Parametric study on heat transfer enhancement and pressure drop of an internal blade tip-wall with pin-fin arrays

One way to cool gas turbine tips is to design serpentine passages with 180° turns inside the blades to fully utilize the coolant potential. It is therefore a desire to improve the cooling of the blade tips to ensure a long durability and safe operation. In the present work, a two-pass channel with a 180° turn and various arrays of pin-fins mounted internally on the tip-cap is considered. The effects of pin-fin height, diameter and pitches on the heat transfer enhancement and pressure drop are investigated numerically. The nominal ratio of height to diameter (H/D) of the pin-fins is 2, and the ratio of tip clearance to pin-fin height is about 10. The inlet Reynolds numbers based on hydraulic diameter are ranging from 100,000 to 600,000. Details of the three dimensional fluid flow and heat transfer over the pin-finned tips are presented. The overall performances of various tips are compared. It is found that due to the combination of turning, impingement and pin-fin crossflow, the heat transfer coefficient of the pin-finned tips is up to a factor of 2.1 higher than that of the smooth tip. This augmentation is achieved at the expense of a penalty of pressure drop around 30%. Results show that the magnitude of the heat transfer enhancement depends upon pin-fin configuration and arrangement. It is suggested that pin-fins are suitable to enhance the blade tip heat transfer and thus to improve the tip cooling.     

Multi‐objective optimization of a rotating cooling channel with staggered pin‐fins for heat transfer augmentation

A rotating channel with staggered pin‐fins is formulated numerically and optimized for performance (heat transfer/required pumping power) using a Kriging meta‐model and hybrid multi‐objective evolutionary algorithm. Two design variables related to cooling channel height, pin diameter, and spacing between the pins are selected for optimization, and two‐objective functions related to the heat transfer and friction loss are employed. A design of experiment is performed, and 20 designs are generated by Latin hypercube sampling. The objective function values are evaluated using a Reynolds‐averaged Navier–Stokes solver, and a Kriging model is constructed to obtain a Pareto‐optimal front through a multi‐objective evolutionary algorithm. Rotation in a cooling channel with staggered pin‐fins induces Coriolis force that causes a heat transfer discrepancy between the trailing (pressure) and leading (suction) surfaces, with a higher Nusselt number on the trailing surface. The tradeoff between the two competing objective functions is determined, and the distribution of the Pareto‐optimal solutions in the design space is discussed through k‐means clustering. In the optimal designs, with a decrease in spacing between the pins, heat transfer is enhanced whereas friction loss is increased. Copyright © 2011 John Wiley & Sons, Ltd.     

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

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. Copyright © 2010 John Wiley & Sons, Ltd.     

Influence of heating load on heat transfer characteristics in micro-pin-fin arrays

Experimental investigations were carried out to explore the convective heat transfer in micro pin-fins with different aspect ratios, and the influence of heating load on Nusselt numbers in micro pin-fins with liquid water as working fluid were investigated. The mechanism of convective heat transfer in micro pin-fins at different heating load were studied by 3-D numerical investigations, and the relationships of thermal physical properties change, the end wall effect and axial thermal conduction with Nu numbers in micro pin-fins were analysed. It was found that the thickness of boundary layer was decreased as much as 33.3 % attributed to the destructive effect of thermal physical properties change, and convective heat transfer in the micro pin-fin channel was more than 20 % enhanced by the flow disturbance caused by the increase of temperature difference. The discrepancy of Nu in micro pin-fin channel with different aspect ratios reached 34.59 %, and this discrepancy was reduced by the increase of heating load. The maximum value of impact factors of dynamic viscosity and thermal conductivity on the Nu in micro-pin-fins reached 25.02 and 7.68 %, respectively.     

Multi-objective optimization of a guide vane in the turning region of a rotating U-duct to enhance heat transfer performance

An optimization has been performed for the design of a guide vane in the turning region of a rotating U-duct using the Kriging meta-model and a hybrid multi-objective evolutionary algorithm. Rotation of the U-duct is accompanied by the Coriolis force that causes a discrepancy in heat transfer between the trailing (pressure) and leading (suction) surfaces of the duct. For the optimization, three geometric variables related to the thickness, angle, and location of the guide vanes are selected as the design variables. A Kriging model is constructed to obtain a Pareto-optimal front through a multi-objective evolutionary algorithm. The values of the objective function at the design points are evaluated by Reynolds-averaged Navier–Stokes analysis. The shear stress transport model is used as the turbulence closure model in the analysis. The tradeoff between the two competing objective functions is discussed for Pareto-optimal solutions in the design space. The optimized guide vanes show an increase in heat transfer performance with a decrease in the friction loss in the turning region and downstream straight passage in comparison with the reference design.     

Shape optimization of staggered ribs in a rotating equilateral triangular cooling channel

A rotating equilateral triangular cooling channel with staggered square ribs inside the leading edge of a turbine blade has been optimized in this work based on surrogate modeling. The fluid flow and heat transfer in the channel have been analyzed using three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations under uniform heat flux condition. Shear stress transport turbulence model has been used as a turbulence closure. Computational results for area-averaged Nusselt number have been validated compared to the experimental data. The objectives related to the heat transfer rate and pressure drop has been linearly combined with a weighting factor to define the objective function. The angle of the rib, the rib pitch-to-hydraulic diameter ratio, and the rib width-to-hydraulic diameter ratio have been selected as the design variables. Twenty-two design points have been generated by Latin Hypercube sampling, and the values of the objective function have been calculated by the RANS analysis at these points. The surrogate model for the objective function has been constructed using the radial basis neural network method. Through the optimization, the objective function value has been improved by 21.5 % compared to that of the reference geometry.     

Multi-objective optimization of a dimpled channel for heat transfer augmentation

Staggered arrays of dimples printed on opposite surfaces of a cooling channel is formulated numerically and optimized with hybrid multi-objective evolutionary algorithm and Pareto optimal front. As Pareto optimal front produces a set of optimal solutions, the trends of objective functions with design variables are predicted by hybrid multi-objective evolutionary algorithm. The problem is defined by three non-dimensional geometric design variables composed of dimpled channel height, dimple print diameter, dimple spacing, and dimple depth, to maximize heat transfer rate compromising with pressure drop. Twenty designs generated by Latin hypercube sampling were evaluated by Reynolds-averaged Navier–Stokes solver and the evaluated objectives were used to construct Pareto optimal front through hybrid multi-objective evolutionary algorithm. The optimum designs were grouped by k-means clustering technique and some of the clustered points were evaluated by flow analysis. With increase in dimple depth, heat transfer rate increases and at the same time pressure drop also increases, while opposite behavior is obtained for the dimple spacing. The heat transfer performance is related to the vertical motion of the flow and the reattachment length in the dimple.     

Surrogate based optimization of a laidback fan-shaped hole for film-cooling

The present work has been performed to evaluate the effects of geometric variables of a laidback fan-shaped hole on the film-cooling effectiveness using a Reynolds-averaged Navier-Stokes analysis, and to optimize the shape of the hole using the Kriging meta-modeling technique. The shape of the laidback fan-shaped hole is defined by four geometric design variables, namely, the injection angle of the hole, the lateral expansion angle of the diffuser, the forward expansion angle of the hole, and the ratio of the length to the diameter of the hole. From the results of a parametric study, effects of design variables on the film-cooling effectiveness are evaluated. The objective function, which is defined as the spatially averaged film-cooling effectiveness, is numerically evaluated through a RANS analysis at design points selected through Latin hypercube sampling. The Kriging model is used to approximate these objective function values at the design points, and sequential quadratic programming is used to search for the optimal point from the constructed Kriging model. The optimizations are carried out for two different blowing ratios, 0.5 and 2.5. The film-cooling effectiveness has been successfully improved with the optimization as compared to the reference geometry.     

Effect of streamwise spacing on periodic and random unsteadiness in a bundle of short cylinders confined in a channel

While flow across long tube bundles is considered classical data, pin-fin arrays made up of short tubes have become a growing topic of interest for use in cooling gas turbine airfoils. Data from the literature indicate that decreasing streamwise spacing increases heat transfer in pin-fin arrays; however, the specific mechanism that causes increased heat transfer coefficients remains unknown. The present work makes use of time-resolved PIV to quantify the effects of streamwise spacing on the turbulent near wake throughout various pin-fin array spacings. Specifically, proper orthogonal decomposition was used to separate the (quasi-) periodic motion from vortex shedding and the random motion from turbulent eddies. Reynolds number flow conditions of 3.0?×?10³ and 2.0?×?10⁴, based on pin-fin diameter and velocity at the minimum flow area, were considered. Streamwise spacing was varied from 3.46 pin diameters to 1.73 pin diameters while the pin-fin height-to-diameter ratio was unity and the spanwise spacing was held constant at two diameters. Results indicated that (quasi-) periodic motions were attenuated at closer streamwise spacings while the level of random motions was not strongly dependent on pin-fin spacing. This trend was observed at both Reynolds number conditions considered. Because closer spacings exhibit higher heat transfer levels, the present results imply that periodic motions may not contribute to heat transfer, although further experimentation is required.     

The Effects of duct height on heat transfer enhancement of a co-rotating type rectangular finned surface in duct

Experiments were performed to investigate the effect of duct height on heat transfer enhancement of a surface affixed with arrays (7 × 7) of short rectangular plate fins of a co-rotating type pattern in the duct. An infrared imaging system is used to measure detailed distributions of the heat transfer at the endwall along with the fin base. An infrared camera of TVS 8000 with 160 × 120 point In–Sb sensor was used to measure the temperature distributions in order to calculate the local heat transfer coefficients of the representative fin regions. Pressure drop and heat transfer experiments were performed for a co-rotating fin pattern varying the duct height from 20?50 mm. The friction factor calculated from the pressure drop shows that comparatively larger friction occurs for the smaller duct cases and the friction factor slowly decreases with increasing Reynolds number. The effect of duct height on the area-averaged heat transfer results show that heat transfer initially increases with duct height and then finally decreases with increasing the duct height. Detailed heat transfer analysis and iso-heat transfer coefficient contour gives a clear picture of heat transfer characteristics of the overall surface. The relative performance graph indicates that a 25 mm duct is the optimum duct height for the highest thermal performance. In addition, a significant thermal enhancement, 2.8?3.8 times the smooth surface, can be achieved at lower Reynolds number with a co-rotating fin pattern in the duct.     

Comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface

This paper presents the comparative studies on the effect of duct height on heat transfer and flow behavior between co-angular and co-rotating type finned surface in duct. Experiments were performed to investigate the effect of duct height on heat transfer enhancement of a surface affixed with arrays (7 × 7) of short rectangular plate fins of a co-angular and a co-rotating type pattern in the duct. An infrared imaging system with the camera of TVS 8000 was used to measure the temperature distributions to calculate the local heat transfer coefficients of the representative fin regions. Pressure drop and heat transfer experiments were performed for both types of fin pattern varying the duct to fin height ratio (H _d/H _f) of 2.0–5.0. The friction factor calculated from the pressure drop shows that friction factor decreases with increasing the duct to fin height ratio (H _d/H _f) regardless of fin pattern and this is expected because the larger friction occurs for smaller duct to fin height ratios. Detailed heat transfer distribution gives a clear picture of heat transfer characteristics of the overall surface as well as the influence of the duct height. In addition, different flow behavior and flow structure developed by both patterns were visualized by the smoke flow visualization technique.     

Numerical modeling of pin–fin micro heat exchangers

A micro heat exchanger (MHE) can effectively control the temperature of surfaces in high heat flux applications. In this study, several turbulence models are analyzed using a 3D finite element model of a MHE. The MHE consists of a narrow planar flow passage between flat parallel plates with small cylindrical pin fins spanning these walls. The pin fin array geometry investigated is staggered, with pin diameters of 0.5, 5.1 and 8.5 mm, height to diameter ratio of 1.0 and streamwise (longitudinal) and spanwise (transverse) to diameter ratios of 1.5 and 2.5, respectively. Pressure loss and heat transfer simulated results for 4,000 ≤ Re ≤ 50,000 are reported and compared with previously published numerical and experimental results. It was found that the flat micro pin fin overall thermal performance always exceeds that of the parallel plate counterpart (smooth channel) by a factor of as much as 2.2 for the 8.5 mm diameter pins, and by 4 for the 0.5 mm diameter pins in the investigated Reynolds number range. Further, among the six turbulence models investigated, the RNG model tends to be the best model to predict both the Nusselt number and the friction factor and capture the main feature of the flow field in MHE.     

Experimental investigation of local heat transfer in a square duct with various-shaped ribs

In the present study, experimental studies are carried out to investigate the heat transfer and friction characteristics in a square duct roughened by various-shaped ribs on one wall. The ribs are oriented transversely to the main stream in a periodic arrangement. Liquid crystal thermography is employed to measure the local and average heat transfer coefficient on the ribbed surface. The rib height-to-duct hydraulic diameter ratio is fixed at 0.1; the rib pitch-to-height ratio varies from 8 to 15 and the test Reynolds number spans from 8,000 to 20,000. The results show that the trapezoidal-shaped ribs with decreasing height in the flow direction (case C) provide the highest heat transfer enhancement factor and are likely to be used to suppress the local hot spot which usually occurs in the region just behind the ribs.     

Transport through baffles in bottom heated top cooled enclosures: parametric studies

This paper presents parametric studies on the heat transfer and fluid exchange through single-hole baffles located at the median height in bottom heated top cooled enclosures. Results indicate that when the baffle area-opening ratio is smaller than 2%, the heat transfer in the enclosure is dominated by the transport through the baffle opening. Even with such small baffle openings, increasing the enclosure aspect ratio still enhances the transport across the baffle. The characteristic length scale of flow in the enclosure is a combination of baffle opening diameter and the chamber height. The Nusselt number that characterize the heat transfer through the baffle-hole is linearly correlated with the Rayleigh number based on baffle opening diameter and the temperature difference between the bulk temperatures in the two chambers, while no effects of Prandtl numbers are observed. The mechanism of transport across the baffle opening varies from conduction dominated, combined conduction and convection, and convection dominated regimes as Rayleigh number increases.     

Experimental and numerical investigation on air-side performance of fin-and-tube heat exchangers with various fin patterns

Air-side heat transfer and friction characteristics of five kinds of fin-and-tube heat exchangers, with the number of tube rows (N = 12) and the diameter of tubes (D_o = 18 mm), have been experimentally investigated. The test samples consist of five types of fin configurations: crimped spiral fin, plain fin, slit fin, fin with delta-wing longitudinal vortex generators (VGs) and mixed fin with front 6-row vortex-generator fin and rear 6-row slit fin. The heat transfer and friction factor correlations for different types of heat exchangers were obtained with the Reynolds numbers ranging from 4000 to 10000. It was found that crimped spiral fin provides higher heat transfer and pressure drop than the other four fins. The air-side performance of heat exchangers with the above five fins has been evaluated under three sets of criteria and it was shown that the heat exchanger with mixed fin (front vortex-generator fin and rear slit fin) has better performance than that with fin with delta-wing vortex generators, and the slit fin offers best heat transfer performance at high Reynolds numbers. Based on the correlations of numerical data, Genetic Algorithm optimization was carried out, and the optimization results indicated that the increase of VG attack angle or length, or decrease of VG height may enhance the performance of vortex-generator fin. The heat transfer performances for optimized vortex-generator fin and slit fin at hand have been compared with numerical method.     

A computational method for geometric optimization of enhanced heat transfer devices based upon entropy generation minimization

A computational fluid dynamics‐based optimization methodology is developed, appropriate for the geometric optimization of enhanced heat transfer devices based upon the principle of entropy generation minimization, in which the objective function is evaluated from a flow field obtained by computational simulation. A quasi‐Newton optimization procedure is employed, with computation of the objective function gradients based upon a finite difference approach. The optimization procedure is developed to be general with regard to the choice of objective function, the details of the problem under consideration, and the computational methodology employed in solving the fluid flow and heat transfer problems. A novel implementation of a Taylor series‐based procedure for the fast solution of nearby problems is presented, which is found to greatly benefit the efficiency of the present methodology. Finally, a numerical experiment is presented, illustrating the use of the present method in the geometric optimization of a practical enhanced heat transfer device on the basis of the criterion of entropy generation minimization. The optimization of the fin spacing of a simple plate fin heat sink is considered, and a comparison of the computational results with results obtained by analytical optimization based upon empirical friction factor and Nusselt number correlations is given. Copyright © 2012 John Wiley & Sons, Ltd.     

自适应Kriging近似模型及其在二维扩压器优化设计中的应用

将均匀设计方法、CFD技术、Kriging近似模型及小生境微种群遗传算法相结合发展了一种自适应全局优化设计方法.优化过程中综合考虑Kriging模型的预测值与预测标准差,引入了EI(Expected Improvement)函数得到校正点,解决了采用近似模型最优策略得到校正点带来的局部收敛问题.分别采用该方法和小生境微...     

Transition Modeling Using Two Different Intermittency Transport Equations

The accurate numerical simulation of the flow through turbomachinerydepends on the correct prediction of boundary-layer transitionphenomena. Especially heat transfer and skin friction investigationsdemand a reliable simulation of the transition process. Therefore, in this work two different one-equation transport modelsfor a transitional weighting factor are selected and modified for theimplementation into a Reynolds-averaged Navier–Stokes solver. Thisfactor is used to modify the eddy viscosity obtained from a turbulencemodel to simulate the transition process. The first model was originallydeveloped by Steelant and Dick [1] to simulate by-passtransition for high free-stream turbulence. The second model wasproposed by Huang and Suzen [2] as a blending of two modelsfor near-wall intermittency and cross-stream variation of intermittency.In contrast to one-dimensional transition models, the new approachesmodel the transition process not only in flow direction but also acrossthe boundary-layer and thus provide a more realistic prediction of thetransition process. Whereas the Steelant and Dick model (SD) allowsturbulent quantities in the free-stream prior and after transition, thesecond model by Huang and Suzen (HS) sets the free-stream turbulence tozero in the whole flowfield. The models are validated on transitional skin friction experimentson a flat plate (T3 test cases of ERCOFTAC SIG 10), on heat transfermeasurements in a linear turbine cascade done at the VKI and on laservibrometer measurements of a linear turbine cascade. Both models showgood agreement with the skin friction data, but the heat transfer canonly be predicted correctly by the Steelant and Dick model due to itsability to consider the free-stream turbulence.     

Effect of adiabatic wall on the natural convection heat transfer from a wavy surface created by attached horizontal cylinders

The effect of a vertical adiabatic wall on the natural convection heat transfer from vertical array of attached cylinders, which can be considered as wavy surface, was investigated experimentally and numerically. The experiments were carried out using Mach-Zehnder interferometer and the commercial FLUENT code was used for numerical study. This paper focuses on the effect of wall-wavy surface spacing and Rayleigh number variation on the local and average free convection heat transfer coefficients from the each cylinder and the wavy surface. Rayleigh number ranges from 2400 to 10,000 and from 300,000 to 1,250,000 based on cylinder diameter and wavy surface height respectively. The local and average Nusselt numbers were determined for the different Rayleigh numbers, and the ratio of wall- wavy surface spacing to cylinder diameter 0.75, 1, 1.5, 2, 3, 4, 5, and ∞. Results are indicated with a single correlation which gives the average Nusselt number as a function of the ratio of the wall-wavy surface spacing to cylinder diameter and the Rayleigh numbers. There is an optimum distance between the wall and wavy surface in which the Nusselt number attain its maximum value. This optimum distance depends on the Rayleigh number.     

Heat Transfer and Pressure loss of a very shallow fluidized-bed heat exchanger Part 1. Experiment with a single row of tubes

A novel gas fluidized-bed heat exchanger with a very small static bed height has been developed for a heat-exchanging system using a low-pressure fan. This fluidized bed is composed of a multislit distributor, a single row of 8 mm diameter tubes, and glass beads 48–195 μm in diameter. The measured performance of heat transfer is excellent and that of fluidization is satisfactory, in spite of the static bed height being as small as 13 mm. In the best case, the test fluidized bed exhibited a heat transfer performance comparable to that of a conventional fluidized bed with a perforated plate distributor and a static bed height of 150 mm, and showed one-fourteenth the pressure loss.