Experimental Study of Impingement-Film Compound Cooling in the Leading Region of a Turbine Vane

Abstract

This study examines the effects of jet Reynolds number (Re) and jet hole diameter (d) on flow and heat transfer in the leading-edge full-impingement cooling channel of a gas turbine nozzle guide vanes (NGV). Experiments via transient liquid crystal and numerical simulations were conducted. Results reveal that the peak Nusselt number (Nu) initially increases and then reaches a fixed value from root to tip in the spanwise direction. The area-averaged Nu presents the descending trend of the shower-head surface, pressure surface, and suction surface. In addition, the bleeding from film holes causes significant local flow acceleration and Turbulence Kinetic Energy (TKE) enhancement of 10.69%, resulting in local heat transfer elevation. The heat transfer enhancement region on both pressure and suction surfaces is inclined towards the shower-head at a 5% span region. Increasing the jet hole diameter (d) results in a decrease in both averaged Nu and TKE on the target surface. Simultaneously, the Nu gradient increases. When d = 1.6 mm, there is a recirculation zone near the hub on the suction surface and a strong crossflow near the hub on the pressure surface. The jet flow on the target surface is bending towards the shower-head. When d = 0.8 mm, the overall heat transfer is highest. However, considering heat transfer uniformity, a jet hole diameter of d = 1.2 mm offers better application.

1. Introduction

Gas turbines are extensively used in aviation propulsion, ship propelling, and ground power generation, and other applications. As the power output of gas turbines continues to increase, the turbine inlet temperatures (TIT) have risen significantly, surpassing the allowable limits of turbine blade super alloy [1]. To maintain turbine safety, there is a continuous need for elevation in cooling technologies. Currently, turbine blade cooling is divided into internal cooling and external cooling [1]. External cooling primarily refers to film cooling, while internal heat-transfer enhancement includes jet impingement, rib turbulator, pin-fin, turbulator, etc. Jet impingement is particularly favored for its high convective heat transfer coefficient, making it appropriate for the high temperature/heat-flux regions such as the leading-edge. However, the high-speed jets create intense turbulent fluctuations near the impingement point, which can compromise blade strength. Furthermore, the non-uniform cooling caused by impingement increases thermal stress on the blade. Therefore, understanding the effect of geometric parameters on the heat transfer performance of jet impingement is crucial for cooling design.

Many researchers have conducted studies to explore the factors affecting impingement cooling and to enhance heat transfer performance. Martin et al. [2] analyzed the effects of jet Reynolds number, impingement-to-target distance, and hole spacing on impingement heat transfer enhancement. Metzger et al. [3] and Florschuetz et al. [4] examined the impact of array arrangements and hole spacing on heat transfer, finding that staggered arrangements improve heat transfer uniformity, especially under cross-flow conditions. Xing [5] further confirmed that staggered arrays provide better heat transfer performance at high Reynolds numbers. Obot et al. [6] demonstrated that larger jet hole spacing exhibits heat transfer in the circumstance of strong cross-flow, while smaller spacing is more effective in weak cross-flow conditions. Additionally, San et al. [7] identified that the optimal ratio of hole spacing-to-hole diameter is 3–4 for the maximum heat transfer. Katti et al. [8] showed that increasing the spacing between jet holes can reduce cross-flow interference and improve heat transfer distribution.

Advances in impingement research have led to an increased focus on impingement cooling over curved surfaces and the impingement-film compound cooling of the turbine blade leading-edge. Guo et al. [9] examined the effects of hole spacing of impingement on surface heat transfer with varying curvatures, highlighting the differences between flat and curved surfaces under impingement. Bunker et al. [10] investigated the effects of hole-to-target distance and streamwise hole spacing in the condition of one-side outflow. Martin et al. [11,12] explored the effects of jet temperature, impingement distance, hole spacing, and target surface curvature on the heat transfer performance of the leading-edge under high-temperature jet conditions. Haider [13] conducted numerical analyses to assess how varying jet hole diameters affect flow characteristics and heat transfer distributions on turbine blade leading-edges. Cao et al. [14] employed numerical simulations to study the cooling performance of compound cooling (impingement + film), analyzing film hole, jet hole diameters, and impact spacings affect overall cooling efficiency and flow dynamics. Yan et al. [15] experimentally examined the internal heat transfer characteristics of leading-edge channel that combines impingement and external film cooling, comparing the effects of central and offset impingement. Kulkarni et al. [16] studied heat transfer and pressure loss in a blade leading-edge channel and discussed the effects of hole spacing, impingement distance, channel curvature, and race-track hole with different rounding radius. Wang et al. [17,18] numerically studied the conjugate heat of impingement/effusion cooling with different ribs in a turbine guided vane, and compared the overall cooling efficiency under different ribs.

Despite advancements in turbine blade cooling techniques, there is a scarcity of detailed experimental studies on the combined impact-film cooling of turbine blade leading-edges. Many existing computational analyses lack experimental validation, and few comprehensively address the interaction between film outflow and impingement cooling. Additionally, the arrangement of the jet holes at the leading-edge of the turbine blade is relatively homogeneous, usually an array of jet holes at the center of the blade spacer, which does not include a full impact study in the leading-edge region of the turbine blade. To bridge these gaps, this study employs transient liquid crystal heat transfer experiments and numerical simulations to investigate the flow and heat transfer characteristics of a fully impinged leading-edge channel on the first-stage static blade of a heavy combustion turbine. The research specifically examines the effects of jet Reynolds number and jet hole diameter on cooling performance.

2. Experimental Setup

2.1. Visualization Test System

The transient liquid crystal technique was used in this study to calculate the heat transfer coefficient distribution on the cooling channel surfaces. The experimental setup, shown in Figure 1, includes an air compressor, gas storage tank, filter, dryer, valve, Venturi flowmeter, heater, pressure and temperature sensors, and liquid crystal thermography system. The heater consists of a double layer of high-power wire mesh that rapidly heats the mainstream gas to 50 °C in less than 1 s and maintains this temperature throughout the experiment. The heater is installed in the mid-portion of the plenum. Dry air from a freezing dryer enters the plenum and then gets heated by the heater. Through a contracting entrance, the heated air flows into the insert with many impingement holes, discharges into the cooling channel, and impacts on different surfaces on the channel, including the showerhead, pressure side, and suction side. The air then exits the channel through film holes into the atmosphere. During the experiment, pressure transducers were used to measure the static pressure, and thermocouples were used to record the temperature of the mainstream. The heat transfer coefficient distribution is calculated from the temperature change captured by the liquid crystal painted on the inner wall of the cooling channel using a camera.

2.2. Models

The cooling channel in this experiment is based on the internal cooling channel in the NGV of a land-based heavy gas turbine. Impingement cooling in the leading region of the vane is achieved by placing a 3D-printed insert inside the cooling channel, as shown in Figure 2 and Figure 3. The experimental channel at the leading-edge features 10 exhaust membrane holes for airflow outlets. These are arranged in six rows for the shower-head surface and two rows each for the pressure and suction surfaces. Each row contains 20 film holes, with the holes arranged in a staggered pattern. The layout of the target surface impact area is shown in Figure 2b. To investigate the impact of hole diameter on cooling effectiveness, three different impact insert designs were tested, with hole diameters of 0.8 mm, 1.2 mm, and 1.6 mm, as shown in Figure 3. The inserts consist of 10 rows of jet holes: three rows on the pressure surface, six on the suction surface, and a single row in the shower-head surface. The flow direction spacing between each jet hole is consistently 4.8 mm.

2.3. Transient Liquid Crystal

In this experiment, the transient liquid crystal technique is used to obtain the temperature variation of the target surface inside the impingement cooling channel, and the 1D semi-infinite conduction is assumed to calculate the heat transfer coefficient (h). According to the analytical solution of 1D semi-infinite conductivity, the heat transfer coefficient h is related to wall temperature (T_w) and time (t):

$${\displaystyle \frac{(T_w-T_i)}{(T_m-T_i)}}=1-exp\left({\displaystyle \frac{h^2\alpha t}{{\kappa }^2}}\right)erfc\left({\displaystyle \frac{h\sqrt{\alpha t}}{\kappa }}\right)$$

(1)

where the thermal diffusion coefficient ɑ = 0.1343 m²·s⁻¹ and the thermal conductivity κ = 0.2172 W·m⁻¹·K⁻¹ are from the material (transparent resin) of the test section. T_m is the mainstream temperature in the channel, and T_i is the initial temperature of the wall, both are measured by thermal couples.

Equation (1) is derived under the assumption of an ideal step change in T_m. However, in experiments, the mainstream temperature does not exhibit an ideal step increase but instead rises gradually over a short period. To account for this, the temperature rise during this period is approximated by a series of temperature steps using the Duhamel superposition principle. Thus, Equation (1) can be modified as follows:

$$T_w-T_i={\displaystyle {\sum }_{j=1}^N\left(\left(1-exp\left(\frac{h^2\alpha \left(t-{\tau }_j\right)}{{\kappa }^2}\right)erfc\left(\frac{h\sqrt{\alpha \left(t-{\tau }_j\right)}}{\kappa }\right)\right)\Delta T_m\left(j,j-1\right)\right)}$$

(2)

A Hallcrest R35C1W narrowband liquid crystal was used in this experiment, and the measurement range of the liquid crystal was roughly 35 °C to 36 °C. Before the experiment, the liquid crystal needs to be calibrated to obtain the correspondence between the calibration temperature and the color hue of the liquid crystal. During the experiment, T_i and T_m are measured by thermocouples, and ɑ and κ are known, so only the temperature of the surface T_w and the time to reach this temperature need to be measured, and the convective heat transfer coefficient h can be obtained by the above Equation (2).

The calibration of transient liquid crystals involves uniformly heating the copper plate with liquid crystal, then measuring the temperature with a thermocouple and recording the color of the liquid crystal with a camera. In the post-processing of the calibration, MATLAB R2023a is used to obtain the (Red-Green-Blue) RGB color values of each pixel point and record the temperature at which the green color value reaches its peak. This temperature is taken as the calibration temperature of the liquid crystals. In the experiment, the RGB values of each pixel point in the video are processed to obtain the time when the green color value reaches its peak. The wall temperature, Tw, at this moment is equal to the calibration temperature.

2.4. Parametric Calculation

This experiment investigated the heat transfer characteristics of the leading-edge channel at inlet Reynolds numbers of 40,000, 50,000, and 60,000. The channel inlet Re was controlled by adjusting the inlet flow rate, while the jet Re was calculated by the averaged jet mass flow rate and jet hole. The experimental working conditions for the impingement cooling channel are summarized in

Table 1. Experimental working conditions.

Channel Inlet Flow \$\dot{\mathit{m}}$ (kg/s)	Channel Inlet Reynolds Number (Re)	Jet Reynolds Number (Rej)
		Model 1	Model 2	Model 3
0.01681	40,000	6665	4443	3332
0.02110	50,000	8366	5578	4183
0.02529	60,000	10,026	6684	5013

.

The parameters involved in this paper are defined below:

• The diameter of the channel D_h is used to define the Reynolds number Re, as below:

$$\mathit{Re}={\displaystyle \frac{\dot{4m}}{\pi \mu D_h}}$$

(3)

where $\dot{m}$ is the total mass flow rate; D_h is the diameter of the channel, and μ is the dynamic viscosity of the gas.

b.

The jet Reynolds number Re_j at the jet hole is described as follows:

$${\mathit{Re}}_j={\displaystyle \frac{2 \dot{m}/N}{\pi \mu d}}$$

(4)

where $\dot{m}$ is the total mass flow rate; N is the number of jet holes; d is the diameter of the jet hole; and μ is the dynamic viscosity of the gas.

c.

The friction coefficient f of the channel is described as follows:

$$f={\displaystyle \frac{\Delta p}{\frac{1}{2}\rho V_j^2}}{\displaystyle \frac{d}{L}}$$

(5)

where Δp is the pressure drop between the inlet of the insert and the exit of the film cooling holes, ρ is the density, and L is the distance between the jet hole and the target surface.

d.

The reference friction coefficient f₀ of the smooth channel can be described as follows:

$$f_0={\left(0.79lnR{e}_j-1.64\right)}^{-2}$$

(6)

e.

The local Nusselt number Nu is defined as follows:

$$Nu={\displaystyle \frac{hd}{\lambda }}$$

(7)

where λ is the thermal conductivity of the fluid; h is the heat transfer coefficient of the target surface measured by the transient liquid crystal technique.

f.

The reference Nusselt number Nu₀ for a fully developed turbulent wall on a smooth surface can be calculated by:

$$N{u}_0={\displaystyle \frac{(f_0/8)(R{e}_j-1000)/Pr}{1+12.7{(f_0/8)}^{1/2}(P{r}^{2/3}-1)}}$$

(8)

where Pr is the molecular Prandtl number of the fluid.

g.

The turbulent kinetic energy TKE can be described as follows:

$$TKE={\displaystyle \frac{1}{2}}\left(\overline{{\left(u^{\prime }\right)}^2}+\overline{{\left(v^{\prime }\right)}^2}+\overline{{\left(w^{\prime }\right)}^2}\right)$$

(9)

h.

The TPF characterizes the degree of intensification of the heat transfer capacity per unit of pump work, which can be described as follows:

$$TPF={\displaystyle \frac{Nu/N{u}_0}{{(f/f_0)}^{1/3}}}$$

(10)

2.5. Uncertainty

The uncertainty of the heat transfer coefficient (h) is attributed to those parameters: channel mainstream temperature (T_m), target surface temperature (T_w), initial wall temperature (T_i), and the time to reach green peak (t). T-type thermocouples are used in the measurement of T_m and T_i with an accuracy of ±0.5 K. Color-changing time t is calculated by the camera frame rate of 100 fps with the maximum uncertainty of 0.01 s. Substitute the formula (2) for h into the uncertainty transfer Equation (11) as follows:

$$U_h=\sqrt{{\left({\displaystyle \frac{\partial h}{\partial T_w}}\right)}^2{u_{Tw}}^2+{\left({\displaystyle \frac{\partial h}{\partial T_i}}\right)}^2{u_{Ti}}^2+{\left({\displaystyle \frac{\partial h}{\partial T_m}}\right)}^2{u_{Tb}}^2+{\left({\displaystyle \frac{\partial h}{\partial t}}\right)}^2{u_t}^2}$$

(11)

The uncertainty of h obtained in this experiment was calculated to be 10.95%.

3. Numerical Calculation

The software Ansys CFX 2020R1 was used to carry out the simulation. In this paper, a 1:1 model as an experiment is adopted, as shown in Figure 4. The inlet boundary conditions are consistent with the experiments, with inlet mass flow rates (0.01681 kg/s, 0.02110 kg/s, and 0.02529 kg/s) and an inlet mean temperature (50 °C). All film holes were defined as pressure outlets with relative pressure (0 kPa). On the target surface, a constant wall temperature (25 °C) is given while all other solid surfaces are adiabatic.

Based on experiences from many previous research studies, such as [14], RANS simulation with the SST k-ω turbulence model is applied. The boundary layer grid follows the requirements of the turbulence model, as shown in Figure 5. The dimensionless distance between the first-layer grid and the solid wall y⁺ < 1 is ensured for the entire computational domain, as shown in Figure 6. In the calculation, the convective terms of the equations are all discretized in 2nd order upwind format. The overall residuals for all equations are less than 1 × 10⁻⁵ for the consideration of convergence. By comparing Nu on the shower-head surface at Re = 40,000 by experiments with numerical simulation, it is shown in Figure 7 that the predicted values are slightly lower than experiments, while the Nu trend remains the same. Considering details, for example, the stagnation due to jets, the trend of Nu from root to tip, and the heat transfer weakening region that deflects from root to shower-head are all captured with satisfaction.

An unstructured mesh is used in this study. The mesh was refined in the shower-head surface, around the jet holes, and near the film holes. Five mesh models with different mesh numbers, as shown in

Table 2. Mesh-independent validation of Model 2.

Mesh	Number of Grids
Mesh1	7.22 M
Mesh2	12.15 M
Mesh3	24.80 M
Mesh4	30.12 M
Mesh5	35.50 M

, were tested to verify mesh independence. The average Nusselt number (Nu_ave) of the pressure surface at Re = 40,000 was chosen as the grid convergence criterion. Figure 8 shows the results of the grid independence test. It can be seen that when the grid number reaches 30,120,000, a further increase in the number of grids results in less than a 2% change in the pressure surface Nu_ave. Therefore, a grid number of 30,120,000 is considered sufficient for accurate simulation of the leading-edge channel.

4. Results and Detailed Discussions

4.1. Heat Transfer Characteristics

Figure 9 presents the Nu distribution on pressure, suction, and shower-head surfaces of Model 2 by experiments at different Re. As shown in Figure 9a, the highest heat transfer zone on the Pressure surface occurs near the stagnation points of the jets at the top of the blade, for all Re. Due to the accumulated cross-flow by used jets, the Nu decreases gradually from the tip to root of the blade, with a reduction in the local high heat transfer region also. Additionally, higher Nu values can be observed in the region adjacent to the shower-head surface. Similar to the pressure surface, Nu in the region next to the showerhead is higher than that near the mid-chord. However, on the suction surface, the variation of Nu from hub to tip is much smaller compared to the pressure surface. Figure 9c illustrates the Nu distribution on the shower-head surface. The four rows of film holes on the shower-head surface form local heat transfer enhancement due to the film extraction effect. Here, from hub to tip, Nu rises initially and then varies little. With increasing Re, the heat transfer enhancement area expands, and the peak Nu in the stagnation region increases. The overall Nu on the target surface also rises, and the local heat transfer enhancement in the region around the film holes becomes more significant.

Figure 10 shows the distribution of the laterally averaged Nu (Nu_lat-avg) with Z/D for pressure, suction, and shower-head surfaces of Model 2 at various jet Reynolds numbers Re_j. The peaks of Nu_lat-avg indicate the heat transfer enhancement by jet arrays, and their overall value increases with Z/d. As Re_j rises, the overall Nu_lat-avg of each surface increases, and the fluctuations become larger. In Figure 10, Nu_lat-avg of the suction surface first increases and then slightly decreases, while for the pressure and shower-head surfaces, Nu_lat-avg steadily increases. Furthermore, Figure 10c shows that the Nu_lat-avg gradient of the shower-head surface is larger than that on the pressure and suction surfaces. This is attributed to the bleeding from film holes, which enhances heat transfer in the shower-head region.

Figure 11 illustrates the variation of area-averaged Nu (Nu_area-avg) on pressure, suction, and shower-head surfaces of Model 2 at different jet Re (Re_j). As Re_j rises, heat transfer is enhanced on all surfaces, which is consistent with the findings in Reference [15] regarding the influence of the Re_j on impingement-film cooling. Notably, the shower-head surface experiences a significantly higher heat transfer due to the bleeding effect, while the heat transfer of the pressure surface is slightly higher than on the suction surface.

Figure 12 shows the Nu distribution on pressure, suction, and shower-head surfaces of all three Models at Re = 60,000. The jet hole diameter (d) is 0.8 mm, 1.2 mm, and 1.6 mm for Models 1, 2, and 3, respectively. All other parameters are kept the same. In Figure 12a, for all three Models, higher Nu can be observed on the side next to the shower-head compared to the side near mid-chord. As the jet hole diameter (d) increases from 0.8 mm to 1.2 mm, the overall heat transfer enhancement due to the jet grows, while the overall Nu decreases as d varies from 1.2 mm to 1.6 mm. Furthermore, varying jet hole d results in different heat transfer distributions on the pressure surface. In Model 1 (d = 0.8 mm), the Nu distribution increases and then decreases along the flow direction (spanwise), while in Model 2 (d = 1.2 mm), Nu gradually increases from root to tip. In Model 3 (d = 1.6 mm), a particularly low heat transfer region exists near the root. In comparison, Model 1 demonstrates a more uniform distribution of Nu on the pressure surface.

In Figure 12b, the overall Nu on the suction surface decreases as jet hole diameter (d) increases, which reveals a different trend than that of the pressure surface. The Nu on the side adjacent to the shower-head is higher than the other side. For Model 3 (d = 1.6 mm), heat transfer is very low near the root, similar to that on the pressure surface. For Models 2 and 3, the rising Nu from root stabilizes at 50% span and above.

Figure 12c presents the Nu distribution on the shower-head surface. As the jet hole diameter (d) increases, the area of the stagnation region grows, with the peak Nu value decreasing, leading to an overall reduction of Nu on the shower-head surface. A rising d improves the uniformity of Nu distribution, while for Model 3, an obviously low heat transfer near the root can be observed.

The distribution of the laterally averaged Nu_{lat_avg} with Z/d on pressure, suction, and shower-head surfaces at Re = 60,000 is shown in Figure 13. It can be seen from Figure 13a that the peak Nu_{lat_avg} in the root region decreases with increasing d. However, in the tip region, an opposite trend can be found. From 50% span of the blade, Nu_{lat_avg} of all three Models are close to each other. The maximum Nu_{lat_avg} of Model 1 appears at 50% span, while that of Models 2 and 3 is in the tip region, and the Nu_{lat_avg} profiles of Models 2 and 3 in the tip region are close to each other. Furthermore, Nu_{lat_avg} will exhibit repetitive variations along the spanwise direction because the heat transfer at the impingement hole is stronger. When Nu_{lat_avg} varies along the spanwise direction, it will reach a small peak at the impingement hole.

In Figure 13b, the peak of the Nu_{lat_avg} on the suction surface decreases gradually with jet hole diameter (d). The Nu_{lat_avg} of each Model 3 increases from the root and reaches a constant value, with its peak value occurring at a 50% span. The Nu_{lat_avg} profile of Models 2 and Model 3 is basically the same level in the tip region. With the increase of d, the region of heat transfer enhancement expands, and the gradient of the Nu_{lat_avg} of the tip decreases gradually.

In Figure 13c, it can be seen that Nu_{lat_avg} gradually decreases as d increases, as well as the gradient of Nu_{lat_avg} decreases. Along the flow direction with increasing Z/d, the Nu_{lat_avg} is elevated in trend, and the Nu_{lat_avg} distribution is more uniform for Model 1 than for Models 2 and 3.

Figure 14 gives the variation of the area-averaged Nu (Nu_area-avg) with respect to jet hole diameter (d) of pressure, suction, and shower-head surfaces. For all three surfaces, the Nu_area-avg decreases with increasing d, which is consistent with the findings in Reference [14] regarding the influence of the impact hole diameter on impingement-film cooling. The phenomenon can be explained as that in the inlet passage, channel Re (Re_c) is unchanged, and rising d leads to the reduction of the jet velocity and consequent impingement heat transfer coefficient on the target surface. Although larger d also leads to an increasing stagnation zone, which is positive to the overall heat transfer, the effect of reduced jet velocity in the current study is dominant compared to that of increased stagnation area. Thus, Nu_area-avg of the target surface decreases as jet hole d increases.

Figure 15 shows the non-dimensional velocity (V/V_j) contours of Models 1, 2, and 3, approximately at 95%, 50%, and 5% span, in which V_j represents the averaged ejecting velocity. Considering Model 2 with jet hole diameter (d) of 1.2 mm for illustration, Figure 15a,b shows that jets are not influenced by the planar cross-flow pointing to the shower-head, and complex vortices are formed near the stagnation points after impinging on the target surface. Figure 15c reveals that near the root, the cooling jet on the suction side rarely reaches the target surface. The jet on the pressure surface is slightly deflected towards the shower-head side due to the near-wall cross-flow. The extraction of coolant from film holes on the shower-head surface promotes local flow-acceleration and boundary layer re-development around them at both the blade tip and blade root. Comparing among Figure 15a–c, from root to tip, the main air velocity inside the inserts decreases and inclines towards the shower-head surface, while the impingement flow velocity increases. At 5% span, the flow inside the insert is basically in the main flow direction, and the impingement velocity is relatively low. Conversely, at the 95% span, the flow is deflected in several directions due to the channel structure, with the highest impingement velocities observed in this region. The flow is more pronounced on the pressure and suction surfaces near the shower-head region, which is consistent with the trend of the Nu distribution.

The overall effect of jet hole diameter d is that for all models, increasing d results in a decrease in jet velocity and heat transfer rate. At 95% and 50% span, all models have similar flow structures, with the jet velocity decreasing with d. At a 5% span, the effect of the cross-flow is more obvious with increasing d. Especially for Model 3, a low-speed recirculation zone develops near the suction surface, and jets near the pressure surface are deflected substantially towards the showerhead. These contribute to the low heat transfer region in the blade root of Model 3.

Figure 16 shows the distribution of turbulent kinetic energy (TKE) for all models at 95%, 50%, and 5% span. As the jet hole diameter d increases, the total TKE decreases in all three spanwise cross-sections due to the reduced shear effect of jets. In addition, decreasing d leads to more uniform TKE distribution, especially at 95% and 50% span planes. At each cross-section, a relatively high TKE profile can be observed compared to both the pressure and suction surfaces. Considering the effects of jet hole diameter, at the 95% plane, Model 1 presents significantly higher TKE compared to Models 2 and 3. At the 5% span of Model 3, on both pressure and suction surfaces, TKE is largely reduced compared to the shower-head region. Both phenomena can be used to explain the heat transfer characteristics shown in Figure 12.

4.2. Friction Coefficient and Combined Heat Transfer Efficiency

In this paper, two pressure points were set at the inlet and outlet of the channel to measure the differential pressure of the channel, from which the friction coefficient of the channel, f, can be calculated and compared with the referenced friction coefficient, f₀, to obtain the friction coefficient ratio, f/f₀. Figure 17 shows the f/f₀ of the channel at different inlet Re for all three models.

In Figure 17, it can be seen that f/f₀ of each model shows a decreasing trend with Re. And f/f₀ increases as the diameter of the jet hole d increases. The f/f₀ of Model 3 with d = 1.6 mm is the largest.

Enhancing the internal cooling of the channel is certainly helpful to elevate the performance of gas turbines, but the pressure drop induced cannot be avoided. The thermal performance factor (TPF) is used to evaluate the increase in heat transfer per pump power. Figure 18 shows the TPF of the heat transfer enhancement suction surface and shower-head surface for the three Models at different inlet Re. The comparison shows that Model 1 (d = 0.8 mm) has the highest TPF on every surface. Between the remaining two Models, Model 2 (d = 1.2 mm) has a higher TPF. From the comprehensive comparison of the heat transfer distribution and pressure drop characteristics, it can be seen that the Nu fluctuation amplitude of Model 1 on each target surface is very large, and thus, the increased thermal stress may bring more consideration of structural strength. Therefore, Model 2 could be more suitable for application.

5. Conclusions

This study investigates the leading portion internal cooling of a nozzle by impingement. Transient liquid crystal was employed to measure the heat transfer distribution of three Models under varying Re. Additionally, numerical simulations were conducted to analyze the corresponding flow field. Effects of jet Reynolds number and jet hole diameter on the flow and heat transfer characteristics are discussed. The findings offer a reference for the cooling design of a nozzle leading-edge. Conclusions are drawn as follows.

• In the spanwise direction, overall Nu distribution initially increases, then continues rising or stabilizes to a constant value, with the highest Nu typically near the tip. The area-averaged Nu generally follows the pattern: shower-head > pressure > suction. Notably, the heat transfer enhanced regions are shifted toward the shower-head on both pressure and suction surfaces. This trend aligns with the velocity and TKE distributions.
• Bleeding from film holes significantly affects the heat transfer enhancement in the stagnation region of the impingement, and there is a significant flow acceleration and TKE enhancement near film holes due to bleeding, where the Nu increases by 10.69% compared to the region without film holes.
• The overall heat transfer of the target surface is elevated with the increase of Re_j. The average Nu and TKE increase with Re_j. However, the flow field structure does not change significantly.
• The average Nu and TKE decrease with jet hole diameter d increased due to the decrease of jet velocity, and the Nu gradient also rises on the target surface. For Model 3 (d = 1.6 mm), recirculation near the suction surface and deflected jets near the pressure surface at 5% span plane weaken heat transfer on both surfaces.
• The f/f₀ decreases with Re_j and increases with d. And, TPF increases with Re_j and decreases with d. The TPF of Model 1 (d = 0.8 mm) is the largest, with a high Nu gradient and non-uniformity. In current research, considering Nu and its uniformity, f/f₀, and TPF, Model 2 (d = 1.2 mm) has a better application prospect.

This study examines the effects of jet Reynolds number and jet hole diameter on flow and heat transfer in the leading-edge full-impingement cooling channel of a gas turbine nozzle guide vane. The influence of spanwise spacing of the impingement holes and the impact spacing on the flow and heat transfer has not been addressed. Additionally, the full impingement cooling study for the trailing edge channel is also one of the future research contents.