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Optimal design and decision making of an air cooling channel with hybrid ribs based on RSM and NSGA-II

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Abstract

The channels roughed by ribs have been widely applied in turbine blade internal cooling. A new concept of cooling channels with hybrid ribs (the combination arrangement of rectangular and semicircular ribs) is proposed in this paper. The optimal design and decision making of the new channels are performed to gain the optimal design variables and corresponding heat transfer and flow performance, combining response surface methodology and non-dominated sorting genetic algorithm II. The objective functions (\(\overline{{{\text{Nu}}}} {/}\overline{{{\text{Nu}}}}_{{\text{s}}} ,\overline{f}/\overline{f}_{{\text{s}}}\), and η) corresponding to the optimized design variables (Re, p/e, e/D) are obtained by a series of numerical simulation calculations. The surrogate models are obtained in quadratic polynomial forms, and then, the analysis of variance is utilized to assess the statistical significance of each term in the surrogate models. Pareto-optimal fronts are obtained by NSGA-II, and the Technique for Order Preference by Similarity to Ideal Situation is used to determine the better Pareto-optimal solution. The results indicate that the quadratic term (p/e)2, linear term Re, and linear term Re are the most significant terms for \(\overline{{{\text{Nu}}}} {/}\overline{{{\text{Nu}}}}_{{\text{s}}} ,\overline{f}/\overline{f}_{{\text{s}}}\), and η, respectively. That the optimum objective functions are \(\overline{{{\text{Nu}}}} {/}\overline{{{\text{Nu}}}}_{{\text{s}}}\) = 2.07 and \(\overline{f}/\overline{f}_{{\text{s}}}\) = 4.00, corresponding design variables are Re = 20,571, p/e = 11.43, and e/D = 0.051. The optimal design variables along for various Re are also gained, which possesses guiding significance for cooling channels optimization design.

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Abbreviations

c p :

Constant pressure specific heat capacity (J kg−1 K−1)

D :

Hydraulic diameter (mm)

e :

Rib height (mm)

f :

Fanning friction factor, approximate function (–)

H :

Channel height (mm)

I :

Turbulence intensity

k :

Turbulence kinetic energy (m2 s−2)

L :

Channel length (mm)

n :

Number of variables (–)

Nu :

Nusselt number (–)

p :

Pressure (Pa), rib pitch (mm)

Pr :

Prandtl number (–)

q :

Heat flux (W m−2)

Re :

Reynolds number (–)

T :

Temperature (K)

W :

Channel width (mm)

u :

Velocity (m s−1)

X :

Design variable (–)

α :

Convective heat transfer coefficient (W K−1 m−2)

λ :

Thermal conductivity (W m−1 K−1)

μ :

Dynamic viscosity (kg m−1 s−1)

ρ :

Density (kg m−3)

η :

Overall heat transfer coefficient (–)

ε :

Turbulence dissipation rate (m3 s−2)

w :

Channel wall

f:

Flow region

in:

Inlet/inside

o:

Outlet/outside

t:

Turbulence

s:

Smooth tube

ANOVA:

Analysis of variance

CCD:

Central composite design

DF:

Degree of model freedom

DOE:

Design of experiments

NSGA:

Non-dominated sorting genetic algorithm

MS:

Mean square

PRESS:

Predicted residual error sum of squares

RSM:

Response surface methodology

SD:

Standard deviation

SS:

Sum of the squares

TOPSIS:

Technique for Order Preference by Similarity to Ideal Situation

References

  1. Chandra PR, Alexander CR, Han JC. Heat transfer and friction behaviors in rectangular channels with varying number of ribbed walls. Int J Heat Mass Transf. 2003;46:481–95.

    Article  Google Scholar 

  2. Gao XF, Sundén B. Heat transfer and pressure drop measurements in rib-roughened rectangular ducts. Exp Therm Fluid Sci. 2001;24:25–34.

    Article  Google Scholar 

  3. Rau G, Monde M, Moeller D, Arts T. The effect of periodic ribs on the local aerodynamic and heat transfer performance of a straight cooling channel. J Turbomach. 1998;120:368–75.

    Article  Google Scholar 

  4. Acharya S, Agarwal P, Nikitopoulos DE. Heat/mass transfer in a 4:1 AR smooth and ribbed coolant passage with rotation in 90-degree and 45-degree orientations. Vienna, Austria; 2008.

  5. Islam SM, Haga K, Kaminaga M, Hino R, Monde M. Experimental analysis of turbulent flow structure in a fully developed rib-roughned rectangular channel with PIV. Exp Fluids. 2002;33:296–306.

    Article  Google Scholar 

  6. Han JC, Park JS. Developing heat transfer in rectangular channels with rib turbulators. Int J Heat Mass Transf. 1988;31:183–95.

    Article  CAS  Google Scholar 

  7. Chang SW, Liou TM, Chiang KF, Hong GF. Heat transfer and pressure drop in rectangular channel with compound roughness of V-shaped ribs and deepened scales. Int J Heat Mass Transf. 2008;51:457–68.

    Article  CAS  Google Scholar 

  8. Chang SW, Liou TM, Lee TH. Thermal performance comparison between radially rotating ribbed parallelogram channels with and without dimples. Int J Heat Mass Transf. 2012;55:3541–59.

    Article  Google Scholar 

  9. Choi EY, Choi YD, Lee WS, Chung JT, Kwak JS. Heat transfer augmentation using a rib-dimple compound cooling technique. Appl Therm Eng. 2013;51:435–41.

    Article  Google Scholar 

  10. Shen Z, Xie Y, Zhang D. Numerical predictions on fluid flow and heat transfer in U-shaped channel with the combination of ribs, dimples and protrusions under rotational effects. Int J Heat Mass Transf. 2015;80:494–512.

    Article  Google Scholar 

  11. Singh P, Ekkad S. Experimental study of heat transfer augmentation in a two-pass channel featuring V-shaped ribs and cylindrical dimples. Appl Therm Eng. 2017;116:205–16.

    Article  Google Scholar 

  12. Singh P, Pandit J, Ekkad SV. Characterization of heat transfer enhancement and frictional losses in a two-pass square duct featuring unique combinations of rib turbulators and cylindrical dimples. Int J Heat Mass Transf. 2017;106:629–47.

    Article  CAS  Google Scholar 

  13. Jaurker AR, Saini JS, Gandhi BK. Heat transfer and friction characteristics of rectangular solar air heater duct using rib-grooved artificial roughness. Sol Energy. 2006;80:895–907.

    Article  CAS  Google Scholar 

  14. Layek A, Saini JS, Solanki SC. Heat transfer and friction characteristics for artificially roughened ducts with compound turbulators. Int J Heat Mass Transf. 2007;50:4845–54.

    Article  CAS  Google Scholar 

  15. Eiamsa-ard S, Promvonge P. Thermal characteristics of turbulent rib-grooved channel flows. Int Commun Heat Mass Transf. 2009;36:705–11.

    Article  CAS  Google Scholar 

  16. Alfarawi S, Abdel-Moneim SA, Bodalal A. Experimental investigations of heat transfer enhancement from rectangular duct roughened by hybrid ribs. Int J Therm Sci. 2017;118:123–38.

    Article  Google Scholar 

  17. Papila N, Shyy W, Griffin L, Dorney D. Shape optimization of supersonic turbines using response surface and neural network methods. Reno, Nevada; 2013.

  18. Shyy W, Papila N, Vaidyanathan R, Tucker K. Global design optimization for aerodynamics and rocket propulsion components. Prog Aerosp Sci. 2001;37:59–118.

    Article  Google Scholar 

  19. Samad A, Kim K-Y, Goel T, Haftka RT, Shyy W. Multiple surrogate modeling for axial compressor blade shape optimization. J Propuls Power. 2008;24:301–10.

    Article  Google Scholar 

  20. Kim HM, Moon MA, Kim KY. Multi-objective optimization of a cooling channel with staggered elliptic dimples. Energy. 2011;36:3419–28.

    Article  Google Scholar 

  21. Kim KY, Shin DY. Optimization of a staggered dimpled surface in a cooling channel using Kriging model. Int J Therm Sci. 2008;47:1464–72.

    Article  Google Scholar 

  22. Samad A, Lee KD, Kim KY. Multi-objective optimization of a dimpled channel for heat transfer augmentation. Heat Mass Transf und Stoffuebertragung. 2008;45:207–17.

    Article  Google Scholar 

  23. Deb K. Multi-objective optimization using evolutionary algorithms multi-objective optimization using evolutionary algorithms. Wiley; 2001.

  24. Samad A, Kim K-Y. Surrogate based optimization techniques for aerodynamic design of turbomachinery. Int J Fluid Mach Syst. 2009;2:179–88.

    Article  Google Scholar 

  25. Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput. 2002;6:182–97.

    Article  Google Scholar 

  26. Esfe MH, Hajmohammad H, Toghraie D, Rostamian H, Mahian O, Wongwises S. Multi-objective optimization of nanofluid flow in double tube heat exchangers for applications in energy systems. Energy. 2017;137:160–71.

    Article  Google Scholar 

  27. Seo JW, Afzal A, Kim KY. Efficient multi-objective optimization of a boot-shaped rib in a cooling channel. Int J Therm Sci. 2016;106:122–33.

    Article  Google Scholar 

  28. Damavandi MD, Safikhani H, Yahyaabadi M. Multi-objective optimization of asymmetric v-shaped ribs in a cooling channel using CFD, artificial neural networks and genetic algorithms. J Braz Soc Mech Sci Eng. 2017;39:2319–29.

    Article  Google Scholar 

  29. Haasenritter A, Weigand B. Optimization of the rib structure inside cooling channels with genetic algorithms. Int J Des Nat. 2007;1:116–34.

    Google Scholar 

  30. Yang YT, Chen PJ. Numerical optimization of turbulent flow and heat transfer characteristics in a ribbed channel. Heat Transf Eng. 2015;36:290–302.

    Article  CAS  Google Scholar 

  31. Hwang CL, Lai YJ, Liu TY. A new approach for multiple objective decision making. Comput Oper Res. 1993;20:889–99.

    Article  Google Scholar 

  32. Orszag SA, V. Yakhot, Flannery WS, Boysan F, Choudhury D, Maruzewski J, et al. Renormalization group modeling and turbulence simulations. int conf near-wall turbul flows, Tempe, Arizona. 1993.

  33. Han JC, Park JS, Ibrahim MY. Measurement of heat transfer and pressure drop in rectangular channels with turbulence promoters. 1986.

  34. Deb K, Agrawal S, Pratab A, Meyarivan T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput. 2002;6:182–97.

    Article  Google Scholar 

  35. Feng Y, Hung TC, Zhang Y, Li B, Yang J, Shi Y. Performance comparison of low-grade ORCs (organic Rankine cycles) using R245fa, pentane and their mixtures based on the thermoeconomic multi-objective optimization and decision makings. Energy. 2015;93:2018–29.

    Article  CAS  Google Scholar 

  36. He C, Zhang Q, Ren J, Li Z. Combined cooling heating and power systems: sustainability assessment under uncertainties. Energy. 2017;139:755–66.

    Article  Google Scholar 

  37. Ge Y, Liu Z, Sun H, Liu W. Optimal design of a segmented thermoelectric generator based on three-dimensional numerical simulation and multi-objective genetic algorithm. Energy. 2018;147:1060–9.

    Article  CAS  Google Scholar 

Download references

Acknowledgements

The authors gratefully acknowledge the support by the scientific research start-up funds for introducing talent in the Sichuan University (Grant No. 20822041C4013); the National Natural Science Fund (Grant No. 51506034)

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  1. School of Chemical and Engineering, Sichuan University, Chengdu, 610065, China

    Ruitian Yu, Huaizhi Han, Chengang Yang & Wen Luo

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  1. Ruitian Yu
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  2. Huaizhi Han
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Yu, R., Han, H., Yang, C. et al. Optimal design and decision making of an air cooling channel with hybrid ribs based on RSM and NSGA-II. J Therm Anal Calorim 147, 5839–5854 (2022). https://doi.org/10.1007/s10973-021-10807-1

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