A signal reconstruction algorithm based on the compressed sensing (CS) theory with dual-uniform sampling point (DUSP) distribution is developed and applied to identify the azimuthal mode of axial compressor. A regular failure signal pattern is found, and the corresponding explanation is presented with validation. Azimuthal mode analysis is applied to both numerical and experimental pressure fluctuation signals of rotating instability (RI) in the axial compressor tip region. For numerical calculations, the signal in the azimuthal mode domain is reconstructed by the CS with random measurement points and DUSP, respectively. The success rates and reconstruction errors are discussed in detail. It is shown that the azimuthal mode reconstruction method based on CS combined with DUSP is capable of identifying the complex flow modes in the tip region of the axial compressor. For the experimental results, high azimuthal mode orders are reconstructed based on dynamic pressure signals measured by DUSP. Azimuthal mode analysis efficiency is thereby significantly improved. The time-resolved characteristics of the RI are discussed. Moreover, a robustness analysis is conducted, demonstrating the ability of the CS-based method with DUSP to address sensor failure problems.

In this paper, error sources affecting the dynamic calibration of fast response pressure probes in shock tubes are examined. In particular, the sensors uncertainty, the uncertainty in the rising point of the pressure step and the nonideality of the step are treated. The latter refers to the presence of pressure oscillations past the shock front, which are particularly important in the case of low-pressure shock tubes, typically used for the calibration of pressure probes for turbomachinery applications. The nonideality effect is investigated using a Linear Time Invariant (LTI) second order model for the transfer function of the probe's line-cavity system and an existing analytical model for the post-shock oscillations. The effect of these uncertainty sources to the experimentally determined transfer function of a fast response probe calibrated in the von Karman Institute (VKI) shock tube are finally presented.

As designers aim to increase efficiency in gas turbines for aircraft propulsion and power generation, spatially resolved experimental measurements are needed to validate computational models and compare improvement gains of new cooling designs. Infrared (IR) thermography is one such method for obtaining spatially resolved temperature measurements. As technological advances in thermal detectors enable faster integration times, surface temperature measurements of rotating turbine blades become possible to capture including the smallest features. This paper outlines opportunities enabled by the latest IR detector technologies for capturing spatially resolved rotating blade temperatures, while also addressing some of the challenges of implementing IR for turbine rigs such as the one in the Steady Thermal Aero Research Turbine (START) Laboratory. This paper documents critical steps in achieving accurate measurements including calibration, integration times, spatial noise, and motion blur. From these results, recommendations are provided for achieving accurate IR measurements collected in a rotating turbine facility to study film cooling.

There is relatively little literature concerning the effect of Reynolds number on multihole aerodynamic probe performance. In particular, there is almost no discussion in the literature regarding the underlying mechanisms of Reynolds number (Re) sensitivity for such probes. In order to close this gap, detailed investigations of the effect of Re on a five-hole probe have been performed using both PIV techniques and oil flow visualizations. Wind- and water-tunnels were used to cover a wide range of Re. The open-access Oxford Probe was used for these studies because of the readily available data-sets and processing routines, and to allow future comparisons by other authors. Complex flow dynamics including flow separation and re-attachment were identified, which cause Re-sensitivity of the calibration map at low Re even for low yaw or pitch angles. By comparing calibration maps across a wide range of Re, we demonstrate that the Oxford Probe can be employed without much loss of accuracy at lower Re levels than initially (conservatively) suggested, and quantify the errors in the extreme low-Re regime. Overall we demonstrate the robustness of the Oxford Probe concept across a wide range of Re conditions, we more clearly defined the low-Re limit for the probe design and quantify errors below this limit, and we illustrate the fundamental mechanisms for Re-sensitivity of multi-hole probes.

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.

In the previous part of the paper, a novel method to reconstruct the compressor non-uniform circumferential flow field using spatially under-sampled data points is developed. In this part of the paper, the method is applied to two compressor research articles to further demonstrate the potential of the novel method in resolving the important flow features associated with these circumferential non-uniformities. In the first experiment, the static pressure field at the leading edge of a vaned diffuser in a high-speed centrifugal compressor is reconstructed using pressure readings from nine static pressure taps placed on the hub of the diffuser. The magnitude and phase information for the first three dominant wavelets are characterized. Additionally, the method shows significant advantages over the traditional averaging methods for calculating repeatable mean values of the static pressure. While using the multi-wavelet approximation method, the errors in the mean static pressure with one dropout measurement are 70% less than the pitchwise-averaging method. In the second experiment, the full-annulus total pressure field downstream of Rotor 2 in a three-stage axial compressor is reconstructed from a small segment of data representing 20% coverage of the annulus. Results show very good agreement between the reconstructed total pressure profile and the experiment at a variety of spanwise locations from near hub to near shroud. The features associated with blade-row interactions accounting for passage-to-passage variations are resolved in the reconstructed total pressure profile.

The present paper focuses on the resilience of 3-hole pressure probes to hot sand fouling in turbomachinery environments. These probes are utilized inside jet engine hot sections for diagnostics and flow characterization. Ingestion of sand and other particulates pose a significant risk to hot section components and measurement devices in gas turbine engines. In this study, wedge, cylindrical, and trapezoidal probes were exposed to hot section turbine aerothermal conditions of 1050 °C and 65–70 m/s flow velocity and fouled with 0–5 µm Arizona Road Dust (ARD). Sand accumulated more rapidly on the surface of the trapezoidal and cylindrical probe geometries than on the surface of the wedge probe geometry. Probe calibrations following sand fouling were performed in an ambient temperature, open air, calibration jet at Mach 0.3 and 0.5. Calibration curves using nondimensional coefficients were used to assess probe error in yaw angle due to sand fouling. Probe error was based on each probe’s ability to accurately measure flow direction over a flow angle range of [−10 deg, 10 deg]. On average, the probes displayed greater error at Mach 0.5 than Mach 0.3. The wedge probe performed the best after sand fouling and displayed a maximum error of less than ±2 deg in yaw angle. In contrast, the cylindrical probe performed the worst after sand fouling and displayed maximum errors of more than ±8 deg in yaw angle. Transient response did not change notably with sand fouling.

The aerothermal characterization of film-cooled geometries is traditionally performed at reduced temperature conditions, which then requires a debatable procedure to scale the convective heat transfer performance to engine conditions. This paper describes an alternative engine-scalable approach, based on Discrete Green’s Functions (DGF) to evaluate the convective heat flux along film-cooled geometries. The DGF method relies on the determination of a sensitivity matrix that accounts for the convective heat transfer propagation across the different elements in the domain. To characterize a given test article, the surface is discretized in multiple elements that are independently exposed to perturbations in heat flux to retrieve the sensitivity of adjacent elements, exploiting the linearized superposition. The local heat transfer augmentation on each segment of the domain is normalized by the exposed thermal conditions and the given heat input. The resulting DGF matrix becomes independent from the thermal boundary conditions, and the heat flux measurements can be scaled to any conditions given that Reynolds number, Mach number, and temperature ratios are maintained. The procedure is applied to two different geometries, a cantilever flat plate and a film-cooled flat plate with a 30 degree 0.125 in. cylindrical injection orifice with length-to-diameter ratio of 6. First, a numerical procedure is applied based on conjugate 3D unsteady Reynolds-averaged Navier–Stokes (URANS) simulations to assess the applicability and accuracy of this approach. Finally, experiments performed on a flat plate geometry are described to validate the method and its applicability. Wall-mounted thermocouples are used to monitor the surface temperature evolution, while a 10 kHz burst-mode laser is used to generate heat flux addition on each of the discretized elements of the DGF sensitivity matrix.

The effects of blade row interactions on stator-mounted instrumentation in axial compressors are investigated using unsteady numerical calculations. The test compressor is an eight-stage machine representative of an aero-engine core compressor. For the unsteady calculations, a 180-deg sector (half-annulus) model of the compressor is used. It is shown that the time-mean flow field in the stator leading edge planes is circumferentially nonuniform. The circumferential variations in stagnation pressure and stagnation temperature, respectively, reach 4.2% and 1.1% of the local mean. Using spatial wave number analysis, the incoming wakes from the upstream stator rows are identified as the dominant source of the circumferential variations in the front and middle of the compressor, while toward the rear of the compressor, the upstream influence of the eight struts in the exit duct becomes dominant. Based on three circumferential probes, the sampling errors for stagnation pressure and stagnation temperature are calculated as a function of the probe locations. Optimization of the probe locations shows that the sampling error can be reduced by up to 77% by circumferentially redistributing the individual probes. The reductions in the sampling errors translate to reductions in the uncertainties of the overall compressor efficiency and inlet flow capacity by up to 50%. Recognizing that data from large-scale unsteady calculations are rarely available in the instrumentation phase for a new test rig or engine, a method for approximating the circumferential variations with single harmonics is presented. The construction of the harmonics is based solely on the knowledge of the number of stators in each row and a small number of equispaced probes. It is shown how excursions in the sampling error are reduced by increasing the number of circumferential probes.

Thin-film heat flux gauges (HFGs) have been used for decades to measure surface temperatures and heat flux in test turbines with the majority being used in facilities that are short-duration. These gauges are typically composed of two resistive temperature devices deposited on opposing sides of a dielectric. However, because these sensors have been traditionally applied for measurements in transient-type facilities, the challenges facing adaptation of this technology for a steady facility warrant investigation. These challenges are highlighted, and the solutions are presented throughout the paper. This paper describes the nanofabrication process for heat flux gauges and a new calibration method to address the potential deterioration of gauges over long runtimes in continuous-duration facilities. Because the primary uncertainty of these sensors arises from the ambiguity of the thermal properties, the emphasis is placed on the property determination. Also, this paper presents a discussion on the use of impulse response theory to process the data showing the feasibility of the method for steady-duration facilities after an initial settling time. The latter portion of the paper focuses on comparing well-established heat flux gauges developed for short-duration turbine test facilities to recently developed gauges fabricated using modern nanofabrication techniques for a continuous turbine test facility. The gauges were compared using the test case of an impinging jet over a range of Reynolds numbers. The comparison between the PSU gauge and the reference device indicated agreement within 14%, and similar results were achieved through comparison with established sensors from partner institutions.

Our investigation raises an important question that is of relevance to the wider turbomachinery community: how do we estimate the spatial average of a flow quantity given finite (and sparse) measurements? This paper seeks to advance efforts to answer this question rigorously. In this paper, we develop a regularized multivariate linear regression framework for studying engine temperature measurements. As part of this investigation, we study the temperature measurements obtained from the same axial plane across five different engines yielding a total of 82 datasets. The five different engines have similar architectures and therefore similar temperature spatial harmonics are expected. Our problem is to estimate the spatial field in engine temperature given a few measurements obtained from thermocouples positioned on a set of rakes. Our motivation for doing so is to understand key engine temperature modes that cannot be captured in a rig or in computational simulations, as the cause of these modes may not be replicated in these simpler environments. To this end, we develop a multivariate linear least-squares model with Tikhonov regularization to estimate the 2D temperature spatial field. Our model uses a Fourier expansion in the circumferential direction and a quadratic polynomial expansion in the radial direction. One important component of our modeling framework is the selection of model parameters, i.e., the harmonics in the circumferential direction. A training-testing paradigm is proposed and applied to quantify the harmonics.

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.

Nonlinear turbulence closures were developed that improve the prediction accuracy of wake mixing in low-pressure turbine (LPT) flows. First, Reynolds-averaged Navier–Stokes (RANS) calculations using five linear turbulence closures were performed for the T106A LPT profile at isentropic exit Reynolds numbers 60,000 and 100,000. None of these RANS models were able to accurately reproduce wake loss profiles, a crucial parameter in LPT design, from direct numerical simulation (DNS) reference data. However, the recently proposed k v 2 ¯ ω transition model was found to produce the best agreement with DNS data in terms of blade loading and boundary layer behavior and thus was selected as baseline model for turbulence closure development. Analysis of the DNS data revealed that the linear stress–strain coupling constitutes one of the main model form errors. Hence, a gene-expression programming (GEP) based machine-learning technique was applied to the high-fidelity DNS data to train nonlinear explicit algebraic Reynolds stress models (EARSM), using different training regions. The trained models were first assessed in an a priori sense (without running any RANS calculations) and showed much improved alignment of the trained models in the region of training. Additional RANS calculations were then performed using the trained models. Importantly, to assess their robustness, the trained models were tested both on the cases they were trained for and on testing, i.e., previously not seen, cases with different flow features. The developed models improved prediction of the Reynolds stress, turbulent kinetic energy (TKE) production, wake-loss profiles, and wake maturity, across all cases.

The measurement accuracy of the temperature/pressure probe mounted at the leading edge of a turbine/compressor blade is crucial for estimating the fuel consumption of a turbo-fan engine. Apart from the measurement error itself, the probe also introduces extra losses. This again would compromise the measurement accuracy of the overall engine efficiency. This paper utilizes high-fidelity numerical analysis to understand the complex flow around the probe and quantify the loss sources due to the interaction between the blade and its instrumentation. With the inclusion of leading-edge probes, three-dimensional flow phenomena develop, with some flow features acting in a similar manner to a jet in cross flow. The separated flow formed at the leading edge of the probe blocks a large area of the probe bleedhole, which is one of the reasons why the probe accuracy can be sensitive to Mach and Reynolds numbers. The addition of 4% free-stream turbulence is shown to have a marginal impact on the jet trajectory originated from the probe bleedhole. However, a slight reduction is observed in the size of the separation bubble formed at the leading edge of the probe, preceding the two bleedhole exits. The free-stream turbulence also has a significant impact on the size of the separation bubble near the trailing edge of the blade. With the addition of the free-stream turbulence, the loss observed within the trailing edge wake is reduced. More than 50% of the losses at the cascade exit are generated by the leading-edge probe. A breakdown of the dissipation terms from the mean flow kinetic energy equation demonstrates that the Reynolds stresses are the key terms in dissipating the counter-rotating vortex pairs with the viscous stresses responsible for the boundary layer.

Machine learning was applied to large-eddy simulation (LES) data to develop nonlinear turbulence stress and heat flux closures with increased prediction accuracy for trailing-edge cooling slot cases. The LES data were generated for a thick and a thin trailing-edge slot and shown to agree well with experimental data, thus providing suitable training data for model development. A gene expression programming (GEP) based algorithm was used to symbolically regress novel nonlinear explicit algebraic stress models and heat-flux closures based on either the gradient diffusion or the generalized gradient diffusion approaches. Steady Reynolds-averaged Navier–Stokes (RANS) calculations were then conducted with the new explicit algebraic stress models. The best overall agreement with LES data was found when selecting the near wall region, where high levels of anisotropy exist, as training region, and using the mean squared error of the anisotropy tensor as cost function. For the thin lip geometry, the adiabatic wall effectiveness was predicted in good agreement with the LES and experimental data when combining the GEP-trained model with the standard eddy-diffusivity model. Crucially, the same model combination also produced significant improvement in the predictive accuracy of adiabatic wall effectiveness for different blowing ratios (BRs), despite not having seen those in the training process. For the thick lip case, the match with reference values deteriorated due to the presence of large-scale, relative to slot height, vortex shedding. A GEP-trained scalar flux model, in conjunction with a trained RANS model, was found to significantly improve the prediction of the adiabatic wall effectiveness.

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

From the efforts of many researchers and engineers related to the S-CO 2 Brayton cycle technology development, the S-CO 2 Brayton cycle is now considered as one of the key power technologies for the future. Since the S-CO 2 Brayton cycle has advantages in economics due to high efficiency and compactness of the system, various industries have been trying to develop baseline technology on the design and analysis of the S-CO 2 Brayton cycle components. According to the previous researches on the S-CO 2 Brayton cycle component technology, the treatment of a thermodynamic property near the critical point of CO 2 is one of the main concerns since conventional design and analysis methodologies cannot be used for the near critical point region. Among many thermodynamic properties, the stagnation to static condition conversion process is important since the flow in a compressor is at high flow velocity. In this paper, the impact of various stagnation to static conversion methods on the S-CO 2 compressor design near the critical point will be evaluated. From the evaluation, the limitation of a certain stagnation to static conversion method will be discussed to provide a guideline for the future S-CO 2 compressor designers.

Problems in turbomachinery computational fluid dynamics (CFD) are often characterized by nonlinear and discontinuous responses. Ensuring the reliability of uncertainty quantification (UQ) codes in such conditions, in an autonomous way, is challenging. In this work, we suggest a new approach that combines three state-of-the-art methods: multivariate Padé approximations, optimal quadrature subsampling (OQS), and statistical learning. Its main component is the generalized least-squares multivariate Padé–Legendre (PL) approximation. PL approximations are globally fitted rational functions that can accurately describe discontinuous nonlinear behavior. They need fewer model evaluations than local or adaptive methods and do not cause the Gibbs phenomenon like continuous polynomial chaos methods. A series of modifications of the Padé algorithm allows us to apply it to arbitrary input points instead of optimal quadrature locations. This property is particularly useful for industrial applications, where a database of CFD runs is already available, but not in optimal parameter locations. One drawback of the PL approximation is that it is nontrivial to ensure reliability. To improve stability, we suggest to couple it with OQS. Our reasoning is that least-squares errors, caused by an ill-conditioned design matrix, are the main source of error. Finally, we use statistical learning methods to check smoothness and convergence. The resulting method is shown to efficiently and correctly fit thousands of partly discontinuous response surfaces for an industrial film cooling and shock interaction problem using only nine CFD simulations.

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.

In the present paper, direct numerical simulation (DNS) data of a low-pressure turbine (LPT) are investigated in light of turbulence modeling. Many compressible turbulence models use Favre-averaged transport equations of the conservative variables and turbulent kinetic energy (TKE) along with other modeling equations. First, a general discussion on the turbulence modeling error propagation prescribed by transport equations is presented, leading to the terms that are considered to be of interest for turbulence model improvement. In order to give turbulence modelers means of validating their models, the terms appearing in the Favre-averaged momentum equations are presented along pitchwise profiles at three axial positions. These three positions have been chosen such that they represent regions with different flow characteristics. General trends indicate that terms related with thermodynamic fluctuations and Favre fluctuations are small and can be neglected for most of the flow field. The largest errors arise close to the trailing edge (TE) region where vortex shedding occurs. Finally, linear models and the scope for their improvement are discussed in terms of a priori testing. Using locally optimized turbulence viscosities, the improvement potential of widely used models is shown. On the other hand, this study also highlights the danger of pure local optimization.