Two notes relating to frazil ice formation

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Two notes relating to frazil ice formation

Williams, G. P.

https://publications-cnrc.canada.ca/fra/droits

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S e r TH1 I N2lr2 no. 1 6 2 c . 2 BLDG

NATIONAL

RESEARCH

COUNCIL

C A N A D A

DIVISION OF BUILDING RESEARCH

P R I C E 1 0 C E N T S

OTTAWA JULY 1962

CANADA

TWO NOTES RELATING TO FRAZIL ICE FORMATION

BY

G.

P.

WILLIAMS

1 . AN EMPIRICAL METHOD OF ESTIMATING TOTAL HEAT LOSSES FROM OPEN - WATER SURFACES. 2. SOME OBSERVATIONS ON SUPER - COOLING AND

FRAZIL ICE PRODUCTION.

PRESENTED TO SEMINAR ON ICE PROBLEMS I N HYDRAULIC STRUCTURES. INTERNATIONAL ASSOCIATION OF HYDRAULIC RESEARCH, HELD I N MONTREAL. AUGUST 1959.

R E S E A R C H P A P E R NO. 1 6 2

OF T H E

DIVISION OF BUILDING RESEARCH

N R C 6 2 2 3 N R C 6 2 2 4

T h i s publication i s being d i s t r i b u t e d by the Division of Building R e s e a r c h of the National R e s e a r c h Council. It should ndt be r e p r o d u c e d in whole o r in p a r t , without p e r m i s - s i o n of the o r i g i n a l publisher. T h e Division would be glad to be of a s s i s t a n c e i n obtaining s u c h p e r m i s s i o n .

P u b l i c a t i o n s of the Division of Building R e s e a r c h may be obtained by m a i l i n g the a p p r o p r i a t e r e m i t t a n c e , ( a Bank, E x p r e s s , o r P o s t Office Maney O r d e r o r a cheque m a d e pay- able a t p a r in Ottawa, to the R e c e i v e r G e n e r a l of Canada, c r e d i t National R e s e a r c h Council) to the National R e s e a r c h Council, Ottawa. S t a m p s a r e not acceptable.

A coupon s y s t e m has been introduced to m a k e pay-

m e n t s f o r publications r e l a t i v e l y s i m p l e . C ~ u p o n s a r e a v a i l -

able i n denominations of 5 , 2 5 and 50 c e n t s , and m a y be ob-

tained by making a r e m i t t a n c e a s indicated above. T h e s e

coupons m a y be u s e d f o r the p u r c h a s e of a l l National R e s e a r c h Council publications including s p e c i f i c a t i o n s of the Canadian Government Specifications B o a r d .

AN EMPIRICAL METHOD O F ESTIMATING TOTAL HEAT LOSSES FROM OPEN-WATER SURFACES

by

G. P. Williams

National R e s e a r c h Council of Canada Division of Building R e s e a r c h

This r e p o r t p r e s e n t s some information on- the h e a t l o s s e s f r o m the s u r f a c e of a tank of w a t e r , 10 f e e t in d i a m e t e r , exposed to various a t m o s p h e r i c conditions a t Ottawa during the p e r i o d J a n u a r y t o April

1959.

T h e r e a r e two approaches to estimating the total h e a t l o s s f r o m open water s u r f a c e s under field conditions. One can attempt to m e a s u r e o r calculate the various components of the heat balance; o r a t t e m p t t o r e l a t e the total heat l o s s by a n e m p i r i c a l f o r m u l a to r e a d i l y observable f a c t o r s s u c h a s the difference between mean a i r t e m p e r a t u r e and m e a n w a t e r s u r f a c e t e m p e r a t u r e . Because of the difficulties of obtaining

r e l i a b l e e s t i m a t e s of the r a d i a t i o n , convective and evaporative components of the heat balance, engineers have usually been s a t i s f i e d with the

e m p i r i c a l approach. T h e s e e m p i r i c a l f o r m u l a e a r e l i m i t e d because a i r t e m p e r a t u r e does not p r o p e r l y account f o r radiation effects.

In a n attempt to improve on these e m p i r i c a l f o r m u l a e the concept of

s o l - a i r t e m p e r a t u r e has been introduced in t h e studies r e p o r t e d h e r e w i t h . Sol-air h a s been d e s c r i b e d a s a fictitious t e m p e r a t u r e which will combine

the effects of h e a t t r a n s f e r by radiation and convection (1)

.

As t h e r e is

a relationship between evaporation a n d convection l o s s e s f r o m w a t e r

s u r f a c e s given by what meteorologists call the Bowen r a t i o (2)

,

the

fictitious s o l - a i r t e m p e r a t u r e is possibly a m e a s u r e of the heat t r a n s f e r by evaporation and condensation a l s o .

Sol-air t e m p e r a t u r e was m e a s u r e d by means of a thermocouple embedded

in the c e n t r e of a d i s c - l i k e , l i g h t - m a s s body approximately 12 inches i n

NRC

6223

10-SI- 1

d i a m e t e r , painted black and mounted 3 f e e t above the ground.

Water t e m p e r a t u r e s w e r e m e a s u r e d by m e a n s of t h e r m o c o u p l e s l o c a t e d

a t 2-inch i n t e r v a l s throughout the 12-inch depth of the w a t e r . The

w a t e r was kept mixed b y m e c h a n i c a l s t i r r e r s

,

to m a i n t a i n uniform

w a t e r t e m p e r a t u r e s throughout the m a s s . The s u r f a c e w a t e r t e m p e r a - t u r e was a s s u m e d equal to that given b y a thermocouple l o c a t e d a p p r o x - i m a t e l y

$

inch below the w a t e r s u r f a c e .

During the p e r i o d f r o m J a n u a r y t o A p r i l 1959, the total h e a t l o s s f r o m the w a t e r s u r f a c e was c a l c u l a t e d f r o m the m e a s u r e d change in w a t e r t e m p e r a t u r e o v e r observatioii p e r i o d s f r o m 5 t o 10 h o u r s in length. During t h e s e s a m e t i m e i n t e r v a l s the m e a n s o l - a i r t e m p e r a t u r e was

obtained by a v e r a g i n g the r e c o r d e d s o l - a i r t e m p e r a t u r e s . The d i f f e r e n c e between the mean s o l - a i r t e m p e r a t u r e and m e a n s u r f a c e w a t e r t e m p e r a - t u r e was c o m p a r e d t o the total h e a t l o s s o r g a i n a s shown on F i g . 1. F i g u r e 1 indicates t h a t t h e r e i s a good c o r r e l a t i o n between t h i s t e m p e r a - tur.e d i f f e r e n c e and the t o t a l h e a t l o s s o r gain a t the w a t e r s u r f a c e .

During the night p e r i o d s m e a n s o l - a i r t e m p e r a t u r e s w e r e s l i g h t l y l o w e r

than m e a n a i r t e m p e r a t u r e s , a s m e a s u r e d in a Stevenson s c r e e n . How-

e v e r , during the daylight h o u r s , the m e a n s o l - a i r t e m p e r a t u r e was u s u a l l y s e v e r a l d e g r e e s ( " C ) h i g h e r than the m e a n a i r t e m p e r a t u r e .

T h e s e e x p e r i m e n t s indicated that d u r i n g daylight p e r i o d s , when r a d i a t i o n effects a r e a m a x i m u m , s o l - a i r t e m p e r a t u r e would have t o be used

i n s t e a d of m e a n a i r t e m p e r a t u r e t o obtain a r e a s o n a b l e c o r r e l a t i o n with Heat l o s s f r o m a n open w a t e r s u r f a c e .

The o b s e r v a t i o n s d u r i n g cooling t r i a l s shown i n F i g . 1 , h a v e been c o m p a r e d with v a r i o u s e m p i r i c a l f o r m u l a ( 3 , 4 , 5) a s shown by F i g . 2. It should be noted t h a t the t e m p e r a t u r e d i f f e r e n c e of t h e s e e m p i r i c a l f o r m u l a i s t h e d i f f e r e n c e between m e a n a i r t e m p e r a t u r e a n d m e a n

w a t e r t e m p e r a t u r e

,

w h e r e a s the t e m p e r a t u r e difference of t h e e x p e r i m e n t - a l o b s e r v a t i o n s i s between s o l - a i r t e m p e r a t u r e a n d m e a n a i r t e m p e r a t u r e .

F i g u r e 2 indicates t h a t the h e a t l o s s e s obtained f r o m the e x p e r i m e n t a l

t a n k c o m p a r e r e a s o n a b l y well with o t h e r r e p o r t e d h e a t l o s s e s . T h e s e r e s u l t s s u g g e s t t h a t the difference between w a t e r s u r f a c e t e m p e r a t u r e and m e a n s o l - a i r t e m p e r a t u r e can be u s e d t o p r e d i c t the r a t e of h e a t l o s s e s f r o m a body of w a t e r and h e n c e be a m e a n s of p r e d i c t i n g fraziP i c e f o r m a t i o n .

R e f e r e n c e s

(1) Mackey, C. 0. _and L. T. Wright J r . The Sol-Air T h e r m o m e t e r

-

A New I n s t r u m e n t . T r a n s . ASHVE, Vol. 5 2 , 1946,

Bowen, I.§. The R a t i o of H e a t L o s s e s by Conduction a n d by E v a p o r a t i o n f r o m Any W a t e r Surface. P h y s i c a l Review, Vol. 2 7 , June 11926, pp. 779-787'.

WemePsfelder, P.

J.

The Influence of a n Ice C o v e r on the

D i s c h a r g e Conditions of a R i v e r ; I. U. G.

G.

h t .

A s s . of Scientific Hydrology, 1954, pg. 182-190. St. L a w r e n c e W a t e r w a y P r o j e c t , R e p o r t of J o i n t B o a r d

of E n g i n e e p s , Ice F o r m a t i o n i n t h e St. L a w r e n c e

a n d o t h e r R i v e r s

,

Appendix E , (1 924) g . 406.

Wardlaw R.L. A Study of H e a t L o s s e s Prom a Water

Surface a s R e l a t e d t o Winter Navigation.

P r o c e e d i n g s E a s t e r n Snow C o n f e r e n c e , Vol. 2, 1953 a n d 1954,

0

JAN

,

FEB

@

A P R

,

M A R

T O T A L H E A T L O S S OR GAIN ( 6

T U /

S Q

F T / H R )

RELATIONSHIP BETWEEN HEAT LOSS OR GAIN FROM

10 FOOT DIAMETER WATER SURFACE AND DIFFERENCE

BETWEEN SOL

-

AIR TEMPERATURE AND WATER

TEMPERATURE

@

EXPERIMENTAL DATA

OTTAWA

-

9959

(SOL- AIR TEMPERATURE

DIFFERENCE)

WEMELSFELDE

JOINT BOARD

(4)

TOTAL HEAT LOSS ( B T

lg

/

SQ F T

/

HR)

A COMPARISON OF EXPERIMENTAL OBSER-

VATIONS WITH VARIOUS EMPIRICAL FORMULA

SOME OBSERVATIONS ON SUPER-COOLING AND FRAZIL I C E PRODUCTION

b y

G , P. Williams

National R e s e a r c h Council of Canada Division of Building R e s e a r c h

This r,eport p r e s e n t s s o m e l a b o r a t o r y i n v e s t i g a t i o n s of the f a c t o r s t h a t d e t e r m i n e the s u p e r - c o o l i n g of w a t e r d u r i n g f r a z i l i c e f o r m a t i o n . F r a z i l i c e was p r o d u c e d in a p l a s t i c v e s s e l ( 2 3 i n c h e s b y 23 inches b y 13 inches d e e p ) f i l l e d with w a t e r . The w a t e r s u r f a c e w a s e x p o s e d to t e m p e r a t u r e s below 0 ° C and w a s kept m i x e d with a m e c h a n i c a l s t i r r e r .

Two methods of m e a s u r i n g w a t e r t e m p e r a t u r e w e r e used. The f i r s t

m e t h o d e m p l o y e d a M u e l l e r b r i d g e and a p l a t i n u m r e s i s t a n c e t h e r m o m e t e r c a l i b r a t e d t o 1/100O0C. The s e c o n d u s e d a s e n s i t i v e Rubicon b r i d g e

with a t h e r m o c o u p l e s u b m e r g e d in t h e c e n t r e of the b a t h , enabling w a t e r t e m p e r a t u r e s t o be r e a d t o 1 / 1 0 0 ° C .

The w a t e r bath was kept i n s i d e a c o l d r o o m , a n d t h e m e a s u r i n g b r i d g e s w e r e kept in a r o o m a t a c o n s t a n t t e m p e r a t u r e of + 7 0 ° F . It was n e c e s s a r y t o c a l i b r a t e the b r i d g e s f o r the long l e a d s t h a t c o n n e c t e d the b r i d g e w i t h the bath. It was a l s o found n e c e s s a r y t o c o v e r t h e t h e r m o c o u p l e with a p l a s t i c c o v e r i n g t o p r e v e n t f r a z i l i c e a d h e r i n g t o it.

When w a t e r t e m p e r a t u r e i s m e a s u r e d to l / l O O ° C f a c t o r s s u c h a s t e m p e r a t u r e l a g of the t h e r m o c o u p l e , m i n u t e q u a n t i t i e s of i c e on t h e t h e r m o c o u p l e , d i s t a n c e of the t h e r m o c o u p l e f r o m the w a t e r s u r f a c e , a m o u n t of conduction down the t h e r m o c o u p l e w i r e n e e d t o be c o n s i d e r e d . Even under l a b o r a t o r y conditions it i s difficult t o c o n t r o l t h e s e f a c t o r s

,

a n d thus obtain e x a c t v a l u e s f o r t h e a m o u n t of s u p e r - c o o l i n g .

N R C

6224 9-SI- 1

F i g u r e 1 shows s o m e t y p i c a l changes of w a t e r t e m p e r a t u r e with t i m e f o r d i f f e r e n t r a t e s of cooling obtained during t h e s e e x p e r i m e n t s . S o m e conclusions c a n be d r a w n f r o m t h e s e c u r v e s which a r e of i n t e r e s t in explaining the h e a t exchange a s p e c t s of f r a z i l i c e f o r m a t i o n .

During t h e f i r s t s t a g e of cooling, a - a ' in F i g u r e 1 , the h e a t r e m o v e d f r o m the w a t e r s u r f a c e by convection, e v a p o r a t i o n , a n d r a d i a t i o n c a u s e s a g r a d u a l cooling of the w a t e r . During the s e c o n d s t a g e of

eooling, a ' - b ' , f r a z i l i c e h a s s t a r t e d t o f o r m , the r e l e a s e d h e a t r e s u l t s in a r e d u c e d r a t e of w a t e r cooling. As the r a t e of i c e f o r m a t i o n

i n c r e a s e s , the h e a t r e l e a s e d a l s o i n c r e a s e s until the point b s i s r e a c h e d w h e r e it m u s t j u s t b a l a n c e the r a t e of h e a t l o s s f r o m the a i r - w a t e r

s u r f a c e . F o r t h e p e r i o d b l - c ' , the h e a t r e l e a s e d through i c e f o r m a t i o n will e x c e e d the l o s s f r o m t h e s u r f a c e until the point c ' i s r e a c h e d , w h e r e the t e m p e r a t u r e i s O0C, a f t e r which t h e y m u s t b a l a n c e .

The a m o u n t of s u p e r - c o o l i n g s h o u l d depend upon t h e r a t e a t which h e a t i s being r e m o v e d f r o m t h e w a t e r m a s s , the a m o u n t of m i x i n g , a n d t h e s u r f a c e a r e a a v a i l a b l e upon which i c e m a y f o r m (i. e. t h e n u m b e r a n d s i z e of f r a z i l i c e p a r t i c l e s p e r unit v o l u m e ) . A t t e m p t s t o m a k e a p r e c i s e a n a l y s i s of t h e s e f a c t o r s w e r e not s u c c e s s f u l . Under the l a b o r a t o r y conditions of t h i s e x p e r i m e n t i t w a s i m p o s s i b l e t o obtain r e a l i s t i c v a l u e s f o r the n u m b e r a n d s i z e of t h e i c e p a r t i c l e s o r to e s t i m a t e the r a t e of g r o w t h of t h e s e p a r t i c l e s ,

T h e s e o b s e r v a t i o n s i n d i c a t e that s u p e r - c o o l i n g of a s t r e a m d u r i n g f r a z i l i c e f o r m a t i o n is a t r a n s i e n t phenomenon depending on the r a t e

of cooling a n d the a m o u n t of i c e s u r f a c e a v a i l a b l e f o r i c e f o r m a t i o n . T h e s m a l l s u p e r - c o o l i n g e f f e c t s o b s e r v e d ( 0 . 0 5 " F ) and t h e difficulties of m e a s u r i n g t e m p e r a t u r e s to the a c c u r a d y r e q u i r e d , s u g g e s t that it w i l l be difficult t o obtain meaningful values f o r t h e a m o u n t of s u p e r - c o o l i n g in r i v e r w a t e r u n d e r f i e l d conditions.

TIME (MINUTES)

COMPARISON OF

DIFFERENT RATES

OF

COOLING