Optimum Design of Micro Bare-Tube Heat Exchanger

Transcription

1 Optimum Design of Micro Bare-Tube Heat Exchanger Tomohisa OKU, Nobuhide KASAGI and Yuji SUZUKI Department of Mechanical Engineering, The University of Tokyo, Hongo 7--, Bunkyo-ku, Tokyo, -8, Japan Micro bare-tube heat exchangers can accomplish high performance and compactness with their simple structure. In general, decreasing characteristic length leads to higher heat transfer area density at the expense of larger pressure drop. The trade-off has been so far optimized by trial and error. In the present study, simulated annealing (SA) is employed to optimize various design parameters of heat exchangers, which composes a multiple-variable highly nonlinear system. Although the heat transfer coefficient and the pressure drop on the air-side make major contribution to the total heat resistence and pumping power, empirical correlations of flow around tube bank can not predict them accurately in the low Reynolds number range, which is characteristic of compact heat exchangers. Hence, we make a series of numerical simulation for heat transfer and pressure drop of flow in the tube bank at various tube spacings and Reynolds numbers, and correlation functions are developed using an artificial neural network. Finally, optimum design is made for three types of micro bare-tube heat exchangers, i.e., heater core and radiator for automobiles, electronic equipement cooling system, and recuperator for micro gas turbine. Key words : Heat Exchanger, Micro Tube, Optimum Design, Numerical Analysis, Neural Network () Paitoonsurikarn () * * - -. * kasagi@thtlab.t.u-tokyo.ac.jp.mm Zukauskas ()

2 NN NN inline SIMPLE CFD FLUENT U max Re max.. 9 () Inlet Periodic Boundary Outlet 9.% 98.% inu i C D,i C p Re max = = = =, = Re max Nu mean C p NN d d PL d Fig. Computational domain. a) PT d d Re max Nu mean C p NN NN NN INPUT b) PT PL Re max Nu NN NN Nu i C D,i OUTPUT Inner nozzle Fig. Typical flow patterns around the tube bank at Re max =. a) = =, b) =, =. C D, ΣC D,i NN Fig. Diagram of neural network. C P Nu mean C P

3 Fig. Contours of Nu mean at Re max = Fig. Contours of C p at Re max = Re max = Nu 8.. () NNNNNN NN Re max Nu C D, NN NN Nu i C D,i Re max i Nu i C D,i (i+) Nu i+ C D,i+ NNRe max C D,i C p NNNNNN Re max =Nu mean C p 8 Re max = C P.... Nu mean C p =.. Re max T a, in, T a, out T w, in, T w, out d, m a m w w, l, t J % d in =.8d. ρu P m l core = Kc + Ke + f () din () u m K C K E f Re in f=/re in t Tw,in mw Ta,out w Tw,out Fig. Micro bare tube heat exchanger. PTd PLd d l Ta,in ma

4 P core P in P in = P core NN () CASE J=W p CASE J=-Q T CASE J=V=wlt () CASE J=W p () CASE J=-η th ) x ) T ) Tr x=x +r ) M x J(x) x x =x ) T T T ln N ( i T ) + = exp Ti N () N Table Specifications of commercial heat exchangers. T x.8nm x a) W P [W] b) x Q T [W] 8 c).x - Volume [m ] CASE Present H H H H CASE Present H CASE Present H Air Water W P [W] 8 x Q T [W] CASE Present R R R CASE Present (NN) R R R Air Water Fig.7 Optimization results in CASE -. a) Optimized pumping power for CASE, b) Optimized total heat transfer in CASE, c) Optimized core volume in CASE. Definition Q T kw) ( ( w) (m c ) W P w l (cm) t (cm) Vol ( cm ) T w,in ( T a,in ( m a m w ( kg/s) kg/s) P a ( Pa) P w) W a) W w) ( ( kpa ( W (W H H R R R Heater Core Heater Core Radiator Radiator Radiator

5 Experiment No w l Table Orthogonal array. LEVEL w, l (m).x Table Three levels for w and l. W a, W w [W] x.x Trial No. W a W w CASE Fig. 8 Optimized pumping power of nine trials in CASE. CASE Q T V W p CASE CASE W p V Q T Q T W p lv 7a CASE l HH W p W w W a CASE HH% 7bCASE / / CASE H =. =.d=. - m Zukauskas () w:l:t V=. - m wl CASE 9 H 8 wl W p wl W p L Fig. 9 Schematic of a cooling system with micro bare-tube heat exchanger and cooling plate. LEVEL w, l (m).9x x.7x Fig. Optimized pumping power of nine trials in CASE. W P [W] w c w w T w,in m w W a, W w, W CP [W].. W Tsurface. δ Z T a,in m a O :.x - m O :.x - m O : 8.x - m O :.x - m O :.8x - m T w,out Q T Table Three levels for w and l. (W).x - m Q T [W] Fig. Total pumping power versus heat exchange rate for various core volume in CASE. w Design Variables l t T a,out Trial No. W a CASE W w W CP 7

6 CPU W/cm () Tuckerman-Pease (7) W/ (cm ) 9 CP MHE LWZwltQ T T surface T a,in m a m w CP W CP MHE W MHE W p V= - m wl 9 CASE Q T =W T surface =CP L=W=.m δ=.m Z=.m CASE W p wlw p W p 9 W p W CP MHE w:l:t=::v W p. - m - m W p Q T 8 TIT RIT (8) kw d m a m w P i T i J=-η th kw kw ε R ( P/P) P P T T ε R = T T P P P P = + P P Fig. Recuperated gas turbine cycle. LEVEL w, l (m).x Table Three levels for w and l. η th [%] Compressor Filter Recuperator Combustor Fuel Turbine x.9x Trial No. CASE Fig. Comparison of cycle efficiency among nine trials. () ()

7 9 ε R MHE Plate Type P/P MHE Plate Type.x -.8 CASE : H H CASE : H H CASE : H ε R [%] Fig. Recuperator temperature effectiveness and pressure drop in CASE. η th [%] Fig. System efficiency of recuperated gas turbine cycle in CASE. 8% V=. - m w l 9 CASE η th w l wl w:l:t=:: ε R ( P/P) η th Volume [m ]. Volume [m ] 8 MHE Plate Type.8 x - P/P [%] 9 d [m] Fig. Optimum tube diameter in CASEs,, and..x - d [m] Fig. 7 Optimum tube diameter in CASE., 7 Fig. 8 Optimum tube pitch versus frontal area in CASE. 7, Fig. 9 Optimum tube pitch versus frontal area in CASE. wl/(wlt) / wl/(wlt) / 8 Q T /Volume [W/m ] Q T /Volume [W/m ] O :.x - m O :.x - m O : 8.x - m O :.x - m O :.8x - m CASE x x

8 NN.NN Nu mean C p CASE -. dcase Hd =. =. (9). - 7 CASE.mm (A) (No. ) 89CASE CASE A=wl () KaysW. M., and London, A. L., Compact heat exchangers, A rd edition, McGraw-Hill Inc., (98). () Paitoonsrikarn, S., Kasagi, N., and Suzuki, Y., Proc. Symp. A Energy Engineering in the st Century, Hong Kong,, (), 97. =. =. () Zukauskas, A., Adv. in Heat Transfer, 8, (97), 9. a () Williamson, C. H. K., Annu. Rev. Fluid Mech., 8, (99), 77. () Suzuki, Y., and Kasagi, N., Proc. th Turbulent Shear Flows, Grenoble, (997), 9.8. () Overall Roadmap Technology Characteristics, ITRS, () (7) Tuckerman, D. B., and Pease, R. F. W., IEEE Electron.mmm /m Device Letters, EDL-, (98),. (8), 8, (),. (9) Paitoonsrikarn, S.,,, ().