plate; V0, jet velocity at a hole; V6, j e t v e l o c i t y at distance 5 f r o m the source; y2, dispersion; NNu, N u s s e l t number; NRe, Reynolds number; and N p r , P r a n d t l n u m b e r . LITERATURE 1.

2.

3. 4. 5.

A

CITED

M. K e r c h e r and V. Tabakov, " H e a t t r a n s f e r f r o m s u r f a c e s t r e a m l i n e d by n o r m a l l y incident r e c t a n g u l a r bundle of a i r jets with c i r c u l a r c r o s s s e c t i o n s , with effect of exhaust a i r taken into account," Energ. Mashinostr. Ustan., No. 1, 87-98 (1970). V. S. Turbin, M. Ya. Panov, and A. T. Kurnosov, " H e a t t r a n s f e r f r o m cylinder during its s t r e a m l i n i n g by j e t s , " in: H y d r o d y n a m i c s of B l a d e - T y p e Machines and General Mechanics [in R u s s i a n ] , Voronezhst. Politekh. Inst., Voronezh (1978), pp. 92-98. B. N. Yudaev, M. S. Mikhailov, and V. K. Savin, Heat T r a n s f e r during I n t e r a c t i o n of J e t s and B a r r i e r s [in R u s s i a n ] , M a s h i n o s t r o e n i e , Moscow (1977). A. G. Prudnikov, M. S. Volynskii, and V. L Sagalovich, Mixing and Combustion in A i r - J e t Engines [in R u s s i a n ] , Moscow (1974). V. V. Snizhko, V. S. Turbin, G. V. Tabachni, et al., " I n d u s t r i a l testing of heat e x c h a n g e r s with finned heat p i p e s , " in: Mineral F e r t i l i z e r and Sulfuric Acid Industry [in R u s s i a n l , No. 9, Izd. N a u c h . - I s s l e d . Inst. Tekh.-Ekon. Khim. P r o m y s h l . , Moscow (1977), pp. 18-20.

TURBULENT

CIRCULAR

JET

IN A

CROSSFLOW

Yu. and

P. V.

Vyazovskii, F. Klimkin

V. A .

Golubev,

UDC 532.525.2

An i n t e g r a l method is p r o p o s e d f o r calculating a c i r c u l a r turbulent jet propagating in a c r o s s flow. The j e t p a r a m e t e r s obtained by a n u m e r i c a l method f o r different values of q w e r e c o m p a r e d with e x p e r i m e n t a l data. S a t i s f a c t o r y a g r e e m e n t between the sets of data was found.

The i n t e r a c t i o n and mixing of j e t s with a c r o s s f l o w is a complex f o r m of j e t flow, and the study of the p r o p a g a t i o n of such jets is i m p o r t a n t f o r planning and designing equipment and devices in which mixing takes place. Several works by foreign and d o m e s t i c authors have been devoted to the t h e o r e t i c a l [1-5] and e x p e r i m e n t a l [6-13] study of the laws of mixing and p r o p a g a t i o n of turbulent j e t s in a c r o s s f l o w . As a rule, the theor e t i c a l studies [ 1-5] a r e b a s e d on i n t e g r a l m e t h o d s , a s s u m e an i n c r e a s e in jet width, and m a k e v a r i o u s other a s s u m p t i o n s r e g a r d i n g the conditions of m o m e n t u m c o n s e r v a t i o n . Most of the investigations have focused on d e t e r m i n i n g the jet axis, and only c e r t a i n studies have examined laws of change in width, axial velocity, app a r e n t additional m a s s , and o t h e r p a r a m e t e r s . It was shown in [ 5] that a j e t p r o p a g a t i n g in a e r o s s f l o w does not p o s s e s s the p r o p e r t y of similitude. This is evidenced f i r s t of all by the f a c t that, in the c o n s t r u c t i o n of lines of equal velocity, the c r o s s sections of the jet change f r o m a c i r c u l a r to a h o r s e s h o e shape. Such a change in jet d e v e l o p m e n t along its length leads to p r o b l e m s in analytically d e s c r i b i n g p r o f i l e s of velocity, t e m p e r a t u r e , and concentration in its c r o s s sections. In connection with this, it was p r o p o s e d in [ 11] that the jet flow region be b r o k e n down into t h r e e sections, within each of which the flow could be a s s u m e d to p o s s e s s the p r o p e r t y of similitude. Meanwhile, according to the data in [ 11], the d e t e r m i n i n g change in the c r o s s - s e c t i o n a l shape of the j e t o c c u r s in the initial section. However, this was not c o n f i r m e d by the e x p e r i m e n t in [7]. In the p r e s e n t work, we a t t e m p t to analytically d e t e r m i n e the above jet p a r a m e t e r s within a b r o a d r a n g e of values of the hydrodynamic p a r a m e t e r ~ (4 ~ q _ 400). The method of calculation is b a s e d on s e v e r a l a s s u m p t i o n s : the jet axis is the locus of the points where the velocity for each section n o r m a l to the d i r e c t i o n of the jet is m a x i m a l ; the jet is bounded by the s u r f a c e on which the e x c e s s velocity in the d i r e c t i o n of the axis d e c r e a s e s to l e s s than a specified low value.

Sergo Ordzhonikidze Moscow Aviation Institute. T r a n s l a t e d f r o m I n z h e n e r n o - F i z i c h e s k i i Zhurnal, Vol. 42, No. 4, pp. 548-554, April, 1982. Original a r t i c l e s u b m i t t e d M a r c h 23, 1981.

0022-0841/82/4204-0371507o50

9 1982 Plenum Publishing C o r p o r a t i o n

37]

~.//~,\x. f X

q

/5

/0

5 .~8~

I.=-/

5

An-3

/o

~r

r

15

7

x/do

Fig. 1. Drawing (a) and t r a j e c t o r y (b) of jets: 1-8) q = 4.75; 10; 16; 25; 50; 125; 200; 400, r e s p e c t i v e l y ; c l e a r p o i n t s - [9]; d a r k points - [ 10]; c u r v e s - e a l e . We will examine an i s o t h e r m a l j e t of i n c o m p r e s s i b l e fluid issuing f r o m a c i r c u l a r hole n o r m a l to the c r o s s f l o w . The propagation of the jet in the u n i f o r m c r o s s f l o w is d e s c r i b e d in a r e c t a n g u l a r s y s t e m of c o o r d i nates, X, Y, Z, withits origin at the c e n t e r of the hole f r o m which the j e t e s c a p e s (Fig. l a ) . The equation of equilibrium of the f o r c e s acting on an isolated e l e m e n t of the jet p r o j e c t e d onto a n o r m a l to the jet axis has the f o r m [ 1] dP = - - d@,

( 1)

where dP is the p r o j e c t i o n onto the n o r m a l of the f o r c e f r o m the p r e s s u r e field acting on the side of the e l e ment; d 4~ is the centrifugal f o r c e which a r i s e s with the motion of the e l e m e n t o v e r the e u r v i l i n e a r t r a j e c t o r y . It can be d e s c r i b e d thus : (2)

d@ = pUsS dt,

R where U is the m e a n m a s s velocity, d e t e r m i n e d f r o m the f o r m u l a U=

1 S N

The f o r c e of the p r e s s u r e dP is d e s c r i b e d by analogy with flow about a solid and is p r o p o r t i o n a l to the e h a r a e t e r i s t i e frontal a r e a and the velocity head, which is calculated f r o m the p r o j e c t i o n of the e r o s s f i o w velocity onto the axis n o r m a l : dP = C~ pfU~ sin2abzdl,

2

(3)

where Cn is the d r a g coefficient, dependent on the dynamic heads of the jet and flow. Allowing for (2) and (3), Eq. (1) takes the f o r m C~ of_U} sin2abzd l 2

pU2S dl.

(4)

R

Equation (4) is solved using v a r i o u s a s s u m p t i o n s r e g a r d i n g c o n s e r v a t i o n of m o m e n t u m . Analysis of c a l culated r e s u l t s shows that a s s u m p t i o n of c o n s e r v a t i o n of the m o m e n t u m p r o j e c t i o n along the Y axis or constancy of e x c e s s m o m e n t u m along the jet does not lead to s a t i s f a c t o r y a g r e e m e n t with the e m p i r i c a l data, e s p e c i a l l y at low ~. At high q, the above a s s u m p t i o n s give r e s u l t s c l o s e to the e x p e r i m e n t a l findings. Thus, we will u s e the a s s u m p t i o n of constant total m o m e n t u m along the jet [4], which leads to the b e s t a g r e e m e n t between the calculated and e x p e r i m e n t a l data: pU2S = pcU~ So = const.

(5)

Allowing for the a s s u m p t i o n (5), Eq. (4) is written: C,~Rb~ sin~a = - - - ~

2

372

(6)

Introducing the well-known relations m

y,,

,

y,

sing --

V 1 4 _ ? ,~

we reduce Eq. (6) to the following f o r m :

We determined the change in jet width bz along the jet f r o m the width of the s u b m e r g e d jet bs using an e m p i r i cal c o r r e c t i o n accounting for the effect of the c r o s s flow: b~ = bs

(

1 + L6-q~

-)

~/2-- ~-arctg Y'

.

.

(8)

The following relation is proposed for finding the coefficient of expansion of the s u b m e r g e d jet: C

2l~bS _C~=x[1.634__0.317(lg100

PHPr~)].

(9)

It follows f r o m (9) that C d e c r e a s e s with i n c r e a s i n g distance f r o m the nozzle edge for a jet with a density at the nozzle outlet Pc which is l e s s than ambient density PH, while it i n c r e a s e s for a jet with Pc > PH. The coefficient of expansion r e m a i n s constant for s u b m e r g e d jets of an i n c o m p r e s s i b l e fluid (Pc = PH = Pro): C = C ~ = 1 = 0.167. The distance f r o m the pole of the jet to the section in question l 1 = lpo + l i n c r e a s e s with the jet density, since the distance f r o m the nozzle edge to the pole /po i n c r e a s e s . F o r a s u b m e r g e d jet of an inc o m p r e s s i b l e fluid, /po = 3dc [13], Substituting e m p i r i c a l relations (8) and (9) into (7) and effecting certain t r a n s f o r m a t i o n s using the new variable p = y ', we obtain P'

41C C+~ P ~=

~

l~~

p2(I+p2"T

(10)

where 7 = ,f VV#p~ax. The following e m p i r i c a l relation is proposed for the drag coefficient Cn on the basis 0

of generalization of the empirieal data on jet axis t r a j e c t o r y : C, = 1.05q~

(11)

Equation (10) was solved on a c o m p u t e r by the finite differences method ( E u l e r ' s broken line) using secondo r d e r boundary conditions: at

dY =

X = O: Y = O, ~ -

tg-~-

T h e relative e r r o r of the calculations was no g r e a t e r than 1% with a m e s h c o r r e s p o n d i n g to 0.01 nozzle d i a m e t e r . The calculations gave us values of jet width bz and jet axis coordinates X and Y. Figure lb shows the t r a j e c t o r y of the jet axis for different values of ~. It is apparent f r o m Fig. lb that the calculations a g r e e with the experimental data. The change in width along the jet -1 is shown in Fig. 2. The rate of i n c r e a s e in width at small distances f r o m the nozzle (T = const) is g r e a t e r at low values of 5, while the change in width at substantial distances f r o m the nozzle is m o r e substantial for jets with high values of q. This pattern of inc r e a s e in jet width is explained by the fact that, at low values of q, velocities at the nozzle outlet and the static p r e s s u r e around the jet a r e r e d i s t r i b u t e d under the influence of the c r o s s f l o w . Interaction of the jet with the c r o s s flow causes an i n c r e a s e in static p r e s s u r e in front of the nozzle and a d e c r e a s e in exhaust velocity in the front part of the jet (orifieing of the top p a r t of the n o z z l e ) , while an i n c r e a s e in velocity in the l a t e r a l r e gions of the jet at the nozzle edge indicates the existence of external r a r e f a c t i o n regions on the sides of the r e a r p a r t of the jet. A p a i r of eddies of opposite rotation is thus c r e a t e d c l o s e to the nozzle, and the g r e a t e s t r a r e f a c t i o n is seen at the sites where the eddies a r e originated, i.e., at the sides of the nozzle. This phenomenon leads to stretching of the jet in the t r a n s v e r s e direction and, thus, to an i n c r e a s e in jet width. The inc r e a s e in width d e c r e a s e s m a r k e d l y with i n c r e a s i n g distance f r o m the nozzle, since - as is evident f r o m Fig. lb - the jet b e c o m e s a c o e u r r e n t s t r e a m f a i r l y rapidly. With high ~, the m o m e n t u m of the jet near the nozzle is significantly higher than that of the erossflow, so the p r e s e n c e of r a r e f a c t i o n regions at the sides of the n o z zle does not cause the expansion of the jet n e a r the nozzle seen with low values of ~. Here, the i n c r e a s e in jet width is not g r e a t l y different f r o m that of the s u b m e r g e d jet. However, due to the d e c r e a s i n g velocity of the jet with i n c r e a s i n g distance f r o m the nozzle, the sides of the jet c o m e to be influenced to the s a m e d e g r e e by the crossflow as in the ease of jets with low q, and the rate of i n c r e a s e in width i n c r e a s e s .

373

;--

@

bz~5

2~

§ o--3

0

A - - G I ~ /" ;-.I~t1"/1 25 , v-- 7 /. ~_o.....L.-.~

5

la

/5

20

z/d c

Fig. 2. J e t half-width: 1, 2) g = 10; 3, 4) 25; 5) 200; 6, 7) q = co (1, 3 - [3]; 6, 7 - [13]; 2, 4, 5 - o u r data; c u r v e s - calculated).

0--4, I--8

"~--/2o--N

q5

~ - lZ

o

e

/o

/5

z/d~

2o

Fig. 3. Axial velocity of jet: 1) ~ = 6; 2) 10; 3-6) 25; 7, 8) 50; 9-11) 100; 12, 13) 200; 14-16) 400; 17) ~ = ~o (1, 2 - [ 3 ] ; 5, 7, 1 1 - [ 8 ] ; 4, 6, 8, 9, 12, 15, 16--[61; 1 4 - [ 2 ] ; 1 7 - [ 1 3 ] ; 3, 10, 13 - our data; c u r v e s - calculated). F i g u r e 3 shows the change in axial r e l a t i v e e x c e s s v e l o c i t y along the jet for different values of q. It follows f r o m the data that a d e c r e a s e in ~ is a c c o m p a n i e d by a reduction in the s i z e of the initial section and an i n c r e a s e in the r a t e of d e c r e a s e in axial velocity. T h e s e f a c t o r s lead to an i n c r e a s e in the r a n g e of the jet with an i n c r e a s e in q. By range, we m e a n the distance f r o m the nozzle to the point on the j e t axis where the e x c e s s velocity is 1070 of the e x c e s s velocity at the nozzle outlet. It follows f r o m Fig. 3 that at ~ = 6 the r a n g e is equal to five nozzle d i a m e t e r s ( / / d c = 5). This effect is connected with the fact that at low ~ the jet rapidly l o s e s its individuality as a r e s u l t of mixing of the working body of the jet with the c r o s s f l o w . The e x p e r i m e n t a l data shown in Fig. 3 is v e r y s a t i s f a c t o r i l y d e s c r i b e d by the e m p i r i c a l f o r m u l a um--uf = Uc - - Uf

[

1 - - exp

(

y2

I / - q + cos q , - 1 (12)

~/~-- 1

The r e s u l t s of calculation of axial velocity along the length of a s u b m e r g e d jet in [ 13] a r e shown by the dashed c u r v e in Fig. 3. The a p p a r e n t additional m a s s of the jet was d e t e r m i n e d with the a s s u m p t i o n of c o n s e r v a t i o n of m o m e n t u m (5), which was d e s c r i b e d in the f o r m (13)

GU = G~Uc.

It follows f r o m (13) that finding the a p p a r e n t additional m a s s r e q u i r e s knowledge of the change in the m e a n m a s s velocity U along the jet for different values of ~. Based on physical c o n s i d e r a t i o n s and the e x p e r i m e n t a l data, the following e m p i r i c a l r e l a t i o n is p r o p o s e d between m e a n m a s s velocity U and axial velocity urn: U--Ufc~ - - 1 - - e x p ( - 0 , 0 3 ~) u ~ - - Uf. cos cr l-~ + In 0.75 .

(14)

Then the e x p r e s s i o n for the r e l a t i v e a p p a r e n t additional m a s s can be written thus: G--Gr

Gc

i

(U--Ofcosat \ u ~ - - Uf cos ~ ]

374

[ 1--exp (

-- 1.

0.5q0"~ -/2 ) ;

cos~ l/q -~

(15)

G-Gc

~ --/ I~

Y

o 'x

u--5

V

fo

o

a--9

~ - -

5

fo

/6

20

I

~/ff'~

Fig. 4. A p p a r e n t additional m a s s of a jet: 1) q = 6; 2, 3) 16; 4) 25; 5) 34; 6) 60; 7) 100; 8) 250; 9) q = (1, 2, 4 - [ 3 ] ; 3, 5, 6 - [ 7 ] ; 9 - [ 1 3 ] ; 7, 8 - o u r data; c u r v e s - cale. ). F i g u r e 4 shows r e s u l t s of calculations with Eqs. (15) and e x p e r i m e n t a l data f r o m [3, 7] on the a p p a r e n t additional m a s s of a jet. The e x p e r i m e n t s in these works, conducted at the s a m e values of q, c a m e up with quite different r e s u l t s . F o r example, f o r ~ = 16 a n d - / = 7, the a p p a r e n t additional m a s s is 9.5 a c c o r d i n g to [3] and 2 according to [7]. T h e s e works also show a qualitative difference in the c h a r a c t e r of change in a p p a r e n t additional m a s s in r e l a t i o n to 5- With T= const and a d e c r e a s e in 5, the a p p a r e n t additional m a s s of the jet inc r e a s e s according to [3] and d e c r e a s e s according to [7]. The d i f f e r e n c e s in a p p a r e n t additional m a s s values in [3] and [7] c o m p l i c a t e s c o m p a r i s o n of t h e s e s e t s of data with the calculated r e s u l t s . However, a qualitative explanation of the calculated data can be found if we follow the b e h a v i o r of jet width (see Fig. 2) and the d e c r e a s e in the axial velocity of the jet (see Fig. 3). The p r e s e n c e of the p a i r of eddies at the sides of the nozzle in the c a s e of low q leads to intensive suction of a i r into the jet f r o m the region n e a r the nozzle [ 12]. The e j e c tion capacity of t h e s e eddies is substantially g r e a t e r than the turbulent mixing of the s u b m e r g e d jet, due to the high d e g r e e of turbulence in the vicinity of the eddies. However, with i n c r e a s i n g distance f r o m the nozzle, d i s sipation of the energy of the eddies and d e c r e a s e of the velocity of the jet r e s u l t i n a d e c r e a s e in the ejection c a p a c i t y of the l a t t e r , and the i n c r e a s e in a p p a r e n t additional m a s s b e c o m e s slight. With high values of q, the reduction in axial velocity and change in jet c r o s s - s e c t i o n a l dimensions at s h o r t d i s t a n c e s f r o m the nozzle diff e r little f r o m the laws of d e v e l o p m e n t of the s u b m e r g e d jet, so that the jet has n e a r l y the s a m e ejection c a pacity. With i n c r e a s i n g d i s t a n c e f r o m the nozzle, the m a s s i n c r e m e n t g r a d i e n t i n c r e a s e s as the j e t is developed in the c r o s s f l o w , b e c a u s e t h e v e l o c i t i e s of the jet and c r o s s f l o w b e c o m e c o m p a r a b l e a n d t h e l a w s of i n c r e a s e in a p p a r ent additional m a s s b e c o m e the s a m e as for jets with low values of ~ at s h o r t d i s t a n c e s f r o m the nozzle. It should be noted in conclusion that, for j e t s with low 5, width (Fig. 2) and a p p a r e n t additional m a s s (Fig. 4) i n c r e a s e m o s t rapidly at s h o r t d i s t a n c e s f r o m the nozzle. Such a mutual change in t h e s e p a r a m e t e r s is connected with the fact that weak jets flowing n o r m a l to a c r o s s f l o w of c o m p a r a b l e v e l o c i t y b e c o m e c o c u r r e n t s t r e a m s not f a r f r o m the nozzle. C o n v e r s e l y , f o r jets with high values of 7, the i n c r e a s e in width and a p p a r e n t additional m a s s and d e c r e a s e in axial velocity close to the nozzle o c c u r in qualitatively the s a m e way as with a s u b m e r g e d jet. Here, the jet is hardly deflected f r o m its initial direction by the e r o s s f l o w . Only with i n c r e a s ing distance f r o m the nozzle, as the jet l o s e s velocity, does it begin to bend; width and a p p a r e n t additional m a s s begin to i n c r e a s e m o r e rapidly. NOTATION de, nozzle d i a m e t e r , m; l, distance along jet axis, m; T, r a t i o of distance along j e t axis to nozzle d i a m e ter; Yaxs, jet axis coordinate, m; Uc, Uf, initial v e l o c i t i e s of jet and flow, r e s p e c t i v e l y , m / s e c ; Pc, Of, d e n s i ties of jet and flows, kgf/m3; ~ = PcUc2/pfU~, r a t i o of velocity heads of j e t and flow. LITERATURE 1. 2. 3.

CITED

G . N . A b r a m o v i c h , T h e o r y of Turbulent J e t s [in R u s s i a n ] , F i z m a t g i z , Moscow (1960). N . I . Akatnov, " C i r c u l a r turbulent jet in a c r o s s f l o w , " Izv. Akad. Nauk SSSR Mekh. Zhidk. Gaza, No. 6, 11-19 (1969). I.B. Palatnik and D. Zh. Temirbaev, "Laws of propagation of an axisymmetric air jet in a uniform erossflow," in: Problems of Heat and Power Engineering and Applied Thermophysics [in Russian], Vol. 4, Alma-Ata, Nauka (1967), pp. 196-216. 375

4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

C. Crowe and H. R i e s e b i e t e r , " A n analytic and e x p e r i m e n t a l study of j e t deflection in a c r o s s f l o w , " AGARD Conf. P r o c . , No. 22, 1-19 (1967). D. A d l e r and A. Baron, " P r e d i c t i o n of a t h r e e - d i m e n s i o n a l c i r c u l a r turbulent jet in c r o s s f l o w , " AIAA J., 1_~7, No. 2, 168-174 (1979). Yu. V. Ivanov, " C e r t a i n laws governing a f r e e c i r c u l a r jet developed in an external c r o s s f l o w , " Icy. Akad. Nauk SSSR, Otd. Tekh. Nauk, No. 8, 37-54 (1954). Yu. Kamatani and I. G r e b e r , " E x p e r i m e n t a l study of the turbulence of a jet d i r e c t e d into a c r o s s f l e w , " Raket. Tekh. K o s m . , No. 11, 43-49 (1972). V. Gendrikson and A. ~pshtein, " E x p e r i m e n t a l study of a n o n i s o t h e r m a l j e t in a c r o s s f l o w , " Izv. Akad. Nauk Est. SSSR Fiz. Mat., 22, No. 3, 304-311 (1973). V . A . Golubev, V. F. Klimkin, and L S. Makarov, " T r a j e c t o r y of single jets of different density p r o p a gating in a c r o s s f l o w , " I n z h . - F i z . Zh., 3_~4,No. 4, 594-599 (1978). T. Okamoto and M. Yagita, " T h e effects of the exit profile on the flow," Bull. Tokyo Inst, Technol., No. 114, 29-47 (1973). I . F . Keffer and W. D. Baines, " T h e round turbulent jet in a c r o s swind," J. Fluid Mech., 1_.55,No. 4, 481496 (1963). S . T . Kashafutdinov and N. F. Polyakov, " F l o w of a weak turbulent jet in a e r o s s f l 0 w , " Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Tekh, Nauk, 1, No. 3, 74-80 (1973). V . A . Golubev and V. F. Klimkin, "Study of turbulent s u b m e r g e d gas j e t s of different d e n s i t y , " Inzh.Fiz. Zh., 3.44, No. 3, 493-499 (1978).

INTENSITY

OF

STAGNATION

HEAT POINT

PERIODIC

EXCHANGE IN

VARIATION

NEAR

THE OF

COURSE THE

A OF

SURFACE

TEMPERATURE V.

L.

Sergeev

and

A.

S.

UDC 536.24.01

Strogii

We p r e s e n t the solution of the n o n s t a t i o n a r y p r o b l e m of heat exchange n e a r a stagnation point of the flow at a b a r r i e r , r e p r e s e n t e d by a s p h e r i c a l s u r f a c e , when the s u r f a c e t e m p e r a t u r e of the body is p e r i o d i c a l l y v a r i e d .

In p r a c t i c e , one often encounters the c a s e of heat exchange between a flow and a b a r r i e r when the p e r i odic v a r i a t i o n of the flow p a r a m e t e r s is close to steplike. An e x a m p l e is the application of o b t u r a t o r devices which p e r i o d i c a l l y cut off the flow f r o m a heated b a r r i e r [ 1 ]. The burning of an e l e c t r i c a r c in a l i n e a r p l a s m o t r o n with s h o r t e l e c t r o d e s r e p r e s e n t s blowing and ignition at high f r e q u e n c y [2], which leads to a periodic change of t e m p e r a t u r e of the g e n e r a t e d jet. T h e r e a r e situations when heat is exchanged in the c o u r s e of p e r i odic v a r i a t i o n of the s u r f a c e t e m p e r a t u r e . The r e s u l t s of investigation of the c h a r a c t e r i s t i c s of a heat exchange with a b a r r i e r on a model of the p r o c e s s , r e p r e s e n t e d by a steplike periodic v a r i a t i o n of the s u r f a c e t e m p e r a t u r e between a r b i t r a r y values, a r e given below. The full p e r i o d is divided into two different t i m e i n t e r v a l s during which the t e m p e r a t u r e is constant. The change of t e m p e r a t u r e takes p l a c e at the ends of the t i m e i n t e r v a l s . In the solution of this p r o b l e m , we have m a d e a p r e l i m i n a r y study of a nonstationary heat exchange at a stagnation point of a s p h e r e a f t e r a stepwise change of t e m p e r a t u r e of the s u r f a c e (or of the flow). As in [3, 4], the flow is a s s u m e d to be subsonic, l a m i n a r , and stationary, and the p r o p e r t i e s of the liquid a r e a s s u m e d constant.

A. V. Lykov Institute of Heat and Mass Transfer, Academy of Sciences of the Belorussian SSR, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 4, pp. 554-558, April, 1982. Original article submitred April 9, 1981.

376

0022-0841/82/4204-0376507.50

9 1982 Plenum Publishing C o r p o r a t i o n