convective heat input, the heat flow into these nodes may be written as (see also Appendix 5.A3, section 5.A3.5):
Heat flow to air node:
Φ–a= Cv(θ–ai– θ–ao) – hcΣA (θ–m–θ–ai) (5.158) Heat flow to environmental node:
Φ–e = Σ(A U) (θ–ei– θ–eo) + haΣA (θ–ei–θ–ai) (5.159) The method also defines the following relationships:
(a) Environmental temperature:
θ–ei= 1/3θ–ai+ 2/3θ–r (5.160) (b) Operative temperature
θ–c= 1/2 θ–ai + 1/2θ–r (5.161) The definition of environmental temperature follows from the introduction of standard heat transfer coefficients (see Appendix 5.A3, section 5.A3.5). It is therefore rational to use the same coefficients in the following derivation. That is:
hc= 3.0 W.m–2.K–1
6/5εhr= 6.0 W.m–2.K–1 ha= 4.5 W.m–2.K–1
Now, all gains to the space have been expressed in terms of gain to the air and environmental temperature nodes.
Therefore to calculate the heating or cooling load to maintain to a specific operative temperature it is necessary to eliminate θ–eiand θ–ai from equations 5.158 and 5.159, while for a specific air temperature, θ–ei and θ–c are not required. Rearranging equation 5.161 and substituting into equation 5.160 provides the following relationships that can be used to eliminate the unwanted variables:
θ–m= 2 θ–c– θ–ai (5.162) θ–ai= 4 θ–c– 3 θ–ei (5.163) Substituting for θ–mand replacing the heat transfer coeffi- cients with the standard numerical values given above, equation 5.158 gives:
Φ–a+ Cvθ–ao+ 6.0 ΣAθ–c
θ–ai= ——————————– (5.164)
Cv+ 6.0 ΣA
Similarly, equation 5.159 gives:
Φ–e + Σ(A U) θ–eo+ 18.0 ΣAθ–c
θ–ei= ————————————–– (5.165)
Σ(A U) + 18.0 ΣA
5.A5.3.1 Convective heating/cooling source for control on operative temperature Equations 5.164 and 5.165 together with equation 5.163 can be manipulated to give the convective heat input (Φ–a) for control at a specific operative temperature as:
Φ–a= Cv(θ–c– θ–ao) + Fcu[Σ(A U) (θ–c– θ–eo) – Φ–e] (5.166) where:
3.0 (Cv+ 6.0 ΣA)
Fcu= ———————— (5.167)
Σ(A U) + 18.0 ΣA
The steady state, or mean, load for control of operative temperature is calculated by including solar gains, occu- pancy gains and equipment and lighting gains in equation 5.161. These gains comprise both radiant and convective components. In the case of radiant gains, 150% is released as a gain to the environmental node and 50% as a gain to the convective node, see Appendix 5.A3, section 5.A3.5. Thus the mean convective cooling load is:
Φ–a= Cv(θ–c– θ–ao) + Fcu[Σ(A U) (θ–c– θ–eo) – Φ–e– 1.5 ΣΦ–rad] – ΣΦ–con+ 0.5 ΣΦ–rad
(5.168) where ΣΦ–radand ΣΦ–conare the sums of the daily mean radiant and convective gains, respectively (cooling loads are negative).
The extension of this calculation to cover a combination of convective and radiant heating or cooling sources is given below, see section 5.A5.3.3.
Note that in equation 5.168 and elsewhere, the shortwave radiant component of lighting, i.e. the visible light, is assumed to form part of the longwave radiant component.
5.A5.3.2 Convective heating/cooling source for control on air temperature
In this case, equation 5.163 is used to provide a value for θ–c in equations 5.164 and 5.165, thus:
Φ–a= Cv(θ–ai– θ–ao) + Fau[Σ(A U) (θ–ai– θ–eo) – Φ–e– 1.5 Σ Φ–rad] – ΣΦ–con+ 0.5 ΣΦ–rad
(5.169) where:
4.5 ΣA
Fau = ———————– (5.170)
Σ(A U) + 4.5 ΣA
The calculation then follows that for control on the operative temperature, see section 5.A5.3.1.
5.A5.3.3 Combined convective and radiant heating/cooling sources for control on operative temperature
If the emitter output is Φp with a radiant fraction of R (where R = 1.0 for a 100% radiant load), then the heat supplied to the air node (Φpa) is:
Φpa= Φp(1 – R) – 0.5 ΦpR = Φp(1 – 1.5 R) (5.171) and the heat supplied to the environmental node (Φpe) is given by:
Φpe= 1.5 QpR – Φsg (5.172)
where Φsgis the solar gain (W).
From equation 5.168, by replacing Φ–aand Φ–eby Φ–paand Φ–pe, respectively, and substituting from equations 5.171 and 5.172, the daily mean, or steady state, load is:
Φ–p= F1cu[Σ(A U) (θ–c– θ–eo) – Φ–sg– 1.5 ΣΦ–rad] + F2cu[Cv(θ–c– θ–ao) – ΣΦ–con+ 0.5 ΣΦ–rad]
(5.173) where:
3.0 (Cv+ 6.0 ΣA)
F1cu= ———————————————–––––––
Σ(A U)+18.0 ΣA+1.5 R [3.0 Cv– Σ(A U)]
(5.174)
Σ(A U) + 18.0 ΣA
F2cu= ———————————————–––––––
Σ(A U)+18.0 ΣA+1.5 R [3.0 Cv– Σ(A U)]
(5.175) For the purposes of calculation of the steady state design heat loss (where all internal gains are ignored), equation 5.173 reduces to:
Φ–p= [F1cuΣ(A U) + F2cu Cv] (θ–c– θ–ao) (5.176) where it is assumed that θ–eoand θ–aoare equal.
The corresponding air temperature, θai, is obtained by substituting Φpafor Φain equation 5.164 and then replacing Φpaby Φpusing equation 5.169, hence:
Φp(1 – 1.5 R) + Cvθao+ 6.0 ΣAθc
θai= ——————————————— (5.177)
Cv+ 6.0 ΣA
5.A5.3.4 Combined convective and radiant heating/cooling sources for control on air temperature
In this case, the emitter load relationships given by equations 5.171 and 5.172 are substituted into equation 5.169 to give:
Φ–p= F1au[Σ(A U) (θ–ai–θ–eo) – Φ–sg– 1.5 ΣΦ–rad] + F2au[Cv(θ–ai–θ–ao) – ΣΦ–con+ 0.5 ΣΦ–rad]
(5.178) where:
4.5 ΣA
F1au= ——————————–––– (5.179)
(1 – 1.5 R) Σ(A U) + 4.5 ΣA Σ(A U) + 4.5 ΣA
F2au= —————————— ––– (5.180)
(1 – 1.5 R) Σ(A U) + 4.5 ΣA
For the purposes of calculation of the steady state design heat loss, equation 5.178 reduces to:
Φ–p= [F1auΣ(A U) + F2auCv] (θ–c– θ–ao) (5.181)
5.A5.4 Alternating component of cooling load
5.A5.4.1 Convective cooling for control on operative temperature
This may be derived in a similar way to that for the mean cooling loads. However, in this case the fabric heat load is dependent on the thermal admittance of the surfaces. Thus the heat flow to the air node is:
Φ~at= Cvθ~ait– hcΣA (θ~mt– θ~ait) (5.182) Note: equation 5.182 assumes that changes in the ventila- tion load due to fluctuations in external temperature are taken into account separately.
Heat flow to the environmental node is:
Φ~et= Σ(A Y) θ~eit+ haΣA (θ~eit– θ~ait)
+Σ(A f Uθ~eo) + Φ~sg (5.183) where Φ~sgis the solar gain at the environmental node (W).
Note: it is assumed that phase differences are not signifi- cant.
Thus the alternating component of the cooling load for control to the operative temperature is:
Φ~at= Cvθ~ct+ Fcy[Σ(A Y) θ~ct+ Σ(A f Uθ~eo) – Φ~sg– 1.5Φ~rad] – ΣΦ~con+ 0.5 Φ~rad (5.184) where:
3.0 (Cv+ 6.0 ΣA)
Fcy= ———————— (5.185)
Σ(A Y) + 18.0 ΣA
Note: θ~ct= 0 for 24-hour plant operation.
5.A5.4.2 Convective cooling for control on air temperature
The alternating component of the cooling load for control to the air temperature is:
Φ~at= Cvθ~at+ Fay[Σ(A Y) θ~at– Φ~et– 1.5 ΣΦ~rad– Φ~sg] – ΣΦ~con+ 0.5 Φ~rad (5.186) where:
4.5 ΣA
Fay= ———————— (5.187)
Σ(A Y) + 4.5 ΣA
Note: θ~at= 0 for 24-hour plant operation.
5.A5.4.3 Combined convective and radiant cooling for control on operative temperature
The emitter load relationships given in section 5.A5.3.3 can also be applied to the alternating component of the emitter
load. In this case substitution of equations 5.171 and 5.172 into equation 5.176 gives:
Φ~pt= F1cy[Σ(A Y) θ~ct+ ΣA f U θ~eo– 1.5 ΣΦ~rad– Φ~sg] + F2cy[Cvθ~ct– ΣΦ~con+ 0.5 ΣΦ~rad]
(5.188) where:
3.0 (Cv+ 6.0 ΣA)
F1cy= ———————————————––––––
Σ(A Y) + 18.0 ΣA+1.5 R [3.0 Cv– Σ(A Y)]
(5.189)
Σ(A Y) + 18.0 ΣA
F2cy= ———————————————–––––––
Σ(A Y) + 18.0 ΣA + 1.5 R [3.0 Cv– Σ(A Y)]
(5.190) Note: θ~ct= 0 for 24-hour plant operation.
5.A5.4.4 Combined convective and radiant cooling for control on air temperature Substitution of equations 5.171 and 5.172 into equation 5.186 gives:
Φ~pt= F1ay[Σ(A Y) θ~at+ ΣA f U θ~eo– 1.5 ΣΦ~rad– Φ~sg] + F2ay[Cvθ~at– ΣΦ~con+ 0.5 ΣΦ~rad]
(5.191) where:
4.5 ΣA
F1ay= ———————————— (5.192)
(1 – 1.5 R) Σ(A Y) + 4.5 ΣA Σ(A Y) + 4.5 ΣA
F2ay= ———————————— (5.193)
(1 – 1.5 R) Σ(A Y) + 4.5 ΣA
Note: θ~at= 0 for 24-hour plant operation.
5.A5.5 Effect of allowing room temperature to rise above set point
The peak cooling capacity can be reduced if the room temperature is allowed to rise above the set point for a period sufficiently short that the effect on the mean temperature is small (e.g. two hours at the time of peak load). Because the mean is not changed, the reduction may be calculated from the alternating component of the gain, i.e. from either equation 5.184 or equation 5.186. Thus for control on the operative temperature, the change in load becomes:
ΔΦk= [cpρqv+ FcyΣ (A Y)] Δθc (5.194) For control on the air temperature:
ΔΦk= [cpρqv+ FayΣ(A Y)] Δθai (5.195) where ΔΦkis the change in cooling load resulting from a small change in temperature (Δθ), cpis the specific heat capacity of air (Jã kg–1.K–1), ρ is the density of air (kgãm–3), qvis the total ventilation (mechanical plus infiltration) rate (m3.s–1), Fcyis the room admittance factor with respect to operative temperatures, Fayis the room admittance factor with respect to the air node, Σ (A Y) is the sum of the products of surface areas and their corresponding thermal admittances (WãK–1), Δθc is the rise in operative tem- perature (K) and Δθaiis the rise in internal air temperature (K).
5.A5.6 Summertime temperatures
The Simple (dynamic) Model may be used to assess peak temperatures when there is no heating or cooling. The method used is essentially the inverse of the cooling load calculation. However, further simplifications are intro- duced to enable rapid hand checks on designs.
The intent of the calculation is to obtain the peak operative temperature, which is achieved using a trans-position of equations 5.166 and 5.167. Thus from equation 5.166 the daily mean operative temperature is:
Cvθ–ao+ FcuΣ(A U) θ–eo+ FcuΦ–e+ Φ–a
θ–c= ———————————————— (5.196) Cv+ FcuΣ(A U)
where:
Φ–a= Φ–con
Note that for glazed surfaces, θ–eo=θ–ao.
The alternating operative temperature follows from equation 5.188:
Φ–a t+ FcyΦ–e t
θ~ct= ——————–– (5.197)
Cv+ FcyΣ(A Y)
where:
Φ–a t= ΣΦ–con
Equation 5.197 is based on the ventilation rate remaining constant throughout the day. An assessment of the effect of a varying ventilation rate is given by Harrington-Lynn(A5.1).
Reference for Appendix 5.A5
A5.1 Harrington-Lynn J The admittance procedure: variable ventilation Building Serv. Engineer 42 99–200 (November 1974)
5.A6.1 Introduction
This appendix describes the way room cooling loads are calculated using the CIBSE admittance method. The solar position and transmission algorithms are those used to produce the cooling load tables in the 1999 and earlier editions of Guide A. Other calculations follow the equations presented in Appendix 5.A5 which, although different in appearance, are identical to those in editions of Guide A preceding the 1999 edition.
The solar cooling load tables are based upon a particular space and rules related to the use of blinds. Details are given in 5.A6.17.
5.A6.2 Input data
The input data required are:
— Latitude of the building: the calculations here are carried out for Local Apparent Time (solar time) and so longitude is not required. CIBSE Guide J(A6.1)provides information on how to correct to clock time.
— Internal design temperature: operative temperature, see chapter 1, Table 1.5.
— Hourly dry bulb temperatures: design values for three UK locations can be found in chapter 2, Tables 2.34 to 2.36.
— Hourly values of direct and diffuse solar radiation: see CIBSE Guide J(A6.1), sections 2.6.2.2 and 2.6.2.3.
Design values can be found in chapter 2 of this Guide, Tables 2.30 to 2.32 for UK locations and Table 2.33 for worldwide latitudes. (Note that editions of Guide A prior to the 1999 edition used theoretical solar data whereas the 1999 edition and the present edition use measured data.)
— Dimensions of the space.
— Material properties: these are the dimensions and thermal properties of the fabric elements bounding the space. For glazing the data must be sufficient to determine the transmission, absorption and reflection for each pane of glass as a function of the solar angle of incidence.
— Internal heat gains: the hourly profile of use and the radiant/convective split are required.
— Infiltration rate/ventilation rate: this is for outside air only and it is assumed here to be constant throughout the day. Harrington-Lynn(A6.2)shows how to allow for a variable ventilation rate.
— Boundary conditions for internal surfaces: this algorithm assumes that internal surfaces are adiabatic. If the temperature in adjacent spaces is known then they can be treated in the same way as external spaces. If not an iterative procedure is required.
— Time plant is switched on and off.
5.A6.3 Overview
The basic process is as follows, for each hour of the day.
Note that if measured climatic data are used the solar radiation at any given hour is, usually, the average over the preceding hour and so calculations should be made on the half hour. Measured temperatures are usually reported on the hour and so interpolation may be required in order to obtain the half hour value.
(1) Calculate the U-value, thermal admittance, decre- ment and surface factor for all fabric elements (see chapter 4).
(2) Calculate the factors required by the method.
The following preliminary calculations are carried out for each hour of the day:
(3) Calculate the position of the sun.
(4) Generate the direct and diffuse radiation normal to the sun (or obtain from tabulated or measured data).
(5) Obtain appropriate hourly dry bulb temperatures.
(6) Calculate the sol-air temperature for all external surfaces.
(7) Calculate the radiation transmitted through and absorbed within the glazing. If necessary allowing for external shading devices and the raising or lowering of blinds. It is assumed here that blinds are lowered because of external conditions (level of solar radiation) and not internal space tempera- ture. Iteration will be necessary if internal temper- ature control is required.
This completes the preliminary calculations.
(8) The following loads at the environmental and air node are needed (see 5.A5.3 and 5.A5.4). Note that in the case of the solar cooling load tables only the solar and infiltration loads are required.
— solar
— infiltration/ventilation
— fabric
— internal gains.
(9) Sum the gains and determine the cooling load for 24-hour plant operation.
(10) Apply correction for intermittent plant operation.
The method of calculation is given in the following sections.
5.A6.4 Correction factors
The calculation requires the following input data for each surface:
VOL Room volume (m3) AWALL Opaque area (m2)