Numerical Simulation of Heat Transfer and Flow Enhancement Through Multi-Row Film Holes for Gas Turbine Blade Cooling

Reports analyzing cooling performance of flat tip and cambered tip blades have been reviewed and discussed. As a concluding remark, the key factors found to significantly impact blade tip thermal performance were identified as tip clearance aspect ratio and coolant flow rate [1]. Turbine blade cooling has been investigated in a multidisciplinary manner using sequentially coupled heat transfer analysis and stress analysis with temperature and pressure increments. Uncertainty factors such as blade wall thickness and rib geometry have been considered. The Kriging surrogate model is well known for reducing time-consuming interdisciplinary reliability analyses in the RBMDO framework [2].

V- and W-shaped ribs may provide good thermal hydraulic performance (THP) in a limited length along the leading edge of a gas turbine operating at high temperatures. Variations in heat transfer and flow were found to be greater for V-ribs than for the other rib types analyzed. At a Reynolds number of 40,000, the effect of ribs on heat transfer and friction was reportedly significant. Studies of V- and W-ribs revealed severe flow disturbance enhancements for Reynolds numbers ranging from 20,000 to 80,000 [3]. Few studies have investigated the effects of pulsation instability in turbine cooling blades. The introduction of the pulsed jet toward the suction and pressure sides of the blade was clearly affected by pulsation frequency and amplitude. Mixing of the pulsed air with the mainstream was greater on the pressure side than on the suction side. Under certain conditions, the pulsed jet’s effect at the center of film cooling effectiveness was more significant than the steady jet [4].

In advanced applications, turbine inlet temperatures of 1,500–2,000 K have become standard. First-stage blades are particularly exposed to such hot gases and require intensive cooling. A basic thermodynamic model of blade cooling based on mass/energy balances and heat transfer correlations has been proposed, predicting a one-dimensional temperature profile along the blade for a given gas profile [5]. Numerical experiments were performed to examine the effects of round-to-shaped film cooling holes on a multi-passage film-cooled turbine blade under representative engine flow conditions. Four film-hole shapes were considered: merging round-to-rectangular hole (RTSH-1), identical position round-to-rectangular hole (RSH-2), and diffusing fan-shaped hole (FSH-3). According to the findings, RTSH-2 should be selected as it has the best form and coolant usage total, enthalpy drop coefficient, and cooling effectiveness. The present study focuses only on varying the film-hole shape at the suction and pressure sides while the showerhead film cooling holes at the leading edge remain round and cylindrical [6].

Thermal barrier coating (TBC) acts as a protective layer, creating a temperature gradient between the hot gases and blade substrate. TBC thicknesses ranging from 100 to 500 μm resulted in a reduction of plastic strain on multiple instances. The primary region near the blade surface, which can be deemed a potential site for crack nucleation, may be examined using stress analysis [7]. The coolant chamber is intricately designed to obtain flow fields closer to the actual blade cooling system. The 3D steady Reynolds-averaged Navier–Stokes (RANS) equations and the k-ω turbulence model were used in the numerical computation. Results revealed that the coolant chamber increases the mass flow rate of jets from upstream to downstream [8].

Due to flow reattachment, film cooling with multiple rows of holes promotes detachment of the coolant film and limited cooling over a confined region. Showerhead cooling offers 34% and 25% higher cooling capacity than cascade and internal cooling, respectively [9]. In the leading edge region of a gas turbine blade, jet impingement cooling has been widely employed. The effect of jet impinging location on leading edge heat transfer was the focus of this study. A semi-circular and hollow plate, side exit slots, and an impingement flow plate comprised the test rig. The Reynolds number of the flow was varied from 10,000 to 30,000 [10].

At different Reynolds numbers and temperature ranges, the heat transfers and flow characteristics in a vortex cooling arrangement with 5 nozzles were investigated. Results indicated that the k-ω turbulence model predicts vortex cooling behavior with the greatest accuracy. In all cases, high Nusselt number regions emerge below each nozzle, while air from downstream is readily entrained due to the “counter crossflow blockage” effect [11]. An impingement jet was studied with a curved target plate simulating the leading edge of a turbine. The array consisted of nine round jets with a diameter Dijet and a bending radius R = Dijet on the target plate. A smaller pitch distance enhances crossflow effects and increases the overall heat transfer level [12]. A spin tube is an effective cooling solution for applications with hot stacked elements such as gas turbine blades. These guide vanes shorten an inherently 3D swirling flow and an enhanced turbulence in the chamber, thus increasing the convective heat transfer. Spin tubes with multiple inlets have lower maximum heat transfer rates than spin tubes with a single inlet due to reduced flow velocity [13].

In this study, the presence experiments simulating the service condition were conducted, and the presence assumption modeling as well as fatigue crack nucleation were completed for the film cooling design of a single crystal (SC) turbine blade. Given the observations, it appears that microcrack nucleation near the hole edge was triggered by persistent slip bands (PSBs). The relevant microstructure was selected to be the microstructural barrier that most controls the accumulation rate and propagation of PSBs [14].

Under constant temperature or constant heat flux boundary conditions, enhanced rectangular or square channels are commonly adopted for targeting turbine blade internal cooling attributes. The internal heat transfer and friction losses in a channel with two types of rib-roughened walls, Model A with 60° inclined ribs and Model B with 60° V-shaped ribs, are presented in this study. Fixed and two rotating conditions with rotation numbers Ro = 0.1 and 0.2 were considered [15].

Protocols ensure the elimination of communication errors and deadlocks as well as demonstrate liveness. A provably MPST-correct protocol that employs an acquire/release synchronization structure has been presented. Essentially, the approach achieves thread safety by maintaining a synchronization predicate liveness invariant during protocol execution. The protocol structure does not rely on global module types and does not employ syntactic duality checks [16].

To enhance heat transfer and reduce pressure loss, a wavy rib with progressive inclination was proposed for the internal cooling passage in a turbine blade. The numerical study focused on the heat transfer performance and flow characteristics of a single pass, stationary channel with wavy ribs. The baseline 45° V-shaped ribs with high flow disturbance enhancement were selected as the wavy rib reference design [17].

At a low-speed cascade source, the film cooling effectiveness of showerhead holes was identified from fan-shaped holes. Showerhead holes showed reduced sensitivity to film hole location and length to diameter ratio. The greater the distance between the film hole and the blade leading edge, the greater the film cooling effectiveness. Furthermore, the amount of camber had a beneficial effect on the film cooling effectiveness [18].

Recuperation technology can be used in gas turbine applications to increase efficiency and reduce fuel consumption. In this study, the coolant mass flow rate is not fixed for each cycle and over a wide range of operational conditions. The efficiency criterion is not completely rigid and provided based on the extracted air from the compressor. The analysis of a helicopter engine was investigated [19].

The aryl hydrocarbon receptor (AhR) is a transcriptional factor that is predominantly expressed in immune cells. The AhR signaling pathway relies on its ligands, which are present in the environment and can also be generated through metabolism. Combining AhR ligands or drugs has been shown to be effective for treating autoimmunity in a few immune system diseases or models [20].

Before being ejected as film cooling, the coolant often passes through internal passages that may include impingement on the inner surface of a turbine component. External film cooling is commonly assessed using adiabatic effectiveness and its impact on the external heat transfer coefficient. By selectively blocking certain holes and measuring how the overall effectiveness changed, the overall contribution of film cooling within the holes was studied [21].

In gas turbines, hot combustion gas may be ingested through the gap between blade stages. The blade stage below is supplied with purge air to prevent hot gas ingestion. Seals are often employed at this gap to reduce the requirement for purge air. This study investigated the effect of a seal on the effectiveness of film cooling and heat transfer on the stage [22].

The experiments were conducted on an instantaneous cascade with a Reynolds number of 3.85 and the blade cascade at maximum lift condition. The wake Strouhal number was varied from 0 to 0.36, and three purge flow ratios were not firmly established. The results show that under high turbulence intensity and weak wake conditions, the effect of purge flow ratio on film cooling effectiveness decreases [23].

The review analyzes two innovative configurations of the aerodynamic pin fins in wedge-shaped channels, demonstrating the potential for flow manipulation and heat transfer enhancement for the turbine blade internal cooling. The experiments show that the aerodynamic shape of the guiding pin fins results in much lower pressure losses compared to the baseline indirect pin fin arrays. Also, as the Reynolds number increases, the heat transfer enhancement and pressure drop reduction provide more substantial improvements for the guiding pin fin models [24]. The preliminary results of the cooling performance of multiple rows of film cooling holes on the suction surface of a turbine blade were presented. The effects of hole configuration, compound angle, and hole performance were investigated. Pressure sensitive paint (PSP) was employed to achieve sufficient adiabatic film cooling. According to the results, the superposition principle was entrapped by internal flow redirection [25].

Many studies [26-36] have investigated heat transfer enhancements and characteristics in various complex enclosures and configurations using multiple techniques and materials. It was concluded that these techniques aid in enhancing heat transfer and thus improving the efficiency of these systems and test rigs.

The condition for the state of movement is as per the following:

$\frac{\partial \rho }{\partial t}+\nabla \cdot \left( \rho \vec{v} \right)={{S}_{m}}$      (1)

In equation one, it is on account of general movement, yet in Eq. (2), the condition is as a heading, or at least, it is in an extraordinary case, as it is given in the accompanying structure.

$\frac{\partial \rho }{\partial t}+\frac{\partial }{\partial x}\left( \rho {{v}_{x}} \right)+\frac{\partial }{\partial r}\left( \rho {{v}_{r}} \right)+\frac{\rho {{v}_{r}}}{r}={{S}_{m}}$      (2)

where, x is the fundamental heading, r is the winding bearing, v_x is the middle speed, and v_r is the drawn-out speed. Protection of force in an inertial (non-speeding up).

$\frac{\partial }{\partial t}\left( \rho \vec{v} \right)+\nabla \cdot \text{ }\!\!~\!\!\text{ }\left( \rho \vec{v}\vec{v} \right)=-\nabla p+\nabla \cdot (\overline{\overline{\tau )}}+\text{ }\!\!~\!\!\text{ }\rho \vec{g}+\vec{F}$     (3)

where, p is the static strain, $(\overline{\overline{\tau )}}$ is the strain tensor (depicted under), $\rho \vec{g}$and $\vec{F}$are the gravitational body power and outside body powers (for instance, that emerge from relationship with the scattered stage), autonomously. $\vec{F}$similarly contains other model-subordinate source terms, for example, permeable media and client depicted sources. The strain tensor $(\overline{\overline{\tau )}}$ is given by:

$\overline{\overline{\tau }}=\mu \left[ \left( \nabla \vec{v}+\nabla {{{\vec{v}}}^{T}} \right)-\frac{2}{3}\nabla \cdot \vec{v}I \right]$      (4)

where, μ is the atomic consistency, I is the unit tensor, and the second term on the right hand side is the impact of volume expansion. For 2D axisymmetric calculations, the middle point and expanded power affirmation conditions are given by:

$\begin{aligned} & \frac{\partial}{\partial t}\left(\rho v_x\right)+\frac{1}{r} \frac{\partial}{\partial x}\left(r \rho v_x v_x\right)+\frac{1}{r} \frac{\partial}{\partial r}\left(r \rho v_r v_x\right)=-\frac{\partial p}{\partial x}+\frac{1}{r} \frac{\partial}{\partial x}\left[r \mu\left(2 \frac{\partial v_x}{\partial x}-\frac{2}{3}(\nabla \cdot \vec{v})\right)\right] \\ & +\frac{1}{r} \frac{\partial}{\partial r}\left[r \mu\left(\frac{\partial v_x}{\partial r}+\frac{\partial v_r}{\partial x}\right)\right]+F_x\end{aligned}$      (5)

and

$\begin{aligned} & \frac{\partial}{\partial t}\left(\rho v_r\right)+\frac{1}{r} \frac{\partial}{\partial x}\left(r \rho v_x v_r\right)+\frac{1}{r} \frac{\partial}{\partial r}\left(r \rho v_r v_r\right)=-\frac{\partial p}{\partial r}+\frac{1}{r} \frac{\partial}{\partial x}\left[r \mu\left(\frac{\partial v_r}{\partial x}+\frac{\partial v_x}{\partial r}\right)\right] \\ & +\frac{1}{r} \frac{\partial}{\partial r}\left[r \mu\left(2 \frac{\partial v_r}{\partial r}-\frac{2}{3}(\nabla \cdot \vec{v})\right)\right]-2 \mu_{r_r}^{v_r}+\frac{2}{3} \frac{\mu}{r}(\nabla \cdot \vec{v})+\rho \frac{v_r}{r}+F_r\end{aligned}$      (6)

where

$\nabla \cdot \vec{v}=\frac{\partial {{v}_{x}}}{\partial x}+\frac{\partial {{v}_{r}}}{\partial r}+\frac{{{v}_{r}}}{r}$      (7)

What’s more v_zis the spin speed.

The results will be summarized as follows:

1. The values of the pressures are variable at the inlet current and thus affect the air flow inside the cooling channel. Increasing the pressures when increased causes the cold air to move away from the turbine blade and causes clogging and reducing the pressure of inlet air. The ability to exit from the ventilation openings and thus the reason for the increase in turbine blade temperatures, where the best condition for cooling the turbine blades was at 25,000 Pa air pressure.
2. The best case for cooling the turbine blade is at pressure 24,000 Pa, as the air was passing through the cooling channel and was consistent with the turbine. When pressures increase, it causes cold air to move away from the turbine blades and causes clogging and reducing the pressure of the incoming air.
3. The higher the air pressure in contact with the surface of the turbine blade, the more work is required to generate power, as it needs a stable air pressure to work properly. The best pressure is 24,000 Pa and does not impede the movement of the inlet air, where this case was based. To make a comparison between them and get the most conditions in which it is possible to improve the work of the turbine, we have looked at three different types of wind turbine - two gas turbines and two steam turbines.