DENSITY AND SURFACE STRUCTURE OF ICE ACCRETIONS

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Submitted on 1 Jan 1987

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DENSITY AND SURFACE STRUCTURE OF ICE ACCRETIONS

F. Prodi, L. Levi

To cite this version:

F. Prodi, L. Levi. DENSITY AND SURFACE STRUCTURE OF ICE ACCRETIONS. Journal de

Physique Colloques, 1987, 48 (C1), pp.C1-383-C1-388. �10.1051/jphyscol:1987153�. �jpa-00226299�

DENSITY AND SURFACE STRUCTURE OF ICE ACCRETIONS

F. P R O D 1

and L.

LEVI'')

Istituto FISBAT-CNR, Reparto Nubi e precipitazioni, Via De' Castagnoli 1, I-40126 Bologna, Italy

Rbsum6

On 6 t u d i e l a d e n s i t 6 l o c a l e de l a g l a c e a c c r 6 t d e s u r c y l i n d r e s f i x e s e t t o u r n a n t s . La dens i t 6 l o c a l e e s t d B t e r m i n 6 e p a r m i c r o g r a p h i e de c o n t a c t en r a y o n s

X

de s e c t i o n s norma l e s ca

l i

b r 6 e s . Les rQsu l t a t s m o n t r e n t que l a dens

i

t 6 l o c a l e e s t p l u s 6

l

ev6e que c e

l l

e donn6e p a r l a r e l a t i o n de Mackl

i

n . Ce

l

l e c

i

do

i

t e t r e va

l

a b l e seu lement p o u r l a d e n s i t 6 moyenne des c y l i n d r e s t o u r n a n t s q u i c o n t i e n n e n t des l o b e s e t des canaux d ' a i r . Les l o b e s s o n t a b s e n t s dans l e s d6pGts f i x e s q u i p r Q s e n t e n t une d e n s i t 6 p l u s u n i f o r m e .

A b s t r a c t

The dependence o f a c c r e t e d i c e d e n s i t y on g r o w t h c o n d i t i o n s has been

i

n v e s t i g a t e d by g r o w i n g d e p o s i t s on r o t a t

i

ng and f i x e d c y

l i

n d e r s . The l o c a l d e n s i t y o f t h e a c c r e t i o n s has been measured b y X-ray c o n t a c t m i c r o g r a p h y on c a l i b r a t e d normal s e c t i o n s . The r e s u l t s show t h a t t h e l o c a l d e n s i t y i s h i g h e r t h a n t h a t g i v e n b y Mackl i n ' s r e l a t i o n s h i p . The l a t t e r may be c o n s i d e r e d v a l i d o n l y f o r t h e mean d e n s i t y o f r o t a t i n g c y l i n d e r s , w h i c h c o n t a i n l o b e s and c o r r e l a t e d a i r c h a n n e l s . Lobes a r e a b s e n t i n f i x e d d e p o s i t s w h i c h show a more u n i f o r m d e n s j t y .

1. l

n t r o d u c t i o n

I t i s known t h a t t h e d e n s i t y o f a c c r e t e d i c e may assume v a l u e s we1

l

below t h e b u l k i c e d e n s i t y . As shown b y Macklinl, t h i s d e n s i t y e may be c o n s i d e r e d a f u n c t i o n o f t h e p a r a m e t e r

X

= - r v,/T

,

where r i s t h e med i an volume drop1 e t r a d i u s , V, i s t h e impac+? s p e e 8 a t t h e s t a g n a t i o n m p o i n t and

T

i s t h e s u r f a c e t e m p e r a t u r e . The

L? ( X )

law o b t a i n e d by t h e s a i d a u t h o r %as u s u a l

l

y been c o n s i d e r e d a g e n e r a l one. However, f o s r i m e depos

i

t e d on f r e e l y f a l

l

i n g i c e

art i

c

l

es,

P f l

aum and P r u ~ p a c h e r more r e c e n t l y found d e n s i t y v a l u e s w h i c h depended on

X

a c c o r d i n g t o a law t h a t d i d n o t c o i n c i d e w i t h t h a t p r o p o s e d by M a c k l i n

1 .

T a k i n g i n t o a c c o u n t t h e s e d i f f e r e n t r e s u l t s ,

i t

was c o n s i d e r e d t h a t t h e dependence of t h e a c c r e t e d i c e d e n s i t y on t h e g r o w t h c o n d i t i o n s was s t i

l l

w o r t h y o f a deeper a n a l y s i s and new e x p e r i m e n t s were p e r f o r m e d where t h e " l o c a l d e n s i t y " was measured i n i c e a c c r e t e d on r o t a t i n g and i x e d c y l i n d e r s . The r a y c o n t a c t m i c r o g r a p h y method d e s c r i b e d by P r o d i

and b y P r o d i e t a l .'-was used f o r t h e d e n s i t y measurements.

The r e s u I t s o b t a

i

ned w

i l l

be d e s c r i b e d and d i scussed

i

n t h e p r e s e n t work.

(''permanent affiliation : Cornisibn Nacional de Energia A t h i c a and Caneejo Nacional de In~estigaciones Cientificas y Tichnicas, Argentina

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987153

CI-384 JOURNAL DE PHYSIQUE

2. E x p e r i m e n t a l methods and r e s u l t s

The a c c r e t i o n e x p e r i m e n t s w e r e p e r f o r m e d i n t h e same w i n d t u n n e l a l r e a d y d e s c r i b e d i n s e v e r a l Only a few d e t a

i l

s o f s p e c i f i c

i n t e r e s t a r e d e s c r i b e d h e r e .

A c c r e t i o n ' o c c u r r e d on a p l a s t i c r o d c o a t e d w i t h b u l k i c e , w i t h a t o t a l d i a m e t e r o f

1

cm. The a i r and d e p o s i t t e m p e r a t u r e s T

, T

were mea u r e d b y a t h e r m i s t o r housed on t h e e x t e r n a l s u r f a c e o f t%e p ? a s t i c r o d

8 .

These were v a r i e d w i t h i n t h e r e s p e c t i v e r a n g e s o f - 1 8 > T > -2!j0c,

- 1 5 > T >

-20°C. The p l a s t i c r o d was p l a c e d i n t h e w o r k i n g s e c t i o t of t h e t u n n e l S where t h e w i n d speed c o u l d be r e g u l a t e d a t f i x e d v a l u e s between 26 and 2.5 m s

- 1 .

Two d r o p l e t s p e c t r a were used. They were d e t e r m i n e d b y measur

i

ng t h e d r o p l e t impr

i

n t s on a g l a s s s l i d e

4

^mm w i d e c o v e r e d w i t h g e l a t i ne and b r i e f l y exposed t o t h e f l o w , by means o f a s p r

i

n g r e l e a s e d e v i c e . The mean and median volume r a d i i were, f o r t h e t w o d r o p l e t s p e c t r a , 10 and

14 p m

o r

1 5

and 21

p m

r e s p e c t i v e l y .

Two s e r i e s o f e x p e r i m e n t s were p e r f o r m e d : i n one o f them t h e c y

l i

n d r

i

c a

l

c o

l

l e c t o r was made t o r o t a t e a b o u t i t s a x i s , normal t o t h e d r o p l e t f l u x , a t a speed o f

4 Hz;

i n t h e second t h e same c o

l

l e c t o r was k e p t i n a f i x e d p o s i t i o n , a f t e r a s h o r t r o t a t i o n p e r i o d a t t h e

i n i t i a t i o n o f each r u n .

The i c e d e n s i t y d e t e r m i n a t i o n s were p e r f o r m e d b y a n a l y s i n g t h e x - r a y c o n t a c t m i c r o g r a p h s o f c a

l i

b r a t e d normal s e c t i o n s o f t h e d e p o s i t s u s i n g an o p t i c a l dens

i

t o m e t e r . The o p t i c a l d e n s i t y o f t h e X-ray m i c r o g r a p h s was k e p t w i t h i n a r a n g e where a l i n e a r r e l a t i o n e x i s t e d between t h e d e n s i t o m e t e r s i g n a l and t h e i c e d e n s i t y . The a r e a r e s o l u t i o n of t h e d e n s i t o m e t e r depended on t h e s e c t i o n o f t h e o p t i c a l beam, w h i c h was i n most c a s e s 640x140 prn. The s t u d i e d s e c t i o n s were a l s o o b s e r v e d i n n a t u r a l r e f l e c t e d l i g h t .

The a s p e c t o f low d e n s i t y d e p o s i t s e c t i o n s , as a p p e a r s i n n a t u r a l r e f l e c t e d l i g h t p i c t u r e s and i n X-ray m i c r o g r a p h s , i s shown i n F i g . 1 and 2. The c o m p a r i s o n o f F i g . l a w i t h l b shows t h a t p e r i o d i c l o b e s , t y p i c a l o f r o t a t i n g d e p o s i t s , do n o t appear i n f i x e d d e p o s i t s . However, rnicroroughnesses a r e d e v e l o p e d b o t h on t h e s u r f a c e o f l o b e s and on t h e g r o w t h f r o n t s o f f i x e d d e p o s i t s .

The i n t e r n a l s t r u c t u r e o f a knobby d e p o s i t i s shown i n F i g . 2a where r a d i a l c l e a r l i n e s i n d i c a t e t h e f o r m a t i o n o f a i r c h a n n e l s between l o b e s . l n h o m o g e n e i t i e s a l s o e x i s t i n s i d e l o b e s , a s i s shown by t h e t h i n , i r r e g u l a r , c l e a r l i n e s , d e p a r t i n g f r o m t h e l o b e a x i s and g i v i n g a dendr

it i

c a s p e c t t o l o b e s

.

F i g . 2b shows t h e more homogeneous s t r u c t u r e o f f i x e d d e p o s i t s , where o n l y t h i n a i r c h a n n e l s may be o b s e r v e d . I n F i g . 2 a and 2b d i a g r a m s s h o w i n g t h e d e n s i t o m e t e r s i g n a l f r o m w h i c h t h e i c e d e n s i t y i s d e r i v e d a r e a l s o g i v e n . I n F i g . 2 a t w o s y m m e t r i c a l r a d i a l p a t h s a r e i n d i c a t e d . The d i a g r a m shows t h e maximum d e n s i t y o f t h e b u l k i c e r i n g , t h e d e n s i t y d e c r e a s e o c c u r r i n g a t t h e b e g i n n i n g o f a c c r e t i o n and t h e n e a r l y s t a t i o n a r y d e n s i t y r e a c h e d a f t e r 1-2 mm g r o w t h . The l o n g i t u d i n a l d i a g r a m i n F i g . 2 b i s s u b s t a n t i a l l y s i m i l a r t o t h a t i n F i g . 2 a . The whole d i a g r a m was o t a i n e d a l o n g t h e s t a g n a t i o n zone o f t h e s e c t i o n . The t r a n s v e r s a l d i a g r a m i n F i g . 2 b shows t h a t t h e l a t e r a l d e n s i t y v a r i a t i o n o f t h e d e p o s i t i s srnal

I,

so t h a t t h e l o c a l and mean d e n s i t y a p p r o x i m a t e l y c o i n c i d e .

The r e s u l t s o b t a i n e d f o r t h e l o c a l i c e d e n s i t y f r o m t h e a n a l y s i s of r o t a t i n g and f i x e d d e p o s i t s a r e g i v e n i n F i g . 3a, b as a f u n c t i o n o f t h e p a r a m e t e r

5

=- r v o / T s . Th

i

s i s a s

l i

g h t

l

y m0d.i

f

i e d Mack

l i

n f s p a r a m e t e r

The c u r v e s , b e i n g v e r y s i m i l a r t o each o t h e r , may be r e p r e s e n t e d w i t h good a p p r o x i m a t i o n b y t h e same e q u a t i o n :

2 -1 oc-ls

v a l i d i n t h e i n t e r v a l

2 4 < 4

mrn s

I n F i g .

3

and eq. ( 1 )

Q

has been g i v e n as a f u n c t i o n o f

5

^because

rn r i s t h e p a r a m e t e r most f r e q u e n t l y used t o r e p r e s e n t n a t u r a l d r o p l e t s p e c t r a 7 . However, when t h e median d r o p l e t r a d i u s r i s used, e q . ( l ) changes t o : m

a b

F i g .

1

Low d e n s i t y s e c t i o n s i n n a t u r a l r e f l e c t e d

l

i g h t : a ) r o t a t i n g depos i t , w i n d speed

5

m s - I ,

T

_{= -2Z0f,}

_T

_=-17OC, g r o w t h t i m e 1980 s;

b ) f i x e d d e p o s i t , w i n d speed o?

5

^{m S -}

, TS;

-19OC, Ts =

- 1 5 O C ,

g r o w t h t i m e 630 s. L i q u i d w a t e r c o n t e n t was

1

gm-3 f o r b o t h d e p o s i t s .

I n n e r c i r c l e i s

1

crn i n d i a m e t e r .

3

D i s c u s s i o n

a ) Comparison w i t h p r e v i o u s r e s u l t s .

The

Q

( X ) c u r v e s o b t a i n e d by ~ r e v i o u s and i n t h e p r e s e n t work have been r e p r e s e n t e d i n F i g . 4 .

I t

must be n o t e d t h a t t h e r e i s a r e m a r k a b l e d i s c r e ~ a n c v between c u r v e

1

o b t a i n e d b y Mackl i n and c u r v e s

4

and

5

o b t a i n e d here: T h i s may be r e l a t e d t o t h e d i f f e r e n c e e x i s t i n g between t h e mean d e n s i t y of r o t a t i n g c y l i n d e r s , measured by M a c k l i n , and t h e l o c a l d e n s i t y measured h e r e . The c o m p a r i s o n o f t h e s e c u r v e s i n d i c a t e s t h a t t h e volume o c c u p i e d b y v o i d s o r a i r c h a n n e l s , i n r o t a t i n g deposits, b e g i n s t o be s i g n i f i c a n t when t h e l o c a l d e n s i t y i s s t i

I

l d 0 . 9 g cm-3 and t h a t

i t

may occupy more t h a n h a l f t h e a c c r e t e d volume when t h i s d e n s i t y i s 4 0.7 g

- 3

cm

.

Curves

2

and

3

a r e t h o s e p r e s e n t e d by P f l a u m and Pruppacher f o r c o m p a r i s o n

w i t h

M a c k l i n ' s c u r v e . T h i s c o m p a r i s o n i s n o t r i g o r o u s , s i n c e t h e d e f i n i t i o n o f t h e impact v e l o c i t y i s n o t e x a c t l y t h e same i n b o t h

C1-386 JOURNAL

DE PHYSIQUE

p a p e r s

8 .

N e v e r t h e l e s s , we c a n e a s i

l y

see t h a t o u r c u r v e s

4

and

5

a r e c l o s e r t o c u r v e s 2 and

3

t h a n t o c u r v e

1.

F i g . 2 C o n t a c t X-ray m i c r o g r a p h s of t h e low d e n s i t y d e p o s i t s i n F i g .

1.

D e n s i t o m e t r i c r e a d i n g s o f t h e m i c r o g r a p h s a r e added.

b ) Use o f t h e mean and median volume d r o p l e t r a d i u s

The more e x t e n d e d use o f t h e median compared t o t h e mean d r o p l e t r a d i u s depends on t h e f a c t t h a t , f r o m a s t a t i s t i c a l p o i n t o f view, t h e median v a l u e o f a q u a n t i t y r e p r e s e n t s a f r e q u e n c y d i s t r i b u t i o n b e t t e r t h a n t h e mean. A c c o r d i n g l y ,

e ^{( X )}

^{has a more} s i g n i f i c a n t

meaning t h a n

Q ( )

so t h a t , whi l e e q . ( 2 ) may be c o n s i d e r e d a g e n e r a l r e l a t i o n s h i p , e q . ( l ) i s s t r i c t l y v a l i d o n l y f o r a d r o p l e t s p e c t r u m w i t h

-

r / r m as i n t h e p r e s e n t w o r k . For a b e t t e r a n a l y s i s o f t h i s problem, we have compared some e x p e r i m e n t a l v a l u e s o f Q w i t h t h o s e o b t a i n e d b y d i v i d i n g t h e d r o p l e t s p e c t r u m i n t o

N

c a t e g o r i e s :

N N

where

e i , E i

,and

f i

m. a r e t h e d e n s i t y , t h e c o l e on f a c t o r and t h e

l

i q u i d mass c o r r e s p o h d i n g t o t h e i - t h c a t e g o r y .

~ , F S .

I t was f o u n d t h a t t h e c a l c u l a t e d and e x p e r i m e n t a l v a l u e s o f t h e mean d e n s i t y d i f f e r e d b y a b o u t

15-18 %

when e q . ( l ) was a p p l i e d , whi l e t h e e r r o r was r e d u c e d t o about

4%

when eq. ( 2 ) was a p p l i e d .

I t

i s c o n c l u d e d t h a t Q i s b e t t e r r e l a t e d t o t h e median t h a n t o t h e mean volume r a d i

i

o f d r o p l e t s , and e q . ( 2 ) i s t h e more g e n e r a l . When t h e e x p r e s s i o n o f Q as a f u n c t i o n o f i s r e q u i t e + t h e c o n s t a n t 0.28 i n e q . ( 2 ) s h o u l d be m u l t i p l i e d by a f a c t o r ( F / r

) ,

n e g l e c t i n g t h e s m a l l v a r i a t i o n o f v, c o r r e s p o n d i n g t o t h e change

Tram F

t o r _m

.

c ) S u r f a c e and i n t e r n a l s t r u c t u r e o f f i x e d and r o t a t i n g d e p o s i t s .

R e c e n t l y , n u m e r i d a l s i m u l a t i o n s have been p e r f o r m e d o f t h e p r o c e s s

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

I t

i s i n t e r e s t i n g t o o b s e r v e t h a t , as a r e s u l t o f such t h e o r e t i c a l s i m u l a t i o n s , d e p o s i t s a r e f o u n d w h i c h a r e s t r i k i n g l y s i m i l a r t o t h e f i x e d d e p o s i t s o b t a i n e d i n t h e p r e s e n t work.

I n f a c t ,

i t

i s shown t h a t t h e a g g r e g a t e d e v e l o p s as a f a n - l i k e s t r u c t u r e , where t h e p a r t i c l e s a r e d e p o s i t e d a l o n g s t r a

i

g h t

l i

nes s e p a r a t e d b y a i r i n t e r s t i c e s . T h i s open s t r u c t u r e o f t h e a g g r e g a t e i s a consequence o f t h e shadow p r o j e c t e d b y each p a r t i c l e o r g r o u p of p a r t i c l e s d e p o s i t e d on a s u r f a c e zone w h i c h i s n o t normal t o t h e p a r t i c l e f l u x . The shadow l e n g t h i n c r e a s e s t o w a r d s t h e s i d e s o f t h e a g g r e g a t e , g i v i n g r i s e t o a d e c r e a s e o f t h e d e n s i t y as t h e a n g u l a r d i s t a n c e from t h e s t a g n a t i o n zone i n c r e a s e s .

Fig.3 Deposit density a s a function of E

^:

^a)

^for

rotating deposits ;

b)

along the stagnation line of fixed deposits.

F i g . 4 Curves o f

@ ( X )

a c c o r d i n g t o v a r i o u s a u t h o r s : 1:Mackl i n ' s c u r v e ;

2

and

3:

P f l a u m and

.t P r u p p a c h e r ' s c u r v e s ;

4

and

5:

1 1

18

100 f i x e d and r o t a t i n g d e p o s i t s r e s - p e c t i v e l y, a c c o r d i n g t o t h e p r e -

-=<,,.m-''

9C-')

T

s e n t r e s u l t s .

Now, i t seems e v i d e n t t h a t t h e s t r u c t u r e o f f i x e d i c e d e p o s i t s , s h o w i n g t h i n l o n g i t u d i n a l a i r c h a n n e l s , i s r e l a t e d t o

t h i s

a g g r e g a t i o n

Cl-388

J O U R N A L DE PHYSIQUE

e f f e c t . However, i n t h e p r e s e n t c a s e t h e phenomenon i s more c o m p l e x t h a n t h a t c o n s i d e r e d i n t h e ment i o n e d model, because t h e d r o p l e t s s p r e a d on i m p a c t i o n w i t h t h e a l r e a d y f o r m e d body, t h e s p r e a d i n g f a c t o r d e p e n d i n g on t h e c o l l i s i o n speed and on t h e t e m p e r a t u r e .

The c o n s i d e r e d model may n o t b e a p p l i e d t o r o t a t i n g d e p o s i t s b e c a u s e i n t h i s c a s e each s u r f a c e p o i n t c o n t i n u a l l y changes

i t s

o r i e n t a t i o n w i t h r e s p e c t t o t h e d r o p l e t f l u x . I n t h i s c a s e , t h i n a i r c h a n n e l s f o r m e d i n t h e l o b e s p r e s e n t a v a r i a b l e d i r e c t i o n a s shown i n F i g . 2 . I n a d d i t i o n ,

i t must be n o t e d t h a t each s u r f a c e p o i n t p e r i o d i c a l l y o c c u p i e s t w o s y m m e t r i c a l p o s i t i o n s a t t h e s i d e s o f t h e d e p o s i t , w h e r e t h e shadow e f f e c t

i s

maximum. Due t o t h i s e f f e c t , l o b e s and c o r r e l a t e d a i r c h a n n e l s a r e f o r m e d , t h e l a t t e r d e t e r m i n i n g a d e c r e a s e i n t h e mean i c e d e n s i t y . 4. C o n c l u s i o n s

We c o n c l u d e t h a t t w o d i f f e r e n t l a w s may be q i v e n f o r t h e d e n s i t y o f -

a c c r e t e d i c e . One i s Mac l i n ' s law r e p r e s e n t i n g t h e mean d e n s i t y o f a r o t a t i n g b o d y . The o t h e r c o r r e s p o n d s t o t h e " l o c a l " d e n s i t y measured i n zones w h i c h do n o t i n c l u d e a i r channe I s . The l a t t e r may be i d e n t i f i e d w i t h t h e mean d e n s i t y when l o b e s a r e a b s e n t , a s o c c u r s

i n

f i x d d e p o s i t s o r i n t h e i n i t i a l a c c r e t i o n l a y e r o f f r e e l y f a l l i n g p a r t i c l e s 5 . However,

i t g i v e s o n l y t h e d e n s i t y i n s i d e l o b e s , when t h e s e a r e we1 I d e v e l o p e d and s e p a r a t e d b y a i r c h a n n e l s .

These r e s u l t s s h o u l d be t a k e n i n t o a c c o u n t when s t u d y i n g n a t u r a l phenomena, such as t h e p r o c e s s o f h a i l s t o n e g r o w t h and t h a t o f i c i n g on s t r u c t u r e s .

R e f e r e n c e s

1-Mack l i n W .C., Q u a r t . J . R . M e t . Soc., 88, ( 1962), 30-50.

2-Pflaum, J.C. and

H . R . P r u p p a c h e r , J.Atmos.Sc.,

36, (19791, 680-689.

3-Prod i ,

F . , J.

App l .Met., 9, ( 19701, 903-910.

4-Prod i , F.,

G . S a n t a c h i a r a

a n d A . F r a n z i n i , Q u a r t . J. R . Met. Soc., 112, (19861, i n p r e s s .

5 - P r o d i , F . , J . A p p l . M e t . , 14, (19751, 120-124.

6 - L e v i , L . and F . P r o d i , J . A t m o s . S c . , 35, (19781, 2181-2189.

7-Heymsf i e I d , A . J., J .Atmos.Sc., 39, f 19821, 2867-2897.

8-Rasmussen, R.M. and A .

J.

Heymsf i e l d , J.Atmos.Sc., 42, ( 1 9 8 5 ) , 2275- 2279.

9-3ain,M. and J . F . G a y e t , J . R e c h . A t m . , 1 7 , ( 1 9 8 3 ) , 299-311.

1 0 - P r o d i , F., L . L e v i and V.Levizzani,Quart.J.X.Met.Soc., 112, (19861, i n p r e s s .

11- Xaman l a I, P. and L. M. Sander, Phys . Rev. L e t t . , 54, ( 1 9 8 5 ) , 1828-1831.

COMMENTS

Remark of K. ITAGAKI

:

Vapor growth is very important in particular most experimental conditions, since vapor pressure of droplets is higher than growing ice surface.

Answer

:

It is well established in cloud physics that riming is dominant with respect to vapor deposition, at list in the conditions typical of growth of hailstones.

In fact ventilation effect cannot overcome the riming effect.