Sauna Simulation by Corentin

EXPERIMENTAL AND COMPUTATIONAL FLUID DYNAMICS STUDY OF A FIRE HEATED SAUNA – VALIDATION, DESIGN AND FIRE RISKS ANALYSIS Corentin Macqueron1 and Perttu Leppänen2 Corresponding author, Computational Fluid Dynamics Engineer 11 place de la convention, 78 280, Guyancourt, France +33 6 98 26 43 77 corentin.macqueron@gmail.com 1

PhD Student, Tampere University of Technology, Department of Civil Engineering Korkeakoulunkatu 10, FI-33720 Tampere, Finland perttu.leppanen@tut.fi

Abstract – An experimental fire heated sauna is built according to the European standard EN 15821, providing results for fire risks analysis and for comparison with a computational fluid dynamics modelling performed with the open source Fire Dynamics Simulator (FDS) software. It is found that the peak flue temperature can reach values well above the temporally averaged temperature which is considered in the EN 15821 testing methodology. This might explain why accidental fires are observed even with chimneys correctly dimensioned according to EN 15821, because this standard is not conservative enough and should hence be modified. It is also found that FDS performs well for flame, air, flue and stones temperatures, as well as for stove mass flow rate and heat fluxes, by comparison to the measurements and other data from the literature. The model performance is less conclusive for stove and wall temperatures, but it is nonetheless shown that FDS can be used for sauna design and fire risks analysis. Keywords – Sauna, Computational Fluid Dynamics, Fire Dynamics Simulator, wood, stove, fire, EN 15821

comparison basis for numerical simulations performed with FDS (Fire Dynamics Simulator), a fire-dedicated open source CFD (computational fluid dynamics) software [9] [10] [11] [12] [13]. The numerical results from the sauna simulations were then compared to the sauna setup measurements and other data from the literature in order to assess the performance of FDS and thus to what extent this new approach might be effectively reliable.

INTRODUCTION

The traditional sauna, very popular in Finland and Scandinavia, is a fire heated insulated room built for dry bath activities that have numerous beneficial physiological effects [1] [2]. During the 2008-2014 period, ~2000 fires broke out from the sauna buildings in Finland [3] [4] [5], representing ~5% of all the building fires in Finland. At the same time, ~700-900 fires ignited from fireplaces and chimneys every year in Finland. The causes of the fires are amongst other things too small protection distances and too high flue gases temperatures. Investigations are required in order to better understand and suppress these causes. In order to do so, an experimental sauna setup has been built in the Tampere University of Technology [6] [7], following the European standard EN 15821 [8] in order to study flue gas temperatures and accidental fire risks.

2. EXPERIMENTAL SETUP 2.1. Sauna An experimental sauna setup has been built in the Tampere University of Technology [6] [7], following the European standard EN 15821 [8] in order to study flue gas temperatures and accidental fire risks. This setup is used as a basis for wood stove and sauna modelling and is shown on Fig. 1-2-3-4.

Following this experimental investigation, the idea arose that numerical simulation could also be used for further inquiry. The experimental sauna setup built in the Tampere University of Technology hence served as a

The volume of the cabin is 20 m3.

The walls are made of 21 mm of plywood (internal side) and 75 mm of insulating rock wool (external side). As required by EN 15821 [8], there is a forced extraction of the air inside the cabin at a rate of 6 vol/h (Fig. 1-2-4).

Figure 3 – Side view of the sauna

Figure 4 – Sauna roof with forced extraction system

2.2. Wood stove The wood stove is a Narvi NC 20 [14], dissipating an average power of 16 kW. It is shown on Fig. 5-6. It is filled with 60 kg of stones. The thicknesses of the stove walls are 3 mm for the firebox and pipes (cast iron), 1.5 mm for the internal walls and 0.75 mm for the external walls (steel). The stove is loaded with a batch of 3 kg of wood at the beginning. Another batch is added 24 min after ignition, and another one 48 min after ignition.

Figure 1 – Top view of the sauna

Figure 2 – Front view of the sauna

Figure 5 – Wood stove (Narvi NC 20)

3. MODELLING 3.1. Software The sauna is modelled with the Fire Dynamics Simulator (FDS) software (version 5.5.3 [9] [10] [11] [12] [13]). FDS is developed by the NIST (National Institute of Standards and Technology) and its partners (VTT for instance) and is an open source fire-dedicated computational fluid dynamics (CFD) software. As summarized in reference [15], FDS solves a special form of the Navier-Stokes equations designed for lowMach and thermally-driven flows, focused on smoke and fires. FDS uses an explicit predictor-corrector scheme (second order in time and space). Turbulence is taken into account with Large Eddy Simulation (LES) (Smagorinsky model) by default. For combustion, FDS generally uses a single step chemical reaction whose products are tracked via a twoparameter mixture fraction model. Radiative heat transfer is taken into account via a radiation transport equation for gray gases solved using a technique similar to finite volume methods. It uses approximately 100 discrete angles by default. The absorption coefficients of the gas-soot mixtures are computed using the narrow-band model from Grosshandler [11]. Post-processing is done with the Smokeview software [12].

Figure 6 – Internal design of the Narvi NC 20 stove (simplified)

The stack is made of a ‘sandwich’ of 50 mm of rock wool between two layers of 0.5 mm of steel. As required by EN 15821 [8], the pressure in the stack of the stove is maintained at -12 Pa (± 2 Pa) (Fig. 7 and Fig. 14).

The choice of FDS for this wood fire heated sauna study over other CFD software was driven by the fact that FDS is specifically designed to handle fire. Sauna simulation is obviously not the core mission of FDS, as accidental fires for which FDS has been developed are of course somewhat different from a wood stove fire in terms of scales, containment and heat release rates, meaning that some characteristics of FDS may not apply very well to a wood fire heated sauna, but the underlying physics remains the same.

Figure 7 – Stack exhaust system with pressure regulation

2.3. Measurements The temperatures are measured with type K thermocouples, at the locations indicated in Table 1 and Fig. 1-2-3. Thermocouple n° Cabin

Flue

2-3

Walls

24-29, 30-35

3.2. Geometry The sauna and stove models are shown on Fig. 8-9-10. The stove and stones geometries are complex and are somewhat pushing the limits of the FDS capabilities in terms of geometry and purely one-dimensional conduction calculations, which were not designed for this kind of study. These limits are well acknowledged in the framework of this study, but it will however be shown in the following that FDS can still produce relevant results.

Table 1 – Temperature measurements

The pressure in the stack is also measured, at location 4 (Fig. 2-3). Stones temperatures were measured during additional tests with thermocouples not listed here. The stove heat release rate has not been measured but it is known from the manufacturer that its average value is 16 kW [14]. The stove mass flow rate has not been measured and is hence unknown. 3

3.3. Mesh The mesh is made of ~220 000 hexahedral cells (cubes of 5 cm width) and is shown on Fig. 11-12.

Figure 8 – Sauna model

Figure 11 – Mesh (front view)

Figure 9 – Real stove on the left, modelled stove on the right (metal structure in black, wood blocks in red, stones in dark grey and stack in light grey)

Figure 12 – Mesh (side view)

As it does not contain any refinement on the walls, the mesh may seem somewhat coarse, especially for LES modelling. FDS is however known to work on relatively coarse meshes, especially because it uses ‘macroscopic’ laws-of-the-wall for velocity profiles and heat exchange coefficients in the boundary layers [9] [10]. The size of the mesh cells (5 cm) has been chosen in order to represent fairly accurately the sauna and stove geometries and to allow for reasonable calculation time. Due to FDS limitations (face-to-face conduction can only occur in solid obstructions if the obstructions are one cell thick maximum [9]), it is not easy to perform a relevant mesh resolution sensitivity study as should be performed for any CFD calculation, because of the complex stove geometry relying on solid obstructions (especially for stones modelling). Finally, as with any CFD study, it is up to the user to prove the adequacy of the mesh for the pursued results, and this will be shown in the following.

Figure 10 – Two views of the modelled stones inside the stove (metal structure in black, wood blocks in red, stones in dark grey and stack in light grey)

3.4. Simulation overview

The entire sauna is modelled, as well as an extra layer of air around it, where ambient temperature (20°C) and atmospheric pressure are prescribed. The physical phenomena taken into account in the present study are the following: - wood combustion - fluid dynamics (free and forced convection) with turbulence - heat transfer (conduction, convection and radiation (with participating gases)) The main parameters and hypotheses of the present study are the following: - turbulence is represented with the Large Eddy Simulation (LES) Smagorinsky model [9] [10] - wood pyrolysis is not simulated: the total heat release rate is not a result but an input of the calculation and is transformed by FDS into a mass flow rate of flammable gases on the surface of idealized wood ‘blocks’ (Fig. 9-10). These gases are transported by fluid dynamics and are burnt according to the instantaneous and irreversible combustion model of FDS [9] [10] - wood combustion parameters are the following: o chemical composition: CH1.7O0.74N0.002 [16] o heat of combustion: 12 600 kJ/kg [17] o soot yield: 0.015 g/g [16] [17] o carbon monoxide yield: 0.004 g/g [16] [17] o average heat release rate per unit area on the wood blocks: 88.8 kW/m2 (this value is consistent with the wood fire literature [18]) o the fire duration is assumed to be one hour and a half - temporal variations of the heat release rate (Fig. 13) have been fitted in order to reproduce fairly accurately the flue temperature profile. These variations are somewhat arbitrary but remain realistic for the following reasons: o the average heat release rate value is maintained at 16 kW in order to be consistent with the characteristics of the stove given by the manufacturer [14] o the variations are following the wood batches o the amplitude of the variations is consistent with the literature (see reference [19] for instance) - the negative exhaust pressure required by the standard [8] is applied as a boundary condition on the stack outlet - conduction in the solids is purely onedimensional, in the solid surface normal direction (FDS limitation [9])

geometry has been simplified, mainly due to FDS limitations (solids can only be horizontal or vertical flat objects and face-to-face conduction can only occur if the solids are one cell thick maximum [9]) (Fig. 8-9-10) stones are modelled as solid obstructions in perfect contact with the stove internal walls or ‘floating’ in the air (Fig. 9-10). This approximation is crude but it is difficult to proceed otherwise, given the limitations of FDS in terms of geometry. As the conduction is only occurring in one dimension and in the surface normal direction, and the stones ‘blocks’ being sometimes more than one cell thick, heat transfer can occur multiple times in the same stone ‘block’. The density of the stones material is modified accordingly in order to represent the correct total stones inertia human beings are represented with solid blocks of the shape and size of a person (Fig. 33-34), sitting on the bench. The skin temperature is kept at 40°C, as this is the equilibrium temperature of the human skin reached in a sauna according to reference [2]. People hence behave as heat sinks. The production of water vapour through perspiration is not modelled. The blocks emissivity is set to 1 (real human skin emissivity is ~0.98 [20]) the gap under the door, which is ~2 cm height on the whole width of the door (~0.014 m2 in total), is represented by six small openings of 5 cm width and 5 cm height at the bottom of the door (0.015 m2 in total)

Figure 13 – Heat release rate

Fig. 13 shows that the required heat release rate to fit the flue temperature during the first batch is quite low compared to the two other batches. This is due to the fact that the combustion was weak during this period 5

(experimental observation). Additional tests have shown much better combustion during the first batch. 3.5. Materials The material properties considered for this study are the following. Plywood: Density: 461.9 kg/m3 [21] Thermal conductivity: 0.13 W/m/K [22] Specific heat: 1250 J/kg/K [23] Emissivity: 0.92 [24] Rock wool: Density: 20 kg/m3 (assumption from [25]) Thermal conductivity: 0.036 W/m/K [26] Specific heat: 1250 J/kg/K (assumption from [25]) Emissivity: 1 (assumption)

Figure 14 – Static pressure in the stack

4.2. Mass flow rate

Stones: Density: 2980 kg/m3 [27] Thermal conductivity: 6.4 W/m/K [27] Specific heat: 980 J/kg/K [27] Emissivity: 0.9 (assumption)

The mass flow rate in the 16 kW stove calculated by the model is ~9 g/s on average. This parameter was not measured during the test but other experimental data following European standard EN 13240 [28] from different stove manufacturers can be found and are in the same order of magnitude, even though the calculated value might be considered a little bit low. For instance, references [29], [30], [31] and [32] indicate 3.3 g/s, 6.3 g/s, 7.2 g/s and 14.5 g/s for 5 kW, 7 kW, 7.8 kW and 16.5 kW stoves respectively.

The stones properties are for steatite sauna stones, whereas the stones used for the tests are made of olivine, because no solid data for olivine sauna stones were found. It is however believed that this should not have a significant impact, as different sauna stones are likely to have quite similar properties, and also because the way the stones are represented in the FDS model is very crude anyway.

4.3. Flame temperature Fig. 15 shows the gas temperature on a vertical slice in the middle of the stove. The flame temperature was not measured during the experiment, but the results are consistent with the data from the literature, which states that typical wood flame temperature is expected to be in the range of 750-1300°C [33] [34] [35] [36].

4. RESULTS AND DISCUSSION 4.1. Stack pressure The negative static pressure in the stack (measure n°4 in Fig. 2-3) is shown on Fig. 14. It appears that the numerical regulation of the pressure is more efficient than the real regulation system. This results in slight differences between the real and the modelled pressure at the stack outlet, and this has an impact on the results of the simulation. For instance, at the end, the experimental pressure is likely to extract less mass flow than the simulated one. This, combined with the assumptions about the heat release rate profile, might explain some of the differences between experimental and numerical flue temperatures.

Figure 15 – Gas temperature (°C) at t ~ 3750 s

4.4. Flue temperature The flue temperature (measure n°3 in Fig. 2-3) is shown on Fig. 16. As explained in § 3.4, the heat release rate has been fitted to reproduce the flue temperature as accurately as possible, following realistic constraints. On average, the model underestimates the flue temperature, but the trends and the peak values are fairly well reproduced. The values of the peaks are ignored by the EN 15821 [8] testing methodology, because this standard only focuses on temporally averaged temperature. The fact that these peaks can be well above this temporally averaged temperature is a major safety concern about chimney fires highlighted in reference [7]: accidental fires can occur even with correctly dimensioned chimneys (according to the standard), simply because the standard is not conservative enough and should hence be modified. The model being able to reproduce the peaks indicates that this kind of numerical simulation could help to produce relevant results for fire safety analysis and chimney dimensioning, using appropriate assumptions for the heat release rate profile.

Figure 17 – Flue temperature (with constant heat release rate)

4.5. Air temperature The air temperature (measure n°21 in Fig. 1-2-3) is shown on Fig. 18. The model appears to be able to reproduce it with a very good accuracy, indicating that this kind of numerical simulation could help to produce relevant results for sauna design analysis, as it is the main temperature felt by the users. The sudden decrease of the experimental temperature around t = 5500 s, circled in red on Fig. 18, is due to a brief opening of the door between the room where the sauna was installed and the outside, which was very cold, causing the sauna inlet temperature to decrease. This was not represented in the modelling, hence the sudden differences between experimental and numerical results. The experimental and numerical trends after this artefact are however very similar, meaning that the model is still producing relevant results. This artefact is also visible on some wall temperatures (Fig. 23 for instance).

Figure 16 – Flue temperature

The same calculation has been performed with a constant heat release rate (16 kW). The corresponding flue temperature is shown on Fig. 17. The flue is logically lower than with the realistic heat release rate profile. This calculation is interesting because it only requires the stove manufacturer’s data and does not need any assumption for the heat release rate profile, but it cannot provide reliable results for safety, the flue temperature being too low. Still, the numerical results are very close to the manufacturer’s data (425°C [14] following EN 15821 [8]), which is another confirmation of the good model behaviour (and of the limitations towards safety of the standard).

Figure 18 – Air temperature

Fig. 19 shows the gas temperature on a vertical slice at the location of the air cabin thermocouple when it reaches 7

its maximal temperature. The stratification of the hot gases is clearly visible.

4.6. Wall temperatures The wall temperatures (measures n°24-29 for the back wall and measures n°30-35 for the left wall in Fig. 1-2-3) are shown on Fig. 21-22-23-24 for the back wall and on Fig. 25-26-27-28 for the left wall. The model appears to be able to reproduce fairly well some of the wall temperatures at medium heights above the stove, but it considerably overestimates the bottom temperatures and underestimates the top temperatures. The overestimated wall temperatures are facing the stove, while the correct or underestimated wall temperatures are above the stove. This may indicate that the stove temperature is overestimated by the model, which could cause an overestimated radiative heat flux towards the walls. Additional tests and measurements on the stove itself have confirmed that the model overestimates the wall stove temperatures close to the firebox and underestimates the others. This is probably caused by the inevitable and sometimes crude geometrical approximations of the modelling of the internal parts of the stove. It is clear that further experimental and numerical tests should be performed in order to investigate this matter. It is also possible that the thermocouples, being installed on the surface of the sauna walls, are exposed to some sort of ‘bound effects’ (the thermal resistance of the wallthermocouple contact might be large and/or the radiative heat flux towards the small sphere of the thermocouple might be different than the one towards the plane wall). Additional tests, with in-depth measurements (thermocouples engulfed in the rock wool), should be performed, and may well lead to better agreement with the simulations. For now, the results tend to show that this kind of numerical simulation should be considered with caution for wall temperature prediction. Overestimating wall temperatures facing the stove is nevertheless on the conservative side for safety analysis. The literature provides data for maximal temperatures that should not be exceeded on wood surfaces in order to avoid ignition: 250364°C for short-term/single exposures according to reference [37], but ignition threshold can be significantly lower for long term/repetitive exposures as can be expected in a sauna (150°C according to reference [38] and even as low as 77°C according to reference [37]). These values could be compared to the simulation results in order to assess the risks of accidental fire.

Figure 19 – Gas temperature (°C) at t ~4760 s

The same calculation has been performed with a constant heat release rate (16 kW). The corresponding air temperature is shown on Fig. 20. This calculation is interesting because it only requires the stove manufacturer’s data and does not need any assumption for the heat release rate profile and it provides a reasonably good prediction for the temperature that can be reached in the cabin (~90-95°C with both realistic and constant profiles) (whereas it is completely flawed for flue temperature prediction as seen earlier (Fig. 17)).

Figure 20 – Air temperature (with constant heat release rate)

Figure 21 – Back wall temperature, n°24

Figure 25 – Left wall temperature, n°30

Figure 26 – Left wall temperature, n°31

Figure 22 – Back wall temperature, n°25

Figure 27 – Left wall temperature, n°33

Figure 23 – Back wall temperature, n°27

Figure 24 – Back wall temperature, n°29

Figure 28 – Left wall temperatures, n°35

Fig. 29 and 30 show the temperature field on the walls (with different scales to emphasise on different locations) at peak temperature. Hot spots are visible on the stove and on the back wall.

Figure 31 – Radiative heat flux (kW/m2) at t ~ 3750 s

Figure 29 – Wall temperature (°C) at t ~ 3750 s

Figure 32 – Radiative heat flux (kW/m2) at t ~ 3750 s

According to reference [39], a value of 25 kW/m2 can ignite wood panels. The calculated heat fluxes on the walls are well under this value, consistent with the fact that no wall fire was ignited during the experiments, but this cannot directly be used as a relevant indicator of the model’s correctness. Heat fluxes were not measured during the experiments. Data can however be found for heat fluxes towards the human body in a sauna (~0.3 to ~0.6 kW/m2 according to reference [40]). These values for a human body might not be of direct interest for fire risks but they are still interesting for safety (skin burns) and design (thermal comfort) and provide data to which the model can be compared. Additional calculations have thus been performed with people inside the sauna (Fig. 33-34). According to the model, at the chest level, at peak temperature, the radiative heat flux towards the body is ~0.19 to ~0.31 kW/m2 and the convective heat flux is ~0.14 to ~0.2 kW/m2, hence a total heat flux of ~0.33 to ~0.51 kW/m2. These values are well within the data from the literature (~0.3 to ~0.6 kW/m2 [40]), indicating that the model can produce

Figure 30 – Wall temperature (°C) at t ~ 3750 s

4.7. Stones temperatures Stones temperatures have been measured in additional tests and are in the range of 200°C to 500°C at peak temperature. The calculated temperatures are well within the same range, except for top stones that are ‘floating’ in the air (these stones are much cooler, ~100°C, which is probably well underestimated). 4.8. Heat fluxes Fig. 31 and 32 show the radiative heat flux on the walls (with different scales to emphasise on different locations) at peak temperature. Negative values correspond to emitting walls while positive values correspond to absorbing walls.

relevant results for heat fluxes (at least towards human bodies). Fig. 33 shows that the spatial variations of the radiative heat flux on the human bodies are significant. Convective heat flux is much more homogeneous (Fig. 34).

Figure 35 – Small ‘human’ parts circled in red

More validation would be required to conclude (with heat fluxes measurements), but it seems that this kind of numerical simulation could be used both for thermal comfort and safety analysis. This kind of calculation could determine the spatial limits for discomfort, skin burns and ignition risk zones.

Figure 33 – Radiative heat flux (kW/m2) at t ~ 3750 s

4.9. Calculation requirements The calculations were performed with FDS 5.5.3 in monoprocessor on a single desktop computer, equipped with an Intel Core i5 4300U CPU and 8 GB of RAM and running on Windows 8.1. It took approximately 500 hours to simulate the 2 hours of the experimental test. Quasi steady-state can be reached within 80 hours (calculation is accelerated by diminishing the thermal inertia of the solids by several orders of magnitude). These calculation durations may seem long, but they are still manageable and huge improvements could probably be made using more powerful processors and running parallel calculations [42]. High-end processors can indeed easily be 5 times faster than the one used for this study and, with a reasonable number of cores (6-8 for instance), it might be possible to bring the calculation duration down to a mere few hours.

Figure 34 – Convective heat flux (kW/m2) at t ~ 3750 s

The results can also be analysed from the pain threshold perspective. Additional calculations have been performed with small solid blocks, kept at 40°C [2], mimicking human parts that would stand very close to the stove (5 cm distance) (Fig. 35). Radiative heat fluxes on these surfaces reach ~8 kW/m2 at peak temperature (~3750 s). According to the Stoll Curve [41], this value would cause pain within ~15 s (and 5 kW/m2 is enough to cause blister burns within 30 s [20]). These results are consistent with typical sauna experience, as one can encounter severe pain when standing very close to the stove.

5. CONCLUSIONS This study has shown that it is possible to represent fairly accurately the physics involved in a wood fire heated sauna with the Fire Dynamics Simulator (FDS) software. It has been shown that flue, air and stones temperatures can be reproduced with good accuracy compared to our experimental results produced following the European standard EN 15821 [8]. Flame temperature, mass flow rate and heat fluxes appear consistent with the data from the literature. The stove and sauna wall temperatures prediction would require further experimental 11

and numerical investigations, as the simulation results are less conclusive for these variables but it nevertheless seems possible to perform fire safety analysis like chimney or stove-wall distance dimensioning in order to avoid accidental fires through wood ignition. It would also be possible to investigate insulation needs, power requirements, design analysis and to perform thermal comfort zone optimisation. The main difficulty of this kind of modelling is the complexity of the stove geometry (the stones are especially difficult to represent). The FDS limitations in terms of geometry and mesh may not apply for all stoves and will always require some assumptions. One of the main drawback of this kind of modelling is that the heat release rate profile has to be foreknown, but it can easily be constructed from the stove manufacturer’s data and a few reasonable assumptions for batch frequency and heat release rate amplitude, as it has been done in the present study. An average profile can be used, requiring no assumption at all and producing relevant results for air and mean flue temperatures, but at the cost of severely underestimating the peak flue temperatures. This kind of modelling, like any computational fluid dynamics analysis, would always require some sort of preliminary experimental tests in order to check that the stove (with its stones) is correctly represented and to supply data for the heat release rate profile, but once this step is validated, simulations could be performed with no other testing. Besides, as the stove is the most cautious part of the modelling, preliminary tests could be limited to the stove, without the whole sauna cabin setup, saving space, time, building material and, consequently, costs. This new simulation approach would hence allow for performing fire safety analysis and design optimisation with reduced experimental tests and costs.

The production of steam cloud by pouring water on the hot stones could also be studied using the sprinkler/nozzle tool included in FDS. The condensation of the hot steam cloud on the ‘cold’ human skin, which is one of the major reasons for the ‘hot’ feeling during sauna bathing, is however not possible to take into account by default, due to software limitation (FDS was designed for fire analysis, in which condensation takes no part). Steam cloud calculations are also interesting for safety analysis, as burn injuries can be caused by steam. ACKNOWLEDGMENT The authors would like to thank Sami Lamminen from the Tampere University of Technology for his helpful contribution to the study and Simo Hostikka from VTT for his helpful comments on the paper. NOMENCLATURE CFD: Computational Fluid Dynamics FDS: Fire Dynamics Simulator NIST: National Institute of Standards and Technology VTT: Technical Research Centre of Finland LES: Large Eddy Simulation REFERENCES

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