integral_kinetic

# integral_kinetic - Integral Kinetic Energy Equation v...

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Unformatted text preview: Integral Kinetic Energy Equation v ." ." ." Idea: Integrate BL ﬂow in y, to “wash out” details in u(y) proﬁle. Converts PDEs in w,y into ODE in :3. Combine Continuity, m-momentum equations: apu (9m) 2_ 2 __ __ _ y (u “an ax ay 0] + 2H [ ’u—83 + va—u — 5%. 6“ 3p“ a“ 39’” du (97' 2— 2 _ 2 _ __ 2 _ 2 __ _ e _ => 2/711 61: + (u ue) 33; + 2puvay + (u ue) 8y 2upeue dx + guay a 2 a 2 2 _ due 87 or am [(“e U W] + 3—y[(Ue-u )pv] — —2(pe—p)uue dx 2125; (*) ye Integrate / (*) dy term by term: m 0 ye 3 2 _ 2 /y6 3 2 2 _ /ye due ye 8T /0 am [(118 U )W] dy + 0 6y [(ue U )W] (111 — 0 2(pe p)uue dm dy 0 2uay dy d ye 2 2 _ due ya ya (9U d—m/o [(ue _ u )pu] dy + 0 - .—2ue day /0 (p6 “ pludy + 2/0 Ta—ydy d 3 * 2 M due , _ E; (peuee ) + 2Peue5 dx = 2D Dimens1onal form Dimensionless form Deﬁnitions “2 0* = / 1 — —2 ’0“ dy kinetic energy thickness ue peue 6" = / < — i) i dy volume ﬂux thickness pe “6 6a . . . . D = 7'6— dy diss1pation integral 9 * 9* . . H = 7 kinetlc energy shape parameter M 6” ' . . H = 7 densrty thickness shape parameter CD = i5 dissipation coefﬁcient (Hk-4)2 2 (Bk-4) ‘1. HR ' “R > 4 l. O.“ (7.4-Hk)2 ‘.067 + 0.01977 W , Hk < 7.4 0.3 Cf k 0'2 067 + o 022 1'4 2 H > 7 . . v k .4 0.1 0.0 -0.1 0.26 S 5 2:3.CD 0.207 + 0.00205 (4-Hk) ' , Hk < 4 2c 0.20 Ree _*D = H 2. 0.207 - 0.003 H -4 , H > 4 0.22 , (k ) k 0. l I I Closure rc/ainons —— iuo—fyua‘ﬁw, /ammar/ mfajm/ Mai/10a”, ..... .. one equation (Thwuites') ...... -- two equation finite difference >ngygﬂarjrson —— Var/bu} BL aka/4&5»: maﬁa/s ...
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## This note was uploaded on 11/07/2011 for the course AERO 16.13 taught by Professor Markdrela during the Fall '03 term at MIT.

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integral_kinetic - Integral Kinetic Energy Equation v...

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