Оперативные методы расчёта характеристик вихревого следа

реклама
184
!"#$% &'(%!)"*%+,+ #'-!+#'.*#+,+ /#!)0("$101/
20(!3 «4'105'1$6#0 5+70.8)'##3. 9#:+(5'-!;#! 10<#+.+,!=. >)1+5'1$?+)'#! "$"105$
/@(').!##3»
D 847, 2009, ".184-190
ABC 533.6
E@0('1$)#F0 501+7F ('"6G1' <'('%10($"1$%
)$<(0)+,+ ".07' ?' "'5+.G1'5$
>. H. I0.'##$%+)
!"##!-$!%&'(#)* +#,"#"-#)* ).)&"/+* +/. 0.1. 2'.!$3.!4!, 5!33+*
6"#7-)89#:; )<-!4+&-!&+#)/+="3.+; +#37+7'7 +/. 0.1. 2'.!$3.!4!, 5!33+*
Methods of modeling the near and far vortex wakes of aircrafts with turbojets and air
propellers are considered separately. The results of predicting vortex wakes of a series
of domestic and foreign aircrafts are presented. The effect of number of factors is
taken into account in this case: turbulence and atmosphere stratification, presence of
side wind at take-off-landing regimes. The mathematical model of a distant vertical
trace behind the airliners, basing on a method of discrete vortices and on N.E.
Zhukovsky's theorem of lifting force is described. Results of researches of
characteristics of a distant trace behind some airliners are presented. The computer
time consumption while modeling the vortex wakes according to the proposed method
is 3–4 orders less than in the case of using the well-known numerical methods.
!"#$ %&'(#)&*+# ,#-#./ / 01 #+(2#34)&'(4
@+".07#00 )(053 )+?(+" $#10(0" % $"".07+)'#$8 )$<(0)F< ".07+) ?'
5',$"1('.*#F5$ "'5+.G1'5$. J1+ ")3?'#+ "+ 5#+,$5$ @($6$#'5$, ,.')#F5$ $?
%+1+(F< 3).381"3 (+"1 $#10#"$)#+"1$ )+?7/K#+,+ 7)$L0#$3 ) (';+#'< %(/@#F<
'M(+/?.+) $ @+3).0#$0 #+)F<, ) 1+5 6$".0 $ ")0(<13LG.F< "'5+.G1+) 5'""+;
N+.00 500 1+##. ")3?$ " M1$5 @+1(0N+)'.$"* @(+"1F0 $ M::0%1$)#F0 501+7F
7.3 ('"6G1' <'('%10($"1$% )$<(0)+,+ ".07' ?' 1'%$5$ "'5+.G1'5$. #'"1+3O00
)(053 @(+:0""$+#'.*#+ )$<(0)F5$ $ "@/1#F5$ ".07'5$ ?'#$5'81"3 ) P>QH
$5. R.S. I/%+)"%+,+, )
H> $5. R.S. I/%+)"%+,+ $ ) THH $5. 4.4. Q(+5+)'
[1,2,8-11,13,14,16-19]. C(+50 1+,+, ) 6'"1$ %'"'8O0;"3 )+?7/K#F< "/7+)
,('L7'#"%+; ')$'-$$ (Q>) )$<(0)F5$ $ "@/1#F5$ ".07'5$ ?'#$5'81"3 )
'%'705$$ Q> $ Q+"RHH Q> [23]. 4'105'1$60"%$0 5+70.$ )$<(0)F< ".07+)
H> 1('7$-$+##+ "1(+$.$"* #' N'?0 501+7' 7$"%(01#F< )$<(0; [1,37,12,15,22].
7'##+; ('N+10 @+%'?F)'01"3, 61+ 7.3 ('"6G1' <'('%10($"1$% 7'.*#0,+
)$<(0)+,+ ".07' ?' 5',$"1('.*#F5$ "'5+.G1'5$ 5+L#+ /@(+"1$1*
5'105'1$60"%/8 5+70.* 7'.*#0,+ )$<(0)+,+ ".07', $?.+L0##/8 ) 5+#+,(':$3<
[2,13] $ ) ('N+10 [14]. U(07.','01"3 ) M1+; 5+70.$ 7.3 ('"6G1' <'('%10($"1$%
7'.*#0,+ )$<(0)+,+ ".07' ?' 5',$"1('.*#F5$ "'5+.G1'5$ ) %'60"1)0 $"<+7#F<
7'##F< $"@+.*?+)'1* -$(%/.3-$$ )$<(0;, ('""6$1'##F0 @+ :+(5/.0 R.S.
I/%+)"%+,+, @+.+L$) (')0#"1)+ @+7VG5#+; "$.F Ya $ 5'""F .01'10.*#+,+
1.
'@@'('1'
G , ($"/#+% 1.
E@0('1$)#F0 501+7F ('"6G1' <'('%10($"1$% …
A6G1
"+"1+3#$3
'15+":0(F
A6G1
N.$?+"1$
?05.$
4'105'1$60"%'3
5+70.* 7'.*#0,+
)$<(0)+,+ ".07'
185
4'105'1$60"%'3
5+70.* N.$L#0,+
)$<(0)+,+ ".07'
Z+(5/.'
R.S. I/%+)"%+,+
Ya
"V!l G
&'('%10($"1$%$
7'.*#0,+ ".07'
5+3'#!. 1. @8!.-3>"/) !A"-)7+$#!; /"7!&+.+ -)3=?7)
>)-).7"-+37+. $+>-"$!4! 38"&).
W'105, M1/ "/55'(#/8 -$(%/.3-$8 #0+N<+7$5+ @(')$.*#+ ('"@(070.$1*
50L7/ )$<(35$, "<+73O$5$ " %(F.', "1'N$.$?'1+(' $ ?'%(F.%+) 7.3 "'5+.G1+) "
1/(N+(0'%1$)#F5$ 7)$,'10.35$ (XYB), ' 7.3 "'5+.G1+) " 1/(N+)$#1+)F5$
7)$,'10.35$ (X B), 0OG $ /60"1* ?'%(/1%/ @+1+%' )$#1'5$, ($"/#+% 2.
5+3'#!. 2. +>-"$:" 3>"/: &8* -)3=?7) &)89#"4! $+>-"$!4! 38"&).
7'##+; ('N+10 @(07.','01"3 ('"@(070.$1* "/55'(#/8 -$(%/.3-$8 Q 7.3
"'5+.G1' " XYB, "+)0(K'8O0,+ @+.G1 #' %(0;"0("%+5 (0L$50 50L7/
186
>. H. I0.'##$%+)
%(F.*0)F5$ )$<(35$ B. $ )$<(35$, "<+73O$5$ "+ "1'N$.$?'1+(' B3
@(+@+(-$+#'.*#+ @.+O'735 %(F.' $ "1'N$.$?'1+('. B.3 )?.G1#+-@+"'7+6#F<
(0L$5+) -$(%/.3-$3 )$<(3, "<+73O0,+ " %(F.' B. ('"@(070.301"3 50L7/
%(F.*0)F5 )$<(G5 B. $ )$<(G5, "<+73O05 " ?'%(F.%' B% @(+@+(-$+#'.*#+
7.$#0 ?'%(F.%'. P$(%/.3-$3 )$<(3, /6$1F)'8O0,+ ?'%(/1%/ @+1+%' B*
('""6$1F)'01"3 ) "++1)01"1)$$ " 501+7$%+; ('N+1F [18].
X'%$5 +N('?+5, 7.3 5'105'1$60"%+; 5+70.$ 7'.*#0,+ )$<(0)+,+ ".07' )
%'60"1)0 $"<+7#F< 7'##F< $"@+.*?/81"3 #0 (0?/.*1'1F ('"6G1' -$(%/.3-$;
5#+L0"1)' 7$"%(01#F< )$<(0; @+ 5'105'1$60"%+; 5+70.$ N.$L#0,+ )$<(0)+,+
".07', %'% M1+ NF.+ ('#*K0, ' 7'##F0 :+(5/.F R.S. I/%+)"%+,+ 7.3 7)/<
%(F.*0)F< )$<(0;.
2. 56&*06+# 6#!&(&'%&'&!)&'(/ 70(&-/+/ / -&'(&*06)&'(/ %&32.#0789
60,234(#(&*
B.3 @+71)0(L70#$3 ('N+1+"@+"+N#+"1$ 1'%+; /@(+OG##+; 5'105'1$60"%+;
5+70.$ $ 7+"1+)0(#+"1$ @+./6'05F< @+ #0; (0?/.*1'1+) NF.$ )F@+.#0#F
('"601F, %+1+(F0 ?'105 "(')#$)'.$"* " (0?/.*1'1'5$ .G1#+,+ M%"@0($50#1'. R'
($". 3 @(07"1').0#F (0?/.*1'1F ('"6G1' -0#1(+) )$<(0)F< L,/1+) ?' "'5+.G1+5
H.-76. W70"* )+"@(+$?)070#F /".+)$3, @($ %+1+(F< @(+$?+K.' %'1'"1(+:'
"'5+.G1' [%-40 16 3#)'(3 1987 ,+7' ) ,. X'K%0#10. U+ 5'10($'.'5
('"".07+)'#$3 NF.+ /"1'#+).0#+, 61+ @($6$#+; %'1'"1(+:F [%-40 "1'. @(')F;
%+#-0)+; )$<(*, %+1+(F; @+7 70;"1)$05 N+%+)+,+ )01(' "@(')' 0.5-1.5 5/"
"50"1$."3 % -0#1(/ )?.G1#+-@+"'7+6#+; @+.+"F $ ?')$" #'7 #0; #' )F"+10 20
501(+). U($ M1+5 H.-76 @(+.010. 50"1+ %'1'"1(+:F #' )F"+10 40 501(+).
5+3'#!. 3. +>-"$!; 38"& %) 3)/!8?7!/ C8-76 A-+ #)8+=++ D!.!$!4! $"7-)
E@0('1$)#F0 501+7F ('"6G1' <'('%10($"1$% …
187
5+3'#!. 4. 5)3A-"&"8"#+" 7)#4"#E+)89#!; 3.!-!37+ $ *&-" $+>-* 3)/!8?7) C8-76.
Y'"6G1F @+%'?F)'81, 61+ 70;"1)$10.*#+ @($ 7'##F< /".+)$3< @+.G1' @(')F;
%+#-0)+; )$<(* ?')$"'01 #' )F"+10 20 501(+) @('%1$60"%$ #'7 -0#1(+5 )?.G1#+@+"'7+6#+; @+.+"F, 61+ %+")0##+ 1'%L0 @+71)0(L7'01 ('N+1+"@+"+N#+"1*
7'##+; 501+7$%$.
R' ($"/#%0 4 @+%'?'#+ ('"@(070.0#$0 1'#,0#-$'.*#+; "%+(+"1$ ) 37(0 )$<(3
"'5+.G1' H.-76 60(0? 60 " @+".0 @(+.G1' 50"1' ?'50(' "%+(+"1$ #' )F"+10 100 5.
Y+5N$%$ – ('"6G1, %)'7('1$%$ – M%"@0($50#1 ()/6 15650).
$7$5
/7+).01)+($10.*#+0 "+,.'"+)'#$0 ('"6G1#F< $ M%"@0($50#1'.*#F< 7'##F<.
5+3'#!. 5. 5)3A-"&"8"#+" 7)#4"#E+)89#!; 3.!-!37+ $ *&-" $+>-* 3)/!8?7) -747.
188
>. H. I0.'##$%+)
R' ($"/#%0 5 @+%'?'#+ ('"@(070.0#$0 1'#,0#-$'.*#F< "%+(+"10; ) 37(0
"'5+.G1' -747 60(0? 10 " @+".0 @(+.G1' 50"1' ?'50(' "%+(+"10; #' )F"+10 100
5. Y+5N$%$ – ('"6G1, %)'7('1$%$ – M%"@0($50#1 (Department of transportation
USA).
$7$5 1'%L0 /7+).01)+($10.*#+0 "+,.'"+)'#$0 ('"6G1#F< $
M%"@0($50#1'.*#F< 7'##F<.
X'%$5 +N('?+5, 5+L#+ "70.'1* )F)+7 + 1+5, 61+ ?' 5',$"1('.*#F5$
"'5+.G1'5$ 5+L#+ ('""6$1F)'1* <'('%10($"1$%$ )$<(0)+,+ ".07' @+ 7'##+;
/@(+OG##+; 501+7$%0.
3. :0,234(#(8 /''30-&*#)/; 9#6#+(06/'(/+ */960*&<& '30-# ,#
'#7&31(#7/ =)-124, >-747 / =-380
U($)+731"3 (0?/.*1'1F $"".07+)'#$3 <'('%10($"1$% 7'.*#0,+ )$<(0)+,+
".07' ?' "'5+.G1'5$ >#-124 (('?5'< %(F.' L=73.6 5, )?.G1#F; )0" G=405 1), 747 (('?5'< %(F.' L=59.64 5, )?.G1#F; )0" G=365 1) $ >-380 (('?5'< %(F.'
L=79.8 5, )?.G1#F; )0" G=560 1). J1+ 1($ "'5F< N+.*K$< ($"%.86'3 >#-225
«4($3») "'5+.G1' ) 5$(0. &'('%10($"1$%$ )$<(0)+,+ ".07' @($)+731"3 )
"(')#0#$$ M1$< "'5+.G1+) 7(/, " 7(/,+5.
5+3'#!. 6. F!8!,"#+" E"#7-!$ $+>-"$:> ,4'7!$ 3)/!8?7!$ G#-124, -747, + G-380
R' ($"/#%0 6 @($)070#F (0?/.*1'1F ('"6G1' @+.+L0#$3 -0#1(+) )$<(0)F<
L,/1+) ?' "'5+.G1'5$ >#-124, -747 $ >-380, .013O$< #' )F"+10 R=1000 5 "+
"%+(+"1*8 V=300 %5/6 @($ +60#* /"1+;6$)+5 "+"1+3#$$ '15+":0(F (2>=1).
Y'"6G1F @+%'?'.$, 61+ ) +60#* "@+%+;#+; '15+":0(0 )$<(0)+; ".07 ?'
"'5+.G1'5$ -747 $ >-380 #' /7'.0#$$ &=15 %5 +@/"1$."3 #' \R=-200 5. W'
"'5+.G1+5 >#-124 #' M1+5 L0 /7'.0#$$ )$<(0)+; ".07 +@/"1$."3 #' \R=-160 5.
U($ M1+5 NF.$ ('""6$1'#F )0(1$%'.*#F0 "%+(+"1$ ) 37(0 %+#-0)F< %(F.*0)F<
)$<(0;. R' ($"/#%0 7 @($)070#F ,(':$%$ ('"@(070.0#$3 )0(1$%'.*#+; "%+(+"1$
?' "'5+.G1'5$ >#-124, -747 $ >-380, .013O$< #' )F"+10 R=1000 5 "+
"%+(+"1*8 V=300 %5/6 @($ 2>=1 #' /7'.0#$$ +1 "'5+.G1+) &=50 5. $7$5, 61+
E@0('1$)#F0 501+7F ('"6G1' <'('%10($"1$% …
189
) M1+5 "./6'0 )0(1$%'.*#F0 "%+(+"1$ ) 37(0 )$<(0; "'5+.G1+) >#-124, -747 $
>-380 #0 @(0)FK'81 (+25) – (-30) 5/".
5+3'#!. 7. 5)3A-"&"8"#+" $"-7+.)89#!; 3.!-!37+ $ *&-" $+>-* 3)/!8?7!$
X'%$5 +N('?+5, @+ @(07.','05+; 501+7$%0 5+L#+ )@+.#0 7+"1+)0(#+ $
,.')#+0 +@0('1$)#+ ('""6$1F)'1* <'('%10($"1$%$ )$<(0)+,+ ".07' ?'
5',$"1('.*#F5$ "'5+.G1'5$.
THXSY>XAY>
1. >/N'%$(+) X.E., ]0.+-0(%+)"%$; 2.4., I0.'##$%+) >.H., R$K1 4.H.
R0.$#0;#'3 10+($3 %(F.' $ 00 @($.+L0#$3. >.5'1F, QF.F5, 1997.
2. >/N'%$(+) X.E., I0.'##$%+) >.H., H)'#+) U.S., R$K1 4.H. 2@/1#F0 ".07F
$ $< )+?70;"1)$0 #' .01'10.*#F0 '@@'('1F. 4+70.$(+)'#$0 #' J 4.
>.5'1F. 1999.230 ".
3. ]0.+-0(%+)"%$; 2.4. X+#%'3 #0"/O'3 @+)0(<#+"1* ) 7+?)/%+)+5 @+1+%0
,'?'. 4., R'/%', 1965.
4. ]0.+-0(%+)"%$; 2.4., R$K1 4.H. E1(F)#+0 $ N0?+1(F)#+0 +N10%'#$0
1+#%$< %(F.*0) $70'.*#+; L$7%+"1*8. 4., R'/%', 1978.
5. ]0.+-0(%+)"%$; 2.4., T$:'#+) H.C. ^$".0##F0 501+7F ) "$#,/.3(#F<
$#10,('.*#F< /(')#0#$3< $ $< @($50#0#$0 ) 'M(+7$#'5$%0, 10+($$
/@(/,+"1$, M.0%1(+7$#'5$%0. 4., R'/%', 1985.
6. ]/K/0) .H., Q'#$0) Z.H., T+%10) ].S., R$K1 4.H., _'5K/($# >.B.
>M(+7$#'5$60"%'3 %+5@+#+)%' $ <'('%10($"1$%$ .01'10.*#F< '@@'('1+).
4., 4'K$#+"1(+0#$0. 1991.
190
>. H. I0.'##$%+)
7.
';#$%%+ Q.4., T$:'#+) H.C., U+.1')"%$; T.R. ^$".0##F0 501+7F )
,$@0("$#,/.3(#F< $#10,('.*#F< /(')#0#$3< $ $< @($.+L0#$3. 4., XEE
«[#/"-C», 2001.
8. FK$#"%$; . . $<(0)+; ".07 "'5+.01', N0?+@'"#+"1* @+.01' $ %($?$"
'M(+@+(1+). – U+.01, P>QH, 1998.
9. FK$#"%$; . ., 2/7'%+) Q.Q. $<(0)+; ".07 "'5+.01' ) 1/(N/.0#1#+;
'15+":0(0. X(/7F P>QH, )F@. 2667, 2006, 155".
10. Q';:/..$# A.M. H"".07+)'#$0 )$<(0)F< "1(/%1/(, +N('?/8O$<"3 @($
+N10%'#$$ 10. L$7%+"1*8 $.$ ,'?+5. H?7. P>QH, 2006, 138".
11. Q';:/..$# A.M., W)+#+)' `.2., 2)$($70#%+ `.R. Y'"601 $#10(:0(0#-$$
1/(N/.0#1#+; "1(/$ 7)$,'10.3 " @.'#0(+5 "'5+.01'. X(/7F P>QH, 2002,
)F@.2655, ". 160-166.
12. Q'#70.* `. ., 4$O0#%+
.E. 4'105'1$60"%+0 5+70.$(+)'#$0 )
M.0%1(+7$#'5$%0 #' N'?0 "$#,/.3(#F< $#10,('.*#F< /(')#0#$; $ @(+0%1
@(+,('55#+; "$"105F. // 4'105'1$60"%+0 5+70.$(+)'#$0. 2N.#'/6.1(./R>R
A%('$#F. H#-1 5'105'1$%$. – C$0), 1996. – 2.70-74.
13. Q$#0)"%$; >.2., I0.'##$%+) >.H. $<(0)F0 ".07F "'5+.G1+). Z$?5'1.$1,
4., 2008.
14. Q+.+)#G) >. ., I0.'##$%+) >.H., S(G50#%+ 2.4., R0%('<' 2.H. A6G1 ?05.$
@($ ('"6G10 #0"1'-$+#'(#+,+ +N10%'#$3 .01'10.*#F< '@@'('1+). 4'10($'.F
XVI K%+.F-"05$#'(' «>M(+7$#'5$%' .01'10.*#F< '@@'('1+)». P>QH, 2005.
15. Q/.30) . ., B0560#%+ E.Z., B+.L0#%+) R.R., 4'1)00) >.H., U+7+N07+)
.>., U+@+) .4. 4'105'1$60"%+0 5+70.$(+)'#$0 @($ :+(5$(+)'#$$
+N.$%' .01'10.*#+,+ '@@'('1'. 4., 4'K$#+"1(+0#$0, 2005.
16. I0.'##$%+) >.H. $<(0)'3 +@'"#+"1*. I/(#'. « 0"1#$% '%'705$$ #'/%
')$'-$$ $ )+?7/<+@.')'#$3», D2. 4., 2003.
17. I0.'##$%+) >.H. R0)$7$5'3 +@'"#+"1*. I/(#'. «U+.G1», D3, 2006 ,., ".1720.
18. I0.'##$%+) >.H., Q/.30)
. ., 4+(+K%$# B. ., AK'%+) 2>.
4'105'1$60"%'3 5+70.* 7'.*#0,+ )$<(0)+,+ ".07' ?' "'5+.G1'5$ "
)+?7/K#F5$ )$#1'5$. R'/6#F; )0"1#$% 4QXA Q> D 111, "0($3
«>M(+50<'#$%' $ @(+6#+"1*», 4+"%)' 2007 ,. ". 16-21., ". 21-27.
19. W'531$# >.R., W')0(K#0) `.>. R'1/(#F0 $"".07+)'#$3 "1(/%1/(F $
('?)$1$3 )$<(0)+,+ ".07' "(07#05',$"1('.*#+,+ "'5+.G1' ) @($?05#+5 ".+0
'15+":0(F. R'/6#+-10<#$60"%$; "N+(#$% D163, THH, 1984.
20. C($-%$; ].2. 4+70.$(+)'#$0 N.$L#0,+ ".07' ?' #0"/O$5 )$#1+5. R'/6#F;
)0"1#$% 4QXA Q>, D37, "0($3 «>M(+50<'#$%' $ @(+6#+"1*», 2001.
21. T$:'#+) H.C. 401+7 "$#,/.3(#F< $#10,('.*#F< /(')#0#$; $ 6$".0##F;
M%"@0($50#1. 4., XEE «[#/"», 1995.
22. 4+(+?+) .H., U+#+5'(0) >.X., YF"0) E. . 4'105'1$60"%+0 5+70.$(+)'#$0
".+L#F< 'M(+/@(/,$< "$"105. 4., H?7. “Z$?5'1.$1”, 1995.
23. Z$.'1+) Q.>., U/50#+)' Q.2., 2$.*)0"1(+) U.H. ]0?+@'"#+"1* @+.G1+) )
)+?5/OG##+; '15+":0(0. 4., «X('#"@+(1», 1992.
R'7!;K.' 30.03.2009.
Скачать