Enhanced multi-objective optimization of a dimpled channel through evolutionary algorithms and multiple surrogate methods

Afzal Husain, Ki Don Lee, Kwang Yong Kim

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21 Citations (Scopus)


Using a multi-objective evolutionary algorithm (MOEA) and enhanced surrogate approximations, the present study demonstrates the numerical analysis and optimization of staggered-dimple channels. Two surrogates, the response surface approximation (RSA) model and the Kriging (KRG) model, are applied in light of the surrogate fidelity of the approximate analysis. An enhanced Pareto-optimal front is obtained by performing local resampling of the Pareto-optimal front, which provides relatively more accurate Pareto-optimal solutions in the design space for each surrogate model. Three dimensionless design variables are selected, which are related to geometric parameters, namely, the channel height, dimple print diameter, dimple spacing, and dimple depth. Two objective functions are selected that are related to the heat transfer and pressure loss, respectively. The objective-function values are numerically evaluated through Reynolds-averaged Navier-Stokes analysis at the design points that are selected through the Latin hypercube sampling method. Using these numerical simulations two surrogates, viz, the RSA and Kriging models, are constructed for each objective function and a hybrid MOEA is applied to obtain the Pareto-optimal front. For the particular implementation of surrogate models, it is observed that Pareto-optimal predictions of the RSA model are better than those of the KRG model, whereas the KRG model predicts equally well at the off-Pareto-region (region away from the Pareto-optimal solutions), which is not the case with the RSA model. The local resampling of the Pareto-optimal front increases the fidelity of the approximate solutions near the Pareto-optimal region. The ratios of the channel height to the dimple print diameter and of the dimple print diameter to the dimple pitch are found to be more sensitive along the Pareto-optimal front than the ratio of the dimple depth to the print diameter. The decrease of the ratio of the channel height to the dimple diameter and the increase of the ratio of the dimple print diameter to the pitch lead to greater heat transfer at the expense of the pressure loss, whereas the ratio of the dimple depth to the print diameter is rather insensitive to Pareto-optimal solutions. Pareto-optimal solutions at higher values of the Nusselt number are associated with higher values of the pressure loss due to the increased recirculation, mixing of fluid and vorticity generation.

Original languageEnglish
Pages (from-to)742-759
Number of pages18
JournalInternational Journal for Numerical Methods in Fluids
Issue number6
Publication statusPublished - Jun 30 2011



  • Dimpled channel
  • Enhanced Pareto-optimal front
  • Multi-objective optimization
  • Surrogate fidelity analysis
  • Turbine-blade cooling

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Mechanics
  • Applied Mathematics
  • Mechanical Engineering
  • Mechanics of Materials

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