Reference pubii

cations

MR.CIR 82-2497 INST. OF STAND & TECH

AiiiDb 2bi32H 5st Method and Calculation

Procedure for Determining

Annual Efficiency for Vented

Household Heaters and Furnaces

Equipped With Modulating-Type

Controls

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Equipment Division

Washington, DC 20234

May 1982

Prepared for;

ldd2

jited States Department of Energy

ashington, DC 20585

NBSIR 82-2497

A TEST METHOD AND CALCULATION

PROCEDURE FOR DETERMINING

ANNUAL EFFICIENCY FOR VENTED

HOUSEHOLD HEATERS AND FURNACES

EQUIPPED WITH MODULATING-TYPE

CONTROLS

J’ATIONAI. -B T pF standAP.L':. IIBKAh. 1 0 198;?

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Esher Kweller

Robert L. Palla, Jr.

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Building Equipment Division

Washington, DC 20234

May 1982

Prepared for: United States Department of Energy

Washington, DC 20585

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
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ABSTRACT

As annual operating efficiency of vented heating equipment is affected by burner

fuel and combustion air modulation, it is important to differentiate between the

various types of controls in determining annual energy requirements. Test procedures for evaluating annual efficiency have already been developed and implemented by the Department of Energy (DoE) for furnaces with single-stage thermostat control. A modified test procedure is necessary to account for operation

with fuel modulation. A revised procedure which accommodates two types of fuel

modulating controls has recently been developed. Tests are conducted at reduced

and maximum firing rates, and along with typical derived values, from a bin

analysis of weather data, the fraction of the total hours for each operating

mode is obtained to calculate a weighted annual efficiency. These test methods

and calculation procedures are based on and are an extension to the current DoE

test procedures for the single-stage type of thermostat control of central warm

air furnaces.

By using the procedures developed in the report, the energy savings impact of

fuel modulating controls when combined with the use of modulated combustion air

is evaluated. Energy savings from 6 percent to 20 percent were determined from

the increase in efficiency with both fuel and combustion air modulation.

Improved efficiency was dependent on the type of thermostat control and the

minimum-to-maximum fueled input; i.e., turndown ratio.

Key Words; annual efficiency; household heaters and furnace test procedures;

hydraulic thermostat control; modulating control gas-fueled;

two-stage thermostat.
TABLE OF CONTENTS

Page

ABSTRACT iii

1. INTRODUCTION 1

2. STEP-MODULATING CONTROLS 3

2.1 MODE OF OPERATIONS 3

2.2 ENERGY CONSIDERATIONS 3

2.2.1 Percent of Operating Time in Each Mode ^ 2.2.2 Average Outdoor Temperature in Each Mode ^ 2.2.3 Average Steady-State Efficiency 3

2.2.4 Infiltration Loss in the Modulating Mode 6

3. TEST PROCEDURE AND CALCULATIONS 7 3.1 CURRENT TEST PROCEDURE 7 3.2 MEASUREMENTS AND CALCULATIONS FOR HEATERS WITH STEPMODULATING CONTROLS 8

3.3 CALCULATIONS FOR HEATERS WITH TWO-STAGE CONTROLS 9

4. IMPACT OF MODULATING CONTROLS ON ENERGY CONSUMPTION 10

4.1 PRESENT DESIGN 10

4.2 HEATERS EQUIPPED WITH THERMAL DAMPERS 10

4.3 HEATERS WITH REDUCED COMBUSTION AIR AT REDUCED HEAT INPUT

RATES 10

5. CONCLUSIONS 12

6. REFERENCES 13

APPENDIX A - Determination of Outdoor Design Temperature for Vented

Room Heaters 29

APPENDIX B - Detailed Calculation Procedure for Annual Efficiency of

Heaters with Step-Modulating and Two-Stage Thermostat ... .. 33

APPENDIX C - Computer Program for the Evaluation of Annual Fuel

Efficiency of Heating Equipment with Single-Stage,

Two-Stage, and Step-Modulating Control 38

iv
LIST OF TABLES

Page

Table 1 . Development of Outdoor Temperatures and Time in Each Mode

from Weather Data for One City 14

Table 2. Outdoor Temperatures and Time in Each Mode — An Average of

Eight Cities Having Total Heating Requirements of

Approximately 4400 Degree Days 13

Table 3. Summary of Stack Losses and Efficiencies for a Room Heater

Rated 45,000 Btu/ h (13,185W) 16

Table 4. Effect of Stack Damper and Operating Input Rate on the Stack

(S) and Flue (F) Temperature and CO2 Values and Stack to Flue

Mass Flow (S/F) for Room Heater Rated 45,000 Btu/h (13,185W)... 17

Table 5. Effect of Type of Thermostat Control on Energy Saving Potential

of Thermal Dampers * 18

Table 6. Effect of Reduced Excess Combustion Air on Efficiency of a 35,000 Btu/h (10,255W) Room Heater Equipped with a Step-Modulating Thermostat 19

LIST OF FIGURES

Figure 1. Typical operating modes for heaters equipped with singlestage, two-stage, and step-modulating controls 20

Figure 2. Outlet gas pressure from a step-modulating thermostat control

in response to changing room temperature 21

Figure 3. Part-load efficiency vs load for a heater with a stepmodulating control 22

Figure 4. Burner output rate vs heating load and associated outdoor

temperature for a heater with step-modulating control 23

Figure 5. Balance point temperature (Tc) as a function of heater output

ratio 24

Figure 6. Example of bin method used to determine percentage of time in

cycling mode 25

Figure 7. Average outdoor temperature in cycling and non-cycling modes

vs balance point temperature (Tc) 26

V
LIST OF FIGURES (Continued)

Page

Figure 8. Average outdoor temperature and percent of time in cycling

mode as a function of heater output ratio 27

Figure 9. The effect of burner fuel input rate on the part-load loss

of a room heater with and without a thermal damper 28

vi
NOMENCLATURE

EFFYA Annual Fuel Utilization Efficiency, in %

^I.OFF Off-cycle infiltration loss, in % of the fuel input rate

Li,on On-cycle infiltration loss, in % of the fuel input rate

^1, ON,min On-cycle infiltration loss, in % of the fuel input rate at

minimum input rate

, ON, max On-cycle infiltration loss, in % of the fuel input rate at

maximum input rate

Latent heat loss, in % of the fuel input rate

1^S,0FF Off-cycle sensible heat loss, in % of the fuel input rate

^^S,ON On-cycle sensible heat loss, in % of the fuel input rate

Ls,ss,a Sensible heat loss at steady-state operation, in % of the

fuel input rate

1 pF Ratio of Qp T = pilot fraction

Qin Fuel energy input rate at steady-state operation (including

any pilot light input), in Btu/h, minimum input,

Qin, max maximum input rate.

Qout Fuel energy output rate - Qout min minimum input rate,

Qout , max ^b maximum input rate.

Qp Fuel energy input rate to pilot light in Btu/h

1 *^OFF Off-time per cycle, in minutes

' ^ON On-time per cycle, in minutes

Tc Balance point outdoor air temperature

^da Average outdoor air temperature applicable to heater operation

at minimum firing rate

’^oa’ Average outdoor air temperature applicable to heater operation

between minimum and maximum rate

Laboratory room temperature, in °F

! ’^ss Steady-state efficiency, in % of fuel input rate

vii
Part-load fuel utilization efficiency, in %

a Oversizing factor

’^ss ,min Steady-state efficiency at minimum input rate

^ss ,max Steady-state efficiency at maximum input rate

’^ss ,hi Average steady-state efficiency between minimum and maximum

input rates

’^ss ,wt Weighted average steady-state efficiency

,Jlo Part load efficiency at the minimum input rate

,hi Part load efficiency at the maximum input rate for two-stage

thermostats or for the non-cycling mode for step-modulating

thermostats

’^y ,WT Weighted part-load efficiency

^lo Percentage of operating time at the low input firing rate

Rhi Percentage of operating time in the non-cycling mode

vlii
1 INTRODUCTION

As annual operating efficiency of vented heating equipment is affected by

burner operating modes, it is important to differentiate between the various

types of controls in determining annual energy requirements. Test procedures

for evaluating annual efficiency have already been developed and implemented

by the Department of Energy (DoE) for heaters with single-stage control [3]*.

I For two-stage and step-modulating units, however, a modified test procedure is

I necessary to account for operation at multiple firing rates, A revised procedure which accommodates modulating-type units has recently been developed and

1 recommended to DoE [1, 2]. A detailed review of the background for the recommendations of tests for modulating heaters in that procedure is the subject of

this report.

jj Modulating controls investigated in this study are generally used with vented

household heaters other than furnaces. However, the methods of test and the

Ll bin analysis procedures developed in this report for vented heaters are also

applicable to central heating systems using the types of modulating controls

described here. The only adjustment that would be needed to these procedures

would be to use bin data based on the population of central furnaces in

j; order to arrive at a national average annual efficiency specific to furnaces.

jl

1

I Three types of thermostatic controls are commonly used on automaticallyi controlled heating equipment. These are;

;!

1 a. single-stage control, which cycles the heater between full input (100

! percent of rating) and off;

b. two-stage control, which operates in an on-off cycling mode at either

, maximum input or at some reduced input which can be as low as 20 percent

of maximum; and

c. step-modulating control, which steps on to a low input and then either

, cycles off and on at the low input if the heating load is light, or grad-

, ually increases the heat input to meet any higher heating load that can-

' not be met with the low firing rate.

(

I Figure 1 illustrates the burner heat output rate and burner on periods (shaded)

area) in response to increasing heating loads for each of these three types of

controls.

The assumptions made in previous work [4] and as depicted by figure 1 that

outdoor temperatures below 65°F would be directly proportional to heating load

is valid only in a broad statistical sense. It should be understood that procedures developed here for calculating annual efficiency as well as current DoE

test procedures for determining annual efficiency of the conventional type

on-off thermostatically controlled heaters is intended for comparison purposes

' Numbers in brackets indicate references in section 6.

|i

I

I

i

I

1
between equipment tested only under laboratory test conditions. A comprehensive

treatment to include internal heat gains, solar radiation, wind, etc., would be

needed in order to be valid for small time thermostatic cycling of the installed

heating system. These procedures should not be considered as being predictive

of the installed annual energy use. It should be understood that a comprehensive treatment of the building and furnace interaction to predict operating

costs after installation is beyond the scope of this work.

2
t

li

2 . STEP-MODULATING CONTROLS

2.1 MODE OF OPERATION

One representation of the operating mode for the step-modulating type control

is its response to room temperature (see figure 2 where room temperature and

outlet gas pressure supplied to the burner from the thermostat control are

shown)

.

Under normal operating conditions, as the ambient air temperature surrounding

the liquid-filled thermostat sensing bulb drops to point A on figure 2, the

control opens to allow minimum fuel flow (point B) . Uhen room air temperature

I rises to point C, the valve closes (point D) . Operations on the ABCD rectangle

is termed the "cycling" mode,

; If more severe weather is encountered while the valve is open to minimum flow

I (point B), room temperature may continue to drop until point E is reached, at

which time any further drop in room temperature would result in an increasing

; fuel flow. If the heating demand continues to increase with subsequent lower

i room temperature, fuel flow would gradually increase to maximum flow (from E to

j G) . In another situation, if the heating demand should just equal heater out-

; put for a prolonged time, the manifold could remain partially open (point F or

'1 any other point between low fire and high fire) until the heating demand changes,

i; Operation at the various firing rates from point B to G is termed the "noncycling"

' mode or modulating mode.

, 1

) 2.2 ENERGY CONSIDERATIONS

In developing test procedures for modulating type heaters, operation in both

, the cycling and non-cycling modes must be addressed. The importance of addressing both modes separately is apparent when one considers the difference in

efficiency between the two modes as illustrated in figure 3. The part-load

^ efficiency curve of figure 3 was plotted using data obtained with a room heater

j having a maximum rated input of 35,000 Btu/h and minimum adjusted input of

j 21,000 Btu/h and with a balance point temperature (T^) of 36°F, (See

section 2.2.1 for discussion of Tp.)

I

J Annual efficiency for step-modulating units depends upon several factors

including:

• percentage of the heating season operating time in each of the two modes,

r • average outdoor temperature for each mode,

® average steady-state efficiency over the various firing rates in the

j; non-cycling mode,

o infiltration loss in the non-cycling mode, and

i'

i| • part-load efficiency in the cycling mode.

I
The first two factors can be developed by considering heater sizing and through

analysis of representative weather data. The remaining factors are determined

via additional test measurements and calculations. Each of the factors is

described in detail in the sections that follow.

2.2.1 Percent of Operating Time in Each Mode

Two assumptions provide a basis for defining the percent of operating time

spent in each of the two modes: (1) at an outdoor temperature of 65°F, heating

requirements no longer exist, and (2) at the outdoor design temperature for

vented room heaters of 15°F (see appendix A for development of this value) the

heater output rate needed to meet the heating requirement is equal to the maximum heater output rate divided by (1+a) where a is the heater oversize fraction.

Here output rate is defined as the product of input rate and steady-state efficiency. A relationship between heater output and outdoor temperature can then

be expressed:

whe re

^out ,max/ ( 1+g) _ 65-15

Qout,min

( 1 )

Qout max rated maximum output rate,

Qout ,min rated minimum output rate.

T^ is the outdoor temperature where the modulating mode begins (see figure 4).

This implies that heating load is a linear function of outdoor temperature. In

these test procedures a is assigned a value of zero. Under this assignment, at

outdoor design temperature of 15°F the heater operates at maximum firing rate.

A plot of Tj, versus the ratio of minimum to maximum output is shown in figure 5 for fixed values of a. The cycling mode (as shown in figure 4) is between outdoor temperature T^ and 65° F. The modulating mode is between T(, and the minimum

outdoor temperature, which for household heaters is typically 15°F, Through

analysis of typical weather data, the time in each mode can then be defined as

a fraction of total heating season degree hours. The analysis involves a bin

method calculation of hours in various temperature ranges. The steps in the

calculation are presented in the column headings of table 1. See column (14)

and columns (1) through (5) of table 1, A graphical example is also shown in

figure 6.

2.2.2 Average Outdoor Temperature in Each Mode

The average outdoor temperature in the cycling and non-cycliiig modes Tq^ and

Toa' > ^respectively (as shown in figures 7 and 8) are developed from representative national average weather data. Tabulated data and temperature calculations]

for one city having a 4200 degree day heating season are shown in table 1. The

average of calculated values for eight cities and the basis for figures 7 and 8 are presented in table two. The eight cities are listed in appendix, table A2

.

These eight cities all fall within a range of +5 percent of the national average

(heater population weighted) of 4400 degree days.

4
Referring to table 1, calculation of Tq^ and Tq^’ is as follows: for each

temperature range, the mean temperature (col. 2) and number of hours spent in

the range (col. 3) are determined from a compilation of historial weather data

[5]. From this the number of degree hours in each range (col. 5) is obtained.

Toa represents the average outdoor temperature between 65°F and T^. To obtain

Tq3 , col. 5 and col. 3 are therefore summed cumulatively (upward in table 1)

from 62°F to yielding col. 6 and col. 7, respectively. For each given in

col. 2, col. 6 divided by col. 7 represents the corresponding number of degrees

below 65°F. This number is given in col. 8. Toa 9) is 65°F minus

col. 8. The same approach is taken in calculating Toa' except that the cumulative summation is from 15°F to T^. rather than from 65°F to T^. The result of

these calculations is a value of Toa ^oa* each T^. A plot of these

parameters for the values in table 2 is shown in figure 7 . For any given

heater, equation (1) can be used to determine Tq , for which values of Toa

Toa' obtained from figure 7. Alternatively, equation (1) and the results

of the previous temperature calculations can be combined to eliminate the intermediate calculations of T^. Toa ^oa' obtained from figure 8 where

percent of time in cycling modes, Toa ^oa' (columns 5, 6a, and 6b of table 2

respectively) are plotted vs the min/max heater output ratio (col. 7 of table 2)

2.2.3 Average Steady-State Efficiency

Due to an Increase in excess air at below maximum firing rates, there is usually

a drop in steady-state efficiency in the non-cycling mode as fuel input rate

is reduced. An average steady-state efficiency is, therefore, needed to represent operation in this mode. The average steady-state efficiency is calculated

by linear interpolation between the steady-state efficiency at the minimum

rated input, which corresponds to temperature, T^, and the steady-state efficiency at the maximum rated input for the heater, which corresponds to a temperature of 15°F. These efficiencies are determined in accordance with the

DoE test procedure using a=0.* The average efficiency (riss^ will correspond to

the efficiency when firing at temperture Tq^' and is given by

'ss 'ss ,max hss ,minj

Tc - Toa’

T^ - 15

+ n ss ,min

( 2 )

In general, the arithmetic mean of the steady-state efficiencies may be used

in place of equation (2) with a resulting error of about one percentage point.

The DoE test procedure [3] lists a value of a=0.7 which was applicable to

central furnaces, and was originally adopted for use with vented heaters.

Since the typical oversize factor is unknown for vented heaters the use of

a=0.7 would be arbitrary. In order to reduce the complexity of the calculation procedures for modulating type heaters, a value of a=o is applied

for all calculated efficiencies reported here.

5
2.2.4 Infiltration Loss in the Modulating Mode

On-period infiltration loss (Lj energy efficiency debit for heaters

using indoor air for combustion and draft hood dilution. The loss of efficiency due to infiltration of outdoor air at Toa' (which is subsequently heated

to an indoor temperature of typically 70°F) is subtracted from the weighted

average steady-state efficiency calculated by the above procedure. Average on- period infiltration loss is calculated in the same manner as steady-state efficiency. On-period infiltration losses are obtained via the current DoE test

procedure [3] and the average infiltration is taken to be the arithmetic mean

of the values determined at the maximum and minimum input rates.
3. TEST PROCEDURE AND CALCULATION

3.1 CURRENT TEST PROCEDURE

The current test procedure for determining the annual efficiency of vented

heaters [ 3] applies only to units equipped with single-stage controls. While

not directly applicable to modulating-type units, only minor modifications to

the procedure are necessary to accommodate these types of controls. A cursory

review of the procedure will, therefore, be provided here. A more detailed

description of the procedure is provided in references [3, 4].

The existing procedure involves conducting a steady-state performance test on

the heater, plus measuring flue gas temperatures at specific times during the

heat-up and cool-down from steady-state conditions. Specific measurements at

steady-state include flue and stack gas temperature and CO2 concentration. Two

temperature measurements during heat-up and three during cool-down provide the

basis for exponential approximations for the temperature-time profiles.

In addition to the above experimental data, a knowledge of several factors

describing mass flow rates through the flue and stack during on- and off-periods

is required. Values for these factors may be either measured or assigned

according to the type of unit under test.

Based upon the experimental data and assigned system factors, thermal losses

associated with heater operation are determined. These losses expressed as a percentage of the fuel input rate are:

Ll = Latent Heat Loss due to the presence of uncondensed water vapor in

the flue gas.

^S,ON “ On-cycle Sensible Heat Loss due to the venting of combustion products

and excess air at a temperature above room temperature.

Ll,ON ~ On-cycle Infiltration Loss due to heating the on-period combustion

and draft control air from outdoor temperature (Tqa) to room

temperature.

Ls,off “ Off-period Sensible Heat Loss due to heating the off-period room air

discharged at a temperature in excess of the room temperature.

^I,OFF “ Off-period Infiltration Heat Loss due to heating the off-period room

air loss from outdoor temperature to room temperature.

Steady-state efficiency is given in terms of latent heat loss, Lj^, and on-perlod

sensible heat loss at steady-state, Lg qn ss* Part-load efficiency, is

expressed as a function of the five losses:

riu = 100 - Ll - — (Ls, 0N + 1^S,0FF + Ll,0N + Li,0FF) (3)

^on X

’^off

7
typical on-period time - minutes,

typical off-period time - minutes.

Pilot fraction (as fraction of total fuel input rate).

^on

^of f

PF

The part-load efficiency is then combined with the steady-state efficiency

(pgs) and pilot fraction to yield the annual fuel utilization efficiency.

EFFYA = ^ss ^ ^u ^ Pgg X 4400 + 2.5 X riu X PF X 4600

( 4 )

where the additional parameters are:

4400 = average annual degree days for vented heaters (see appendix A)

4600 = average non-heating season hours per year that all the energy

to the pilot is assumed wasted.

3 . 2 MEASUREMENTS AND CALCULATIONS FOR HEATERS WITH STEP-MODULATING CONTROLS

For single-stage heaters there is only one fuel input rate at which measurements can be made (the maximum input rate). Modulating- type heaters, however,

operate both at reduced firing rate during the cycling mode and anywhere between

the reduced and maximum rates during the non—cycling mode. Accordingly, test

measurements must be made at the maximum input rate as well as the reduced setting. Since the heater with step-modulating control cycles on-off only at the

reduced input rate, all part-load cycling losses must be determined at the

reduced input. In addition, to account for operation in the non-cycling mode,

as described in sections 2.2.3 and 2.2.4, Lg^oN ^I,0N be determined at

maximum fire as well. It is not necessary to know either of the off-cycle

losses at high fire (Lg qfF OFF^ because no off period loss occurs at

that input rate with the step-moduiating-type control.

The recommended procedure for calculating the annual fuel utilization

efficiency for modulating type heaters essentially involves determination of

losses and efficiencies for each of the operating modes — cycling and noncycling and weighting of these parameters according to the fraction of time

spent in each mode.

The procedure for calculating annual efficiency for the step-modulating heaters

is summarized below in nine steps. The detailed procedure consisting of 20

steps is included in appendix B, along with a sample calculation. A computer

program (FBVH) for conducting the complete calculation applicable to furnaces,

boilers, and vented heaters is included in appendix C.

(a) Determine minimum and maximum heater outputs from the minimum and maximum

input rates and measured steady-state efficiency at these two input

rates. (For details see steps 1-7 of appendix B.)

8
(b) Using Tnlniraum/ maximum heater output from step (a) , determine the percent

of heating season in each mode. Find the percent of time in cycling mode

from figure 8. Percent of non-cycling mode is 100 percent less the

percentage of cycling mode.

(c) Determine the average outdoor temperature in the cycling mode, Tq^, and in

the non-cycling mode, Tq^'

,

from figure 8 at the point corresponding to the

min/max output determined from (a).

(d) Determine part-load efficiency in the cycling mode using the value of Toa

and the prescribed DoE test procedure [3].

(e) Determine the average steady-state efficiency in the non-cycling mode.

Use the average of steady-state efficiency measured at the maximum and

minimum input rates from step (a).

(f) Determine part-load efficiency in the non-cycling mode by subtracting

infiltration loss, qN» the average steady-state efficiency in

step (e). Use Tq^*

,

to calculate infiltration loss in the non-cycling mode.

(g) Determine weighted average steady-state efficiency using steady-state

efficiencies at the minimum input rate from step (a) and the average determined for the non-cycling mode from step (e). Weight each by the percent

of heating season in each mode (determined from step (b)).

(h) Determine average part-load efficiency for the heating season using the

corresponding part-load efficiencies for the cycling and non-cycling modes

and the percent of heating season in each mode.

(i) Determine annual efficiency using average part-load efficiency and average

steady-state efficiency.

3.3 CALCULATIONS FOR HEATERS WITH TWO-STAGE CONTROLS

This type of control cycles the burner at low fire for outside air temperatures

between 65°F and T^ and at higher fire for temperatures T^ and below (see figure

1). Evaluation of the annual fuel efficiency of heaters with two-stage controls

involves the same test measurements required for step-modulating type units, and

only slightly different calculations. The calculations are described in detail

in appendix B.

9
4 IMPACT OF MODULATING CONTROLS ON ENERGY CONSUMPTION

4.1 PRESENT DESIGN

Figure 3 shows that modulating controls will indeed affect annual efficiency

as evidenced by the variation in part load efficiency with heating load. As

shown, efficiency improves as the heating load is increased. This is due both

to a reduction in heater cycling (see Modulating Mode of figure 4) and therefore, off-cycle losses, and also in the higher steady-state efficiency at the

higher full input rates. The maximum efficiency of currently designed heaters

is realized in the non-cycling mode.

4.2 HEATERS EQUIPPED WITH THERMAL DAMPERS

Measured on-period and off-period stack losses of a room heater with and without

a thermal stack damper installed were measured. Detailed test results and data

are in tables 3 & 4. Data for damper A is presented graphically in figure 9.

See [6] for additional information including description of tracer gas test

method use to measure the off period losses. The shaded area represents energy

savings due to the damper. Figure 9 shows for that heater, as fuel input rate

is reduced from maximum to lower input rates, energy savings due to the damper

continuously increase. The significance of these findings is that a test con- ducted per the DoE test procedure [3] only at the maximum input rate does not

reflect the potential energy savings of the thermal type stack damper when it

is installed on a heater having a step-modulating or two-stage thermostat

control

.

A summary of energy savings calculated using the calculation procedure of

appendix C for three heaters with three different models of thermal dampers is

shown in table 5. Results presented in table 5 show that energy savings is

dependent on type of heater and stack damper as well as type of thermostat used,

and the reduced fuel input rate of the step-modulating type thermostat.

4.3 HEATERS WITH REDUCED COMBUSTION AIR AT REDUCED HEAT INPUT RATES

Although heaters tested have shown a reduced part-load efficiency at reduced

input rates, it is possible that heaters can be designed to use less excess air

at the reduced input rate, thereby, actually increasing part-load cycling mode

efficiency at the lower rate to above the non-cycling mode operating efficiency.

This is possible because at reduced input rates the ratio of heat transfer sur- face area to combustion products mass flow rate is greater. Test procedures

outlined here will allow credit for any such innovative designs that result in

reduced excess combustion air at reduced fuel input rate.

The potential for energy savings with reduced excess air has been demonstrated

in the laboratory by intentionally reducing the excess air at reduced input

rate. The excess combustion air values at a minimum input are presented in

table 6 for a heater in "as received" condition and after reducing excess com- bustion air. Excess air was reduced in these test by using a flue baffle placed

in the exit of the heat exchanger. Baffling of the heat exchanger was limited

10
in order not to increase carbon monoxide in the flue gases above the amounts

found prior to any restriction of the flue. Data obtained at the maximum firing

rate and at the minimum input rate with restricted excess combustion air is

shown in table 6.

The effect of reduced excess air on efficiency can be quite significant. As

shown in table 6, energy savings of from 6 to 22 percent were calculated.

11
5 . CONCLUSIONS

A procedure for evaluating the annual operating efficiency

teen^develeaulpment with a step-modulating thermostat or two-stage control has been devel

oped. This procedure is essentially the same as the existing

dLe for venLd heaters, but calls for tests and calculations to performed

at maximum as well as mlnumum firing rates. Analyses of weather data typl

cal cities, and assumptions concerning heater siring, provide a means of com blnlng the cycling and non-cycling efficiencies to yield a weighted annual

fuel efficiency.

This rated annual efficiency is considered to be reflective of differences

Inherent with cycling and non-cycling modes of operation which apply with

mLulatlng-type^ont?ols. Since procedures developed here

current DoE test procedures, these procedures are believed to be “seful o cLparing the annLl efficiency of heaters with modulating type

conventional on-of thermostat control used with some types of

The bln calculation procedures developed here are also expected to be applicable

w certain furnaces equipped with the types of fuel modulating controls Investigated in this study. Predicted annual energy with any of these

^ should be considered valid only for comparison purposes between equipment teste

under laboratory conditions. These procedures as well as the current D

procedures should not be considered predictive of installed

costs. Comprehensive treatment of the building and furnace

are unique to each installation would be needed for that prediction and Is

beyond the scope of these procedures.

Comparison of heater efficiencies with single-stage and with

controls Indicates that substantial Improvements can be made. ®

j

combustion air to fuel ratio with reduced Input rate is a promlstng means of

reducing energy consumption for heaters with step-modulating and two stage

controls.

12
6 . REFERENCES

[1] Kweller, E.R., and Mullis, W.F., "Proposed Amendments to Test Procedures

for Vented Household Heaters," Letter Report prepared for Department of

Energy, March 1980.

[2] Kweller, E.R., and Mullis, W.F., ’’Recommendations to DoE on Modifications

of Test Procedures for Vented Gas and Oil Fueled Heaters," Letter Report,

June 1979.

[3] Appendix 0 - Uniform Test Method for Measuring the Energy Consumption of

Vented Home Heating Equipment, Federal Register, Vol. 43, No. 91, May 10,

1978.

[4] Kelly, G.E. , et al., "Recommended Testing and Calculation Procedures for

Determining the Seasonal Performance of Residential Central Furnaces and

Boilers," NBSIR 78-1543, National Bureau of Standards, September 1978

[5] Engineering Weather Data, Department of the Air Force, AFM 88-29, the

Array (TM 5-785) and the Navy (NAVFAC P-89), July 1978, Washington, DC 20330.

[6] Kweller, E.R. , and Mullis, W.F., "Determination of Annual Efficiency of

Vented Heaters Equipped with Thermally Activated Vent Dampers," ASHRAE

Trans., Vol. 87, Pt . 1, 1981.

13
Table

1.

Development

of

outdoor

temperatures

and

time

In

each

mode

from

weather

data

for

one

city

(Bishop,

California)

(lA) Z

Cycling

Mode

[(6)U00,784] co»^rsfc0^o^%5^ or^cocN

•• tH

CO r> o 1 ^

r-l Hotn

\D

2.0 5.6

10.8 14.8 19.3 23.5 27.0 30.4 33.6 36.7 39.4 42.5 45.3

1—1 1—

1

fsl

r-l w O

rH

63

59.4 54.2 50.2 45.7 41.5 38.0 34.6 31.4 28.3 25.4 22.5 19.7

(11)

1

T.

=

65°F

A

E

(3)

=

0”F

Cumulative Hours 2 7 39109 288 634

1083 164 6

2280 2956 3654 4391 5113

(10) T

=

65”F

A

L

(5)

T^=

0°F

Cumulative

Deg.

Hours

1

126 416 2106 5466

13163 26311 41128 56892 71474 83642 92716 98612

100778

(9) T

oa

65-(8)

^

;

45.3 45.3 45.3 45.6 46.0 46.9 48.4 50.2 52.3 54.7 57.1 59.5 62.0

X Nw' CD

vD

19.7 19.7 19.7 19.4 19.0 18.1 16.6 14.8 12.7 10.3 7.9 5.5 3.0

(7) T

=

0"F

A

T

=65'F

A Cumulative Hours 5114 5111 5106 5074 5004 4825 4479 4030 3467 2833 2157 1459 722

0) CO > >-• [t, ^ pj -H D

o iD O -U O

/-X O lP) CO 3^ ^ "< w "< i ci H H 3 OJ o o

100778 100652 100362 98672 95312 87615 74467 59650 43886 29304 17136 8062 2166

(5) (3)x(4)

Deg.

Hours

126 290

1690 3360 7697

13148 14817 15764 14582 12168 9074 5896 2166

y—\ CN

-X

'

1 N--' OnD

63 58 53 48 43 38 33 28 23 18 13 8 3

1

(3) Total Hours 2 5 32 70 179 346 449 563 634 676 698 737 722

(2)

Midpoint 2 7 12

•

17 22 27 32 37 42 47 52 57 62

(1) Outdoor

Temperature Range

'F

0-4 5-9 10-14 15-19 20-24 25-29 30-34 25-39 40-44 45-49 50-54 55-59 60-64

«

1 C

14
(30

O

CO

0) <f >

CO > I C (U

CO 4J

CO I e 1 -H

<u o

13 >-4 I O P- 1 B a

cO ; U >4-:

[i COO

Il cn ' c 4-1 o c

03

03

B

B 03

3-1 1' 4J •H 1 P : XJ cr 1 C 03

CO 3-4

cn bC 1 0) C : p H 3 4J 4J CO . to 03

3-1 0) rC j C- i-H 1 B CO ' 03 4-1 LJ O

Ij

.i l-l

4-1 0 C3C . o c ! T3 •H

4-1 > p CO o o I1 (U i t-i ' CO H 2O

O) X)co

+-> <c3

CT(1)

<D

0) GO

u CD U.

>3 o w CO IT) o TO) VO

60

•H 03 -o

03 03 c

TO

<+- t30 o 03

L

03 TO) h-C

0)O)2+-> O)

J=>

(U -aoE

03co

>>u

O)

s-3

4-> fO

t.(UQ.E

(U

+->

5-oo

T3

+-> 3O

X>

03 4->

032

03 2o

03

03 MOC

03

03

C/3 2o

03 JQCo

4J

TO3

O'

03

03

03

t/3 oLD

•oC

TOUc

03

032

-M

03

03 -oO

03

4-> TO

4->

C/3 >3

"O

TO

03

+->

C/3

03

S-3

+-> TO

i.

03CLE

03

+-> 0 03 03 3 03 03 O TO “

«V ^ 0 <13 D > - TO

TO

l-03>

TO

II II

TOO

TOO

II II

LT3 CO

CO

TO

4-> 3 3

Q. l=L +3 +3 VO VO VO VO VO VO CO VO 3 3 CTt 00 VO in CO CM O o O o O o o o o o c X

•r“ TO s:

(33 - 1 C cn CO f— r-^ cn

fO

C •!- r— r— CVJ C\J CO CO CO ro o O 1—

— 2: o

>-, C_3 O

•r“ lO VO cn r— VO

TO

U in in in

>3 O

C 03

•I- c

LO <+-o

03 03 U -O

>3O

I— o s:

c/3 sOLf)<o<oa30jcoTO- oo>oor^ir)»^CMi

CO C'J

PC CO VO CO r-~ in in cn o C\J CO Lf) CO CO cn o CO to o

<v CO CO o CO VO r~ CO CO to 0) CO CO m CO m CO in VO

II cn o o cn CO VO

M 1 0) CO

-o

sz

O CM p—

+3 »—

W VO o

•r“

—oX—,

to •

s- CO CO CM cn o r>* CO VO

u

CO 3 o cn in in CO CM CO cn in 1— c o r— CO in VO VO in in ro o PC 1 •f“

-!-> in r—

03 VO o 3 U cr . O CM u

0) CM

u CM CM CM CM CM 1 h- to VO 1— [O (— r~ CM CM CO CO in in VO EO 1 s-

<+- LO

03 VO

-a s03 3 II c +3 cn <n cn cn cn

•r“ TO CM CM CO CO in in VO CL) fO r— $- 1 1 1 1 1 1 1 1 1 1 o 4-> 03 03 cn O in o in o in o in o O

-Q CL cn-—.

CM CM CO CO in in VO E o E C Ll_ 03 TO O o

CO h- CC'-' •P”

roou

<-) I—I lO

CO o- w ,

COoo

to

<o

03 -oo

03 +3

TO +3

C/3I >3 -o

TO03

-1-3 C/3

(Z>

TOOo

>3o o o O (_) oo

CSj

TOO

15

NOTE:

All

calculated

values

in

this

table

are

based

on

no

oversizing

(a=0)

Each

line

of

Col, 6

represents

the

average

from

eight

cities

with

individually

calculated

values

from

specific

data

for

each

city.
Table

3.

Summary

of

stack

losses

and

efficiencies

fora

room

heater

rated

45,000

Btu/h

(13,185W)

•KbO

5-1 OJC 6^ W CO I vO I 00 a^ I ^ ro I a

CO CL) <3 \0 CM CN 00 CNJ 00 rH rH cn 3 >4 /—s • • • • • • • » • 3 O p4 6^ fH LO <r 00 <r o CH 5 •H rH \0 vO in vD \D < 4-1 W C w

rC3

4-1 CQ bO o > o ^3

T3

a < o CO 3 - in 3 00 00 in 3 CN O CU X) 1—1 • » • 4-J • • • 4J • • • t-J *H 3 mT (N rH pq CO o pq m O 1 O 4-1 ^ \D r^ VO vO

4J

H -3 3 4-1

OO 5-1 4-( bO fr 3 O o CO 4-4 •H '-4 O o

P4

W 3 Qi 13 X) cO o O CN 1—1 B

4-1 4-1 bO 3 3 3

TO •H 3 3

0) o 1 N 1—1 5-1 b4

4-) bO

O •H •H

x: cO Xi CD

w 44 4-4 bO 3 4J o O 00 o^ <r OV

*H 0) 3 3 3 • • •' • • 15 • • • 0) > 4-1 4-1 m cn <r cn O Ov CO CO O cr> CvJ o\

:s < CO CO cr 3 1—1 vD 1—1 vD r-- vD

4-1 3 1 1 4J3 3 3 O 33 33 B O O

fH

u

B

B

IH 3 o 44 OV in 1 1 bO

m 1 1 bO rH

m CO

»• ^s

u • • • 3 • • • 3 • • • M CN CN CN •H CO CN CN •H <r rH CN

t-J 3 U XJ bO 3 3 3 iH rH

4-J 3 3 3 33 33

U

O

O 3 3 6 e 3 P4 rH 3 B o bO 00 00 cn PC CO CJv VO P4 vD CN & 3 3 • • • 3 • • • 3 • • • B 33 M •H rH o o u CN O o U CN rH o 3

1-4 3 3 3 33 42

4-1 3 3 3 O •H 3 •H •H 3

bO bO bO <1 < 3 3 3 >4 >4

(H *H •H •H pH o 4J CNl CN 3 CT> CTi o 3 CN CO CJv fH (H 3 • • » 3 • • • 3 • • • w w

CO 3 CM CN CN 54 CN t 1 CN 3 -cr CN

h4 3 3 3

3- 3- PC O O O rH 1 /—S

2; rH rH CO I 1 CN 00

O vO CO

m o o 'w' • • • 'w' • • • 'w' • • • o »• r-v m vO o vO CN C3V CO rH

CO rH 1—I

rH CN !—1

tH CN t 1 CN

h4 1bO

•r4h>3 3 5-1 u 3 O 3 < pq 3 C pq 3 <1 pq 'H & C4 3,

5-4 3 B 3 3 B 3 3 bO

•H 3 3 cd 3 3 Cd 3 3 3

4-1 t3

Q 3- 3. pq C4 PC pq PU 3- 3 3 3 B 6 B B B B 3 3 O O 3 ci3 o 3 3 o 3 3 W H C3 2; O Q 2 Q O 2 Q O ^c

16
^—s 0 LO 3 P PQ • • • m x: 3 s >o- cn 1—!

00

p pQ) 1—! 1 r! 6

5-4 1 12 3 r cn

m LO 3 CO Q < • * •K z. cn cn d ^u

[p

(U Xi C/0

p

ex'-.

p 'H

B =1 1 3 I—1

eg 3

QJ 4J 1 0 a. • • • P M a B vO m 3 3 •H O 0 P

IP o *• P O w 3

#s t—1

go •H 0

a>

m

p :

rH 0 3 <r 1 Ip 3 'W' vD to cn 3 •H 1—1 1 0 & = 0 X

fp T3 e M •H 0

QJ 3 3 : <3^ a^ P •H

T) P In P 0 cn

m cn a> 3 0 C n3 w 3 Nw/ CM Csl 1—1 3 P

CO !-i P cr CO 3 3 3 \ Vj 3 P 0 c/0 OJ P 3 3 P w 4J Ip O- CM 0 x:

cO

B P cO 0 eg

p 3

(U 3 3 3 pz^ vD

m cn P

cj .c P H Q-- 3

CO 3 B < CO P p e P 3 = 3 r

CO o CO CO

Q /—s

CM eg 3 ^ w o v_/ CO iH \o rH 0 3

(U

p N-X CM eg rH 3 X 3 4:: 3 Xi > P X p p 3 3 3 0 3 3 m > C M-l P P /*~\ CM 0 0 CO m 0 CO CO PL| VO LO eg 3 CM

/~v P ''w' vO

m cn 0 0

0) Ip 1 3 3 CM C_) P 1 3 0 a 0 P

CO CO 3 2 B CJX 0 P 3 /-*S r— 0 vO 3 p P cn 0 CJ\ cn 3 p 5

s-x CM iH rH 3 3 X 3 0 3 0 3

CCi r—1 X 3 3 P-i P 0

•H /-N CM 0 IPw

X

CO PCH » •- • 3 P

00 CO 1 P r- eg

X P 3 3 1 3 CM 0 0

•H S 6^ &- 0 0 ex P B w CJ 0 0 3 3 IP I 3 = cn 0 1^ P P 3 P C/!J * • • 3 p ex 3 iH CM Nw' eg eg rH x: 0

ex P 3 0 p 0 3 CJ f \ W

X 0 P 00 0 3

'3 P 1 3 •V

XM 3 /*N eo v£> •H pT P P 3 Xi 3 p • • • M 3 3 0 P CO 3 >s^ eg 3 P > P 3 3 ' p = CO 3 3 P p B < 3 r' 3 X

ex

m CO

M 3 r /-N 'vO 0 3 X

B 0 P CO • • • P P 3 3 "3 3 'w' eg rH 3 (_J P 3 3 P I—1 3 3 3 3 CO 3 cn P 3 0 • 3 m

CJ

w P 3 (T\ 00 rH rH 3 3 3 CO 3 p /--s • • • 3 M 3 P 3 3 3 pZH r-- 1—I 0 II 3 X

C/3 iH 1 0 P 3 3 3 1 Z B 3 X > P > 3 t—1

go P 3 0 P cn • • • 3 zn > H

CN iH 1—! 0 Pi P 0 0 CJ

CO3 pT 3 3 • P "3 rH 3 S P 3 3 3 X 0 W 3 3 > P X P P

00 3 3 3 « 3 3 Pi u W p

m

'd- •H P d 3 3 3 P 3 P a 1—1

00 eg

X

X 3

0» •H Pi 0 c OS uO eg

H 5 0

rH P M

CTl S'? •jc H

17
Table

5.

Effect

of

type

of

thermostat

control

on

energy

saving

potential

of

thermal

dampers

M

W)

C! •H>

cO CO

ocM

0) M

4-t C

0)o

cu

P-i

(U

do

t—

I

CO CJ

QJO

tl3 C

Pm

Oi e (U o 4-t • o cd o

Pi 0) z

X

Jm 1—

I

B oj O 4J • o cd o

Pi 0) z

0) 0) O- cu

E-i cd Q

LO CS

fO LO

vO fO

PQ U

CM

<r m fo

00 cTN

<1 PQ C_>

I I I

<Ti vC CNI

vD n iH

PQ O

00 a' 6^ cu

fi S-. m }-l rH •H (>j •H

CU d cu 4-1 Pm Pm

4-1 00 o X3 Cd o o o

Cd cd 4-1 O 1—

1

4-1 4-t vO 6 4-1 E 4-t 4J Cd cu s 3 Cd 3 3 m CO 4J P4 T3 4-1 TJ 4J B no B

a. o CO •H oo O CO CU Cd •H (U •H B cu o c s O +J X 4J H S-i I—

i

B •H B CO cu cd CO cd

d) 00 5-t x: X u 3 r-4 Z 3 S X c cu bO CJ cu cu •1—) CJ •r-) H •H JQ •H 4-1 x: TJ 14-1 M-4 CO H C_3 CO H C C^ O <d o

18

NOTE:

For

additional

details

on

test

results

and

calculation

procedures

for

heaters

equipped

with

thermal

dampers,

see

Ref

[6].
Table

6.

Effect

of

reduced

excess

combustion

air

on

efficiency

ofa

35,000

Btu/h

room

heater

(10,255W)

equipped

with

(1)

step-modulating

thermostat,

or

(2)

two-stage

thermostat

GOC

•H>

cd CO

0)

t)C cd I ^

0) CO a Io U {>0 •w C C *H O 4J o cd

0)00

<d COI I o o cu 5 C G. H

0) >>

•H

H

4-<

O *H Mh M 4J

ClJ 4-) cd C <H

rH o D

CdO TJ 3 I O C S

0)

4J

U <D 3

•H

O D. < 3 C

TJ

M

CO (U

CO Cd

0> -U O 3 X X a

Cd

C S M ^ 3 U *3 C QJ

(U oi •H

CJ

0) 4-1

X

4J 4-i cd CO M s3 .X a o

T3(1) o33 Cd a 4-» C CO X <u

cd 3 S 'H

PiH

•3 /-s

Q>

O

0>

U

O 4J 3

Cd 3 iH

C»S <U

X pc: ^ 4= 3 ^ a 3 C X -U M Cd CQ 63 3 S u 3 a -H Cd •H 3 3

(0 00 4-1 3 •H »H CO

u 3 cd c CO 0) a (0 •H 4J O •H 3 O 3 cu Cd 3

•H V4

O 43 3 0)

O

a

a

•uU (U 3 s 3 CJ 4J

X 3 3

CO •Hu 3 o (U 3 0)

O •H

d) 3 cd 3 (U

uM 3 3 •H

H

C cu <u

U 0) dJ 3 4J

a

O 4= > (0

U ^ 4J cu CO 3

CJ •H

U CO Cd 4-> <0 CJ 3 a

4= 0> 0) cu 3 4= 3 3 43 •H U O U o M a 4-t •(—) 3 a 3

•H (U CM

X 'H 3 •H 3 CU o •H

M < (U Cd •H S cd pc:

u

a

r—4

CM ro i
LU

ct:

\'

\

N \ ^\\

I., VV'

x\

' ^ \

J I L

o

a:O

C_)

COo

LU

(J<

I—CO

UJ_J

CO

o o

<0 <N

o

tn

<c

om

o

a:o

(_)

CO

oO

Q.LU

om

UJ

a:<

cn

a.

2:LU

q;O

Q

Q

<

omJo

z

»-<LUz

o

o

a:O

c_>

LU

CD<

tcoo

om

o

*XVW JO % 31VH ifldino iVlH

20

HEATING

LOAD—

(outdoor

temperature)

Figure

1.

Typical

operating

modes

for

heaters

equipped

with

single-stage,

two-stage,

and

step-modulating

controls
Figure 2

ROOM TEMPERATURE

OR SENSING BULB TEMP.

Outlet gas pressure from a step-modulating thermostat control in response to changing room temperature

21
o

22

lodulating

control
Heater

Output

B

Design

Heater

Output

A

)

O

h"

<1

o

Q>

O

>» o—o

o

XBIAI |0 o/^

e\B\i indjno lean

o

“O

cco

O)£MM

CO0

Q

h"

d

OH

<1

o

LO

CD

23

Figure

4.

Burner

output

rate

versus

heating

load

and

associated

outdoor

temperatures

for

a

heater

with

step-modulating

control
OUTDOOR

TEMPERATURE

0.20 0.30 0.40 0.50 0.60 0.70 0.80

MINIMUM HEAT OU T PU T / MAX I MU M HEAT OUTPUT

Figure 5. Balance point temperature as a function of heater output ratio

24
Cycling Mode Fraction = 2530 -f- 4400

or 58%

Non-Cycling Mode = 100-58 - 42%

800

700

600 h

g

500

o

^ 400

o>

i= 300

200

100

0

65 60 55 50 45 40 35 30 25 20 15

Figure 6. Example of bin method used to determine percentage of time

in cycling mode

25
AVERAGE

OUTDOOR

TEMPERATURE,

IN

STEADY

STATE

AND

CYCLING

MODES

Figure 7. Average outdoor temperature in cycling and non-cycling modes

versus balance point temperature (T^^)

26
56

54

52

50

48

4 6

44

42

40

38

36

34

32

30

28

26

24

22

20

1 8

1 6

1 4

T CYCLING

oa

1 n

.0 0.1 0.2

1 00

T_ I I p

0.3 0.4 0.5 0.6

RATIO: MIN/MAX OUTPUT

Figure 8. Average outdoor temperature and percent of time in cycling

mode as a function of heater output ratio

27

OF

TIME

IN

CYCLING

MODE
cd

xndNi land jo %'ssoi >i3Vis

28

Figure

9.

The

effect

of

burner

fuel

input

rate

on

the

part-load

loss

of

room

heater

with

and

without

a

thermal

damper
APPENDIX A

Determination of Outdoor Design Temperature and

Typical Annual Heating Degree Days

for Vented Household Heaters

29

I
Appendix A

Determination of Average Heating Degree Days and Design

Temperature for Vented Room Heaters

The 97 1/2 winter design temperature is that dry-bulb temperature which will

probably be exceeded 97 1/2 percent of the time for winter months (December,

January, February). Through consideration of the geographic distribution of l| vented room heaters throughout the U.S., combined with analyses of weather

data, a single value or design temperature, representative of a

"National ;j Average" condition, can be obtained. This value will be different than the ! corresponding value of 5°F for furnaces used in [4]

,

since the geographic ; distribution of furnaces and room heaters is not the same.

Based on 1970 census data, the total number of room heaters installed in each

of the nine geographic regions of the United States is presented in table A1 . j Also presented in table A1 are representative average number of heating season degree days for each of the nine regions. Based on these two pieces of information, a heater population weighted average of space heating degree days for

room heaters can be obtained. Results of the average are presented at the

bottom line of column (4) (4438 is rounded to 4400 degree-days, as the weighted

national average) . Although these data are based on the 1970 census now 11 years ' i old, results are expected to be little affected if more recent census data were

to be used since most vented heaters sold are replacement units for existing

installations

.

The outdoor design temperature can be approximated as the average of the

design temperatures of a representative number of cities having heating seasons

of about 4200 to 4600 degree-days. The heating degree-days and outdoor design

temperatures for 13 cities falling in this range are presented in table A2.

The average design temperature for the group is 15.7°F.

30
Table A-1 Population Weighted Average Space Heating Degree Days

(1) (2) (3) (4)

Census

Region

Population

of Vented

Heaters

% of

Total

Regional

Average

Degree Days

Population

Weighted

Degree Days

Pacific 3,672,950 26.6 3820 1016

Mountain 649,618 4.7 5780 271

East So. Cntrl

.

1,007,956 7.3 3795 277

So. Atl. 2,683,320 19.5 3380 659

W. No. Cntrl. 1,179,377 8.6 6825 587

E. No. Cntrl. 1,640,383 11.9 6610 787

Mid. Atl. 800,859 5.8 6100 354

New Eng. 369,041 2.7 6820 184

W. So. Cntrl. 1,783,762 12.9 2350 303

Total 13,787,266 4438

31
Table A-2 Design Temperatures from 97 1/2% Column of ASHRAE

Handbook of Fundamentals (1972)

DEGREE

CITY DESIGN TEMP

°F

DAYS

Charlestown, SC 14 4476

Huntington, WV 14 4446

Philadelphia, PA 15 4486

St. Louis, MO 8 4484

Albuquerque, NM 17 4348

Evansville, IN 10 4435

Bishop, CA 15 4275

Washington, DC 15 4551

Sandberg, CA 25 4209

Eureka, CA 35 4643

Prescott, AZ 15 4654

Dover, DE 12 4660

Louisville, KY 9 4620

Avg. 15.7
APPENDIX B

Detailed Stepwise Procedure for Calculation of Annual

Efficiency for Heaters Equipped with Step-Modulating

or Two-Stage Thermostat Controls
Appendix B

Detailed Stepwise Procedure for Calculation of Annual

Efficiency for Heaters Equipped with Step-Modulating

or Two-Stage Thermostat Controls

The first 11 steps deal with the calculation of minimum and maximum heat

outputs, and fraction of time and outdoor temperature in each mode. Each

of the following steps refers to a similarly numbered block in figure B-1.

1 . Enter the maximum fuel input rate (including fuel supply to

pilot flame)

.

2 .

3.

Enter the steady state efficiency at the maximum input rate

(determined in accordance with the DoE test procedure).*

Calculate and enter the maximum heat output rate Step 1 X Step 2 100

4. Enter the minimum (reduced) fuel input rate (including fuel supply

to pilot flame)

.

5.

6 .

Enter the steady state efficiency at reduced fuel input rate

(determined in accordance with the DoE test procedure).*

Calculate and enter the minimum heat output rate

Step 4 X Step 5

100

7. Calculate and enter ratio of minimum to maximum output

RATIO

Qout ,min

0 _ out ,max

or Step 6

Step 3

8. Read the percentage of time in the low fire cycling mode fi^om the

graph of figure 7 for the minimum/maximum ratio corresponding to the

ratio determined in step (7)

.

9. Calculate percentage of time in the non-cycling mode (Rj^^) .

R^. . 100 - (Step 8)

10. Read the average outdoor temperatures for the cycling and non-cycling

11. mode, T and Tq^' respectively, from figure 7 at the point corresponding

to min/max ratio determined in step (7)

.

In the next four steps, the average steady state efficiency and on-cycle

infiltration losses for the non-cycling mode are determined.

*References 1 and 3.

34
12.

Calculate and enter average steady state efficiency (%) for the non- cycling mode,

13. Enter the on-perlod infiltration loss (Lj 0N,niin) at the minimum input

rate (determined in accordance with the £>oE test procedure for an outdoor temperature equal to (Step 11),

14. Enter the on-cycle infiltration loss at the maximum input rate

(determined in accordance with the DOE test procedure for an outdoor

temperature equal to T , (Step 11)

.

oa

15. Calculate and enter the average on-cycle infiltration loss (%) for the

non-cycling mode

, _ ON, min ON,max Step 13 + Step 14

h,ON,avg 2 2

The part load efficiency, n,j, for both the cycling and non-cycling modes are determined next, and the weighted average efficiencies are then calculated.

16.

Calculate and enter the part load efficiency for the non-cycling

mode

nu,hi ”ss,hi (Step 12) - I-I, ON,

(Step 15) av

17. Calculate and enter the percentage part load efficiency (%) for the

iwii^-cycling mode

20

^u,lo

" t^^ + PFxt^pp ^^S,0N h,0N S,0FF h,0FF^

where the thermal losses are determined in accordance with the DOE

nrocedure for the minimum firing rate, at outdoor temperature equal

to T (Col 10), and t^j^ = tQpj. = 20 min. Alternatively ,Lg Qpp and

Li qpj, can be measured using the tracer gas technique [6]. PF is the pilot

fraction (the ratio of pilot input Qp to total fuel input .

18. Calculate and enter the weighted average part load efficiency for the

cycling and non-cycling modes

u,wt

or Step

R, X n , + R, , X n lo u,lo ni

8 X Step 17 + Step 9,

u ,hi

Step 16

Appendix B (cont)

35
19. Calculate and enter the weighted average steady state efficiency for

the cycling and non-cycling inodes.

"ss.wt

'

"lo == "ss.mln *hl "ss,hl ^ ^tep 5 + Step 9 X Step 12

The annual fuel efficiency for modulating type heaters is finally calculated

using the weighted efficiencies from steps 18 and 19.

20. EFFYA = ssjWt X nU,wt

X 4400

n X 4400 + 2.5 n X PF X 4600

SSjWt u,wt

Procedure for Calculating Annual Efficiency for Heaters with Two-Stage Controls

The calculations listed above for heaters with step-modulating controls will,

with slight modification, accommodate heaters with two-state controls. The

modifications are as follows:

o replace step (12) with the equality: n u* ~ ^

s s y m ss^ni3x

o delete steps (13) through (15) , and

o replace step (3fT} with a calculation similar to that of step (JPfr) but for the maximum input rate and an outdoor temperature equal to

The annual fuel efficiency given by step (20) will then be for a heater with

two-stage contol.

Appendix B (cont)

36
For

Step

Modulating

Type

Heaters

(Operating

ina

Cycling

Mode

at

Reduced

Input

Rate

(Low

Fire)

and

Non-Cycling

Mode

at

Intermediate

Input

Rates

Between

Low

and

Maximum

Rated

Input

ro

f\i 2 CM O 1—» nJ

T*“

(Uto -r

CuP ro

(U>< 1 1 o

a.C

O • -X

•Xi(Uo3

0) Pi

<SJ 6^

•U 2: 3 o cx,

•> 3o

s:

<u CO -I rsj CO o c —> u ^ (1) I m

to

d

CO o + U 'Z

(U CM > c ^

-< -H I—I O

O) -oo - s:

COO CD

I— c

•I- CD

<uCD fO «J I—

i~ 3

OJ -o o > o s- c s:

O)

fO "O I

o o

d)CD

«3

s-

<u>

<c

CD

I— E o o

s- o u_

CS7 COC o

OJ “tM o c rH 1—{

•H o H

D o

M-i 1 OJ O c •c o o

5^ 2 Z o

00 <>

p-l Pxw o

CO

CO 33

to

COVj

(U><

00 c

0)tlc

cu><

soIC CJ o

tocoo • ' ^ d "3 CO 30 O z z s

37

ycling

mode [(

9)(1

6)-K1

7)

(8) ]

ilOO [U

2)(

9)+(

5)(

8) ]

MOO

From (1

g)&

(1

9)
APPENDIX C

Computer Program for the Evaluation of Annual Fuel Utilization

Efficiency and Energy Consumption of Vented Heating Equipment

With Single-Stage, Two-Stage, and Step-Modulating Thermostats
Appendix C

Computer Program for the Evaluation of Annual Fuel Efficiency of Heating

Equipment With Single-Stage, Two-Stage, and Step-Modulating Control

Program Description

The computer program to be described here is based on the original program

NBSFBS5 developed in 1978 by Kelly, et al [2]. While maintaining the previous

structure of NBSFBS5, the present program handles heating equipment with singlestage, two-stage, and step-modulating input, and permits the use of tracer gas

measurements in determining off-cycle losses (see Reference ) . The computer

program consists of a main program, entitled FBVH, and four subroutines: SENLOS,*

WEIGHT, OFFLOS, and FUNT4. It is written in ASCII Fortran and should be

compatible with most Fortran V processors with a minimum of change.

The main program FBVH, as its predecessor, chooses calculation paths, makes

appropriate calls to subroutines, and performs calculation steps based on input

information. The theoretical calculations and the order in which the calculations

proceeds are essentially the same as in NBSFBS5. For single-stage controls, a straight-through path, identical to that in NBSFBS5, is taken. For step-modulating

and two-stage controls, outdoor temperatures and time in each mode are determined

via a call to t,jeIGHT, and two passes through the calculation stream are then

taken. In the first pass, input data for the maximum firing rate and outdoor

temperature T^^, are used. In the second pass, required parameters are saved,

and data for the minimum firing rate and outdoor temperature To^f are used.

Weighted efficiencies are calculated in accordance with section 3.2.

Subroutine SENLOS determines values for steady state: latent heat loss

sensible heat loss Lg and steady state efficiency Tgg as well as other

parameters. This SENiOS ’version contains the stack to flue mass flow ratio S/F

(SFR) computed from stoichiometric relationships and is used in place of the

input value of SFR for all calculations (the computed value was previously used

only if it was greater than the input value of SFR)

.

Subroutine WEIGHT assigns values for average outdoor temperatures in the cycling

and non cycling modes (Toa and Toa' respectively) , and the fraction of time in the

cycling mode. WEIGHT is called only for step-modulating and two-stage heaters.

The subroutine OFFLOS calculates off-cycle sensible heat and infiltration losses

based on the tracer gas technique described in Reference 6, For this calculation,

which is optional, twenty measurements of tracer concentration in stack gas are required at one-minute intervals, along with the initial tracer concentration, and

tracer gas flow rate and temperature.

Subroutine FUNT A calculates functions required for the analytical determination

of off-cycle stack losses (the current DOE and default means of calculating offcycle losses) . FUNT 4 is unchanged from the NBSFBS5 version.

*SENLOS used in this procedure is modified from another form of the

SENLOS given in Reference 2 with NBSFBS5.

39
A flow chart of FBVH including corresponding statement numbers from the

program listing, is shown in figure Cl. This figure does not include all

program details but only those essential differences between FBVH and NBSFBS5.

The majority of the theoretical calculations are performed in statements 132

through 256 and are described in detail in Reference k . The complete program

listing, with subroutines, is shown in figure C2.

Input Data Format

The input data file or element for FBVH must be consistent with the format

shown in figure C3. A sample data form is presented as figure C4 for comparison

It should be noted that when ICTRL and LOSOPT are selected such that some lines

in figure C3 are omitted in the data file, blank lines should not be inserted;

the line numbers in the data file will therefore differ from those in figure C3

in certain cases.

Sample Input and Output

Sample sets of computer program output for a heater with a step-modulating and

with a two-stage control are presented in figures C4 and C5 respectively.

Appendix C (cont)

40
Figure Cl. Flow chart of main program FBVH

16

21

49

54

66

84

99

100
132

257

274

275

276

305

313

314

316

Figure Cl (cont)

42
Figure C2. Main program and subroutine listings; main program FBVH

HTRS*B0IL6A(

12

34

5

6

78

9

10

1 1 12

13

14

15

16

17

1 ) .FBVH(3)

C PROGRAM FOR THE EVALUATION OF FURNACE/BOILER/VENTED HEATER

C SYSTEMS WITH SINGLE. TWO-STAGE. OR STEP -MODU LATED INPUT.

C THIS PROGRAM IS BASED ON THE ORIGINAL PROGRAM NBSFBVH

C (BOILS) DEVELOPED IN 1978 BY KELLY . CHI . AND KUKLEWICZ.

C WHILE MAINTAINING THE STRUCTURE OF B0IL6. THE PRESENT

C PROGRAM PERMITS THE USE OF TRACER GAS MEASUREMENTS IN C DETERMINING OFF-CYCLE LOSSES. AND HANDLES HEATING EOUIPC MENT WITH SINGLE. TWO-STAGE. OR STEP-MODULATED INPUT.

C

DIMENSION TITLE(20.2) . CONC ( 20 ) . TS ( 20 ) . CONCM( 20 ) .TSM(20)

DATA PHI.REFTRM /0.7.70./

C

C INPUT NUMBER OF DATA SETS

C WRITE (6.500)

READ (5.*) NRUN

DO 310 1=1 .NRUN

18

1 9 20

2122

23

24

C

C INITIALIZE COUNTER AND HIGH-FIRE VARIABLES

C NPASS=1

QS0FFH=0.

QICFFH=0.

0S0FFM=0.

25 0I0FFM=0.

26

27

28

29

30

3132

QINH=0.

EFYSSH=0.

EFFYUH=0.

QI0NH=0.

CC I/O SYSTEM PARAMETERS

C 33

34

35

36

37

38

39

40

4142

43

44

45

46

47

48

READ (5.510) TITLE

WRITE (6.520) (

( T I T LE ( 1 1 . J J ) . 1 1 = 1 . 20 ) . d J= 1 . 2

)

READ (5.+) IFB. INST . ICTRL. LOSOPT

IF ( IFB. EO. 1 ) WRITE (6.530)

IF (IFB.EQ.2) WRITE (6.540)

IF (1FB.E0.3) WRITE (6.550)

IF (INST.E0.1) WRITE (6.560)

IF (INST.E0.2) WRITE (6.570)

IF (ICTRL. EO.O) WRITE (6,580)

IF (ICTRL. E0.1) WRITE (6.590)

IF (ICTRL. EO-2) WRITE (6.600)

IF (LOSOPT. EO.O) WRITE (6.610)

IF ( LOSOPT . EO. 1 ) WRITE (6,620)

C

C I/O DATA FOR MAXIMUM FIRING RATE AND CALL SENLCS

C

49

50

5152

53

54

55

56

57

58

59

60

6162

63

64

65

66

67

68

69

70

7172

73

74

75

READ (5.*) NSYS,IFUEL.HHV.0IN.0P.P£,BE.XC02S

WRITE (6.630) NSYS . I FUE L , HHV . QI N . QP . PE . BE . XC02S

READ (5.*) TSSSX.XC02F.TFSS.TF0N1 .TF0N2.TF0FF3.TF0FF4. TF0FF5

WRITE (6,640) TSSSX . XC02F . T FSS . T FON 1 . TF0N2 . TF0FF3 . TF0FF4 . TF0FF5

READ (5.*) TRA.Od.SFR.DF.DS.Y

CALL SENLOS ( I FUE L . NSYS . XC02S . TSSSX . XC02F . T FSS . HHVA . AFR . OL . RT

,

2 OSSS.EFFYSS.TRA. IFB.SFR)

WRITE (3.650) TRA.Od.SFR.DF.DS.Y

READ (5.*) TON. TOFF. TOA

WRITE (6.660) TON. TOFF. TOA

PF=QP/QIN

Cd=3.3

IF (IFB.EQ.2) Cd=4.7

IF (INST.E0.1) Cd=0.

C

C I/O data FOR MINIMUM FIRING RATE. CALL SENLOS AND WEIGHT

C

IF (ICTRL. EO.O) GO TO 10

NPASS=2

READ (5.*) 0INM.XC02SM

WRITE (6.670) 0INM.XC02SM

READ (5,

) TSSSXM. XC02FM, TFSSM.TFONIM, TF0N2M. TF0F3M. TF0F4M, TF0F5M

WRITE ( 6 . 640 ) TSSSXM . XC02FM . TFSSM . T F0N1 M . TF0N2M . TF0F3M . T F0F4M

.

2 TFCF5M

RE/D (5.*) TRAM.SFRM.DFM.DSM

CALL SENLOS ( I FUE L . NS V S . XC02SM . TSSSXM . XC02FM , TFSSM . HHVA . AFR . QL

.

2 RTM.OSSSM. EFYS3M . TRAM. IFB.SFRM)

43
76

77

78

79

80

8182

83

84

85

86

87

88

89

90

9192

93

94

95

96

97

98

99

100

101 102

103

104

105

106

107

108

109

110

1 1 1

1 1 2 113

1 14

1 1 5 116

1 1 7

1 1 8

1 1 9 120

121 122

123

124

125

126

127

128

129

130

131 132

133

134

135

136

1 37

138

139

140

141 142

143

144

1 45

146

147

148

149

150

WRITE (6,680) TRAM . SFRM . DFM . DSM

CALL WEIGHT ( 0 1 N . E FF YSS . 0 1 NM . EF YSSM . PLOW . TOA LO . TOAH I

)

RHIGH=1 . -RLOW

WRITE (6,690) R LOW , RH IGH , TOALO , TOAH

I

TOA=TOAHI

C

C I/O TRACER GAS DATA AND CALCULATED OFF-CYCLE LOSS IF L0S0PT=1

C

10 IF (LOSOPT.EO.O) GO TO 20

READ (5,*) (CONC(d) ,TS( J) , J=1 ,20) ,CONCI ,VTTT,TROOM

CALL OFFLOS ( CONC . TS . CONC I , VTTT , TROCM , TOA , 0 1 N . OSOF FH . 0 1 OF FH

)

WRITE (6,700) (CONC( J ),d=1.10),(TS(d),d = 1,10), (CONC( J) ,d=11 ,20)

,

2 (TS(J),d=11.20) .CONC I . VTTT ,TR00M,0S0FFH,0I0FFH

IF (ICTRL.EO.O) GO TO 20

READ (5,*) (CONCM(d) ,TSM( J) ,d=1 ,20) ,CONCIM,VTTTM,TROOMM

CALL OFFLOS ( CONCM , TSM , CONC IM , VTTTM , TROOMM , TOA LO , 01 NM . QSOFFM

,

2 OIOFFM)

WRITE (6,710) (CONCM( J) ,d=1 ,10) , (TSM( J) ,J=1 . 10) . (CONCM(d) ,d=11 ,20)

2 , (TSM( J) ,d=1 1 .20) . CONC IM. VTTTM, TROOMM. QSOFFM, OIOFFM

20 WRITE (6.720)

C

C LOOP THRU B0IL6 WORKING CALCULATIONS NPASS TIMES

C DO 270 J=1 .NPASS

IF ( J . EO. 1 ) GO TO 30

C

C HOLD NECESSARY VARIABLES FOR MODULATING AND TWO STAGE CALCULATIONS

C QINH=0IN

EFYSSH=EFFYSS

EFFYUH=EFFYU

OIONH=OION

C

C REPLACE MAXIMUM FIRE VARIABLES WITH MINIMUM FIRE VARIABLES

C OIN=OINM

TFSS=TFSSM

TF0N1 =TF0N1M

TF0N2=TF0N2M

TF0FF3=TF0F3M

TF0FF4=TF0F4M

TF0FF5=TF0F5M

TRA=TRAM

SFR=SFRM

DF=DFM

DS=DSM

RT=RTM

OSSS=QSSSM

EFFYSS=EFYSSM

TOA=TOALO

WRITE (6,730)

30 REFTOA=TOA

WRITE (6,740) PF . HHVA . AFR . OL . CJ . RT . QSSS . EFFYSS

C

C *** COLUMNS 31 THROUGH 43 IN NBSIR 78-1543

C TSSS=(TFSS-TRA)/SFR+TRA

IF ( IFB. EQ.2) GO TO 40

Cl =2.

C2=0.

5

C3=7.5

C4=1 .5 GO TO 50

40 C1=4.5

C2=1 . C3=18.75

C4=3. 75

50 IF (TFSS.E0.TF0N1 . AND.TFSS.E0.TFON2) GO TO 60

TA0N=C1/AL0G( ( TFSS-TF0N1 ) / ( T FSS - T F0N2 )

)

ZETF0X=( TFSS-TF0N1 ) * EXP ( C2/TA0N

)

GO TO 70

60 TA0N=0.

ZETF0X=0.

70 CONTINUE

TA0FF=C3/AL0G( ( T F 0FF3 - T FOF F5 ) / ( T FOF F4 - T F0FF5 )

)

Figure C2 (cont)

44
151

152

153

154

155

156

157

158

159

160

161 162

163

164

165

166

167

168

169

170

171 172

173

174

175

176

177

178

179

180

101 182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

21 1 212

213

214

215

216

21 7 218

219

220

221

222

223

224

225

SIF0X=(TF0FF3-TF0FF5)*EXP(C4/TA0FF)

SIF1X=TF0FF5-TRA

IF (NSYS.GT.8) GO TO 90

IF (NSYS.GT.4. AND.DS. LE. (DF/SFR) ) GO TO 80

DSF=DF/(SFR»DS)

SISIX=DSF*SIFIX

SISOX=DSF*SIFOX

GO TO 100

80 SISIX=SIFIX

SISOX=SI FOX

GO TO 100

90 SISIX=0.

SISOX=0.

100 CS=1 .+(REFTRM-REFTOA)*EFFYSS/( 100. ‘(TFSS-REFTRM)

)

IF (NSYS.LT.9) CS=0.

CS0N=24.»(1 .+RT»AFR)/HHVA

IF (NSYS.GT.8) GO TO 120

IF (NSYS.GT.4) GO TO 110

CSOFF=DF*CS0N*(TFSS+460.+REFTRM-TRA)**1 . 1 9/ ( T FSS - TRA ) * *0 . 56

GO TO 130

110 CS0FF = DS'»SFR»CS0N»(TSSS+460.+REFTRM-TRA)**1 . 1 9/ ( TSSS- T RA+REFTRM2 REFT0A)**0.56

GO TO 130

120 CSOFF = DF*CSON* ( T FSS+460 . +REFTRM- TRA ) * 1 . 1 9/ ( T FSS - TRA+R EFTRM2 REFTOA) »*0. 56

130 IF (NSYS.GT.8) GO TO 140

CION=PHI*SFR»CSON

CIOFF=DS*CION* ( TSSS-TRA+530. ) **1 . 1 9/ ( TSSS - TRA+RE FTRM- REFTOA ) • *0 . 56

GO TO 150

140 CI0N=0.

CI0FF=0.

150 WRITE (6.750) TSSS . TAON . 2ETF0X . TAOFF . SI FOX . S I FIX . SISIX . SI SOX

WRITE (6.760) CS . CSON . CSOF F . C I ON , C lOFF

C

C COLUMNS 44 THROUGH 53 IN NBSIR 78-1543

C

IF ( (HHV/HHVA) . LE.0.95) WRITE (6.770)

IF ( (HHV'/HHVA) .GE. 1 .05) WRITE (6,780)

IF (TFSS.EO.TFON1 . AND.TFSS.E0.TF0N2) GO TO 160

TTON=TON/TAON

GO TO 170

160 TT0N=10.**20

170 TT0FF=T0FF/TA0FF

FON=SIFOX*EXP( -TTOFF)/( TFSS-TF0FF5)

F0FF=2ETF0X*EXP( - TTON ) / ( TFSS- T F0FF5

)

F0N0F=1 . - FON'FCFF

FF0N=(1 . -F0N)/F0N0F

FFOFF=( 1

. -FOFF )/FONOF

C CII=.90 IF no EQUIPPED UNIT **

IF (OP.LT.0.1) FFOFF=FFOFF* .90

IF (NSYS.GT.8) GO TO 180

2ETF0=FF0N*ZETF0X

SIFO=FFOFF*SIFOX

SIFUSIFIX

SISO=FFOFF*SISOX

SISI=SISIX

GO TO 190

180 2ETF0=CS*FF0N-2ETF0X

SIF0=1 . 22»SI FOX^FFOFF

SIFI=1 .22»SIFIX

SIS0=0.

SISI=0.

190 WRITE (6.790) TOA . TON . TOF F . TTON , TTOFF . 2ETF0 . S I FO . S I FI C

C COLUMNS 54 THROUGH 59 IN NBSIR 7B-1543

C

IF (NSYS.GT.8) GO TO 210

IF (NSYS.GT.4) GO TO 200

N = 4 CALL FUNT4 ( N . SI FO . TTOFF . REFTOA . REFTRM . F3 . F4

)

F5 = 0. F6 = 0. N = 8

CALL FUNT4 ( N . S I SO . TTOFF . REFTOA . REFT RM . F7 . F8

)

OSON=OSSS-CSON»2ETFO* ( 1

. -EXP( -TTON) )/TTON

Figure C2 (cont)

45
226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

0S0FF = CS0FF* ( F3+S I F I * F4 ) *T0FF/T0N

0ION=CION*( REFTRM-REFTOA)

OIOFF=CIOFF*(REFTRM-REFTOA)*( F7+SISI*F8)*T0FF/T0N

GO TO 220

200 CONTINUE

F3 = 0. F4 = 0. N = 6

CALL FUNT4 ( N . S I SO . TTOFF . RE FTOA , REFTRM , F5 . F6

)

N = 8

CALL FUNT4 ( N . S I SO . TTOF F , REFTOA . REFTRM . F7 . F8

)

QSON=0SSS-CSON*2ETFO* ( 1

. -£XP( -TTON) )/TTON

QSOFF=CSOFF* ( F5+S1 SI » F6 ) *TOFF/TON

0ION=CI ON* {REFTRM- RE FTOA)

OIOFF=CIOFF*(REFTRM-REFTOA)*( F7+S IS I* F8)* TOFF/TON

GO TO 220

210 CONTINUE

F3 = 0. F4 = 0. F7 = 0. F8 = 0. N = 6

CALL FUNT4 ( N . S I FO . JTOF F . REFTOA . REFTRM , F5 , F6

)

OSCN = CS*QSSS-CSON*ZETFO*( 1 . - EXP ( -TTON) )/TTON

QSOFF=CSOFF*( F5+SI FI*F6)*T0FF/T0N

0ION=0.

0IOFF=0.

220 CONTINUE

C

C USE MEASURED VALUES FOR OFF-CYCLE LOSS IF L0S0PT=1

C

IF (LOSOPT.EO.O) GO TO 240

IF (J.E0.2) GO TO 230

QSOFF=OSOFFH

OIOFF=OIOFFH

GO TO 240

230 QSOFF=OSOFFM

OIOFF=OIOFFM

240 IF (NSYS.GT.8) QI0FF=0.

CC FINISH UP B0IL6 CALCULATIONS

C

IF (INST.E0.2) GO TO 250

EFFYU=100. -QL-TON* (OSON+OSOFF+OION+QIOFF)/( TON+PF*TOFF

)

GO TO 260

250 EFFYU=100. -OL-CJ*Od- TON* (OSON+OSOFF )/(TON+PF* TOFF)

260 WRITE (6,800) S I SO , S I S I . F3 . F4 . F5 . F6 . F7 . F8

WRITE (6.810) OSON.OSOFF.OION.QIOFF.EFFYU

IF (ICTRL.GE. 1 ) GO TO 270

EFFYA=EFFYU*EFFYSS*4400/( EFFYSS*4400+2. 5*EFFYU*PF*4600)

WRITE (6.820) EFFYA

GO TO 300

270 CONTINUE

C

C CALCULATE WEIGHTED EFFICIENCIES FOR MODULATING AND TWO-STAGE

C

IF (ICTRL.EQ.2) GO TO 280

EFYSSA=( EFYSSH+EFYSSM)/2.

QIONA=(OIONH+OION)/2

.

EFYU=EFYSSA-OIONA

EFYUW=EFYU*RHIGH+EFFYU*RLOW

EFYSSW=EFYSSA*RHIGH+EFYSSM*RLOW

GO TO 290

280 EFYUW=EFFYUH*RHIGH+EFFYU*RLOW

EFYSSW=EFYSSH*RHIGH+EFYSSM*RLOW

EFYU=EFFYUH

290 EFFYAW=EFYUW*EFYSSW*4400/( EFYSSW*4400+2.5*EFYUW*PF*4600)

WRITE (6,830) E FYU . EFFYU . EFYUW

WRITE (6.840) EFYSSH . EFYSSM . EFYSSW

WRITE (6.850) EFFYAW

C

C RELOAD HIGH-FIRE VARIABLES

C 0IN=01NH

EFFYSS=EFYSSH

Figure C2 (cont)

46
301 EFFYU=EFYUW

302 C 303 C 304 c 305 300

306

307

308

309

310

31 1 312

313

314 310

315

316

31 7 C 318 C 319 C 320 500

321 510

322 520

323 . 530

324 540

325 550

326 560

327 570

328 580

329 590

330 600

331 610

332 620

333 630

334

335

336 640

337

338

339 650

340

341 660

342 670

343

344

345

346 680

347

348 690

349

350

351

352 700

353

354

355

356

357

358

359

360

361 710

362

383

364

365

366

367

368

369

370 720

371 730

372 740

373

374 750

375

CALCULATE ANNUAL FUEL REQUIREMENTS

A= 100000./ (34 1300. * ( PE+Y* BE )+ ( QIN -OP ) EFFYU

)

B=2 . *A*QP*EFF YU/1 00000.

IF (OP. LT .0. 1 ) B=0.

C=0.3B

DHR=EFFYSS*QIN/ 100000.

B0H=2080. *( A*C+DHR-B)

AFUEL=(OIN-QP) *B0H+8760.*0P

AELEC=(PE+Y*BE)’*BOH

WRITE (6.860) AFUEL.AELEC

CONTINUE

WRITE (6,870)

STOP

FORMAT STATEMENTS

FORMAT (/5X.31HINPUT DATA -- ©ADD F I LE . ELEMENT/

)

FORMAT (20A4)

FORMAT (//2(5X,20A4/)

)

FORMAT (/5X.7HFURNACE)

FORMAT (/5X.6HB0ILER)

FORMAT (/5X. 13HVENTED HEATER)

FORMAT (5X. 16HINSTALLED INDOOR)

FORMAT ( 5X. 1 7HINSTALLED OUTDOOR)

FORMAT (5X. IBHSINGLE STAGE INPUT)

FORMAT (5X.20HSTEP MODULATED INPUT)

FORMAT (5X.15HTW0 STAGE INPUT)

FORMAT ( 5X . 30HASS1GNED VALUES FOR OFF-LOSSES)

FORMAT (5X.30HMEASURED VALUES FOR OFF-LOSSES)

FORMAT (///5X. 13H1NPUT VALUES //5X . 6H1 ) NS YS4X . 7H2 ) I FUE L3X

.

2 5H3)HHV5X.5H4)0IN5X.4H5)0P6X,4H6)PE6X.4H7)BE6X.7H8)XC02S/I7. 110,

3 6X.8(1PE10.2) ) FORMAT (/5X .6H9)TSSS4X .8H10)XC02F2X .7H1 1 ) T FSS3X . 8H 1 2 ) T FON 1 2X

.

2 8H13)TF0N22X. 9H14)TF0FF31 X.9H15)TF0FF41X.9H1 6)TF0FF5/3X.

3 8( 1PE10.2) ) FORMAT ( /5X . 6H 1 7 ) T R A4X . 5H 1 8 ) 0U5X . 6H 1 9 ) S/F4X , 5H20 ) D F5X . 5H2 1 ) DS . 5X

.

2 8H22)Y /3X,8( 1 PE10.2)

)

FORMAT (/5X.4HT0N=F6.2.4X.5HT0FF=F6.2,5X,4HT0A=F5. 1

)

FORMAT (///5X.47HADDITI0NAL INPUT VALUES FOR MINIMUM FIRING RATE//

2 5X.6H1 )NSYS4X . 7H2 ) I FUE L3X . 5H3 ) HHV5X , 5H4 )QI N5X . 4H5 ) QP6X , 4H5 ) PE6X

.

3 4H7)BE6X.7H8)XC02S/3(7X,3H--- ) . 3X . 1 PEI 0 . 2 . 4X . 3H - - - . 2 ( 7X . 3H - - - )

.

4 3X.1PE10.2)

FORMAT ( /5X . 6H1 7 ) TRA4X . 5H1 8 )0J5X . 6H1 9 ) S/F4X . 5H20 ) DF5X . 5H2 1 )DS . 5X

,

2 8H22)Y /3X. 1PE10.2.4X.3H--- ,3X,3( 1PE10.2) .4X.3H---

)

FORMAT (//5X.49HFRACTI0N OF TIME IN LOW FIRE/CYCLING MODE = . 2 F5.3/5X.49HFRACTI0N OF TIME IN HIGH F I RE/NON - C YC L I NG MODE = F5.3/

3 5X.40H0UTD00R AIR TEMP FOR CYCLING MODE = F6.2/5X,

4 40H0UTD00R AIR TEMP FOR NON-CYCLING MODE = F6.2)

FORMAT (///5X.22HFLUE LOSS MEASUREMENTS//

63H TIME

13H 8-9

63H TIME

13H 18-19

26HINITIAL

0-1 1-2

9- 10/6H CONC

10-11 11-12

19-20/6H CONC

2-3 3-4 4-5

10( IX. F6. 1 )/6H TEMP

12-13 13-14 14-15

10( IX. F6. 1 )/6H TEMP

5-6 6-7 7-8

10( 1X.F6. 1 )//

15-16 16-17 17-18

10( IX. F6. 1 )//5X.

CONC( ENTRATION) = 1PE10.2/5X.

27HMETER VOLUME/BUBBLE TIME = 1PE10.2/5X.

24HTEST ROOM TEMPERATURE = 1PE10.2//5X.

17HQS0FF MEASURED = 1 PE 1 0 . 2/5X . 1 7HQI0FF MEASURED = FORMAT (//5X, 19HMINIMUM FIRE VALUES//

63H TIME

13H 8-9

63H TIME

13H 18-19

26HINITIAL

0-1 1-2 2-3

9- 10/6H CONC 10( IX,

10-11 11-12 12-13

19-20/6H CONC 10( IX,

C0NC( ENTRATION)

3-4 4-5

F6. 1 )/6H TEMP

13-14 14-15

F6, 1 )/6H TEMP

1 PE10.2)

6-7

F6. 1 )//

16-17

5-6 7-8

10( IX 15-16 16-17 17-18

10(1X.F6.1 )//5X,

1 PE10. 2/5X,

27HMETER VOLUME/BUBELE TIME = 1PE10.2/5X.

24HTEST ROOM TEMPERATURE = 1PE10.2//5X.

17H0S0FF MEASURED = 1 PEI 0 . 2/5X , 1 7HQI0FF MEASURED = 1PE10.2)

FORMAT ( ///5X , 1 8HCALCULATED VALUES-/)

FORMAT (///5X .40HCALCULATED VALUES -- MINIMUM FIRING RATE/)

FORMAT (/5X.5H23)PF5X,7H24 )HHVA3X ,6H25)A/F4X.5H26)0L5X,5H27)CJ5X.

2 5H23)RT5X.7H29)0SSS3X.9H30)EFFYSS/3X.8(1PE10.2)

)

FORMAT ( /5X . 7H3 1 ) TSSS3X . 8H32 ) TAU0N2X . 9H33 ) ZET FOX 1 X . 9H34 ) T AUOFF , 1 X

.

2 9H35)PSIF0X1X ,9H36)PSIFIX1X.9H37)PSISIX1X,9H38)PSIS0X/3X

.

Figure C2 (cont)

47
37 6 377 760

373

379 770

380

381 780

382

383 790

384

385

386 800

387

388 810

389

390 820

391 830

392

393

394 840

395

396

397 850

398 860

399

400 870

401

IS*B0IL6A( 1 ) .1^

12 C

3 C

4 C

5 C

6 c

7 c

8

910

1 1

1 2 c

1 3

1 4

1 5 16

1 7 c

18 c

1 9 c 20

2122

23

24

25

26

27

28

29

30

3132

33

7H47)TT0N3X.

IPSIFI/3X,

3 1PE10.2)

)

FOR'.UT ( /5X . 5H39)CS5X . 7H40 ) CSON3X . 8H4 1 )CSOFF2X . 7H42 )CI0N3X , 2 8H43)CI0FF/3X.5( 1 PE10.2)

)

FORMAT (///5X.46H*** WARN I NG- HEAT I NG VALUE OF TEST FUEL IS TOO

2 7HLOW ***///)

FORMAT (///5X.46H*** WARN I NG- HEAT I NG VALUE OF TEST FUEL IS TOO

2 8HHIGH ***///)

FORMAT ( /5X . 6H44 ) T0A4X . 6H45 ) TON4X . 7H46 ) TOFF3X

,

2 8H48)TT0FF.2X,8H49)ZETF02X.8H50)PS1F02X,8H51

:

3 8( 1PE10.2) ) FORMAT ( /5X . 8H52 ) PSIS02X . 8H53)PSISI2X , 5H54 ) F35X . 5H55) F45X

.

2 5H56)F55X.5H57)F65X.5H58)F75X,5H59)F8/3X.8( 1 PE 10. 21)

FORMAT ( /5X . 7H50 ) QS0N3X . 8H6 1 )0S0FF2X . 7H62)0I0N3X . 8H63)QI0FF2X

.

2 8H64)EFFYU/3X,5( 1 PE10.2)

)

FORMAT (///5X.25HANNUAL FUEL EFFICIENCY = F6.2)

FORrMT ( ///5X . 35HPART - LOAD EFFICIENCY -- HIGH FIRE = F6.2/5X,

2 35HPART-L0AD EFFICIENCY -- LOW FIRE = F6.2/5X,

3 40HWEIGHTED AVERAGE PART-LOAD EFFICIENCY = F6.2)

FORMAT {/5X.39HSTEADY-STATE EFFICIENCY -- HIGH FIRE = F6.2/5X,

2 33HSTEADY-STATE EFFICIENCY -- LOW FIRE = F6.2/5X.

3 43HWEIGHTED AVERAGE STEADY-STATE EFFICIENCY = F6.2)

FORMAT (/5X.42HWEIGHTED AVERAGE ANNUAL FUEL EFFICIENCY = F6.2)

FORMAT (5X.33HANNUAL FUEL ENERGY CONSUMPTION = 1 PEI 0 . 3 . 1 X . 3HBTU/

2 5X.39HANNUAL ELECTRICAL ENERGY CONSUMPTION = 1 PEI 0 . 3 . 1 X . 3HBTU

)

FORMAT (///5X. 16HPR0GRAM COMPLETE//)

END

Subroutine I-7EIGHT

SUBROUTINE WE I GHT ( 01 N . EFFYSS . 01 NM . E FYSSM , R LOW . TCALO . TO AH I ) SUBROUTINE TO DETERMINE THE FRACTION OF HEATING SEASON IN MINIMUM FIRE/CYCLING MODE AND IN MAXIMUM FiRE/NON-CYCLING

MODE, AS WELL AS THE CORRESPONDING OUTDOOR AIR TEMPERATURE

FOR EACH MODE. I .E. .TOALO AND TOAHI

DIMENSION RL0(9) . TOALO) ,T0AH(9)

DATA RLO/0.01 .0.09.0.21.0.33.0.45.0.57.0.69.0.81 .0.89/

DATA TOAL/59.4.57.9.55.2.53.0.51 .1.49.5.47,7.45.9.45.0/

DATA TOAH/42. 1,40.6.38.2.36.1.33.9.31.6.28.6.24.3.21.7/

HIMAX=OIN* EFFYSS/ 100.

himin*oinm*efyssm/ioo.

RATIC=HIMIN/HIMAX

N = 0

ASSIGN VALUES FOR RLOW. TOALO. AND TOAHI

IF(RATIO. LE.O.

IF(RATI0. LE.O,

IF(RATI0. LE.O,

IF(RATIO. LE.O.

IF(RATIO. LE.O.

1F(RATI0. LE.O,

IF(RATIO. LE.O.

IF(RATI0. LE.O.

IF(RATIO.GT.O.

RLOW=RLO(N)

TOALO=TOAL(N)

TOAHI=TOAH(N)

RETURN

END

15) N=1

26. AND. RATIO. GT.O. 15) N=2

35. AND. RATIO. GT. 0.26) N=3

43. AND. RATIO. GT.O. 35) N=4

50. AND. RATIO. GT.O. 43) N=5

57. AND. RATIO. GT .0. 50) N=6

66. AND. RATIO. GT.O. 57) N=7

79. AND. RATIO. GT.O. 66) N=8

79) N=9

Figure C2 (cont)

48
Subroutine SENLOS

HTRS*BOI L6A(

123

4

56

78

910

1 1 12

13

14

15

16

1 7 18

19

20

2122

23

24

25

26

27

20

29

30

3132

33

34

35

36

37

38

39

40

41

1 ) .SENLOS( 1

)

SUBROUTINE SENLOS ( I FUE L . NSYS . XC02S . TSSSX . XC02 F . T FSS , HHVA , APR . OL , RT

* .QSSS.EFFYSS.TRA. 1 FB.SFR)

C ***CALCULATI0N OF HHVA AFR OL RT QSSS EFFYSS *+*

C ***APRIL 1978+** FOR USE WITH NBSFBS 5 **

DIMENSION HHV(6) .AF(6) ,0(6) ,ART(6) ,BRT(6) . CA ( 5 ) . CF ( 6 . 5

)

DATA (HHV(J) ,d=1 ,6)/19800. . 19500. .20120. . 18500. .21500. .20890./

DATA (AF(J).J=1,6)/14.56.14.49.14.45.11.81.15.58, 15.36/

DATA (0( J) .0=1 .6)/6.55.6.50.9.55. 10. 14,7.99.7.79/

DATA (ART(J) , J=1 .6)/. 0679. .06668. .09194, .09646. .0841 . .0808/

DATA (GRT(d) ,d=1.6)/14.22.14.34.10.96,10.10, 12.60.12.93/

DATA (CA(d) .d=1 .5)/2.5462121E-1 . - 3 . 02601 26E - 5 . 2 . 760857 1 E - 8

, -7.4253

321E-12.6.4307377E-16/

DATA (CF( 1 ,K) ,K = 1 . 5)/2 . 441 6834E-01 . 3 . 37 1 1 449E - 6 . 8 . 8906305E - 9

. -1.36

* 1 901 SE- 12,-1 . 43674 10E- 16/

DATA (CF(2.K) ,K=1 . 5 ) /2 . 4361 1 63E- 1 . 3 . 6702686E - 6 , 8 . 7098897E - 9

. - 1 .309

*437SE-12. -1 .5029209E- 16/

DATA (CF(3.K) , K=1 , 5 ) /2 . 5949478E- 01 . - 4 . 9475802E - 06 . 1 .3885838E-8. -2. *C059994E- 1 2.3. 7682444E - 1 7/

DATA (CF(4.K) . K=1 . 5 ) /2 . 6598442E- 1

. - 7 . 7561 435E -6 . 1 . 5833852E - 8

. - 3 . 41 94210E-12.1 .2158977E-16/

DATA (CF(5,K) ,K=1 , 5 ) /2 . 51 63639E- 1

. - 6 . 4 1 44604E - 7 . 1 . 1 31 5073E-8 . -2 . 06

56792E-12.-5.4897330E-17/

DATA (CF(6.K) ,K=1 . 5 ) /2 . 501 1 247E - 1 ,1 . 7737005E - 7 . 1 . 0820337E-8 . - 1 .922

*0641 E- 12. -7.3013274E- 17/

HHVA=KHV( IFUEL)

AFR=AF( IFUEL)

QL=0( IFUEL)

RT=(BRT( IFUEL)/XC02F)+ART{ IFUEL)

XC02=XC02F

TSS=TFSS+459.69

C ** SFR TEST ONLY FOR VENTED HEATERS WITH DRAFT HOODS *** IF(IFB.NE.3.0R.XC02S. LT.O. 1 ) GO TO 30

RTS= (BRT( IFUEL)/XC02S)+ ART(IFUEL)

CALSFR = 1 .3*(RTS/RT)

SFR = CALSFR

30 IF(XC02S. LT .0. 1 .OR. TSSSX. LT.O. 1 ) GO TO 50

XC02=XC02S

TSS=TSSSX+459.69

50 CONTINUE

RTX = ART( IFUEL) + (BRT( IFUED/XC02)

Qr = 0. 42 0A = 0. 43

44

45

46

47

48

49

50

DO 100 1=1.5

QF = QF+CF( IFUEL. I

) * ( TSS* * I - ( TRA+459 . 69 ) * * I

)

100 OA=QA+CA( I)*(TSS**I-( TRA+459 . 69 )* I

)

QSSS=(1 .+AFR)*0F+(RTX-1 . )*AFR*QA

0SSS=100. *0SSS/HHVA

EFFYSS=100. -QL-OSSS

RETURN

END

Subroutine OFFLOS

HTRS+BOI L6A( 1 ) .0FFL0S(2)

1 SUBROUTINE OFF LOS ( CONC . TS . CONC I . VTTT , TROOM , TOA . QIN . QSOFF , OIOFF

)

2 C

3 C SUBROUTINE TO CALCULATE OFF-CYCLE FLUE LOSSES BASED ON MEASURED

4 C VALUES OF TRACER GAS CONCENTRATION AND STACK TEMPERATURE

5 C

78910

1 1

1 2

1 3

1 4

1 516

1 7 18

DIMENSION C0NC(20) ,TS(20)

0FFLS=0.0

0FFLI=0.0

DO 10 J=1 ,20

R,ATI0=(C0NCI -CONC(U) )/CONC(d)

r LCL'^O. 01 * VTTT’ RAT 10/60.

0FFLS=0FFLS+0 . 24* F LOW* ( TS ( J )- TROOM

)

0FFLI=0FFLI+0. 24*FL0W*( 70.0-T0A)

10 CONTINUE

QS0FF=3C0. *0FFLS/QIN

0IOFF=30O,*1 .3*0. 7*OFFLI/0IN

RETURN

END

Figure C2 (cont)

49
Subroutine FUNT4

HTRS*B0IL6A( 1 ) . FUNT4( 1

)

12

34

B

6

78

910

1 1 12

13

14

15

16

17

18

1 9 20

2122

23

24

25

26

27

28

29

30

3132

33

100

110

120

SUBROUTINE FUNT4(N.SI . TTOFF . REFTOA . REFTRM, FI , F J

)

T1=REFTRM-REFT0A

C1 = 1 . T2=REFTRM+460.

IF(N.E0.4) T1=0.

IF(N.EQ.8) C1=0.0

X = 0.

FI =0. FU =0.

DX =TTOFF /500.

FF1 1 = (SI + T1 )**0.56*SI**C1/(SI+T2)**1 .19

FF21 = (SI+T1+100. )**0.56’»(SI + 100. ) *C1 / ( SI+T2+1 00 . )**1 . 19

DO 100 1=1 .250

X=X+DX

XX=SI *EXP(-X)

FF12=(XX+T1 )**0.56*XX**C1/(XX+T2)**1 .19

FF22=(XX+T1+100. ) * *0 . 56* ( XX+1 00 . ) • *C1 / ( XX+T2+ 1 00 . )**1 . 19

X=X+DX

XX=SI *EXP(-X)

FF13=(XX+T1 )**0.56*(XX)**C1/(XX+T2)**1 . 19

FF23=(XX+T1+100. ) * *0 . 56* ( XX+1 00 . )**C1/(XX+T2+100. )**1 . 19

FI =FI +(FF11+4.*FF12+FF13)

Fd =FJ +(FF21+4.*FF22+FF23)

FF1 1=FF13

FF21=FF23

IF( (ABS( Fd-FI )). LE. 0.0000001 ) GO TO 110

Fd =(Fd -FI )/( 100. *TTOFF ) Fd =DX *Fd /3.

GO TO 120

Fd =0.

FI =FI *DX /(3.*TT0FF ) RETURN

END

Figure C2 (cent)

50
Figure C3 . Input data format for FBVH

Line 1: NRUN (integer)

NRUN = number of sets of test data to be analyzed. Lines 2 through 53

should be repeated NRVN times in the stored data file/element

Line 2: TITLE

TITLE = one to 80 alphanumeric characters describing the test conditions/data

Line 3: SUBTITLE

SUBTITLE = one to 80 alphanumeric characters describing the test conditions/data

Line 4: IFB, INST, ICTRL, LOSOPT (all integers)

IFB = 1 for furnaces

= 2 for boilers

= 3 for vented heaters

INST = 1 for vented heating equipment installed indoors

= 2 for vented heating equipment installed outdoors

and floor furnaces

ICTRL = 0 for single stage controls

= 1 for step modulating controls

= 2 for two stage controls

LOSOPT = 0 for analytic determination of off-cycle stack losses

(method used in References 1 and 4) = 1 for determination of off-cycle stack losses from tracer

gas technique (see Reference 6)

Line 5: NSYS, IFUEL, HHV, QP, PE, BE, XC025

Line 6: TSSS, XC02F, TFSS, TFONl, TFQN2, TF0FF3, TF0FF4, TF0FF5

Line 7: TRA, QJ , SFR, DF, DS , Y

Measured quantities/assigned values defined in Reference 4, evaluated

at maximum firing rate

Line 8: TON, TOFF, TOA

TON = 20 min

TOFF = 20 min For Vented Heaters

TOA = 45°F J

See Reference 4 for values for other types of heating equipment.

51
OMIT LINES 9-11 for single stage controls (ICTRL = 0)

Line 9: QINM, XC02SM

Line 10: TSSSM, XC02FM, TFSSM, TFONIM, TFON2M, TFOF3M, TFOF4M, TFOF5M

Line 11: TRAM, SFRM, DFM, DSM

Measured quantities /assigned values evaluated at minimum firing rate

OMIT LINES 12-53 for Analytic Determination of Off-Cycle Losses (LOSOPT = 0)

Lines 12-31- CONC, TS

CONC = measured concentration of tracer gas in sample taken from stack, PPM

TS = measured stack gas temperature, “F

Twenty sets of concentration and temperature measurements for a cooldown following

steady state operation at maximum fire. For more details on tracer measurements

see Reference 3.

Line 32: CONCI, VTTT, TROOM

CONCI = concentration of active traver gas in the tracer gas in PPM, eg, , for

a carbon monoxide/nitrogen tracer gas mixture consisting of 50.8

percent carbon monoxide, CT = 508,000 PPM

3

VTTT = volumetric flow rate of tracer gas, cm /sec

TROOM = test room temperature, **F Values for test at maximum firing rate.

OMIT LINES 33-53 For Single Stage Controls (ICTRL = 0)

Lines 33-52: CONCM TSM

Twenty sets of concentration and temperature measurement for a cooldown following

steady state operation at minimum fire.

Line 53: CONCIM, VTTTM, TROOMM

Values for test at minimum firing rate.

Figure C3 (cont)

52
MAXIMUM

INPUT

MINIMUM

INPUT

MAXIMUM

INPUT

Figure C4. Input data form for FBVH

LINE

1

2

3

4

5

6

7

8

9

10

11

f

~~ FBVH DATA~ ~

| ^N IK | DATE

NRUN

TITLE

SUBTITLE

IFB INST ICTRL LOSOPT

NSYS IFUEL HHV QIN QP PE BE XC02S

TSSS XC02F TFSS TFONl TF0N2 TF0FF3 TF0FF4 TF0FF5

TRA QJ SFR DF DS Y

TON TOFF TOA

QINM XC02SM

TSSSM XC02FM TFSSM TFONIM TF0N2M TF0F3M TF0F4M TF0F5M

TRAM SFRM DFM DSM

'12

13

1415

16

17

18

1920

212223

24

25

262728

29

30

31

32

TIME CONC TS

0-1 1-2 2-3

3-4

4-5

5-6 6-7

7-8

8-9

9-10

10-11 11-12

12-13

13-14

14-15

15-16

16-17

17-18

18-19

19-20

CONCI VTTT TROOM

LINE ’33

34

35

363738

3940

414243

44

4546

4748

49

50

5152

53

TIME CONCM TSM

0-1 1-2 2-3

3-4

4-5

5-6

6-7

7-8

8-9

9-10

10-11 11-12

12-13

13-14

14-15

15-16

16-17

17-18

18-19

19-20

CONCIM VTTTM TROOMM ]

53
Figure C5. Program output for a heater with step-modulating control

in o U. CM o U. CM

to o U. o tn o u. O

CN O O O CJ o o o

o + U. + O -f U. + o o *- 00 u o J- 00 ^

X O) — o X <0 -.o . u> • to • 00 — — CO ^ —

'T 'T CM U. CM U. CM o u. O U. O

o o o O • u. + 1 U. +

UJ in t- ^ UJ 1 1- 00 m CM ^ m CD t — CO

. in • *—

»

in • *- — —

CO CO

tl. CM o U. CM

u- O o U. O O O o o o

u. + + « UL + • Ul o J- T >- 00 UJ • J- in >- < • o. o -.00 — to a • — o <— • Ul . . >T • CM • J—>» 'T • CM

cr (O r- CM CM ^ CO ^ CM CM

u.

CM CM CM O CM CM O

X o Z O o UJ Z O O

o o O O o »- o o O »—« + u. + to + < 1 u. + to + X a. in J- in Q O (r a I 1- to Q O O GO cn — O a • -.CO -. o

& . CO • — o to • — . in m in CM *- z tn r- O’ CM •- z

3 o a o — CM O • l-H — CM O

o O z o O in U. o z o O «l o o o O o o o o o z + u. U. + s z + U- + u. + o •-< CO t~ C7) O O 11 -• o 4- O’ Q O

o o c lo — O < s o m — c^ — O

CM • O • o •—

1

J—s . CM • O • 1- T- CM — *- z ^ cs — CO CM T- z < (/) »—

4

UJ UJ 5

s ££ If) CM O CM O

LU o If) o to O O q: to o O

—I Z UJ o o in o U. O O to o U. O

UJ > + u. + \ + o u. > 1 u. + \ +

• o • 1 X — 1- O) to CM o X • J- — to cn

UJ UJ u. u. I o —. — CD • </) X • — O) — CM 2 o 11. . —• 0> • o UJ — 0) •

1 -J o o CO CM — in CO — T- y

iJL »-4 UJ t- I Q. S 3 ir <

a CQ OL o U. o U. > u. o

a o> Q a Z U. —i CM o u. «J CM O

< tu O' t-t UJ o o o J“ UJ O O

u z o to 3 u + 3 »- 3 3 • O + 3 I r* O 3S o a UJ u. X lO O O a U. 1 X O o • « o o ce o UJ 3 ~ CO ~ o z ^ 1 — ^ <— • X • UJ a UJ Z t- -1 C/) — CO o • 00 • »-« o CO > a -J »-•-<<< UJ CM — a T» m < o < -j > o

u. o UJ O 3 o <

< u X UJ o o < CM — z CM —

< o -J O UJ > o o o o o o

(£> _J O -J s z to m o < o CJ in to o < o

r— < Ul < O 1- >- to + ct + 1— >• I to + CC + s 1- t- a >-< to to o H- O II {/) I to in 4- O

O a cr Z (/) Ul to a z 1- CO — CM z o z » 1- CO — CM z Q. g

Ul Z J- to z —. »• —. . • o o —

s

—. . • •—

<

- z > •-• to < V— a CM — c* < OJ — r- o

a

X <

&

54

FRACTION

OF

TIME

IN

LOW

FIRE/CYCLING

MODE

*

.690

FRACTION

OF

TIME

IN

HIGH

FIRE/NON-CYCLING

MODE

.310

OUTDOOR

AIR

TEMP

FOR

CYCLING

MODE

=

47.70

OUTDOOR

AIR

TEMP

FOR

NON-CYCLING

MODE

=

28.60
tA

X to

K

1/) •*- o »- -< X— in to XO X- 1—1 X— in > O «) o U. O o > o (O o U. o o

u.

O HH

O •- o o 11. o MO I-I

O o u- + w + CO + 00 • u. + to + to + 00 1 LLl Q a. 00 CL O U- c^ ID O' a. CO a o li. CM

cn <9- -x CO ~ 00

— 10 CM o • 00 - X- cn • o • CO • cn X fO ro ^ m CO in CM to r-x to CM in CO in CO X X »- — o O CM to »- « o O CM to

CO o in o u.

O o CO o to o u. o o

CO

O

M

O 1-

O o to o >-X

O I-I o o tA + Crt + to + CO + CO + CO + C' 1 C7 O a CL o U. fx- O X- Q. cn a CO U. CM ^(0 'f -^co -—X ^ ^ f' -'to -'CM — 00

C» • r' • o • oo • cn • C" • O • 00 • CN (Ti in CM in in CM X- to 00 m •- in CO X X O X- O CM o LH X— O CM o u. o u. o o ti. o U. o o -< o t- o o « o 1- o + in + UJ + CD + to + UJ + CO

cr COa o N 'T u.

O cr 00

a o M 4 u. o

'—in x-X<0 ^co— tn ^ to— in— o 3

cn • ID • cn • • 00

X toX tnX f'

X

K

Oi ^ n cn o- CM in CM CM to to 4 CM in CQ X X .. O CJ a. -r- U- O 3 — O CM li. X- u. O 3 X- r- O

liL

O u. o u.

O >-

O UO u.O U. o > O ^ 3 o i-t O o o o o u. o M o o o o o u. O (O 00 • f- +

“D to + •-> + H- + m u. + 3 to + •-< + V- + in u. + in in 00 T— u o a o cj in 1- 00 u. o UJ <0 CJ o CL to O X- h- CO u. o ID r- • CO 0) CO — o ^ CO ~ CM in ''O in CM — o .—,

'-'O

— to • CO o • in • CO • CO • to • o^ • X in X to X CD • CO X 4 X (Ti 10 00 • It o • CN cn CM «T »- O' to in CO CO CM to X- 4 CM 4 to tn CO to o ^ CO II o 00

LLl • > +

U- t- u.

O • H o > T- o o CM to U. o 4 o u. o T- to u. O <0 II z u o u o o o Z O z o o u. O cr o o o z o z o o li. o <D > H Ui z t- o 3 o O O o o o o o o 3 O o o o o o o o o LU LU • z

-i + < + i-i 1 *- + O’ • + O -> + 4 + 1 1- + 4 1 I-I + II z a LU o I-* CO o O LO H- cn O <T) t- to ll cm O CO z o in I- Oi O C' t- in U. O' o to U UJ •*4 Of U »-* * in lO ^ m 00 -^o -'f' H -xin to — to X— — <o — 00 UJ u. u. HCO • ^ CM • • in • to • cr to • «T • CM • r* • in • to X q: Lu o u. u. U. II o.

CM cn 00

m cn <? •<- in CD CO CM CM cn CO CO 4 X- 4 to in t' CD X- •-* cc »-< I LD u. s

U. u. »-« u.

O 3 UJ z 3 X X u. u. I-I O ID o LO - O CM U- o x~ o S O CM u- O X- X- o X UJ X -1 1- -J t-H z o u- O ti- o u. O o z o 3 o ti- O u. O IL O o z o a 3 4 UJ l~ o

u.

O t- o o o U.

O o o o s u. o 1- o o o u. o o o o o o 1 1 »- 3 a o \ + LJ + to + o + to • •-« + \ + UJ + to + o + CO 1 I-I + I -j < 1 1 tn U. S < in M 0~ O 00 h- O ti. 00 ot' z 4 in Nl f* CJ CO 1- o U. X- O CO o 1 > ^ tg- to — CO ^ r- cn ^ o -'in — 4 — o — 00 — o 1 1 ^ >- > >* •J to o m • CO • •w- CD • «T • CM • £ in X to X CO X 4 X CM X 1 • 1 U U Q < z o:

CM T- CO CM 'T CO >3- CM in CO CO CO CM *- CO CM 4 in 4 CM in X- CO CO i~ z z < 3 o LU » >- >- c: UJ LU LU z u z « o u < z UI Z O CM <-) o U. O o z »- CM X— M o U. o z z a u.a tn < >

<l

O

O

O Z O o cn o u.

O tn 4 O o o z O o CO o u.O UJ UJ

a .J > o 13 O O O z o —I O o o UJ > O 3 O O O z o *-i O o o ^ Hi Li. U. UJ UJ cr < lU X + <. + CO t o + to + CO + 3 I + 4 • CO • o + to + to + o o o U. u. O O LU o H* I *r. t- cn tj ^ *- o ti. !«. o in _J X X- - 4 CJ t' 1- o CL cn O 00 ^ < UJ LU < < z •—1 lU — o —X 00 — o O’ CM 4 ~o — to — in — o — cn 4 ii. Li. o: Ct CC LU q: .J ^ • CM • o • in • to • T- « > O X CM X O X in X to X X— X Ll- Li. LU tu LU LU LU I- o.

CN CM to »-

V CM

V CM in O' to CM CM CM CO CO 4 4 4 CM in 00 CO CM UJ LU > K 1- > > -1 o s O < < < < < UJ LU o

ID o o IK

u

CM CM X- o - 1- CM CM . XO X- X- < < Q to in

QQ lu LU

O LOO o to o z o 4 O to

O ' o m o z o O

O UJ • 1 UJ UJ s o to o < o *- o o o _l o to O 4 O -1 o o o -J -j h- > > K- 1- -J .J <x

O. I to + tO o + CO + to + 3 li. 1 to + to o + to + to + • • X

QQ

XX < < cr

c. in ID CJ o f- 'D

a 00

O CMU Cl in 1-O o o 1- r*

a CD

O 1^

K

O < < O

O Zi 3 o ^ o o CD t^ ^ 10 —1 — o — t" — o — t' — 00 — to cc a H4 LU lU Z o

ro • cn • • CM • o • 4 toX tn

X 4 X CMX

O

X < < LU lU lU z z cr

CN ^ to ^ to 'T CM in O’ to x- CJ CM X- to X- to 4 4 in CM CO Xa D. 3 to CO .3 s < < Q.

Figure C5 (cont)

55
Figure C6. Program output for a heater with two-stage control

in in O U. CM O U. CM to o u. o in o u. o

CM O o o cx o o o

O + u. + o + u. + o o *- 00 u o h- 00 X o> X CO '-'O

. to • to • CO »- — *“ CO *-

tj- c< II. CM U. CM o U. O u. O

o O O O

• u. + 1 U. +

UJ in 1- '0- UJ * J- (D a cj -^m GO • — CO

.-K . m • in • -- *- Xto to

U. CM o U. CM

LL O o U- O

o o o o o

u. + + • u. + • UJ o »- ^ > CO UJ • *- in >- I • a o — 00 CO a. • — o —. • UJ • • CM • «T • CM IX to — CM CM — ID CM CM

u.

rv CM CM O CM CM O

X o Z O O UJ z o O

o o o o O 1- o o O I-* + u. + to + < « U. + to + X CL in *- in a o a a. 1 1- to Q O O 00 o> -^o O ' -'CD -'O

<» . CO • »- a CO • in in T- in CM — z in — tj- CM — z

3 o q: o «»• — CM O — CM O Q o z o o in u. o z o O -1 o o o o o o o O

O z + u. + u. + S z + u. + u. + o —• to t- o> o o H 3 o »- n- o o

u oo .^to < S o in -- c~ —V . CM • o • o •-H CM o

h- —I — tj- CM — »- z V cx — to CM —

z < to

UJ 2 UJ 2

IX </) tj- CM O CM O

UJ o (/) o to O O q: to O O

Z UJ o o to O U. O o t/3 O U- o

UJ r— a -i > + u. + \ + o u. > • U. + \ + • a - H.* 1 I *- t- a> to CM o X « 1- T- to C33 UJ tu 1- u. u. X o ^ 03 to X 1 03 CM s O u. . <n • o UJ 1—IL at •

1 -> o o CO C4 *- to — V CN 3 w — "T u. —• UJ X a. s ce M < o 01 O U. o u. > u. O

o a> O ft u. CM O li. •J CM O < _j UJ ce UJ o o O »- UJ o o

3 u z o t- to 3 o + 3 h- 3 3 • o + 3 • s 3 3 O 3 UJ u. X to o o Q. u. • X O O •

1 Q O a: o a. 3 to ~ o Z < — tr —' • X 1 UJ O UJ z Z -I to — 00 o • 03 • —X o • 00 > O' -1 t— «-4 M < UJ CN — 1^ CM —

CD < O < > 3 o _J

U. o UJ o UJ o <I < u X UJ O O < CM r- z CM r~ < o -1 < UJ > O o o o O o

CO Q -1 Z to to o «1 o cx to to O < o

_J K < UJ < to O »- > ^ + 13: + >- • to + CE +

Z) s 1— 1- >- 3 to to o f- o If tn • to in h- o o a ce z to o to a z »- CO CM z Q z • 1- 03 CM CQ z CL o UJ Z 3 (/) z — T- . . • o Q ^ . f' • • z at CM 1- < 03 — — I'- H- o

o o

X <

0,

56

fraction

of

time

in

low

fire/cycling

mode

=

,690

FRACTION

OF

TIME

IN

HIGH

FIRE/NON-CYCLING

MODE

*

.310

OUTDOOR

AIR

TEMP

FOR

CYCLING

MODE

=

47.70

OUTDOOR

AIR

TEMP

FOR

NON-CYCLING

MODE

=

23.60
•J)

X inX

</> ^ O »—< T—m tn »-

O T- •-4 T- in > o CO O Ll- O o >- o cn o u. o o

u.

O o o o U. o o •- o o

u» + to + CO + ro < u. + cn + tn + CO • uj cn O- CO C- o UJ ^ CL CO CL O U. CN ^ CO ^ 10 '-'t — to ^ 00 -^lO ^CN o * CD • Cl • o • 00 • »— • cn • CO CO ^ in n in CN CO t'- CO CN in to in to X X — o O CN to .r- — o O CN to

CO

O to o u.O o in o 10 o u. o o

CO

O o KHO o tn o o 1-4 o o

lO + to -f CO + r* • in + in + in + C' 4 a e 0. a- O 11. o -r- CL 0) CL CO u. Cl ^ {D ^ ro .—- T— —' CO — CN 00

O) • O cO - cn • O' • o • 00 • CN ^ in r'i LO tn CN T- CO 00 LO »- in CO X X O »-« *“ O CN o T- O CN o U- O L. o o U- O U O o o t- O o O H- O

h- CO + UJ + CO - + tn + to to

Cl CO

a o NJ Cf U.

O QC CO 0.O IM cf u.O ^ in ^ CD CO -'O '-'in .-'to '-'in '-'O 3

CO • (D . o> • • 00 • CO • tn • t' • »-

CV «r- CO CO c rj tn CN CN to CO cf CN in 00 X X CM y- O CM u. u- o Z3 »- O CN u. »- IJ. o 3 — in CD O

f- o U- o u- o >-

O U.O u. o u.O 3-O • T- 3 O •-« o o o o o U. o I- O o o o o U. O to CO • 1— +

“D lO + -f 1- )- in u- + 3 to + + 1- '!• in u. + CD tn 4f

m CN o o CL o o in I-- m u- o UJ CO o o CL CO o »- t- CO u. o UJ t' • 00 CO 4" ^ o ^ CO CM ^ in -'O ^in — CN — o -r- — m to • OD t' CN • in • CO • 00 • CO • «3- • in to ' 00 • CO • 4f • to CO • 11 o • CH CO CM ^ CO in to CO CN to -- If CN cf CO in CO CO If) ^ CO H O 00

lii • >- •{* Li. I- LL in • II a >- CN o u. o CM T~ CO u. o < O U. O T- V- to U. o to to 11 z O O'

H o a o z o 2 O o u. O cr O o o z o z o o U. o to > II LU 2 t' o ZD O o o O O o o o O D O o o o o o o o o IJLI HH UJ • z

*f < + 1 H- + T • •"1 + O -t + < + .* 1 1- + ^ 4 4-4 + li z or UJu

H CO

O o m I- cn U (J) t- to 11. rj O 00. z o in 1- tn o 1- in U. t'- O CO II UJ «~i q: i“* O 4-4 ^ m n't —- in — 00 '-a ^ fl. ~ I.O CO — CO T- (O 00 UJ H-4 U. u. 4-4 t—

CO • CM • O' • in • (0 • cr CO O’ • CN • r- • in • CO • cr UJ cj U. LU U. li O. <N O) CO Lfi ^ cn <tr >- tn CO CO CN *-4 CN tn CO CO «f •- ^ to m t' CO T- »-» o: •-« X UJ u. S

Li. U. t-H LL.

a 3 UJ Z 3 X X u. u. O LU o cn

»-

O CM U- o O s TO CN u. o y— V- o X UJ

X 1- 3 4-4 2:

O u_ o IL

O 11. o o 2 O 3 o u.

O U.O U.O o z o O 3 <t UJ 1- o

uO i- o o o u. o o O

O S u. o 1- o o o U. o o o o *-•O

Q • • 1- 3 a o \ + UJ </) + o + to • <-• + + UJ + tn + o + to 4 4-4 -»• X -J < 1 « m u. S < to Nl O GO »- o U. GO O f- z < tn tsi tj to 1- o U. r~ O CO o • 3 > ^ CO CO o '-'CD l-H ^Xf in — «f — o '-'CO "'O « 1 ^ >- > >• 3 tn (3 m • CO • • IC • M • CN • s tn • to • CO • ^ • CN • 1 1 1 U O Q <c z cc CM ^ CO CM ^ CO <!T CN in CO CO CO CN T- CO CN cf in 'T CN in CO CO 1- z z < 3 O UJ « > > cr UJ LU UJ Z CJ z 1 u o <c *-• *-t 1-* Z lU n ::z o CM <-• o U. O «r z «- Cl 4r- 4-4 o u. O z z o. u o tn < >- < o o o Z O o tn o U. O l/> < o o o z o o in o u. O UJ LU IM tM a 3 > o ID O o o z o t~t o O O LU > o 3 O o o z o 4-4 o o o t-H UJ U. U. LU UJ cc < I - <t + (O • o + cn + cn + 3 I + «* • cn • o + cn + cn + o u o U. UL (0 O UJ CJ X ^ f- O) u ^ 1- o a t'' o m I r- 1- O' O C' H- O CL m O 00 UJ UJ < < Z 4-4 ^ o ^ o ^ 00 o ^ <T '-'CN < O ~ CO -^in -^o "'to "'O’ u. u. cr cr cc UJ q:

*T • CM • o • in • (O • - • > V • CN • o • in • to • U. U. UJ UJ U1 lU LU 1- CM CM CO — rt CM CN in C' CO CN CN CN CO to O’ ^ 4f CN in 00 CO CN UJ UJ > 1- 1- > >30 Q < < < < < LU lU UJ o o 3 3

CM CM r- o - t— - CN CN yy o — 44- < < Q . tn tn

QO u. lU

O 10

O o CO o Z O' < O in o o LO o 2 O

O

O UJ * I UJ LU o (/i O •3 O •-• o o o .J O in o < o 4-4 O o o -J -1 I- >- >- 1- 1- 3 _l

u. * (O f 1/) o + cn + tn + 3 ti. I in + in o + cn + tn + • • X

O

O

XX < < a u) r- lO o o 1- to ft. CO O CN O CL in t- o o o h- t' CL CO O t' h- f- C3 < < o 0 3 3 ^ CO o — CO — to .J ~ «T — o — CO .-V lO CG QC *-• UJ UJ <M -4 Z Z

fO • CD • NT • CN • o • < to • V- tn • ’f • CN • o • < < LU 1- UJ LU z z

CM ^ CO CO 'T CN in ^ CO— o CN »- co »- to f in CN to »- CL CL 3 LO tn 3 3 < <

Figure C6 (cont)

57
NBS»n4A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instruction s)

1. PUBLICATION OR

REPORT NO.

NBSIR 82-2497

2. Performing Organ. Report No. 3. Publication Date May 1982

4. TITLE AND SUBTITLE

A TEST METHOD AND CALCULATION PROCEDURE FOR DETERMINING ANNUAL EFFICIENCY FOR

VENTED HOUSEHOLD HEATERS AND FURNACES EQUIPPED WITH MODULATING TYPE THERMOSTAT

CONTROLS

5. AUTHOR(S)

Esher Kweller and Robert Palla

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7 . Contract/Grant No. NATIONAL BUREAU OF STANDARDS

D EPA RTM ENT OFCOMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

U.S. Department of Energy

1000 Independence Avenue

Washington, DC 20585

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11.

ABSTRACT (A 200~word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here)

As annual operating efficiency of vented heating equipment is affected by burner

fuel and combustion air modulation, it is important to differentiate between the

various types of controls in determining annual energy requirements. Test procedures

for evaluating annual efficiency have already been developed and implemented by the

Department of Energy (DoE) for furnaces with single-stage thermostat control.

A modified test procedure is necessary to account for operation with fuel modulation.

A revised procedure which accommodates two types of fuel modulating controls has

recently been developed. Tests are conducted at reduced and maximum firing rates, and

along with typical derived values from a bin analysis of weather data, the fraction

of the total hours for each operating mode is obtained to calculate a weighted annual

efficiency. These test methods and calculation procedures are based on and are an extension to the current DoE test procedures for the single-stage type of thermostat

control of central warm air furnaces.

By using the procedures developed in the report, the energy savings impact of

fuel modulating controls when combined with the use of modulated combustion air is

evaluated. Energy savings from 6 percent to 20 percent were determined from the

increase in efficiency with both fuel and combustion air modulation. Improved

efficiency was dependent on the type of thermostat control and the minimum-to-maximum

fuel input; i.e., turndown ratio.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

annual efficiency; household heaters and furnace test procedures; hydraulic thermostat

control; modulating control gas-fueled; two-stage thermostat.

13. AVAILABILITY

^3] Unlimited

I I For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

65

15. Price

$9.00

USCOMM-DC 6043-P80