Multi-Objective Optimization on the Fluid Flow and Heat Transfer of Semi-Attached Rib-Channels

Rib-turbulators have been widely used in turbine blade cooling designs to enhance internal heat transfer. However, application of the ribs in blade cooling channels inevitably causes large pressure losses and lower heat transfer areas behind the ribs and at the joint parts of the ribbed wall with sidewalls in comparison to smooth channels. Semi-attached rib having two rectangular holes at the bottom of the ribs at the joint regions of the ribbed wall and two sidewalls is able to reduce friction losses and alleviates lower heat transfer in the channels. This paper presented a method of combining computational fluid dynamic simulation with an optimization method to optimize the performance of a channel with semi-attached ribs and to discuss the effects of hole geometric variables on both pressure losses and heat transfer enhancement. A fully automatic multi-objective genetic algorithm based on the Non-dominated Sorted Genetic Algorithm-II is applied for a one-pass squared channel with 60° inclined semi-attached ribs. Four geometrical variables are widths and heights of the two rectangular holes, and two objective functions are the maximum of area-averaged Nusselt number on the rib roughend wall and the minimum of friction factor. The Kriging model is constructed by using the Latin hypercube sampling method to choose 15 experimental points in the design space. The results showed that the optimization method helps to increase the channel performance and to eliminate nearly all low heat transfer areas by appropriately adjusting the heights and widths of the holes. Compared to solid ribs, the optimal semi-attached rib increases the area-averaged Nu number on the rib-roughened walls by 9.45%, whereas the friction factor in the channel is decreased by 6.95%, which corresponds to an increase of 12.13% in thermal performance. In the optimal model, the existence of large holes on the right side of the optimal semi-attached ribs moves the vortex core of the secondary flow downstream of the ribs from the right side of the solid-ribbed channel to the middle, which causes a large increase in Nu number on the middle and left side of the rib roughened walls and only a moderate reduction in Nu number on the right part of the walls. In the whole range discussed, heat transfer coefficient on the rib-roughened walls increased with the height of the right holes, but it increases with the width of the hole only in the range of 8–10mm. For the holes on the left, heat transfer coefficient deteriorates as the height and width increase. Increasing width and height of the holes on both sides of the semi-attached ribs reduces the channel friction losses.

Calibration of κ-ε turbulence model for thermal–hydraulic analyses in rib-roughened narrow rectangular channels using genetic algorithm

Nowadays, applications of turbulent fluid flow in removing high heat flux in rib-roughened narrow channels are drawing much interest. In this work, an improved version of the κ-ε turbulence model is proposed for better prediction of thermal–hydraulic characteristics of flow inside rib-roughened (pitch-to-rib height (p/k) ratio = 10 and 20) narrow channels (channel height, H = 1.2 mm and 3.2 mm). For this, the four turbulence model parameters, Cμ, Cε1, Cε2, and σk, are calibrated. These parameters are adjustable empirical constants provided for controlling the accuracy of the turbulence model results when needed. The simulated data are used to develop correlations between the relative errors in predicting the friction factor (f), Nusselt number (Nu), and the model parameters using a multivariate nonlinear regression method. These correlations are used to optimize the errors using genetic algorithm. Results reveal that the calibrated parameters are not the same for all the narrow channel configurations. After calibration, the overall predictive improvements are up to 35.83% and 27.30% for p/k = 10 and p/k = 20 respectively when H = 1.2 mm. Also, up to 15.48% and 18.05% improvements are obtained for p/k = 10 and p/k = 20 respectively when H = 3.2 mm. The role of the two parameters Cε1 and Cε2 are found to be of primary importance. Furthermore, three types of nanofluids i.e. Al2O3-water, CuO-water, and TiO2-water are studied using the calibrated model to check the potentiality of heat transfer enhancement. Among them, CuO-water nanofluid is predicted to have around 1.32 times higher value of Nu than pure water for the same narrow channel configuration. Article Highlights κ-ε turbulence model is calibrated for rib-roughened narrow rectangular channels using genetic algorithm. Cε1 and Cε2 are the most influential parameters on the performance of the model inside rib-roughened narrow channel. Suggested calibration process is more effective for channel height of 1.2 mm than 3.2 mm.