sz., Zhou, Ys., Wei, S.X., Tan, Z.H. A mathematical model of thermal channel glazing curtain wall. Building Energy & Environment 25 (2006) 10-5. [6] DesignBuilder v.2.4.2.026. [Online], Available: http://www.designbuilder.es/descargas/ software-designbuilder [17 June 2013]. [7] EnergyPlus v.6.0. U.S. Department of Energy (DOE). [Online], Available: http://apps1.eere.energy.gov/buildings/energyplus/energyplus training.cfm [2 September 2013]. [8] Faggembauu, D., Costa, M., Soria, M., Olivia, A. Numerical analysis of the thermal behaviour of ventilated glazed fa¸cades in Mediterranean climates. Part I. Development and validation of a numerical model. Solar Energy 75 (2003) 217-28. [9] Fernandez, V., Gallo, E. La Cit´e de Refuge de Le Corbusier, une ´etude men´ee sur la demande de Fran¸cois Chatillon, ACMH. S´eminaire Efficacit´e ´energ´etique. [Online], Available: http://www.futursurbains.fr/fichiers/S%202013.pdf [13 May 2013]. [10] FreeFem++ v.-3.20. [Online], Available: http://www.FreeFem.org/ff++/ [30 October 2011]. [11] Fondation of Le Corbusier. [Online], Available: http://www.fondationlecorbusier.fr. [7 January 2012]. [12] Gallo, E., Fernandez, V. A factory for well-being, innovation in the heating system and the curtain-wall in Le Corbusier’s Salvation Army City of Refuge, Paris 1933. (2010) Toulouse: CDHTE-CNAM, Ecole Nationale d’Architecture. [13] Ghadimi, M., Ghadamian, H., Hamidi, A.A., Shakouri, M., Ghahremanian, S. Numerical analysis and parametric study of the thermal behavior in multiple-skin fa¸cades. Energy and Buildings 67 (2013) 44-55. 33 [14] Hecht, F. New development in freefem++. J. Numer. Math. 20 (2012), no. 3-4, 251-265. 65Y15. [15] Ismail, K.A.R., Henr´ıquez, J.R. Modeling and simulation of a simple glass window. Solar Energy Materials & Solar Cells 80 (2003) 355-374. [16] Ismail, K.A.R., Henr´ıquez, J.R. Two-dimensional model for the double glass naturally ventilated window. International Journal of Heat and Mass Transfer 48 (2005) 461-475. [17] Ismail, K.A.R., Henr´ıquez, J.R. Simplified model for a ventilated glass window under forced air flow conditions. Applied Thermal Engineering 26 (2006) 295-302. [18] Joe, J., Choi, W., Kwak, Y., Huh, J-H. Optimal design of a multi-story double skin fa¸cade. Energy and Buildings 76 (2014) 143-150. [19] Le Braz, J. La transmission de la chaleur gr`ave `a travers le verre: Des id´ees nouvelles sur le chauffage des habitations. Glaces et Verres 20 (1933) 12-18. [20] Liu, M., Bjarne Wittchen, K., Kvols Heiselberg, P., Vildbrad Winther, F. Development and sensitivity study of a simplified and dynamic method for double glazing facade and verified by a full-scale fa¸cade element. Energy and Buildings 68 (2014) 432-443. [21] Oliveti, G., Arcuri, N., Bruno, R., De Simone, M. An accurate calculation model of solar heat gain through glazed surfaces. Energy and Buildings 43 (2011) 269-264. [22] R.L. La maison de verre de MM. Le Corbusier et Jeanneret et le mur neutralisant. Glaces et Verres 20 (1933) 10-12. [23] Saint Gobain, [Online], Available: http://www.saint-gobain- sekurit.com/SP/index.asp?nav1=AU&nav2=AUSM/ [13 September 2012]. [24] Shameri, M.A., Alghoul, K., Sopian, M., Fauzi M., Sain, Elayeb, O. Perspectives of double skin fa¸cade systems in buildings and energy saving. Renewable and Sustainable Energy Reviews 15 (2011) 1468-1475. [25] Taylor, B. Technology, society, and social control in Le Corbusier’s Cit´e de Refuge, Paris 1933. Oppositions 16 (1979)168-185. [26] Zanghirella, F., Perino, M., Serra, V. A numerical model to evaluate the thermal behaviour of active transparent fa¸cades. Energy and Buildings 43 (2011) 1123-1138. [27] Zhou, J., Chen, Y. A review on applying ventilated double-skin fa¸cade to buildings in hot-summer and cold-winter zone in China. Renewable and Sustainable Energy Reviews 14 (2010) 1321-1328. 34