Unsteady Flows In Turbomachinery Research Articles

Analyzing Unsteady Turbomachinery Flow Simulations With Mixing Entropy

Abstract The prediction of unsteady aerodynamic loads is a central problem during the design of turbomachinery. Over the last 20 years, harmonic balance methods have been shown to be highly efficient for this task. A CPU-cost optimal setup of a harmonic balance simulation, however, requires knowledge of relevant harmonics. In the case of a single blade row with a periodic disturbance this question amounts to the classical problem of harmonic convergence, a problem which is solely due to the nonlinearity of the unsteady flow physics. In contrast, for multi-stage configurations, the choice of harmonics is further complicated by the fact that the interactions of disturbances with blade rows may give rise to a vast spectrum of harmonics that possibly have important modal content, e.g., Tyler–Sofrin modes. The aim of this paper is to show that the mixing entropy attributed to circumferential modes of a given harmonic can serve as a disturbance metric on the basis of which a criterion could be derived whether a certain harmonic should be included or not. The idea is based on the observation that the entropy due to the temporal and circumferential mixing of the flow at a blade row interface may be decomposed, up to third-order terms, into independent contributions from different frequencies and mode orders. For a given harmonic balance (and steady) flow result, the mixing entropy attributed to modes that are simply mixed out, rather than resolved in the neighboring row, is shown to be a natural indicator of a potential inaccuracy. We present important features of the mixing entropy for unsteady disturbances, in particular a close relationship to sound power for acoustic modes. The problem of mode selection in a 1.5-stage compressor configuration serves as a practical example to illustrate our findings.

SIMD vectorization for simultaneous solution of locally varying linear systems with multiple right-hand sides

Developments in numerical simulation of flows and high-performance computing influence one another. More detailed simulation methods create a permanent need for more computational power, while new hardware developments often require changes to the software to exploit new hardware features. This dependency is very pronounced in the case of vector-units which are featured by all modern processors to increase their numerical throughput but require vectorization of the software to be used efficiently. We study the vectorization of a simulation method that exhibits an inherent level of vector-parallelism. This is of particular interest as SIMD operations will hopefully be available with std::simd in a future C++ standard. The simulation method considered here results in the simultaneous solution of multiple sparse linear systems of equations which only differ by their main diagonal and right-hand sides. Such structure arises in the simulation of unsteady flow in turbomachinery by means of a frequency domain approach called harmonic balance.

Loss Analysis of Unsteady Turbomachinery Flows Based on the Mechanical Work Potential

Abstract Loss analysis is a valuable technique for improving the thermodynamic performance of turbomachines. Analyzing loss in terms of the “mechanical work potential” (Miller, R.J., ASME Turbo Expo 2013, GT2013-95488) provides an instantaneous and local account of the thermal and aerodynamic mechanisms contributing to the loss of thermodynamic performance. This study develops the practical application of mechanical work potential loss analysis, providing the mathematical formulations necessary to perform loss analysis using practical Reynolds-averaged Navier–Stokes (RANS) or large eddy simulations (LES). The analysis approach is demonstrated using RANS and LES of a linear compressor cascade, both with and without incoming wakes. Spatial segmentation is used to attribute loss contributions to specific regions of the flow, and phase-averaging is performed in order to associate the variation of different loss contributions with the periodic passage of wakes through the cascade. For this un-cooled linear cascade, viscous dissipation is the dominant source of loss. The analysis shows that the contribution of the viscous reheat effect depends on the operating pressure of the compressor stage relative to the ambient “dead state” pressure—implying that the optimal blade profile for a low-pressure compressor stage may be different from the optimal profile for a high-pressure compressor stage in the same engine, even if the operating conditions for both stages are dynamically similar.

Accuracy and Efficiency Assessment of Harmonic Balance Method for Unsteady Flow in Multi-Stage Turbomachinery

With the relative movement of neighboring blade rows, flows in multi-stage turbomachinery are unsteady and periodic in time at the design condition. As an alternative to the widely used time domain time marching method, the harmonic balance (HB) method has been successfully applied to simulate the essentially unsteady flow of multi-stage turbomachinery. By modelling various number of harmonics, the accuracy of this method could be adjusted at different level of computational cost. In this article, accuracy of the harmonic balance method is not only validated against the time domain time marching method, as in most previous works on this topic, but also against the data from an experiment campaign of a two-stage high-pressure turbine where strong tip leakage flow exists. Efficiency of this method is also assessed in detail by adjusting the number of harmonics and comparing with time domain time marching solution results. Results show that the harmonic balance method is a flexible tool with adjustable accuracy for fast-turnaround unsteady flow simulation of multi-stage turbomachinery. Results from this work can provide a guidance in applying the harmonic balance method with balance between accuracy and computational cost.

Leveraging LDV techniques for the investigation of unsteady turbomachinery flows

ABSTRACTSteps required for proper acquisition and processing of laser Doppler velocimetry data for turbomachinery research applications are addressed. Turbomachinery applications are difficult due to the small internal passages, high-frequency fluctuations, large turbulence intensities, and strong secondary flows resulting in low overall signal-to-noise ratios and narrowband noise sources that cannot be removed by simple band-pass filters. Special aspects that must be considered for successful and accurate laser Doppler velocimetry studies to be conducted in turbomachinery are discussed. Specifically, the design of the measurement volume size, reflection mitigation, engineering of seed particle size and injection schema, and alignment of the traverse mechanism are addressed in terms of their importance (from literature sources) and the solutions implemented by the authors. These techniques have been applied to successfully obtain three-component, unsteady velocity data in a high-speed centrifugal compressor for aeroengine application. Processing techniques are also presented including a novel mixture-model-based statistical method for narrowband noise isolation developed by the authors. The method, validation steps, and example results are presented, showing the successful rejection of noise with high accuracy, a low failure rate, and a significant reduction in required manual inspection. This newly developed method elucidated flow features that were not clear prior to the noise removal.

Two-Scale Methodology for URANS/Large Eddy Simulation Solutions of Unsteady Turbomachinery Flows

A general issue in turbomachinery flow computations is how to capture and resolve two kinds of unsteadiness efficiently and accurately: (a) deterministic disturbances with temporal and spatial periodicities linked to blade count and rotational speed and (b) nondeterministic disturbances including turbulence and self-excited coherent patterns (e.g., vortex shedding, shear layer instabilities, etc.) with temporal and spatial wave lengths unrelated to blade count and rotational speed. In particular, the high cost of large eddy simulations (LES) is further compounded by the need to capture the deterministic unsteadiness of bladerow interactions in computational domains with large number of blade passages. This work addresses this challenge by developing a multiscale solution approach. The framework is based on an ensemble-averaging to split deterministic and nondeterministic disturbances. The two types of disturbances can be solved in suitably selected computational domains and solvers, respectively. The local fine mesh is used for nondeterministic turbulence eddies and vortex shedding, while the global coarse mesh is for deterministic unsteadiness. A key enabler is that the unsteady stress terms (UST) of the nondeterministic disturbances are obtained only in a small set of blade passages and propagated to the whole domain with many more passages by a block spectral mapping. This distinctive multiscale treatment makes it possible to achieve a high-resolution unsteady Reynolds-averaged Navier–Stokes (URANS)/LES solution in a multipassage/whole annulus domain very efficiently. The method description will be followed by test cases demonstrating the validity and potential of the proposed methodology.

Solution Stabilization and Convergence Acceleration for the Harmonic Balance Equation System

This paper presents an efficient approach for stabilizing solution and accelerating convergence of a harmonic balance equation system for an efficient analysis of turbomachinery unsteady flows due to flutter and blade row interaction. The proposed approach combines the Runge–Kutta method with the lower upper symmetric Gauss Seidel (LU-SGS) method and the block Jacobi method. The LU-SGS method, different from its original application as an implicit time marching scheme, is used as an implicit residual smoother with under-relaxation, allowing big Courant–Friedrichs–Lewy (CFL) numbers (in the order of hundreds), leading to significant convergence speedup. The block Jacobi method is introduced to implicitly integrate the time spectral source term of a harmonic balance equation system, in order to reduce the complexity of the direct implicit time integration by the LU-SGS method. The implicit treatment of the time spectral source term thus greatly augments the stability region of a harmonic balance equation system in the case of grid-reduced frequency well above ten. Validation of the harmonic balance flow solver was carried out using linear cascade test data. Flutter analysis of a transonic rotor and blade row interaction analyses for a transonic compressor stage were presented to demonstrate the stabilization and acceleration effect by the combination of the LU-SGS and the block Jacobi methods. The influence of the number of Jacobi iterations on solution stabilization is also investigated, showing that two Jacobi iterations are sufficient for stability purpose, which is much more efficient than existing methods of its kind in the open literature.

A Double-Passage Shape Correction Method for Predictions of Unsteady Flow and Aeroelasticity in Turbomachinery

AbstractIn this paper, a double-passage shape correction (DPSC) method is presented for simulation of unsteady flows around vibrating blades and aeroelastic prediction. Based on the idea of phase-lagged boundary conditions, the shape correction method was proposed aimed at efficiently dealing with unsteady flow problems in turbomachinery. However, the original single-passage shape correction (SPSC) may show the disadvantage of slow convergence of unsteady solutions and even produce nonphysical oscillation. The reason is found to be related with the disturbances on the circumferential boundaries that can not be damped by numerical schemes. To overcome these difficulties, the DPSC method is adopted here, in which the Fourier coefficients are computed from flow variables at implicit boundaries instead of circumferential boundaries in the SPSC method. This treatment actually reduces the interaction between the calculation of Fourier coefficients and the update of flow variables. Therefore a faster convergence speed could be achieved and also the solution stability is improved. The present method is developed to be suitable for viscous and turbulent flows. And for real three-dimensional (3D) problems, the rotating effects are also considered. For validation, a 2D oscillating turbine cascade, a 3D oscillating flat plate cascade and a 3D practical transonic fan rotor are investigated. Comparisons with experimental data or other solutions and relevant discussions are presented in detail. Numerical results show that the solution accuracy of DPSC method is favorable and at least comparable to the SPSC method. However, fewer iteration cycles are needed to get a converged and stable unsteady solution, which greatly improves the computational efficiency.

Space–Time Gradient Method for Unsteady Bladerow Interaction—Part I: Basic Methodology and Verification

For advanced turbomachinery development, there is increasing interest to carry out unsteady analyses for flows through multiple bladerows during a design stage. Even with the huge increase in computer processing power currently available, direct unsteady calculations in a whole annulus domain are still very time consuming. Efficient alternative methods with truncations in time and/or in space have been developed for unsteady turbomachinery flows in the past 20 years or so, but they all are associated with related limitations. The present development is motivated to maintain as many modeling fidelities of direct unsteady solution methods as possible while still have a significant speed-up. To this end, a new steady-solution-like unsteady time-domain methodology has been developed for bladerow interactions. No circumferential domain truncation is required so that a direct periodic (repeating) condition can be applied. For each mesh cell, the temporal gradient term as required to balance the discretized unsteady flow equation is obtained by specially sequenced spatial variations of corresponding cells in multiple-passages. Consequently, the rotor–stator interface treatment becomes completely compatible to that of a direct unsteady solution. Thus a fully conservative interface is easily achieved, in contrast to existing truncated models where interface treatments tend to be complicated and nonconservative. The simultaneous solution procedure with the space–time gradient (STG) link enables an unsteady flow solution to converge at a rate compatible to a steady solution. The background, motivation/justification, basic methodology, and some preliminary verifications are described in this paper as Part I. Further validations and applications with extension to more complex configurations and flow conditions will be presented in Part II.

Reduced Passage Method for Multirow Forced Response Computations

This paper presents a time-domain Fourier method for modeling steady and unsteady nonaxisymmetric flows in turbomachinery on a reduced computational domain. The method extends well-established single-passage multirow methods, which efficiently model periodic unsteadiness in single stages, to assemblies with stationary circumferential perturbations with periodicity different from the blade count. Such perturbations are caused, for example, by rotor–rotor/stator–stator interaction or geometric circumferential variations. The method is therefore suitable to study low-engine-order forcing problems, flow past nonuniform assemblies, and clocking problems. The proposed method solves the flow inside several discrete passages, located at different circumferential positions, using a time-accurate scheme. Boundary conditions at the azimuthal and interrow surfaces are approximated via time–space Fourier series and couple the individual passages. The reduced passage model is validated against the whole annulus solution for three test cases: 1) a row of outlet guide vanes with stagger pattern, 2) a high-pressure turbine stage with throat area variation in the stator, and 3) a 1.5-stage compressor. It is demonstrated that the time-domain Fourier method yields results equivalent to the whole annulus model but at a much reduced computational cost.

Multiblock residual-based compact schemes for the computation of complex turbomachinery flows

A flexible multiblock implementation of second and third-order accurate residual-based compact (RBC) schemes is proposed and validated for turbomachinery flows of increasing complexity. Applications to complex transonic unsteady flows in turbomachinery show the advantages of using such schemes in terms of increased accuracy and better insight into the flow physics.

Validation of an analysis method for particle image velocimetry of turbulent unsteady flows in turbomachinery

This paper presents a post-processing analysis that combines several statistical tools to validate experimental results in a particle image velocimetry analysis on unsteady flows in the turbomachinery field. The method was developed in three steps: verification of the number of acquired images, verification of the meaningfulness of the velocity averages, and identification of the zones characterized by the greatest error on the average estimation. The statistical approach allows one to identify the possible error sources, discriminating between experimental problems due to the test rig, the turbulent nature of the flow, and structures unidentifiable by a single frequency.

Aerodynamic Asymmetry Analysis of Unsteady Flows in Turbomachinery

A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of 2. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.

Recent German Research on Periodical Unsteady Flow in Turbomachinery

The main source of flow unsteadiness in turbomachinery is the aerodynamical interaction of the rotor and stator blade rows. The blades and vanes, moving relatively to each other, interact because of the viscous wakes and the potential effects of the blades. In addition, the wakes and potential effects superimpose with other flow patterns, for instance the tip clearance vortices and other secondary flow phenomena. Furthermore in transonic compressors the interaction of wakes and shocks plays an important role. As a result, the real flow field is highly periodically unsteady and very complex, especially in multistage turbomachinery. Although this fact has received increasing attention within recent years, blade row interactions effects are not yet typically addressed in current design systems of turbomachinery. Actually, there is a requirement of the ability of modern design methods to predict unsteady flow features. With increasing aerodynamic loading of the blades and higher Mach numbers the consideration of rotor-stator-interactions gains in importance. It is therefore one of the challenges of the present and future design of compressors and turbines to include beneficial unsteady effects to improve the engine parameters. This requires a detailed physical understanding of the unsteady flow field and the resulting effects on the performance and flow stability. In 2000 the joint research program “Periodical Unsteady Flow in Turbomachinery” was initiated. Partners of this project are five research groups from four german universities: Technische Universitat Berlin (Prof. Hourmouziadis), Universitat der Bundeswehr Munchen (Prof. Fottner, Prof. Pfitzner), Universitat Karlsruhe: Institut fur Thermische Stromungsmaschinen (Prof. Wittig, Dr. Dullenkopf), Institut fur Hydromechanik (Prof. Rodi), Technische Universitat Dresden (Prof. Vogeler), and a research group from the: German Aerospace Centre (Deutsches Zentrum fur Luft- und Raumfahrt), (Prof. Weyer, Prof. Monig). This 5-year program was funded by the German Research Foundation (Deutsche Forschungsgemeinschaft) and coordinated by Professor Hourmouziadis (Technische Universitat Berlin). The aim of this joint project is to contribute to an improved physical understanding of the periodical unsteady flow phenomena and to provide more reliable prediction methods of these complex flow conditions in turbomachinery. Selected aspects of flow unsteadiness in turbomachines were investigated with complementing experimental and numerical investigations. Different flow conditions of different complexity were investigated in detail. After a 3-year period of the project, first results of the research group are published in a special issue of the Journal of Flow, Turbulence and Combustion (Flow Turbulence Combust 69, 2002). After the end of the joint project, in the present paper selected results of each research group, which addresses different aspects of periodical unsteady flow in turbomachinery, are discussed. However, it is not the intention of the present paper to give a general survey on this field of research. The following topics are selected to provide insight into the work of the joint research group: (1) Experimental Investigation of Rotor-Stator-Interactions in an Axial Compressor, (2) Influence Of Periodically Unsteady Flow On The Boundary Layer Development Of A Highly Loaded Linear Turbine- And Compressor Cascade, (3) Flow Conditions on a Flat Plate under Oscillating Inlet Conditions, (4) Simultaneous Measurements of Flow and Heat Transfer in a Periodically Unsteady Flow, (5) Turbulence- and Transition Modelling for Unsteady RANS simulations, and (6) Direct Numerical Simulations of Transitional Flow in Turbine-Related Geometries.

Nonlinear Frequency-Domain Analysis of Unsteady Flows in Turbomachinery with Multiple Excitation Frequencies

A harmonic balance technique for the analysis of nonlinear unsteady flows in turbomachiney arising from several excitation sources, possibly with frequencies with irrational ratios, is presented in this paper. This method uses a mixed time-domain/frequencydomain approach that allows one to model the blade row on a computational grid spanning just a single blade passage, no matter the interblade phase angles of the original disturbances. Using this approach, we compute several solutions, each one corresponding to one of several times over one period for periodic flows, or over a representative time interval for aperiodic flows. These time levels are coupled to each other through a spectral time derivative operator in the interior of the computational domain, and through the far-field and periodic boundary conditions around the boundary of the domain. In this paper, we apply the method to the two-dimensional Euler equations (although the method can be applied to three-dimensional and viscous flows), and examine the nonlinear interaction of wake passing with blade vibration.

Fast Estimation of Unsteady Flows in Turbomachinery at Multiple Interblade Phase Angles

T IME-LINEARIZED computational fluid dynamic (CFD) models for the computation of unsteady flows in turbomachinery are now used routinely in the design and analysis of turbomachinery blade rows, particularly to predict the onset of flutter. A typical flutter analysis of a rotor requires one to compute unsteady flow solutions over the full range of interblade phase angles, and hence requires significant computational time even for relatively efficient time-linearized flow solvers. Typically, onemight compute the unsteady aerodynamic damping at several dozen interblade phase angles to ensure that no single interblade phase angle will flutter. In this note, we describe a fast technique that significantly reduces the computational time required to perform such a flutter clearance analysis. In recent years, researchers have developed models to reduce the time required to compute multiple unsteady flow solutions when one or more parameters is varying. In many (but not all) cases, the varying parameter is the frequency of airfoil vibration [1,2]. For example, Florea and Hall [3] computed the dominant eigenfrequencies and mode shapes of the unsteady fluid motion within a twodimensional cascade of airfoils using a nonsymmetric Lanczos algorithm, and then used these eigenmodes to construct a lowdegreeof-freedom reduced-ordermodel of the unsteadyflowfield around an airfoil. Kim [4] developed a frequency-domain proper orthogonal decomposition (POD) technique and applied it to both mechanical and fluid dynamic models. Hall et al. [5] developed reduced-order models of small-disturbance unsteady flows around airfoils and turbomachinery cascades using a POD technique. Similarly,Willcox et al. [6] developed an efficient frequency-domain proper orthogonal decomposition method for low order aeroelastic control of turbomachines. Cizmas and Palacios [7] used a POD technique to construct reduced-order models to examine a turbine rotor-stator interaction problem. (For a complete review of ROM/PODmethods, see Lucia et al. [8]). In most of these investigations, the reduced-order model is constructed in such a way that estimates of the unsteady flow can be constructed rapidly over a wide range of (possibly undetermined) vibrational frequencies. In the turbomachinery flutter problem, however, because of the high mass ratio associated with turbomachinery blading, the frequency of flutter is known a priori. Instead, the interblade phase angle of flutter is not known, and one must examine all possible interblade phase angles to insure that a rotor is flutter free. This suggests that for flutter problems, reducedorder model should be constructed in which the interblade phase angle is the free parameter. One notable exception is the work of Epureanu et al. [9]. Here, a POD technique was used to form a reduced-order model of two-dimensional viscous flow based on an inviscid boundary-layer coupled flow solver. Both frequency and interblade phase angle were allowed to vary. In this note, we present a fast technique that allows us to estimate the unsteady flows for many interblade phase angles very efficiently. Note that the base CFD solver used here is an iterative, threedimensional time-linearized flow solver.

Multistage Coupling for Unsteady Flows in Turbomachinery

Multistage Coupling for Unsteady Flows in Turbomachinery

Large eddy simulation of unsteady flows in turbomachinery

Unsteady computations of flows through a rotor of turbomachinery are very essential, and another challenge is to predict performances at off-design points, and to provide information on source fields as an input to the Ffowcs Williams-Hawkings (FW-H) equation for noise prediction. A deductive dynamic SGS modelling in large eddy simulation (LES) is proposed that does not impose averaging of the SGS model coefficients in homogeneous directions. This approach is tested and applied to the unsteady simulation of turbomachinery flow. The LES results from three typical cases of unsteady flows in turbomachinery, namely a NACA0018 airfoil, a compressor cascade and an axial fan, are reported. The flow characteristics on and around a symmetrical NACA0018 airfoil at moderate Reynolds number are simulated to establish the mechanism of discrete tone noise by unsteady flows near the trailing edge (TE) of the airfoil in a uniform flow. The flow past a compressor blade cascade is simulated to predict aerodynamic losses and self-noise by unsteady flows at off-design points. As a third example, the flowfields around rotating fan blades are simulated and used as an input to the FW-H equation to predict their farfield noise, which is in good agreement with experimental data.

Algorithm Developments for Discrete Adjoint Methods

This paper presents a number of algorithm developments for adjoint methods using the 'discrete' approach in which the discretisation of the non-linear equations is linearised and the resulting matrix is then transposed. With a new iterative procedure for solving the adjoint equations, exact numerical equivalence is maintained between the linear and adjoint discretisations. The incorporation of strong boundary conditions within the discrete approach is discussed, as well as a new application of adjoint methods to linear unsteady flow in turbomachinery.

A Three-Dimensional Linearized Euler Analysis of Classical Wake/Stator Interactions: Validation and Unsteady Response Predictions

A comprehensive validation of the linearized Euler analysis, LINFLUX, for wake/blade row interaction is carried out. The flow configuration is that of the benchmark problem for rotor-stator interaction proposed at the Third Computational Aeroacoustics Workshop. It consists of an unstaggered, annular, flat-plate blade row excited by the vortical gusts associated with the wakes shed from an upstream rotor. The numerical results for the unsteady pressure responses of the stator are compared with semi-analytic lifting surface and lifting line solutions. The validation is first conducted for narrow-annulus flows, where the numerical results are shown to agree well with classical two-dimensional solutions over a range of frequencies. We then carry out a detailed comparison of the three-dimensional LINFLUX results with the lifting surface results of Namba and Schulten for a blade row with a hub-to-tip ratio of 0.5. This study encompasses gust excitation frequencies for which the stator responses vary from cut off to propagating, as well as gusts with varying degrees of spanwise variation. The numerical and semi-analytical analyses yield results for the stator pressure response, including the complex amplitudes of the propagating and least attenuated, evanescent, pressure modes that are in very good agreement. The effect of increasing the spanwise phase variation of the gust is generally, but not necessarily, to reduce the power associated with the acoustic response of the blade row. A comparison of the present numerical results with those obtained from a stripwise application of classical linear theory reveals that the latter approach can be erroneous and, therefore, of questionable applicability to realistic turbomachinery unsteady flows.