Search

The tip leakage flow passed over the tip clearance makes the flow very complicated near the tip gap, and the interaction of the tip leakage vortex and endwall vortex enhances the instability of the flow. Accurately capturing detailed flow structures and investigating the relationship between the flow structures and loss are beneficial for understanding the flow physics and providing guidance on reducing the loss. Due to the conventional Reynolds Averaged Navier-Stokes (RANS) methods is limited to predict the complex turbulence structures of the tip clearance flow, high fidelity simulation approaches are needed. In this work, the hybrid RANS/Large Eddy Simulation (LES) is adopted to simulate the tip leakage flow in linear cascade and demonstrates its ability to capture the small-scale flow structures. With the POD method, the time-averaged flow field and the dominating modes are obtained. Based on the analysis of the POD modes, it is found that the induced vortex generated by the interaction between the leakage vortex and the endwall vortex has strong turbulence characteristics. Based on the entropy generation rates, viscous loss mechanism is further analyzed. It is found that the shear strain rates dominate the viscous dissipation losses, and the fluctuation dissipation has a strong local enhancement effect.

Accurate predictions of Shock Waves and Boundary Layer Interaction (SWBLI) and strong Shock Waves and Wake Vortices Interaction (SWWVI) in a highly-loaded turbine propose challenges to the currently widely used Reynolds-Averaged Navier-Stokes (RANS) model. In this work, the SWBLI and the SWWVI in a highly-loaded Nozzle Guide Vane (NGV) are studied using a hybrid RANS/LES strategy. The Turbulence Kinetic Energy (TKE) budget and the Proper Orthogonal Decomposition (POD) method are used to analyze flow mechanisms. Results show that this hybrid RANS/LES method can obtain detailed flow structures for flow mechanisms analysis. Strong shock waves induce boundary layer separation, while the presence of a separation bubble can in turn lead to a Mach reflection phenomenon. The shock waves cause trailing-edge vortices to break clearly, and the wakes, in turn, can change the shocks intensity and direction. Furthermore, the Entropy Generation Rate (EGR) is used to analyze the irreversible loss. It turns out that the SWWVI can reduce the flow field loss. There are several weak shock waves in the NGV flow field, which can increase the irreversible loss. This work offers flow mechanisms analysis and presents the EGR distribution in SWBLI and SWWVI areas in a transonic turbine blade. Keywords: Boundary layer, Hybrid RANS/LES, NGV, Shock waves, Wakes

Efficient method to handle the geometric constraints in the optimization of turbomachinery blade profile is required. Without constraints on the blade thickness, optimal designs typically yield thinner blade to reduce the friction loss, however, at the risk of degraded strength and stiffness. This issue is seldom discussed and existing literature always treat the blade thickness constraint in an indirect manner. In this work, two different geometric constraints on the blade thickness are proposed and applied in the adjoint optimization: one is on the maximum blade thickness and the other is on the blade area. Methods to compute sensitivities of both constraints are proposed and they are integrated into an optimization system based on a finite volume code and a solver for the discrete adjoint equation. Adjoint optimization is conducted to minimize the entropy production in a transonic compressor stage. Results for the adjoint optimization without geometry constraint and two comparative cases are detailed. It is indicated that three cases yield similar performance improvement; however, if geometry constraints are properly handled, the optimal designs have almost the same maximum thickness as the original design, compared to a thinner blade profile with 14% reduction of maximum thickness in the case without geometry constraint. The cases considering geometry constraints also consume slightly reduced Central Processing Unit (CPU) cost. Result of this work verifies the effectiveness of the proposed method to treat geometric constraints in adjoint optimization.

Film cooling is a typical three-dimensional fluid phenomenon, where the coolant with lower temperature is ejected from discrete holes to protect metal walls from being burnt by the hot mainstream. It is a great challenge for Reynolds-averaged Navier–Stokes (RANS) methods to accurately predict the coolant coverage on the wall because the turbulent thermal diffusion tends to be under-predicted due to inherent assumptions behind RANS models. In this paper, a framework of integrated field inversion and machine learning is built to enhance RANS prediction of turbulent thermal diffusion. A neural network (NN) is trained in this framework to predict the spatially varying turbulent Prandtl number ([Formula: see text]) and to improve the prediction of RANS models. The temperature distribution obtained from the large eddy simulation is used as the learning target, and the discrete adjoint method is used as the inverse model that helps calculate derivatives of mean square error of the temperature distribution to NN parameters. The training process of NN shows good convergence properties. The results show that the obtained NN effectively increases the insufficient turbulent thermal diffusion by predicting much lower [Formula: see text] than the commonly used value of 0.9. The NN-enhanced RANS provides significant improvements on predicting experimental temperature distributions compared with general RANS models not only on the training data but also on the unseen testing data. In addition, the obtained NN can be implemented into general-purpose software with minimal effort and no numerical stability problem.

In modern aero-engine and gas turbine, the highly loaded turbine leads to strong secondary flow by which the main flow and the film cooling jets are driven from the pressure side to the suction side. As a result, the cross flow has considerable influences on the performance of film cooling jets in the endwall region. In this work, the effects of cross flow on the shaped-hole film cooling performance are investigated both experimentally and numerically. Experimental studies are conducted in a curved channel which simulates the real turbine blade environment with the blowing ratio from 0.5 to 2.5. Numerical studies are also conducted to obtain detailed information about vortical structures. Results show that the cross flow changes the relative position of the two pairs of kidney vortices generated at the outlet of the shaped hole. The negative kidney vortices are stuck to the endwall due to the lift force and they decay faster downstream. The coolant is driven by the cross flow to migrate along the radial pressure gradient direction. And the coolant near the endwall migrates further. The peak value of the cooling effectiveness is suppressed; however, the laterally averaged cooling effectiveness is increased, especially at high blowing ratio. An analytical model describing the flow topology about coolant jets with cross flow is proposed and results from this work may help to understand the film cooling behaviour affected by real complicated flow structures in the engine environment.

Strong secondary flow results in substantial aerodynamic loss for highly-loaded turbine. Accurate prediction of the complicated flow structures proposes challenges to the widely used Reynolds Average Navier-Stokes (RANS) approach. This work employs the hybrid RANS/Large Eddy Simulation (LES) method to study the unsteady flows for a highly-loaded turbine blade, with both flat endwall and optimized contoured endwall. Evolution of the unsteady flows in the endwall region is analyzed, with emphasis on the loss generation mechanism. Results show that for the flat endwall, the horseshoe vortex system is highly unsteady and is a significant source of unsteadiness in both the passage and the wake region. It contributes to the unsteady passage vortex, also the earlier breakdown of the trailing edge shedding vortex. The Probability Density Function (PDF) histogram of velocity in the wake region is bimodal, implying the perturbations from two mechanisms. For the contoured endwall, the unsteady evolution of the horseshoe vortex is blocked, which results in significantly reduced unsteadiness, also the merge between the horseshoe vortex with the passage vortex is prevented. Effect of the flow unsteadiness on the loss generation is assessed based on the entropy generation rates contributed by the time-averaged flow and the fluctuations. The effect of unsteadiness is two-fold: unsteady perturbations trigger the vortex breakdown into small-scale structures and thus weakened wake velocity deficit and loss generation; however, in both the passage and the wake region the entropy generation by the fluctuations are remarkable. For the contoured endwall, due to the reduced flow unsteadiness, loss generation contributed by the fluctuations are much smaller compared to the flat endwall. The results highlight the importance of including the loss generation by the fluctuations, also a possible mechanism to reduce the secondary loss by attenuating the flow unsteadiness with the contoured endwall.

This work presents the implementation and study of the quadratic constitutive relation nonlinear eddy-viscosity model with representative compressor application, for which the corner separation has been poorly predicted with the widely used linear Boussinesq eddy-viscosity model. With the introduction of the Reynolds stress anisotropy, the secondary flow of the second kind and its effect on the corner flow can be well captured and this results in greatly improved prediction of pressure coefficient, total pressure loss coefficient and the corner separation size. Without the quadratic constitutive relation model, the separation size and loss are generally over-estimated. The mechanism of the improvement is studied using both the vortex dynamics and the momentum equation. It is proved that quadratic constitutive relation model consumes low CPU time and provides much improved compressor corner separation prediction without worsening the convergence property.

In the modern highly-loaded gas turbine, due to the large pressure difference between the suction side and the pressure side of the turbine blade, strong cross flow is formed and it strongly affects the aerodynamic and cooling performances in the end-wall region. The film cooling behavior in the environment of strong cross flow is different from the straight channel environment widely studied in the literature. In this research, the effect of cross flow on film cooling is investigated by Large Eddy Simulation (LES) using subgrid-scale (SGS) model. Numerical simulation is carried out in a curved passage to simulate the turbine blade passage. Shaped cooling hole with blowing ratio 1 is studied. The time-averaged friction line results are compared with existing experimental ink trace results. The vortex structures, both time-averaged and instantaneous, are analyzed to study the effect of cross flow on film cooling. At the exit of the cooling hole, the hanging vortices with negative y-vorticity are more flat in shape and closer to the wall in position in contrast to hanging vortex with positive y-vorticity, which is caused by cross flow and results in the asymmetry of hairpin vortices downstream as well as the asymmetry of the distribution of coolant. It has been shown that the vortices from mainstream have a significant impact on the field near the exit of the cooling hole. Those vortices interact with the hairpin vortices from the cooling hole and directly lead to the asymmetry of the hairpin vortices. Proper Orthogonal Decomposition (POD) analysis is further conducted to extract the dominant flow structures and the physical mechanisms of primary POD modes are given to explain the distribution of film cooling effectiveness affected by cross flow. Based on the specific situation in this work, a fast incremental POD (iPOD) approach is adopted since the rank of the field matrix is far less than the rows, which is caused by the tall and thin character of the matrix, which makes the analysis less costly and more effective. This research helps to understand the cooling performance in the real turbine blade passage and to explain the coolant mixing process based on the instantaneous flow field obtained using high precision LES simulation and powerful iPOD.

The complex leakage flow structure in the tip region of unshrouded rotor is a main source of turbine aerodynamic loss. Due to the complex turbulence characteristics of the tip leakage flow, the widely used Reynolds Averaged Navier-Stokes (RANS) approach may fail to accurately predict the multi-scale turbulent flow and the related loss. In order to effectively improve the turbine efficiency, more insights into the turbulence characteristics and the loss mechanism in the tip leakage flow are required. In this work, a Delayed Detached Eddy Simulation (DDES) study is conducted to simulate the flow inside a high pressure turbine blade, with emphasis on the tip region. DDES results are in good agreement with the experiment and the comparison with RANS results verifies the advantages of DDES in resolving finer flow structures of leakage flow, also in capturing the complex turbulence characteristics. The snapshot Proper Orthogonal Decomposition (POD) method is used to extract the dominant flow features. The flow structures and the distribution of Reynolds stress help to reveal the process of leakage flow and its interaction with the secondary flow. Meanwhile, it is found that the separation vortex (SV) forms from leading edge to trailing edge, and the strong interactions between tip leakage vortex (TLV) and passage secondary vortex (PSV) significantly enhance the turbulence intensity. Based on the DDES results, loss analysis of tip leakage flow is conducted based on entropy generation rates. For the leakage flow related loss, the largest local entropy generation rate occurs at 50 % of axial chord, and the interaction between the leakage vortex and up passage vortex promotes the loss generation. To sum up, the current DDES study about the tip leakage flow provides helpful information about the loss generation mechanism and may guide the design of low-loss blade tip.

The wake vortex is an important origin of unsteadiness and losses in turbines. In this paper, the development and underlying mechanisms of the shedding vortex of a high-pressure transonic turbine vane are studied and analyzed using the delayed detached eddy simulation (DDES) and proper orthogonal decomposition (POD). The goal is to understand the unsteadiness related to the wake vortex shedding and the wake evolution and mixing. Special attention is paid to the development of the wake vortex and the mechanisms behind the length characteristics. Interactions of the wake vortex with the shock wave and pressure waves are also discussed. First, the DDES simulation results are compared with published experimental data, Reynolds Averaged Navier-Stokes, and large eddy simulation (LES) simulations. Then, the development of the vane wake vortex, especially the different length characteristics from the cylinder vortex, is discussed. The reason of stronger pressure-side vortex shedding compared to suction-side vortex shedding is revealed. Wake-shock wave interaction and wake-pressure wave interaction are also investigated. The pressure waves are found to have a stronger effect than the shock wave on the spanwise motion and the dissipation of the wake vortex. An analysis of the losses through the turbine vane passage is carried out to evaluate the contributions of thermal and viscous irreversibilities. Losses analysis also confirms the strong interaction between the wake vortex and pressure waves. After that, POD study of the wake behavior was carried out. The results indicate that the shedding vortex is dominant in the unsteady flow. The phase relation between the pressure side wake vortex (PSVP) and the suction side wake vortex (SSVP) is confirmed.

The influence of the cross flow in mainstream on film cooling performance and jet flow field is investigated experimentally and numerically. To show the effect of cross flow in mainstream without the influence of the other secondary flows, a curved test section is constructed to generate a cross flow, simulating the curved turbine passage. Both the straight and the curved passage are used to show the differences of cooling performance for shaped holes with and without the cross flow, with blowing ratio varying from M = 0.5 to M = 2.5. Pressure sensitive paint is used to measure the adiabatic cooling effectiveness, and the ink trace measurement is conducted to present the friction lines on the endwall platform. Numerical simulations are performed to show the flow field. The cross flow is accelerated in a curved passage and migrates the fluid near the endwall platform. Due to the cross flow in the mainstream, the deflection angle changes a lot along the normal direction to the endwall, and dominates the spatial distribution of coolant. Although the cooling trace follows the trend of wall surface streamlines, the migration of coolant is slower than the deviation of the friction line, and the difference increases with increasing blowing ratios. The cross flow enhances the lateral dispersion, decreasing the peak value of cooling effectiveness but increasing the laterally averaged cooling effectiveness. Higher blowing ratios lead to a higher intensity of a counter-rotating vortex pair that limits lateral dispersion near the outlet of cooling hole. But the effect of cross flow dominates the flow pattern downstream. The cooling performance has a significant difference with the influence of the cross flow. This study is essential to understand the interaction of the cross flow and the film cooling in gas turbines.

Film cooling is an important technology in protecting the turbine blade of modern aero-engine and gas turbine. Besides the widely studied parameters including the cooling hole geometry and blowing ratio, film cooling effectiveness is also affected by the crossflow in the internal cooling channel, which causes off-design inflow directions of the cooling hole. In-hole counter-rotating vortex pair is observed which accounts for the effect of internal crossflow on the film cooling. The current paper numerically studies the effect of internal channel flow on the film cooling performance by comparing the results of three configurations. A theoretical model about the boundary layer deformation is proposed to explain the formation of in-hole vortices based on the vortex dynamics, and two comparative cases with slip and no-slip channel wall respectively are used to highlight the importance of internal channel flow boundary conditions. By comparing adiabatic film cooling effectiveness under varying blowing ratios and internal crossflow velocities, it is shown that internal crossflow plays an important role in film cooling performance. Enhanced cooling effectiveness can be obtained at internal co-flow conditions where in-hole vortices has the opposite direction with downstream kidney vortices. Due to the competitive effects of distorted velocity profile and in-hole vortices, an optimal velocity of internal crossflow can be found at given blowing ratio and the optimal velocity magnitude slightly increases with increasing blowing ratio.

The strong secondary flow and the interaction between multiple vortices result in substantial aerodynamic losses in the endwall region of the highly-loaded turbine. Accurate predictions of complex turbulence characteristics propose severe challenges to the widely used Reynolds-Averaged Navier-Stokes (RANS) approach. This work adopts a high accuracy hybrid RANS/Large Eddy Simulation (LES) method on a highly-loaded turbine blade for which the Reynolds number is 611,000 and the exit Mach number is 0.8. Results verify that, in contrast with the RANS method, the hybrid method can provide more accurate predictions and detailed small-scale flow structures than the RANS simulation. Analysis of the Reynolds stresses predicted by the hybrid method reveals the complex turbulence characteristics in the endwall region and highlights shortcomings of Reynolds stresses predictions existing in the RANS method in the highly-loaded turbine blade environment. To analyze turbulence characteristics near the blade endwall, the Lumley triangle method is applied to quantify the turbulence anisotropy degree. Based on fine flow field structures, the proper orthogonal decomposition (POD) method is used to extract the dominant flow structures from the unsteady hybrid method results. The turbulence kinetic energy budget is employed to study dominant terms in turbulent flow. The total pressure loss coefficient based on the first law of thermodynamics and the entropy generation rate (EGR) based on the second law of thermodynamics are both used to study the loss generation mechanism in the endwall region. Predicted turbulence characteristics and flow mechanism can provide guide towards low loss design and flow control of the turbine blade.

In this paper we explore a new hybrid method for the near-wall treatment of turbulent flow computation with Cartesian mesh. Cloud of points are generated to resolve the boundary layer and they are generated along wall-normal directions. Special attention is paid at the treatment of singular point for the use of current method for complex geometry. Multiple marching directions are defined for enough resolution and smooth transition between near-wall and off-wall solvers. These points demonstrate one dimensional structure in the wall-normal direction and it offers the opportunity of improved accuracy. By exploring this property, a hybrid methodology combines high order scheme in the wall-normal direction and meshless method in the streamwise direction is proposed. Also a hybrid LU-SGS/line-implicit time integration method is developed based on this property. The use of high order scheme for the wall-normal flow derivative significantly improves the overall accuracy, especially in the area with curved solid surface. The current hybrid method is verified using Method of Manufactured Solution (MMS) and a series of turbulent test cases. Results indicate good agreement with available experimental values and improved predictions and robustness compared to the meshless method.

Gas turbines are important energy-converting equipment in many industries. The flow inside gas turbines is very complicated and the knowledge about the flow loss mechanism is critical to the advanced design. The current design system heavily relies on empirical formulas or Reynolds Averaged Navier–Stokes (RANS), which faces big challenges in dealing with highly unsteady complex flow and accurately predicting flow losses. Further improving the efficiency needs more insights into the loss generation in gas turbines. Conventional Unsteady Reynolds Averaged Simulation (URANS) methods have defects in modeling multi-frequency, multi-length, highly unsteady flow, especially when mixing or separation occurs, while Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES) are too costly for the high-Reynolds number flow. In this work, the Delayed Detached Eddy Simulation (DDES) method is used with a low-dissipation numerical scheme to capture the detailed flow structures of the complicated flow in a high pressure turbine guide vane. DDES accurately predicts the wake vortex behavior and produces much more details than RANS and URANS. The experimental findings of the wake vortex length characteristics, which RANS and URANS fail to predict, are successfully captured by DDES. Accurate flow simulation builds up a solid foundation for accurate losses prediction. Based on the detailed DDES results, loss analysis in terms of entropy generation rate is conducted from two aspects. The first aspect is to apportion losses by its physical resources: viscous irreversibility and heat transfer irreversibility. The viscous irreversibility is found to be much stronger than the heat transfer irreversibility in the flow. The second aspect is weighing the contributions of steady effects and unsteady effects. Losses due to unsteady effects account for a large part of total losses. Effects of unsteadiness should not be neglected in the flow physics study and design process.

The flow in a generic, high-pressure turbine vane was simulated using an in-house DDES code. Two different operating conditions were simulated with one leading to a shock wave while the other does not. One case was used to validate the capability of the DDES method to capture shock waves and other flow structures using an inlet Reynolds number of 271,000 and an exit Mach number of 0.840. The test conditions for the other case were an inlet Reynolds number of 265,000 and an exit Mach number of 0.927, which is representative of a transonic, high pressure turbine vane which was used to further investigate the flow field. The DDES simulations from the first case are compared with published experimental data, RANS simulations and LES simulations. Then, DDES results for two cases with adiabatic and isothermal boundary conditions are compared. The numerical simulations with the isothermal boundary condition are further used to study the flow phenomena with wake vortices, shock waves, pressure waves, wake-shock interactions, and wake-pressure wave interactions. The effects of the pressure waves on the vane heat transfer are also analyzed.

Unsteady blade row interactions considerably affect the performance of turbomachinery consisting of multiple blade rows. However, most aerodynamic optimizations of turbomachinery are based on mixing-plane steady flow simulations which cannot account for the unsteady effects of blade row interactions. In this work, the rotor of a two-dimensional transonic turbine stage is optimized using an in-house unsteady aerodynamic optimization system that allows for a more accurate modeling of the unsteady flow features occurring in multi-row turbomachinery configurations. The gradients of the objective function and constraint to the design variables are efficiently calculated with the discrete adjoint method. In the developed adjoint-based unsteady aerodynamic optimization system, the unsteady Reynolds-Averaged Navier-Stokes equations are solved using the harmonic balance method with an in-house code. The adjoint equations are derived by hand from the discrete form of the unsteady flow equations. The present results demonstrate the efficiency and capability of the unsteady aerodynamic optimization system for turbomachinery with multiple blade rows.Copyright © 2016 by ASME

In this paper we explore a new hybrid method for the near wall treatment of viscous computation with block structured Cartesian mesh. Cloud of points are generated to resolve the near wall boundary layer and most of the points are distributed on one-dimensional lines along the wall normal directions, thus enabling the usage of high order scheme for the wall-normal flow derivative. In streamwise direction the flow derivative is approximated using second order least-square meshless method. Compared to the existing wall treatment methods for block structured Cartesian mesh, the current approach retains the flexibility of the least-square method and also offers the opportunity of high order accuracy along the wall-normal direction. A simple method is proposed to generate the near-wall points and it relieves the burden of body-fitted near-wall mesh generation. The current approach is tested with several high Reynolds number flows and the results are discussed.

Unsteady blade row interactions play an important role in the performance of the compressor stages. However, due to the large cost of the unsteady flow simulation, most aerodynamic optimizations of the compressor are based on the steady flow simulation. This paper adopts the time spectral method to reduce the cost of the unsteady flow simulation and a discrete adjoint solver based on the unsteady flow solver has been developed. The unsteady flow equations and the adjoint equations are solved using an in-house code. The in-house code is based on the finite volume method and solves the URANS (Unsteady Reynolds Averaged Navier-Stokes) equations on the multi-block structured mesh. For spatial discretization the 3rd order WENO (Weighted Essentially Nonoscillatory) upwind scheme is used for reconstruction and the convective flux is computed with Roe’s approximate Riemann solver. The widely used one-equation Spalart-Allmaras turbulence model is adopted for the flow simulation. For the adjoint solution, the constant-eddy viscosity assumption is adopted and only the main flow adjoint equations are solved. The adjoint equations are formed in a discrete manner, which leads to more accurate discrete objective function sensitivity than the continuous adjoint method. The present work serves as an essential part of the system for efficient unsteady aerodynamic optimization of turbomachinery.

The corner separation in the high-loaded compressors deteriorates the aerodynamics and reduces the stable operating range. The flow pattern is further complicated with the interaction between the aperiodic corner separation and the periodically wake-shedding vortices. Accurate prediction of the corner separation is a challenge for the Reynolds-Averaged Navier–Stokes (RANS) method, which is based on the linear eddy-viscosity formulation. In the current work, the corner separation is investigated with the Delayed Detached Eddy Simulation (DDES) approach. DDES results agree well with the experiment and are systematically better than the RANS results, especially in the corner region where massive separation occurs. The accurate results from DDES provide a solid foundation for mechanism study. The flow structures and the distribution of Reynolds stress help reveal the process of corner separation and its interaction with the wake vortices. Before massive corner separation occurs, the hairpin-like vortex develops. The appearance of the hairpin-like vortex could be a signal of large-scale corner separation. The strong interaction between corner separation and wake vortices significantly enhances the turbulence intensity. Based on these analyses, entropy analysis is conducted from two aspects to study the losses. One aspect is the time-averaged entropy analysis, and the other is the instantaneous entropy analysis. It is found that the interaction between the passage vortex and wake vortex yields remarkable viscous losses over the 0–12% span when the corner separation has not yet been triggered; however, when the corner separation occurs, an enlarged region covering the 0–30% span is affected, and it is due to the interaction between the corner separation and wake vortices. The detailed coherent structures, local losses information and turbulence characteristics presented can provide guidance for the corner separation control and better design.