This study comprehensively illustrates the effect of Reynolds number, hole spacing, jet-to-target distance, and hole inclination on the convective heat transfer performance of an impinging jet array. Spatially resolved target surface heat transfer coefficient distributions are measured using transient liquid crystal (TLC) measurement techniques, over a range of Reynolds numbers from 5000 to 25,000. Considered are effects of streamwise and spanwise jet-to-jet spacing (X/D, Y/D: 4–8) and jet-to-target plate distance (Z/D: 0.75–3). Overall, a test matrix of 36 different configurations is employed. In addition, the effect of hole inclination (θ: 0–40 deg) on the heat transfer coefficient is investigated. Optimal hole spacing arrangements and impingement distance are pointed out to maximize the area-averaged Nusselt number and minimize the amount of cooling air. Also included is a new correlation, based on that of Florschuetz et al., to predict row-averaged Nusselt number. The new correlation is capable to cover low Z/D ∼ 0.75 and presents better prediction of row-averaged Nusselt number, which proves to be an effective impingement design tool.

The film cooling holes in the blade of modern gas turbines have commonly been manufactured by laser drilling, Electric Discharge Machining (EDM), and Additive Manufacturing (AM) in recent years. These manufacturing processes often result in small geometric deviations, such as conical angles, filleted edges, and diameter deviations of the hole, which can lead to deviations on the distribution of adiabatic cooling effectiveness (η) values, the value of the discharge coefficient (C_d), and the characteristic of the in-hole flow field. The current study employed flat plate fan-shaped film cooling holes with length-to-diameter values (L/D) equal to 3.5 and six to investigate the effects of these manufacturing deviations on the distribution of η values, the value of C_d, and the characteristic of in-hole flow field. An Uncertainty Quantification (UQ) analysis using the Polynomial Chaos Expansion (PCE) model was carried out to quantify the uncertainty in the values of η and C_d. The statistical characteristics (mean values, standard deviation (Std) values, and Probability Density Function (PDF) values) of η and C_d were also calculated. The results show that conical angle deviations exert no visible changes on the value of η. However, the C_d value decreases by 6.2% when the conical angle changes from 0–0.5°. The area averaged adiabatic cooling effectiveness ( $\stackrel{=}{\eta }$ ) decreases by 3.4%, while the C_d increases by 15.2% with the filleted edge deviation existing alone. However, the deviation value of $\stackrel{=}{\eta }$ is 7.6%, and that of C_d is 25.7% with the filleted edge deviation and the diameter deviation existing.

An experimental investigation of the geometrical parameter effects on the film cooling performance of a fan-shaped hole was conducted on a low speed flat-plate facility. The pressure sensitive paint (PSP) technique and steady liquid crystal (SLC) technique were employed to determine the adiabatic film cooling effectiveness and heat transfer coefficients, respectively, for a blowing ratio ranging from 0.3 to 3 and a density ratio of DR = 1.5. Several geometrical parameters were investigated, including lateral expansion angle, length-to-diameter ratio, and hole entrance shape. Local, laterally averaged, and area-averaged adiabatic film cooling effectiveness, heat transfer coefficients, and net heat flux reduction (NHFR) were shown to provide a comprehensive understanding on the geometrical parameter effects on the thermal performance. A novel method was proposed for designing a fan-shaped hole with short length-to-diameter ratio to design to achieve high film cooling performance. The original and optimized fan-shaped holes were compared in terms of adiabatic film cooling effectiveness, heat transfer coefficients, and NHFR. Results showed that the optimized fan-shaped hole with short length-to-diameter ratio, large lateral diffusion angle, and slot hole entrance shape obtained highest overall thermal performance. It demonstrated the feasibility of adopting the proposed design method to design fan-shaped holes applied in thin wall gas turbine blades.

This study comprehensively illustrates the effect of Reynolds number, hole spacing, nozzle-to-target distance, and target plate thickness on the conjugate heat transfer (CHT) performance of an impinging jet array. Test models are composed of a specific thermal-conductivity material which exerts a matched model Biot number to that of engine condition. High-resolution temperature measurements are conducted on the impinging-target plate utilizing steady liquid crystal (SLC) with Reynolds numbers ranging from 5000 to 27,500. Different streamwise and spanwise jet-to-jet spacing (i.e., X/D and Y/D: 4–8), nozzle-to-target plate distance (Z/D: 0.75–3), and target plate thickness (t/D: 0.75–2.75) are employed to compose a total of 108 different geometries. Experimental measured temperature is utilized as boundary conditions to conduct finite element simulation. Local and averaged nondimensional temperature and averaged temperature uniformity of target plate “hot side” are obtained. Optimum hole spacing arrangements, impingement distance, and target plate thickness are pointed out to minimize hot side temperature, amount of cooling air and to maximize temperature uniformity. Also included are 2D predictions with different convective boundary conditions, i.e., local 2D distribution and row-averaged heat transfer coefficients (HTCs), to estimate the accuracy of temperature prediction in comparison with the conjugate results.