Manufactured blades are inevitably different from their design intent, which leads to a deviation of the performance intended value. To quantify associated uncertainty, many approaches have been developed. The traditional Monte Carlo method based on Computational Fluid Dynamics solver (MC-CFD) for three-dimensional compressor is prohibitively expensive. Existing alternatives MC-CFD, such as surrogate models and second-order derivatives adjoint method, can greatly reduce computational cost....

The aerodynamic design and optimization of modern centrifugal compressors are inseparable from computational fluid dynamics (CFD) tools. In a environment, CFD simulations expected to predict compressor performance characteristics with reasonable accuracy. Turbulence models model simplification can play significant role in the discrepancy between analysis reality. To investigate influence turbulence on results compressors, National Aeronautics Space Administration's high efficiency stage is...

This paper proposes an approach that combines manual differentiation (MD) and automatic (AD) to develop efficient accurate multi-row discrete adjoint solver. In this approach, the structures of codes generated using AD tool are first analyzed. Then, AD-generated manually adjusted reduce memory CPU time consumption. adjustment is performed by replacing automatically low-efficient differentiated with developed ones. To demonstrate effectiveness proposed single-stage transonic compressor–NASA...

A forced response induced by inlet distortion and blade row interactions can lead to high-cycle fatigue failure, especially when the unsteady excitation frequency is close natural vibration of a blade. This paper presents study sensitivity analysis minimization using full-viscosity discrete adjoint method. The goal improve aeroelastic performances turbomachinery blades simultaneously constrain/improve aerodynamic performances. decoupled modal reduction method used compute response, which...

This paper presents an efficient approach for stabilizing solution and accelerating convergence of a harmonic balance equation system analysis turbomachinery unsteady flows due to flutter blade row interaction. The proposed combines the Runge–Kutta method with lower upper symmetric Gauss Seidel (LU-SGS) block Jacobi method. LU-SGS method, different from its original application as implicit time marching scheme, is used residual smoother under-relaxation, allowing big Courant–Friedrichs–Lewy...

This paper presents a combined experimental and computational study of unsteady flows in linear turbine cascade oscillating three-dimensional bending/flapping mode. Detailed data are obtained on seven-bladed rig. The middle blade is driven to oscillate using an influence coefficient method. numerical simulations performed by 3D nonlinear time-marching Navier–Stokes flow solver. Single-passage domain computations for arbitrary interblade phase angles achieved the Fourier shape correction Both...

This paper presents efficient alternative numerical methods for an implicit solution of the harmonic balance equation system analysing temporal periodic unsteady flows. The proposed method employs approximate factorisation to decouple common residual term and time spectral source a when it is discretised implicitly. With this factorisation, complexity discrete greatly reduced. can be dealt with using lower-upper symmetric-Gauss-Seidel (LU-SGS) integrated Jacobi iteration (JI) or one step...

This paper documents an investigation into unsteady flow in a three-dimensional oscillating turbine cascade with emphasis on the influence of tip clearance. Systematic experimental measurements were acquired low-speed rig. The consists seven prismatic blades, middle blade being driven to oscillate bending/flapping mode. Blades instrumented pressure tappings at six spanwise sections facilitate steady and surface. are complemented by computational fluid dynamics simulations. Both good...

Adjoint methods are widely used for turbomachinery aerodynamic shape optimization. However, industrial applications, the degradation of robustness and efficiency adjoint solvers edge-of-the-envelope conditions still poses a challenge to successful deployment in industry. This work attempts alleviate such problems by using Newton–Krylov method solve both flow equations. The developed parallel solver reuses Jacobian matrix computed obtains matrix–vector product via an accumulative...

Conventional blade flutter prediction is normally based on an isolated row model, however, little known about the influence of adjacent rows. In this article, investigation presented into upstream stator aero-elastic stability rotor blades in last stage a low pressure (LP) steam turbine. The computed directly by time-marching, unsteady, Navier-Stokes flow solver stator-rotor coupled computational domain. three-dimensional solution obtained, with adequate mesh resolution, single passage...

Abstract The paper presents a time-space spectral method for an efficient analysis of rotor–rotor/stator–stator interactions in the framework time form harmonic balance method. treats and space harmonics coherent way allows easy choice passage through introduction pseudo-shaft frequency composite frequency. proposed can accommodate to variation time-averaged flow field amplitude unsteady given as needed interactions. Minimum change is required extend existing solver incorporate most concise...

Precise and inexpensive uncertainty quantification (UQ) is crucial for robust optimization of compressor blades to control manufacturing tolerances. This study looks into the suitability MC−adj−nonlinear, a nonlinear adjoint-based approach, precisely rapidly assess performance discrepancies transonic blade section, arising from geometric alterations, building upon previous research. In order practicality illustrate benefits its proficiency precision are gauged against two other...

Abstract With increasing requirements for high-loading and high-efficiency turbomachines, blades become thinner thus design optimizations considering both aerodynamic performances aeroelastic stability more necessary. In this study, a full viscosity discrete adjoint harmonic balance solver has been developed using algorithmic differentiation (AD), verified by linear based upon duality property, then adopted to perform multi-disciplinary coupled optimizations. To end, framework of...

This paper presents a thorough study of the effect Constant Eddy Viscosity (CEV) assumption on optimization discrete adjoint-based design system. First, algorithms adjoint methods with and without CEV are presented, followed by discussion two methods’ solution stability. Second, sensitivity accuracy, stability, Root Mean Square (RMS) residual convergence rates at both off-design operating points compared between full viscosity in detail. Finally, multi-point steady aerodynamic...

Abstract The paper proposes a novel numerical method called coupled time and passage spectral for an efficient resolution of far upstream wakes in unsteady analysis flow field within generic multiple blade rows. proposed is very simple natural extension the form harmonic balance method. By including inter phase angle index truncated Fourier series, capable circumventing limitations dealing with zero frequency harmonics same but different angles. Different from method, which seeks solution at...

The conventional inverse method possesses several disadvantages: experience-dependence, inconvenience for multi-row application and lots of human intervention. This hinders it from becoming a routine design tool. In the present paper, those mentioned shortcomings are conquered by combining with adjoint method, which could give an automatic optimized in enviroment. principles first introduced. Then derivation equation based on Euler is conducted, corresponding boundary conditions deeply...

This paper revisits the Space-Time Gradient (STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents from an alternative time-clocking perspective. The STG requires reordering blade passages according their relative clocking positions with respect blades adjacent row. As space-clocking is linked equivalent time-clocking, passage can be performed time-clocking. With perspective, flow solutions different same row are mapped at time...

Abstract Manufactured compressor blades deviate from their intended design, leading to a shift in the mean and scattering of aerodynamic performance. To mitigate performance deterioration without escalating manufacturing costs, accurate efficient evaluation uncertainty, known as uncertainty quantification (UQ), is crucial. The computational cost three-dimensional fluid dynamics (CFD) simulations has prompted UQ studies predominantly target two-dimensional cases or extend three dimensions...

A multi-operating-point adjoint aerodynamic optimization of the fan a high bypass-ratio aero-engine is presented in this paper. Flow solutions at both design and off-design operating points are firstly obtained using an in-house Newton— Krylov flow solver, compared with commercial solver to verify their accuracy. Subsequently, automatic gradientbased workflow established perform optimization. Three typical related bypass performance, i.e. design, near stall choke considered order achieve...

Abstract Manufactured compressor blades deviate from their intended design, leading to a shift in the mean and scattering of aerodynamic performance. To mitigate performance deterioration without increasing manufacturing costs, an accurate efficient evaluation uncertainty, known as uncertainty quantification (UQ), is crucial. The high cost three-dimensional computational fluid dynamics (CFD) simulations has prompted UQ studies predominantly target two-dimensional cases or extend three...

This paper documents an investigation into unsteady flow in a three-dimensional oscillating turbine cascade with emphasis on the influence of tip clearance. Systematic experimental measurements were performed low-speed rig. The consists seven prismatic blades, middle blade being driven to oscillate bending/flapping mode. Blades instrumented pressure tappings at six span-wise sections facilitate three dimensional steady and surface. are complemented by CFD simulations. Both good agreement...

Hyperbolic metamaterials (HMMs) are artificial subwavelength-structured media that exhibit excellent hyperbolic properties. The Casimir force for HMMs can be predicted by effective medium theory (EMT), which simplifies the calculations considerably. However, conditions of EMT in between have not been investigated. In this work, we compare exact results calculated transfer matrix method (TMM) with those from EMT. numerical suggest accurately calculate only when gap distance is 100 times...