IAE-Annex 41, Subtask 1, Meeting May 12-14, 2004, Zurich

CFD-modelling of

Temperature and Humidity Distribution

in the St. Pieter’s Church

W. Uyttenhove1, M. De Paepe1, A. Janssens2

1Department of Flow, Heat and Combustion Mechanics, Ghent University,Sint-Pietersnieuwstraat 41, B-9000 Gent, Belgium

2Department of Architecture and Urban Planning, Ghent University,J. Plateaustraat 22, B-9000 Gent, Belgium

1 Introduction

This paper gives a brief overview of heat and moisture modelling using FLUENT, a widely used CFD-toolfor modelling and simulating flows. The effect of heating and moisture sources on the temperature andhumidity distribution is simulated in 2D and 3D models.

These techniques are used on a particular example, the St. Pieter’s Church in Ghent. An extensivemeasurement campaign is set up to determine the climate characteristics of the church. Several heatingsystems are studied using FLUENT and the consequences on the indoor church climate are indicated. Avery important issue is the impact of heating systems on historical works of art in monumental churches.

2 The St. Pieter’s Church, Ghent

About 630 Saint Amandus founded the Sint-Pieters abbey on the highest point of Ghent. The abbeybecame very famous during the Middle Ages, but in 1566 the church and the abbey became badly damagedduring the iconoclastic fury. Only in 1629 the first stone of the current baroque church was laid. Today,the church is used for services and cultural manifestations and the abbey is a tourist attraction in Ghent,also used for exhibitions and conferences.

The St. Pieter’s Church is decorated with many paintings and sculptures of famous artists. Themonumental organ, built by Van Peteghem in 1849, is famous for his marvellous sound.

The floor plan is given in Fig. 2. The church has a total length of 88 m and a maximal width of 30 m.The internal height is about 17 m in the side aisles, about 32 m in the nave and about 52 m in the dome.With its 74 m, the steeple is the highest point of Ghent. The church walls are made of sandlimestoneand masonry, and have an average thickness of about 1 m.

At the moment, there is no fixed heating system in the church. Gas burners fueled by propane are usedto heat the church for services and cultural manifestations during wintertime, but they are insufficientand produce water vapor. The installation of a heating system is planned.

3 Measurements

In October 2003 an extensive measurement campaign has been started in the St. Pieter’s Church.Temperature and relative humidity (RH) loggers have been placed at several points in the building.

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Figure 1: The St. Pieter’s Church seen from the Nord-West

Figure 2: Floor plan of the St. Pieter’s Church

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The global results are given in Fig. 3. The temperature decreases from 18 ◦C in the beginning ofOctober 2003 till 5 ◦C in January 2004. From March 2004 the temperature is increasing. The relativehumidity (RH) varies between 40 and 90 % and the absolute humidity (AH) varies between 3 and 7gram H20/kg air. There is a time delay between the changes in the indoor and outside climate.

Measurements confirm that the church has a stable climate and the loss of heat by leakage is limited.The temperature and humidity differences in the volume of the church are small. The actual heatingmethod (propane burners) does not influence the indoor church climate, which is necessary for the con-servation of the historical works of art and the famous Van Peteghem organ. So the church approximatelycan be represented as a large, homogeneous volume, with a low moisture content. With a thermographicalcamera pictures of the wall temperature were taken. No cold bridges were found.

4 Modelling Temperature and Humidity in FLUENT

4.1 FLUENT

FLUENT is a computational fluid dynamics (CFD) software package to simulate fluid flow and heattransfer in complex geometries. It uses the finite-volume method to solve the governing equations formass, impuls and energy transfer. It provides the capability to use different physical models such asincompressible or compressible, viscous or non viscous, laminar or turbulent, etc. Geometry and gridgeneration is done using GAMBIT which is the preprocessor bundled with FLUENT.

4.2 Models

In order to shorten the calculations, simple 2D and 3D models of the St. Pieter’s Church have beenmade in GAMBIT and used in FLUENT (Fig. 4). They give a good indication of the usefullness ofFLUENT to simulate temperature and humidity distribution in monumental churches and are in globalrepresentative for the St. Pieter’s Church.

4.3 Heat loss

Measurements in the church (see also § 3) indicate the restricted loss of heat by leakage. The main partis caused by heat transport through de wall. It is not easy to determine little losses through cracksand windows and their influence in this model is neglected. Therefore we approximately model the wallas a fixed temperature surface and use this boundary condition in FLUENT. The wall temperature isdependent of the outside temperature. The estimated U-coefficient of the wall is 0.98 W

m2.K .

4.4 Underfloor Heating

Modelling underfloor heating in FLUENT can preliminary be done in a 2D model (§ 4.2). The wholefloor is implemented as a fixed temperature wall boundary condition.

FLUENT solves the energy equation by searching an equilibrium of the incoming and outgoing heatflows. De heat flow through a wall is calculated by FLUENT ([Flu03], Chapter 6) as

q = hf (Tw − Tf ) + qrad (1)

with

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Figure 3: Evolution of temperature, relative humidity (RH) and absolute humidity

(AH) in and outside the St. Pieter’s Church

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Figure 4: 2D and 3D model

• hf fluid-side local heat transfer coefficient

• Tw wall surface temperature

• Tf local fluid temperature

• qrad radiative heat flux

The radiative heat flux is neglected in this case.With an outdoor temperature of 1,35 ◦C and a floor temperature of 25 ◦C the temperature distribution

is simulated in a model (Fig. 5). The balanced temperature is 7 ◦C in the church, so it is impossibleto heat the St. Pieter’s Church sufficiently without reaching an excessively high floor temperature. Theheight of the church is too big in comparison with the surface that can be heated. With a moisturecontent of 4,87 g water/kg air the relative humidity (RH) varies from 60 to 85 %.

It is clear that for detailed simulations, a more precise determination of the wall characteristics isnecessary. Although this model gives a general view on the heat loss, suitable for this church.

4.5 Convector Heating

A convector heating system is planned for the renovation of the St. Pieter’s Church. Hot water will bedistributed to convector wells on several places in the church, where a heat exchanger will create hot air.Through the grille on floor level, cold air will be heated and the hot air will be expulled (Fig. 6), asdescribed in [MAH04]. This decentralised heating system can produce a maximal heat power of 35 kWper convector.

To simulate the effect of this heating system in FLUENT, the inlet of a convector well is defined inFLUENT as a velocity inlet, with a velocity magnitude of 0,4 m/s and an incoming temperature of 25 ◦C.The outlet is defined as a pressure outlet. The heat loss by the wall is defined as in § 4.3. The heat inputfrom a well can be calculated using

Q = mCp∆T (2)

with

• m mass flow of the fluid

• Cp volumetric heat capacity of the fluid

• ∆T the temperature difference between incoming and outgoing fluid

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Figure 5: 2D floor heating effect

Figure 6: Convector heating - Mahr system

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andm = ρAv (3)

with

• ρ density of the fluid

• A grille surface

• v velocity of the fluid normal to the grille surface

In Fig. 7 and Fig. 8 the balanced situation is indicated in the 3D model for a simulation with 18convector wells with a heat input of about 5 kW each. The convector wells create a very homogenoustemperature distribution and the church is heated till 11 ◦C. The relative humidity (RH) varies between25 and 63 %. Despite the approximations, it is clear that sufficient heating causes low local relativehumidities (Fig. 8). Problems with heating concerning conservation of historical artworks are a wellknown problem ([Sch02]).

4.6 Moisture Sources

The influence of people in a room has been examined. In order to see preliminary results, a simulation isdone in a 3D block (14 m x 18 m x 40 m) (Fig. 9). On the floor a group of people is modeled as a massflow inlet of water, with a mass flux of 0,0583 g

m2.s . This corresponds with a group of 300 people sittingon a 100 m2 surface, each producing 70 g H2O/h. There are two convector wells in the 3D block with thesame characteristics as in § 4.5. The distribution of temperature and humidity is calculated with bothlaminar and turbulent flow pattern.

The results of the laminar case are given in Fig. 10. The average temperature is 13,3 ◦C and themass fraction of H2O (AH) varies from 0,0047 to 1 (on the water surface) g H2O/kg air. There is alittle temperature fluctuation through the volume of the block. The results of the turbulent model aregiven in Fig. 11. The flow goes immediately from the velocity inlet to the outlet, and there is a quickermixing of water and air. In the balanced situation the whole block is filled with water (mass fraction 1),except near the outflow. Instationary simulations are recommended for more realistic simulations andwill bring clarity about the effect of moisture sources in monumental buildings. It is clear that the resultsare different, and the chosen flow model has a big influence on the final result. The most reasonablesimulation is the turbulent one, because of the high Reynolds number. This application demonstratesthe importance of a good model and parameters choice in FLUENT.

5 Conclusion and Perspectives

Installing a good heating system in the St. Pieter’s Church is not obvious. Two possibilities are evaluatedin FLUENT. In view of the building characteristics of the church, underfloor heating is inadequate.Convection wells can deliver enough heat, but the evolution in the relative humidity has to be taken intoaccount.

The use of FLUENT for modelling temperature and humidity distribution is evaluated in this paper.The results are shown and demonstrate the power of FLUENT as CFD package. It is clear that for detailedsimulations, a more precise determination of the wall and inlet conditions is necessary. Instationary caseshave to be evaluated. Modelling moisture transport in FLUENT has to be looked into.

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Figure 7: Global temperature distribution in a 3D model of the St. Pieter’s Church

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Figure 8: Temperature distribution at a convector well and global humidity distribu-

tion in a 3D model of the St. Pieter’s Church

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Figure 9: Moisture source in a 3D block

References

[Flu03] Fluent Inc. Fluent 6.1 User’s Guide, January 2003.

[MAH04] MAHR. Mahr church heating systems. http://www.mahr-heizung.de, 2004.

[Sch02] H. Schellen. Heating of Monumental Churches. Number ISBN 90-386-1556-6. Technische Uni-versiteit Eindhoven, December 2002.

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Figure 10: Temperature and humidity distribution in a 3D block - laminar model

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Figure 11: Temperature and humidity distribution in a 3D block - turbulent model

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