PresentationPDF Available

Thermo-Aeraulics CFD 3D Modeling of an Electric Sauna

Authors:
  • ORANO (ex-AREVA)

Abstract

Thermo-Aeraulics CFD 3D Modeling of an Electric Sauna : Comparison with experimental data and analysis
Thermo-Aeraulics CFD 3D
Modeling of an Electric Sauna
Corentin Macqueron
Computational Fluid Dynamics Engineer
corentin.macqueron@gmail.com
Context
Sauna Bathing
Sauna bathing is a cultural and
wellness activity in many countries
such as Finland or Sweden [15]
There are some thermal studies
dedicated to the thermo-aeraulic
behavior of saunas, such as
[1][2][3][4][5][6][7][29][30][32],
but there are still many things to
discover on this topic
That’s why we decided to create a
3D thermo-aeraulic model of our
own home sauna to get some
further insights
(and to have some fun )
Our Sauna
Our Sauna
Our sauna, known as ‘Sauna des Mésanges,
has the following dimensions :
Length : 2.19 m (internal)
Width : 2.19 m (internal)
Height : 1.68 m minimum, 2 m maximum,
1.83 m average (internal)
Internal wall thickness : 9 mm
External wall thickness : 25 mm
Insulation thickness (Isover rock wool) :
100 mm
Door thickness : 25 mm
Glass window thickness : 4 mm
Natural ventilation openings : 100x100 mm
(inlet and outlet altitudes : 0.25 m and 1.56 m)
Wooden floor thickness : 3 cm
Floor insulation thickness (extruded
polystyrene foam) : 4 cm
Lower and upper benches altitudes : 45 cm
and 75 cm
Our Sauna
The sauna is heated by an
electric stove (Harvia Cilindro
PC 70 [8], 1 phase/230 V, max
thermal output : 6800 W, stones
mass : 60 kg (77 stones of
6.5-18 cm, mean equivalent
diameter of ~7.5 cm),
height : 93 cm, diameter : 32 cm,
‘open’ and ‘mesh’ design
Cellular concrete thickness
(walls protection) : 7 cm
Our Sauna
Our sauna is somewhat ‘short’ (~2 m height, whereas
a Finnish sauna is usually ~2.3-2.6 m [31][32], because
we had building constraints), but its volume is
somewhat ‘classic’ because it is ~8.8 m3which is close
to the ‘classic’ 8 m3volume saunas that are frequently
built and because it has a ~1 kW/m3heating power in
accordance with the good practice
Its insulation thickness of 100 mm and its insulation
thermal conductivity of 0.045 W/m/K [10] at 100°C
has a thermal resistance of
2.22 m2K/W which is well comprised between the
values recommended by the EN15821 norm
(1.875 m2K/W and 2.5 m2K/W) [11]
Methodology
Methodology
The thermo-aeraulic and radiative behavior of the sauna is
studied with a steady-state turbulent Computational Fluid
Dynamics 3D model built with Ansys Fluent 18.1 [16]
Natural openings are inlet and outlet vents to the outside
atmosphere, so the natural convection ventilation mass flow
rate is not given but solved by the solver (equilibrium between
natural draught and pressure drop)
The full sauna model is built with a simplified stove model,
based on a detailed stove model representing the stove with all
its elements (grid, heating resistances, stones) located in a small
enclosure maintained at a typical sauna temperature (80°C) and
typical sauna walls (wood with insulation) exposed to an outside
air temperature of 20°C. The detailed stove geometry is taken
from the CAD file given in reference [20]
Model Geometry
Full sauna model with simplified stove
Model Geometry
Detailed stove model : small sauna enclosure, stove, heating resistances and dodecahedral stones
Model Mesh
The mesh is built with Ansys Fluent 2021 R2 [24] in
meshing mode
The Ansys Mosaic polyhexcore technology is used [17] to
create perfect hexahedral cells for the core of the fluid
flow (far from the walls), with prismatic boundary layers
on the walls and polyhedral cells at the transition from
the boundary layers to the core of the flow
~17 millions cells in total for the sauna with the
simplified stove, with 10 cells in the boundary layers
thickness (y+max ~3, y+average ~0.05, so the thermal
and hydrodynamic boundary layers are correctly solved
to capture the natural convection dynamics [18])
Minimal orthogonal quality : 0.075
Model Mesh
The mesh is built with Ansys Fluent
2021 R2 [24] in meshing mode
The Ansys Mosaic polyhexcore
technology is used [17] to create perfect
hexahedral cells for the core of the fluid
flow (far from the walls), with prismatic
boundary layers on the walls and
polyhedral cells at the transition from
the boundary layers to the core of the
flow
~1.6 million cells in total for the detailed
stove model, with 5 cells in the
boundary layers thickness (y+max ~3, y+
average ~0.5, so the thermal and
hydrodynamic boundary layers are
correctly solved to capture the natural
convection dynamics [18])
Minimal orthogonal quality : 0.045
Modeling
Modeling
Navier-Stokes, Turbulence, Energy & Radiation
equations activated
Turbulence model :
RANS k-ε realizable, enhanced wall treatment (low
Reynolds approach to solve natural convection [18])
Radiation model : Discrete Ordinates [16],
Theta & Phi Divisions and Pixels : 3x3-3x3 (air is
assumed to be fully transparent to radiation, this
might not be entirely true during steam production,
but radiation gases are extremely hard to model [6],
and our approximation seems still largely
acceptable)
Incompressible ideal gas, air molecular mass :
28.966 g/mol
Gravity activated (9.81 m/s2)
Pressure scheme : PRESTO! [18]
All equations : 2nd order
Pressure-Velocity Coupling : Coupled [16]
Pseudo-transient activated [16]
Modeling
External temperature : 20°C
External walls boundary conditions : free convection and
radiation with the external temperature
(h = 1,31ΔT1/3 [19][25] and ε = 0,9 [19][25])
Insulation thermal conductivity :
λ = 0.036 W/m/K at 20°C, 0.045 W/m/K at 100°C [10]
Wood thermal conductivity :
λ = 0.13 W/m/K [19][25]
Wood emissivity : 0.9 [19][25]
Soil thickness, thermal conductivity and temperature : 1 m,
λ = 1 W/m/K [19][25] and 10°C
Stones thermal conductivity :
6,4 W/m/K [14]
Cellular concrete thermal conductivity :
0.1 W/m/K [19][25]
Depron thermal conductivity :
0.035 W/m/K [19][25]
Glass thermal conductivity :
0.78 W/m/K [19][25]
Natural ventilation inlet and outlet pressure drop
coefficients : 0.5 and 1 [21]
No leakage apart from the natural inlet and outlet
There is no air gap between the wooden planks of the
benches and between the walls and the benches
Modeling
Modeling
In the full sauna model, stones are modeled as an isotropic porous
media in thermal equilibrium with the fluid flow [16], using the
Ergun law for the pressure drop. The Ergun parameters of the
porous media have been determined by comparison to a detailed
model of the stove, representing the grid, the heating resistances
and the individual stones
The stones porous media cannot radiate energy (Ansys Fluent
limitation [16]), but it is enclosed in an airtight cylindrical shell
(while the real stove is not closed on its side but rather open) and
this shell is capable to radiate energy
Measurements
Measurements
Some measurements were performed on our
sauna with commercial sauna thermometers
placed at different altitudes and an infrared
thermometer
External temperature was ~20°C and stove
power was set at ~1720 W (~25% of the full
power) and quasi steady-state was reached
Measurements
At ~steady-state, the following temperatures were
measured :
External temperature : ~20°C
Stove resistances temperatures : ~350-450°C
Stones temperatures : ~50°C (bottom), ~200°C (top)
Internal ceiling temperature above the stove : ~96°C
Internal cellular concrete max temperature close to the
stove : ~100°C
Air temperature :
Floor level : ~30-40°C
Lower bench level : ~40-60°C
Upper bench level : ~50-70°C
Head level : ~90°C
Thermal images are not our own
401°C
86°C 64°C
339°C
114°C
Measurements
Our measurements were certainly not
performed in a very ‘scientific’ way but they
are nonetheless in good agreement with the
literature :
- Stones : 260-310°C [2]
- Floor level : 30-38°C [2][22]
- Lower bench level : 38-49°C [9][22]
- Upper bench level : 60-63°C [9][22]
- Ceiling level : 91°C [9]
- Lower walls : 58°C [2]
- Upper walls : 80°C [2]
- Overall air : 75-90°C [1][2][5]
Images are not our own
401°C
Measurements
Air temperature vertical profiles from the literature [1][2][6][12][13] are shown below.
Literature is scarce, some data are from real scientific sources, and some are just from everyday users.
Our measures are in good agreement with the literature.
Results
Detailed Stove Model
The detailed and simplified stove models are run at ~25% of full power (realistic
value for steady-state) to determine the porous characteristics of the simplified
media. Using the original Ergun equations [16] with a porosity of 0.583 (based on a
stone mass of 60 kg and a stone density of 2980 kg/m3) would lead to viscous and
inertial resistances of 23 401,04 1/m2and 98,21 1/m, respectively. These values
would lead to an overestimated air mass flow rate through the stones and too
much heat dissipated in the hot plume of gas and too little heat radiated towards
the walls. By comparing the detailed and the simplified models in identical
configurations (sauna at ~80°C), the porous parameters have been adjusted to
45000 1/m2and 225.1 1/m, respectively (x1.92 and x2.3, respectively). The stones
thermal conductivity has also been adjusted to 150 W/m/K and the thermal
emissivity of the stove shell has been adjusted from 0.9 to 1. These adjustments
allows for a similar (but not fully identical) representation of the fluid flow through
the stones and of the radiated energy towards the walls. The full sauna model is
based on the simplified adjusted model.
Detailed Stove Model
We do not claim that our ‘adjustment’ or ‘correction’ is
universal, because the underlying physics is complex and
there are an infinite possibilities for stones sizes, shapes and
packing, but modifying the Ergun law as we did here should
be considered for this kind of study
It might not be surprising that the Ergun law, built for spheres,
is too ‘smooth’ for angular rocks, but building a new and
universal law for packed stones would be a full time work of
research
3D-scans of real stones could be used but would probably
lead to very hard meshing difficulties
Detailed stove model, full
power (6800 W) :
- Max/mean heating
resistances temperature :
655/558°C
- Max/mean stones
temperature : 620/383°C
- Max/mean stove
temperature : 332/176°C
Detailed Stove Model
Temperatures (°C)
Detailed stove model, ~25% of full
power (1700 W) :
- Max/mean heating resistances
temperature : 314/264°C
- Max/mean stones
temperature : 303/192°C
- Max/mean stove temperature :
166/107°C
Actual temperatures should be
somewhere between 25% and 100%
of full power, because stoves rarely
work in steady state, they are
regulated and are thus usually
‘oscillating’ by working on/off
The resistances and stones
temperatures calculated by the model
are consistent with what to be
expected (260-310°C expected for
stones [2] and up to more than 500°C
for the resistances)
Detailed Stove Model
Temperatures (°C)
Pathlines colored by velocity (m/s)
The detailed stove model shows that the air flow in the stove is almost entirely 1D in the vertical direction,
indicating that ‘open’ and ‘meshed’ stove designs does not create very different air flows than ‘closed’ stove
designs. During steam production, things might be different though
Detailed Stove Model
Detailed stove model : velocities (zoom on the
stove and the spaces between the stones)
Detailed Stove Model
Velocities (m/s)
In a sauna at ~80°C with insulated wooden walls exposed to a 20°C outside air, the following max
temperatures are obtained with the detailed stove model :
The previous pictures and these table values are in good agreement with our measurements (~350-450°C for
the resistances and ~200°C for the stones) and with the literature (260-310°C for the stones [2]). The model
can hence be considered validated
25% power 100% power
Resistances 314 655
Stones 303 620
Stove 166 332
Ceiling 100 135
Walls 119 227
Floor 93 132
Max Temperatures (°C)
Detailed Stove Model
The porous model underestimates the
maximal stove/stones temperature (only
~230°C versus ~303°C, underestimation of
~26% of the temperature rise)
Temperature field on the symmetry plane (°C)
Left : simplified model with original Ergun parameters, center : simplified model with adjusted Ergun
parameters, right : detailed model. Very similar (but not identical) results are obtained
Simplified Stove Model Adjustment
Velocity field on the symmetry plane (m/s)
Left : simplified model with original Ergun parameters, center : simplified model with adjusted Ergun
parameters, right : detailed model. Very similar (but not identical) results are obtained
Simplified Stove Model Adjustment
Wall temperatures (°C)
Left : simplified model with original Ergun parameters, center : simplified model with adjusted Ergun
parameters, right : detailed model. Very similar (but not identical) results are obtained
Simplified Stove Model Adjustment
Radiation heat flux (W/m2)
Left : simplified model with original Ergun parameters, center : simplified model with adjusted Ergun
parameters, right : detailed model. Very similar (but not identical) results are obtained
Simplified Stove Model Adjustment
Simplified model with original Ergun parameters is not ‘hydraulically resisting’ enough
and leads to an overestimated air mass flow rate within the stones, and too much energy
advected towards the ceiling and not enough energy radiated towards the walls
The simplified model with the adjusted parameters correctly predicts the air mass flow
rate within the stones, leading to correct air and somewhat correct walls temperatures
and advected and radiated energies (radiation is a little bit underestimated), compared
to the detailed model, and can hence be used in the full sauna model
There are obviously infinite possibilities for the arrangement of the stones of various
shapes and dimensions, tightly or loosely packed, etc. but the model built here should be
a very reasonable approximation of an actual sauna stove
Simplified Stove Model Adjustment
Full Sauna Model
Mean air temperature : 84°C
(obtained with ~1720 W, only ~25%
of the full stove power)
Natural ventilation mass flow rate :
0.0118 kg/s (~4 vol/h, close to the
requirements of EN 15821 [11])
Outlet ventilation mean
temperature : 98°C
Stove mass flow rate through the
stones : 0.0086 kg/s
Mean/max external stones
temperatures : 140/156°C
Max internal stones temperatures :
158°C
External walls temperature (°C)
Full Sauna Model
Max/mean internal floor temperature : 62/83° C
Max/mean internal ceiling temperature : 105/86°C
Max/mean external ceiling temperature : 23/24°C
Internal floor
temperature C)
Internal ceiling
temperature C)
External ceiling temperature (°C)
Full Sauna Model
Max/mean internal door temperature : 73/61° C
Max/mean external door temperature : 51/35°C
Max/mean internal window temperature : 65/55° C
Max/mean external window temperature : 56/53°C
Internal door and window
temperature C) External door and window
temperature C)
Full Sauna Model
Max/mean internal walls temperature : 119/80° C
Mean external walls temperature : 22°C
The cellular concrete protects the wooden wall : it reaches 119°C while the wooden wall behind reaches only 88°C
Internal walls temperature (°C) External walls temperature (°C)
Full Sauna Model
The temperature inside one of the wall, at sauna’s mid height and in the
center of the sauna, is shown below :
Insulation
External wood wall
Internal wood wall
Full Sauna Model
Max/mean lower bench temperature : 67/84° C
Max/mean upper bench temperature : 74/103° C
Bench temperature (°C)
Full Sauna Model
The floor is cooled by the air inlet and, close to the hot stove, the radiative heat flux on the floor is very high
The walls that are the closest to the hot stove also receive a very high radiative heat flux
The ceiling above the stove, being in the hot plume, is maintained at very high temperature and thus emits a lot of radiative
heat flux
Internal walls and ceiling radiative heat flux (W/m2)
Floor and bench radiative heat flux (W/m2)
Full Sauna Model
Pathlines colored by air temperature,
coming from the air inlet (°C) Pathlines colored by air velocity, coming from the air inlet (m/s)
Full sauna model
Pathlines colored by fly time, coming from the air inlet (s)
The vertical air temperature gradient in the sauna is very strong, in good agreement with the
literature. Mean air temperature on a vertical centerline is equal to the mean air temperature in
the whole sauna within a ~1°C accuracy.
Profile taken at the center of the sauna
(gradient is ~29°C/m)
Full Sauna Model
Temperature (center slice and stove slice) (°C)
Full Sauna Model
Comparison between our simulation results (‘Mésanges’) and the literature[1][2][6][12][13] :
Full Sauna Model
Air temperature at different locations for
a user sitting on the lower bench and on
the upper bench :
Feet : 50°C and 66°C
Knees : 66°C and 83°C
Chest : 80°C and 92°C
Head : 86°C and 95°C
Head to feet difference is 36°C for a user
on the lower bench and 29°C for a user
on the upper bench
These temperature differences might be
a little too large for a traditional Finnish
sauna, because our sauna is a little bit
too ‘short’ in height [31]
‘Law of Löyly
By adding a small removable
bench as a third level, one person
can sit higher and fully enjoy a
much more homogeneous heat
(head temperature : ~95°C and
head to toe difference : ~15°C)
and have the steam gently engulf
his entire body, down to his feet,
fulfilling the ‘law of löyly’ [31]
‘Law of Löyly
Adding a small thermoelectric fan,
using the Seebek effect, is very silent,
but it does not produce any
measurable difference in the
homogenization/stratification, and is
therefore not enough to ensure the
‘law of löyly’ for too small saunas
Horizontal temperature gradients are quite small :
for a given altitude, the temperature is roughly homogeneous (except very close to the stove
and of the fresh air inlets), in accordance with experimental findings [32]
Horizontal temperature
slices at z=0.15, 0.85 and 1.55 m (°C)
Full Sauna Model
Horizontal temperature
slices at z=1.55 m (°C)
Convective heat transfer coefficient on
the external walls (W/m2/K)
Outside air is assumed to be still
In windy conditions, the convective heat
transfer coefficient can be much higher,
but the overall thermal resistance is
mainly due to the insulation thickness
and would not be very different
Full Sauna Model
The velocity in the sauna is very heterogeneous.
Average velocity is 0.06 m/s and max velocity is 1.75 m/s.
Inlet and outlet velocities are 0.98 m/s and 1.26 m/s
Max velocity in the hot plume is 0.9 m/s.
Average velocity in the stove is 0.13 m/s.
The air rises above the stove, spreads across the ceiling, and descends along the walls.
Profile taken at the center of
the sauna
Velocity (center slice and stove slice) (m/s)
Full Sauna Model
Center slice (m/s) Stove slice (m/s)
Full Sauna Model
The heat loss is the following :
- Walls : 284 W
- Ceiling : 116 W
- Floor : 116 W
- Door : 103 W
- Window : 166 W
- Natural ventilation : 934
The natural ventilation should be closed during heating to avoid
unnecessary loss
Full Sauna Model
Heat loss (W/m2)
The heating power of the stove is dissipated as follows :
- Total : 1720 W
- Advection in the hot gases through the stones and in
the hot plume : 640 W (~37%)
- Advection on the lateral cylindric walls of the stove :
245 W (~14%)
- Radiation : 835 W (~49%)
The stove radiates up to ~1050 W/m2
The floor receives radiation up to ~270 W/m2
Radiation is a very important component of the heat
transfer from the stove, which is consistent with the
literature [2]
These values are for steady-state. During the heating
phase, instantaneous values might be very different
(stove temperature and radiation should be much higher)
Full Sauna Model
Radiative heat flux from the stove and on the floor (W/m2)
A ~90% obturation of the inlet and the outlet is performed in
order to study a sauna with no ventilation but with still a few
leaks (it’s impossible to completely eliminate leaks)
Total power is decreased from 1720 W to 895 W to keep the
mean air temperature at the same temperature (84°C)
The ventilation loss is now 0 W and the leak loss is 79 W
Leak mass flow rate is 0.0011 kg/s (~10x less) and stove mass
flow rate is 0.007 kg/s
With leaks only, the vertical air temperature profile is much
flatter
(the gradient is much lower)
Full Sauna Model Temperature (center slice) (°C)
With forced mechanical ventilation, we can reverse the ventilation, with
the air outlet becoming the air inlet, and vice-versa
By keeping everything constant, especially power and air flow rate
(~0,0118 g/s, ~4 vol/h) and reverting the air flow, we obtain a different
stratification and temperature gradients (temperature is more
homogeneous [except very close to the cold jet entering the sauna])
We also obtain higher temperatures (average air temperature : ~92°C vs
~84°C), simply because, being reversed from top to bottom, and because
hot air rises, the temperatures at the outlet level are lower (~84°C vs
~98°C), so the ventilation is exhausting colder air than a bottom-to-top
ventilation and, exhausting at lower temperature means
exhausting/losing less power (~764 W vs ~934 W, i.e. ~-18%)
Mean air velocity is increased (~0,085 m/s vs ~0,061 m/s, i.e. ~+40%)
Full Sauna Model
With forced mechanical ventilation, we can reverse the ventilation, with the air outlet becoming the air inlet, and vice-versa
Temperatures are shown below, forced downward ventilation leads to smaller gradients, more homogeneous and higher
temperatures
Full Sauna Model
Temperature (center slice and stove slice) (°C)
Natural upward ventilation
Temperature (center slice and stove slice) (°C)
Forced downward ventilation
With forced mechanical ventilation, we can reverse the ventilation, with the air outlet becoming the air inlet, and vice-versa
Velocities are shown below
Full Sauna Model
Velocity (center slice) (m/s)
Natural upward ventilation
Velocity (center slice) (m/s)
Forced downward ventilation
With forced mechanical ventilation, we can reverse the ventilation, with the air outlet becoming the air inlet, and vice-versa
Velocities are shown below
Full Sauna Model
Velocity (stove slice) (m/s)
Natural upward ventilation
Velocity (stove slice) (m/s)
Forced downward ventilation
With forced mechanical ventilation, we can reverse the ventilation, with the air outlet becoming the air inlet, and vice-versa
Pathlines are shown below
Full Sauna Model
Pathlines (°C)
Natural upward ventilation
Pathlines (°C)
Forced downward ventilation
With forced mechanical ventilation, we can reverse the ventilation, with the air outlet becoming the air inlet, and vice-versa
Air temperature profiles taken on a vertical axis in the center of the sauna are plotted, forced downard ventilation leads to
higher temperatures, especially in the bottom region, and leads to more homogeneous temperatures, with a lesser gradient
Full Sauna Model
With a stove represented by a solid, non-porous, perfectly airtight block, the
modeling is simplified compared to a porous stove model or a fully detailed stove
model. The results obtained with an airtight stove show a much weaker thermal
plume, with significantly lower upward velocities.
This results in much weaker advective thermal pumping upwards and a higher
radiation from the stove.
This approach is not realistic from the point of view of fluid mechanics, the plume,
and stratification, but it has the advantage of being simple and allows the wall
temperatures near the stove to be maximized (152°C vs 119°C with the porous
stove), making it a safe approach. Representing the stove in all its details (casing,
stones, resistances) is cumbersome and complex but can hence be approximated
by a much simpler porous model that represents fluid mechanics and stratification
relatively well, at the cost of underestimating the temperatures of the solids near
the stove, but this underestimation can be compensated for by using a non-porous
modeling approach. With these two models, it is possible to easily model in an
acceptable way a fully detailed stove.
It is interesting to note that the non-porous model leads to a much lower vertical
thermal gradient in the upper part of the sauna, which is desirable from the
perspective of thermal comfort [31] and could hence be interesting. However,
constructing a truly non-porous stove would likely result in unreasonably extended
air heating durations, but there must be an optimal stove design to balance
heating time and stratification.
Full Sauna Model
Discussion & Conclusion
Discussion
All the numerical results provided by the 3D model
are in very good agreement with the literature and
our own measurements.
There are some discrepancies of course, because
each sauna is different, because measurements are
not always very accurate, because the model is in
steady-state, and so on, but the model can be
considered validated.
The full sauna model provides reliable results in
every aspect of the sauna, except for resistances,
stones and stove temperatures that are too low,
because of the simplified averaged porosity
approach.
For reliable resistances, stones and stove
temperatures, it is required to model the stones and
stove geometry in details (work in progress), but an
airtight, non-porous stove model provides maximized
wall temperatures.
Conclusion
A 3D thermo-aeraulic Computational Fluid
Dynamics and Radiation model of an electric sauna
has been built.
The model results are in very good agreement with
experimental results from the literature, indicating
that this approach could and should be used for
sauna engineering and design (for safety and
comfort studies for instance).
This approach could also be used for design
optimization, commercial, marketing and
communication efforts.
Modeling the resistances, stones and stove as a
simplified porous zone is possible and lead to
reliable results in every aspect of the sauna
(provided that the porosity parameters are
adjusted), except for the resistances, stones and
stove themselves
A detailed approach with all stones and stove
details is required to provided reliable results for
these elements (work in progress)
References
[1] E. Äikäs et al., Saunan lämpötilat ja ilmanvaihto (Sauna temperatures and
ventilation), VTT, 1992
[2] Y. Fan et al., CFD simulation on the airflow in a sauna, Building Research and
Information, 1994
[3] C. Macqueron, Computational Fluid Dynamics Modeling of a wood-burning stove-
heated sauna using NIST's Fire Dynamics Simulator, arXiv, 2014
[5] K. Nore et al., The principles of sauna physics, Energy Procedia, 2015
[4] C. Macqueron et al., Experimental validation of a computational fluid dynamics
modelling of a wood fire heated sauna with Fire Dynamics Simulator, ResearchGate,
2017
[6] H. Ishibashi et al., Evaluation of radiative absorption effect to estimate mean
radiant temperature in environments with high water vapor concentration such as in a
sauna, Building and Environment, 2023
[7] M. Ringh, The Heat Is On : Modeling Temperature Distribution in a Sauna, COMSOL,
2023, https://www.comsol.com/blogs/the-heat-is-on-modeling-temperature-
distribution-in-a-sauna/
[8] PC70…, Instructions for Installation and Use of Electric Sauna Heater,
25042013/ZSC-192, Harvia
[9] https://www.finlandiasauna.com/sauna-ceiling.html
[10] https://www.isover-technical-insulation.com/products
[11] Multi-firing sauna stoves fired by natural wood logs Requirements and test
method, European norm EN 15821, ISSN 0335-3931, AFNOR, 2010
References
[12] https://www.reddit.com/r/Sauna/comments/o5x86l/tech_minded_only_temperature_stratification_graph/
[13] https://www.reddit.com/r/Sauna/comments/mi0qv3/sauna_heat_stratification_measurements/
[14] https://www.tulikivi.com/en/tulikivi/Properties_of_soapstone
[15] M. Aaaland, Sweat, Capra, 1978
[16] Ansys Fluent Theory Guide, Version 18.1, Ansys, 2017
[17] Ansys Fluent Mosaic Technology, White Paper, Ansys, 2020
[18] Natural Convection, Advanced Fluent Training, Ansys, 2006
[19] J. P. Holman, Heat Transfer, McGraw Hill, 2010
[20] https://grabcad.com/library/sauna-heater-harvia-cilindro-pc90e-1
[21] I. E. Idelchik, Handbook of Hydraulic Resistance, BHB, 2008
[22] Owner’s/Operator’s Manual, 23052019/Y05-0571, Harvia
[23] https://www.harvia.com/en/sauna/heaters/electric-heaters/
[24] Ansys Fluent Theory Guide, Version 2021 R2, Ansys, 2021
[25] F. P. Incropera et al., Fundamentals of Heat and Mass Transfer, Wiley, 2007
[26] J. Leppäluoto, Human thermoregulation in sauna, Ann. Clin. Res., 1988, https://pubmed.ncbi.nlm.nih.gov/3218894/
[27] A. Bouslimani et al., Molecular cartography of the human skin surface in 3D, Applied Biological Sciences, 2015
[28] Harvia, FAQ about the energy consumption of sauna bathing
https://www.harvia.com/en/ideas-and-trends/sustainability-and-safety/faq-about-the-energy-consumption-of-sauna-
bathing/#:~:text=In%20total%2C%20the%20consumption%20of,about%207%2D9%20kilowatt%20hours.
[29] C. Macqueron, Numerical simulation of a wood-stove-heated sauna using ‘Fire Dynamics Simulator’, presentation at the
University of Tartu, ResearchGate, 2015
[30] C. Macqueron et al., Does sauna research have a future? (Onko saunatutkimuksella tulevaisuutta), Sauna Magazine, vol.
121, 2017
[31] https://localmile.org/trumpkins-notes-on-building-a-sauna/
[32] E. Äikäs, Ilman lämpötilat ja niiden jakaantuminen saunassa (air temperature and its distribution in the sauna), Sauna
Magazine, 1965
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
Appendix Sauna Construction
... A stove evacuates ~50% [28] to ~75% [2] of its power in the form of radiation, the rest being evacuated by convection. Radiation can be unpleasant if it is too intense (causing discomfort or even pain), and if it is not sufficiently uniform (it is uncomfortable to be heated on one side but not the other) [104]. ...
... For example, a surface at 1000°C in a fire at 1000°C will receive zero flux (equal to 0 W/m 2 ) because the temperature difference is zero. Similarly, a sauna wall at 95°C exposed to a hot source at 100°C will only receive a weak flux (~25 W/m 2 [28]). A cold surface (such as human skin (~33°C [3]), or a window (~60°C [28]) without double glazing and directly exposed to outside air on its outer side), on the other hand, will receive a very significant flux (~300-600 W/m 2 for human skin [67], ~300 W/m 2 for a "cold" window [28]). ...
... Similarly, a sauna wall at 95°C exposed to a hot source at 100°C will only receive a weak flux (~25 W/m 2 [28]). A cold surface (such as human skin (~33°C [3]), or a window (~60°C [28]) without double glazing and directly exposed to outside air on its outer side), on the other hand, will receive a very significant flux (~300-600 W/m 2 for human skin [67], ~300 W/m 2 for a "cold" window [28]). The wall closest to the stove, if well insulated, will thus be very hot (~140°C, for example [28]), and will receive intense radiative flux (up to ~400 W/m 2 locally [28]), but will ultimately only receive a relatively moderate total flux (convective and radiative) (~20 W/m 2 [28]), because, being very hot but in contact with relatively cold air, it will transfer most of what it received radiatively back into the sauna air in the form of convective flux, and will thus release only a small amount of total flux to the outside. ...
Technical Report
Full-text available
Sauna & Steam Traditions: A Scientific, Historical, Cultural and Medical Literature Review on the Art of Sweating
... Sauna bathing is a cultural and wellness activity in many countries such as Finland or Sweden [15] There are some thermal studies dedicated to the thermo-aeraulic behavior of saunas, such as [1] [2][3] [4][5] [6][7] [8][23], but there are still many things to discover on this topic ...
... We recently built a 3D Computational Fluid Dynamics (CFD) model of an electric sauna [8] that works very well in steady state but that would be too computationally expensive for transient calculations That's why we decided to build a 'lighter' model, based on 0D-1D calculations, to be able to study transient states in a computationally efficient manner (and to have some fun ☺) ...
... Calculating the thermal stratification is only possible through CFD (Computational Fluid Dynamics), such as in reference [8], and is too computationally expensive to perform transient calculations. Stratification is hence simplified here, with an empirical polynomial correlation fitted on experimental and numerical data from ...
Presentation
Full-text available
Thermo-Aeraulics 0D-1D Transient Modeling of a Sauna : Validation, Analysis, Design & Artificial Intelligence
Article
Full-text available
Sauna engineering and simulation, published in "Sauna Magazine", vol. 121, 2017
Presentation
Full-text available
Numerical simulation of a wood-stove-heated sauna using ‘Fire Dynamics Simulator’
Article
Full-text available
Significance The paper describes the implementation of an approach to study the chemical makeup of human skin surface and correlate it to the microbes that live in the skin. We provide the translation of molecular information in high-spatial resolution 3D to understand the body distribution of skin molecules and bacteria. In addition, we use integrative analysis to interpret, at a molecular level, the large scale of data obtained from human skin samples. Correlations between molecules and microbes can be obtained to further gain insights into the chemical milieu in which these different microbial communities live.
Article
Finnish sauna is heated by the radiation energy of an electrical or wood burning stove resulting in high air temperature, 80-100 degrees C, and low air humidity levels, 50-60 g/kg of air. Sauna bathing is divided into several 5-20 min sessions and between the sessions several minutes are spent at normal room temperature. Finnish sauna presents a heat load of 300-600 W/m2 of skin surface area. This increases mean skin temperature to 40-41 degrees C, causes strong heat sensations and starts thermoregulatory mechanisms. Evaporative heat transfer by sweating is the only effective channel dissipating heat from the body in sauna. Sweating is usually 0.6-1 kg/h and represents a heat loss of about 200 W/m2. The body cannot compensate for the heat load of sauna and the temperature of viscera begins to increase. A 30-minute stay in a sauna with a temperature of 80 degrees C increases rectal temperature by about 0.9 degrees C in adults whereas in children less intensive sauna (10 min at 70 degrees C) increases rectal temperature by 1.5 degrees C. The subjective feelings after Finnish sauna are usually described in positive terms such as "calm" and "pleasant".
FAQ about the energy consumption of sauna bathing
  • Harvia
Harvia, FAQ about the energy consumption of sauna bathing https://www.harvia.com/en/ideas-and-trends/sustainability-and-safety/faq-about-the-energy-consumption-of-saunabathing/#:~:text=In%20total%2C%20the%20consumption%20of,about%207%2D9%20kilowatt%20hours.
Onko saunatutkimuksella tulevaisuutta, Sauna Magazine
  • C Macqueron
C. Macqueron, Onko saunatutkimuksella tulevaisuutta, Sauna Magazine, vol. 121, 2017 https://issuu.com/corentin/docs/sauna_magazine_macqueron
Ilman lämpötilat ja niiden jakaantuminen saunassa (air temperature and its distribution in the sauna), Sauna Magazine
  • E Äikäs
E. Äikäs, Ilman lämpötilat ja niiden jakaantuminen saunassa (air temperature and its distribution in the sauna), Sauna Magazine, 1965