Expanded psychrometric landscapes for radiant cooling and natural ventilation system design and optimization

Abstract

Maintaining the thermal comfort of building occupants is a challenge typically negotiated by air based heating and cooling systems that rigidly maintain supply air temperatures and humidity levels. Such a practice overlooks several other design variables, including the mean radiant temperature, TMRT , which is responsible for a significant portion of an occupant’s thermal comfort, or air velocity, v(air). The increased deployment of low exergy cooling strategies such as evaporative cooling and radiant cooling allows temperature potentials to be efficiently and effectively leveraged. However, the precise execution and subsequent control of these potentials in air based or radiant systems is driven by incomplete empirically based standards, removing heuristic guiding. Deciding where system setpoints should be for systems that go beyond simple air based cooling is difficult to arrive at through intuition and current metrics, as the inclusion and modulation of other thermal comfort variables such as air velocity, skin temperature, skin wettedness and metabolic rate are not entirely independent variables. The focus of this research is to approach thermal comfort with an occupant-centered stance, comparing heat loss through primary modes of heat transfer generated by an occupant’s metabolic rate. In doing so, the holistic integration of all comfort variables currently missing from the literature opens a window into an integrated design landscape including air temperature, T(MRT) , and relative humidity as the relevant independent variables for thermal comfort. Building on the array of low exergy building systems with integrated evaporative and radiative cooling systems in the literature, this new landscape will be presented as a tool for assessing a new radiant cooling system.

Full text

Available online at www.sciencedirect.com
Energy Procedia 00 (2016) 000–000
www.elsevier.com/locate/procedia
CISBAT 2017 International Conference Future Buildings & Districts Energy Efficiency from
Nano to Urban Scale, CISBAT 2017 6-8 September 2017, Lausanne, Switzerland
Expanded psychrometric landscapes for radiant cooling and natural
ventilation system design and optimization
Eric Teitelbauma,∗, Forrest Meggersb,c
aCivil and Environmental Engineering, Princeton University, Princeton, NJ, 08544, USA
bSchool of Architecture, Princeton University, Princeton, NJ, 08544, USA
cAndlinger Center for Energy and the Environment, Princeton University, Princeton, NJ, 08544, USA
Abstract
Maintaining the thermal comfort of building occupants is a challenge typically negotiated by air based heating and cooling sys-
tems that rigidly maintain supply air temperatures and humidity levels. Such a practice overlooks several other design variables,
including the mean radiant temperature, TMRT , which is responsible for a significant portion of an occupant’s thermal comfort,
or air velocity, vair. The increased deployment of low exergy cooling strategies such as evaporative cooling and radiant cooling
allows temperature potentials to be efficiently and effectively leveraged. However, the precise execution and subsequent control of
these potentials in air based or radiant systems is driven by incomplete empirically based standards, removing heuristic guiding.
Deciding where system setpoints should be for systems that go beyond simple air based cooling is difficult to arrive at through
intuition and current metrics, as the inclusion and modulation of other thermal comfort variables such as air velocity, skin temper-
ature, skin wettedness and metabolic rate are not entirely independent variables. The focus of this research is to approach thermal
comfort with an occupant-centered stance, comparing heat loss through primary modes of heat transfer generated by an occupant’s
metabolic rate. In doing so, the holistic integration of all comfort variables currently missing from the literature opens a window
into an integrated design landscape including air temperature, TMRT , and relative humidity as the relevant independent variables for
thermal comfort. Building on the array of low exergy building systems with integrated evaporative and radiative cooling systems
in the literature, this new landscape will be presented as a tool for assessing a new radiant cooling system.
c
2016 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the CISBAT 2017 International Conference Future Buildings &
Districts Energy Efficiency from Nano to Urban Scale.
Keywords: Thermal comfort; Psychrometrics; Radiant Cooling; Mean Radiant Temperature
1. Introduction
In a broad sense, buildings act as barriers between biological thermal engines and ambient environmental condi-
tions, providing protection from undesirable conditions that would otherwise direct heat and coupled mass transfer
to the engine at rates incongruent with engine output. In this analogy, a building is abstracted as a heat and mass
∗Corresponding author. Tel.: +1-609-408-7786.
E-mail address: eteitelb@princeton.edu
1876-6102 c
2016 The Authors. Published by Elsevier Ltd.
Peer-review under responsibility of the scientific committee of the CISBAT 2017 International Conference Future Buildings & Districts Energy
Efficiency from Nano to Urban Scale.

2Author name /Energy Procedia 00 (2016) 000–000
exchanger for a human body, with dynamically linked conductive, convective, and radiative modes available to tune
the rate of heat loss or gain. Yet despite the depth of our understanding regarding thermoregulation and radiant heat
transfer, the majority of HVAC systems control for comfort using air based metrics. And when radiant systems are
installed, they rarely are controlled adequately with TMRT values. Even if such controls existed, our familiarity with
air based systems has led to an intuition for air temperature set points, however the same could not be said for radiant
systems or air velocities. As such, the overarching goal of this research is to reimagine comfort criteria with intuitive
visualizations for design and control of more complex systems.
Nomenclature
A area
MR metabolic rate
P partial pressure
Q heat
T temperature
h heat transfer coefficient
v air velocity
w skin wettedness
emissivity
σStefan-Boltzmann constant
wb wet bulb
dp dew point
eevaporative
cconvective
rradiative
skin skin property
air air property
MRT mean radiant temperature
Heat transfer in buildings occurs through radiative and convective exchanges, convection linked explicitly to evap-
orative mass transfer, and conductive exchanges. However, standard practice attempts to maintain historically-dictated
stringent guidelines, referred to as the “comfort zone”, which uses operative temperature and moisture content in air
as the two tunable parameters through which comfort is achieved. Academically, thermal comfort is well researched,
and empirical and analytical relationships exist between thermal comfort and a full set of climatic conditions for a
building space [1,2]. A full framework for human comfort has been proposed through the frame of exergy destruction
[3,4].
Using the heat transfer analogy, it becomes clear that a static comfort zone is true for a subset of conditions only.
Such a dimensional reduction, however, excludes many facets of heat transfer that could more efficiently maintain
comfort. Still, a conventional comfort zone dictated by air temperature and relative humidity only. This approach
neglects the influence of mean radiant temperature, air velocity, skin wettedness, and an individual’s metabolic rate.
A phenomenal tool was created by the Berkeley Center for the Built Environment that takes inputs for each of these
parameters, however variables are still fixed and trends are not easily discerned with precision [5].
2. Methods
Applying a reductionist approach to thermal comfort yields seven key variables acting within 3 interconnected
modes of heat and mass transfer (radiative, convective, and evaporative, neglecting conduction for this analysis). The
7 variables are air temperature, Tair, mean radiant temperature, TM RT , relative humidity, %RH, skin temperature, Tskin ,
air velocity, vair , skin wettedness, w, and metabolic rate, MR. Clothing level is also an important factor to consider,
however this is a variable parameter that can easily be added later to calibrate a specific model.
For this abstracted model of human comfort, the comfort condition is defined as equality between heat removed
and metabolic rate. Metabolic rates are well defined and independent of size, and are therefore a robust metric to serve
as the basis of this analysis [2]. Specifically 1.2 met (69.8 W/m2) is the metabolic rate of an individual performing
light office work such as typing, and 2 met (116.3 W/m2) is one’s metabolic rate when walking briskly. These values
of metabolic rate were chosen to serve as the boundary of the office space comfort zone, or in other words this range
describes the range a building system must be able to operate within to remove heat between 69.8 and 116. 3 W/m2
from an individual.

Author name /Energy Procedia 00 (2016) 000–000 3
Heat transfer between a building and an occupant can occur through radiative and convective exchanges, as well
as convection linked explicitly to evaporative mass transfer, and conductive exchanges. Conduction was neglected for
this paper, since conduction tends to be situational and therefore difficult to quantify, rather than the other three modes
which are always present and empirically calculable. The following equation demonstrates the objective function for
analysis.
Qevap +Qconv +Qrad =MR (1)
In equation 1, Qrepresents heat transfer in W/m2with subscripts for the particular mode of heat transfer. Parametriz-
ing this model in equation set 2 reveals interconnectedness between the relevant modes of heat transfer.
Qevap =f(w,%RH,Tskin,vair)Qconv =f(vair,Tair ,Tskin)Qrad =f(TM RT ,Tskin) (2)
Each mode is coupled by a dependence on skin temperature, and evaporative and convective modes have a dependence
on vair.
In models presented by Arens and deDear [2,6], the three modes are simply portrayed as potential-driven transfer
mechanisms as depicted in equation sets 3 through 5. Equation set 3 shows Qconv divided into a two regimes, forced
and free convection. Free convection occurs for vair ≤0.1m/sand forced convection occurs for vair >0.1m/s. For
this paper, free convection assumes an individual is sitting, and forced convection assumes an individual is standing
(walking) thereby changing the form of hc[2].
Qconv =hc(Tskin −Tair)hc,fr ee =0.78(Tskin −Tair)0.56 hc,f orced =10.4v0.56
air (3)
Equation set 4 shows the dependence of evaporatively generated heat transfer on convective heat transfer as shown
in the heterm, in addition to partial pressure differences, P. In this model, Pskin,sat is the partial pressure of water at
the skin’s surface and therefore at Tskin, and Pair is the partial pressure of water in the air at Tair. For an individual that
is not sweating but transporting moisture at a background rate, it is assumed that w=0.06. At the onset of sweating,
this number increases to a maximum practical threshold of 0.80 [2].
Qevap =w∗he(Pskin,sat −Pair )he=16.5hc(4)
Equation set 5 is an empirical simplification of radiant heat transfer that is possible due to relatively small temper-
ature differences at building scales. AR
ADrepresents the effective area through which radiative heat transfer can occur,
chosen for a seated, clothed occupant.
Qrad =hr(Tskin −TMRT )hr=4 σ AR
AD
[273.15 +Tskin +TMRT
2]3AR
AD
=0.70 (5)
The challenge is presenting these empirical models as a comprehensive, holistic, and intuitive model, rather than a
disparate set of equations.
Additionally, a significant amount of research has been conducted measuring skin temperature as a function of air
temperature [7], a useful equation to begin reducing parameters among the modes of heat transfer. While there is a
nonuniform relaxation period during which the skin temperature approaches the equilibrium value, a simple linear
expression can be defined to more accurately model Tskin as a function of Tair as follows in equation 6, which fits data
with R2=0.99.
Tskin =0.3182Tair +22.406 (6)
Using these fundamental relationships, a model was developed using Python scripting that allowed for the funda-
mental parameters to be varied and the resulting topology change plotted. Similar to the models created by Shukuya
[3] and Fanger [1], these topologies were created with the intent of defining a comfort zone and performing a gener-
alized system optimization. However unlike other work in the field, the intended goal of this analysis is to provide a
user with an intuitive picture of his or her surroundings, adding more complexity than just air temperature and relative
humidity.

4Author name /Energy Procedia 00 (2016) 000–000
3. Results
The generalized heat transfer models have the flexibility to incorporate any set of the 7 fundamental parameters.
Since heat flux via radiative, evaporative, and convective modes are treated equally, comfort is defined as when the
sum of these three equals an individual’s metabolic rate. For using radiant systems to address thermal comfort, the
design space was able to be dimensionally reduced parametrizing %RH and eliminating forced convection entirely.
This allowed for TMRT to be solved implicitly for a given MR,w, and Tskin . Figure 1 demonstrates this result for
MR =2 met, w=0.6, and Tskin =f(Tair ). This assumes that air is entering a room with a known Tair and %RH, and
these values are used to solve implicitly for the required TMRT for the given metabolic rate. In figure 1, the standard
psychrometric chart is superimposed on the calculated TMRT at each (Tair ) and %RH, for a fixed MR and w. Equation
6 was used to make Tskin a dependent variable in this model.
5 10 15 20 25 30 35 40
Air Temperature ◦C
0
5
10
15
20
25
Humidity Ratio (g water/kg dry air)
10%
20%
30%
40%
50%
60%
70%
80%90%
100%
MRT ◦C
18.8
19.2
19.6
20.0
20.4
20.8
21.2
21.6
22.0
22.4
22.8
23.2
23.6
24.0
24.4
24.8
25.2
25.6
26.0
18.5
19.7
20.9
22.1
23.3
24.5
25.7
26.9
5 10 15 20 25 30 35 40
Air Temperature ◦C
0
5
10
15
20
25
Humidity Ratio (g water/kg dry air)
10%
20%
30%
40%
50%
60%
70%
80%90%
100%
MRT ◦C
20.8
21.6
22.4
23.2
24.0
24.8
25.6
26.4
27.2
28.0
28.8
29.6
30.4
31.2
32.0
32.8
33.6
34.4
35.2
20.2
22.4
24.6
26.8
29.0
31.2
33.4
35.6
Fig. 1. (a) Expanded comfort zone for free convection at MR =1.2 met and w=0.06 when TMRT , shown by the gradient, is solved for, expanding
the comfort zone to encompass many air temperature and humidity regimes. (b) Expanded comfort zone for forced convection at MR =1.2 met for
forced convection at vair =0.5 m/s. The nearly vertical white line corresponds to TMRT =Tair , the middle white line as TMRT =Twb, and the top
white line corresponds to TMRT =Td p.
In figure 1 the comfort zone has been greatly expanded with the inclusion of radiant cooling and heating. For any
Tair and %RH on the x,yplane, there is now a corresponding TMRT which must be achieved to satisfy the comfort
condition, indicated by the color gradient. Practicalities associated with deriving particularly low values for TMRT set
aside for this study, this assessment of thermal comfort provides visual confirmation of the narrow approach associated
with air-based design only.
Figure 1 also includes white lines for different TMRT scenarios. Namely The nearly vertical white line corresponds
to TMRT =Tair , the middle white line as TMRT =Twb, and the top white line corresponds to TM RT =Tdp . Therefore,
any point that lies above the top white line could expect condensation on surfaces providing the required TMRT . While
typically a design constraint, there are commercially available radiant cooling panels that allow cooling below the dew
point [8,9].
Interpretation of the figure would require knowing the mean radiant temperature perceived by an occupant, some-
thing not typically available but certainly obtainable [10]. For a given Tair, %RH, and TMRT , the plotted point would
have an (x,y) coordinate, and a color determined by the mean radiant temperature. A mismatch between the tempera-
ture of the datapoint and the background TMRT would imply the occupant could be more comfortable, and either Tair
or TMRT should be adjusted accordingly.
The same approach can be used to visualize the effects of a forced convection based system, i.e. fans, by solving
for a required air velocity. Here, the function used to reduce the dimensionality of the problem is TM RT =Tair, a
standard HVAC assumption. For cooling demand, air velocities can be determined.
Figure 2 demonstrates some nonlinearities experienced with air based comfort, as moving from 2a to 2b demon-
strates sweat’s ability to shed heat. 2 met and 20% skin wettedness is not a likely steady state office environment
scenario, and likely implies a transitional period such as arriving to work from a bike ride or climbing many flights of
stairs. Therefore an office maintained at conditions presented in figure 2b would not be desirable.

Author name /Energy Procedia 00 (2016) 000–000 5
5 10 15 20 25 30 35 40
Air Temperature ◦C
0
5
10
15
20
25
Humidity Ratio (g water/kg dry air)
10%
20%
30%
40%
50%
60%
70%
80%90%
100%
m/s
0.1
0.3
0.5
0.7
0.9
1.1
1.2
1.4
1.6
1.8
5 10 15 20 25 30 35 40
Air Temperature ◦C
0
5
10
15
20
25
Humidity Ratio (g water/kg dry air)
10%
20%
30%
40%
50%
60%
70%
80%90%
100%
m/s
0.1
0.3
0.5
0.7
0.9
1.1
1.2
1.4
1.6
1.8
Fig. 2. (a) Expanded comfort zone for forced convection at MR =1.2 met and w=0.06 when TM RT =Tair, and vair shown by the gradient is
solved for. (b) Expanded comfort zone for forced convection at MR =2 met and w=0.2.
5 10 15 20 25 30 35 40
Air Temperature C
0
5
10
15
20
25
Humidity Ratio (g water/kg dry air)
10%
20%
30%
40%
50%
60%
70%
80%90%
100%
MRT C
18.8
19.2
19.6
20.0
20.4
20.8
21.2
21.6
22.0
22.4
22.8
23.2
23.6
24.0
24.4
24.8
25.2
25.6
26.0
18.5
19.7
20.9
22.1
23.3
24.5
25.7
26.9
5 10 15 20 25 30 35 40
Air Temperature C
0
5
10
15
20
25
Humidity Ratio (g water/kg dry air)
10%
20%
30%
40%
50%
60%
70%
80%90%
100%
m/s
0.1
0.3
0.5
0.7
0.9
1.1
1.2
1.4
1.6
1.8
Fig. 3. (a) Cooling in San Francisco’s Federal Building modeled with a radiant system operating under Tair =TMRT , and (b) more aggressive
natural ventilation system. Singapore climate data is also shown.
4. Discussion
This work provides a new set of visualizations for thermal comfort, and familiarity with radiant and air velocity
setpoints for system control and design can be achieved. To put the model into perspective, San Francisco’s moder-
ate climate was compared to climate conditions in tropical Singapore. Figure 3b uses TMY3 weather data for San
Francisco and Singapore, plotting air temperature and humidity ratio on the xand yaxes, with the color assignment
determined by the prevailing wind speed. A mismatch between the color of a point and the background implies an
uncomfortable condition. If the wind speed is too great, the occupant would likely feel cold, or too blue for slow
wind, and the occupant would feel hot. Figure 3b shows that passive cooling through natural ventilation should be
sufficient, implying solutions should be built in so occupants can reduce the air volume, rather than restrict the air into
the building. Free cooling could also be accomplished with a wet-bulb hydronic radiant cooling system, as shown in
figure 3a. This figure was generated similar to figure 3b, but instead with the assumption that TMRT =Tair for some
type of hydronic radiant system maintaining a TMRT as dictated by Tair . Only a small subset of points are mismatched
as being too warm, which could be addressed with a wet bulb evaporative cooling system for the radiant system.
However this still some form of active system incurring parasitic power costs, unlike the completely passive natural
ventilation system, making radiant cooling in San Francisco less desirable.
Singapore is a good contrasting example, as maintaining occupant thermal comfort is a more challenging endeavor.
Conditions are always hot and humid, and figures 3a and b shows that wind alone and evaporatively driven wet-bulb
cooling cannot always generate comfort. High humidity makes evaporative cooling difficult, and often radiant systems

6Author name /Energy Procedia 00 (2016) 000–000
are avoided as the risk of condensation is believed to be too high. However, a new class of radiant cooling panels [8]
that allow supply temperatures to go below the dew point while avoiding condensation could be used to cool surfaces,
rather than incoming air. And when combined with a desiccant dehumidification system rather than a conventional
sub dew point driven system, power consumption is considerably lower than with conventional systems [11].
However, visualizing the climate conditions in terms of required setpoints for unconventional systems, i.e. radiant
cooling or natural ventilation, helps engineers and architects achieve realistic design opportunities truly based on local
climate. Using the expanded psychrometric chart as a tool, one easily identifies methods other than standard vapor
compression air conditioning approaches that could be used to maintain occupant thermal comfort. Since Singapore
and San Francisco have such different climatic conditions, it makes sense that radiant cooling and natural ventilation,
respectively, may be the most sensible alternative choices. But most importantly, it is also clear that prescribing the
same standard air conditioning systems to the two extraordinarily different design opportunities is also a mistake, and
using such a tool can remedy such situation in the future.
Going one step further in the context of actual buildings, the Federal Building in San Francisco uses passive ven-
tilation where air velocities cannot be set. Unfortunately, the design narrative was not translated in to a comfortable
space with only 32% of occupants reporting feeling comfortable due the lack of freedom with the air velocity. In
Singapore, the 3for2 [11] installation was used as pilot program for desiccant dehumidification with radiant panels,
however radiant temperature cannot be modulated. (The 3for2 post occupancy comfort studies are currently under-
way.) Using a more holistic approach such as the proposed expanded psychrometrics to system design should help
elucidate the methods for better control and design of sustainable building systems.
5. Conclusions
This work was particularly successful at designing a new radiant cooling and natural ventilation framework allow-
ing HVAC engineers and architects design for systems that do not change the air temperature or humidity to provide
comfortable living or working conditions. The theoretical governing equations for controlling such systems were syn-
thesized, and a thermal comfort reference framework within which both air and radiant systems may be adjusted was
developed, intuitively and quickly allowing occupants and operators to visualize which parameters could be modified
to become more comfortable. Future work could look more closely at materials for sub-Td p radiant cooling panels. A
rigorous thermal comfort study should be performed in the high humidity, high temperature, low radiant temperature
region of the expanded thermal comfort zone to fully verify the model.
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