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.
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.
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ɘ.ȼ. Ȼɪɹɧɫɤɚɹ
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Ɋɚɫɫɦɨɬɪɟɧɵɝɢɞɪɚɜɥɢɱɟɫɤɢɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢɬɟɱɟɧɢɹɜɬɪɭɛɚɯɩɪɢɩɟɪɟɯɨɞɧɨɦ
ɪɟɠɢɦɟ ɝɢɞɪɚɜɥɢɱɟɫɤɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɧɚ ɨɫɧɨɜɟ ɦɨɞɟɥɢ, ɭɱɢɬɵɜɚɸɳɟɣ
ɩɟɪɟɦɟɠɚɟɦɨɫɬɶɬɟɱɟɧɢɹɜɜɹɡɤɨɦɩɨɞɫɥɨɟ. ɉɨɥɭɱɟɧɚɮɨɪɦɭɥɚɞɥɹɤɨɷɮɮɢɰɢɟɧɬɚ
ɫɨɩɪɨɬɢɜɥɟɧɢɹɜɩɟɪɟɯɨɞɧɨɦɪɟɠɢɦɟ, ɫɨɞɟɪɠɚɳɚɹɤɨɷɮɮɢɰɢɟɧɬɩɟɪɟɦɟɠɚɟɦɨɫɬɢ.
ɉɨɥɭɱɟɧɵ ɡɚɜɢɫɢɦɨɫɬɢ ɞɥɹ ɬɨɱɧɨɝɨ ɢ ɩɪɢɛɥɢɠɟɧɧɨɝɨ ɪɚɫɱɟɬɚ ɤɨɷɮɮɢɰɢɟɧɬɚ
ɩɟɪɟɦɟɠɚɟɦɨɫɬɢ. Ʉɨɷɮɮɢɰɢɟɧɬɫɨɩɪɨɬɢɜɥɟɧɢɹ, ɪɚɫɫɱɢɬɚɧɧɵɣɫɢɫɩɨɥɶɡɨɜɚɧɢɟɦ
ɩɨɥɭɱɟɧɧɵɯɮɨɪɦɭɥ, ɞɚɟɬɯɨɪɨɲɟɟɫɨɜɩɚɞɟɧɢɟɫɨɩɵɬɧɵɦɢɞɚɧɧɵɦɢ.
Ʉɥɸɱɟɜɵɟ ɫɥɨɜɚ: ɬɟɱɟɧɢɟ ɜ ɬɪɭɛɚɯ, ɝɢɞɪɚɜɥɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ,
ɩɟɪɟɯɨɞɧɵɣɪɟɠɢɦ, ɤɨɷɮɮɢɰɢɟɧɬɩɟɪɟɦɟɠɚɟɦɨɫɬɢ.
(
)
,
.
[1],
k
,
-,
-.
—
.
,
k
,
.
Re
u
* вδ
,
δ
=
ν
(1)
0 *
u
—
;
0—
.
-* .
u k
-,
-,
δ
* в
u
ν
~10 [2, 3].
,
,
-δ
* в
u
ν
50…70 [4].
[5].
max,
,
[6].
[4],
,
[7, 8]
[9].
,
-,
.
[8]
,
,
,
,
:
δ
* в
3...5,
u
<
ν
.
-.
.
,
.
-.
,
,
(
,
-,
).
t
0
:
т
0
,
t
T
γ =
(2)
.
γ
= 0
,
γ
= 1 —
.
γ
= 1
(
)
(
).
γ
= 0
(
>
k
).
,
,
—
,
,
-,
γ
,
l,
,
-, . .
γ
:
(
)
п г 1 к,
λ = λ − γ + γλ
(3)
,
,
—
,
-.
1
,
,
γ
:
(
)
п г к
1 1 1
1 .
= − γ + γ
λ λ λ
(4)
(3) (4)
-γ
,
,
,
(3)
(4),
10 %.
g
(4)
г п
1
1
.
γ =
−
λ
λ
(5)
.
,
[10, 11].
.
г г
1
2 lg Re 0,8,
= λ −
λ
(6)
cp
Re
V d
;
d
—
; —
,
* 0
г
1
2 lg
u r
0, 7.
=
+
ν
λ
(7)
.
0
к
1
2 lg
r
1, 74
k
=
+
λ
(8)
0 * 0 *
к
*
г
1
2 lg
1, 74
2 lg
0, 7
2 lg
1, 04
1
2 lg
1, 04 ,
r
u r
u k
k
u k
⎛
⎞
=
+
=
+
−
⎜
−
⎟
=
ν
ν
λ
⎝
⎠
⎛
⎞
=
−
⎜
−
⎟
ν
λ
⎝
⎠
(9)
«
»
,
(5) (9)
*
п г
1 1
2 lgu k 1, 04 .
⎛ ⎞
= − γ⎜ − ⎟
ν
λ λ ⎝ ⎠
(10)
,
-r
0k
-V
cp,
(10),
γ
,
,
γ
.
γ
,
.
,
. 1.
. 1.
.
0
r
k
:
*
0,12 3
1
.
u k
e
(11)
.
,
,
,
(6),
-γ
u k* .
(10),
(11)
u k*
,
. 1
. 1
* u k
4
6
8
10
15
20
25
30
35
40
50
* 2lgu k 1,04
0,018 0,156 0,345 0,545 1,00 1,359 1,631 1,835 2,005 2,138 2,350
-1 -0,5 0 0,5 1 1,5 2 2,5 3
0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8
-по (12)
. 2.
(10)
(12)
*
u k
> 8
* *
2 lgu k 1, 04 2, 64 lgu k 2,10.
(12)
(10)
*
п г
1
1
2, 64 lg
u k
s2,1.
=
−
+
ν
λ
λ
(13)
(13)
(7) (8)
*
п к
1
1
0, 64 lg
u k
1, 07.
=
−
+
ν
λ
λ
(14)
(13)
u k*
= 8
-,
u k*
= 47
-.
,
(13) (14)
,
-.
-,
.
(11)
(10)
-* .
u k
(11) (10),
*
0,12 3
*
п к
1
1
2 lg
1, 04 .
u k
u k
е
⎛ − ⎞ ⎜ ν ⎟
⎝ ⎠
⎛
⎞
=
+
⎜
−
⎟
ν
λ
λ
⎝
⎠
(15)
0,12 3 **
2 lg
1, 04 ,
u k
u k
F k
e
:
( )
п к
1
1
.
F k
=
+
λ
λ
(16)
k
F
u k*
. 2.
. 2
* u k
4 6 8 10 15 20 25 30 35 40 50
F k 0,145 0,360 0,421 0,415 0,311 0,203 0,125 0,075 0,043 0,026 0,0085
(8),
(16)
( )
0
п
1
2 lg
r
F k
1, 74,
k
−
=
+
λ
(17)
,
. 2,
.
(
. 3).
0 0,5 1 1,5 2 2,5
0 0,5 1 1,5 2 2,5 3 3,5 4
r/k = 507 r/k = 252 r/k = 126 r/k = 60 r/k = 30,6 r/k = 15 (по 17(
. 3.
-.
.
пер шер
1 1
−
λ λ
*
lgu k
,
.
,
.
,
.
,
.
Ȼɢɛɥɢɨɝɪɚɮɢɱɟɫɤɢɣ
ɫɩɢɫɨɤ
1.
Ʉɢɫɟɥɟɜ
ɉ
.
Ƚ
.
.
. . :
, 1980. 360 .
2.
Ƚɭɪɠɢɟɧɤɨ
Ƚ
.
Ⱥ
.
//
. 1936.
. 303. 56 .
3.
Ɂɟɝɠɞɚ
Ⱥ
.
ɉ
.
.
- . :
.
-
, 1957. 278 .
4.
ɒɥɢɯɬɢɧɝ
Ƚ
.
. . :
, 1969. 742 .
5.
Narahari Rao K., Narasimha R., Badri Narayanan M.A.
The “bursting” phenomenon
in turbulent boundary layer // J. Fluid Mech. 1971. Vol. 48, part 2. P. 339—352.
6.
Carino E.R.,
Brodkey R.S.
A visual investigation of the wall region in turbulent
fl
ow
// Journal of Fluid Mechanics. 1969. v. 37, N 1. p. 1—30.
7.
Einstein H.A., Li H.
The viscous sublayer along a smooth boundary // ASCE, Journal
Engineering Mechanical Division. V. 82. N 2, 1956. p. 945-1—945-27.
8.
Ȼɪɹɧɫɤɚɹ
ɘ
.
ȼ
.,
Ɇɚɪɤɨɜɚ
ɂ
.
Ɇ
.,
Ɉɫɬɹɤɨɜɚ
Ⱥ
.
ȼ
.
. . :
;
-
, 2009.
263 .
9.
Ȼɨɪɨɜɤɨɜ
ȼ
.
ɋ
.,
Ȼɪɹɧɫɤɚɹ
ɘ
.
ȼ
.
//
.
2001.
№
7. . 20—22.
10.
ɇɢɤɭɪɚɞɡɟ
ɂ
.
//
. - . :
-
, 1936. . 75—150.
11.
Nikuradse I.
Stromungsgesetze in rauhen Rohren // Forschungs-Heft 361, 1933. Pp. 1—22.
ɉɨɫɬɭɩɢɥɚ
ɜ
ɪɟɞɚɤɰɢɸ
ɜ
ɨɤɬɹɛɪɟ
2012
ɝ
.
:
Ȼɪɹɧɫɤɚɹ
ɘɥɢɹ
ȼɚɞɢɦɨɜɧɚ
—
,
,
,
ɎȽȻɈɍ
ȼɉɈ
«
Ɇɨɫɤɨɜɫɤɢɣ
ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ
ɫɬɪɨ
-ɢɬɟɥɶɧɵɣ
ɭɧɢɜɟɪɫɢɬɟɬ
» (
ɎȽȻɈɍ
ȼɉɈ
«
ɆȽɋɍ
»)
, 129337, .
,
, . 26, 8(499)-261-39-12, mgsu-hydraulic@yandex.ru.
:
Ȼɪɹɧɫɤɚɹ
ɘ
.
ȼ
.
//
. 2013.
№
1. . 177—184.
Y.V. Bryanskaya
FLOW INTERMITTENCY PATTERN IN CASE OF THE TRANSITIONAL MODE OF HYDRAULIC RESISTANCE
The author considers hydraulic characteristics of the fl ow inside pipes in case of the transitional mode of hydraulic resistance on the basis of the model taking account of the
fl ow intermittency coeffi cient as its quantitative characteristic. The proposed coeffi cient represents the ratio of the time period of the turbulent fl ow near the pipe surface to the total observation time. The author discusses the relationship between the coeffi cient of the fl ow intermittency and the characteristics of resistance. The author has obtained depende ncies applicable to exact and approximate calculations of the coeffi cient of inter-mittency. The coeffi cient of resistance, calculated on the basis of the formulas proposed for the coeffi cient intermittency of fl ow, refl ects peculiarities of the behavior of the
coef-fi cient of resistance in the transition zone. Its application provides suffi cient convergence with the experimental data.
Key words: fl ow in pipes, hydraulic resistance, transitional mode of hydraulic resis-tance, coeffi cient of fl ow intermittency.
References
1. Kiselev P.G. Gidravlika. Osnovy mekhaniki zhidkosti [Hydraulics. Fundamentals of Liquid Mechanics]. Moscow, Energiya Publ., 1980, 360 p.
2. Gurzhienko G.A. O vliyanii vyazkosti zhidkosti na zakony turbulentnogo dvizheniya v pryamoy tsilindricheskoy trube s gladkimi stenkami [About the Infl uence of the Viscosity of Liquids onto Regularities of the Turbulent Motion inside a Straight Cylindrical Pipe That Has Smooth Walls]. Works of Central Aerohydrodynamic Institute. Moscow, 1936, no. 303, 56 p.
3. Zegzhda A.P. Gidravlicheskie poteri na trenie v kanalakh i truboprovodakh [Hydrau-lic Resistance in Channels and Pipelines]. Moscow-Leningrad, Gos. izd-vo po stroitel’stvu i arkhitekture publ., 1957, 278 p.
4. Shlikhting G. Teoriya pogranichnogo sloya [Boundary Layer Theory]. Moscow, Nauka Publ., 1969, 742 p.
5. Narahari Rao K., Narasimha R., Badri Narayanan M.A. The “Bursting” Phenomenon in Turbulent Boundary Layer. J. Fluid Mech. 1971, vol. 48, part 2, pp. 339—352.
6. Carino E.R., Brodkey R.S. A Visual Investigation of the Wall Region in Turbulent Flow. Journal of Fluid Mechanics, 1969, vol. 37, no. 1, pp. 1—30.
7. Einstein H.A., Li H. The Viscous Sublayer along a Smooth Boundary. ASCE, Journal Engineering Mechanical Division, 1956, vol. 82, no. 2, pp. 945-1—945-27.
8. Bryanskaya Yu.V., Markova I.M., Ostyakova A.V. Gidravlika vodnykh i vzvesenesush-chikh potokov v zhestkikh i deformiruemykh granitsakh [Hydraulics of Water and Suspension-bearing Flows within Rigid and Deformable Boundaries]. Moscow, ASV Publ., 2009, 263 p.
9. Borovkov V.S., Bryanskaya Y.V. Raschet soprotivleniya v perekhodnoy oblasti s uchet-om peremezhaemosti techeniya v vyazkuchet-om podsloe [Transitional Resistance Calculation in the Transitional Zone with Account for the Flow Intermittency inside the Viscous Sublayer]. Gidrotekhnicheskoe stroitel’stvo [Hydraulic Engineering]. 2001, no. 7, pp. 20—22.
10. Nikuradze I. Zakonomernosti turbulentnogo dvizheniya v gladkikh trubakh [Turbulent Motion Regularities in Smooth Surface Pipes]. Problemy turbulentnosti [Problems of Turbu-lence]. Moscow-Leningrad, ONTI NKTP Publ., 1936, pp. 75—150.
11. Nikuradse I. Stroemungsgesetze in rauhen Rohren. Forschungs-Heft (Forschungs auf demGebiete des Ingenieur-Wesens). No. 361, 1933, pp. 1—22.
A b o u t t h e a u t h o r : Bryanskaya Yuliya Vadimovna — Candidate of Technical Sciences, Associate Professor, Department of Hydraulics, National Research University Moscow State University of Civil Engineering (MGSU), 129337, Moscow, 26 Yaroslavskoe shosse; mgsu-hydraulic@yandex.ru; +7 (499) 261-39-12.
