INTRODUCTION
Introduction
In the aviation industry, enhancing aircraft performance is crucial for reducing operating costs and emissions, with a significant focus on engine improvements, particularly turbine efficiency Turbines are vital components of engines, directly influencing overall performance Turbine blades operate under extreme conditions, including high temperatures, aerodynamic loads, and substantial centrifugal forces, making experimental research costly and challenging To address these difficulties, numerical simulation methods have been developed, utilizing complex calculation models This project specifically analyzes turbine stage performance through Computational Fluid Dynamics (CFD) simulation.
Improving turbine performance is crucial in both the jet engine and power sectors Research in turbine blade technology focuses on methods such as reducing tip clearance, implementing casing grooves, and optimizing airflow injection A notable approach is the use of squealer tips, which effectively minimize tip leakage losses This paper analyzes the configuration of squealer tips, extensively investigating the leakage flow through the tip gap using computational fluid dynamics (CFD) methods and examining its effects on the aerothermal performance of the axial turbine.
This study evaluates the efficiency and Nusselt number of two turbines, focusing on an axial annular turbine named “LISA,” which was experimentally tested at the Laboratory for Energy Conversion (LEC) at ETH Zürich, Switzerland Utilizing 3-D Reynolds Averaged Navier-Stokes (RANS) equations with the shear stress transport (SST) turbulence model, numerical calculations were conducted with a “total energy” option and a “mixing-plane” approach for rotor and stator interfaces The research discusses the impact of various geometric parameters, specifically the height and width of the cavity at the tip, on aerothermal performance and leakage loss Results indicate that the generated vortex significantly influences the turbine's aerothermal performance, with most cavity sizes outperforming the original configuration lacking a squealer tip, achieving maximum efficiency.
This research utilized CFD simulation to examine the impact of tip clearance on the aerodynamic performance of an axial turbine, resulting in a 0.88% increase in efficiency and a 9.64% rise in the averaged Nusselt number Additionally, two methods were implemented, including the use of a squealer tip, to enhance the turbine's performance.
Previous research
The flow structure in turbomachinery passages is highly intricate, particularly in turbines where the rotor, a rotating component, maintains a small space known as tip clearance between its tip and the casing Research indicates that this tip clearance can lead to significant losses and the formation of vortices, ultimately diminishing turbine performance Additionally, the curved passages create a gap between the blades and end walls, resulting in non-uniform velocity profiles, pressure gradients, and temperature gradients These unsteady flow conditions contribute to leakage flows, further reducing turbine efficiency.
Recent studies have focused on aerodynamic enhancement methods to mitigate the effects of tip leakage flow, with the squealer tip design emerging as a prominent solution Research by Heyes et al demonstrated that optimized blade tip geometry significantly improves the aerodynamic performance of axial turbine cascades by reducing the negative impacts of tip leakage flow Additionally, Ameri et al found that squealer tips effectively slow down leakage flow while enhancing overall heat transfer, highlighting their thermodynamic benefits.
Recent studies on turbine blade tip designs reveal significant advancements in aerodynamic performance Camci et al demonstrated that suction side squealers outperform cavity squealers in low-speed axial flow turbines Numerical simulations by Kavurmacioglu et al indicated reduced aerodynamic losses with suction side squealers compared to conventional flat tips Key and Arts found that squealer tips can lower aerodynamic losses under specific conditions when compared to flat tips Newton et al measured heat transfer coefficients and found a decrease in heat transfer with squealers Krishnababu et al concluded that cavity tips enhance both aerodynamic performance and heat transfer Lee and Kim examined the impact of tip gap height on performance with cavity squealers, while Schabowski and Hodson identified lower aerodynamic losses associated with cavity squealer tips in low-speed turbine cascades.
Current research on the simultaneous effects of aerodynamics and heat in tip leakage flow is limited Lee and Chae found that increasing the height of the squealer rim reduced aerodynamic losses downstream of a high-turning turbine rotor, specifically noting that the loss decreased until the height-to-chord ratio reached 2.75% Zhou and Hodson conducted both experimental and numerical studies on the impact of squealer geometry on the aerothermal performance of tip leakage flow, revealing a complex relationship where increased squealer height led to a decrease in the heat transfer coefficient, while narrower widths helped mitigate aerodynamic losses Kang and Lee also explored these effects further.
Recent studies have shown that the height of the squealer rim significantly affects heat transfer on the floor of the cavity at the squealer tip in high-turning turbine blade cascades, with findings indicating that an increase in height leads to a decrease in average heat transfer rate Additionally, research by Senel et al explored the impact of both squealer width and height on the aerothermal performance of high-pressure turbine blades, examining four different heights and seven widths The results underscored the importance of selecting the appropriate squealer dimensions to enhance aerothermal performance.
This study investigates the impact of different squealer tip configurations, specifically varying widths and heights, on the aerodynamic efficiency, thermodynamic performance, and leakage mass flow rate of an axial turbine The findings are compared to a baseline case without a squealer tip, highlighting the significance of these configurations in enhancing turbine performance.
Tip clearance of rotor blade
Tip clearance must be carefully maintained; it should not be excessively large to avoid losses, yet it cannot be too small either Insufficient clearance can lead to rotor blade expansion due to thermal effects and inertial forces during operation, potentially causing damage to the casing.
A common technique to reduce excessive leakage flow is the use of a shroud on the rotor blade As illustrated in Fig 2 [11], one rotor blade is shrouded while the other features a free tip Both blades have orifices that release fluid (air bled from the high-pressure compressor) to form a boundary layer of cooled air (~700 K), which provides film cooling to protect the metal from overheating and combustion byproducts.
Figure 2 High pressure shrouded (left) and unsrhouded (right) turbine rotor blades
The structure of shrouded and unshrouded turbine blades presents distinct advantages and disadvantages While shrouded blades enhance aerodynamic efficiency, they also introduce significant centrifugal stresses at the blade root due to the added weight, resulting in a lower rotational speed limit compared to unshrouded blades This limitation highlights the benefit of unshrouded blades, as work output is proportional to the square of the blade rotational speed according to the Euler turbine equation However, shrouded blades offer the advantage of reduced blade vibrations, making them beneficial in certain applications.
Tip leakage flow
To enhance turbine stage performance, it is crucial to reduce aerodynamic losses, particularly those caused by over the tip leakage flow (OTL) in rotor blades Minimizing these losses is vital for achieving optimal efficiency in turbine operations.
Figure 3 Illustration of tip leakage flow over a flat tip
Over the tip leakage (OTL) flow originates from the static pressure difference on either side of the rotor airfoil at its tip In this gap, the fluid is not deflected by the blade, resulting in no contribution to the stage's work output The fluid enters the gap on the pressure side of the rotor blade, then mixes with the core flow and forms a vortex Additionally, an outer passage vortex, created by the endwall boundary layer of the casing, interacts with the OTL vortex, as illustrated in Fig 4.
Figure 4 Outline of the flow in the region of an unshrouded turbine rotor blade
Recent research has focused on tip leakage flows in turbines, highlighting theoretical studies in this area Notably, Rain [1] has developed models to analyze the flow through the tip gap of an axial compressor, providing insights into the flow structure within these systems.
Moore et al investigated the impact of Reynolds number on the flow dynamics within the tip gap surface of a compressor Their research revealed that at high Reynolds numbers, significant flow separation occurs at the sharp edge of the blade, highlighting the critical relationship between flow characteristics and compressor efficiency.
Moore et al [2] calculated turbulence models for high Reynolds numbers ranging from 100 to 10,000 Bindon [3] identified the development of vortex formation along the blade from leading to trailing edge, detailing the measurement of tip clearance loss in a linear turbine cascade This study quantified the contributions of mixing, internal gap shear flow, and endwall secondary flow, revealing that only 13 percent of the total loss is attributed to endwall secondary flow, with 48 percent due to mixing and 39 percent from internal gap shear The dominant loss mechanisms are linked to gap separation bubbles Yamamoto [4] emphasized the significance of clearance gap size and cascade incidences in affecting these mechanisms, utilizing a micro five-hole pitot tube for detailed flow surveys Tallman and Lakshminarayana [5, 6] demonstrated that reduced tip clearance leads to decreased mass flow and aerothermal losses The incorporation of outer casing motion significantly alters the structure of aerothermal losses while maintaining overall loss levels Comprehensive studies by Prasad and Wagner [7], Stephan et al [8], Xiao et al [9], McCarter et al [10], and Blanco [11] have further explored these phenomena Sjolander [12] provided an overview of tip leakage flow and its impact on axial turbine stage performance, while Storer and Cumpsty [13] conducted investigations revealing that tip leakage flow and vortex formation are major loss sources in compressors Gao et al [14] examined the effects of casing contouring on the aerodynamic performance of an unshrouded turbine rotor, highlighting the influence of curved passages on secondary flows and vorticity distribution.
Over the tip leakage (OTL) flow in rotor blades is a significant contributor to turbine stage losses, accounting for more than one-third of the total losses At the trailing edge of each turbine blade, a phenomenon known as wake occurs, characterized by a momentum deficit in the flow field Meyer defined this wake as a negative jet directed at the trailing edge of the blade profile.
The present work investigated the performance of turbine “LISA” and the variation of rotor blade tip, using three-dimensional (3D) Reynolds-averages
Navier-Stockes (RANS) equations to find its effect on the aerodynamic performances.
Flat tip and squealer tip
In rotor blade manufacturing, flat tips are commonly used, prompting research into how different tip profiles affect turbine performance One effective design enhancement is the squealer tip, which minimizes losses by incorporating a specific profile This article will compare the performance of the flat tip and the squealer tip, as illustrated in Fig 5.
Figure 5: Rotor tip with flat and squealer show clearly the cavity squealer tip with a small figure at the tip region
The squealer tip method has been researched to enhance aerodynamic performance in compressor blades and to boost cooling capacity in turbine blades This project focuses on modifying the end tip configuration from a flat shape to a squealer shape, aiming to assess its impact on the vortex behavior within the turbine passage and to improve overall turbine performance.
9 case We will also evaluate the impact of this method on thermal performance in the later part of the study
NUMERICAL ANALYSIS
Turbine model Error! Bookmark not defined Turbine “LISA”
The turbine studied in this investigation is an axial annular turbine named
“LISA” This turbine was tested at the Laboratory for Energy Conversion (LEC)
The LISA facility at the ETH Zürich Institute in Switzerland features a continuously operating scaled subsonic turbine test rig that effectively releases generated power to a generator, maintaining stable operating conditions This setup enables steady-state turbine operation, achieving lower temperatures and flow velocities, which allows for the accurate use of intrusive measurement techniques.
Figure 6: Schematic view of LEC’s LISA research axial turbine
The air in the system circulates in a nearly closed loop, with an opening to the atmosphere at the turbine exit The mass flow rate through the compressor is adjusted using variable inlet guide vanes and is accurately measured by a calibrated venturi nozzle To regulate the turbine inlet temperature, the air is cooled in a water-cooled heat exchanger The turbine's rotational speed is precisely controlled by a DC generator, achieving an accuracy of ±0.1 rpm Key characteristics of the LISA turbine are outlined below.
Table 1 LISA research turbine facility controlling parameters
Compressor power 750 kW Turbine speed (max.) 3000 rpm
flow rate 6 to 13 kg/s Turbine inlet temperature 33 to 55 ⁰C Generator power 400 kW Turbine exit pressure Atmospheric
Working fluid Air Turbine tip diameter 800 mm
Therefore the measurement planes positions are defined as follows:
Where is the axial chord distance of the respective blade rows as demonstrated in Fig 7:
Figure 7 Sketch of the turbine first stage with the relevant dimensions :
At the position, there are measurement probes to mersure some characteristics needed
2.1.2 Stator and rotor blade geometry
Every blade has a different parameters, based on these parameters we design the turbine using design module ANSYS Design Modeler 19.1 Stator and rotor blade row is shown in Fig 8
Figure 8 Rotor blade (left) and stator blade (right) :
Figures 9 and [insert figure number] illustrate the stator and rotor profiles at three span sections, along with their pressure distribution during the designed operation The design parameters for both blades are detailed in Table 2 [10].
Figure 9 Stator blade geometric parameters and profile pressure distribution :
Figure 10 Rotor blade geometric parameters and profile pressure distribution : Tab 2 presents some design parameters of the rotor and stator blade:
Table 2 Design parameters of the first stage blades
Tip Midspan Hub Tip Midspan Hub Radius [m] 0.400 0.365 0.330 0.400 0.365 0.330
Axial chord length [mm] 49.61 49.71 49.82 43.41 46.83 50.08 Chord length [mm] 85.37 80.88 76.40 59.68 59.72 60.46 Pitch [mm] 69.81 63.70 57.60 46.54 42.47 38.40
Trailing edge thickness [mm] 1.21 1.30 1.38 0.98 1.10 1.28 Throat diameter [mm] 20.01 18.53 17.07 16.08 14.42 13.25
Based on these parameters, the geometry was designed by using ANSYS Design Modeler 19.1 as illustrated in Fig 11
Figure 11 Stator and rotor blade design in Ansys Design Modeler :
The design of the blades features a significant thickness at the leading edge, resulting in acceleration and deceleration on the front suction side, as shown in the pressure distribution profiles Both the stator and rotor profiles are aligned along radial lines that intersect the axis of rotation, with the stator positioned at its leading edge and the rotor aligned with its center of gravity to mitigate bending stresses caused by centrifugal forces during rotation.
The current design features distinct rotor and stator fillets, with a rotor hub fillet radius of 3 mm and a stator fillet radius of 2 mm, enhancing structural integrity and preventing operational damage These fillets also contribute to more accurate simulations by refining the flow phenomena, marking a significant improvement over the design presented in the validated paper by Blanco.
Figure 12: Conceptual view of rotor blade without squealer tip (WST) and with cavity squealer tip (CST)
The turbine geometry without a squealer tip (WST) features a turbine stage with 36 stator blades and 54 rotor blades operating at 2700 rpm, designed with a tip clearance of τ/b = 1% This study examines two geometric parameters of the cavity squealer tip (CST): the depth (h) and width (w) The experimental fillet radius for the stator and rotor blades was set at 2 mm and 3 mm, respectively, which is an enhancement over Blanco's design that did not consider these values The inclusion of fillets in the blade design aims to mitigate structural failure and damage, marking an improvement in the overall design Detailed design specifications for both the axial turbine and cavity squealer tip are provided in Tables 2 and 3.
Figure 13: Rotor blade with cavity squealer tip and fillet radius at the hub
The operating conditions at the turbine's design point, as outlined in Table 3 [9], will serve as the boundary conditions for the CFD analysis, with the results being compared to experimental measurements.
Table 3: Design specifications of cavity squealer tip
Table 4 Measured operating condition at turbine design
Pressure ratio (1.5 stages, total to static) [-] 1.60
Total inlet pressure [bar- absolute Norm] 1.405
Rotor tip clearance/ blade span ratio [%] 1.0
Pressure ratio (total to total) [-] 1.35
Blade row relative exit Mach number (average) [-] Stator 0.54
Numerical method
In general, the operating characteristics of a turbine, or turbine performance, can be deduced from two important parameters: total pressure ratio, adiabatic efficiency
Total pressure ratio is commonly calculated as follow:
17 in which, and are the total pressure at outlet and inlet of a turbine, respectively
The formula for turbine’s adiabatic efficiency is:
Adiabatic efficiency is determined by the temperature at the turbine's outlet and inlet, as well as the absolute pressure at both points The specific heat of the working air, particularly for ideal gases, plays a crucial role in this process At a constant rotational speed, the turbine's operating point adheres to a characteristic curve that illustrates the relationship between pressure decline and mass flow rate.
As the mass flow rate increases, the pressure ratio typically decreases There comes a point where the pressure increase is maximized, and any further rise in mass flow can result in instability.
Thermal performance of squealer tips is evaluated calculating average Nusselt number, , is given by:
(3) where kt is the thermal conductivity of the air and is average heat transfer coefficient Local heat transfer coefficient defined as,
(4) where is wall heat flux, Tw is wall temperature and Ti is total temperature at the inlet Average heat transfer coefficient, is defined as:
(5) where A is the area of the rotor blade While calculating the mass flow averaged total temperature at the inlet section
2.2.2The fundamental equations of fluid dynamics
Based on the conservation of mass, we obtain the continuity equation for the fluid flow [30] :
We apply the Newton’s 2rd law to a model of flow therefore we have the momentum equation [30]:
Since energy is conserved, we obtain the energy equation [30]:
The Navier-Stokes equations serve as the foundational equations for Computational Fluid Dynamics, rooted in the conservation laws of fluid properties These laws dictate that changes in physical attributes such as mass, energy, and momentum within a fluid are determined by the balance of inputs and outputs.
We obtain the Navier-Stockes equations in Cartesian coordinates ]: [30
Mathematical equations can effectively solve laminar flow problems with straightforward boundary conditions, such as Poiseuille and Couette flow However, in cases of viscous flow characterized by high turbulence, both velocity and pressure components experience temporal fluctuations.
In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity Nowadays turbulent flows may be computed using several different approaches:
The Reynolds-averaged Navier Stokes equations (RANS) –
The Reynolds-averaged Navier Stokes equations (RANS) are most popular – and widely used in calculating fluid flow The RANS equations are described below [30]:
To tackle the complexity of equations in Computational Fluid Dynamics (CFD), numerical methods are employed for calculations The process of solving CFD problems involves four key components: generating the geometry and grid, establishing a physical model, performing the computations, and post-processing the resulting data The methods for generating geometry and grids, computing the set problems, and presenting the acquired data are well-established in the field.
The K-epsilon (k-ε) turbulence model is widely utilized in Computational Fluid Dynamics (CFD) to simulate mean flow characteristics under turbulent conditions This model emphasizes the mechanisms influencing turbulent kinetic energy, represented by the first transported variable, k, while the second variable, ε, indicates the rate of turbulent dissipation, which determines the turbulence scale The K-epsilon model is particularly effective for free-shear layer flows with minimal pressure gradients and also performs well for wall-bounded and internal flows when the mean pressure gradients are small.
The K-omega (k-ω) model is a widely utilized turbulence model that incorporates two transport equations to capture the turbulent characteristics of fluid flow This two-equation framework effectively accounts for historical influences, such as the convection and diffusion of turbulent energy The model features turbulent kinetic energy (k) as the first transported variable, while the second variable is the specific dissipation rate (ω).
20 variable that determines the scale of the turbulence, whereas the first variable, k, determines the energy in the turbulence
The SST k-ω turbulence model, introduced by Menter in 1993, is a widely adopted two-equation eddy-viscosity model that effectively combines the strengths of both k-ε and k-ω formulations This model utilizes a k-ω approach in the inner boundary layer, allowing it to be applied directly to the wall without the need for additional damping functions, making it suitable for low Reynolds number turbulence simulations.
Therefore an ideal model should introduce the minimum amount of complexity into the modeling equations, while capturing the essence of the relevant physics
In order to validate the correctness of the model, the y-plus value was used
Y-plus is a non-dimensional distance It is often used to describe how coarse or fine a mesh is for a particular flow pattern It is important in turbulence modeling to determine the proper size of the cells near domain walls The turbulence model wall laws have restrictions on the y-plus value at the wall For instance, the standard K-epsilon model requires a wall y-plus value between approximately 300 and 100 A faster flow near the wall will produce higher values of Y-plus, so the grid size near the wall must be reduced The y-plus value is defined by:
Friction velocity is a crucial parameter in fluid dynamics, representing the shear stress within a specific layer of fluid It is influenced by factors such as fluid density, near wall distance, and dynamic viscosity, measured in kg/m·s Understanding these components is essential for analyzing fluid behavior near surfaces.
This study utilized the k-ω SST model to assess turbine performance, highlighting the importance of achieving a low y-plus value for optimal results A smaller y-plus, ideally approaching zero, enhances the accuracy of the SST model However, achieving this smaller y-plus necessitates a significantly reduced first grid size near the wall, which leads to a substantial increase in the overall mesh count.
21 elements Moreover, due to the possibility of computers are not so strong, SST model is used with y-plus less than 5.
The numerical calculations were performed using three-dimensional RANS equations with the SST k-ω model and mixing plane, utilizing the commercial CFD software ANSYS-CFX 19.1 The design of the stator, rotor blades, diffuser, and cavity squealer tip was accomplished with Design-Modeler® Mesh generation for the rotor, stator passages, diffuser domain, and cavity squealer tip domain was carried out using Turbo-Grid® and ICEM The analysis was conducted through ANSYS CFX-Pre and CFX-Solver.
The CFX-Post software was utilized to establish boundary conditions, solve governing equations, and post-process results in a computational domain divided into four sections: stator, rotor, cavity squealer, and exhaust diffuser The stator and annular diffuser domains remained stationary, while the rotor and cavity domains rotated at 2700 rpm Meshing employed hexahedral elements, with an O-type grid near the blades and H/J/C/L-type grids in other rotor and stator regions, created using Turbo Grid The diffuser and cavity squealer domains featured structured hexahedral meshes generated by ICEM Air was modeled as an ideal gas, consistent with conditions at the LEC LISA test facility, and specific boundary conditions were outlined in Tab 4 The inlet boundary conditions for the k-ω SST model were set with a Fractional Intensity of 0.01 and an Eddy Viscosity Ratio of 1, while periodic conditions were applied at the computational domain's side boundaries The General Grid Interface (GGI) method facilitated connections between the stator and rotor domains, as well as between the rotor and diffuser The rotor pitch angles were set at 6.6667° for the rotor and 10° for the stator at their interface, and the SST k-turbulence model was employed, maintaining ω values near the walls at a maximum of 5.
The computational domain is divided into three distinct parts: the stator domain, the rotor domain, and the exhaust diffuser domain The stator remains stationary, while the rotor operates at a rotational speed of 2700 rpm, and the annular diffuser is also stationary.
Meshing
The mesh of stator computational domains was created using TurboGrid, illustrated in Fig 14 Hexahedral elements were used to mesh the rotor and stator blocks
The number of nodes and elements for stator domain are 519456 nodes and
The turbine stator stage consists of 36 blades, but for efficiency in reaching a steady-state solution, only one blade with a 10˚ pitch is modeled The stator interfaces with the downstream rotor domain using either a "Mixing plane" or "Frozen rotor" approach, depending on the specific case.
Figure 14 3D mesh of the stator blade :
The mesh of rotor computational domain was generated using Turbo Grid, illustrated in Fig 15 As with the stator domain, the hexahedral cells were used to mesh the rotor block
Figure 15: 3D mesh of rotor blade
The number of nodes and elements for rotor domain are 796510 nodes and
The turbine rotor stage consists of 54 blades, but for efficiency in achieving a steady state solution, only one blade with a pitch of 6.67˚ is modeled Similar to the stator/rotor interface, the rotor is linked to the downstream diffuser domain through a "Mixing plane" or "Frozen rotor" interface, facilitating the connection between the stator, rotor, and diffuser.
The diffuser domain utilizes a structured grid composed of hexahedral cells, created using the meshing software ANSYS ICEM CFD v19.1, which is part of the ANSYS CFX package The meshing process involved a 2D profile that was extruded around the axis of rotation to generate the 3D domain, as illustrated in Fig 16.
For practical reasons, especially when performing unsteady computations, the entire diffuser domain is split in 36 parts with a circular pitch of 10˚ in circumference, the same as the stator row domain
It is important that the mesh near wall is properly sized to ensure accurate simulation of the flowfield
Figures 17 and 18 illustrate the computational domain of the turbine stage, featuring mirrored blocks of the stator, rotor, and diffuser around the rotational axis to offer a comprehensive view of the turbine stage.
Figure 17: The computational domain of turbine with WST
At the stator inlet, we set up boundary conditions, air characteristics The stator domain is stationary, the rotor domain rotate with a speed of 2700 rpm The diffuser is stationary
Figure 18 : 3D mesh of the computational domain with CST
Figure 19: Complete computational domain when mirrored around the rotational axis
When mirror the whole parts around the rotational axis, we obtain a turbine stage as Fig 19.
Boundary conditions
The working fluid was considered as 100% air, which is the same gas as the one used at the LISA test stand of LEC
The gas thermodynamic properties utilized are summarized in Tab 5 [9]:
Table 5 Thermodynamic properties of the gas used in the CFD analysis 100% air, at a pressure ref of 1.013 bar and temperature ref of 298.15 K
Heat capacity at const pressure (Cp) 1004.4 J/(kg.K)
Fluid model Total energy in Heat transfer
The boundary conditions used in this investigation are specified in Tab 6 [9]:
Table 6 Boundary conditions in CFD analysis
Inlet conditions Inlet total pressure 1.405 bar
Inlet total temperature 328.0 K Inlet turbulence intensity [-]
Outlet conditions Mass flow rate Variable
Interface between stator and rotor 1/ Mixing plane
2/ Frozen rotor Interface between rotor and diffuser 1/ Mixing plane
Interface at rotor tip gap G GI
The setting of the inlet boundary conditions for the k-ω SST model is
“Intensity and Eddy Viscosity Ratio” with the Fractional Intensity is 0.01 and the Eddy Viscosity Ratio is 1 The turbulence intensity is used to estimate the initial
27 turbulent kinetic energy k, and the viscosity ratio to calculate the specific dissipation ω.
Convergence criteria
To ensure high simulation quality, key convergence parameters include outlet and input mass flow rates, total pressure ratio, and adiabatic efficiency A deviation of less than 0.5% between inlet and outlet mass flow rates, along with an adiabatic efficiency variation of less than 0.3% over 100 steps, is required For simulations near peak efficiency, 1000 interactions are necessary, while 3000 interactions are needed for near stall conditions.
RESULTS AND DISCUSSIONS
Grid dependency test and validation
A mesh dependency study was conducted for a case without a cavity squealer tip, featuring a tip clearance of τ = 1% The results were analyzed and compared with the initial design parameters shown in Table 7, under a flow rate of 11.7 kg/s and a pressure ratio of 1.35 Table 7 details the number of elements and the calculated pressure ratio As the number of elements increased from Mesh 1 to Mesh 4, the discrepancy between numerical and experimental pressure ratios diminished Given the minimal differences between Mesh 3 and Mesh 4, Mesh 3 was selected for further calculations to optimize computation time For Mesh 3, the averaged y+ value is 0.8629, and the SST model shows a blade value of less than 5, indicating that the results' accuracy is satisfactory for subsequent computations.
Table 7 : Mesh dependency test results
Figure 20: Mesh dependency test results a) Mesh 1 b) Mesh 2 c) Mesh 3 d) Mesh 4
Figure 21: contours on stator and rotor blade for Mesh 1 to Mesh 4
The results were analyzed using ANSYS CFX-Post, employing a "Frozen rotor" interface between both the stator and rotor, as well as the rotor and diffuser The mass flow rate was established at 11.7 kg/s, and the blade configuration utilized was WST.
At a given rotational speed, the turbine operating point follows a characteristic line in pressure rise versus mass flow rate It is common that when
As the mass flow rate increases, the pressure ratio also rises until a maximum point is reached, beyond which further increases in mass flow can lead to instability Operating the turbine past this limit may result in detrimental conditions such as rotating stall, characterized by a significant drop in pressure rise, or surge, marked by violent flow oscillations These phenomena can severely impact the turbine's efficiency, pressure ratio, and structural integrity.
With variable mass flow rate in diffuser outlet, we receive a diagram of total pressure ratio and adiabatic efficiency
In Fig , two speed line of the turbine performance map are calculated The 22 Blanco’s results and one measured operating point are given for comparison [10]
Fig 22 shows the numerical performance curves of the total pressure ratio and the adiabatic efficiency for the single stage axial turbine
The analysis presented in Figure 22 compares the measured points and computed total pressure ratios across two interface cases alongside Blanco's computed results As detailed in Table 8, the pressure ratio values for these cases were evaluated at a consistent mass flow rate of 11.7 kg/s.
Table 8 Pressure ratio compared to Blanco’s results and measured point
Mixing plane Frozen rotor Blanco’s numerical results
The total pressure ratio peaks at different mass flow rates, with the Mixing Plane interface achieving a maximum of 13.815 kg/s before stall, compared to 13.74 kg/s for the Frozen Rotor interface Below a mass flow rate of 4 kg/s, turbine performance becomes unstable At 11.7 kg/s, the computed total pressure ratios are 1.362 and 1.371, closely aligning with the measured value of 1.35 This indicates that the computed ratios are in good agreement with experimental data at that flow capacity As the turbine chokes, the local flow becomes supersonic, and further increases in pressure ratio occur through a series of expansion waves The Mixing Plane case demonstrates a lower pressure ratio but supports a higher mass flow rate before stall, suggesting that the movement equations were effectively solved and the phenomena were accurately simulated.
The pressure ratio tolerance in “Mixing plane” connection:
The pressure ratio tolerance in “Frozen rotor” connection:
The total pressure ratio variation is quite small so the simulation method is acceptable
Fig 23 shows the adiabatic efficiency curve in two cases:
Figure 23: Measured point and computed adiabatic efficiency compare two interface cases
Tab 9 shows the peak and stall point in efficiency of turbine stage compared two cases:
Table 9 Maximum efficiency and stall point of turbine stage
CFD simulation values slightly exceed Blanco's results and measurements, particularly with a total pressure ratio peak of 2.52 and 2.48 compared to 2.11 This discrepancy may arise from factors such as steady-state computations versus unsteady measurements or turbulence modeling Additionally, the "fillet" designs appear to positively influence simulation outcomes The data indicates that as the mass flow rate increases, the total pressure ratio rises until the turbine reaches choking conditions.
Pressure, velocity and temperature contours
The following result from the 11.7 kg/s mass flow rate case, “Frozen rotor” interface are chosen between stator and rotor, rotor and diffuser.
Figure 24 illustrates the static pressure contours of both the stator and rotor at the mid-span plane, clearly distinguishing between the suction and pressure sides of the blades.
Figure 24: Static pressure contour of the stator and rotor at the mid-span plane
Figure 25 displays the relative Mach numbers between the blades in both rows, revealing that high Mach number areas align with low pressure zones and vice versa The fluid accelerates through the passages, reaching its peak at the throat of each channel Following the throat, there is a slight pressure recovery on the suction side of the blades, attributed to their geometric curvature.
Figure 25: Relative Mach number of the stator and rotor at the mid-span plane
Figure 26 illustrates the total pressure and entropy at the stator's outlet plane A noticeable deficit in total pressure and an increase in entropy are evident at the blade's trailing edge, indicating the wake region characterized by turbulence following flow separation Additionally, the presence of two passage vortices near the stator is highlighted.
34 hub and casing and connected to the stator wake on the suction blade side are appreciated
Figure 26: Total pressure and Static entropy at the outlet plane of the stator
Fig 27 represents the total pressure (left) and the static entropy (right) at the outlet plane of the rotor:
Figure 27: Total pressure and Static entropy at the outlet plane of the rotor
Three secondary flow structures can be identified in this context: the two passage vortices and the over-the-tip leakage vortex, all of which are linked to the rotor blade wake The over-the-tip leakage vortex notably influences the tip passage vortex, while the vortex generated from the rotor clearance contributes significantly to losses, thereby reducing turbine performance Additionally, a momentum deficit in the flow field, known as the wake, occurs at the trailing edge of each turbine blade, characterized as a negative jet directed at the blade profile's trailing edge, as defined by Meyer [18].
In Fig 28, static temperature on the surface of the blades and hub are shown:
Figure 28: Temperature contour on the surface of stator and rotor blades
Certain regions exhibit higher temperatures due to heat generated by passage vortices and tip leakage vortices As these vortices reach the rotor blade's trailing edge, they lift off the end walls, highlighting their interaction with the blade surface and demonstrating their intensity Notably, the tip leakage vortices are larger and possess greater intensity compared to the other vortices.
The contour of static pressure at the rotor's end wall reveals a significant pressure gradient on either side of the blade near the trailing edge, which influences fluid movement through the clearance and leads to the generation of over tip leakage.
Figure 29: Static pressure contour at the end wall of the rotor
The recirculating fluid trapped in the separation bubble located at the rotor blade tip corner in the pressure side was captured in the numerical simulation as
36 seen in Fig 29 This phenomenon was also captured in the turbine teststand as the visualization of oil deposits on the rotor blade tip confirm in Fig 30
Figure 30: Flow visualization of the recirculation bubble over the rotor tip surface
Table 10 summarizes the flow angles calculated at the inlet and outlet locations Under normal conditions, a lower flow angle indicates more effective thrust at the diffuser outlet For the compressor, the flow angle is approximately 10 degrees This calculated flow angle demonstrates that the turbine achieves efficient thrust following the diffuser.
Table 10 Flow angle at the inlet and outlet locations
Quantity Inlet Outlet Out- In
Effect of tip cl earance
This section evaluated the effects of blade tip clearance on the performance of a turbine by modifying the tip clearance belongs to the rotor blade
The boundary conditions were set with the same case as interface between the blocks was set to ‘Frozen rotor’.
In this study, the rotor tip was adjusted to 0.07 cm, while the shroud tip was varied across five different cases, set at 0.5%, 1%, 1.5%, 2%, and 2.5% of the blade diameter.
Table 11 Values of tip clearance investigated and computed adiabatic efficiency
Mass flow rate at peak efficiency (kg/s) 8.55 8.53 8.61 8.62 8.67
Fig 31 and Fig 32 present the efficiency curve at different tip clearance:
Figure 31: Peak efficiency at different rotor blade tip clearance
Figure 32: Efficiency at mass flow rate of 11.7 kg/s
As previous research, the tip leakage vortex increase when the tip clearance increases
To optimize efficiency, a tip clearance limit of 2.5% was established, as exceeding this threshold significantly increases losses The tip clearance is influenced by the mechanical constraints of the turbine blades, with heat and centrifugal forces causing rotor blade expansion that ultimately restricts the tip gap.
Reduce tip leakage flow using squealer tip
Tip leakage due to tip clearance is identified as the primary contributor to turbine efficiency loss To address this issue, we implemented a recessed tip design on the blade surface, which features a concave profile achieved by compressing the blade tip This design maintains dimensions expressed as a percentage of blade height for ease of calculation.
The distance to the tip margins (w) is 1%, 0.75%, 0.5% and 0.25%
As shown in Fig 33, two parameters are described:
Figure 33: Squealer tip parameters After calculating 7 cases, we obtain T 12 which compare performance at ab mass flow rate of 11.7 kg/s:
Table 12 Aerodynamic performance at different cases
Fig 34 shows the pressure contour (left) and the static entropy contour (right) at the rotor outlet plane:
Figure 34: Pressure and Static entropy contour at the rotor outlet plane
The analysis of the squealer tip reveals a reduction in the low-pressure area, signifying decreased wing tip losses Furthermore, the three regions of losses are now more evenly distributed, and the intensity of the swirl at the tip has diminished These findings demonstrate the effectiveness of the squealer tip design in minimizing vortex and tip losses.
In the case of non-recessed designs, the performance values indicate a tip value of 84,443 and a pressure ratio of 1.36 When compared to other configurations, it is observed that the pressure ratio in most instances is slightly lower at 1.35 than that of the squealer tip design.
In all cases, the performance value is greater than the value when the tip is
flat This minimizes the probability of concluding that the simulation results deviate from the error of simulation
Performance values in cases of slight variation Maximum value is obtained in case w/τ [%] = 1 and 00 h/τ [%] 25 6,743%) = (8
Effects of the squealer tip on aerothermal performance
Table 13 outlines the numerical findings related to total pressure ratio, adiabatic efficiency, Nusselt number on rotor blades, and leakage flow rate ratios for various cavity squealer tip configurations Notably, the introduction of the squealer tip significantly reduces leakage flow rates compared to scenarios without it Figure 35 further elucidates the impact of cavity squealer tip depth (h) and width (w) on the aerothermal performance of the LISA turbine The results indicate that an increase in cavity squealer tip depth leads to a decrease in total pressure ratio and average Nusselt number on the rotor blade, while adiabatic efficiency improves Conversely, increasing the cavity squealer tip width enhances both total pressure ratio and average Nusselt number, but results in a decline in adiabatic efficiency The presence of tip leakage flow contributes substantially to aerodynamic losses Additionally, Figure 35(d) illustrates that the rotor leakage mass flow rate decreases with greater cavity squealer tip depth, whereas it increases with wider cavity squealer tips.
Table 13: Effect of cavity squealer on aerodynamic and aerothermal performances for
(c) Averaged Nusselt number on the rotor blade
(d) Tip leakage mass flow rate
Figure 35: Aerothermal performance of LISA turbine with cavity squealer tip
Figure 36 Distribution of temperature [K] on the stator blade a) WST b) w100h50 c) w100h100 d) w100h150 e) w100h200
Figure 37: Pressure [Pa] contours on the shroud casing of rotor blade without squealer and with w/τ = 100%
The minimal variation in the rotor tip cavity geometry leads to comparable effects on the stator blade across all cases As illustrated in Fig 36, the airflow striking the leading edge (LE) of the stator blade results in the highest temperatures in those areas, which subsequently decrease progressively.
In the absence of a squealer tip, low-pressure areas are evident on the shroud casing, as illustrated in Fig 37 As the height of the cavity increases, the static pressure on the shroud casing also rises The presence of the squealer cavity gradually reduces these low-pressure areas, compensating for the initial deficiency.
44 of this air shortage This drop in pressure can be contributed to the resulted fast velocity of the air flow through the gap
Figure 38 illustrates the streamlines of leakage flow with a fixed squealer width at w/τ = 100% and varying heights h/τ of 50%, 100%, 150%, and 200% The incoming flow enters at the leading edge, traverses the squealer rim, and is directed into the cavity As the squealer height increases, the cavity volume expands, resulting in larger and more pronounced cavity vortices before exiting through the tip gap After leaving the gap, the leakage flow divides into two main streams, characterized by a significant vortex with high turbulence, as indicated by the pink areas in the figure Generally, increasing the height while reducing the width of the squealer leads to relatively larger cavity vortices This expansion of cavity volume creates multiple eddy structures that obstruct airflow from the pressure side to the suction side, effectively reducing the tip leakage mass flow rate.
Figure 38: Streamline through the tip clearance of rotor blade with w/τ 0% a) w100h50 b) w100h100 c) w100h150 d) w100h200
Figure 39: Static entropy contours on the blade with w/τ = 100%
Tip leakage flow significantly contributes to aerodynamic losses and enhances convective heat transfer on the blade tip platform exposed to hot gas streams This leakage flow, occurring between the stationary turbine casing and the rotor surface, leads to notable aerothermal performance degradation The Nusselt number distribution on the blade tip, depicted in Fig 40 for a fixed squealer height, reveals the formation of a local high heat transfer region due to intrusion Increasing the squealer height enlarges the cavity vortex, which subsequently decreases thermal transport in both the encroachment zone and the high heat transfer region Consequently, extending the cavity vortex limits the boundaries of the high heat transfer area beneath.
Figure 41 illustrates the Nusselt number distribution on the blade tip as a function of squealer height, revealing that a reduction in squealer height improves heat transfer at the blade tip, where leakage flow exits the tip gap without reattachment The Nu contours indicate a significant heat transfer region on the top surface of the squealer rim, particularly near the leading-edge zone, which exhibits a peak Nusselt number of approximately 950 This high thermal zone extends further along the leading edge as the rim width increases from 50% to 200% However, wider squealer rims may experience increased thermal loads and oxidation in these high heat transfer areas.
Research indicates that increasing the height of squealers on cavity floors leads to a reduction in the average heat and mass transfer rates, as demonstrated by Kang and Lee in their linear cascade experiments Additionally, Zhou and Hodson's numerical study revealed that decreasing the width while increasing the height of squealers results in a lower average heat transfer coefficient Our numerical analysis further explores the thermal performance of squealer rims across various width and height dimensions, with results presented in Table 6 and Figure 8, highlighting the variation of the Nusselt number on the rotor blade The findings show that reducing squealer width and increasing height significantly lowers the Nusselt number, aligning well with the previous studies by Kang and Lee and Zhou and Hodson.
Figure 40: Nu contours on the blade with h/τ= 150% b) w200h100 a) w200h50 c) w200h150 d) w200h200
Figure 41: Nu contours on the blade with w/τ = 200%
Due to time constraints and limited computational capabilities, the number of cases that can be analyzed is quite small To gain a clearer understanding of the impact of this change, it is essential to evaluate a larger number of cases.
Conclusion and future work Conclusion
The investigation analyzed the impact of squealer tip dimensions on the aerodynamic and aerothermal performance of an axial turbine through numerical analysis The study utilized stator and rotor blades resembling those of an axial annular turbine Findings showed that numerical results aligned with initial predictions and experimental data, indicating that this passive control system enhances aerodynamic and aerothermal efficiency Notably, increasing the height of the squealer tip improved adiabatic performance, while reducing the width of the squealers led to a decrease in adiabatic performance, although it remained superior to configurations without a squealer tip.
Numerical methods have been developed to simulate and evaluate the performance of axial turbines The study has achieved some results as follows:
Determine the effect of the blade tip gap on the efficiency of an axial turbine
As the gap increases, turbine efficiency significantly decreases, with the smallest gap of 0.5% achieving the highest efficiency of 93.46%, which is 1.81% greater than the standard clearance efficiency of 91.65% Additionally, the turbine's vortex zones are influenced by the distributions of pressure, static entropy, and temperature.
The research explored the impact of recessed tips on turbine performance, revealing an overall increase in turbine efficiency across all cavity profiles examined The most significant improvement was observed in the case with w/τ = 100 and h/τ [%] = 25 Despite this enhancement, the specific governing laws were not analyzed Additionally, the study found that the reduction of the over-the-tip vortex contributed to decreased losses when compared to flat tips, as evidenced by the pressure and static entropy distribution.
The study examined the impact of adding current to the tips of rotor blades on turbine performance Results indicated that both single-tube and three-tube flow configurations yielded higher efficiency compared to flat tips, although performance was lower than that of squealer tips.
The optimal survey of tip configurations was conducted on the "LISA" turbine, as well as on a compressor and an aircraft turbine By analyzing the impact of the squealer tip on turbine efficiency, we further explored additional parameters of the cavity squealer design and investigated new shapes for the cavity.
To enhance the thermal effectiveness of the axial turbine, additional cool air flow can be supplied to the cavity squealer tip via pipes within the rotor blades While this modification improves efficiency, it is crucial to assess how it affects other performance metrics of the turbine, ensuring that the overall performance remains stable despite changes in efficiency.
A total area of rotor blades [m 2 ]
C chord length of rotor blades [m]
The axial chord length of rotor blades is measured in meters (m), while the rotor blade span is also expressed in meters (m) The local heat transfer coefficient is denoted as h0, with an averaged local heat transfer coefficient represented as h Thermal conductivity is indicated by kt, measured in watts per meter per Kelvin (W/(m.K)) Additionally, the leakage mass flow rate is quantified in kilograms per second (kg/s), alongside the inlet mass flow rate, which is similarly measured in kilograms per second (kg/s).
Nu Nusselt number averaged Nusselt number on rotor blade
PR pressure ratio p pressure [Pa] p t total pressure [Pa] wall heat flux [W/m 2 ] h squealer height or cavity depth [m]
Ti averaged temperature at inlet [K]
Tw wall temperature [K] w squealer width [m] dimensionless wall distance maximum dimensionless wall distance η adiabatic efficiency [%] τ tip clearance rotor blade [m]
WST without squealer tip (or flat tip)
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