Sauna Modeling Conference

Numerical simulation of a wood-stove-heated sauna using ‘Fire Dynamics Simulator’ Corentin Macqueron Computational Fluid Dynamics Engineer University of Tartu, Estonia, may 2015

FDS presentation (1/4)  FDS : Fire Dynamics Simulator

 Developed by NIST : National Institute of Standards and Technology, USA  Computational Fluid Dynamics software  Entirely dedicated to fire modelling  Open source code

FDS presentation (2/4)  Turbulence by LES-Smagorinsky or DNS, no RANS  Instantaneous and irreversible combustion model for organic compounds  Limited to low-Mach numbers  Surface and gas radiation (soots, CO, H2O, etc.)  1D heat transfer in walls  Cartesian structured mesh : only ‘cubic’ geometry

Different turbulence approaches

An example of a FDS mesh

FDS presentation (3/4)  Almost no numerical parameters to setup  Automated time-stepping, with CFL < 1, explicit integration methods  Simplified wall treatment  “Plane wall” for heat transfer coefficients  Werner-Wengle for velocity profiles  No boundary layers in the mesh !

Heat transfer law in FDS : simple [1] > No boundary layer

Heat transfer law in FLUENT : much more sophisticated ! > Requires boundary layer meshing

FDS presentation (4/4)  Interface  Text file for modelling  Smokeview for 3D post-processing

An example of a FDS text file

An example of a Smokeview post-processing

Why FDS for sauna modelling?  “Simply” because a wood-stove sauna is nothing but a “fire” after all  The sauna physics is complicated for a general CFD software (FLUENT for instance) but FDS already has it all with no coding required :    

Combustion Radiation, especially from flames and soots Fluid dynamics Water sprinkling and steam cloud tracking

 And also because FDS is :  robust (no convergence problems)  extremely fast to calculate  and easy to use

 (… and it’s free !)

Sauna simulation : the context  I am an engineer in Computational Fluid Dynamics in nuclear engineering  I really love simulation & modelling  I love sauna : I’ve been in Russia, Sweden, Norway and I even built my own sauna in France, Normandy  I enjoy FDS a lot  Only one similar scientific study has already been performed, and it’s old (1994)[11]  I understood that there was something to do so I just decided to give it a try !  I published a paper on arXiv : C. Macqueron, Computational Fluid Dynamics Modeling of a

wood-burning stove-heated sauna using NIST’s Fire Dynamics Simulator, arXiv, 2014, http://arxiv.org/abs/1404.6774

 This is a 100% personal project, my employer isn’t involved at all

My own sauna in France, Normandy

Main sauna characteristics    

L*l*H : ~2.5*1.8*1.8 m Volume : ~8 m3 Wood-stove : ~10 kW Insulation : 7 cm rock wool sandwich between 10 mm wood panels

Sauna

Insulation

Wood-stove (pretty old guy!)

Modelling : geometry  Geometry simplified with “cubic” shapes

Sauna

Wood-stove (Soon to be replaced by a modern one!)

Bench

Modelling : meshing  4 cm hexaedral homogeneous cells  ~170 000 cells  A small volume of the outside surrounding air is meshed for atmospheric pressure boundary conditions

Reference mesh ~170 000 cells

Refined mesh ~1 250 000 cells

Modelling : fire (1/6)  First : what exactly is a fire ?

Flame : “secondary combustion” : the flammable gases produced by pyrolysis finally ignite if enough oxygen and temperature

Burned wood : char Pyrolysis zone : “primary combustion” : under heat flux, wood degrades into pyrolysis flammable gases, propagates from surface to core Wood “waiting” for pyrolysis to degrade it from surface to core

Modelling : fire (2/6) ď&#x201A;§ How is a fire modelled in FDS ?

REALITY Flame

Char

Pyrolysis

Wood

FDS Calculated : FDS estimates if pyrolysis gases ignite or not depending on oxygen concentration and ambient temperature, resulting in 3D volume power heating zones Not modelled, but soot yield is given by the user and then transported by fluid flow calculations Could be calculated, but the models are still in R&D and are not really reliable. So, for practical applications, pyrolysis gases composition and quantity are an input, related to the total power defined by the user 3D solid block

Modelling : fire (3/6)  So, unless you are doing research, in practical, the fire power, as well as soot, carbon monoxide or other combustion by-products, are just an input data from the user to the software  The power desired by the user is silently “translated” by FDS into a pyrolysis gases volume flux  FDS calculates if these gases ignite or not depending on oxygen concentration and ambient temperature, if they ignite they release the power desired by the user  The combustion is instantaneous and irreversible  FDS then calculates the fluid dynamics and heat transfers occurring from this combustion  All the chemical species from the reaction below are transported by fluid dynamics The chemical reaction modelled in FDS :

Modelling : fire (4/6)  Fire radiation modelling :  The fire combustion releases power (of course!)  This power is transported from conduction,

convection and radiation  Conduction is negligible in gas movement  Convection is the buoyant hot gases movement  Radiation comes from :

 hot solid soot particles  hot gases that are not fully transparent to radiation

 The radiation is caused by the soots and gases

temperatures elevated at the fourth power (typical radiation behaviour)  Combustion and radiation often occur in very small zones, typically only a few millimetres thick

Modelling : fire (5/6)  Fire radiation modelling :  The mesh cell size in FDS is generally 5-10-20 cm, which is way too large to correctly represent these small combustion zones  By averaging the gas temperature over a “large” cell mesh, the radiation zones are generally too “cold”  The radiation is hence generally highly underestimated by a “fourth power” calculation  This is why FDS releases the radiation according to the following formulae [1] :

 So, FDS chooses the maximal value between the “fourth power” formula and an empirical relationship  This empirical relationship is very simple : it says that X% of the total

combustion power is radiated  Surprisingly (and luckily…) the value of X is generally constant and is roughly 30-40% for ‘classic’ organic fires

Modelling : fire (6/6)  So, back to the sauna model :  Solid wood ‘block’ inside the stove (in red on the picture)  Pyrolysis gases are injected from the surface of the    

wood block Wood chemical composition : CH1.7O0.73 [2] Heat of reaction : 12.6 MJ/kg [2] Soot yield : 1.5% [2] Radiative fraction : 35% (default value in FDS)

 Finally :  The total power is adjusted in order to reproduce

the usual measured temperature on the walls, which is ~80°C  The found corresponding power is ~8.75 kW  This value is in very good agreement with woodstove manufacturers’ data for a sauna of ~8 m3 [3]

Wood-stove model

Modelling : walls & materials  Walls are thin walls as for the geometry (zero width)  Real width taken into account for thermal conduction and inertia  Multi-layer walls (wood-insulation-wood) are modelled as an homogeneous equivalent monolayer material  Thermal properties are taken from technical literature

Modelling : ventilation    

Wood stove air intake from the outside Air leakage under the door (area somewhat arbitrary) Outside air temperature : 20°C No outside wind

Wood-stove outside air intake

Leakage under the door

Modelling : human body

 Not always present in the calculation  Taken into account only as an impact study  Only one person modelled  ‘Cubic’ body  Inert blocks at fixed temperature (40°C according to [4])

Results : sauna temperatures

 Air temperature : ~100°C  Quite homogeneous except in the lower part  These results are consistent with common experience and literature [4]

Results : sauna temperatures

 Wall temperatures far from the stove : ~80°C  Quite homogeneous except in the lower part  These results are consistent with common experience and literature [4]

Results : sauna temperatures

 Stove wall temperatures : ~150-270°C  Wood wall temperature just behind the stove : ~180°C  These results are consistent with the literature [5] even if stove wall temperatures could be considered a little ‘cold’

Results : flame temperature

 Flame temperature does not exceed 270°C  This is clearly underestimated  Values from 750 to 1300°C are expected [6][7][8][9]  Refined mesh does not lead to hotter flame  It is surprising that such a ‘cold’ flame can lead to correct temperatures inside the sauna with a correct 8.75 kW power  There is additional research to do

Results : gas mass flow rate    

Gas flow rate in the stove : ~38 g/s This value is overestimated Gas flow is expected to be closer to 15 g/s [3] This overestimation of the air flow rate might partly explain the low flame temperature  The air leakage area under the door might be to big  The pressure drop in the stove might be too weak  There is additional research to do, may be by adjusting leakage area and stove power

Results : heat transfer coefficients  Variations consistent with the flow (high values with high velocities)  Values in the range of 2-10 W/m2/K  May be a little weak inside the stove and the stack  Otherwise in very good agreement with typical free convection  These results are rather consistent with common experience and literature [10]

High velocity from door leakage flow clearly visible

Results : steam cloud ď&#x201A;§ Liquid water is poured on the bricks on the stove using the sprinkler-extinguisher FDS feature ď&#x201A;§ ~250 mL

Cold spot on the stove during water pouring

Liquid particles water flowing on the stove

Results : steam cloud  The steam cloud originates from the stove bricks surface, elevate, circulate and spread in the sauna  There is also water inside the stove because wood burning produces water  The behaviour of the steam cloud is consistent with “personal” experience

Steam cloud rising from the stove

Steam cloud spreading in the sauna

Results : impact of the human body  Its seems that one person can decrease the temperature from 100°C to 90°C (in steady-state, maybe not that much in transient-state)  No data to confirm this or not?

With human body

Without human body

Results : impact on the human body  Heat flux towards the human body  Radiation : ~300 W/m2  Convection : ~180 W/m2  Total : ~480 W/m2

 Theses results are in very good agreement with the literature [4], which indicates a total heat flux of 300-600 W/m2

Results : close the door !  What happens if we let the door permanently open ?  It’s of course way cooler (~40°C instead of 80°C) !  And there are more gradients, too

Results : air inlets and outlets design ď&#x201A;§ Many air inlets and outlets can be tested ď&#x201A;§ It might be possible to look for an optimum design

Results : mesh size sensitivity study  Results with the refined mesh are compared with the results from the reference mesh  There are some differences but the results are roughly the same  (Here, the time is accelerated so its values are not relevant)  The results from the reference mesh can be considered rather correct

Temperature (°C)

Wall temperature (thermometer location)

Refined Reference

Time (s)

What still need to be done  Additional work should be performed in order to correct :  the flame temperature which is clearly too low  the air mass flow rate in the stove which is too big (this may be connected to the flame temperature problem)  a model of a simple wood-stove, without the sauna cabin, should be considered as a starter  Experimentations should be setup in order to measure accurately :  Temperatures (air, walls, stove, chimney, etc.)  Radiative and convective heat flux (walls close and far from the stove, floor, ceiling)  Air mass flow rates (stove and sauna cabin)  All this could lead to a scientific validation of the model

Perspectives  Scientific publication of the physical validation work  Engineering design could be performed in order to help manufacturers to improve stove and sauna cabin  Technical demos could be setup to bring attention to the sauna world and to help manufacturers to present their equipment  What I am looking for :  Collaboration with professors and students for research and teaching  Collaboration with manufacturers from the sauna industry to “go pro”

Conclusion  A huge amount of work has been done and has proven conclusive in many ways but there is still work and research to do  A fully validated 3D modelling might be ahead of us  There is room for industrial application

References (1/2) [1] Kevin Mc Grattan et al., Fire Dynamics Simulator â&#x20AC;&#x201C; Technical Reference Guide, National Institute of Standards and Technology (NIST), 2010 [2] James G. Quintiere, Fundamentals of Fire Phenomena, Wiley, 2011 [3] Harvia Woodburning Products, http://www.harvia.fi/files/document_pdf/5429/PK_EN.pdf [4] Minna L. Hannuksala et al., Benefits and Risks of Sauna Bathing, American Journal of Medicine, vol. 110, 2001 [5] Robert Scharler et al., CFD based design and optimisation of wood log fired stoves, 17th European Biomass Conference and Exhibition, 2009 [6] Simo Hostikka, Kevin Mc Grattan, Large Eddy Simulation of Wood Combustion, National Institute of Standards and Technology (NIST), 2001 [7] James G. Quintiere, Principles of Fire Behavior, Delmar Publishers, 1997 [8] JoĹže Urbas, William J. Parker, Surface Temperature Measurements on Burning Wood Specimens in the Cone Calorimeter and the Effect of Grain Orientation, Fire and Materials, vol.

17, 1993 [9] V. Novozhilov et al., Computational Fluid Dynamics Modeling of Wood Combustion, Fire Safety Journal, vol. 27, Elsevier, 1996 [10] J.P. Holman, Heat Transfer, McGraw Hill, 2009 [11] Y. Fan, R. Holmberg, J. Heikkinen, CFD simulation on the air flow in a sauna, Building Research and Information, vol. 22, 1994

References (2/2) Please also see my personal work : [12] C. Macqueron, Computational Fluid Dynamics Modeling of a wood-burning stove-heated sauna using NIST’s Fire Dynamics Simulator, arXiv, 2014 http://arxiv.org/abs/1404.6774 [13] C. Macqueron, Modélisation thermo-chimico-aéraulique d’un sauna à bois avec le logiciel Fire Dynamics Simulator, Issuu, 2013 http://issuu.com/corentin/docs/rapport_technique_bania_dynamics