Cascade Flow Research Articles

Effect of Local Concave Non-axisymmetric Endwall Profiling on Endwall Secondary Flows of a Highly-Loaded Turbine Cascade

Effect of Local Concave Non-axisymmetric Endwall Profiling on Endwall Secondary Flows of a Highly-Loaded Turbine Cascade

Shock waves characteristics and losses estimation of non-equilibrium condensation flow in nozzle and steam turbine cascade

The investigation of transonic non-equilibrium condensation is paramount due to its profound influence on the shock patterns and the distribution of losses. This study numerically investigates the shock wave morphology, evolution, and quantitative loss calculation under the influence of non-equilibrium condensation within the Moses-Stein nozzle and Dykas cascade. The results indicate that the vapor near the nozzle wall undergoes phase transition first and forms “X-shaped” condensation shock, which impervious to back pressure variations. Conversely, the “λ-shaped” aerodynamic shock moves towards the throat with increasing back pressure, triggering boundary layer separation. The entropy generation of “λ-shocks” accounts for over 98% and represents the primary source of shock losses. Strong pressure side shock induces shock wave-boundary layer interactions with the blade suction wall, resulting in reflected shocks. However, the latent heat released by non-equilibrium condensation mitigates this effect, increasing the total pressure loss coefficient by 0.188. The decrease in Mach number under high back pressure causes a notable increase in the trailing edge shock angle, with the wave foot shifting upstream. Notably, the proportion of shock losses attributed to the suction side of trailing edge exceeds 80%, significantly surpassing other regions, which progressively increases with rising back pressure. Therefore, it is crucial for cascade optimization. The findings can provide references for the optimization design of low-pressure steam turbine blade profiles. The results can serve as a guide for optimizing the blade profiles of low-pressure steam turbine.

Research on compressor cascade flow field modeling method based on finite volume flux-informed neural network

For compressor cascade flow field modeling, there exists strong velocity shear in the leading edge separation flow, boundary layer, and wake, which leads to increased modeling errors. To improve the accuracy of the flow field modeling method, this paper introduces the concept of numerical flux from the finite volume method into the loss function to implement Euler equation physics-informed learning, and a finite volume flux-informed neural network (FVFI-net) is constructed. Selecting a high-load, large-turning-angle compressor cascade as the study object, a comparative analysis is conducted on the advantages and disadvantages of purely data-driven, weak physical constraint, and finite volume flux-informed methods in compressor cascade flow field modeling. The study found that compared to purely data-driven and weak physical constraint methods, FVFI-net can reduce the average error of aerodynamic parameters in the flow field by approximately 45.6% and 29.5%, respectively, at a 0° angle of attack. For the flow separation problem occurring at the suction side leading edge and the blade wake area caused by a 5° angle of attack, FVFI-net can effectively reduce modeling errors near the leading edge, in the wake region, and near the periodic boundaries, thus reducing the average error of the aerodynamic parameters of the flow field by about 49.2%and 31.3%, respectively, compared to pure data-driven and weak physical constraint methods.

Flow field reconstruction of compressor blade cascade based on deep learning methods

In the design process of compressors, calculating the S1 flow surface involves solving the Navier-Stokes equations, which results in slow convergence and makes determining cascade characteristics time-consuming. However, deep learning offers significant advantages in flow field reconstruction by not only automatically extracting complex flow features and reducing prediction time but also providing high accuracy in reconstruction. This paper implements the rapid reconstruction of the compressor S1 flow surface cascade flow field using two deep learning models: U-Net and 1D-CNN. Using a double-circular arc airfoil as an example, we selected four key design parameters that define the geometry and position of the airfoil, ultimately designing 5,292 sets of cascade geometries. By performing batch meshing and CFD simulations, we built a cascade flow field dataset. The U-Net neural network uses design parameters as input and outputs the aerodynamic distribution of the cascade flow field. After training, it can directly predict the flow field based on the design parameters. Since the U-Net model cannot directly obtain the aerodynamic parameter distribution and flow field aerodynamic coefficients on the airfoil surface, a 1D-CNN model is used as a complementary approach. The 1D-CNN model takes the design parameters as input and outputs the aerodynamic parameter distribution on the airfoil surface and the flow field aerodynamic coefficients. The prediction results show that the U-Net model achieves an average relative error of less than 1% in cascade flow field reconstruction, while the 1D-CNN model achieves an average relative error of less than 1% in predicting the pressure recovery coefficient and less than 2% in predicting the total pressure loss coefficient. This study presents a method for the rapid reconstruction of compressor blade cascade flow fields, which helps improve design efficiency and shorten the design cycle.

Position query-guided cross-modal flow field prediction model of a transonic compressor cascade

The gradient of flow parameters in a transonic compressor cascade flow field varies significantly, especially in the region of shock waves, which causes a significant challenge to its high-precision flow field prediction. In this study, the position query-guided cross-modal flow field prediction model (PGCM) is proposed to effectively predict the flow field parameter distribution of a transonic compressor cascade. The PGCM utilizes the self-attention mechanism for the global and deep geometric feature extraction of configurations, which contributes to an in-depth understanding of the spatial relationships between coordinate points within the flow field, accurately capturing and analyzing the structural complexity of a compressor cascade flow. In addition, the PGCM integrates the cross-attention mechanism that establishes correlations between different input sequences, which enhances the performance of the model in querying and interpreting flow parameters at specific coordinates. The flow field prediction models are developed to predict the flow parameter distributions of different cascade geometries at Mach numbers of 0.78 and 0.93, respectively. The validation results indicate that the PGCM performs significantly better than the existing convolutional neural network and vision transformer, especially in the prediction of the pressure coefficient Cp distribution. The PGCM is adaptable to the variation of flow conditions and geometrical configurations efficiently and accurate in predicting the flow field of a compressor cascade. This paper demonstrates the promising potential of conducting the multi-modal information fusion to enhance the capability of flow field prediction.

Numerical simulation on energy characteristics of pump-turbine under pump condition

Abstract To investigate the energy characteristics of the pump turbine in pump mode, we selected the pump turbine as the research object and employed the SST k-ω turbulence model to conduct three-dimensional steady numerical simulations of the internal flow field of the pump turbine under several typical flow conditions. Our findings indicate that the unit’s energy loss is primarily concentrated in the runner and guide vane areas. In the small flow condition area, the energy loss of the draft tube basin cannot be ignored, while the energy loss in the stay guide vane and spiral casing areas is relatively small due to their low flow velocity. As the flow rate decreases, the energy loss in the draft tube, runner, and guide vane areas increases continuously. Additionally, complex flows such as vortex flow and backflow appear in the double-row cascade flow channel, which obstructs the flow channel and increases dissipation energy. In typical flow conditions, the energy loss in the draft tube, runner, and guide vane areas is a significant factor contributing to the decrease in head.

Fluid–acoustic–structure resonance mechanism of a plane cascade via a low-speed wind tunnel test

Acoustic resonance is an important factor that contributes to aeroengine compressor failure. In this study, a plane cascade of compressor blades was designed to reproduce acoustic resonance via a low-speed wind tunnel test. A high-frequency hot-wire, microphone and strain gauge were used to synchronously measure the fluid, acoustic and structural parameters. We analysed the variation in the amplitude and frequency of the multi-field parameters with increasing mean flow velocity and explored the multi-field interaction mechanism that induces the acoustic resonance of the plane cascade. The plane cascade effectively reproduced the acoustic resonance phenomenon. The first-order acoustic-mode frequency of the plane cascade flow duct, second-order torsional vibration mode frequency of the blade and shedding mode frequency of the tip clearance leakage vortex were equal under acoustic resonance. The fluid, acoustic and structural fields showed a strong interaction effect, achieving the maximum blade vibration amplitude and causing fatigue cracks of torsional vibration at the blade root. The frequency lock-in region of the compressor plane cascade was divided into an ‘acoustic–structure’ interaction region, a ‘fluid–acoustic–structure’ interaction region and a first-order acoustic-mode dominant region with increasing mean flow velocity, which demonstrates an interesting phenomenon in which the fluid–acoustic–structure modes compete: acoustic mode > blade vibration mode > vortex shedding mode. The results demonstrate a unique approach to the study of acoustic resonance that provides insight into the acoustic resonance mechanism in a cascade of compressor blades.

Investigation of irreversible losses in subsonic compressor cascade flow field: A study on viscous dissipation and temperature gradient term in entropy production rate

The entropy generation rate is a widely employed loss characterization approach in the design and optimization of fluid machinery. This approach is utilized to quantitatively determine various types of losses in the flow field, and it is considered that the temperature gradient term in the entropy generation rate can characterize irreversible losses. This research paper aims to address the question of whether the temperature gradient term in entropy production rate can represent the irreversible losses in a flow field. By employing the Reynolds-Averaged Navier-Stokes (RANS) numerical simulation method, the flow field of a subsonic compressor cascade, both with and without wall heating, was investigated. Statistical analysis was conducted to examine the contributions of viscous dissipation, the temperature gradient term in entropy production rate, wall shear stress work, and global power loss. The study reveals the distribution differences of viscous dissipation and the temperature gradient term in entropy production rate within the separated flow region. The research results demonstrate that, under wall heating conditions, viscous dissipation increased by approximately 45%, and the ratio of the temperature gradient term to global power loss increased from 4% to 125%, exceeding the mechanical energy loss in the flow field. The distribution of the temperature gradient term within the separated flow region cannot be explained by irreversible losses, and it exhibits significant discrepancies with the distribution of viscous dissipation losses. Therefore, the temperature gradient term in entropy production rate cannot represent the local irreversible losses, whereas viscous dissipation serves as an accurate measure of local irreversible losses. The research results provide theoretical support for accurately determining the irreversible losses in the flow field.

Numerical investigation of tip bifurcation on aerodynamic characteristics and flow field structure in a compressor cascade

In this study, the tip bifurcation of the compressor cascade is proposed, referring to the biological characteristics of bird wing bifurcation. The influence of tip bifurcation with different structural parameters on the aerodynamic performance and flow field structure of compressor cascade at different incidence angles is studied by numerical simulation. The research shows that the tip bifurcation can make the starting position of the corner separation move backward, inhibit the separation along the pitch and blade height direction, and reduce the flow loss of the cascade. The separation control effect of the corner region first increases and then decreases as the bifurcation height increases, and gradually diminishes as the arrangement position approaches the trailing edge. When the tip bifurcation is set at the starting position of the corner separation and its height is equal to 4 %H, the flow improvement effect in the passage is the most obvious, and the cascade flow loss is reduced by 14.4 %. At the same time, the tip bifurcation cascade has effective positive incidence angle characteristics, but when the incidence angle is less than the minimum loss incidence angle, the tip bifurcation increases the cascade loss.

Numerical Study on the Influence of Inlet Turbulence Intensity on Turbine Cascades

The turbulence intensity of the high-pressure turbine inlet plays an important role in the development of secondary flow and boundary layer evolution in the turbine passage. Unfortunately, current research often overlooks the coupling effect between boundary layer separation and endwall secondary flow, and lacks comprehensive exploration of loss variation. To complement existing research, this study utilizes numerical simulation techniques to investigate the evolution of the boundary layer and secondary flow in high-pressure turbine cascades under varying turbulence intensities, with experimental research results as the basis. Furthermore, the relationship between profile loss and endwall secondary flow loss is analyzed. The research results indicate that higher turbulence intensity can enhance the anti-separation ability of the boundary layer, thereby reducing the blade profile loss caused by separation in the boundary layer. However, higher turbulence intensities (Tu) enhance the development of secondary flow within the cascade, leading to a significant increase in secondary flow losses. Q-criterion methods are employed to display the vortex structures within the passage, while loss decomposition is leveraged to uncover the variations of different losses under different turbulence intensities (Tu of 1% and 6%).With the exception of a minor decrease in total pressure loss (Yp) when Tu increases from 1% to 2%, Yp demonstrates a substantial increase in all other cases with increasing Tu. Additionally, this study explains why the loss of high-pressure turbine cascades shows a trend of first increasing and then decreasing with the increase in inlet turbulence intensity.

The Unsteady Shock-Boundary Layer Interaction in a Compressor Cascade – Part 3: Mechanisms of Shock Oscillation

Abstract The shock-boundary layer interaction in transonic flows is known to cause strong unsteady flow effects that negatively affect the performance and operability of blade and cascade designs. Despite decades of research on the subject, little is still known about the physical mechanisms that drive the different oscillation frequencies observed with different designs. In the conclusion of this three-part series, the experimental and numerical data obtained with the Transonic Cascade TEAMAero are analyzed together in detail in order to test the main theories of continuous shock oscillation. This analysis exposes a main mechanism of shock oscillation, where pressure waves generated inside the passage of the cascade propagate upstream and interact strongly with the main shock when the latter is also in the passage. The interaction of these features causes a breakdown of the flow that is shown to propagate upstream, inevitably causing strong variations in the inflow angle and therefore on the operating conditions of the cascade. The high frequency content of these pressure waves is also shown to be responsible for weaker high-frequency variations of the shock movement throughout the cycle. Parallels are also drawn with previous experimental campaigns in order to search for a global understanding of the different observations made. Although various parts of the described interaction are not fully understood yet, and the dataset of experimental measurements compiled is still rather small, a good basis is provided on which to further study the underlying mechanisms of unsteady flows in transonic cascades.

Enhancing Aerodynamic Performance of a Non-Axisymmetric Endwall Contoured Cascade Through Section Profiling Method

Abstract Endwall contouring and 3D blade configurations are effective techniques for enhancing turbomachinery performance. The integration of these technologies is an important area of investigation. To continue the numerical and experimental validations of the non-axisymmetric endwall contoured cascade (Du et al., 2024, “Endwall Contouring for Improving Aerodynamic Performance in a High-Pressure Turbine Cascade,” ASME J. Turbomach., 146(10), p. 101001), the present study redesigns the cascade via section profiling using optimization methods to maximize performance gains. To improve the control effect of endwall contouring, blade section parameters are strategically adjusted during optimization. The experimental flow field traverses at cascade exits demonstrate the control of the cascade flow field by the optimized design. The redesigned cascade exhibits decreased overturning near the shroud and reduced underturning near the hub, as well as reduced profile loss in the mainstream, compared to the endwall contoured cascade. The modification of section parameters enhances the control of losses and the secondary flow intensity. Computational fluid dynamics is used to provide a detailed analysis of the flow field, providing insights into how flow structures vary when the blade profile is modified. The numerical results further elucidate the effect of blade section profiling on both the performance characteristics of the cascade and the configuration of the secondary flows.

Hybrid LES/RANS Simulations of Compressible Flow in a Linear Cascade of Flat Blade Profiles

The paper reports on 3D numerical simulations of unsteady compressible airflow in a blade cascade consisting of flat profiles using a hybrid LES/RANS approach including a transition model. As a first step towards simulation of blade flutter in turbomachinery, various incidence angle offsets of the middle blade were modeled. All simulations were run for the flow regime characterized by outlet isentropic Mach number Mis=0.5 and zero incidence. The results of the LES/RANS simulations (pressure and Mach number distributions) were compared to a baseline RANS model, and to experimental data measured in a high-speed wind tunnel. The numerical results show that both methods overpredict flow separation taking place at the leading edge. In this regard, the hybrid LES/RANS method does not provide superior results compared to the traditional RANS simulations. Nevertheless, the LES/RANS results also capture vortex shedding from the blunt trailing edge. The frequency of the trailing edge vortex shedding in CFD simulations matches perfectly the spectral peak recorded during wind tunnel measurements.

Experimental study of flow control on tip leakage flow in variable geometry linear turbine cascades with different pivot layouts

Variable geometry turbines are essential for adjusting operational conditions in industrial gas turbines and variable cycle engines. These adjustments necessitate partial gaps at both ends of the variable guide vanes to alter the turning angle, consequently introducing an aerodynamic performance penalty. Moreover, the pivot layout profoundly influences aerodynamic losses. Research on turbine cascades that considers various partial gap layouts is limited, particularly in terms of experimental studies, which are rarely conducted. This study aims to diminish aerodynamic losses and augment the efficiency of gas turbines by examining the impact of pivot layouts on partial gap clearance and secondary flow. It further investigates the effectiveness of flow control strategies at the blade tip across different pivot configurations within a variable geometry turbine cascade, utilizing pneumatic probe scanning and surface oil flow visualization techniques. The results reveal that employing a cavity at the tip can significantly reduce aerodynamic losses in schemes both with and without a pivot, achieving maximum loss reductions of 15.8% and 3.7%, respectively. Additionally, a narrower squealer width can further decrease these losses. However, with a pivot located at the tip, the resulting separation flow and wake vortex become predominant sources of losses. The presence of the pivot weakens the tip leakage flow rate and the intensity of the tip leakage vortex (TLV), thus diminishing the effectiveness of cavity tip flow control. The cavity moderates TLV and enhances the interaction between TLV and the wake vortex, leading to increased aerodynamic losses.

Controlled Delivery of H2O2: A Three-Enzyme Cascade Flow Reactor for Peroxidase-Catalyzed Reactions.

Peroxidases are promising catalysts for oxidation reactions, yet their practical utility has been hindered by the fact that they require hydrogen peroxide (H2O2), which at high concentrations can cause deactivation of enzymes. Practical processes involving the use of peroxidases require the frequent addition of low concentrations of H2O2. In situ generation of H2O2 can be achieved using oxidase-type enzymes. In this study, a three-enzyme cascade system comprised of a H2O2 generator (glucose oxidase (GOx)), H2O2-dependent enzymes (chloroperoxidase (CPO) or horseradish peroxidase (HRP)), and a H2O2 scavenger (catalase (CAT)) was deployed in a flow reactor. Immobilization of the enzymes on a graphite rod was achieved through electrochemically driven physical adsorption, followed by cross-linking with glutaraldehyde. Modeling studies indicated that the flow in the reactor was laminar (Reynolds number, R e < 2000) and was nearly fully developed at the midplane of the annular reactor. Immobilized CAT and GOx displayed good stability, retaining 79% and 84% of their initial activity, respectively, after three cycles of operation. Conversely, immobilized CPO exhibited a considerable reduction in activity after one use, retaining only 30% of its initial activity. The GOx-CAT-GRE system enabled controlled delivery of H2O2 in a more stable manner with a 4-fold enhancement in the oxidation of indole compared to the direct addition of H2O2. Using CPO in solution coupled with GOx-CAT-GRE yields of 90% for the oxidation of indole to 2-oxyindole and of 93% and 91% for the chlorination of thymol and carvacrol, respectively.

Sensitivity of the endwall flow in a linear vane cascade to blade fillet geometry

Based on the blade chord and inlet velocity, the current computational study uses a linear vane cascade with a large filleted blade-endwall junction with a 2.01 x 105 Reynolds number. Three fillets with related profiles are explored. To evaluate the upshots of geometric differences in a fillet attached to the endwall flow-field, the height and endwall-width of the fillets are changed. The RANS k-ω turbulent model is used in the computations, and the results are compared to experimental results from a similar cascade without the fillet. The computed results of the secondary flow-field in the endwall region along the cascade are compared for baseline (no fillet) and filleted passages. As a result of diminished leading-edge and passage vortices, the fillets lower pitchwise pressure gradients, flow separation, axial vorticity, and overall pressure losses when compared to the baseline. The pros of fillets on endwall secondary flows are however unaffected by fillet's geometric changes.

PIV experimental study on water-sediment two-phase flow in NACA0012 cascade

Abstract Sediment wear is one of the important reasons for the damage of hydraulic machinery components, and the motion characteristics of sediment are the key factors to determine the degree of wear damage. In order to reveal the mechanism of sediment wear of turbine guide vane, motion characteristics of sediment near the wall of NACA0012 cascade were studied by PIV test method. In this research, fluorescent and sediment particles were used as tracer particles respectively, and the particle images of solid and liquid phases were recorded by double-camera synchronous imaging method. Finally, the synchronous velocity field of solid and liquid phases was determined by correlation analysis of particle images. The experimental results show that the PIV test method can accurately determine the motion characteristics of the solid phase. There is velocity slip between the solid phase and the liquid phase, and the velocity deviation is related to the factors of particle characteristics and Reynolds number.

Analyses of non-clean surface compressor blade cascades’ aerodynamic performance deterioration

Abstract The efficiency and dependability of the engine are directly impacted by the compressor’s performance, which is a crucial part of gas turbines. The blade cascade is significantly influenced by surface roughness in terms of flow characteristics and aerodynamic performance. In this study, the NACA65-410 airfoil is selected as the research object to investigate the variations in blade cascade performance and flow characteristics under different inflow and roughness conditions. The results show that the smooth surface blade cascade performs optimally when the Reynolds number increases from 120,000 to 200,000. As the angle of attack increases from -5° to 8°, the blade cascade performance deteriorates, and the degree of performance degradation increases with the increase in angle of attack. For the roughened blade cascade surface, the performance initially improves and then decreases as the equivalent sand grain density increases, and there exists a critical equivalent sand grain density that maximizes the blade cascade performance. When the Reynolds number is 120,000, the critical equivalent sand grain density is 225 μm, and when the Reynolds number is 160,000, the critical equivalent sand grain density is 111 μm. Based on the findings of this study, the degradation pattern of blade cascade performance can be predicted, and it can be utilized to enhance the overall performance of the compressor.

Numerical study of shock wave boundary layer interaction flows using a novel turbulence model

This study proposes a novel partial average fluctuation velocity (PAFV) turbulence based on the PAFV and the average strain rate tensor, which is used to calculate the shock wave boundary layer interaction flows, including cascade flow and transonic compressor flow. In order to illustrate the adequacy, the calculation results of several other turbulence models were also compared with PAFV, including k-ω, shear stress transport, SA-neg (negative Spalart-Allmaras), and stress-BSL (ω-based Reynolds stress model). The suitability of the PAFV turbulence model was initially tested by calculating the transonic flow in the L030-4 cascade. Subsequently, numerical computations were performed for the 3D (three-dimensional) National Aeronautics and Space Administration Rotor 67 transonic compressor rotor. In the numerical simulation, the flow control equations were transformed in a general curvilinear coordinate system for precision enhancement, and the spatial discretization of control equations was executed using the finite difference method. The convection term was processed using the Steger–Warming flux vector splitting method, the diffusion term was discretized using a second-order central difference scheme, and the time derivative term was discretized using the third-order Runge–Kutta method. A parallel computing strategy with multi-block partitioning was employed to speed up the calculations and facilitate faster convergence alongside a local time step method. All numerical computation procedures were written in Python, revealing the following: (1) The PAFV turbulence model aptly simulates the transonic flow within the cascade channel. The shock wave pattern in the cascade channel aligns well with the experimental schlieren images. (2) During the Rotor 67 transonic compressor rotor calculation, the flow–pressure ratio, flow efficiency, and inlet and outlet total temperatures and pressures align well with the experimental data. Furthermore, the resolution of the flow field structure related to the interaction between the tip leakage vortex and channel shock wave is high. (3) The turbulence model uses PAFV as the turbulence velocity scale, thereby suppressing the fluctuation velocity and turbulence viscosity near shock wave areas, preventing excessive turbulence viscosity. Moreover, PAFV inherently exhibits transport properties and anisotropic characteristics, making it well-suited for handling transonic compressor flows.

Multi-fidelity CFD for obtaining the runner blade profile parameters of a Francis turbine for optimum hydrodynamic performance

The high fidelity Navier Stokes equations based CFD codes precisely take care of the turbulent and viscous effects of complex flows passing through the hydraulic turbines. However, for preliminary design synthesis and analysis purposes, this full 3D flow can be assumed as a combination of two 2D flows (meridional axi-symmetric flow and blade-to-blade or cascade flow) which is the basis of low fidelity potential flow theory for hydraulic turbines. This paper presents the utilities of high as well as low fidelity CFD analyses for obtaining a runner blade design which yields an optimum hydrodynamic performance of a prototype Francis Turbine. The complete flow domain of the Francis turbine has been considered for the high-fidelity analysis which is carried out by using ANSYS CFX 16.0 for different operating conditions. Whereas, for the low fidelity investigations, full three-dimensional flow domains of different blade rows (i.e., stay vanes, guide vanes and runner) of the Francis turbine is divided into two 2D flow domains (i.e., an axisymmetric annulus of the turbine space for meridional flow analysis and cascades at different sections from hub to shroud for blade-to-blade analysis). By using the low fidelity analysis, runner blade design parameters have been adequately varied in order to obtain a population of different promising runner blade designs. Performances of these promising designs are evaluated, and the obtained results are thoroughly analysed through the response surface analysis. An optimized hydrodynamic performance design of the runner is obtained for the target values of responses (here, swirl velocity at trailing edge of the runner (Cu2) and stagnation pressure at trailing edge of the runner (P02/ρ)) at different sections from hub to shroud by determining the design parameters of blade profiles at different sections. The adopted multi-fidelity CFD approach is found very effective and has the potential to yield reasonably accurate hydraulic designs of the Francis turbine in considerably lesser time and cost.