3 ȼɿɫɧɢɤ ɏɚɪɤɿɜɫɶɤɨɝɨ ɧɚɰɿɨɧɚɥɶɧɨɝɨ ɭɧɿɜɟɪɫɢɬɟɬɭ ɋɟɪɿɹ «Ɇɚɬɟɦɚɬɢɱɧɟ ɦɨɞɟɥɸɜɚɧɧɹ. ȱɧɮɨɪɦɚɰɿɣɧɿ ɬɟɯɧɨɥɨɝɿʀ. Ⱥɜɬɨɦɚɬɢɡɨɜɚɧɿ ɫɢɫɬɟɦɢ

3
ȼɿɫɧɢɤ ɏɚɪɤɿɜɫɶɤɨɝɨ ɧɚɰɿɨɧɚɥɶɧɨɝɨ ɭɧɿɜɟɪɫɢɬɟɬɭ
ɋɟɪɿɹ «Ɇɚɬɟɦɚɬɢɱɧɟ ɦɨɞɟɥɸɜɚɧɧɹ. ȱɧɮɨɪɦɚɰɿɣɧɿ ɬɟɯɧɨɥɨɝɿʀ. Ⱥɜɬɨɦɚɬɢɡɨɜɚɧɿ ɫɢɫɬɟɦɢ
ɭɩɪɚɜɥɿɧɧɹ»
ʋ 780, 2007, ɫ.3-8
ɍȾɄ 519.68
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɫɬɪɭɣɧɨɝɨ ɨɛɬɟɤɚɧɢɹ
ɬɟɥ ɰɢɥɢɧɞɪɢɱɟɫɤɨɣ ɮɨɪɦɵ
Ⱥ. ȼ. Ⱥɮɚɧɚɫɶɟɜ, ȼ. ȼ. Ⱥɮɚɧɚɫɶɟɜɚ
Ɇɨɫɤɨɜɫɤɢɣ ɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣ ɭɧɢɜɟɪɫɢɬɟɬ ɥɟɫɚ, Ɋɨɫɫɢɹ
Target setting and numerical method of solution two-dimensional task of impingement
circular horizontal cylinder with slot jet of viscous incompressible fluid have been
done. On the base of method realized program of numerical experiment. Good
coincidences with the experimental data have been achieved for test examples.
1. ȼɜɟɞɟɧɢɟ
ɇɚɫɬɨɹɳɚɹ ɪɚɛɨɬɚ ɩɨɫɜɹɳɟɧɚ ɦɚɬɟɦɚɬɢɱɟɫɤɨɦɭ ɦɨɞɟɥɢɪɨɜɚɧɢɸ ɨɛɬɟɤɚɧɢɹ
ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɰɢɥɢɧɞɪɚ ɩɥɨɫɤɨɣ ɫɬɪɭɟɣ ɜɹɡɤɨɣ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ.
ɒɢɪɨɤɨɟ ɩɪɢɦɟɧɟɧɢɟ ɜ ɨɯɥɚɠɞɟɧɢɢ ɦɢɤɪɨɱɢɩɨɜ ɢ «ɬɟɩɥɨɜɵɯ ɬɪɭɛɨɤ»,
ɧɚɯɨɞɹɳɢɯɫɹ ɜɧɭɬɪɢ ɩɟɪɫɨɧɚɥɶɧɵɯ ɤɨɦɩɶɸɬɟɪɨɜ, ɧɚɲɥɢ ɢɦɟɧɧɨ ɥɚɦɢɧɚɪɧɵɟ
ɫɬɪɭɢ [1], ɬɚɤ ɤɚɤ ɨɧɢ ɨɛɟɫɩɟɱɢɜɚɸɬ ɩɪɚɤɬɢɱɟɫɤɢ ɩɚɫɫɢɜɧɨɟ ɬɟɩɥɨɜɨɟ
ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɢ ɩɨɡɜɨɥɹɸɬ ɷɤɨɧɨɦɢɬɶ ɡɚɪɹɞ ɛɚɬɚɪɟɢ.
Ɂɚɞɚɱɚ ɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɩɥɨɫɤɨɣ ɫɬɪɭɢ ɫ ɬɟɥɚɦɢ ɪɚɡɥɢɱɧɨɣ ɮɨɪɦɵ
ɦɧɨɝɨɩɚɪɚɦɟɬɪɢɱɟɫɤɚɹ, ɩɨɷɬɨɦɭ ɩɪɢɦɟɧɟɧɢɟ ɦɚɬɟɦɚɬɢɱɟɫɤɨɝɨ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɢ
ɜɵɱɢɫɥɢɬɟɥɶɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ ɤɚɤ ɢɧɫɬɪɭɦɟɧɬɚ ɢɫɫɥɟɞɨɜɚɧɢɹ ɞɚɧɧɨɣ ɡɚɞɚɱɢ ɜ
ɧɚɫɬɨɹɳɟɟ ɜɪɟɦɹ ɹɜɥɹɟɬɫɹ ɚɤɬɭɚɥɶɧɵɦ.
ɉɪɢ ɢɡɭɱɟɧɢɢ ɨɛɬɟɤɚɧɢɹ ɤɪɭɝɨɜɨɝɨ ɰɢɥɢɧɞɪɚ ɫɬɪɭɟɣ ɠɢɞɤɨɫɬɢ ɦɨɠɧɨ
ɜɨɫɩɨɥɶɡɨɜɚɬɶɫɹ ɞɚɧɧɵɦɢ ɨɫɧɨɜɚɬɟɥɶɧɨ ɢɡɭɱɟɧɧɨɣ ɡɚɞɚɱɢ ɨɛ ɨɛɬɟɤɚɧɢɢ
ɰɢɥɢɧɞɪɚ ɛɟɫɤɨɧɟɱɧɵɦ ɩɨɬɨɤɨɦ ɠɢɞɤɨɫɬɢ [2-5], ɷɬɚ ɡɚɞɚɱɚ ɹɜɥɹɟɬɫɹ ɱɚɫɬɧɵɦ
ɫɥɭɱɚɟɦ ɫɬɪɭɣɧɨɝɨ ɨɛɬɟɤɚɧɢɹ ɩɪɢ ɭɫɥɨɜɢɢ, ɱɬɨ ɲɢɪɢɧɚ ɫɬɪɭɢ ɦɧɨɝɨ ɛɨɥɶɲɟ
ɞɢɚɦɟɬɪɚ ɰɢɥɢɧɞɪɚ.
Ⱦɚɧɧɚɹ ɪɚɛɨɬɚ ɹɜɥɹɟɬɫɹ ɩɪɨɞɨɥɠɟɧɢɟɦ ɢɡɭɱɟɧɢɹ ɫɦɟɲɚɧɧɨɣ ɤɨɧɜɟɤɰɢɢ ɩɪɢ
ɫɬɪɭɣɧɨɦ ɨɛɬɟɤɚɧɢɢ ɰɢɥɢɧɞɪɚ. Ɉɫɧɨɜɧɵɟ ɪɟɡɭɥɶɬɚɬɵ ɢɫɫɥɟɞɨɜɚɧɢɣ, ɩɨɥɭɱɟɧɧɵɟ
ɚɜɬɨɪɚɦɢ, ɩɪɟɞɫɬɚɜɥɟɧɵ ɜ ɪɚɛɨɬɚɯ [6-8].
ɐɟɥɶɸ ɧɚɫɬɨɹɳɟɣ ɪɚɛɨɬɵ ɹɜɥɹɟɬɫɹ ɩɪɢɦɟɧɟɧɢɟ ɦɟɬɨɞɚ «ɜɢɯɪɟɣ ɜ ɹɱɟɣɤɚɯ»
ɞɥɹ ɦɨɞɟɥɢɪɨɜɚɧɢɹ ɫɬɪɭɣɧɨɝɨ ɨɛɬɟɤɚɧɢɹ ɰɢɥɢɧɞɪɚ ɫɬɪɭɟɣ ɜɹɡɤɨɣ ɧɟɫɠɢɦɚɟɦɨɣ
ɠɢɞɤɨɫɬɢ. Ⱦɚɧɧɵɣ ɦɟɬɨɞ, ɤɚɤ ɩɨɤɚɡɚɧɨ ɜ ɪɚɛɨɬɟ [9], ɛɨɥɟɟ ɷɮɮɟɤɬɢɜɟɧ, ɱɟɦ
ɦɟɬɨɞ, ɨɩɢɫɚɧɧɵɣ ɜ [7], ɞɥɹ ɨɬɫɥɟɠɢɜɚɧɢɹ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɫɬɪɭɢ ɫ ɥɨɛɨɜɨɣ
ɡɨɧɨɣ ɰɢɥɢɧɞɪɚ.
2. ɉɨɫɬɚɧɨɜɤɚ ɡɚɞɚɱɢ
Ɋɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɞɜɭɦɟɪɧɚɹ ɡɚɞɚɱɚ ɨ ɥɚɦɢɧɚɪɧɨɦ ɨɛɬɟɤɚɧɢɢ ɰɢɥɢɧɞɪɚ
ɩɥɨɫɤɨɣ ɫɬɪɭɟɣ ɠɢɞɤɨɫɬɢ (ɪɢɫ. 1ɚ). ɇɚ ɝɨɪɢɡɨɧɬɚɥɶɧɵɣ ɰɢɥɢɧɞɪ, ɞɢɚɦɟɬɪ
ɤɨɬɨɪɨɝɨ D, ɢɡ ɫɨɩɥɚ ɲɢɪɢɧɨɣ H ɧɚɬɟɤɚɟɬ ɫɬɪɭɹ ɠɢɞɤɨɫɬɢ. Ɋɚɫɫɬɨɹɧɢɟ ɨɬ ɫɪɟɡɚ
ɫɨɩɥɚ ɞɨ ɰɢɥɢɧɞɪɚ ɪɚɜɧɨ ɜɟɥɢɱɢɧɟ h. ɉɪɨɮɢɥɶ ɫɤɨɪɨɫɬɢ ɧɚ ɫɪɟɡɟ ɫɨɩɥɚ
ɩɪɹɦɨɭɝɨɥɶɧɵɣ. ɋɤɨɪɨɫɬɶ ɢɫɬɟɱɟɧɢɹ ɠɢɞɤɨɫɬɢ ɢɡ ɫɨɩɥɚ V – ɞɨɡɜɭɤɨɜɚɹ.
ȼ ɨɫɧɨɜɭ ɦɨɞɟɥɢ ɩɨɥɨɠɟɧɵ ɭɪɚɜɧɟɧɢɹ ɇɚɜɶɟ-ɋɬɨɤɫɚ ɫ ɩɟɪɟɯɨɞɨɦ ɤ ɮɭɧɤɰɢɢ
ɬɨɤɚ (Ȍ) ɢ ɮɭɧɤɰɢɢ ɢɧɬɟɧɫɢɜɧɨɫɬɢ ɜɢɯɪɹ (Ȧ) – (2.1-2.2). ɂɫɩɨɥɶɡɨɜɚɥɚɫɶ
4
Ⱥ. ȼ. Ⱥɮɚɧɚɫɶɟɜ, ȼ. ȼ. Ⱥɮɚɧɚɫɶɟɜɚ
ɩɨɥɹɪɧɚɹ ɫɢɫɬɟɦɚ ɤɨɨɪɞɢɧɚɬ ɫɨ ɫɝɭɳɟɧɢɟɦ ɪɚɫɱɟɬɧɨɣ ɫɟɬɤɢ ɭ ɰɢɥɢɧɞɪɚ ɫ
ɩɨɦɨɳɶɸ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ [ e k ˜r , ɝɞɟ k const - ɩɚɪɚɦɟɬɪ ɫɝɭɳɟɧɢɹ.
Ɋɢɫ.1. ɋɯɟɦɚ ɡɚɞɚɱɢ
a) ɪɚɫɱɟɬɧɚɹ ɫɯɟɦɚ ɡɚɞɚɱɢ;
b) ɫɯɟɦɚ ɪɚɫɩɨɥɨɠɟɧɢɹ ɭɡɥɨɜ ɫɟɬɤɢ (ɜ ɤɨɨɪɞɢɧɚɬɚɯ
[ ,M
)
Ɉɩɪɟɞɟɥɹɸɳɢɦɢ ɩɚɪɚɦɟɬɪɚɦɢ ɹɜɥɹɸɬɫɹ: ɱɢɫɥɨ Ɋɟɣɧɨɥɶɞɫɚ Re V ˜ D Q ,
H D — ɨɬɧɨɲɟɧɢɟ ɲɢɪɢɧɵ ɫɨɩɥɚ ɤ ɞɢɚɦɟɬɪɭ ɰɢɥɢɧɞɪɚ, h H — ɨɬɧɨɲɟɧɢɟ
ɪɚɫɫɬɨɹɧɢɹ ɨɬ ɫɪɟɡɚ ɫɨɩɥɚ ɞɨ ɰɢɥɢɧɞɪɚ ɤ ɲɢɪɢɧɟ ɫɨɩɥɚ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɭɪɚɜɧɟɧɢɹ ɩɪɢɦɭɬ ɜɢɞ:
DZ
1
'Z ;
(2.1)
Dt
Re
'< Z .
(2.2)
ɍɪɚɜɧɟɧɢɟ ɩɟɪɟɧɨɫɚ ɜɢɯɪɟɣ (2.1) ɩɪɟɞɫɬɚɜɢɦ ɜ ɜɢɞɟ ɞɜɭɯ ɱɚɫɬɟɣ.
Ʉɨɧɜɟɤɬɢɜɧɚɹ ɱɚɫɬɶ ɩɪɢɦɟɬ ɜɢɞ
DZ
0,
(2.3)
Dt
ɞɢɮɮɭɡɢɨɧɧɚɹ ɱɚɫɬɶ
wZ
1
'Z .
(2.4)
Re
wt
ɍɪɚɜɧɟɧɢɟ (2.3) ɚɩɩɪɨɤɫɢɦɢɪɨɜɚɥɨɫɶ ɜɢɯɪɟɜɵɦɢ ɷɥɟɦɟɧɬɚɦɢ, ɩɨɥɨɠɟɧɢɹ ɢ
ɰɢɪɤɭɥɹɰɢɹ ɤɨɬɨɪɵɯ ɨɩɪɟɞɟɥɹɥɢɫɶ ɫɨɝɥɚɫɧɨ ɭɪɚɜɧɟɧɢɹɦ:
dx p
(2.5)
up xp ;
dt
d*
0.
(2.6)
dt
Ƚɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ ɞɥɹ ɫɢɫɬɟɦɵ ɭɪɚɜɧɟɧɢɣ ɫɬɚɜɢɥɢɫɶ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɫɬɪɭɣɧɨɝɨ ɨɛɬɟɤɚɧɢɹ …
ɇɚ ɰɢɥɢɧɞɪɟ
<
const
; Vr
<
0 ; Vr
0 ; VM
0 ; VM
0
5
ɢ ɜɧɟɲɧɢɯ ɫɬɟɧɤɚɯ ɫɨɩɥɚ
0 – ɭɫɥɨɜɢɹ ɩɪɢɥɢɩɚɧɢɹ. ɇɚ ɫɪɟɡɟ ɫɨɩɥɚ –
ɛɟɡɜɢɯɪɟɜɨɟ
ɬɟɱɟɧɢɟ
ɢ
ɪɚɜɧɨɦɟɪɧɨɟ
ɪɚɫɩɪɟɞɟɥɟɧɢɟ
ɫɤɨɪɨɫɬɢ
<
0 . 5 h D ˜ sin M , Z ɧɚ ɝɪɚɧɢɰɟ ɢɡ ɭɪɚɜɧɟɧɢɹ (2.2) ɫ ɭɱɟɬɨɦ ɜɵɲɟ
ɫɤɚɡɚɧɧɨɝɨ. ɇɚ ɜɧɟɲɧɟɣ ɝɪɚɧɢɰɟ – ɭɫɥɨɜɢɹ ɩɨɥɧɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ:
w VM
wZ
wVr
0 . ȼɢɯɪɢ ɝɟɧɟɪɢɪɨɜɚɥɢɫɶ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ
0;
0 ;
w[
w[
w[
ɰɢɥɢɧɞɪɚ ɢ ɧɚ ɤɪɨɦɤɚɯ ɫɨɩɥɚ.
3. Ɇɟɬɨɞ ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ
ȼ ɤɚɱɟɫɬɜɟ ɦɟɬɨɞɚ ɪɟɲɟɧɢɹ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ ɚɜɬɨɪɵ ɩɪɢɦɟɧɢɥɢ ɦɟɬɨɞ
«ɜɢɯɪɟɣ ɜ ɹɱɟɣɤɟ». ȼ ɷɬɨɦ ɦɟɬɨɞɟ ɢɧɬɟɝɪɢɪɭɟɬɫɹ ɭɪɚɜɧɟɧɢɟ ɬɪɚɟɤɬɨɪɢɢ
ɞɜɢɠɟɧɢɹ ɤɚɠɞɨɝɨ ɞɢɫɤɪɟɬɧɨɝɨ ɜɢɯɪɹ, ɬɨ ɟɫɬɶ ɫɤɨɪɨɫɬɢ ɜɵɱɢɫɥɹɸɬɫɹ ɩɨ
ɡɧɚɱɟɧɢɹɦ ɮɭɧɤɰɢɢ ɬɨɤɚ, ɤɨɬɨɪɚɹ ɜ ɨɬɥɢɱɢɟ ɨɬ ɦɟɬɨɞɚ ɞɢɫɤɪɟɬɧɵɯ ɜɢɯɪɟɣ
ɨɩɪɟɞɟɥɹɟɬɫɹ ɧɟ ɩɭɬɟɦ ɫɭɦɦɢɪɨɜɚɧɢɹ (ɧɚɥɨɠɟɧɢɹ, ɫɭɩɟɪɩɨɡɢɰɢɢ) ɜɤɥɚɞɨɜ ɨɬ
ɨɬɞɟɥɶɧɵɯ ɞɢɫɤɪɟɬɧɵɯ ɜɢɯɪɟɣ, ɚ ɢɡ ɪɟɲɟɧɢɹ ɭɪɚɜɧɟɧɢɹ ɞɥɹ ɮɭɧɤɰɢɢ ɬɨɤɚ ɫ
ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɫɟɬɨɱɧɨɣ ɮɭɧɤɰɢɢ ɡɚɜɢɯɪɟɧɧɨɫɬɢ, ɨɩɪɟɞɟɥɟɧɧɨɣ ɩɭɬɟɦ
ɨɫɪɟɞɧɟɧɢɹ ɜɤɥɚɞɨɜ ɞɢɫɤɪɟɬɧɵɯ ɜɢɯɪɟɣ ɩɨ ɹɱɟɣɤɚɦ ɫɟɬɤɢ.
Ⱦɥɹ ɩɟɪɟɯɨɞɚ ɨɬ ɫɢɫɬɟɦɵ ɞɢɮɮɟɪɟɧɰɢɚɥɶɧɵɯ ɭɪɚɜɧɟɧɢɣ ɢ ɤɪɚɟɜɵɯ ɭɫɥɨɜɢɣ,
ɤ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦ ɤɨɧɟɱɧɨ-ɪɚɡɧɨɫɬɧɵɦ ɫɨɨɬɧɨɲɟɧɢɹɦ, ɪɚɫɫɦɚɬɪɢɜɚɟɦɚɹ
ɨɛɥɚɫɬɶ ɢɡɦɟɧɟɧɢɹ ɛɟɡɪɚɡɦɟɪɧɵɯ ɤɨɨɪɞɢɧɚɬ [ ,M ɛɵɥɚ ɡɚɦɟɧɟɧɚ ɪɚɜɧɨɦɟɪɧɨɣ
ɫɟɬɤɨɣ ɭɡɥɨɜɵɯ ɬɨɱɟɤ ɫ ɧɨɦɟɪɚɦɢ i, j, ɤɨɬɨɪɵɟ ɢɡɦɟɧɹɥɢɫɶ ɜ
ɞɢɚɩɚɡɨɧɚɯ: 0 d i d n 1, 0 d j d m 1 (ɪɢɫ. 1b). ɋɟɬɤɚ ɡɚɞɚɜɚɥɚɫɶ ɤɚɤ n, l u m , ɝɞɟ
n ɢ m - ɤɨɥɢɱɟɫɬɜɨ ɜɫɟɯ ɭɡɥɨɜ ɜ ɪɚɞɢɚɥɶɧɨɦ ɢ ɬɚɧɝɟɧɰɢɚɥɶɧɨɦ ɧɚɩɪɚɜɥɟɧɢɹɯ
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ, ɚ l - ɤɨɥɢɱɟɫɬɜɨ ɭɡɥɨɜ, ɩɪɢɯɨɞɹɳɢɯɫɹ ɧɚ ɫɨɩɥɨ, ɜ ɪɚɞɢɚɥɶɧɨɦ
ɧɚɩɪɚɜɥɟɧɢɢ. ɉɚɪɚɦɟɬɪ ɫɟɬɤɢ
ɜɵɛɢɪɚɥɫɹ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ:
k
k D h ˜ ln l n .
Ɋɢɫ. 2. ɋɯɟɦɚ ɜɟɫɨɜ ɞɥɹ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɡɚɜɢɯɪɟɧɧɨɫɬɢ
ɂɧɬɟɧɫɢɜɧɨɫɬɶ ɜɢɯɪɹ ɜ ɭɡɥɨɜɵɯ ɬɨɱɤɚɯ (ɪɢɫ. 2) ɢɡɦɟɧɹɥɚɫɶ ɫɨɝɥɚɫɧɨ
S q *p
Z q ¦ 2 , q 1,2,3,4
S
p
(3.1)
Ⱥ. ȼ. Ⱥɮɚɧɚɫɶɟɜ, ȼ. ȼ. Ⱥɮɚɧɚɫɶɟɜɚ
6
ɐɢɪɤɭɥɹɰɢɹ ɤɚɠɞɨɝɨ ɞɢɫɤɪɟɬɧɨɝɨ ɜɢɯɪɹ ɨɩɪɟɞɟɥɹɥɚɫɶ ɩɨ ɮɨɪɦɭɥɟ:
*p Z ɝɪ Z 6w ˜ S ,
ɝɞɟ
(3.2)
Z ɝɪ - ɡɚɜɢɯɪɟɧɧɨɫɬɶ ɧɚ ɝɪɚɧɢɰɟ ɨɩɪɟɞɟɥɹɥɚɫɶ ɢɡ ɭɪɚɜɧɟɧɢɹ (2.2),
S - ɩɥɨɳɚɞɶ ɹɱɟɣɤɢ, ɜɧɭɬɪɢ ɤɨɬɨɪɨɣ ɧɚɯɨɞɢɬɫɹ ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɣ
ɜɢɯɪɶ,
Z 6w - ɡɚɜɢɯɪɟɧɧɨɫɬɶ, ɝɟɧɟɪɢɪɭɟɦɚɹ ɨɬɫɨɟɞɢɧɟɧɧɵɦɢ ɜɢɯɪɹɦɢ,
ɤɨɬɨɪɵɟ ɧɚɯɨɞɹɬɫɹ ɜ ɬɨɣ ɠɟ ɹɱɟɣɤɟ.
ɉɨɫɥɟ ɭɱɟɬɚ ɜɤɥɚɞɨɜ ɜɫɟɯ ɞɢɫɤɪɟɬɧɵɯ ɜɢɯɪɟɣ (3.1) ɡɚɜɢɯɪɟɧɧɨɫɬɶ
ɨɤɚɡɵɜɚɥɚɫɶ ɨɩɪɟɞɟɥɟɧɧɨɣ ɜɨ ɜɫɟɯ ɭɡɥɚɯ ɫɟɬɤɢ, ɢ ɮɭɧɤɰɢɹ ɬɨɤɚ ɦɨɝɥɚ ɛɵɬɶ
ɧɚɣɞɟɧɚ ɢɡ ɭɪɚɜɧɟɧɢɹ (2.2), ɤɨɬɨɪɨɟ ɪɟɲɚɥɨɫɶ ɦɟɬɨɞɨɦ ɭɫɬɚɧɨɜɥɟɧɢɹ ɩɨ ɧɟɹɜɧɨɣ
ɫɯɟɦɟ ɫ ɢɫɩɨɥɶɡɨɜɚɧɢɟɦ ɩɪɨɞɨɥɶɧɨ – ɩɨɩɟɪɟɱɧɵɯ ɩɪɨɝɨɧɨɤ.
Ɂɚɬɟɦ ɨɩɪɟɞɟɥɹɥɨɫɶ ɩɨɥɟ ɫɤɨɪɨɫɬɟɣ ɢ ɞɥɹ ɤɚɠɞɨɝɨ ɞɢɫɤɪɟɬɧɨɝɨ ɜɢɯɪɹ
ɨɩɪɟɞɟɥɹɥɚɫɶ ɟɝɨ ɫɤɨɪɨɫɬɶ ɫɨɝɥɚɫɧɨ
4 U ˜S
4 V ˜S
q
q
q
q
; vp ¦
.
(3.3)
up ¦
S
S
q 1
q 1
Ⱦɚɥɟɟ ɢɧɬɟɝɪɢɪɨɜɚɧɢɟɦ ɩɨ ɜɪɟɦɟɧɢ ɭɪɚɜɧɟɧɢɹ ɬɪɚɟɤɬɨɪɢɣ ɜɢɯɪɟɣ (2.5)
ɨɩɪɟɞɟɥɹɥɢɫɶ ɢɯ ɧɨɜɵɟ ɩɨɥɨɠɟɧɢɹ:
x p t 't x p t u p t ˜ 't ; y p t 't y p t v p t ˜ 't .
(3.4)
ɇɚ ɨɫɧɨɜɟ ɞɚɧɧɨɣ ɦɟɬɨɞɢɤɢ ɪɚɫɱɟɬɚ ɪɚɡɪɚɛɨɬɚɧɨ ɩɪɨɝɪɚɦɦɧɨɟ ɨɛɟɫɩɟɱɟɧɢɟ
ɩɨɞ Windows ɞɥɹ ɩɪɨɜɟɞɟɧɢɹ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ ɞɥɹ ɢɫɫɥɟɞɨɜɚɧɢɹ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɥɨɫɤɨɣ ɫɬɪɭɢ ɜɹɡɤɨɣ ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɫ
ɝɨɪɢɡɨɧɬɚɥɶɧɵɦ ɤɪɭɝɨɜɵɦ ɰɢɥɢɧɞɪɨɦ. Ɍɟɤɫɬ ɩɪɨɝɪɚɦɦɵ ɧɚɩɢɫɚɧ ɧɚ ɹɡɵɤɟ
ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ ɋ++. ȼɪɟɦɹ ɪɚɫɱɟɬɚ ɨɞɧɨɝɨ ɜɚɪɢɚɧɬɚ ɡɚɞɚɱɢ ɧɚ ɩɟɪɫɨɧɚɥɶɧɨɦ
ɤɨɦɩɶɸɬɟɪɟ ɜ ɫɪɟɞɧɟɦ ɫɨɫɬɚɜɥɹɥɨ ɨɤɨɥɨ ɧɟɫɤɨɥɶɤɢɯ ɱɚɫɨɜ.
4. Ɍɟɫɬɢɪɨɜɚɧɢɟ ɦɟɬɨɞɚ ɢ ɪɟɡɭɥɶɬɚɬɵ
Ɉɰɟɧɤɚ ɞɨɫɬɨɜɟɪɧɨɫɬɢ ɩɨɥɭɱɚɟɦɵɯ ɪɟɡɭɥɶɬɚɬɨɜ ɩɪɨɜɨɞɢɥɚɫɶ ɩɭɬɟɦ
ɫɪɚɜɧɟɧɢɹ ɪɟɡɭɥɶɬɚɬɨɜ ɜɵɱɢɫɥɢɬɟɥɶɧɵɯ ɷɤɫɩɟɪɢɦɟɧɬɨɜ (ɪɢɫ. 3) ɫ ɢɡɜɟɫɬɧɵɦɢ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ [2]. ȼ ɤɚɱɟɫɬɜɟ ɬɟɫɬɨɜɨɝɨ ɩɪɢɦɟɪɚ
ɪɚɫɫɦɚɬɪɢɜɚɥɨɫɶ ɨɛɬɟɤɚɧɢɟ ɤɪɭɝɨɜɨɝɨ ɰɢɥɢɧɞɪɚ ɛɟɫɤɨɧɟɱɧɵɦ ɩɨɬɨɤɨɦ.
Ⱥɜɬɨɪɵ ɩɪɨɜɟɥɢ ɩɪɟɞɜɚɪɢɬɟɥɶɧɵɟ ɪɚɫɱɟɬɵ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɨɣ ɤɚɪɬɢɧɵ
ɬɟɱɟɧɢɹ ɜɛɥɢɡɢ ɰɢɥɢɧɞɪɚ ɞɥɹ Re = 500. ɂɡ ɪɢɫ. 4 ɜɢɞɧɨ, ɱɬɨ ɫɥɟɞ ɡɚ ɰɢɥɢɧɞɪɨɦ
ɞɥɹ ɫɬɪɭɣɧɨɝɨ ɨɛɬɟɤɚɧɢɹ (ɪɢɫ 4ɛ, 4ɜ) ɨɬɥɢɱɚɟɬɫɹ ɨɬ ɫɥɟɞɚ ɩɪɢ ɨɛɬɟɤɚɧɢɢ
ɰɢɥɢɧɞɪɚ ɛɟɫɤɨɧɟɱɧɵɦ ɩɨɬɨɤɨɦ (ɪɢɫ. 4ɚ), ɚ ɬɚɤ ɠɟ ɡɚɜɢɫɢɬ ɨɬ ɲɢɪɢɧɵ ɫɬɪɭɢ ɢ
ɪɚɫɩɨɥɨɠɟɧɢɹ ɰɢɥɢɧɞɪɚ ɨɬɧɨɫɢɬɟɥɶɧɨ ɫɪɟɡɚ ɫɨɩɥɚ.
Ɍɚɤ ɠɟ ɦɨɠɧɨ ɨɬɦɟɬɢɬɶ, ɱɬɨ ɩɪɢ ɲɢɪɢɧɟ ɫɬɪɭɢ ɛɨɥɶɲɟ ɞɢɚɦɟɬɪɚ ɰɢɥɢɧɞɪɚ
ɤɨɝɟɪɟɧɬɧɵɟ ɫɬɪɭɤɬɭɪɵ, ɝɟɧɟɪɢɪɭɟɦɵɟ ɫɬɪɭɟɣ, ɜɥɢɹɸɬ ɬɨɥɶɤɨ ɧɚ ɫɥɟɞ ɡɚ
ɰɢɥɢɧɞɪɨɦ, ɜ ɬɨ ɜɪɟɦɹ ɤɚɤ ɩɪɢ ɲɢɪɢɧɟ ɫɬɪɭɢ ɦɟɧɶɲɟ ɞɢɚɦɟɬɪɚ ɰɢɥɢɧɞɪɚ ɨɧɢ
ɜɡɚɢɦɨɞɟɣɫɬɜɭɸɬ ɫ ɩɨɜɟɪɯɧɨɫɬɶɸ ɰɢɥɢɧɞɪɚ, ɱɬɨ, ɧɟɫɨɦɧɟɧɧɨ, ɫɤɚɡɵɜɚɟɬɫɹ ɧɚ
ɟɝɨ ɝɢɞɪɨɞɢɧɚɦɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ.
Ɇɚɬɟɦɚɬɢɱɟɫɤɨɟ ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɫɬɪɭɣɧɨɝɨ ɨɛɬɟɤɚɧɢɹ …
7
Ɋɢɫ. 3. Ʉɚɪɬɢɧɚ ɬɟɱɟɧɢɹ Re=13.1;
a) ɞɚɧɧɵɟ ɧɚɬɭɪɧɨɝɨ ɷɤɫɩɟɪɢɦɟɧɬɚ [1]; ɛ) ɮɭɧɤɰɢɢ ɬɨɤɚ; ɜ) ɜɢɯɪɢ
Ɋɢɫ. 4. Ʉɚɪɬɢɧɚ ɬɟɱɟɧɢɹ Re=500;
a) ɛɟɫɤɨɧɟɱɧɵɣ ɩɨɬɨɤ; ɛ) H D 0.4 , h H 2 ; ɜ) H D
2, h H
1
5. ȼɵɜɨɞɵ
ȼ ɞɚɧɧɨɣ ɪɚɛɨɬɟ ɨɩɢɫɚɧ ɪɚɡɪɚɛɨɬɚɧɧɵɣ ɢ ɪɟɚɥɢɡɨɜɚɧɧɵɣ ɚɜɬɨɪɚɦɢ ɚɥɝɨɪɢɬɦ
ɱɢɫɥɟɧɧɨɝɨ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɨ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɩɥɨɫɤɨɣ ɫɬɪɭɢ ɜɹɡɤɨɣ
ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɫ ɝɨɪɢɡɨɧɬɚɥɶɧɵɦ ɤɪɭɝɨɜɵɦ ɰɢɥɢɧɞɪɨɦ. ɇɚɥɢɱɢɟ
ɤɨɝɟɪɟɧɬɧɵɯ ɫɬɪɭɤɬɭɪ ɩɪɢ ɫɬɪɭɣɧɨɦ ɨɛɬɟɤɚɧɢɢ ɰɢɥɢɧɞɪɚ ɫɥɭɠɢɬ ɢɥɥɸɫɬɪɚɰɢɟɣ
ɬɨɝɨ, ɱɬɨ ɫ ɩɨɦɨɳɶɸ ɪɚɡɪɚɛɨɬɚɧɧɨɝɨ ɚɥɝɨɪɢɬɦɚ, ɨɫɧɨɜɚɧɧɨɝɨ ɧɚ ɦɟɬɨɞɟ «ɜɢɯɪɟɣ
ɜ ɹɱɟɣɤɚɯ», ɦɨɠɧɨ ɦɨɞɟɥɢɪɨɜɚɬɶ ɨɬɞɟɥɶɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɫɥɨɠɧɨɝɨ
ɧɟɫɬɚɰɢɨɧɚɪɧɨɝɨ ɬɟɱɟɧɢɹ ɜɛɥɢɡɢ ɰɢɥɢɧɞɪɚ.
ɋɪɚɜɧɟɧɢɟ
ɪɟɡɭɥɶɬɚɬɨɜ
ɬɟɫɬɨɜɵɯ
ɪɚɫɱɟɬɨɜ
ɫ
ɢɡɜɟɫɬɧɵɦɢ
ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦɢ ɞɚɧɧɵɦɢ ɩɨɡɜɨɥɹɟɬ ɫɞɟɥɚɬɶ ɜɵɜɨɞ ɨ ɬɨɦ, ɱɬɨ
ɪɚɡɪɚɛɨɬɚɧɧɚɹ ɚɜɬɨɪɚɦɢ ɪɟɚɥɢɡɚɰɢɹ ɚɥɝɨɪɢɬɦɚ ɞɚɟɬ ɜɨɡɦɨɠɧɨɫɬɶ ɤɨɪɪɟɤɬɧɨ
8
Ⱥ. ȼ. Ⱥɮɚɧɚɫɶɟɜ, ȼ. ȼ. Ⱥɮɚɧɚɫɶɟɜɚ
ɦɨɞɟɥɢɪɨɜɚɬɶ ɞɜɢɠɟɧɢɟ ɜɹɡɤɨɣ ɠɢɞɤɨɫɬɢ ɜɛɥɢɡɢ ɩɨɜɟɪɯɧɨɫɬɢ ɰɢɥɢɧɞɪɚ ɞɥɹ
ɫɥɭɱɚɹ ɨɛɬɟɤɚɧɢɹ ɰɢɥɢɧɞɪɚ ɛɟɫɤɨɧɟɱɧɵɦ ɩɨɬɨɤɨɦ.
Ⱥɜɬɨɪɵ ɩɥɚɧɢɪɭɸɬ ɩɪɨɜɟɫɬɢ ɜɟɪɢɮɢɤɚɰɢɸ ɦɟɬɨɞɚ ɞɥɹ ɫɥɭɱɚɹ ɫɬɪɭɣɧɨɝɨ
ɨɛɬɟɤɚɧɢɹ ɰɢɥɢɧɞɪɚ, ɚ ɬɚɤ ɠɟ ɢɫɫɥɟɞɨɜɚɬɶ ɜɥɢɹɧɢɟ ɤɨɝɟɪɟɧɬɧɵɯ ɫɬɪɭɤɬɭɪ ɫɬɪɭɢ
ɧɚ ɫɥɟɞ ɡɚ ɰɢɥɢɧɞɪɨɦ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɜɡɚɢɦɧɨɝɨ ɪɚɫɩɨɥɨɠɟɧɢɹ ɫɬɪɭɢ ɢ
ɰɢɥɢɧɞɪɚ. ȼ ɞɚɥɶɧɟɣɲɟɦ ɩɥɚɧɢɪɭɟɬɫɹ ɪɚɫɩɪɨɫɬɪɚɧɢɬɶ ɦɟɬɨɞ «ɜɢɯɪɟɣ ɜ ɹɱɟɣɤɚɯ»
ɢ ɧɚ ɫɥɭɱɚɣ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɥɨɫɤɨɣ ɫɬɪɭɢ ɜɹɡɤɨɣ ɬɟɩɥɨɩɪɨɜɨɞɧɨɣ
ɧɟɫɠɢɦɚɟɦɨɣ ɠɢɞɤɨɫɬɢ ɫ ɝɨɪɢɡɨɧɬɚɥɶɧɵɦ ɢɡɨɬɟɪɦɢɱɟɫɤɢ ɧɚɝɪɟɬɵɦ ɰɢɥɢɧɞɪɨɦ.
ɅɂɌȿɊȺɌɍɊȺ
1. Guarino J.R., Manno V.P. Characterization of laminar jet impingement
cooling in portable computer applications. // Semiconductor Thermal
Measurement and Management Symposium. San Jose (California, USA),
2001 (http://www.rostenaward.org/manno1.pdf).
2. Ⱥɥɶɛɨɦ ɬɟɱɟɧɢɣ ɠɢɞɤɨɫɬɢ ɢ ɝɚɡɚ: ɩɟɪ. ɫ ɚɧɝɥ./ɫɨɫɬ. Ɇ. ȼɚɧ-Ⱦɚɣɤ. – Ɇ.:
Ɇɢɪ, 1986. – 184 ɫ.
3. ɒɥɢɯɬɢɧɝ Ƚ. Ɍɟɨɪɢɹ ɩɨɝɪɚɧɢɱɧɨɝɨ ɫɥɨɹ. – Ɇ.: ɇɚɭɤɚ, 1974.
4. Roshko. A. On the development of turbulent wakes from vortex streets. Report
1191 national advisory committee for aeronautics. – 1954.
5. Ȼɪɞɥɢɤ ɉ.Ɇ., ɋɟɦɟɧɨɜ ɘ.ɉ., ɏɪɨɦɟɧɤɨ Ⱥ.ȼ. ɇɟɤɨɬɨɪɵɟ ɨɫɨɛɟɧɧɨɫɬɢ
ɬɟɩɥɨɨɛɦɟɧɚ ɢ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɩɪɢ ɜɵɧɭɠɞɟɧɧɨɦ ɨɛɬɟɤɚɧɢɢ
ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɰɢɥɢɧɞɪɚ // Ƚɢɞɪɨɞɢɧɚɦɢɤɚ ɢ ɬɟɩɥɨɦɚɫɫɨɨɛɦɟɧ ɜ
ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɩɪɨɰɟɫɫɚɯ. – Ɇ.: ɆɅɌɂ, 1988. – ʋ 207. ɋ. 5-15.
6. Ⱥɮɚɧɚɫɶɟɜ Ⱥ.ȼ., Ⱥɮɚɧɚɫɶɟɜɚ ȼ.ȼ. Ɋɚɫɱɟɬ ɝɢɞɪɨɞɢɧɚɦɢɤɢ ɢ ɬɟɩɥɨɨɛɦɟɧɚ
ɩɪɢ ɫɬɪɭɣɧɨɦ ɨɛɬɟɤɚɧɢɢ ɰɢɥɢɧɞɪɚ. // Ɍɪɭɞɵ ɑɟɬɜɟɪɬɨɣ Ɋɨɫɫɢɣɫɤɨɣ
ɇɚɰɢɨɧɚɥɶɧɨɣ Ʉɨɧɮɟɪɟɧɰɢɢ ɩɨ Ɍɟɩɥɨɨɛɦɟɧɭ (ɊɇɄɌ-4) Ɍ. 2.
ȼɵɧɭɠɞɟɧɧɚɹ ɤɨɧɜɟɤɰɢɹ ɨɞɧɨɮɚɡɧɨɣ ɠɢɞɤɨɫɬɢ. – Ɇ.: ɂɡɞ-ɜɨ Ɇɗɂ,
2006. – ɋ. 50-53.
7. Ⱥɮɚɧɚɫɶɟɜ Ⱥ.ȼ., Ⱥɮɚɧɚɫɶɟɜɚ ȼ.ȼ., ɏɪɨɦɟɧɤɨ Ⱥ.ȼ.. ɑɢɫɥɟɧɧɨɟ
ɢɫɫɥɟɞɨɜɚɧɢɟ ɫɨɜɩɚɞɚɸɳɟɣ ɫɦɟɲɚɧɧɨɣ ɤɨɧɜɟɤɰɢɢ ɩɪɢ ɨɛɬɟɤɚɧɢɢ
ɝɨɪɢɡɨɧɬɚɥɶɧɨɝɨ ɰɢɥɢɧɞɪɚ ɩɥɨɫɤɨɣ ɫɬɪɭɟɣ ɜɹɡɤɨɣ ɧɟɫɠɢɦɚɟɦɨɣ
ɠɢɞɤɨɫɬɢ // ȼɵɱɢɫɥɢɬɟɥɶɧɵɟ ɦɟɬɨɞɵ ɢ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɟ. – Ɍ. 8. ʋ 1.
2007. – ɋ. 65-72.
8. Ⱥɮɚɧɚɫɶɟɜ Ⱥ.ȼ., Ⱥɮɚɧɚɫɶɟɜɚ ȼ.ȼ. ɂɫɫɥɟɞɨɜɚɧɢɟ ɥɨɤɚɥɶɧɨɝɨ ɢ ɫɪɟɞɧɟɝɨ
ɬɟɩɥɨɨɛɦɟɧɚ ɩɪɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɢ ɩɥɨɫɤɨɣ ɫɬɪɭɢ ɠɢɞɤɨɫɬɢ ɫ
ɝɨɪɢɡɨɧɬɚɥɶɧɵɦ ɰɢɥɢɧɞɪɨɦ ɜ ɪɟɠɢɦɟ ɥɚɦɢɧɚɪɧɨɣ ɫɦɟɲɚɧɧɨɣ
ɤɨɧɜɟɤɰɢɢ. //Ɍɪɭɞɵ XVI ɲɤɨɥɵ ɫɟɦɢɧɚɪɚ ɦɨɥɨɞɵɯ ɭɱɟɧɵɯ ɢ
ɫɩɟɰɢɚɥɢɫɬɨɜ ɩɨɞ ɪɭɤɨɜɨɞɫɬɜɨɦ ɚɤɚɞɟɦɢɤɚ ɊȺɇ Ⱥ.ɂ. Ʌɟɨɧɬɶɟɜɚ
«ɩɪɨɛɥɟɦɵ ɝɚɡɨɞɢɧɚɦɢɤɢ ɢ ɬɟɩɥɨɨɛɦɟɧɚ ɜ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɭɫɬɚɧɨɜɤɚɯ».
– Ɍ. 1. Ɇ.: ɂɡɞ-ɜɨ Ɇɗɂ, 2007. – ɋ. 62-65.
9. Ⱥɮɚɧɚɫɶɟɜ Ⱥ. ȼ., Ⱥɮɚɧɚɫɶɟɜɚ ȼ. ȼ., Ⱥɮɚɧɚɫɶɟɜ ȼ. Ƚ. ɑɢɫɥɟɧɧɨɟ
ɦɨɞɟɥɢɪɨɜɚɧɢɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɥɨɫɤɨɣ ɫɬɪɭɢ ɫ ɝɨɪɢɡɨɧɬɚɥɶɧɵɦ
ɢɡɨɬɟɪɦɢɱɟɫɤɢɦ ɰɢɥɢɧɞɪɨɦ ɜ ɪɟɠɢɦɟ ɫɦɟɲɚɧɧɨɣ ɥɚɦɢɧɚɪɧɨɣ
ɤɨɧɜɟɤɰɢɢ// Ɍɪɭɞɵ XIII Ɇɟɠɞɭɧɚɪɨɞɧɨɝɨ ɫɢɦɩɨɡɢɭɦɚ «Ɇɟɬɨɞɵ
ɞɢɫɤɪɟɬɧɵɯ ɨɫɨɛɟɧɧɨɫɬɟɣ ɜ ɡɚɞɚɱɚɯ ɦɚɬɟɦɚɬɢɱɟɫɤɨɣ ɮɢɡɢɤɢ»
(ɆȾɈɁɆɎ-2007). ɏɚɪɶɤɨɜ-ɏɟɪɫɨɧ, 2007. – ɋ. 35-42