## 5.3 B5.1. Hourly Recirculation Loop Pipe Heat Loss Calculation

Hourly recirculation loop pipe heat loss (HRLLk) is the hourly heat loss from all six pipe sections. There are two pipe heat loss modes, pipe heat loss with non-zero water flow (PLWF) and pipe heat loss without hot water flow (PLCD). The latter happens when the recirculation pump is turned off by a control system and there are no hot water draw flows, such as in recirculation return pipes.

Compliance software shall provide four options of recirculation system controls listed in Table B-2. A proposed design shall select a control type from one of the four options. The standard design shall use demand control.

#### Table B-2. Recirculation Loop Supply Temperature and Pump Operation Schedule

Hour | No Control | Demand Control | Temperature Modulation | Temperature Modulation with Continuous Monitoring
T in,1 (oF) | SCHk,m | T in,1 (oF) | SCHk,m | T in,1 (oF) | SCHk,m | T in,1 (oF) | SCHk,m
1 | 130 | 1 | 130 | 0.2 | 120 | 1 | 115 | 1
2 | 130 | 1 | 130 | 0.2 | 120 | 1 | 115 | 1
3 | 130 | 1 | 130 | 0.2 | 120 | 1 | 115 | 1
4 | 130 | 1 | 130 | 0.2 | 120 | 1 | 115 | 1
5 | 130 | 1 | 130 | 0.2 | 120 | 1 | 115 | 1
6 | 130 | 1 | 130 | 0.2 | 125 | 1 | 120 | 1
7 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
8 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
9 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
10 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
11 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
12 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
13 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
14 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
15 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
16 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
17 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
18 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
19 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
20 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
21 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
22 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
23 | 130 | 1 | 130 | 0.2 | 130 | 1 | 125 | 1
24 | 130 | 1 | 130 | 0.2 | 125 | 1 | 120 | 1

Pipe heat loss modes are determined by recirculation control schedules and hot water draw schedules. For each pipe section, hourly pipe heat loss is the sum of heat loss from the two heat loss modes.

Hourly heat loss for the whole recirculation loop (HRLLk) is the heat loss from all six pipe sections, according to the following equation:

HRL L k =∑n é ë PLW F n + PLC D n ù û | Equation 12

where

PLWFn= Hourly pipe heat loss with non-zero water flow (Btu/hr), see Equation 13.

PLCDn= Hourly pipe heat loss without water flow (Btu/hr), see Equation 18.

n= Recirculation pipe section index, 1 – 6PL W F n = Flow n × (1 − f noflow,n ) × ρ × C p × (T n,in − T n,out ) | Equation 13

where

Flown = Flowrecirc + Flown,draw (gph), assuming

Flown,draw = Average hourly hot water draw flow (gph). For supply sections, n=1, 2, or 3, Flown,draw = GPHk/NLoopk. For return pipes, n=4, 5, and 6, Flown,draw = 0.

Flowrecirc = Hourly recirculation flow (gph). It is assumed to be 360 gallons based on the assumption that the recirculation flow rate is 6 gpm.

fnoflow,n = Fraction of the hour for pipe section n to have zero water flow, see Equation 14

ρ = Density of water, 8.345 (lb/gal).

Cp = Specific heat of water, 1 (Btu/lb-oF).

Tn,in = Input temperature of section n (oF). For the first section (n=1), T1,in shall be determined based on Table B-2. The control schedule of the proposed design shall be based on user input. The standard design is demand control. For other sections, input temperature is the same as the output temperature the proceeding pipe section, Tn,in = Tn-1,out

Tn,out = Output temperature of section n (oF), see Equation 15

f noflow,n = (1 − SCH k ,m ) × NoDraw n | Equation 14

where

NoDrawn = Fraction of the hour that is assumed to have no hot water draw flow for pipe section

n. NoDraw1 = 0.2, NoDraw2 = 0.4, NoDraw3 = 0.6, NoDraw4 = NoDraw5 = NoDraw6 = 1.

SCHk,m = Recirculation pump operation schedule, representing the fraction of the hour that the recirculation pump is turned off, see Table B-2. SCHk,m for the proposed design shall be based on proposed recirculation system controls. Recirculation system control for the standard design is demand control.

− UA n T = T + (T − T ) × e ρ C p Flow n out,n amb,n in,n amb,n | Equation 15

where

TAmb,n = Ambient temperature of section n (oF), which can be outside air, underground, conditioned or semi-conditioned air. Outside air temperatures shall be the dry-bulb temperature from the weather file. Underground temperatures shall be obtained from Equation 10. Hourly conditioned air temperatures shall be the same as conditioned

space temperature. For the proposed design, Tamb,n options shall be based on user input. The standard design assumes all pipes are in conditioned air.

UAn = Heat loss rate of section n (Btu/hr-°F), see Equation 16.

UA n = L e n n × min (U bar e,n , f UA ×U i nsul ,n )

Equation 16

where

Lenn = Section n pipe length (ft). For the proposed design, use user input; for the standard design, see Equation 27.

Ubare,n, Uinsul,n = Loss rates for bare (uninsulated) and insulated pipe (Btu/hr-ft-oF), evaluated using Equation 17 with section-specific values, as follows --

Dian = Section n pipe nominal diameter (inch). For the proposed design, use user input; for the standard design, see Equation 28.

Thickn = Pipe insulation minimum thickness (inch) as defined in the Title 24 Section 120.3, TABLE 120.3-A for service hot water system.

Condn = Insulation conductivity shall be assumed = 0.26 (Btu inch/h∙sf∙F)

hn = Section n combined convective/radiant surface coefficient (Btu/hr-ft2-F) assumed = 1.5.

fUA = Correction factor to reflect imperfect insulation, insulation material degradation over time, and additional heat transfer through connected branch pipes that is not reflected in branch loss calculation. It is assumed to be 2.0.

Equation 17 defines general relationships used to calculate heat loss rates for both loop and branches using appropriate parameters.

Dia o = Dia + 0.125

U bare = h × π × Dia o 12

Dia x = Dia o + 2 × Thick

U = π

Equation 17

insul

ln ( Dia x Dia o ) + 12

2 × Cond 12 h × Dia x

where

Dia = Pipe nominal size (in)

Diao = Pipe outside diameter (in)

Diax = Pipe + insulation outside diameter (in) Thick = Pipe insulation thickness (in)

Cond = Insulation conductivity (Btu in/hr-ft2- oF)

h = Combined convective/radiant surface coefficient (Btu/hr-ft2- oF).

Pipe heat loss without water flow shall be calculated according to the following equations:

PLC D n = Vol n × ρ × C p × (T n,st art − T n,end ) | Equation 18

where

Vol n = Volume of section n (gal). It is calculated as 7.48 × π × ( Dia o

n

24)2 × Len

where 7.48 is the

volumetric unit conversion factor from cubic feet to gallons. Note that the volume of the pipe wall is included to approximate the heat capacity of the pipe material.

Tn,start = Average pipe temperature (oF) of pipe section n at the beginning of the hour. It is the average of Tn,in and Tn,out calculated according to Equation 15 and associated procedures.

Tn,end = Average pipe temperature (oF) of pipe section n at the end of pipe cool down . See

Equation 19

− UA n × f noflow,n T = T + (T − T ) × e Vol n ×ρ ×C p n,end amb,n n,start amb,n | Equation 19

Equation 19 calculates average pipe temperature after cooling down, so the pipe heat loss calculated by Equation 18 is for pipe with zero flow for fraction fnoflow,n of an hour. Recirculation pumps are usually turned off for less than an hour and there could be hot water draw flows in the pipe. As a result, recirculation pipes usually cool down for less than an hour. The factor fnoflow, n calculated according Equation 14 is used to reflect this effect in Equation 19.