more sizing of spa.pdf

7/25/2019 more sizing of spa.pdf

1/13

APPENDIX D

APPLYING THE SIZING METHODS

D.O

THE DESIG

~~_.IGNMENT

The managE

~r

of a Daytona Beach oceanfront motel plans to install a

solar pool heatE

r with

a full-load capability, LPG-fired, backup heater

The motel is oW]

ed by a major chain which owns another motel in Ormond

Beach -- six mi

les north of the Daytona Beach site.

The buildings, site

layou t , pool size

and relative pool location and climate are almost identical

for the two

motels. Monthly LPG consumption figures for pool heating at

the Ormond Bea

That pool

h motel are available for the past six years.

does not have

Both ~1s are to be

kept

at a minimum

olar heater.

water temperature of 80F

The manage

~r of the Daytona Beach motel has two estimates from solar

contractors for

installed solar pool heaters. One contractor proposes to

use 2500 ft2 of

unglazed, flexible-mat collectors laid flat against the insu-

lated roof deck.

His bid for the installed system is $20 t 000.

The other

contractor plans

to use forty 4' x 10' flat black, insulated solar collectors

with

and

single-glass cover plates.

They

be

re to

opper passages

mounted facing

south at a 40 slope.

His bid is $25,600.

Neither contract

includes the LP(

It will be installed by the swimming pool

; backup heater

Bot}:

good reputations

ontracto~

contractors have

Both systems use

s;m;l;~r flow con

trol strategy (differentially controlled l~-hp booster pumps

and automatic valving)

Freeze protection is adequately provided in both

The chemical balance of the pool is carefully

the

ases

controlled so

contact of pool

water with the copper passages in the glazed collectors is

not seen as a problem

D-l


2/13

Both contractors contend that their system represents the best return

on the initial in

vestment and the manager has asked you to help him decide

He has requested an estimate of monthly and

ontract to accept.

annual savings

based on average weather conditions and the history of

ed tor pool heating at the Ormond Beach motel Finally he

nergy consum~

has requested

that you advise his

construction foreman so that he can

effectively supe

rvise the installation

THE CALCULATIONS REQUIRED

D.l..1

STEP

Analyze the annual energy consumption of the Ormond

Beach pool

The average monthly energy consumption for pool heating at

the Ormond Bea

,ch motel is reported in Table D. 1

TABLE D.l

:)rmond Beach Motel Pool Energy Consumption

Month

Gal LPG

$/Mo

Energy Consupmtion

($l.20/gal)

B tu/Mo B u/Day

1,288,000

00

$ 720

38,640,000

$1620

350

86,940,000

2,804,516

1500

$1800

96,600,000 3,116,129

1455

$1746

93,702,000 3,346,500

450

$540

28,980,000 934,839

~

D.l.2

STEP 2:

Tabulate the Required Weather Data

$:r_EJ>~

Tabulate wind conditions using Table D. 2

D-2


3/13

TABLE D.2

Site-specific Wind Conditions

Direction Site Wind Speed (in MPH) Rooftop Sp~ed (in l\'IPH)onth

51

from Table C .4, page C-13)

(site speed x [. 33 to

NW

4.4 - 6.65

3.3

NW

13.3

4.4 -

6.65

Jan

NE

4.5 - 6.9

3.'7

NNE

4.9 - 7.5

4.9

ssw

15.2

5.0 - 7.6

Because 160

0 ft2 to 2500 ft2 of collectors will be installed on the 5200

ft2 roof, which

is wind mapped in Figure C. 9 , some of the collectors will

as much as .5 times the

unobstructed wind speed.

Others

e subjected to

receive the

full protection afforded by the building and its parapet

)f roof top wind speeds is tabulated in Table D. 2

Their

hus, a range c

arithmetic averag;e will be used in subsequent calculations.

Tabulate daytime temperatures using information from the

TEP 2b

table on page E.10.

Table D.3

Daytime Temperature Data

Month

Tar

( 2"'4fij

npa Day time Mean

r Average mean + 5OF)

Daytona 24hr Average

Max Mean

Nov

Dec

Jan

Feb

Mar

71.2

65.8

65.8

65.8

71.2

74.8

69.8

68.8

69.3

14.6

68.2

59.5

57.9

58.8

64.6

D-3


4/13

'eather data does not appear in Appendix E

Thus, data

aytona w

Jacksonville

h the most similiar weather should be chosen

or the city wi

mri is too hot. Gainesville is mlaDd and north of Daytona so

s too cold., Mt

Tampa appears to be a good choice.

TemperatuJ

:'e data for Daytona Beach is available from NOAA (see page

idress) and is tabluated in the right hand two columns of

-7 for the ac

Table D.3 Th1

correlation between the calculated daytime average temper-

ature for Tamp.

a and the average of measured mean and high temperat~res

tor Daytona Be~ch is good.

Tabulate monthly available insolation data using the table

TEP 2c

on page E-10

TABLE D.4

Insolation Data (tor Tampa)

Average B ultt2 .

ay

(Horizontal)

Average B tu/ft2 . day

South facing-, 400 slope

Month

1913

1722

1799

1870

1939

Nov

Dec

Jan

Feb

Mar

1314

1112

1204

1439

1756

In this case. too. we will select Tampa weather data because it is the

city with availa

Lble insolation data listed in Appenidx E whose climate most

found in Daytona Beach..

esembles that

We now have tabulated the weather data that we will use to calculate

the two solar pool heating systems which require evaluation

he output of

performance

of

the

competing

.l..3

STEP 3

the

thermal

stimate

solar systems

D-4


5/13

STEP 3a

collector performance

data for

the

collectors

ssemble

under consideration

Performance

data for both the glazed and unglazed collectors under

evaluation have

been made available by the two competing solar contractors

~d in Figure D.l

nd are presentE

1.00

.80

.80

.70'

.80

.50

.40

.30

.20

.10

Unglazed Perf

" 8 .808 3.60

,-Low temperatl

ormance Equation:

: .

< 3 MPH

I

'

ure rating: aeo BTU/Ft2.0ay

Glazed Performance Equation:

.,. .72 -1.003 : .


6/13

TABLE D.S

Unglazed Collector Output

(Btu/tt2.day)

Corrected Collector Output

Wind

Speed

Temp/lnsol from Wind Speed

Correction Table Correction

from Fig. D.2 from

(A.S) (A.6)

~~

Fig.(5.3)

80-71 = 9

80-66 = 14

80-66 = 14

80-66 = 14

80-71 = 9

1314

1112

1204

1439

1756

5.5

5.5

5.7

6.2

6.3

700

380

450

630

1080

Nov

Dec

Jan

Feb

Mar

785*

500(A.5)

580(A.5)

750(A.5)

1110*

lues from Figure A.5 (AT = 14) and Figure A.6 (AT = 5) is used

a AT of goF.

*Average of va

to approxmate

The dotted lines on Figures A. 5 and A. 6 trace the rerating path for

a 860 B u/ft2 .

standard-Florida-day unglazed collector through the nomo-

graphs for No~

The same proce-

ember temperature/insolation conditions.

.propriate nomographs is used for .each month during which

ure, using aJ:

pool heating is

expected to be required.

The dotted lines on Figure 5. 3 indicate the path through the

785 B u/ft2 . ay rating (the modified

speed

correctic

.n nomograph tor a

ctor rating, obtained by averaging values from AT = 14 and

November colle-

Table D. 6 lists the monthly output. of

T = 5 temp/iI

lsolation nomographs)

the 2500 ft2

I1nglazed-mat-type system which has been proposed

collector output has been multiplied by the nwnber of days

redicted daily

and by the appropriate system correction factor, .95 (from

n each month

Table 5.4), wh:

ich corresponds to 0 slope and no heat exchanger

D-6


7/13

Therma

. Table D.6

1 Output of Unglazed Solar Pool Heating System

System Correction

Factor

Collelation rate = 1600 Btu/ft2 -day -- the predicted perform-

t of 14, inS(

rhe same situation holds for all the pool heating months in

nce improves

this sample problem but certainly not for all months, locations and winter

weather condition:

in Florida.

ou~ut

of glazed collectors does not require correction for wind

speeds

likely

to be encountered during periods of operation in Florida

Table D.9 lists

the predicted monthly output of the 1600 ft2 glazed

collector system ~

Ihich has been proposed

D~8

1913

1722

1799

1870

1939


9/13

Table D.9

Thenr tal Output of Glazed Solar Pool Heating System

(Btu x lO6/month)

System

Output

Nov

Dec

Jan

Feb

Mar

61.9

55.1

57.5

54.2

65.5

.95

.95

.95

.95

.95

58.8

52.4

54.6

51.5

62.2

In this

the appropriate system correction factor is .95 (from

ase

Table 5.~).

This is a more favorable system factor than that assigned to

a horizontal surf

'ace

because the collector slope (30) improves the collec-

The incident angle of the incoming radiation is near 300

ion geometry.

(o : l~s) during

winter collection hours The incident angle on a horizon-

tal surface durin:

g win ter collection hours is 30 (or more)

Table D .10 tabulates the monthly energy requirements of the pool and

the energy predi

lcted to be available from the glazed pool heating system.

Poo]

Table D .10

Energy Requirements/Glazed System Output

(Btu x 106/month)

Pool

Requirt

(Table

Savings

($)

~ment

~

Cost

~

onth

Available

from

Solar System

Nov

Dec

Jan

Feb

Mar

38.6

86.9

96.6

93.7

29.0

58.

52.

54.

51.

62.

720

975

1016

958

540

4209

720

1620

1800

1746

540

6426

*Cannot aU be used

D-9

(30)

(31)

(31)

{28)

(31)

8*

4

6

5

2*


10/13

D.2 STEP 4

C_9_r1~~~EHE ECONOMICS OF BOTH PROPOSED SYSTEMS

Under

the

assumed

weather conditions,

characteristics and

ystem

both

systen1S offer an equally good return on initial investment

about

15%.

The

actual

figures are:

3178/20000

= 15.9% for the unglazed

system and 4209/

The portion of the

26500 = 15.9% for the glazed system.

annual pool heati

ng load is: 3162/ 6426 = 49% in the case of the unglazed

collectors and 42

09/6426 = 65% in the case of the more expensive array of

FSEC suggests a solar fraction range of roughly. 5 - .8

lazed collectors

(50%-80%) as heir

kg cost effective for solar' service or domestic water heat-

It fairly may

be argued that pool heating should not be

ystems

limited to the smme range of solar fractions.

~ether such ar~ents are

valid or invalid, both systems are reasonably close to the suggested range.

STEP 5 COMPARE CALCULATOR (APPENDIX F) WITH NOMOGRAPH

(APPENDIX A) RESULTS

Table D-ll

gives monthly inputs and outputs for the unglazed collec-

ideration as calculated using Program

"A" for a HP 15C

ors under cons:

calculator

INSOLATION WIND

~Btu/ft2day) ~)

ONTH TO of t.

1

71 80

66 80

66 80

66 80

71 80

Nov.

Dec.

Jan.

Feb.

Mar.

1314

1112

1204

1439

1756

5.5

5.5

5.7

6.2

6.3

3.6 x 1.2*

= 4.32

3.6 x 1.2 = 4.32

3.6 x 1.22 = 4.40

3.6 x 1.28 = 4.60

3.6 x 1.29 = 4.65

.808

.808

.808

.808

.808

737

444

506

653

1055

*Wind speed modifiers

ed annual solar savings using the calculator program equalhe predict

$3178

LlSing the nomographs--very close agreement

s

D-1O


11/13

A similar

malysis

for the glazed collector array under consideration

shows

a differen

ce of less than 1%

It should

be noted that the comparisons are for collectors with first

order

thermal performance equations, either exactly like (unglazed) or

very close to (2

~lazed) those for which the nomographs were derived

The

agreement will n.01 be this close if the thermal performance equations vary

substantially from

808 - 3.60 (t. - t ) (unglazed)

1 a

r

1}

s

67 - 1.03 (ti -.ta) (glazed)

I

tt

=

D.4

UNCERTA J

~rI~S ASSOCIATED WITH USING "AVERAGE" VALUES

If January

consisted of 31

equally

days with 66F average

unny

ture, actual solar heater performance would closely follOW

aytime tempera

the calculated p

,erfonnance. Its more likely however,

that some January

days will be clo

,udy, some clear, some unseasonably warm and some cold.

the perfonnance of both solar system and may cause major

his will aft ect

differences

If half of

the month has 55F average daytime temperatures and half

the month

has

75F

temperatures the monthly

verage daytime

daytime

average will reI

nain at about 66F

It may

be interesting to calculate

changes in the

January

contribution of the two solar systems when ad-

justed on the b asis of half a month of each of the new temperature pro-

files

D..,U


12/13

75 F

(AT:5)

55 F

(6.T = 25)

unglazed output

820 Btu/ft2 -day

200 Btu/ft2.day

ating modified

(from Figure

[or temp/ingot

~.6 or A.4)

90 Btu/ft2.day

ating modified f

(from Figure 5

~or wind speed

.3)

725 B u/ft2 . day

85 = 3.0

5 = 23.9

31 x 90 x 2500 x

2

31 x 725 x 2500 x

-2

half month outpu

(Btu x 106)

t

Total = 26.0

So the out]

put of the unglazed system drops 21% and becomes very

unbalanced with

respect to time of mon h

55 F

5 F

lazed output

1065

ating modified

(from Figure

ror temp/insol

~.13 or A.1 .)

1260

95 = 29.7

31 x

1065

x

1600 x

95

= 2

31 x 1260 x 1600 x

2

half month outpu

(Btu x 106)

.t.:

""2

Total = 54.8

;>ut of the system remains about the same and is reasonably

o the out]

well balanced wi1

h respect to time of month

rIONSHIP BETWEEN SYSTEM SIZE AND ENERGY AND

.S THERELA1

DOLLAR SAVINGS

orthy that in November and March both proposed solar pool

t is notew

produce more energy than the Ormond Beach pool used

heating systems

Yet during December, January and February both

uring those months

The selection of an economically op timized

n is required.

roduce less tho

system must takl

e the following factors into account

er square fo?t of solar heating systems tends to rise as the

he cost p

This is because certain costs -- engineering and

system size is reduced.

D-12


13/13

ove~head, controllers,esign, company

valves and supply lines -- do not

decrease linearly

with a reduction in system size

Additionally

the fraction of

the thermal load carried by the solar

(solar

does

increase linearly with

ystem

fraction) collector

ot area

Witness Novembe

and March when a system twice as large as those pro-

posed

would

For these and otherontribute no extra

usable energy

reasons, a syste:

m that meets about 50% - 80% of the annual thermal load is

in a size and co;

st range that maximizes return on the buyer's investment

Another imJ:

ortant fact is apparent from a close examination of tables

D.7 and D.I0 The maximum ~ at which either solar system can con-

tribute energy d

luring the period when it is needed is about 2 million Btu

on a clear,

seasonally

temperate day.

During and immediately after a

during which the motel-sized pool may lose 5-6 million

evere cold snal=

Btu/day, the LPG-fired heater will have be used to maintain a comfortable

pool temperature

Such heaters are able to supply the pool with heat at

the rate

of 200,0

100 o 600,000 B tu per hour (depending on their size) on a

If an unseasonable cold snap occurs in November or

4-hour-a-day basis.

March,

some LPG utilization

be

during those

osts may incurred even

months which on

a 3D-day basis have excess solar heating capacity avail~

able

Thus,

caution must be exercised in predicting the dollar savings

that will result f]

Those savings are effectedom solar pool heating system.

~rns

as well as by

monthly

average conditions

y weathe~ patte

Fortuna tely swimming pools have high thermal storage capacity and

may be heated to 50

-

7F over the minimum acceptable temperature with-

out causing use A 50,000 discomfort.

gal pool has a thermal storage

capacity of 432,

)00 Btu per of and thus can maintain a minimum tempera-

ture

of 80F (ai

.ded by normal daily solar system input) through several

days of

cold weather

in November or March if preheated to say 87F

D-13

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