. . .
0 . _
. . . " ~ _ . _ . _ '_ . _ -
DOCUMENTATION GUIDE TABLE' OF CONTENTS", Chapter I - Thermal LO Introduction U Wall and Roof Transmission Loads L2 Glass Transmission 1.3 Solar Gain Loads 1.4 Heat Gains due to People 1.5 Lighting Heat 1.6 Miscellaneous Electrical Heat Gains L 7 Miscellaneous Intemal Gains L8 Transmission Loads through P~ lrWions L9 Infiltration Loads 1.10 Ground Element Transmission Loads 1.11 Safety Factor Chapter 2 - Design System Calculations 2.0 Introduction 2.1 Analysis for Design Cooling Conditions 2.].] Thermal Load Calculations 2.1.2 Supply Air Sizing Calculations 2.1.3 Air System Simulation Calculations
2.2 Analysis for Design Heating Conditions 2.2. IThermal Load Calculations 2.2.2 System Analysis and Sizing Calculations
!-J
1]·2 ]·2 ]-3 ! A IA
,
1-4 1-5 1-5 ]-6 ]·8 2-] 2-J 2- I 2-2 2-4
2-7 2-7 2·8
._J
.
'
+
+ .
, _ '
•
++ _.,~ ~ .
A key facet of the design load and energy analyses is A "thermal" load is the sum of transmission, for a region of the building. In the program the as a "space load".
calculation of thermal loads. internal and solar gain loads load is sometimes referred to
The thermal load is distinguished from a coil load. A removed or added at the coil. It incorporates the f an g ai n a nd p 1e nu m lo ad c ha ra ct eri st ic s.
load is the amount of heat load as well as ventilation,
The purpose of this chapter is to document the basic thyrmalload calculation procedures used in HAIP. These calculations apply to design as well as average load analyses. The procedures here are based on the Carrier rQ O Load Estimating Method. The primary reference for the method is the Carrier Sys'lem Design Manual Pari I: Lo ad E"! :;tim at in g. Separate sections of this chapter deal with each thermal load component. Specific details concerning design thermal !()
Heat transmission through walls and roofs is due to the indoor-outdoor temperature difference and to the transmission of absorbed solar energy. The fundamental transmission equation is: Qw where: Qw I\w
E TD
==
Uw
-
Wall transmission load (lHU/IJr or Wall LJ..value (BTLJ/(hr-sqft-F) or W I(sqm-K))
--
Wall area (sqft or sqm).
--
E quivalent
T em perature
D ifference
or K ).
The ETD value incorporates the considerations of heat transfer due to both the actual indoor-outdoor temperature difference and absorbed solar energy. The basic ETD equation may be expressed as: ET D
= =
K w (R s/R m)C [em "
T es ) + Tes +
where: Kw
= =
Wall or accounts surfaces. 1.00 for 0.78 for 0.55 for
roof color correction factor (dimensionless). This factor for varied absorptivity characteristics of different color dark color surfaces (reference color). medium color surfaces. light color surfaces.
Solar heat gain for wall or roof exposure (BTU/(hr-sqft) or W Isqm). This value is a peak solar heat gain (IPSHG) for design calculations; it is an s olar g ain (A SH G) fo r ty pic al calcu la tio ns. Solar heat gain for the reference condition (BTU I(hr-sqft) or W Isqm). The reference conditions are 40 deg. north latitude, July, s ea le ve l, d es ig n d ew po in t t em pe ra tu re o f 6 7 F (1 9. 4 a nd c le ar s k y conditions. Thus, the (Rs/Rm) ratio COHects for the magnitude of the solar flux on the surface.
LOAD CALCULATIONS
Equivalent temperature difference for sunlit exposures for the reference condition (F or K). Values are obtained from the Carrier Design Manual Tables! 9 and 20. Valucs vary for cach hour, for wall or roof weights and by exposure. Equivalent temperature difference for sh',lded exposures for the reference condition (F or K). Values are.lobtained from the Carrier Design Manual Tables 19 and 20. Values vary for each hour, for wall or roof weights and by exposure.
Tes
Temperature correction factor (F or K). Tern and Tes valucs arc based on a reference outdoor air tempenHure profile. To adapt the ETDs to actual outdoor conditions, corrections for the amplitude and magnitude of the actual temperature pro~ le must be made. This factor is derived in part from Table 20A of the Carrier Design Manual. Tam -Ti - .5 - 5 for English units. Tam - .5 - 2.78 for S.I. Metric Maximum
Tam
temperature
in outdoor
Indoor air temperature
Ti
air temperature
profile (F or C).
(F or C).
Daily temperature range (F or K). This is the difference between maximum and minimum temperatures in the daily profile.
The equation
for heat transmission
through
glass is:
Qg:;;: Ug Ag (T a - Ti) where: Glass transmission
Qg
Ug
--.
Glass U-value
load (BTU/hr
(BTU/(hr-sqft-F)
or W). or W /(sqrn-K».
Glass area (sqft or sqm).
Ag ::;:
Outdoor
--
Indoor air temperature
air temperature
(F or C). (F or C).
Throughout the day the sun shines through windows in the building. This solar energy is absorbed by interior floors, walls and ceilings and is released by convection and radiation over time. To analyze this transient heat gain a set of hourly solar response factors are These factors been normalized for the maximum daily solar flux. Different sets of factors are defined in the Carrier Design Manual for various building weights and for bare glass elements and glass with internal shading devices. The basic solar gain equation for glass with no external shading is: Qsg ::;:(SHG)(SLF)
Fg Ag
where: Qsg SHG
Solar gain load (RTU/hr
or W).
I\Aaximum solar heat value (BTU/(hr-sqft) or W /sqm). This value is the peak solar heat gain for design cooling calculations or the
SLF
=
Storage load factor (dimensionless). This is the solar response value obtained from Carrier Design Manual. Tables 7 through I I for the appropriate glass condition, building weight, cooling equipment operation schedule, exposure and hour.
Fg
=
Glass factor (dimensionless). SHG values are derived for solar nux through a single pane of ordinary glass. To account for different transmission and reflection characteris~ i cs of other types of glass and internal shading devices a correction f
Ag
0 -
Glass area (sqft or sqm).
For solar gains for glass with external shading, the equation Qsg
=
(FeSHGe
+ FsSHGs)(SLF)
is: Fg Ag
where: Fe
_.
Fraction of glass area exposed to sunlight (dimensionless). This value is determined first by evaluating the angIe of incidence for the beam component of solar flux for the hour. Using the angle of incidence with the physical characteristics of the external shading device, the portion of the glass pane exposed to sunlight can be computed. Fraction
of glass area shaded (dimensionless).
I - Fe Maximum (hr-sqft)or .
solar heat gain for the exposed glass (BTU/ W /sqm).
Maximum solar heat gain for shaded glass (BTU/(hr-sqft) or W /sqm). Different SHG values are used because the exposed glass receives beam and diffuse components of the solar flux; the shaded glass receives only diffuse solar.
The human body continuously releases quantities of sensible heat and nlOisture. The magnitude of these heat gains depends upon the level of physical exertion. It is assumed body heat is released directly to the surrounding air. The basic sensible and latent heat gain equations are as follows: Qps = Np Qs
Qp!
= N p QI
where: Sensible component
Qps
of heat gain (BTU/hr
--
Latent component
of heat gain (BTU/hr
--
Scheduled
of people occupying
number
Sensible heat gain rate (BTU/(hr-person) defined by the user.
=
Latent heat gain rate (BTU/(hr-pcrson) defined by the user.
or W). or W).
space for the hour. or W /person). or W /person).
This value is This value is
LOAD CALCULATIONS
LIGHTING HEAT GAIN
Heat gain lights is assumed lighting heat gain is:
to be instantaneous.
The basic equation
for the total
where: =:
Lighting heat gain (BTU/hr
=:
Scheduled
=:
Ballast multiplier (dimensionless). When fluorescent lights are used, the heat gain from the ballast starter device must be considered also. A ballast multiplier factor is used to increase the lighting power PI accordingly. This multiplier is defined by the user and typically ranges from 1.0 to 1.25. For incandescent lights the multiplier is not used.
Fu
lighting power
Unit conversion (3.4]2
or W). level for the hour (W).
factor used to provide heat gain in proper
BTU/hr)/(W)
units.
for English units.
1.0 fOf S.L Metric units.
This load element is used to model heat gain due to miscellaneous electrical machinery such as computers, typewriters, vending machines, etc ... Heat gain from these machines is assumed to be instantaneous. The basic heat gain equation is:
HEAT GAINS
=:
where: Miscellaneous Pme
=:
Scheduled
electrical
or W).
electrical power level for the ham (W).
factor used to provide load in proper units.
12 BTU/hr)/(W) =
heat gain (BTU/hr
miscellaneous
Unit conversion
Fu
INTERNAL HEAT GAINS
Fu Pme
for English units.
1.0 for S.L Metric units.
This load element is used to consider heat gain from miscellaneous non-electrical sources. Heat gai,n is assumed to be instantaneous. Gains considered for both sensible and latent load components. Hourly heat gain quantities are directly specified by the user in the form of a maximum heat gain and hourly scheduling factors. Heat values may be positive or negative. Negative heat values are used to model loads due to refrigeration cases or similar equipment.
L LOAD CALCULA '. --
~ -
Heat transmission through partitions adjacent to a non-conditioned region are considered with this load element. non-conditioned we mean such regions as adjacent parking garages, freezer storage rooms and unconditioned warehouses, The air temperature in these regions may vary in different ways. Therefore two options for analyzing transmission loads through partitions are offered,
AND
Adjacent Region Temperature. The first option is to consider the temperature in the adjacent region as being fixed, This option should be used for regions such as a refrigerated storeroom or an equipment room in which the temperature is relatively constant. The transmission load for this case is computed Qpl = Up Ap (T",-Tj) where:
Transmission
Ap
= = =
Tar
=
Air temperature user.
in adjacent
'Ii
=
Air temperature
in conditioned
Qpt Up
load through
partition
Partition
U-value (BTU/(hr--sqft-F)
Partition
area (sqft or sqm).
(BTU/hr
or W).
or W I(sqm-K»,
region (F or C). This value is defined by the
01 ' huJoor-O!!hloor Pcrcenlage Tempen!lure evaluates the partition temperature difference temperature difference. This method may be garage or unconditioned warehouse in which temperature. The basic transmission equation
space (F or C),
Dillercnce. Thc second option as a fraction of the indoor-outdoor used to model regions such as a parking the temperature varies with outdoor air is:
Qpt ::::Up where: Partition
transmission
Partition
U-value (BTU/(hr-sqft-F)
::::
Partition
area (sqft or
--.
Temperature difference fraction (dimensionless), The fraction of indoor-outdoor ternpcraturc difference to be applied to the partition. Values may range from 0 (0%) to 2,0 (200%).
Qpt
Outdoor
'Ii
load (IBTU/hr or W),
air temperature
Indoor air temperature
or W I(sqm-K)).
or C). (F or C).
Sensible and latent heat gains due to infiltration air arc considered with this load element. Infiltration air is assumed to enter the space at outdoor conditions and leave at the room conditions. The basic equations for this load are:
Qis ::::Pa Vi Cpa Fu (Ta -
Tn
Qil ::::Pa Vi hfg Fu (wa - wi) where:
Qis Qil
=
Sensible infiitration Latent infiltration 1-5
(BTlJ lor or W). load (BTU/hr
or W).
LOAD CALCULATIONS
Pa
= =
::::
Ps!
= =
Density
of
Value is adjusted
for site elevation.
Psi Pba / Psi De'o.sity of air
standard
sea leve! conditions
(0.075 Ibm/ft3
pressure at site elevation
(psia or kPa).
or 1.201 kg/m
3).
Pba
-
Standard
atmospheric
--
14.696 (l - 6.87535
5
10 1.3 (1 - 2.25569 PsI
==
Standard
x J 0-6E)5.256! x 1O- E)5.2561
atmospheric
for English units. for Metric units.
pressure at sea !eve! (14.696
psia or
101.3 kPa). E
Site elevation Infiltration
Cpa
(fed or meters above sea level).
air flow rate (CFM
Specific heat of air. Standard
or Lis). values used arc 0.24 BTU/(lbm-F)
or
lO04.832 J/(kg-K). Fu
Conversion
factor used to provide
60 min/hr
for English units.
m3 /(lOOO
L) for SJ. Metric units.
Ta
Outdoor
Tj
Indoor air temperature
hfg
load in correct units.
air temperature
Heat of vaporization
2.4535x10
6
or C). or C).
for water. Values used are 1054.8 BTU/lbm
or
J/kg.
Heat loss through floors on or below grade and through walls below grade are computed only for the heating design condition. Heat transmission through ground clements for other conditions is not evaluated. Transmission loads are computed using empirical equations derived for the Carrier QO Method. This method is appropriate only for heat loss through concrete or ~ masonry walls and floors, and only for the heating design condition. A study of ground heat loss showed that ground temperatures below 8 ft (2.44 m) are relatively stable regardless of outdoor air temperature. Between the 8 ft (2.44 m) depth and the surface, ground temperature varies with outdoor temperature more appreciably. Further, research showed that heat loss through floor elements was relatively independcnt of depth below grade, while heat loss through the perimeter of the floor was dependent upon depth. Because of these considerations, the E20 method analyzes ground transmission loads ill components. These arc floor loss, perimeter floor loss, wall transmission below an 8 ft (2.44 depth and wall transmission abovc an 8 ft (2.44 m) depth. These load components are discussed below.
Floor Loss. Heat transmission
through
the floor to the ground
below is evaluated
with the following equation. = =
Uf(Tg _ Tj)
Perimeter Floor Loss. To evaluate heat loss through the perimeter
of floors, a set of thermal resistance factors were derived to account for the insulating effcct of the floor material and of the ground at various depths. Heat loss is computed Ilsing the following equation: Qfp
= =
Lfp Fp (Tad - Tn
~ . __ ._ ~ ~ _ . _ . _ _ . _ -
THERMAL LOAD CALCULAI10NS
Wall Loss Above a Depth of 8 n m). To analyze heat loss through the portion of the wall between grade level and 8 ft (2.44 m) below grade, a set of factors were empirically derived to account for the insulating effect of the wall and ground at various depths. The basic tra~ s mission equation for this load component is:
=
Qw!
Lwp Fp (Tad - Ti)
Heat Loss for Wails More thalli 8 n (2.44 m) Below Grade. If basement walls exist below a depth of 8 ft (2.44 m), a separate analysis is used to determine the heat I.oss for this section of waIL The transmission equation for this section of the wall is:
=
Qw2 Variable
Uw Aw (Tg - Ti)
Defilliitiollls:
Qn
Floor transmission
load (BTU/hr
Qfp
Heat loss through
floor perimeter
1
=
Af
=
wall area below 8 ft (2.44 m) depth (BTU/hr
Floor area (sqft or sqrn).
Floor U-value. An assumed value of .05 BTU/(hr-sqft-I<') or .28 W I(sqm-K) is used. This value models a concrete or masonry floor.
Uf
Wall U·~ v alue. An assumed value of .08 BTU/(hr-sqft-F) or .45 \V I(sq m-K ) is used to mode! concrete or masonry walls.
Uw =
Lwp IFp
grade and 8 ft (2.44 m) below
Basement wall area (sqft or sqrn). For Qw I this is the area between grade and an 8 ft (2.44 m) depth. For Qw2 this is the area below an 8 ft (2.44 m) depth.
Aw
Lfp
(BTU Ih r or W).
Heat loss through wall area between grade (BTU/hr or W). Heat loss through or W).
Qw2
or Vv').
=
Floor perimeter
(ft or
Wall perimeter
length
or m).
Perimeter factor (BTU/(hr-ft-F) or W I(m-K»). This factor accounts for the thermal resistance of the floor or wall and the ground at varying depths. The perimeter factor is applicable from grade level to 8 ft (2.44 m) below grade. For floors more than 8 ft (2.44 m) below grade, the perimeter factor at the 8 ft (2.44 m) level is used. The empirical equation for the factor is: 0.60 - + 0.075(D) for English Units 1.0384 - + .4259(D) for S.I. Metric Units Ground temperature below floor (IF or C). This value is obtained from an empirical equation: 55 - + . s Tad for English units. 21.67 - + .5 Tad for SJ. Metric units. Indoor air temperature
(F or C).
Heating design outdoor
air temperature
Depth below grade grade level to the
or C).
or m). For floors, this is the distance from of the walL
CALCULATIONS
F or d es ng n l oa d c al cu la ti on s a f ac to r i s i nt ro du ce d t o p ro vi de a m ar gi n o f s af et y in the design. The safety factor is defined by the user. The safety load is computed by multiplying each·of"the space sensible and latent thermal load componenl<; by the factor.
~ _ ._ _ ._ _ ._ _ ._ ._ _ ._ ._ _ .-
..-
CIIAPTER
DESIGN SYSTEM ANALYA-9IS CALCULATIONS 'h..._J ~
-
'~ -'''''~ ~ '_'-;'' '_'_''''_'T'k~ . . . -
..
The purpose of the design analysis is to determine system coil loads and air flow characteristics for cooling or heating design conditions. The analyses typically involve three stages: The Thermal Load Calculation Stage determines the heat quantity or removed from the spaces in order to maintain comfort conditions.
to be added
The Sizing Stage involves computation of supply air characteristics required to meet the thermal loads. In the special case of hydronic heating system design, sizing involves computing a required water flow rate. The System Analysis Stage. System operation is simulated to determine the cooling or heating coil load. Coil loads arc in turn used to size the cooling or heating plant The purpose of this chapter is to describe procedures for both cooling and heating design analyses. The following discussions will be useful in interpreting and utilizing data on program printouts. Separate sections arc devoted to each analysis.
YSIS FOR DESIGN COOLING CONDITIONS
Design cooling analyses are performed onan hourly basis. Each of the three analysis stages is described below. For these calculations the indoor temperature is fixed at the specified cooling setting. The outdoor conditions are obtained from the design temperature profiles.
1.1 Thermal Load Calculations The first stage in the analysis involves the calculation of thermal loads. General thermal load calculation procedures were described in Chapter!. To apply these procedures for cooling design conditions, loads arc computed using considerations listed in the Table 2.1.
2-1
DESIGN
ANALYSIS
CALCULATIONS
TABLE 2.1 Considerations
For Cooling Design Thermal Loads _ .
T l J er m a l lo a d
C onsiderations
C om ponent
-
W all
&
C o m p u t e n o s u s in g p e a k s o l a r g a in s . c o o li n g d e s ig n l em p e r at u re p r o fi le d a ta a n d t h e d a il y r a n g e l o r d e s ig n d a y s.
R oof T ransm ission
-
C o m p u t e u s i n g d e s i g n t e m p e r a t u re
G lass T ransm ission
p r o f i le d a t a . " . -
S o!ar G ains
U t il i ze p e a k s o l a r g a i n d a t a t o m o d e ! c l e a r s k y conditions. ______
!otem al
H
_
C o m p u t e u s i n g d e s i g n d a y s c h e d u l es . ~ . _ " -
U i if i z e s p e c i fi e d c o o l in g v a l u e s f o r t h e t e m p e r a tu r e d i ll e r en c e a c r o s s t h e p a r t it io n .
P ar!i!ioo T ransm ission
-----------------
. . ----.< ---"---.-
In filtra tio n
U se sp ecified c o o lin g d esig n in filtra tio n air !low rales.
G r o u n d E l e m e n t T r a n sm i ss io n
T h i s l o ad i s n o t c o n si d er e d l o r c o o li n g c a lc u la l io n s . T i m E 2 0 l o a d c a l c u l a ti o n p r o c e d u r e l o r t h i s e l e m e n t i s a p p r o p r ia t e o n l y lo r h e al i n g d e s i g n c a l c u la t io n s .
.
S a fe ty F a clo r lo ad
_ . _ _ . ~ -
C o m p ute usin g sp ec ifie d c oo lin g sa le ly l ac to r. ~
P le n u m lo ad
-
C o m p u ted a s a p erc en ta g e 0 1 t h e t o l a l m o l a n d I o t a ! l ig h t in g l o ad s . I n d iv i d ua l p e rc e n ta g e s l o r e a c h c o m p o n e n t a r e l is e I ' - s u p p l ie d . -
1.2 Supply
Sizing
The next stage in the analysis is to derive supply air characteristics. The purpose of the cooling system is to provide conditioning to meet a thermal load. To do this a quantity of chilled air at a certain temperature is provided to the space. Thus, characteristics of supply air are air How quantity and temperature. The user has specified one of these characteristics. It is the program's job to compute the other quantity. uppIy ~ airf1Qw rates are computed both on a space and zone basis. Supply temperature iscomputed ol1Iyon basis. SIzing calculations on the zone and space levels are described below.
DESIGN SYSTEJv! ANALYSiS
Space Slupply Air Calculations. These computations depending upon the user supply air specification.
take one of three forms
I. Given the supply flow rate per unit !loor area, the flow rate is computed as shown below. Note that this quantity is not ,elated 1. 0 a specific system supply temperature, or even to the space load.
V sa
Vaf Afs
==
where: Vsa
'.
Supply air flow rate (CFM or Lis).
Vaf
= =
Supply !low rate per unit nom area (CFM/sqft
= =
Space floor area (sqft or sqm).
or L/(s·sqm)).
2. If the total supply air flow rate is given for the zone, the program has no basis for computing a space How rate. Consequently, none is computed or reported. 3. Given the supply temperature, the following equation for
the space supply flow rate is computed
by solving
Qss::: Pa Vsa Cpa Fu (Tc ..Tsa) where:
\ /
'"
Qss
include plenum pa
Density
= =
Co
/
load
( .~) ~ or W). This load does not
heat gains.
of air. Value is adjusted
for site elevation.
Psi Psi/ Pba
--
Density of air for standard
Ps I
sea leve! conditions
(0.075 Ibm/ft.3
or 1.201 kg/m]). Standard -
--
atmospheric
14.696 (! - 6.87535 J
Psi
%
Space sensible t hermal
0 1. 3 (I .. 2.25569
Standard
pressure at site elevation x lO-6E)5.256!
x I O-~ : E)5.2561
atmospheric
(psia or kPa).
for English units. for Metric units.
pressure at sea leve! (i 4.696 psia or
lOJ.3 kPa). E Cpa
-
Site elevation
(feet or meters above sea level).
= =
Specific heat of air. Standard
values used are 0.24 BTU/(lbm-F)
or
1004.832 J/(kg-K). Fu
= =
Con version f~ l ctor 60 min/hr
--
3 /(1000
01
to provide load in proper units.
for English units. L) for S.!. Metric units.
Tc
Indoor air temperature
for cooling (F or C).
Tsa
Supply air temperature
(F or C).
Zone Supply
Air Calculations.
the user supply air specification.
Calculations
again take three forms depending
upon
SYSTEM ANALYSIS CALCULAI10NS
i. Given the supply air flow rate per unit 1100r area, the zone flow rate is computcd as: Vsa:::: Vsf Afz where: Vsa
=
Zone supply air flow rate (CFM or Lis).
Vsf
Supply air flow per unit floor area (CFM/sqft
Afz
Zone floor area (sqft or sqm). This is the sum of space floor areas for all spaces in the zone.
Next, the required equation for Tsa.
supply air temperature
is computed
or LI(s-sqrn)).
by solving the following
Qzs ::::Pa V sa Cpa Fu (T c - Tsa) where: Q 5 ZL 7
: :: :
Zone sensible thermal
load (BTU /hr or W).
Density of air (lbm/ft3 or kg/m3). Values arc adjusted elevation. See previous discussion for calculation.
Pa
Specific heat for air. Values used are .24 BTU/(lb-F) 1004.832 J/(kg-K).
Cpa
Fu
Conversion
for site or
factor used to provide load in proper units.
(60 min)/hr
for English units.
m3 /(l000 L) for S.L Metric units.
Tc
--
Tsa
Indoor air temperature
for cooling (F or C).
Supply air temperature
(F or C).
2. If given the total supply air flow rate, only the supply temperature determined. The following equation is solved for Tsa.
needs to be
Qsz:::: Pa V sa Cpa Fu (Tc - Tsa)
3. If given the supply air temperature, determined.
only supply air flow rates needs to be equation is solved for Vsa.
The following Qsz
=
Pa Vsa
(Tc - Tsa)
1.3 Air System Simulation Calculations The final stage is the system simulation. The analysis procedure involves computing air flow rates, dry-bulb temperatures and humidities at all key points in the system. The coil inlet and outlet conditions are then used to determine the cooling coil load. Space sensible, latent and plenum thermal loads, supply air characteristics, system operating characteristics and weather conditions are utilized in the analysis. Individual aspects of the simulation are discussed below. Zone Thermal Loads are computed as the sum of space thermal loads for all spaces in the zone. Separate totals are determined for the sensible, latent and plenum load components.
""---_._-----~
~ _ .-
-
._ ~ -
DESIGN SYSTEM ANALYSIS
CALCULATIONS
Ventilation Loads. The quantity of air entering the system through the ventilation duct and quantities of air exhausted directly from the zone and exhausted from the return duct result in a heat gain or loss for the system. The ventilation load is computed separately for sensible and latent components: Qvs = , Pa Vva Cpa Fu (Ta - Tzc) + Pa Vre Cpa Fu (Tze - Tre) Qvl '" Pa Vva hlg Fu (wa - we) where: Sensible ventilation
Qvs Qvt
-~
Vva
Latent ventilation Ventilation
load (BTU/hr load (BTU/hr
or W). or W).
air flow rate (CFM or Lis).
Air flow exhausted
from return duct (CFM or
Air density (lbm/ft3 or kg/013). This value is adjusted elevation, See 2.1.2 for calculation details.
Pa
Heat capacity
Cpa
of air (.24 BTU/(lbm-F)
Heat of vaporization
hfg
2.4535
or 1004832 J/(kg-K».
for water. Values used are 1054.8 BTU/lbrn
or
106 J/kg.
x
Outdoor
for site
air temperature
(F or C).
Air temperature for air exhausted from return duct or return plenum (F or C). This temperature may differ fro-m-T-ze-'d~ l e to-plenum heat gains. Air temperature for air exhausted directly from the zone (F or This is the specified indoor temperature for cooling. Outdoor
air specific humidity
Exhaust air specific humidity Conversion
Fu
60 min/hr m3 /(l000
(Ibm/Ibm (Ibm/Ibm
or kg/kg). or kg/kg).
factor used to provide load in proper units. for English units. for S.I. Metric units.
Supply Fan Heat Gain is due to friction between air and the 1~ lI1 blades, energy added to the air by compression, energy loss in the drive mechanism and heat gain from the fan motor. Assuming the fan motor is in the air stream, the fan heat gain equation is:
where: Qf
'
Fan heat gain (BTU/hr Air !1ow rate through
or W). fan (CFM or L/s).
Ts
Total static pressure across fan (in wg or Pa).
flf
Fan drive and mechanical to be 0.55 (55%).
Fan motor efficiency (dimensionless). 0.90 (90%).
11m Fu
efficiency (dimensionless).
= =
Conversion
= =
.4003 for English units.
'"
factor used to provide
(62.3 Ibm water/cuft)(ft/J2
Value assumed
Value assumed to be
heat gain in proper units.
io)(60 min/hr)(.00J285
BTU/ft-Ib)
SYSTEM ANALYSIS
CALCULATIONS
Cooling Coil Loads. Once coil inlet and outlet conditions are defined, the cooling coil load is computed. Sensible and latent load components are calculated separately.
= =
Qcs QcI
pa Vsa Cpa Fu (Tci - Tco) Pa Vsa hfg Fu (wci - wco)
where: Qcs QcI pa
= =
Coil sensible load (BTU/hr
-.
Air density (lbm/H3 or kg/m3).
Vsa
-
Values are adjusted
Heat of vaporization of water (1054.8 or 2.4535 x !O 6 J/kg).
Tci
Air temperature
at coil inlet (F or C).
Tco
Air temperature
at coil outlet (F or C).
Wco Fu
or 1004.832 J/(kg-K).
Supply air flow rate (CFM or L/s).
hfg
Wci
for site elevation.
details.
of air (.24 BTU/(lbm·-F)
Heat capacity
Cpa
or W).
Coil latent load (BTU/hr See 2.1.2 for calculation
or W).
= = = =
(60 min)/hr
--
m 3 /(1O O O
BTU/lbm
Air humidity
ratio at coil inlet (Ibm/Ibm
Air humidity
ratio at coil outlet (Ibm/Ibm
Conversion
factor used to provide
or kg/kg). or kg/kg).
load in proper units.
for English units. L) for SJ. Metric units.
The coil outlet humidity is computed using the bypass factor relations. The coil bypass factor is a measure of the approach of the outlet coil state to the apparatus dew point (AD?) condition. The first step in computing Wco is to determine the AD? state. It is computed using the equations: BF:::: (T co-T adp)/(T
ci-Tadp)
::::(wco-wadp)/(wci-wac!p)
::: (Tco - TciBF)/(I
- BF)
where: BF
--
Coil bypass factor (dimensionless).
Tadp
Apparatus
dew point dry buJb temperature
wac!p
Apparatus
dew point humidity
(F or C).
ratio (Ibm/Ibm
or kg/kg).
Since the apparatus dew point state is a saturated condition, we can determine wadp using Tadp and psychrometric relations. Next, Wco is computed using the equation: Wco
=
BF (wci - wadp) + wadp
Finally, the total coil load is the sum of sensible and latent load components.
. . . . -
DESIGN SYSTEM ANALYSIS CALCULATIONS
Design heating loads are computed for one design condition. This condition is not associated with a particular hour. For these calculations the outdoor winter design dry-bulb temperature, and the specified indoor heating temperature are utilized. The analysis stages are discussed separately below.
2.2.1 Thermal Load Calculations The first stage in the analysis is the calculation of thermal loads. General thermal load calculations were described in Chapter 1. Heating design thermal load calculations follow the traditional procedure of considering only transmission and infiltration loads. Internal heat gains are not evaluated. Individual considerations for each load component are listed in Table 2.2.
Table 2.2 Thermal Load Calculations For Heating Design Condition
\ -~ _ ..._._._._-_.
-..... . . . . . . -
load Com ponent
.....--..-.--.-..---.------
.. . ' . . -. .-
Considerations
Wall & Roof Transmission
An actual temperature difference is used in place of the equivalent temperature difference (EHI). This eliminates the consideration of the transmission of stored sofar hea!.
Glass Transimssion
Computed using outdoor air temperature for design condition.
Solar Gains
Not considered. ---~ ._---"-------------------'------_._----_
Intema! Gains
-------.--_._---------------_. .._------------~
_ _ ._ - - _ ..-
Nol considered.
~ _ . _ . -
Partition T rallsmission
Utilizes specified heating values for the temperature difference across the partition.
~ ~ ~ _ . _ . _ ~ _
Infiltration -
Ground E!ement Transmission
.. ------.----------.------ ... -.---.
Infiltration air flow fate for heating condition utilized. ~ _ . _ _ . _ -
Considered as discussed in Chapter 1. _ .." _ .-
Safely F actor load -
Computed using specified heating safety factor. -
. ..
-
SYSTEM ANALYSIS
CALCULATIONS
2.2.2 System Analysis and Sizing Calculations The final two stages of the analysis are performed in different orders depending upon the heating system type. These stages define system sizing characteristics and the design heating coil load. The purpose of the heating system is to provide conditioning to meet a thermal load. For warm air systems, this is done by providing the proper quantity of air at a specified temperature. For hydronic systems, it is accomplished by providing a quantity of hot water at a certain temperature level. Given sizing characteristics, the heating coil load can be computed and used to size the heating plant Calculations for the two types of heating systems are discussed below. Warm Air Heating Systems. Given space sensible thermal loads and the userspecified supply temperature, the required air now rate is computed by solving the following equation for Vsa .. Qss
=
Pa Vsa Cpa Fu (Th - Tsa)
where: Qss
Space sensible thermal load (BTU/hr or W). This load includes both space and plenum sensible thermal load components. By CtH1\('n(i\\\~ , a heating load is a negative quantity denoting heat loss from the space. Air density (lbm/ft3 or kg/m 3 ). Values are adjusted See 2.1.2 for calculation details.
Pa Cpa
Specific heat of air (.24 BTU/(lbm-F)
Vsa
Supply air flow rate (CFM or Lis). Indoor temperature
Th Tsa Fu
Supply air temperature
=
Conversion
(F or C).
factor to provide load in proper units. for English units.
m 3 /(lO O O
The zone
or 1004.832 J/(kg-K).
for heating (F or C).
--
60 min/hr
for site elevation.
L) for S.L Metric units.
now rate is simply the sum of space flow rates.
Having sized the system, the heating coil load can be computed. Instead of simulating system operation, the coil load is computed as the sum of space thermal loads and the ventilation load. This procedure is used because fan heat gain is not considered for the heating design condition. The design load is: Qhc = - (Sum of Qss values) - Pa Vva Cpa Fu (Ta - Th) where: Qhc
Design heating coil load (BTU/hr or W). For convenience, we report the heating coil load as a positive quantity. Note that in this equation, Qss values are negative indicating a thermal heating load.
Vva
Ventilation
= Ta
air flow rate (CFM
Indoor temperature Outdoor
or L /s )_
for heating (F or C).
air temperature
for heating design condition
(F or C).
DESiGN SYSTEM
NALYSIS CALCULA110NS
Hydronic Heating Systems. Given space sensible thermal loads and a user-defined hot water temperature drop across heating coils, required water flow rates are computed by solving the following equation for V w: - Qss = Pw Vw Cpw Fu (WTD) where: Space sensible thermal load (BTU/hr or W). Note that by convention a sensible heating load is a negative quantity. Pw Cpw
Vw WTD
Density of water (62.0 Ibm/ft3 at 100 1 7 (37.8 C) are used.
--
Specific heat ofwater(J.O
= =
Fu
or 993. I kg/m3).
Hot water temperature Conversion
Of
for water
or 4186.8 J/(kg-K».
BTU/(lbm-F)
Hot water flow rate (gallons/min
Conditions
L/s).
drop across coil (F
Of
K).
factor used to provide load in proper units.
=
(60 min/hr)(.
-
m3 /(1000
J
3668 ft3/gaI) for English units.
L) for SJ. Metric units.
In addition, a water flow rate is computed to meet the ventilation load. The total zone hot water flow rate is the sum of space and ventilation load flow rates. F"inally, the design ventilation
load.
Mathematically,
heating
Fan
coil load
heat gains
is the slim of space
are not considered
sensible
thermal
loads
and
the
for this calculation.
the design load is: Qhc
= -
(Sum ofQss
values) - Pa Vva Cpa Fu (Ta - Th)
where: Design heating coil load (BTU/hr or W). Note that for convenience we report the heating coil load as a positive quantity. In this equation, Qss values arc negative since they represent thermal healing loads.
Qhc
Ventilation -.
air flow rate (CFM or Us).
Indoor temperature Outdoor
for heating (F or C).
air temperature
for heating design condition
(F or C).
