Data-driven techniques have proved their effectiveness in many engineering applications. Machine-learning has gradually become a paradigm to explore innovative designs in turbomachinery. However, industrial Computational Fluid Dynamics (CFD) experts are still reluctant to embed similar approaches in standard practice and very few solutions have been proposed so far. The aim of the work is to prove that standard wall treatments can obtain serious benefits from machine-learning modelling. Turbomachinery flow modelling lives in a constant compromise between accuracy and the computational costs of numerical simulations. One of the key factors of process is defining a proper wall treatment. Many works point out how insufficient resolutions of boundary layers may lead to incorrect predictions of turbomachinery performances. Wall functions are universally exploited to replicate the physics of boundary layers where grid resolution does not suffice. Despite their popularity, these functions are frequently applied in flows where the ground assumptions cease to be true, such as rotating passages or swirled flows. In these flows, the mathematical formulations of wall functions do not account for the distortion on the boundary layer due to the combined action of centrifugal and Coriolis forces. Here we will derive a wall function for rotating passages, through means of machine-learning. The algorithm is directly implemented in the N-S equations solver. Cross-validation results show that the machine-learnt wall treatment is able to effectively correct the turbulent kinetic energy field near the solid walls, without impairing the accuracy of the k-epsilon model.

The flow field in a compressor is circumferentially non-uniform due to the wakes from upstream stators, the potential field from both upstream and downstream stators, and blade row interactions. This non-uniform flow impacts stage performance as well as blade forced vibrations. Historically, experimental characterization of the circumferential flow variation is achieved by circumferentially traversing either a probe or the stator rows. This involves the design of complex traverse mechanisms and can be costly. To address this challenge, a novel method is proposed to reconstruct compressor nonuniform circumferential flow field using spatially under-sampled data points from a few probes at fixed circumferential locations. The paper is organized into two parts. In the present part of the paper, details of the multi-wavelet approximation for the reconstruction of circumferential flow and use of the Particle Swarm Optimization algorithm for selection of probe positions are presented. Validation of the method is performed using the total pressure field in a multi-stage compressor representative of small core compressors in aero engines. The circumferential total pressure field is reconstructed from 8 spatially distributed data points using a triple-wavelet approximation method. Results show good agreement between the reconstructed and the true total pressure fields. Also, a sensitivity analysis of the method is conducted to investigate the influence of probe spacing on the errors in the reconstructed signal.

As a consequence of constant volume combustion in gas turbines, pressure waves propagating upstream the main flow into the compressor system are generated leading to incidence variations. Numerical and experimental investigations of stator vanes have shown that active flow control (AFC) by means of adaptive blade geometries is beneficial when such periodic incidence variations occur. A significant risk reduction in a compressor facing disturbances can thereby be achieved concerning stall or choke. Experimental investigations on such an AFC method with simultaneous application of a closed-loop control are missing in order to demonstrate its potential. This work investigates a linear compressor cascade that is equipped with a 3D-manufactured piezo-adaptive blade structure. The utilized actuators are piezoelectric macro-fiber-composites. A throttling device is positioned downstream the trailing edge plane to emulate an unsteady combustion process. Periodic transient throttling events with a frequency of up to 20 Hz cause incidence changes to the blade’s leading edge. Consequently, pressure fluctuations on the blade’s surface occur, having a significant impact on the pressure recovery downstream of the stator cascade. Experimental results of harmonically actuating the piezo-adaptive blade with the corresponding disturbance frequency show that the impact of disturbances can be reduced to approximately 50%. However, this is only effective if the phase shift of the harmonic actuation is adjusted correctly. Using an inadequate phase shift reverses the positive effects, causing the aforementioned stall, choke, or significant losses. In order to find the optimum phase shift, even under varying, possibly unpredictable operating conditions, an extremum seeking controller is presented. This gradient-based approach is minimizing the pressure variance over time by carefully adjusting the phase shift of the harmonic actuation of the AFC system.

This paper presents a multipoint optimization of the LS89 cascade. The objective of the optimization consists in minimizing the entropy losses generated inside the cascade over a predefined operating range. Two aerodynamic constraints are imposed in order to conserve the same performance as the original cascade. The first constraint is established on the outlet flow angle in order to achieve at least the same flow turning as the LS89. The second constraint limits the mass-flow passing through the cascade. The optimization is performed using a hybrid algorithm which combines a classical evolutionary algorithm with a gradient-based method. The hybridization between both methods is based on the Lamarckian approach which consists in incorporating the gradient method inside the loop of the evolutionary algorithm. In this methodology, the evolutionary method allows to globally explore the design space while the gradient-based method locally improves certain designs located in promising regions of the search space. First, the better performance of the hybrid method compared to the performance of an evolutionary algorithm is demonstrated on benchmark problems. Then, the methodology is applied on the LS89 application. The optimization allows to find a new profile which reduces the entropy losses over the entire operating range by at least 9.5 %. Finally, the comparison of the flows computed in the baseline and in the optimized cascades demonstrates that the reduction of the losses is due to a decrease of the entropy generated downstream the trailing edges and within the passages between the optimized blades.

The design of low-pressure turbines (LPTs) must account for the losses generated by the unsteady interaction with the upstream blade row. The estimation of such unsteady wake-induced losses requires the accurate prediction of the incoming wake dynamics and decay. Existing linear turbulence closures (stress–strain relationships), however, do not offer an accurate prediction of the wake mixing. Therefore, machine-learnt, nonlinear turbulence closures (models) have been developed for LPT flows with unsteady inflow conditions using a zonal-based model development approach, with an aim to enhance the wake mixing prediction for unsteady Reynolds-averaged Navier–Stokes calculations. High-fidelity time-averaged and phase-lock averaged data at a realistic isentropic Reynolds number and two reduced frequencies, i.e., with discrete incoming wakes and with wake “fogging,” have been used as reference data for a machine learning algorithm based on gene expression programing to develop models. Models developed via phase-lock averaged data were able to capture the effect of certain prominent physical phenomena in LPTs such as wake–wake interactions, whereas models based on the time-averaged data could not. Correlations with the flow physics lead to a set of models that can effectively enhance the wake mixing prediction across the entire LPT domain for both cases. Based on a newly developed error metric, the developed models have reduced the a priori error over the Boussinesq approximation on average by 45%. This study thus aids blade designers in selecting the appropriate nonlinear closures capable of mimicking the physical mechanisms responsible for loss generation.

Current turbulent heat flux models fail to predict accurate temperature distributions in film cooling flows. The present paper focuses on a machine learning (ML) approach to this problem, in which the gradient diffusion hypothesis (GDH) is used in conjunction with a data-driven prediction for the turbulent diffusivity field α t . An overview of the model is presented, followed by validation against two film cooling datasets. Despite insufficiencies, the model shows some improvement in the near-injection region. The present work also attempts to interpret the complex ML decision process, by analyzing the model features and determining their importance. These results show that the model is heavily reliant of distance to the wall d and eddy viscosity ν t , while other features display localized prominence.

In film cooling flows, it is important to know the temperature distribution resulting from the interaction between a hot main flow and a cooler jet. However, current Reynolds-averaged Navier–Stokes (RANS) models yield poor temperature predictions. A novel approach for RANS modeling of the turbulent heat flux is proposed, in which the simple gradient diffusion hypothesis (GDH) is assumed and a machine learning (ML) algorithm is used to infer an improved turbulent diffusivity field. This approach is implemented using three distinct data sets: two are used to train the model and the third is used for validation. The results show that the proposed method produces significant improvement compared to the common RANS closure, especially in the prediction of film cooling effectiveness.

This work newly proposes an uncertainty quantification (UQ) method named sparse approximation of moment-based arbitrary polynomial chaos (SAMBA PC) that offers a single solution to many current problems in turbomachinery applications. At the moment, every specific case is characterized by a variety of different input types such as histograms (from experimental data), normal probability density functions (PDFs) (design rules) or fat tailed PDFs (for rare events). Thus, the application of UQ requires the adaptation of ad hoc methods for each individual case. A second problem is that parametric PDFs have to be determined for all inputs. This is difficult if only few samples are available. In gas turbines, however, the collection of statistical information is difficult, expensive, and having scarce information is the norm. A third critical limitation is that if using nonintrusive polynomial chaos (NIPC) methods, the number of required simulations grows exponentially with increasing numbers of input uncertainties: the so-called “curse of dimensionality.” It is shown that the fitting of parametric PDFs to small data sets can lead to large bias and the direct use of the available data is more accurate. This is done by propagating uncertainty through several test functions and the computational fluid dynamics (CFD) simulation of a diffuser, highlighting the impact of different PDF fittings on the output. From the results, it is concluded that the direct propagation of the experimental data set is preferable to the fit of parametric distributions if data is scarce. Thus, the suggested method offers an alternative to the maximum entropy theorem to handle scarce data. SAMBA simplifies the mathematical procedure for many different input types by basing the polynomial expansion on moments. Its moment-based expansion automatically takes care of arbitrary combinations of different input data. It is also numerically efficient compared to other UQ implementations. The relationship between the number of random variables and number of simulation is linear (only 21 simulations for ten input random variables are required). It is shown in this paper that SAMBA's algorithm can propagate a high number of input distributions through a set of nonlinear analytic test functions. Doing this, the code needs a very small number of simulations and preserve a 5% error margin. SAMBA's flexibility to handle different forms of input distributions and a high number of input variables is shown on a low-pressure turbine (LPT) blade-based on H2 profile. The relative importance of manufacturing errors in different location of the blade is analyzed.

Self-adaptive stability control with discrete tip air injection and online detection of prestall inception is experimentally studied in a low-speed axial flow compressor. The control strategy is to sense the cross-correlation coefficient of the wall static pressure patterns and to feed back the signal to an annular array of eight separately proportional injecting valves. The real-time detecting algorithm based on cross-correlation theory is proposed and experimentally conducted using the axisymmetric arrangement of time-resolved sensors. Subsequently, the sensitivity of the cross-correlation coefficient to the discrete tip air injection is investigated. Thus, the control law is formed on the basis of the cross-correlation as a function of the injected momentum ratios. The steady injection and the on–off pulsating injection are simultaneously selected for comparison. Results show that the proposed self-adaptive stability control using digital signal processing (DSP) controller can save energy when the compressor is stable. This control also provides protection when needed. With nearly the same stall margin improvement (SMI) as the steady injection (maximum SMI is 44.2%), the energy of the injected air is roughly a quarter of the steady injection. Unlike the on–off pulsating jet, the new actuating scheme can reduce the unsteady force impinging onto the compressor blades caused by the pulsating jets in addition to achieve the much larger stability range extension.

This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier–Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

Online line-of-sight (LOS) pyrometer is used on certain jet engines for diagnosis and control functions such as hot-blade detection, high-temperature limiting, and condition-based monitoring. Hot particulate bursts generated from jet engine combustor at certain running conditions lead to intermittent high-voltage signal outputs from the LOS pyrometer which is ultimately used by the onboard digital engine controller (DEC). To study the nature of hot particulates and enable LOS pyrometer functioning under burst conditions, a multicolor pyrometry (MCP) system was developed under DARPA funded program and tested on an aircraft jet engine. Soot particles generated as byproduct of combustion under certain conditions was identified as the root cause for the signal burst in a previous study. The apparent emissivity was then used to remove burst signals. In current study, the physics based filter with MCP algorithm using apparent emissivity was further extended to real-time engine control by removing burst signals at real time (1 MHz) and at engine DEC data rate. Simulink models are used to simulate the performances of the filter designs under engine normal and burst conditions. The results are compared with current LOS pyrometer results and show great advantage. The proposed model enables new LOS pyrometer design for improved engine control over wide range of operating conditions.

In this paper, a novel global optimization algorithm has been developed, which is named as particle swarm optimization combined with particle generator (PSO–PG). In PSO–PG, a PG was introduced to iteratively generate the initial particles for PSO. Based on a series of comparable numerical experiments, it was convinced that the calculation accuracy of the new algorithm as well as its optimization efficiency was greatly improved in comparison with those of the standard PSO. It was also observed that the optimization results obtained from PSO–PG were almost independent of some critical coefficients employed in the algorithm. Additionally, the novel optimization algorithm was adopted in the airfoil optimization. A special fitness function was designed and its elements were carefully selected for the low-velocity airfoil. To testify the accuracy of the optimization method, the comparative experiments were also carried out to illustrate the difference of the aerodynamic performance between the optimized and its initial airfoil.

Sensitivity and numerical stability of an algorithm are two of the most important criteria to evaluate its performance. For all published turbine flow models, except Wang method, can be named the “top-down” method (TDM) in which the performance of turbines is calculated from the first stage to the last stage row by row; only Wang method originally proposed by Yonghong Wang can be named the “bottom-up” method (BUM) in which the performance of turbines is calculated from the last stage to the first stage row by row. To find the reason why the stability of the two methods is of great difference, the Wang flow model is researched. The model readily applies to TDM and BUM. How the stability of the two algorithms affected by input error and rounding error is analyzed, the error propagation and distribution in the two methods are obtained. In order to explain the problem more intuitively, the stability of the two methods is described by geometrical ideas. To compare with the known data, the performance of a particular type of turbine is calculated through a series of procedures based on the two algorithms. The results are as follows. The more the calculating point approaches the critical point, the poorer the stability of TDM is. The poor stability can even cause failure in the calculation of TDM. However, BUM has not only good stability but also high accuracy. The result provides an accurate and reliable method (BUM) for estimating the performance of turbines, and it can apply to all one-dimensional performance calculation method for turbine.

This paper describes the development and validation steps of a characteristics-based explicit along with a novel fully implicit mixing plane implementation for turbomachinery applications. The framework is an unstructured 3D RANS in-house modified solver, based on open-source libraries. Particular attention was paid to mass-conservation, accurate variables interpolation, and algorithm stability in order to improve robustness and convergence. By introducing a specific interface, allowing the use of algebraic multigrid solvers together with multiprocessor computation, a speed up of the numerical solution procedure was achieved. The validation of both mixing plane algorithms is carried out on an industrial radial compressor and a cold air 1.5 stages axial turbine.

A Defense Advanced Research Projects Agency (DARPA)-funded multicolor pyrometry (MCP) experiment was carried out on a government-provided aircraft engine to study the nature of hot particulate bursts generated from the combustor at certain engine conditions. These bursts of hot particulates lead to intermittent high-voltage signal output from the line-of-sight (LOS) pyrometer that is ultimately detected and used by the onboard digital engine controller (DEC). The investigation used a high-speed MCP system designed to detect bursts and identify their properties. Results of the radiant temperature, multicolor temperature, and apparent emissivity are presented. The results indicated that the apparent emissivity calculated during the signal burst was lower than that of the blade. The root cause for the signal burst was identified as soot particles generated as a by-product of combustion under certain conditions. This conclusion was drawn based on both experimental and simulation results. Technical strategies to separate, reduce, or remove the burst signal are proposed.

This is the first part of a series of two papers on unsteady computational fluid dynamics (CFD) methods for the numerical simulation of aerodynamic noise generation and propagation. In this part, the stability, accuracy, and efficiency of implicit Runge–Kutta schemes for the temporal integration of the compressible Navier–Stokes equations are investigated in the context of a CFD code for turbomachinery applications. Using two model academic problems, the properties of two explicit first stage, singly diagonally implicit Runge–Kutta (ESDIRK) schemes of second- and third-order accuracy are quantified and compared with more conventional second-order multistep methods. Finally, to assess the ESDIRK schemes in the context of an industrially relevant configuration, the schemes are applied to predict the tonal noise generation and transmission in a modern high bypass ratio fan stage and comparisons with the corresponding experimental data are provided.

Traditional hot gas path film cooling characterization involves the use of wind tunnel models to measure the spatial adiabatic effectiveness (η) and heat transfer coefficient (h) distributions. Periodic unsteadiness in the flow, however, causes fluctuations in both η and h. In this paper we present a novel inverse heat transfer methodology that may be used to approximate the η(t) and h(t) waveforms. The technique is a modification of the traditional transient heat transfer technique that, with steady flow conditions only, allows the determination of η and h from a single experiment by measuring the surface temperature history as the material changes temperature after sudden immersion in the flow. However, unlike the traditional transient technique, this new algorithm contains no assumption of steadiness in the formulation of the governing differential equations for heat transfer into a semi-infinite slab. The technique was tested by devising arbitrary waveforms for η and h at a point on a film cooled surface and running a computational simulation of an actual experimental model experiencing those flow conditions. The surface temperature history was corrupted with random noise to simulate actual surface temperature measurements and then fed into an algorithm developed here that successfully and consistently approximated the η(t) and h(t) waveforms.

A computational method for performing aeroelastic analysis using either a time-linearized or an unsteady time-accurate solver for the compressible Reynolds averaged Navier--Stokes (RANS) equations is described. The time-linearized solver employs the assumption of small time-harmonic perturbations and is implemented via finite differences of the nonlinear flux routines of the time-accurate solver. The resulting linear system is solved using a parallelized generalized minimal residual (GMRES) method with block-local preconditioning. The time accurate solver uses a dual time stepping algorithm for the solution of the unsteady RANS equations on a periodically moving computational grid. For either solver, and both flutter and forced response problems, a mapping algorithm has been developed to map structural eigenmodes, obtained from finite element structural analysis, from the surface mesh of the finite element structural solver to the surface mesh of the finite volume flow solver. Using the surface displacement data an elliptic mesh deformation algorithm, based on linear elasticity theory, is then used to compute the grid deformation vector field. The developed methods are validated first using standard configuration 10. Finally, for an ultra-high bypass ratio fan, the results of the time-linearized and the unsteady module are compared. The gain in prediction time using the linearized methods is highlighted.

Integral bladed disks (also known as blisks) are more widely used in modern aeroengine compressor designs because of the potential weight savings, but there are challenges in controlling the extreme vibration response levels in mistuned blisks, which are blisks with blades slightly different from each other. As blisks lack the uncertainty and variability of friction properties related to joints, the maximum vibration response level of a blisk test piece in operation can be predicted prior to installation. A previously proposed response-level prediction procedure for mistuned blisks is outlined, and its robustness is studied. A method of improving the results, given noisy experimental data, is proposed. Some of the issues discussed are validated by using experimental data.

A new three-dimensional Navier–Stokes solver for flows in turbomachines has been developed. The new solver is based on the latest version of the Denton codes but has been implemented to run on graphics processing units (GPUs) instead of the traditional central processing unit. The change in processor enables an order-of-magnitude reduction in run-time due to the higher performance of the GPU. The scaling results for a 16 node GPU cluster are also presented, showing almost linear scaling for typical turbomachinery cases. For validation purposes, a test case consisting of a three-stage turbine with complete hub and casing leakage paths is described. Good agreement is obtained with previously published experimental results. The simulation runs in less than 10 min on a cluster with four GPUs.