Comsol Perfusion Heat Transfer

Air Collector And Trombe Wall Design

H. Boyer, F. Miranville, D. Bigot, S. Guichard, I. Ingar, A. P. Jean, A. H. Fakra, D. Calogine and T. Soubdhan Physics and Mathematical Engineering for Energy and Environment Laboratory,

1. Introduction

The aim of this paper is to briefly recall heat transfer modes and explain their integration within a software dedicated to building simulation (CODYRUN). Detailed elements of the validation of this software are presented and two applications are finally discussed. One concerns the modeling of a flat plate air collector and the second focuses on the modeling of Trombe solar walls. In each case, detailed modeling of heat transfer allows precise understanding of thermal and energetic behavior of the studied structures.

Recent decades have seen a proliferation of tools for building thermal simulation. These applications cover a wide spectrum from very simplified steady state models to dynamic simulation ones, including computational fluid dynamics modules (Clarke, 2001). These tools are widely available in design offices and engineering firms. They are often used for the design of HVAC systems and still subject to detailed research, particularly with respect to the integration of new fields (specific insulation materials, lighting, pollutants transport, etc.).

2. General overview of heat transfer and airflow modeling in CODYRUN

2.1 Thermal Modeling

This part is detailed in reference (Boyer, 1996). With the conventional assumptions of isothermal air volume zones, unidirectional heat conduction and linearized exchange coefficients, nodal analysis integrating the different heat transfer modes (conduction, convection and radiation) achieve to establish a model for each constitutive thermal zone of the building (one zone being a room of a group of rooms with same thermal behaviour).

For heat conduction in walls, it results from electrical analogy that the nodal method leads to the setting up of an electrical network as shown in Fig. 1, the number of nodes depending on the number of layers and spatial discretization scheme :

3

Fig. 1. Example of associated electrical network associated to wall conduction

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The physical model of a room (or group of rooms) is then obtained by combining the thermal models of each of the walls, windows, air volume, which constitute what CODYRUN calls a zone. To fix ideas, the equations are of the type encountered below:

(4)

Equations of type (1) and (2) correspond to energy balance of nodes inside and outside surfaces. Nw denote the number of walls of the room, and correspond to the following

Fig. 2. Wall Boundary Conditions

ϕ being heat flux density, lw, sw, and c indices refers to long wave radiation, short wave radiation and convective exchanges. Indices e and i are for exterior and indoor. Equation (3) comes from the thermo-convective balance of the dry-bulb inside air temperature Tai, taking into account an air flow m through outside (Tae) to inside. (4) represents the radiative equilibrium for the averaged radiative node temperature, Trm. The generic approach application implies a building grid-construction focus. Following the selective model application logic developed (Boyer, 1999), an iterative coupling process is implemented to manage multi-zone projects. From the first software edition, some new models were implemented. They are in relation with the radiosity method, radiative zone coupling (short wavelength, though window glass) or the diffuse-light reduction by close solar masks (Lauret, 2001). Another example of CODYRUN evolution capacity could be illustrated by a specific study using nodal reduction algorithms (Berthomieu, 2003). To resolve it, a new implementation was done: the system was modified into a canonic form (in state space).

Heat Transfer in Buildings: Application to Solar Air Collector and Trombe Wall Design

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From a user utilization point of view, this thermal module exit is mainly linked to the discretizated elements temperatures, the surfacic heat flows, zone specific comfort indices, energy needs, etc.

2.2 Airflow Modeling

Thermal and airflow modules are coupled to each other thanks to an iterative process, the coupling variables being the air mass flows. It is useful to implement the inter zones flows

Then Qualifies The Mass Transfer From The Zone

i to the zone j, as it is depicted .

Fig. 3. Interzonal Airflow Rates Matrix

Then, a pressure model for calculating previous airflow rates is set and takes into account wind effect and thermal buoyancy. To date, the components are integrated ventilation vents, small openings governed by the equation of crack flow, as :

(5)

S is aperture surface, Cd and n (typically 0.5- 0.67) depends on airflow regime and type of

Δ

the pressure drop. Therefore, the following scheme can be applied for encountered cases.

Fig. 4. Exterior And Interior Small Openings

Taking into account the inside air volume incompressibility hypothesis, the mass weight balance should be nil. Thus, in the established system, called pressure system, the unknowns are the reference pressure for each of the zones. Mechanical ventilation is simply taken into account through its known airflow values. In this way, ventilation inlets are not taken into detailed consideration which could have been the case owing to their flow- pressure characteristics.

0

...

Vmc

is the flow extracted from zone k (by vents) and N the total number of zones. After the setting up of this non linear system, its resolution is performed using a variant of the Newton-Raphson (under relaxed method). This airflow model has recently been supplemented by a CO2 propagation model in buildings (Calogine, 2010).

2.3 Humidity Transfers

For decoupling reasons, zones dry temperatures, as well as inter zone airflows, have been previously calculated. At this calculation step, for a given building, each zone's specific humidity evolution depends on the matricial equation :

+

. .

(7)

According to Duforestel’s model, an improvement of the hydric model (Lucas, 2003) was given by the use of a hygroscopic buffer. If we consider N as the number of zones, a linear system of dimension 2N is obtained and a finite difference scheme is used for numerical solution.

3.1 Inter Model Comparison

A large number of comparisons on specific cases were conducted with various softwares, whether CODYBA, TRNSYS for thermal part, with AIRNET, BUS, for airflow calculation or even CONTAM, ECOTECT and ESP. To verify the correct numerical implementation of models, we compared the simulation results of our software with those from other computer codes (Soubdhan, 1999). The benchmark for inter-comparison software is the BESTEST procedure (Judkoff, 1983), (Judkoff, 1995). This procedure has been developed within the framework of Annex 21 Task 12 of the Solar Heating and Cooling Program (SHC) by the International Energy Agency (IEA). This tests the software simulation of the thermal behavior of building by simulating various buildings whose complexity grows gradually and comparing the results with other simulation codes (ESP DOE2, SERI-RES, CLIM2000, TRNSYS, ...). The group's collective experience has shown that when a program showed major differences with the so-called reference programs, the underlying reason was a bug or a faulty algorithm.

Heat Transfer in Buildings: Application to Solar Air Collector and Trombe Wall Design

3.1.1 Iea Bestest Cases

The procedure consists of a series of buildings carefully modeled, ranging progressively from stripped, in the worst case, to the more realistic. The results of numerical simulations, such as energy consumed over the year, annual minimum and maximum temperatures, peak power demand and some hourly data obtained from the referral programs, are a tolerance interval in which the software test should be. This procedure was developed using a number of numerical simulation programs for thermal building modeling, considered as the state of the art in this field in the US and Europe. After correction of certain parts of CODYRUN, an example output from this confrontation is the following concerns and energy needs for heating over a year, for which the results of our application are clearly appropriate.

Fig. 5. Exemple Of Bestest Result

The procedure requires more than a hundred simulations and cases treated with CODYRUN showed results compatible with most referral programs, except for a few. We were thus allowed to reveal certain errors, such as the algorithm for calculating the transmittance of diffuse radiation associated with double glazing and another in the distribution of the incident radiation by the windows inside the envelope. As in the reference codes, two points are to remember: the majority of errors came from a poor implementation of the code and all the efficiency of the procedure BESTEST is rechecked, errors belonging to modules that have been used for years.

Concerning airflow validation, IEA multizone airflow test cases describe several theoretical and comparative test cases for the airflow including multizone cases. It was developed within the International Energy Agency (IEA) programs: Solar Heating and Cooling (SHC) Task 34 and Energy Conservation in Building and Community Systems (ECBCS) Annex 43.

The tests are designed for testing the capability of building energy simulation programs to predict the ventilation characteristics including wind effect, buoyancy and mechanical fan. CODYRUN passed all the test cases.

3.1.2 Tn51 Airflow Case

In (Orme, 1999), a test case composed of a building with three storeys is described and first published in (Tuomala, 1995). All boundary conditions are imposed (wind, external temperature) and indoor conditions are constant, i.e. in steady state.

Fig. 6. Tn 51 Test Case

Next figure shows solution of 3 references codes, i.e. COMIS, CONTAM93 and BREEZE. CODYRUN’s results were added on the figure extracted from the paper (Orme, 1999).

Fig. 7. Intermodel Airflow Comparison

Heat Transfer in Buildings: Application to Solar Air Collector and Trombe Wall Design

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As it can be seen, in terms of numerical results, CODYRUN gives nearly the same values as the other codes, little differences being linked to numerical aspects as algorithms or convergence criteria used.

3.2 Experimental Confrontation

As part of measurement campaigns on dedicated cells and real homes, a set of elements of models have been to face action (and for some improved), mostly concerning thermal and humidity aspects. Not limited to, some of these aspects are presented in the articles (Lauret, 2001) (Lucas, 2001) and (Mara, 2001), (Mara, 2002).

4.1 Air Solar Collector

An air solar collector is used to heat air from solar irradiation. More precisely, it allows to convert solar energy (electromagnetic form) into heat (Brownian motion). This type of system can be used to heat buildings or to preheat air for drying systems. Air solar collector is constituted by an absorber encapsulated into an isolated set-up (Fig. 8). To avoid heat loss by the incoming flux side, a glass is located above the absorber, letting a gap between them. This glass allowing to catch long wavelength emitted by the set-up when its temperature rises-up. Air temperature improvement is mostly done by air convection at the absorber interface. This heat is then carried by air in the building or in the drying system.

Fig. 8. Air solar collector principle, adapted from (Sfeir, 1984) The enclosure is not strictly speaking a building, but the generic nature of the software allows to study this device. This is a zone (within the captation area), a glazed windows, exterior walls and an inner wall of absorber on which it is possible to indicate that solar radiation is incident.

It should be noted that this is part of a class simulation exercise allowing students to learn collector physics basis.

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4.1.1 Collector modeling and description of the study It is assumed that before initial moment, there is no solar irradiation and the collector is at thermal equilibrium, i.e. outside air temperature is the set-up temperature. At t=0, an irradiation flux Dh is applied without interactions with the outside air temperature. In a simplified approach, a theoretical study is easily obtained. Some equations below are used to understand the functioning of the collector. In steady state, the incoming irradiation flux reaching the absorber is fully converted and transmitted to the air (assumed to uniform

(8)

Where Kp is the thermal conductance (W.m-2.K-1) of each wall through which losses can pass, m dot is a constant air mass flow through the collector, Tai is the inside air temperature, Tae is the outside air temperature, and ρas (1.2 kg.m-3) and Cas (1000 J.kg-1.K-1) are respectively the air thermal conductivity and density. By knowing initial conditions (at t=0, Tai=Tae), the

(10)

The studied collector is horizontal, the irradiated face has a surface of 1m, and an air gap thickness of 0.1m. The meteorological file is constituted of a constant outside air temperature (25°C) and a constant direct horizontal solar irradiation of 500W (between 6 am and 7 pm). It is assumed (and further verified) that the steady state is reached at the end of the day.

Concerning the building description file, the collector is composed by 1 zone, 3 boundaries (1 for the upper face, 1 for the lower face, and 1 for all lateral faces), and 4 components (glass, lateral walls, lower wall and absorber). Walls are made - from inside to outside - of wood (1cm), polystyrene (5cm) and wood (1cm). Wood walls have a short wave absorptivity of α = 0.3.

0

τ = 0.85), and the absorber is a metallic black sheet of 2mm (α = 0.95). The solar irradiation absorption model of the collector is a specific one. This has to be chosen in CODYRUN, because traditionally in buildings the solar irradiation doesn’t impact directly an internal wall (absorber), but the floor.

Even if this solar air heater is considered as a very simple one, the following figure gives some details about heat exchanges in the captation area. Heat Transfer in Buildings: Application to Solar Air Collector and Trombe Wall Design

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Fig. 9. Solar irradiation absorption process. 4.1.2 Simulation results in the case of forced convection in air gaps An air flow of 1 m3.h-1 is set. After running simulations, the following graph is obtained for

Two Identical Days :

Fig. 10. Evolution of air temperature at the output of the solar collector with forced convection (1m3.h-1).

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