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The performance of turbomachinery is largely affected by the nonuniform boundary conditions caused by the coupling between neighboring parts, such as the inlet distortion and hot streak. Existing works study this problem by comparing the flow fields with uniform and nonuniform boundary conditions, which is cost extensive. In this work a new and efficient method is developed by computing the sensitivities of arbitrary performance metric relative to the boundary conditions and this method quantitatively describes how the disturbance on the boundary surface affects the performance. The adjoint method popular in the design optimization is extended to current field for the efficient computation of the sensitivity. The extra cost is independent of the number of parameters describing the nonuniform distribution. Accuracy of the adjoint boundary sensitivity is validated against analytical results for a converging–diverging nozzle case. Its applications in a representative case are detailed and discussed in this paper. Current method provides a new tool, also direct guides to minimize the negative effect and improve the performance utilizing the adjoint boundary sensitivity.

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

An optimization framework is developed for the film cooling hole shape design to achieve highest film cooling effectiveness with affordable cost. A key to this design method is the development and applications of a multi-fidelity model (MFM) to improve the efficiency of surrogate model construction. To construct multi-fidelity model, empirical correlations from existing literature are utilized as low-fidelity data and Reynolds-Averaged Navier-Stokes (RANS) simulations provide high-fidelity data. Compared with single-fidelity surrogate models, multi-fidelity model developed in this work combines vast existing knowledge about shaped film cooling hole and three dimensional numerical simulation. As a result, the computation cost has been substantially decreased by 64.5% while accuracy is maintained with similar level, which provides a firm basis for the optimization. Considering three geometric parameters as design variables, i.e. laidback angel, lateral angle, and hole length-diameter ratio, the shaped hole is optimized with genetic algorithm (GA) combined with sequential quadratic programming (SQP) algorithm. After the optimization, an experiment campaign is further carried out to validate the optimization result using pressure sensitive paint (PSP) technology. With current multi-fidelity model, the spatially averaged film cooling effectiveness has been improved by 39 % compared to the baseline, which is an already well-designed shaped hole and the improvement is also verified by experiment. This work verifies the effectiveness of current multi-fidelity model for the design and optimization of shaped film cooling hole for better performance.

In modern aero-engine and gas turbine, the hot streak and residual swirl caused by the combustor have strong impact on both aero and thermal performances of the high-temperature turbine. Due to different design philosophies of combustors and turbine, one combustor usually matches two or more vanes and the resultant mismatching effect is numerically investigated with unsteady simulation where one nonuniform core faces two Nozzle Guide Vane (NGV) blades. Results indicate that the nonuniformity clocking position dominates the averaged-temperature, while the swirl orientation dominates the radial distribution. The mismatching effect strongly impacts both time-averaged and instantaneous performances, in that neighboring blades of NGV have averaged-temperature difference of 10.5 K, and it also halves the base frequency and amplifies unsteady variation in the rotor passage. By analyzing both aero and thermal results from a matrix of four cases, the LE-pos configuration has the best performance. The complex transportation of the nonuniformity in the LE-pos case is detailed and the unsteady interactions between the inlet nonuniformity and the complex flow topology are analyzed. The residual swirl carries the hot streak fluctuating radially in rotor passages and redistributes the temperature on rotor surface. Results from this work highlight the necessity of considering the mismatching effect in gas turbine design optimization.

The performance of film cooling is influenced by many parameters, and the nonuniform flow caused by the internal cooling system is found to largely affect the film cooling, which further complicates the in-hole flow and draws new difficulties in predicting the cooling performance. In this study, we find a very interesting phenomenon that there always exists an in-hole interface, on which distributions of many parameters, including the velocity and kinetic energy, are seldom affected by the mainstream. The existence of this specific interface can be observed for both cylindrical and shaped film cooling holes under most operating conditions. The theoretical analysis of this interface is conducted in this study based on the characteristic decomposition of the Navier–Stokes equation, and this interface is named as the characteristic interface. Theoretical analysis and numerical observations suggest the film cooling system can be simplified to two weakly coupled regions separated by this interface. It also explains why existing source term models for film cooling may fail. Based on these findings, a new prediction model is developed, which uses the convolutional neural networks (CNN) model to predict the boundary conditions on the characteristic interface. The new model outperforms existing source term models and yields similar accuracy as full-mesh computational fluid dynamics (CFD), while reducing the computational cost by one order of magnitude. This model is further evaluated in large eddy simulation (LES), showing moderate success. To sum up, the current work reports the characteristic interface phenomenon in the film cooling hole, based on which a new and efficient prediction model is developed and verified.

Purpose Adopting large eddy simulation (LES) to simulate the complex flow in turbomachinery is appropriate to overcome the limitation of current Reynolds-Averaged Navier–Stokes modelling and it provides a deeper understanding of the complicated transitional and turbulent flow mechanism; however, the large computational cost limits its application in high Reynolds number flow. This study aims to develop a three-dimensional GPU-enabled parallel-unstructured solver to speed up the high-fidelity LES simulation. Design/methodology/approach Compared to the central processing units (CPUs), graphics processing units (GPUs) can provide higher computational speed. This work aims to develop a three-dimensional GPU-enabled parallel-unstructured solver to speed up the high-fidelity LES simulation. A set of low-dissipation schemes designed for unstructured mesh is implemented with compute unified device architecture programming model. Several key parameters affecting the performance of the GPU code are discussed and further speed-up can be obtained by analysing the underlying finite volume-based numerical scheme. Findings The results show that an acceleration ratio of approximately 84 (on a single GPU) for double precision algorithm can be achieved with this unstructured GPU code. The transitional flow inside a compressor is simulated and the computational efficiency has been improved greatly. The transition process is discussed and the role of K-H instability playing in the transition mechanism is verified. Practical/implications The speed-up gained from GPU-enabled solver reaches 84 compared to original code running on CPU and the vast speed-up enables the fast-turnaround high-fidelity LES simulation. Originality/value The GPU-enabled flow solver is implemented and optimized according to the feature of finite volume scheme. The solving time is reduced remarkably and the detail structures including vortices are captured.

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.

The swirl generator is widely used in lean-burn combustor to guarantee flame stability and reduce NOx emissions. Thus, the non-uniformities induced by the swirler would affect and damage film-cooling effectiveness on the turbine components, even blow-off coolant coverage, to some certain extent. The arrangement of film-cooling holes was normally designed to be perpendicular to the axial direction and in standard straight row. In this work we experimentally studied the effects of inlet swirl and mass flow ratio on traditional film cooling holes arrangement and a new arrangement pattern whose holes are located along the isobars. Results indicated that the swirl perturbation would damage film coverage. The film-cooling effect of endwall on which the holes are along the isobars, is invariably more promising than that of endwall on which hole arrangement is perpendicular to axial with the same mass flow of coolant, whether the inlet conditions is uniform or not. Keywords: Films-cooling, Holes locating, Isobaric, Swirling flow, Turbine design

With the development of computational power, large eddy simulation (LES) method is increasingly used in simulating complex flow. However, there still exist many factors affecting the LES quality and appropriate mesh resolution is among one of them. This work aims to develop an automatic procedure to refine the LES mesh by combining adaptive mesh refinement (AMR) and LES quality criteria. An LES refinement criterion is developed by estimating the proper grid length scale which meets the accuracy requirement of LES method. With this criterion, the baseline mesh is automatically refined with the AMR method. In this work, an efficient one-shot refinement strategy is also proposed to reduce the overall simulation time. Current AMR-based LES method is verified with the typical LES test case about the flow past circular cylinder at Re D = 3900. Results show that the automatically refined mesh provides systematically better agreement with experimental results and with current method the balance between ac...

Summary Adaptive Mesh Refinement (AMR) shows attractive properties in automatically refining the flow region of interest, and with AMR better prediction can be obtained with much less labour work and cost compared to manually re-meshing or the global mesh refinement. Cartesian AMR is well established; however, AMR on hybrid unstructured mesh which is heavily employed in the high-Reynolds number flow simulation, is less matured and existing methods may result in degraded mesh quality, which mostly happens in the boundary layer or near the sharp geometric features. User intervention or additional constraints, such as freezing all boundary layer elements or refining the whole boundary layer, are required to assist the refinement process. In this work, a novel AMR strategy is developed to handle existing difficulties. In the new method, high-order unstructured elements are first generated based on the baseline mesh; then the refinement is conducted in the parametric space; at last the mesh suitable for the solver is output. Generating refined elements in the parametric space with high-order elements is the key of this method and this helps to guarantee both the accuracy and robustness. With the current method, three-dimensional hybrid unstructured mesh of huge size and complex geometry can be automatically refined, without user intervention nor additional constraints. With test cases including the two-dimensional airfoil and three-dimensional full aircraft, the current AMR method proves to be accurate, simple and robust. This article is protected by copyright. All rights reserved.

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.

Shock wave and tip leakage are important flow features at small length scales. These flow phenomena and their interactions play important roles in the performance of modern transonic fans and compressors. In most numerical predictions of these features, mesh convergence studies are conducted using overall performance data as criteria. However, less effort is made in assessing the quality of the predicted small-scale features using a mesh that yields a fairly accurate overall performance. In this work, this problem is addressed using the adaptive mesh refinement (AMR) method, which automatically refines the local mesh and provides very high resolution for the small-scale flow feature, at much less cost compared with globally refining the mesh. An accurate and robust AMR system suitable for turbomachinery applications is developed in this work and the widely studied NASA Rotor-37 case is investigated using the current AMR method. The complex interactions between the shock wave and the boundary layer, as well as those between the shock wave and the tip vortex, are accurately captured by AMR with a very high local grid resolution, and the flow mechanisms are analyzed in detail. The baseline mesh, which is considered to be “acceptable” according to the commonly used mesh convergence study, is unable to capture the detailed interaction between the shock wave and the boundary layer. Moreover, it falsely predicts the tip leakage vortex breakdown, which is a consequence of inadequate resolution in the tip region. Current work highlights the importance of a careful check of the mesh convergence, if small-scale features are the primary concern. The AMR method developed in this work successfully captures the flow details in the transonic compressor in an automatic fashion, and has been verified to be efficient compared with the globally mesh refinement or manually mesh regeneration.

A bleeding system is necessary for gas turbines and may largely affect the compressor performance. In the existing literature the circumferentially uniform bleeding is widely studied; however, it is different from the industrial bleeding geometry and may not fully reflect the effects on the compressor. We conducted a numerical study to investigate the flow mechanism of the real industrial bleeding geometry in a single-stage high-speed axial compressor environment. Results show that bleeding effects increase the adiabatic efficiency and slightly reduce the total-to-static pressure ratio. Furthermore, it is discovered that a locally aperiodic flow field in the rotor passages is generated due to the real bleeding geometry. In the tip region the maximum incident angle difference can reach 1 degree. Locally aperiodic bleeding makes the tip leakage strength and blockage different in various rotor passages.

Film cooling is an important cooling method for the high-temperature components of modern aero-engines. There have been many previous studies on the influences of compound angle on film cooling performance, most of which are conducted in the ideal flat plate environment with zero pressure gradient, and the results indicate that at high blowing ratios, a large compound angle tends to improve the film cooling performance. However, in this work, it is found that a large compound angle tends to decrease the film cooling performance significantly with the influences of endwall lateral pressure gradient. A curved tunnel with constant width is employed to generate lateral pressure gradient similar to that in the endwall region of real turbine blade. It is shown that the crossflow near the endwall surface is the most obvious flow characteristic in this flow environment. Based on this discovery, we further conduct research on the influences of compound angles on film cooling performance in a curved tunnel both with numerical and experimental approaches. A well-designed laidback fan-shaped film cooling hole is used in this work. The experimental results show that for a film cooling hole with a large compound angle under blowing ratios ranging from 1.0 to 3.0, film cooling performance is reduced significantly under the environment of endwall lateral pressure gradient compared with zero pressure gradient environment. Detailed numerical results further indicate that due to the interaction between endwall crossflow and the strong single kidney vortex created by the large compound angle hole, large amounts of coolant are lifted away from endwall surface, which results in poor cooling performance. A topological model on the interaction between endwall crossflow and kidney vortices is proposed to help illustrate this phenomenon. The results of this work suggest that turbine cooling designers carefully consider the negative influence of large compound angles on endwall film cooling due to the lateral pressure gradient.

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.

In this work, the flows inside a high-pressure turbine (HPT) vane and stage are studied with a delayed detached eddy simulation (DDES) code. The fundamental nozzle/blade interaction is investigated with special attention paid to the development and transportation of the vane wake vortices. There are two motivations for this work. First, the extreme HPT operation conditions, including both transonic Mach numbers and high Reynolds numbers, impose a great challenge to modern computational fluid dynamics (CFD), especially for scale-resolved simulation methods. An accurate and efficient high-fidelity CFD solver is very important for a thorough understanding of the flow physics and the design of more efficient HPT. Second, the periodic wake vortex shedding is an important origin of turbine losses and unsteadiness. The wake and vortices not only cause losses themselves, but also interact with the shock wave (under transonic working condition), pressure waves, and have a strong impact on the downstream blade surface (affecting boundary layer transition and heat transfer). Based on one of our previous DDES simulations of a HPT vane, this work further investigates the development and length characteristics of the wake vortices, provides explanations for the length characteristics, and reveals the transportation of the wake vortices in the downstream rotor passages along with its impact on the downstream aero-thermal performance.

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.

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.

Unsteady blade row interactions play an important role in the performance of multistage turbomachinery. However, most aerodynamic optimizations of multistage turbomachinery are based on mixing-plane steady flow simulations. To take into account the unsteady flow features in the optimization cycle, this paper develops an adjoint-based unsteady aerodynamic optimization system for multistage turbomachinery. To the authors' best knowledge, this is the first work in the literature conducting the unsteady adjoint aerodynamic optimization of multistage turbomachinery. The unsteady flow equations and the discrete adjoint equations are solved using a finite volume code, with the harmonic balance method adopted to reduce the cost of unsteady simulations. The system is applied to the unsteady aerodynamic optimization of a 1.5-stage compressor. Results show the efficiency and capability of the proposed framework for the unsteady aerodynamic optimization of multistage 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.