Keywords

1 Introduction

In the contemporary landscape of power generation, gas turbines have evolved into indispensable components, playing a pivotal role in diverse industrial sectors, especially in the production of electrical energy [1,2,3]. The increasing prevalence of gas turbines has spurred a heightened interest among researchers and designers, propelling them to delve deeper into every aspect associated with this machinery, all with the overarching goal of effecting necessary improvements [4, 5]. This comprehensive study is dedicated to the intricate simulation of the flow of compressible transonic fluid through a configuration consisting of eight blades, mirroring the design commonly found in gas turbines. The focal point of our investigation revolves around the meticulous analysis and determination of the pressure and temperature distribution near each turbine blade. The chosen configuration for examination aligns with the experimental study conducted by T. Arts [6], providing a foundation for our numerical simulations. By leveraging the Fluent code, we aim to generate accurate and insightful numerical results. These results will then be subjected to thorough discussion, offering a nuanced understanding of the fluid dynamics at play within this specific turbine blade arrangement. This research aspires to contribute not only to the theoretical understanding of gas turbine performance but also to provide practical insights that can inform the ongoing efforts to enhance the efficiency and effectiveness of gas turbines in real-world applications. Through this exploration, we anticipate uncovering valuable knowledge that will contribute to the continuous advancement of gas turbine technology.

2 Problem Statement and Equations

This work focuses on the numerical modeling of transonic flow around the VKI-CT2 8-profiles located in the stator of an axial turbine. The numerical simulation of the flow is conducted using Fluent software based on the Navier-Stokes equations. Turbulence is accounted for using first-order and second-order turbulence models. The discretization method employed is the finite volume method, and an unstructured tetrahedral mesh is adopted for a generalized Cartesian coordinate system.

The system of averaged Navier-Stokes equations can be expressed in the following conservative form [Refer to [6]]:

$$\frac{\partial w}{\partial t}+div(Fc-Fd(w, wx, wy ,wz))=S(w)$$
(1)

3 Meshing and Boundary Conditions

In the simulation process, meshing and defining appropriate boundary conditions are crucial aspects. The mesh serves as a discretized representation of the computational domain, while boundary conditions prescribe the behavior of the flow at the domain boundaries. For this study, an unstructured tetrahedral mesh of the computational domain is utilized. The choice of mesh type and refinement is particularly important near the walls (Fig. 1), and it is influenced by the Reynolds number and turbulence model applied. In cases where viscous effects are significant, such as at a Reynolds number of approximately Re = 105, a refined mesh is employed to capture the details of the flow near the surfaces accurately.

Fig. 1.
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Mesh of the domain studied

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Additionally, specifying proper boundary conditions is essential to mimic real-world scenarios. These conditions might include the inflow and outflow conditions, as well as the treatment of solid surfaces like the turbine blades. The accuracy and reliability of the simulation results depend on the careful consideration and application of these meshing and boundary condition parameters.

The flow is assumed to be steady, compressible, and viscous. At the inlet of the domain, both the velocity and static temperature of the fluid are considered as specified boundary conditions. At the outlet, the static pressure of the fluid is captured. On the walls, it is assumed that the temperature is known. The obtained results are validated against the wall 251 (test) [1], providing a confirmation of the simulation outcomes. This validation against a known case helps ensure the accuracy and reliability of the numerical model in replicating real-world fluid dynamics, especially under the given assumptions and boundary conditions.

4 Results and Discussions

4.1 Mach Number

The Mach number is a dimensionless quantity that represents the ratio of the speed of an object, in this case, the fluid flow, to the speed of sound in that fluid. It is a crucial parameter in aerodynamics and fluid dynamics, providing insight into the compressibility effects of the fluid. In the context of the results obtained using the Shear-Stress Transport (SST) model, the Mach number gives us valuable information about the speed of the fluid at different locations within the computational domain (Fig. 2).

Inlet of the Domain: The fluid enters the domain at a low velocity. This initial condition is crucial as it sets the baseline for the subsequent flow behavior.

Leading Edge of the 8-Blade Configuration: As the fluid encounters the leading edge of the 8-blade configuration, it undergoes deceleration. This deceleration is likely influenced by the presence of the blades, causing changes in the flow pattern and velocity distribution.

Inter-Blade Space (especially on the Upper Surface): The fluid then begins to accelerate in the inter-blade space, with a particular emphasis on the upper surface or extrados. This acceleration could be attributed to the aerodynamic shape of the blades and the consequent pressure differences on the upper surface, leading to increased flow velocity.

Trailing Edge: At the trailing edge of the blades, there is a sudden decrease in velocity. This reduction in speed might be a result of the interaction between the fluid from the extrados and intrados, causing a difference in momentum (QM) between the two regions.

Swirling Zone Formation: The sudden decrease in velocity at the trailing edge is accompanied by the formation of a swirling zone. This swirling motion is likely induced by the difference in momentum between the fluid from the upper surface (extrados) and that from the lower surface (intrados).

Shockwave Near the Trailing Edge: Additionally, a shockwave is noted near the trailing edge. Shockwaves often occur when there is a sudden change in flow conditions, such as a rapid decrease in velocity. The presence of a shockwave indicates a significant change in the flow dynamics at this location.

Understanding the Mach number distribution and its variations at different points along the flow path provides valuable insights into the aerodynamic characteristics of the 8-blade configuration. It helps in optimizing the design and predicting the performance of the system, considering compressibility effects and shockwave formations.

Fig. 2.
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Variation of the Mach number obtained by the SST-model (case MUR251)

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Pressure/Temperature.The interplay between pressure and temperature is crucial for understanding the behavior of a system, such as the flow around turbine blades (Fig. 3 and 4).

High Inlet Pressure: The excessively high pressure at the inlet of the domain could be attributed to various factors, including upstream conditions, geometry of the inlet, or operational parameters. Understanding the source of this high pressure is essential for optimizing the system's performance and preventing potential damage.

Pressure Degradation in Inter-blade Region: The decrease in pressure within the inter-blade region suggests that there might be interactions between the fluid and the blades leading to energy losses. This phenomenon could be caused by the complex aerodynamic interactions occurring between adjacent blades or the presence of turbulent flows. Investigating and mitigating these pressure losses are vital for improving overall efficiency.

Different Pressure Changes on Extrados and Intrados: The discrepancy in pressure changes between the extrados and intrados indicates an asymmetry in the flow field around the blades. This could be a result of uneven blade loading, non-uniformities in the incoming flow, or blade design considerations. Identifying the cause of this asymmetry is essential for achieving a more uniform distribution of pressure and optimizing the aerodynamic performance of each blade.

Temperature Increase at Shockwave Location: The sudden increase in temperature at the shockwave location near the trailing edge is indicative of compression heating. As the flow accelerates and encounters a shockwave, there is a conversion of kinetic energy to thermal energy, resulting in a temperature rise. This temperature spike should be carefully monitored, as excessive heating can lead to material degradation and affect the overall durability of the blades.

Inconsistent Effect Among Blades: The variability in the impact of the shockwave among the eight blades suggests that there might be differences in their individual aerodynamic loading or geometrical characteristics. Investigating these variations and their influence on the pressure and temperature distribution will help in optimizing the design and ensuring uniform performance across all blades.

Fig. 3.
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Pressure variation (P) obtained by the SST-model

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Fig. 4.
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Temperature variation (T) obtained by the SST-model

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5 Conclusions

The preliminary results obtained in the course of this research work are promising. The viscous calculation of transonic flow around the 8 blades has revealed the presence of a shockwave and its varying effects. This observation prompts the need for further exploration, both in terms of theoretical understanding and practical implications, in future research. These early findings offer a glimpse into the complex behavior of transonic flow around the turbine blades. The identification of a shockwave introduces a layer of intricacy to the study, necessitating a deeper dive into the physical and practical aspects associated with its presence.

Future research endeavors could focus on:

Shockwave Dynamics: Investigating the precise characteristics and dynamics of the shockwave. Understanding how it evolves and interacts with the surrounding flow will contribute to a more comprehensive comprehension of the transonic flow phenomena.

Impact on Turbine Performance: Delving into the effects of the shockwave on the overall performance of the turbine. This includes assessing its influence on efficiency, pressure distribution, and potential structural implications on the blades.

Optimization Strategies: Exploring potential optimization strategies to mitigate any adverse effects caused by the shockwave. This could involve adjustments to blade design, flow control mechanisms, or other engineering solutions.

Validation and Comparison: Validating the computational results against experimental data and comparing them with other established numerical models. This step is crucial for ensuring the accuracy and reliability of the simulation outcomes.

Practical Applications: Extending the research to address practical applications, such as turbine design improvements or the development of guidelines for handling transonic flows in similar contexts.

In summary, while the current results provide a foundation, there is a rich landscape for exploration in understanding and harnessing the dynamics of transonic flow around turbine blades. The identified shockwave serves as a focal point for future investigations, inviting a multidimensional analysis encompassing theoretical, numerical, and practical considerations.