This document discusses using computational fluid dynamics (CFD) to model thermal comfort in buildings. It presents a CFD study of transient heat transfer over a mixed radiative/convective system with time- and space-varying boundary conditions. The study analyzes natural convection, forced convection, and heat radiation phenomena. CFD is proposed as a method to model these phenomena and design new conditioning terminal products through simulation-based design. Integrating CFD with design allows simulation of physical fluid dynamics that are difficult to test experimentally.

1. Modeling and engineering a conditioning terminal:
a CFD approach to thermal comfort in houses
ModutechS.r.l.
October 28° 2014
CAE Conference
International CAE Conference
October 28th 2014
Ing. Alessandro Cariani
ModutechS.r.l.

2. Cooling houses means handling not only generators but even heat terminals as fan
coils or brand new philosophy fan radiators as soon as integrated cooling systems.
This analisys has the aim to present a detailed CFD study of the transient forced
laminar convective heat transfer over a complex mixed radiative/convective/forced
convective system, when the thermal field is due to different kinds of variations – in
time and space – of some boundary conditions, i.e. plate temperature or wall heat
flux. The governing equations are solved using extensions either of the differential
method, or the Karman – Pohlhausen integral approach.
Artistic approach is the first part of integration of R&D to find the state of the art of
technology, comfort and design: CFD is the basis of a brand new product.
Abstract

3. HEAT TRANSMISSION
PHENOMENA
1. Natural convection
2. Heat Radiation
3. Forced convection

4. Natural convection

5. The natural convection flow field is a self-sustained flow generated by
the presence of a temperature gradient.
As a result of this gradient, we obtain a density gradient of flux, typically
air.
A surface with a difference in temperature will induce a flow current
with the influence of the gravitational field and the density field gradient.
Room air heating, wall heating and turbulence inside the room is one of
the results of these phenomena
THERMAL POWER Q, transmitted by convection between a
surface and a surrounding fluid, can be calculated using
Newton's law:
QC = S hc (Ts - T∞)
Natural convection

6. Heat amount transmitted depends on:
• Surface geometry;
• Surface orientation;
• Difference of temperature between air and surface;
• Surface roughness
Air temperature behave in a quite similar way in free
and forced convection, while air relative speed tends
to increase up to a distance of 3 mm from the surface
of a plate and then again tend to zero
S = heat exchange surface (m2)
h = coefficient of convective heat exchange (W/m2 K)
Natural convection
QC = S hc (Ts - T∞)

7. Natural convection
Among the types of convective transfers, forced convection is often used because of its
efficiency. Aa soon as the natural convection has the advantage to be free in terms of energy
expense it generates low heat transfer coefficient. Thus it will be interesting to improve free
convection heat transfer, by the mean of time-dependent boundary conditions.
Laminar free convection problem on a vertical wall has been plentifully investigated as the
dynamic behaviour of free convection flows is poorly documented in literature.
These CFD analisys of mixed flow behaviuor indicates that:
1. Radiative systems could increase overall efficiency using concrete wall to cooperate with
other heat flux phenomena;
2. Control of natural and forced convection can increase the perceived comfort of users.

8. Natural convection
In natural convection, the fluid motion occurs by natural means such as buoyancy.
Since the fluid velocity associated with natural convection is relatively low, the heat
transfer coefficient encountered in natural convection is also low. Consider a hot
object exposed to cold air. The temperature of the outside of the object will drop (as a
result of heat transfer with cold air), and the temperature of adjacent air to the object
will rise. Consequently, the object is surrounded with a thin layer of warmer air and
heat will be transferred from this layer to the outer layers of air. The temperature of the
air adjacent to the hot object is higher, thus its density is lower. As a result, the heated
air rises. This movement is called the natural convection current. Note that in the
absence of this movement, heat transfer would be by conduction only and its rate
would be much lower. In a gravitational field, there is a net force that pushes a light
fluid placed in a heavier fluid upwards. This force is called the buoyancy force.

9. Natural convection
Note that the net force is proportional to the difference in the densities of the fluid and the body. This is known
as Archimedes’ principle. We all encounter the feeling of “weight loss” in water which is caused by the
buoyancy force. Other examples are hot balloon rising, and the chimney effect. Note that the buoyancy force
needs the gravity field, thus in space (where no gravity exists) the buoyancy effects does not exist. Density is a
function of temperature, the variation of density of a fluid with temperature at constant pressure can be
expressed in terms of the volume expansion coefficient β, defined as:
It can be shown that for an ideal gas:
where T is the absolute temperature. Note that the parameter βΔT represents the fraction of volume change of
a fluid that corresponds to a temperature change ΔT at constant pressure. Since the buoyancy force is
proportional to the density difference, the larger the temperature difference between the fluid and the body, the
larger the buoyancy force will be. Whenever two bodies in contact move relative to each other, a friction force
develops at the contact surface in the direction opposite to that of the motion. Under steady conditions, the air
flow rate driven by buoyancy is established by balancing the buoyancy force with the frictional force.

10. Forced convection
Convection is the mechanism of heat transfer through a fluid in the presence of bulk fluid motion. As in natural
convection the fluid motion is caused by natural means such as the buoyancy effect, in forced convection, the
fluid is forced to flow over a surface or in a tube by external power.
Study of convective heat transfer is one of the most complicated problem in fluid-dynamics since it involves
fluid motion as well as heat conduction between solids (typically plates of heat sinks) and fluid: turbulent flows
increase the effects of fluid heat transfer (higher is the flow speed the higher is heat transfer rate).
Convection rate heat transfer can be expressed by Newton’s law of cooling:
The convective heat transfer coefficient h strongly depends on the fluid properties and roughness ( of the solid
surface, and the type of the fluid flow (laminar or turbulent).

11. Forced convection
It is assumed that the velocity of the fluid is zero at the wall, this assumption is called noslip condition. As a
result, the heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction,
since the fluid is motionless. Thus,
The convection heat transfer coefficient, in general, varies along the flow direction. The mean or average
convection heat transfer coefficient for a surface is determined by (properly) averaging the local heat transfer
coefficient over the entire surface.
Bigger is roughness of plate, lower is heat transmission, as soon as higher is Prandlt number better heat
propagates due to bigger sublayer.

12. 𝑄 𝑎𝑖
𝑄 𝑎𝑜
𝑄 𝑎𝑖=𝑆𝑖 𝑉𝑖 (𝑎𝑖𝑟 𝑖𝑛𝑙𝑒𝑡) 𝑄 𝑎𝑢=𝑆 𝑢 𝑉𝑢 (𝑎𝑖𝑟 𝑜𝑢𝑡𝑙𝑒𝑡)
Volume control
Forced convection

13. 𝑆𝑖 𝑉𝑖=𝑆 𝑢 𝑉𝑢
𝑉𝑢=𝑉𝑖 𝐶𝑒
𝐶𝑒 = flux coefficient
𝑆𝑖 𝑉𝑖=𝑆 𝑢 𝑉𝑖 𝐶𝑒
∆𝑄=m 𝑐 𝑝(∆𝑇)
∆ 𝑄=Qu−Qi = 𝑚 𝑢 𝑐 𝑝 𝑇𝑢 − 𝑚𝑖 𝑐 𝑝 𝑇𝑖
𝑄 𝑎𝑢 = 𝑆 𝑢 𝑉𝑢 = 𝑆 𝑢 𝑉𝑖 𝑐 𝑒 𝑇𝑜=?
Forced convection

14. 𝑆 𝑒𝑥𝑐
𝑄 𝑎𝑖
𝑄 𝑎𝑜 (𝑇𝑜)
(𝑇𝑖)
𝑇 𝑤𝑖 𝑇 𝑤𝑜
𝑇𝑜=𝑇𝑖 +(𝑇 𝑤𝑖 − 𝑇𝑖)(𝑐ℎ𝑒 𝑆 𝑒𝑥𝑐)
Forced convection

15. • Radiation is the transfer of energy (heat) between two throught
electromagnetic waves.
• Instead of conduction and convection, radiation does not need
direct contact between exchangers, and does not require a
medium to propagate throught.
Qr = S ε σ ΔT4
THERMAL POWER Q, transmitted by radiation can be calculated
using Boltzmann's law:
Heat radiation

16. σ = 5,67 x 10-8 W/m2 K4 Boltzmann constant
material emissivity ε
Polished gold 0,02
Copper tube 0,30
Polished steel 0,17
Water 0,96
S = heat exchange surface
Heat radiation

17. The main parameters for the efficiency of the heat
exchange both free convective that irradiation are the
exchange surface and the thermal jump:
• greater is surface greater is the heat input;
• greater is thermal jump greater is the radiation
heat output.
Heat radiation

18. quadratic trend of the
thermal radiance
linear trend of
temperature rise in
free convection
Overall convection

19. 𝑵𝒂𝒕𝒖𝒓𝒂𝒍 𝒄𝒐𝒏𝒗𝒆𝒄𝒕𝒊𝒐𝒏 𝑭𝒐𝒓𝒄𝒆𝒅 𝒄𝒐𝒏𝒗𝒆𝒄𝒕𝒊𝒐𝒏
Fluid dynamic simulation
∆𝑸
Overall heat
R𝒂𝒅𝒊𝒂𝒕𝒊𝒐𝒏

20. Why use CFD in cooling ?
• Analysis and Design
1. Simulation-based design instead of “build & test”
More cost effective and faster than EFD
CFD provides high-fidelity database for diagnosing flow
field
2. Simulation of physical fluid phenomena that are
difficult for experiments
Full scale simulations
Environmental effects (wind, weather, etc.)
Simulation in case of different living conditions (party ?)

21. Modeling
• Modeling is the mathematical physics problem
formulation in terms of a continuous initial
boundary value problem (IBVP)
• IBVP is in the form of Partial Differential
Equations (PDEs) with appropriate boundary
conditions and initial conditions.
• Modeling includes:
1. Geometry and domain
2. Coordinates
3. Governing equations
4. Flow conditions
5. Initial and boundary conditions
6. Selection of models for different applications

22. Modeling (geometry and domain)
• Simple geometries can be easily created by few geometric
parameters
• Complex geometries must be created by the partial
differential equations or importing the database of the
geometry(e.g. airfoil) into commercial software
• Domain: size and shape
• Typical approaches
• Geometry approximation
• CAD/CAE integration: use of industry standards such as
Parasolid, ACIS, STEP, or IGES, etc.
• The three coordinates: Cartesian system (x,y,z), cylindrical
system (r, θ, z), and spherical system(r, θ, Φ) should be
appropriately chosen for a better resolution of the geometry
• Effect: mesh analisys in commercial software MUST be checked
before CFD run: garbage in, garbage out.

23. Mesh
• Meshes should be well designed to resolve important
flow features which are dependent upon flow condition
parameters (e.g., Re), such as the grid refinement
inside the wall boundary layer
• Mesh can be generated by either commercial codes
(Gridgen, Gambit, etc.) or research code (using
algebraic vs. PDE based, conformal mapping, etc.). A
check is always needed !!
• The mesh, together with the boundary conditions need
to be exported from commercial software in a certain
format that can be recognized by the research CFD
code or other commercial CFD software.

24. Solve
• Setup appropriate numerical parameters
• Choose appropriate Solvers
• Solution procedure (e.g. incompressible flows)
Solve the momentum, pressure Poisson
equations and get flow field quantities, such as
velocity, turbulence intensity, pressure and
integral quantities (lift, drag forces)

25. x
y
z
x
y
z
x
y
z
(r,,z)
z
r
(r,,)
r

(x,y,z)
Cartesian Cylindrical Spherical
General Curvilinear Coordinates General orthogonal Coordinates

26. • Navier-Stokes equations (3D in Cartesian coordinates)





























2
2
2
2
2
2
ˆ
z
u
y
u
x
u
x
p
z
u
w
y
u
v
x
u
u
t
u






























2
2
2
2
2
2
ˆ
z
v
y
v
x
v
y
p
z
v
w
y
v
v
x
v
u
t
v

      0











z
w
y
v
x
u
t

RTp 
L
v pp
Dt
DR
Dt
RD
R


 2
2
2
)(
2
3
Convection Piezometric pressure gradient Viscous termsLocal
acceleration
Continuity equation
Equation of state
Rayleigh Equation





























2
2
2
2
2
2
ˆ
z
w
y
w
x
w
z
p
z
w
w
y
w
v
x
w
u
t
w


27. CFD Process – How to proceed
Viscous
Model
Boundary
Conditions
Initial
Conditions
Convergent
Limit
Contours
Precisions
(single/
double)
Numerical
Scheme
Vectors
StreamlinesVerification
Geometry
Select
Geometry
Geometry
Parameters
Physics Mesh Solve Post-
Processing
Compressibl
e
ON/OFF
Flow
properties
Unstructure
(automatic/
manual)
Steady/
Unsteady
Forces
Report
XY Plot
Domain
Shape and
Size
Heat
Transfer
ON/OFF
Structured
(automatic/
manual)
Iterations/
Steps
Validation
Reports
Check mesh

28. consider a system made by a fan and a radiator into a room
𝝎 = 𝟏𝟒
𝒓𝒂𝒅
𝒔
Boundary Conditions:
𝒎𝒊𝒏 = 𝟎, 𝟎𝟏𝟔
𝑲𝒈
𝒔
𝒎 𝒐𝒖𝒕 = 𝟎, 𝟎𝟏𝟔
𝑲𝒈
𝒔
1) Inlet mass flow;
2) Outlet mass flow;
3) Real wall (T=293,2 K);
4) Rotating region;
5) Fluid Subdomain:
1) Air
2) Water
6) Radiative Surface;
7) Solid materials
𝑻 𝒉𝒇 = 𝟑𝟐𝟑, 𝟐 𝑲
CFD simulation of the MDTCH/1

29. CFD simulation: room positioning

30. TEMPERATURE
CFD simulation

31. VELOCITY
CFD simulation

32. VELOCITY
CFD simulation

33. Flow Simulation Analysis
Report
Gases: Air
Path: Gases Pre-Defined
Specific heat ratio (Cp/Cv): 1,399
Molecular mass: 0,0290 kg/mol
Dynamic viscosity
Liquids: Water
Path: Liquids Pre-Defined
Density
0
0.00002
0.00004
0.00006
0.00008
0.0001
0.00012
0 500 1000 1500 2000 2500 3000 3500
Dynamicviscosity[Pa*s]
Temperature[K]
0
200
400
600
800
1000
1200
0 100 200 300 400 500 600
Density[kg/m^3]
Temperature[K]
Optimization

34. CFD room simulation.
Example of CFD simulation on a room with
big glasses and one cooling terminal

35. CFD analisys results
1. Mixed heat phenomena in cooling terminals can assure better performances if
compared to single heat transfer technologies as the efficiency of heating behavior
changes depending on plate, air and heat exchange fluid temperature;
2. Natural convection is “low energy depending” thanks to buoyancy effect, but heat
rate is low: as soon as the request of fast heating is present (i,.e. in hotels rooms)
this process need a continuous heat power to heat fluid to be appreciated by
users;
3. Forced convection is “medium energy depending” thanks to blower generated air
speed, and heat rate is high: as soon as the request of fast heating is present (i,.e.
in hotels rooms) this process need a continuous blower power to be appreciated
by users;
4. Radiative power phenomena is low when heat exchange fluid does not reach
approximately 50 celsius (see Boltzmann equation): radiative heat is perceived as
“nice” by users when surface is big, so heating of wall must be an important part of
heating processes.
5. Mixed cooling process can assure a perfect flexibility in cooling rooms adding air
parameters controls.

36. CFD analisys results:
Temperature change
(medium value)
inside a room heated
at different heat fluid
temperature

37. CFD analisys results:
Room stratigraphy temperature inside a room – Natural convection and radiation on a cooling terminal

38. CFD analisys results: MDTCH/1 at
different power
Heat (J)
Time (s)

39. Comfort ?
Relative moisture index (%)

40. Comfort ?
0
1
2
3
4
5
6
0 10 20 30 40 50 60
natural convection
forced convection
radiation
Overall heat exchanged
Heat
power
(kW)
Delta temperature of heat exchangers surface and air (Kelvin)

41. And at the end, the art of
cooling systems…

48. Modeling and engineering a conditioning terminal:
a CFD approach to thermal comfort in houses
Thank you
ModutechS.r.l.
October 28 th 2014
CAE Conference
International CAE Conference
October 28th 2014
Ing. Alessandro Cariani
ModutechS.r.l.