:536.24(075.8) , ANSYS FLUENT STAR CCM+ , , ISBN
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1
2 .. КИК ЧЕЕ ИЕ 07
3 5.56:56.4(075.8) 66 :,,..,,.... :. /....:., ,,,,.,,. ANSYS FLUENT STAR CCM+ ().,.0.0,.0.0,.04.0,.04.0И ISBN , 07, 07
4 ,,,. ( ),.,,.,,, ,, ().
5 .,.,. ( ). TW,.. ( ) w,.,. ( ). Ч (). ( ) (Conjugate eat Transfer CT) []., 4
6 . ().,, Д4].,,., Д 8Ж. []. ANSYS FLUENT STAR CCM+ [5,6].,,,,., 5
7 ( 5, %)., Д4],, :?,., (error, residual),.,.,, (,, ). (...,......,...),.....,.....,
8 .,.... (), w( x, ) T T. w w x x, T T, w (.) (, ),.,.,,, ( ) s.,. (,,, )., () 7
9 ., T T u x, y,, (,).. () (),, (,). T w / x<0,,,.. 8
10 ,,, T w / x>0,..,. ( ): w T, w x, x, T T Nu T T, (.) y w w w L Nu,, L.,,,,.,,,., T w / x=0,..,., T w > T.,,, Nu., Tw < T,,, (.), Nu>0. 9
11 ,,, (.)..,,, s,,.,,,. (.). (.. ) [], 0
12 ,.,.,,,.,,,. :, ;, ; ; ;..., : (, ); (, ); (, ).,,, ( );
13 ,. (, ). (,, ).,.,,. ( ), ( ). (). ( )., [0], ; ;....,,
14 , []: 0 τ ρ j j j j (.) k j k j j jj jk k j j k j j k k j k j k j k j j j k j j k (.4) e j k k j k j k jj k j k j j jk j k j jk j T j j j j j j j e e ρ (.5) : ;,, j ; k ; j
15 ;,, j, jk ; T j ; e.,. (.) (.5) T,,. S, : j j S k jj ( j,, ) (.6) j j k j k k S jk j k k j j k j j k k ( j, k,,; j k) (.7) : 4
16 5 4 p (.8) 4 p (.9) 4 p (.0) (.)
17 6 (.) (.) T ( j e ) j j T j e j T (.4)... : z, r,, (.5) z. : r,,. z, r, u,, w. 0.
18 7 []: 0 r r ur z (.6) ; r r z z p r u z u u zr zr zz (.7) z; rr zr rr r z r r p r z u (.8) r; r z r r r z r w r w z w u (.9) φ;
19 8 r r z u zz 4 (.0) r z u r rr 4 (.) r z u r 4 (.) z r u zr (.) r w r w r r (.4) z w z z (.5) : r r z u p r T r r T r z T z r T z T u c V (.6)
20 9 : r r z u z r u r r z u (.7).4.. :,. 0 y x u (.8) y u x p y u x u u u (.9) y u y T y y T x T u T p c (.0)
21 T T T s s s s c s (.) y s y x s x V y 0, u 0; y, u U, T T ; (.) y 0, T T ; s w T T s. (.) s y y y 0 y 0,, : z 0, u 0, w r z,, w 0 T T,(.4) z=0.,., << L /s /. Bi / s,, 0
22 . (.),.,. : a s T s t T s x w w s V s 0 (.5), w ; V w..5. (.6) T T w w w. (.6),., [,]: w k k d * g x w, k k w w x d w k g w k dx k * k k,(.6) dx k w w
23 * w, g k. * / * w w w (error, residual),. * dp / dx /, W dp / dx ( * ; W ).. g
24 ,,.. * Re u * / ( ). g.. g : = 0,; 0,0;,0; 4 0,0 ( Re * =0, 0 4, 0 5 )
25 w x g x w g w g x w 0 x 0 u t 0 x x g g w 0 u u xt w x (.7) 4 u / x, Д]. g ki 4. g ki u / x : Pr=.0; g ; 0 g ; g ; 4 0 g 0 4
26 ,,,,.,,,.,,..., (.6) (.7),. (.6,.7),. [,4,8], ( ).,,,.,. []. 5
27 ,,.,., (.6), : d T w s g x Bi y w, (.8) dx / y 0. (.8), Bi Bi 0,, ( ).,, d (.8), w. dx, ( ),,. 6
28 ( Bi 0) :,, ( ),.,,.,,,,..,.. ДЖ / Br Pr Re, [8Ж x s Br s / Pe.6..,, :. a s T T s s x * s w g 0 x u w 0, (.9), w. V 7
29 , w T s. a s T s * x >> g 0 u s w T s >> x g 0 Nu * Pe c p c s s w, (.40) (.40), Nu * Pe cp / s c s, [Ж.. Lu c p / s c s. (.40) T s >> L g 0 Nu * Pe Lu w, (.4),. 8
30 ,, (.4),,. L /,.,,, ( ).. (Ni 90%, Cr 0%) =,7/( ), =0,004 L / =00 (Pr=0,7) (Pr=0,0074). t 00 o C u,0 /. t 00 o C u 0, /., 5. L Nu *. g Lu 0 Pe, 4,,0 04 0, 64.,.. 5,8 0,0Re Pr 0, 8 Nu * 0, Re 0,5 Pr 0, Nu * Д4]. 9
31 y y t a t dy y u t t x (.) a c p /, p c,,. : / y y u u y d y c y b a w T T (.) (.) (.), : y T w y T w w y w w s (.)
32 z 0, w z z, (.4) s T 0.,, y, : d 4 a z u, / (.5) 0 dx ( z) z 4z 4 z T,, z 0 (.5) : d dx 0a T (.6) z z 4 Pr (.6) [,]: Br x Pr m Re n x s
33 Nu x Nu x * 0,Br x Br <,5; x Nu x Nu x * 0,4,66 Br, 5(.7) Nu x x * Nu 0, Re 0,5 Pr / x * x... d T dt r r T T dy ar, (.8) dr 0 dy y0 5. r Д]
34 49 y y r r, 60, 5 (.9) w w y y, w y w, (.0) T w T T T b, b, T b b const. (.0) : y T, T Tb, 0; (.) y y 0, s, y y, (.) w y, 0, (.), z, w, T z z / s / T.
35 (.9) (.0) (.8), k T / []: d k a Br k r r dr k Br 49 0 (.4) Br 0 S. / / (.4) : k 0,908 Pr /, Br 0 0. Nu 0,47Re / Pr / r, r, (Pr=0,7) Д7] ( 6%). Nur r /, Re r /, r. (.4) Br 0 k / 0,908 Pr / z, (.5) 4
36 Nu 0.47Re / Pr / / r, r z (.6) (.6),., T T w T T b z ( z). T ДЖ..., T c c. u. u a,, (.7) x y 5
37 T T 0, T 0, T c. 0, x >0, y >0 c T c T 0 (.8) x 0, >0, y >0, =0 (.9) ( T s ) (.5) (.7) y=0,τ>0, x>0, r s ( ), (.0) y r c /. s s (step) [5]: 6
38 T T W c T T 0 c step u exp erf [ ] erf, (.) 0, u., u x / au / r ; x []; c ax/u erf t ) dt [7]. 0 ; exp( Q w step w ( T c T0 ) u /( ax) : 0,, Q (.) w step exp erf, exp erf (ramp) 7
39 T T W c T T 0 c ramp, exp( ) erfc[ ] i erfc[ ] i erfc[ ], (.) T T exp( ) erfc[ ] i erfc[ ] W c, (.4) T T 0 c ramp i erfc[ ]. ;, erfc[ ] erf [ ] i erfc[ ] erfc( t) dt, : erfc( t) dt exp( ) erfc[ ]. exp Q w ramp T W T c T 0 T c step T W T c ramp, (.5) T 0 T c. 8
40 Q w ramp exp erf erf T T W c T T 0 ramp c ( ), (.6). (Quasi steady Q.s.) (.) (.) : Q. s. T T W c T T 0 c step exp( ) erf erf (.7) Q Q. s. exp exp erf erf w step (.8) 9
41 ,. Ж.,.., ( ): w T T w T T w ( T T ) Bi / Bi, (.) Bi T w, T, T ;, ; Bi / s, Bi / s ; ; s. Nux 0, Pr / Re /, x Nux 0,095 Pr 0.4 Re 0.8 (.) x 40
42 ., Bi D x n, Bi D x m. dbi Bi dbi ( / Bi ) dx n n m Bi dx Bi g x g Bi Bi / Bi (.) Bi Bi gn n x D D D / D m x g n m n x D / D D m x D / D x m (.4) (.4), x 0 max n, m 0; g n m 0, m 0 g n max max n (.5), n 0, m 0, 4
43 , n, m 0. max max g / max g /5. Pr>0.5 g 0,6 ( ). max 0%. g =0, ( ) max =4%., Pr=0,0 g =0,5 max =0%.,, ( Pr>0.5).,, 0 5%; 7% []. Д],,.,, max.. (Ni 90%, Cr 0%) =,7/( ), s =0,04 L =0,4.. 4
44 t 0 o C u 0, 5/,, ; t 50 o C u 0, /.,,, x=0,.. 0,5 u D 0, Pr 0, n m 0, 5. s D =0,67( 0,5 ), D =0,0( 0,5 ), =,%.. t 00 o C u 0 / ;,, t 00 o C u 50 /.,,. D =0,046( 0,5 ), x=0, =%. D =0,0( 0,5 ). 4.,.. =56,8% x=0,. 5.,.. x=0, =4,7%. 4
45 ..,, ( x 0) ( 0), w ( x L) T w. T T x w w ch( Bi ) T (.6) T w ( L) ch( Bi) L (.6) : x d x x g w g Bi th Bi, (.7) w dx L L ( g =0.6, Re ) x L Bi =.64, (.7) max =00%.,,, 00%. 44
46 .. w, (.8) w / / w. F / F ;.. F F c ze ;. F F... z ; F.. F zfp ; F p ; F ; c ;, E. : Bi ; s Bi c c s. Bi ; : Bi c D x k 4, Bi, c Bi. s Bi. F Bi c D x k D,. F
47 F F Ez p Bi D.,,..... Bi Bi F c F Bi Bi k n Bi n g (.9) (.9), k x D F c F D k x D D n x nd g 5.. / 4 / + + / D n x k x F c F D D F c F D k x D F F D k n g (.0)
48 , n, k 0,... g n x 0. max n 0; k 0,,, max,.. g n x 0. max 6. Д.5, 4].. (.9) g n Bi. Bi n k Bi. Bi Bi. F c F.. 0,6,55 0,5 5,5 0,5 0,479 6,6 085, =6,7%.. 0, 0,5 0,5 0, Pr,5 L Re Pr Re Pr Nu L L, w u u L Re, Re L, L 47
49 . 0 <Re L <, , (.) w T T, w, () T T,, ; T T,., T T,,,. T.,,, d x w w dx d x x d dx g g (.) dx w w 6, 48
50 M=0,5 M=0,68. M ( u ) /( u ) ( ) ( ). M=0,5 0,68 DR = ρ/ρ = 0,95 ( R / d =47, R, d ), ( R / d = 44,5), []. =0 ( ) P/d=. 6., M=0,6.,,.,, 49
51 . M=.0, ( 7). 7.,. ( 8 9). 8., 50
52 =0, ( 9). 9., ( 8 9),. M =, M =,7 x x / d = 6 5. D x l 6, l >0 ( 6 7) l <0 ( 8 9). l M x / d. (.), : Bi D x n D x l 6 5
53 5 w nbi w dx dbi x dx w d x ; l dx d x, w w w l w nbi g w w dx w d x w dx d x g (.), / Bi Bi, (.) n x D l x D n x D l x D l x D n x D l n x D l x D n x nd g = = D n x n x D D n x n l x D D D n x n x l D n x n x D n l x nd g (.4)
54 x 0 n >0 l g l max n >0; g n max n >0 l n <0 (.5) 7., ( 0). L 5 h =,0,5 Д6Ж. d =0,8,, P / d =,5,0. L.5,0. 0. ( ) 5
55 =0 0 P / d =. ( g =0,; n=0,).. (.). l, 7, M=,05 DR=,0: l ln ln ln x lnx =0,. 5 0,8. L / d =8,7. : =0, =0,5. w Bi = 5,0 [6].,, x = 8,7: l w nbi g w w w =5,8%. 0, 5,0 0,5 0,78 0, 0,5 0, 0, 0, 0,5 0,5 0, ,5. x / d =40. : =0, =0,. w Bi =,0 [0]. 54
56 . l, 8, M=, DR=,0: 0,5. l w nbi g w w w =,% l ln ln ln x lnx 0,,0 0, 0,88 0,5 0,7 0, 0, 0, 0, 0, 0, =.5.,, : g x w 0 u w (.6) g 0 ( 4), u. d i erfc x / dx erfc x :, 55
57 erfc erfc i erfc i erfc ramp g 0 erfc (.7) ramp g 0 erfc erfc erfc i erfc i erfc[, (.8) ]. Q.s. step Q. s. step g 0 erf erf exp (.9) (.9),. 9. Q.s.. step 50% Ni 50% Fe,75, L =76,, =0,. 56
58 (,9,5). 0 5,6, Pr,. : Re,0 5 ( ) L ( ).. : Re L Re L,45 0 6,0 5. 0, 8 4 g =,. Д4] : 0 995,9 /, 0, 687 /(), 450 /(), p,5 0 7 /, a, /. 50% Ni 50% Fe : 8900 / s, 40 /(). s Nu L / 0,664Re 0,5 Pr 0, 4, 6; L c L Lu c p /( s c s ),09 ; Nu L / =0,09. Pe L =0,66, erf(0,7)=0,695 erf(0,66)=0,67 (. 7). Q.s. (.9): step Q. s. step g 0 exp, 0,09 erf erf 068 0,597 0, = 6%, 5 Q.s. =6,%. step 57
59 0. : Re L, , 8. Nu L / 0,07 Re 0,8 Pr 0,4 48; L c L Nu L / Pe L =,54 =0,0. erf(,564)=0,97 erf(,54)=0,967 (. 7). Q.s. (.9): step Q. s. step g 0 exp, 0,09 erf erf 004 0,009 0, =,6% Q.s., step Д8] 0, 8.. ramp,., >, 9, : =0,66 =0,09. =0,8 =,0. 0, <. (.7) =0, : 58
60 erfc(0,66)= erf(0,66)=0,7; erfc(0,6578)= erf(0,6578)=0,55; i erfc(0,66) =0,94; i erfc(0,6578) =0,6; erfc 0,66 =0,008. 0,7 0,55, 0,09 ramp 0,008 0, 0068 =7%. erfc :.,. =5 (.8), >. =0,8. 4,.. : erfc ( ) = erfc(,098); erfc(,007)= 0,57; i erfc(,098) =0,06; i erfc(,007) =0,0506; erfc 0,66 =0,707. 0,57 0,,4 0,09 ramp 0,707 0,06 0, 0506 =5,7%. erfc : 59
61 : ;, [4,7].,.,,...,. : ()., ( ).,. 60
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65 In place interface,,. Air interface Solid interface Type contact interface Interface. STAR CCM+ (.,),,.,.. STAR CCM+ 64
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68 5. (); : Д Ж,, () : Velocity inlet=0 /, Gauge pressure outlet=0. Second Order Upwind. Coupled. k RNG. 5, ( ), ( ).,, 5,. ( 6),. ДЖ,,,. (). 6, 67
69 () x > 0, ДЖ 6,. 68
70 4.4.,.,, ( 5) 0 4 ( ), ( 0 ).,,. Д]: u Y a 00, s s 0. 5, (4.) ( Y ) s, s,., Y = Y s =0,00.,, 00/, s / 00., 69
71 ,.,,.,. STAR CCM+ Simulation, ( 7). Implicit Unsteady model,, T T 00 0 ( 8). c Field Functions Tools C *$ Time 00 0*$Time. Restart,., s Implicit Unsteady model. 7 C++ : ($Time > = 0.0)? 000: *$Time. =0,
72 , >0, , ( 8)., / ( 9,)
73 ;. 0,4 0,04. 50% Ni 50% Fe : 8900 / s, 40 /(). s , Y + =0,6.. =0, =0, s 8. 9., 7
74 5, (); (),. (.7), 0 : ramp g 0 exp, ramp %. 7
75 5. 5..,,,,..,. Д9,0Ж,,,,...,,,., ,88 0,99,4,6 0,6 74
76 , 664 Q = ): d. =50 (, Q ,8( /. ) F.. 0,99,. Q 000 4, ( / ) ( / 4), d., [Ж 664 ( 0) 9/0 SEMIKRON
77 ё ё (, ). GAMBIT ё. Z Y X ё / ) (. 664: ( ); ( ) Д9Ж,, ANSYS FLUENT. (, ), 76
78 ( ). ( 40 ).,, , /. 77
79 0 (. ),,.. ё 664 u (/) R / T RNGKE 0, 0,87 RNGKE P 0, 0,8 RNGKE DO 0, RNGKE,0 0,8 5 SKE,0 0,097 6 RNGKE P,0 0,096 7 RNGKE DO,0 0,8 8 RNGKE P,5 0,079 9 SKE 5,0 0,058 0 RNGKE 5,0 0,065 RNGKE k ε RNG, SKE k ε. P DO Д5]. R T T Q T max /, 78
80 () Q., ё k ε RNG DO ( ).. ё 664 9/0 SEMIKRON ( 000 ).,,, ( ). 79
81 5.., ( ),,.,.,, Д0Ж,. ( ) Д0], d=0,4, P ( 4, ). P/d=,,5, : 4,7 7,
82 ( 70) () (), P/h=0. h 0.4, 0...,,., d =,,. d =. 8
83 ,, , d, 0,4 0,4 0,4 0,4 0,4 0,4 0,4 0,4, t/d,5 4,67 4,67,, 4,67 4,67,8,66,84,87,87,87,87,86,8, DR, M,,8,,95,0,98,0,4 0,88, 64C, 0%, 0,68. I V 0,5; 0,09; 0,0; 0,; 0,80 (90,, 5, 99, 54)C, 0%. (D),.,,. (, ANSYS FLUENT, STAR CCM+) D ( 8
84 ),,,.. Unigraphics NX. 5. Cyclic. 0,8,8. Stagnation ( P* = 0,88, T* = 887, 47, Tu=0%, L= ). Mass Flow Inlet ( 64,6%, 0,5%, 6,9%, 8%, T* = 45, Tu=%, Turbulent Viscosity Ratio ( t / 0). Pressure Outlet ( P = 0,68 )., (In Place). ( Д0]). 8
85 ( ). 5. : (); () STAR CCM+. (. 4).,,. 4 84
86 Y +,0 ( 6). 4.,. Y + Coarse mesh,8,4, Fine mesh 9,5 5,0 4, Finer mesh 8,6,9 6, Finer mesh,5 5, 8, (),, Cp=Cp(T) ( ),, Д6]. 85
87 8760 /, 90 /(),. 6. 4: (); () 86
88 ,. Д9]. : VF ally +, SST ally +, RKE ally +, SST swf, KE swf. (standard wall function swf), «ally +», Y +.,..., Y +,. Segregated,..,.. 9,5. 8,5.,..,,7 48, ,5,5,..,, ,5. 87
89 4 4 ( 7 ). : ( 0 5 ),, ( );, ;,. ( 5). 5., Y+ [ ]. k SST all Y+,8 00 9,5 0 8,5 5,5 4 4 RKE all Y+, , , ,5 8 8 VF,5 9 9 k SST swf, KE swf,8 00 k SST LowRe Re,5 0 88
90 .,8.,,5. ( 4). (,5 ), 6.,,5.,% ( ) ( T * * * T ) /( T T ).,. 7,,% T,,,. 7,,,%,. 5%,, T.,,, RKE.,8. Y + = 00. (SST, VF) 5%, (0 5)%. 89
91 7. : (), (), (), (): SST all Y + (, ), RKE all Y + (, ), VF (, ), SSTsWF ( ), KWsWF ( ), SST LowRe γ Re ( ). ( 8,). 8,, 50., ( 8,). 90
92 8. (); (); () 9., ( 4).,,, D,. ( ),, D. 9
93 T, C Экеие L :, D, D, 4 D 0,, ,. 0 40,
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100 , Re, r r / i, G =.9 07, D c Re =. 0 4, r,,. D c G ( ) Re G D =.0 0 4,, i, D G,, t , Re i, ( 4). (D ).,. M =0, ( 4,). []. 99
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106 7.. Conjugate Problems in Conectie eat Transfer/Dorfman A. Sh. Taylor & Francis Group, LLC. London New York p..,.. /..,..,... :., c..,.. /.....:, ,.. /.. :, ,.. /..,... :, ,.. /....: c. 7.. /..,..,...;.....: :..:, ,..,....: ,.. :....,..: : :. 06. c. 05
107 ..., :.. (.)..:...IV 9/..,..,...: ,..... /....: User Guide ANSYS FLUENT ersion 4.0. USA STAR CCM+ Documentation. CD adapco. Version pp. 7.,..,....: /..,..,..,...: ,....: :.., , ;., ,..,
108 ..., :.. /..: Sucec J. Unsteady heat transfer between a fluid with time arying temperature and a plate: an exact solution//international Journal eat Mass Transfer. Vol pp /..,..,..,..... : ,...:. (... ) /..: ,.... (9) ,..,
109 8. 7 [7]. Итр x x t e dt 0 x (x) x (x) x (x) x (x) x (x) x (x) 0, 0, 0, 0, 0, 0, 0, , ,0 86 0, , , , ,0 70 0, , , , ,0 46 0,5 76 0, , , , , ,0 86 0, , , ,
110 7. р x (x) x (x) x (x) x (x) x (x) x (x) 0, 0, 0, 0,9 0,9 0,9 0,9 8088, 885, 9606,5 678,7 844, , ,5 896,5 9476,55 76, , , ,0 90,40 959,60 765, , , ,5 990, ,65 808,85 9, ,0 880,0 940,50 966,70 879,90 979,
111 7. р x (x) x (x) x (x) x (x) x (x) x (x) 0,99 0,99 0,99 0,99 0,99, 755,6 8607,4 946, ,7 987, ,5 769,0 8857, , , , ,0 87,5 9,50 959,65 98,80 995, ,5 857,40 9, , , , ,99 0,99 0,99 0,99 0,99 0,99 0
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CHAPTER 7 NUMERICAL MODELLING OF A SPIRAL HEAT EXCHANGER USING CFD TECHNIQUE
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