Shape Optimization of a Rotating Rectangular Channel With Pin-Fins by Kriging Method

2010 ◽  
Author(s):  
Mi-Ae Moon ◽  
Afzal Husain ◽  
Kwang-Yong Kim
Keyword(s):  
Heat Transfer ◽  
Objective Function ◽  
Rectangular Channel ◽  
Latin Hypercube Sampling ◽  
Weighting Factor ◽  
Diameter Ratio ◽  
Reference Case ◽  
Pin Fins ◽  
Meta Modeling ◽  
Rans Analysis

This paper presents numerical optimization of a rotating rectangular channel design with the staggered arrays of pin-fins using Kriging meta-modeling technique. In the reference case, the channel aspect ratio (AR) is 4:1, the pin length to diameter ratio (H/D) is 2.0, and the pin spacing to diameter ratio is 2.0 in both the streamwise and spanwise directions. The rotation number is 0.15, while the Reynolds number based on hydraulic diameter is fixed at 10,000. Rotation of the channel slightly reduces the heat transfer on the leading surface and increases it on the trailing surface due to Coriolis effects. Two non-dimensional variables, the ratio of the height to diameter of the pin-fin and the ratio of the spacing between the pin-fins to diameter of the pin-fins, are chosen as design variables. The objective function defined as a linear combination of heat transfer and friction loss related terms with a weighting factor is selected for the optimization. Twenty training points generated by Latin hypercube sampling (LHS) are evaluated by three-dimensional Reynolds-averaged Navier-Stokes (RANS) analysis with the shear stress transport (SST) model for the turbulence closure. The predictions of objective function by Kriging meta-modeling at optimum point show reasonable accuracy in comparison with the values calculated by RANS analysis. The results of optimization show that the cooling performance of the optimized shape is enhanced significantly through the optimization.

Optimization of a Dimpled Channel Using a Surrogate Model

2007 ◽  
Author(s):  
Kwang-Yong Kim ◽  
Dong-Yoon Shin
Keyword(s):  
Heat Transfer ◽  
Objective Function ◽  
Rectangular Channel ◽  
Optimization Technique ◽  
Numerical Procedure ◽  
Weighting Factor ◽  
Diameter Ratio ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Design Variables

A numerical procedure to optimize the shape of a staggered dimpled surface to enhance the turbulent heat transfer in a rectangular channel is presented in this work. A Kriging model-based optimization technique is used with Reynolds-averaged Navier-Stokes analysis of the fluid flow and heat transfer with Shear Stress Transport turbulence model. The dimple depth-to-dimple print diameter ratio, channel height-to-dimple print diameter ratio, and dimple print diameter-to-pitch ratio are chosen as design variables. The objective function is defined as a linear combination of terms related to heat transfer and friction loss with a weighting factor. Latin Hypercube Sampling is used to determine the training points as a mean of the Design of Experiment. Through a sensitivity analysis, it was found that the objective function is most sensitive to the ratio of the dimple depth to dimple print diameter. Optimal values of the design variables were obtained in a range of the weighting factor.

Computation of Flow and Heat Transfer in Rotating Rectangular Channels (AR=4:1) With Pin-Fins by a Reynolds Stress Turbulence Model

2006 ◽  
Vol 129 (6) ◽  
pp. 685-696 ◽  
Author(s):  
Guoguang Su ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rotation Number ◽  
Rectangular Channel ◽  
Density Ratio ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Mean Velocity ◽  
Flow And Heat Transfer ◽  
Pin Fins

Computations with multi-block chimera grids were performed to study the three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with staggered arrays of pin-fins. The channel aspect ratio (AR) is 4:1, the pin length to diameter ratio (H∕D) is 2.0, and the pin spacing to diameter ratio is 2.0 in both the stream-wise (S1∕D) and span-wise (S2∕D) directions. A total of six calculations have been performed with various combinations of rotation number, Reynolds number, and coolant-to-wall density ratio. The rotation number and inlet coolant-to-wall density ratio varied from 0.0 to 0.28 and from 0.122 to 0.20, respectively, while the Reynolds number varied from 10,000 to 100,000. For the rotating cases, the rectangular channel was oriented at 150deg with respect to the plane of rotation to be consistent with the configuration of the gas turbine blade. A Reynolds-averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure for detailed predictions of mean velocity, mean temperature, and heat transfer coefficient distributions.

Computation of Flow and Heat Transfer in Rotating Rectangular Channels (AR=4:1) With Pin-Fins by a Reynolds Stress Turbulence Model

2005 ◽  
Author(s):  
Guoguang Su ◽  
Hamn-Ching Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Rotation Number ◽  
Rectangular Channel ◽  
Density Ratio ◽  
Three Dimensional ◽  
Diameter Ratio ◽  
Mean Velocity ◽  
Flow And Heat Transfer ◽  
Pin Fins

Computations with multi-block chimera grids were performed to study the three-dimensional turbulent flow and heat transfer in a rotating rectangular channel with staggered arrays of pin-fins. The channel aspect ratio (AR) is 4:1, the pin length to diameter ratio (H/D) is 2.0, and the pin spacing to diameter ratio is 2.0 in both the stream-wise (S1/D) and span-wise (S2/D) directions. A total of six calculations have been performed with various combinations of rotation number, Reynolds number, and coolant-to-wall density ratio. The rotation number and inlet coolant-to-wall density ratio varied from 0.0 to 0.28 and from 0.122 to 0.20, respectively, while the Reynolds number varied from 10,000 to 100,000. For the rotating cases, the rectangular channel was oriented at 150 deg with respect to the plane of rotation to be consistent with the configuration of the gas turbine blade. A Reynolds-Averaged Navier-Stokes (RANS) method was employed in conjunction with a near-wall second-moment turbulence closure for detailed predictions of mean velocity, mean temperature, and heat transfer coefficient distributions.

Heat Transfer Experiments in High Aspect Ratio Rectangular Channel With Epoxied Short Pin Fins

1983 ◽  
Author(s):  
S. C. Arora ◽  
W. Abdel Messeh
Keyword(s):  
Heat Transfer ◽  
Rectangular Channel ◽  
Temperature Drop ◽  
Diameter Ratio ◽  
Heat Transfer Surface ◽  
Published Data ◽  
Pin Fin ◽  
Pin Fins ◽  
The Cost ◽  
End Wall

In an attempt to reduce the cost of testing many configurations of short pin fins in a rectangular channel, a technique has been identified whereby the pins are epoxied to the end wall and can be easily removed to form a new configuration at the end of a test. Analytical and experimental results indicate that the temperature drop across a thin layer of epoxy (∼.005–.006 cm) (K = 22.5 W/m°C) with copper pin and endwalls was less than 1% of the heat transfer surface temperature. The technique was then used to test 4 pin fin configurations of height to diameter ratio of about unity. The heat transfer results showed excellent agreement with earlier published data, thus confirming the validity of this technique.

Jet Impingement Heat Transfer in a Rectangular Channel With Smooth and Pinned Target Walls

2021 ◽  
Author(s):  
Yasser S. Alzahrani ◽  
Lesley M. Wright ◽  
Andrew Chen ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Rectangular Channel ◽  
Cross Flow ◽  
Jet Impingement ◽  
Target Surface ◽  
Reynolds Numbers ◽  
Impinging Jets ◽  
Reference Case ◽  
Impingement Heat Transfer ◽  
Pin Fins

Abstract An experimental study was completed to quantify heat transfer enhancement, pressure loss, and crossflow effect within a channel of inline impinging jets. The jet diameter is 5.08 mm and the jet-to-jet spacing in the streamwise and spanwise directions is fixed at x/d = 11.1 and y/d = 5.9, respectively. The effect of jet-to-target surface spacing was considered with z/d = 3 and 6. For both of the jet-to-target surface spacings, a smooth surface, the reference case, and a surface roughened with partial height pins were investigated. The roughened surface has a staggered array of 120 partial height copper pin fins. The pin to jet diameter and the pin height to diameter ratios are D/d = 0.94 and H/D = 1.6, respectively. Regionally averaged heat transfer coefficient distributions were measured on the target surface, and these distributions were coupled with pressure measurements through the array. The heat transfer augmentation and pressure penalty were investigated over a range of jet Reynolds numbers (10K–70K). The results show high discharge coefficients for all the cases. The channels with the tight jet-to-target surface spacing experience double the cross-flow effect of its increased spacing counterpart. The addition of surface roughness showed a negligible effect on the crossflow. The best heat transfer performance was observed in the impingement channel with the pinned target surface at z/d = 3.

Comparison of Pin Surface Heat Transfer in Arrays of Oblong and Cylindrical Pin Fins

2013 ◽  
Vol 136 (4) ◽  
Author(s):  
Kathryn L. Kirsch ◽  
Jason K. Ostanek ◽  
Karen A. Thole
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Boundary Layer Separation ◽  
Diameter Ratio ◽  
Pin Fin ◽  
The Third ◽  
Spacing Effects ◽  
Pin Fins ◽  
Turbine Airfoils ◽  
Pin Fin Arrays

Pin fin arrays are most commonly used to promote convective cooling within the internal passages of gas turbine airfoils. Contributing to the heat transfer are the surfaces of the channel walls as well as the pin itself. Generally the pin fin cross section is circular; however, certain applications benefit from using other shapes such as oblong pin fins. The current study focuses on characterizing the heat transfer distribution on the surface of oblong pin fins with a particular focus on pin spacing effects. Comparisons were made with circular cylindrical pin fins, where both oblong and circular cylindrical pins had a height-to-diameter ratio of unity, with both streamwise and spanwise spacing varying between two and three diameters. To determine the effect of relative pin placement, measurements were taken in the first of a single row and in the third row of a multirow array. Results showed that area-averaged heat transfer on the pin surface was between 30 and 35% lower for oblong pins in comparison to cylindrical. While heat transfer on the circular cylindrical pin experienced one minimum prior to boundary layer separation, heat transfer on the oblong pin fins experienced two minimums, where one is located before the boundary layer transitions to a turbulent boundary layer and the other prior to separation at the trailing edge.

Effect of Rotation on Heat Transfer in Narrow Rectangular Cooling Channels (AR = 8:1 and 4:1) With Pin-Fins

2003 ◽  
Author(s):  
Lesley M. Wright ◽  
Eungsuk Lee ◽  
Je-Chin Han
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Rotation Number ◽  
Rectangular Channel ◽  
Density Ratio ◽  
Pin Fin ◽  
Aspect Ratios ◽  
Rectangular Channels ◽  
Smooth Channel ◽  
Pin Fins

The effect of rotation on smooth narrow rectangular channels and narrow rectangular channels with pin-fins is investigated in this study. Pin-fins are commonly used in the narrow sections within the trailing edge of the turbine blade; the pin-fins act as turbulators to enhance internal cooling while providing structural support in this narrow section of the blade. The rectangular channel is oriented at 150° with respect to the plane of rotation, and the focus of the study involves narrow channels with aspect ratios of 4:1 and 8:1. The enhancement due to both conducting (copper) pin-fins and non-conducting (plexi-glass) pins is investigated. Due to the varying aspect ratio of the channel, the height-to-diameter ratio (hp/Dp) of the pins varies from two, for an aspect ratio of 4:1, to unity, for an aspect ratio of 8:1. A staggered array of pins with uniform streamwise and spanwise spacing (xp/Dp = sp/Dp = 2.0) is studied. With this array, 42 pin-fins are used, giving a projected surface density of 3.5 pins/in2 (0.543 pins/cm2), for the leading or trailing surfaces. The range of flow parameters include Reynolds number (ReDh = 5000–20000), rotation number (Ro = 0.0–0.302), and inlet coolant-to-wall density ratio (Δρ/ρ = 0.12). Heat transfer in a stationary pin-fin channel can be enhanced up to 3.8 times that of a smooth channel. Rotation enhances the heat transferred from the pin-fin channels 1.5 times that of the stationary pin-fin channels. Overall, rotation enhances the heat transfer from all surfaces in both the smooth and pin-fin channels. Finally, as the rotation number increases, spanwise variation increases in all channels.

Identifying Inefficiencies in Unsteady Pin Fin Heat Transfer Using Orthogonal Decomposition

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Markus Schwänen ◽  
Andrew Duggleby
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Basis Function ◽  
High Energy ◽  
Diameter Ratio ◽  
Orthogonal Decomposition ◽  
Turbulent Heat ◽  
Internal Cooling ◽  
Turbulent Heat Exchange ◽  
Pin Fins

Internal cooling of the trailing edge region in a gas turbine blade is typically achieved with an array of pin fins. In order to better understand the effectiveness of this configuration, high performance computations are performed on cylindrical pin fins with a spanwise distance to fin diameter ratio of 2 and height over fin diameter ratio of one. For validation purposes, the flow Reynolds number based on hydraulic channel diameter and bulk velocity (Re = 12,800) was set to match experiments available in the open literature. Simulations included a URANS and LES on a single row of pin fins where the URANS domain was 1 pin wide versus the LES with 3 pins. The resulting time-dependent flow field was analyzed using a variation of bi-orthogonal decomposition (BOD), where the correlation matrices were built using the internal energy in addition to the three velocity components. This enables a detailed comparison of URANS and LES to assess the URANS modeling assumptions as well as a flow decomposition with respect to the flow structure’s influence on surface heat transfer. This analysis shows low order modes which do not contribute to turbulent heat flux, but instead increase the heat exchanger’s global inefficiency. In the URANS study, the forth mode showed the first nonzero temperature basis function, which means that a considerable amount of energy is contained in flow structures that do not contribute to increasing endwall heat transfer. In the LES, the first non zero temperature basis function was the seventh mode. Both orthogonal basis function sets were evaluated with respect to each mode’s contribution to turbulent heat exchange with the surface. This analysis showed that there exists one distinct, high energy mode that contributes to wall heat flux, whereas all others do not. Modifying this mode could potentially be used to improve the heat exchanger’s efficiency with respect to pressure loss.

Turbulent Flow Heat Transfer and Friction in a Rectangular Channel With Varying Numbers of Ribbed Walls

1997 ◽  
Vol 119 (2) ◽  
pp. 374-380 ◽  
Author(s):  
P. R. Chandra ◽  
M. E. Niland ◽  
J. C. Han
Keyword(s):  
Heat Transfer ◽  
Turbulent Flows ◽  
Rectangular Channel ◽  
Reynolds Numbers ◽  
Channel Length ◽  
Diameter Ratio ◽  
Hydraulic Diameter ◽  
Published Data ◽  
Flow Heat ◽  
Turbulent Air Flow

An experimental study of wall heat transfer and friction characteristics of a fully developed turbulent air flow in a rectangular channel with transverse ribs on one, two, and four walls is reported. Tests were performed for Reynolds numbers ranging from 10,000 to 80,000. The pitch-to-rib height ratio, P/e, was kept at 8 and rib height-to-channel hydraulic diameter ratio, e/Dh, was kept at 0.0625. The channel length-to-hydraulic diameter ratio, L/Dh, was 15. The heat transfer coefficient and friction factor values were enhanced with the increase in the number of ribbed walls. The friction roughness function, R(e+), was almost constant over the entire range of tests performed and was within comparable limits of the previously published data. The heat transfer roughness function, G(e+), decreased with additional ribbed walls and compared well with previous work in this area. Friction data obtained experimentally for the case with four ribbed walls compared well with the values predicted by the assumed theoretical relationship used in the present study and past publications. Results of this investigation could be used in various applications of internal channel turbulent flows involving different numbers of roughened walls.

Sign in / Sign up

Export Citation Format

Share Document