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Summary of Heat, air and moisture transfer (HAM)_CFD 2 (7LS6M0)
Clear and concise summary of the complete course.
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Summary Heat, air and moisture transfer / CFD2 (7LS6M0)Overview HAM 2 (CFD not in exam)
Condensation takes place against cold surface with a low RH
2 moisture states: vapor/gas (diffusion, convection), water/liquid (capillary, gravity, pressure)
So three main mechanisms for moisture transport: flow by vapor pressure differences/concentration
differences, diffusion caused by movement of molecules in air, advection (dragging along of vapor
and droplets by air/convection)
Mass flow in kg/s
Air and vapor can be considered as ideal gas with gas constants Rv and Ra, with this pa and pv can be
calculated. , and humidity ratio x
For every temperature there is a maximum vapor pressure, after that concentration occurs psat(T),
higher at higher temps. RH=pv/psat*100%. Below dew point temperature, condensation occurs in
room, pv=psat(dew temp). RH in museum max 60%, normally 80%. Use calcium silicate
for the redistribution of water
In porous materials water vapor condensates already below psat, the relation between
the moisture content w and RH can be found in the sorption curve. Below 98% RH
moisture transfer is dominated by diffusion (potential vapor pressure pv), above 98%
moisture flow is caused by capillary suction (potential pc). Kelvin’s law: relation
between pc and RH
For liquid (above 98%) plot moisture content vs capillary suction, moisture retention
curve
3 potentials for moisture transfer: vapor pressure + temperature, relative humidity +
temperature, capillary suction + temperature. 4th potential is moisture
content+temperature.
Vapor conductivity in porous materials
Vapor transfer equation (density mass flow rate by pv=Ficks law): with u vapor
diffusion resistance factor (always above 1, 1 for stagnant air, relates the vapor resistance of a
material to the vapor resistance of a layer of stagnant air with the same thickness), depends
on porosity and moisture content, decreases with RH. Vapor transfer equation
Water transfer equation by capillary suction (density mass flow rate by pc = Darcy law):
with k moisture permeability which increases with moisture content. Capillary transport equation:
Change of moisture content<0.98 RH , above .g
equation + these equations give vapor/capillary transport equations mentioned above.
3 Boundary conditions:
, - Condition at the surface, from air to surface
- Vapor into wall:
- Liquid into wall
Air flow in porous materials:
- Density mass flow rate , if air is compressible and gravity is neglected
the convective transfer equation is
- Convective heat and vapor transport
Similarities heat and moisture: moisture transfer and heat conduction are both diffusion processes,
boundary conditions are similar; conservation of mass vs conservation of energy and moisture flows
caused by gradients in moisture potential vs heat flows caused by temperature gradients
Differences: vapor pressure has a maximum value psat, moisture content has a maximum value,
moisture diffusion occurs in form of water (potential suction) and vapor (potential vapor pressure),
airflow much more important to vapor transfer, relationship between moisture content and
potential is non-linear and there is hysteresis, transfer coefficients depend strongly on moisture
content (non-linear), temp gradients influence moisture transfer much more than moisture
gradients on heat transfer, gravity important for water transport, pore structure determines
moisture properties.
Porosity: volume pores dry material/total volume, open porosity: open pores/total volume. Porosity
decreases the thermal conductivity and density.
If the adhesion (forces of wall on fluid) are bigger than the cohesion of the fluid molecules, the fluid
will be attracted by the wall (concave meniscus). Otherwise rejection (convex meniscus).
This depends on the contact angle between the fluid and surface, if 0 much wetting
(glass) if 180 no wetting (polysterene). Materials angle<90 are hydrophilic (concave,
much sucking/adhesion), >90 hydrophobic (convex, more force needed for suction.
Capillary pressure pc is higher with smaller angle and radius , σ is the
surface tension coefficient.
Kelvin’s law: lowering of equilibrium water vapor pressure (where condensation equals
evaporation), from this follows the earlier mentioned relation with RH and pc
The higher the RH, a larger amount of capillaries are filled
In equilibrium state the amount of moisture in the pores depends on the RH, higher RH, more water.
This is dependent on absorption and condensation in pores. Types of moisture content depending
on RH, can be expressed in w (kg/m3), u=(w/density)*100 (in m3/m3), volume w/10 (kg/kg):
- Hygroscopic moisture content w: until 98% RH, (measured by weighing at RH increasing
from 1-100 and decreasing from 100-0% or determine based on the absorption and
desorption curve)
- Critical moisture content wcr: lowest moisture content at which there are still continuous
water filled capillaries, below the critical content vapor transport dominates, above water
, transport (cannot be measured as it is a transition trajectory from vapor to liquid, so no
specific breakpoint)
- Capillary moisture content wc: at 100% RH, when a material is put into water and there is no
change of weight, when all air entrapped in capillaries (cannot get out) (measure by putting
a material under water and measure when there is no change of mass)
- Maximum moisture content: above RH 100%, when all entrapped air is extracted, only water
present (vacuum submerging), all capillaries will be filled with water
- Wh is the moisture content at equilibrium
- Wi, initial moisture content
Hysteresis/ink bottle effect: moisture content is higher when RH is decreased step by step, than
increased step by step
3 equations for moisture (vapor+liquid) transport:
RH , Capillary pressure , moisture content
Moisture content is not continuous at the interface (jump at intersection), as Dw (moisture
diffusivity strongly depends on the material), so don’t use this with more than 1 material
Moisture diffusivity Dw curve: minimum at critical moisture content, e increases with
moisture content and E decreases with moisture content
Influence of temperature on vapor transfer (beside pv
as potential) when RH is chosen as potential
Influence moisture on heat transport (extra heat sink term), often small influence:
Wetting:
- Step change in moisture content at surface of semi-infinite thick slab (when put
into water step change from dry to capillary moisture content), for one material
- Weight increase by moisture uptake as a function of time
with a sorption coefficient
- The front between the wet and material with B penetration coefficient
- Step change at constant density (rain): rise of moisture content near the surface
or
- Time needed to reach the capillary moisture content at the surface
and dripping starts
- Time at which the wall is completely wetted (max absorbed)
assumed that w=0, V(wc-wi)=dmw
Drying:
- First drying time, time to reach the critical content: constant drying rate,
w>wcr
- Second drying time, below critical content (vapor), vapor diffusion at front, t2 =
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