Abstract Pressurised solid oxide fuel cell (SOFC) systems are a sustainable opportunity for improvement over conventional systems, featuring high electric efficiency, potential for cogeneration applications and low carbon emissions. Such systems are usually analyzed in deterministic conditions. However, it is widely demonstrated that such systems are affected significantly by uncertainties, both in component performance and operating parameters. This paper aims to study the propagation of uncertainties related both to the fuel cell (ohmic losses, anode ejector diameter and fuel gas composition) and the gas turbine cycle characteristics (compressor and turbine efficiencies, recuperator pressure losses). The analysis is carried out on an innovative hybrid system layout, where a turbocharger is used to pressurise the fuel cell, promising better cost effectiveness then a microturbine-based hybrid system, at small scales. Due to plant complexity and high computational effort required by uncertainty quantification methodologies, a response surface is created. To evaluate the impact of the aforementioned uncertainties on the relevant system outputs, such as overall efficiency and net electrical power, the Monte Carlo method is applied to the response surface. Particular attention is focused on the impact of uncertainties on the opening of the turbocharger wastegate valve, which is aimed at satisfying the fuel cell constraints at each operating condition.

Abstract Nowadays, Computational Fluid Dynamics (CFD) simulations play an increasingly important role for turbine airfoil design. This high-fidelity approach is capable to provide accurate information of flow fields. Meanwhile, the calculation accuracy is always gained at the expense of numerical cost. This gap limits opportunities for design space exploration. To address this problem, surrogate models (also known as metamodels) are introduced to approximate high-fidelity CFD models. However, traditional surrogate models, such as Kriging or Radial Basis Function, construct response surface on a design space with limited dimensions. This prevents users from predicting the flow fields directly from the geometry and performing interactive design of airfoil. In the present work, we propose a Convolutional Neural Network (CNN) based surrogate model to predict flow properties on turbine vane airfoil surface from 3D airfoil profile defined by point cloud. The proposed CNN architecture adopts a symmetric expanding path that is similar to the so-called U-Net. The geometries in the training and testing dataset are generated via varying the parameters defined by the Free-Form Deformation approach. The corresponding flow fields are obtained through high-fidelity CFD simulations performed in a finite volume context. Furthermore, a gaussian process based Bayesian optimization technique is utilized to tune automatically the hyperparameters of the network. In this work, we trained the CNN based surrogate model with static pressure and temperature on the mean section of turbine vane airfoil surface. The trained model is able to predict in a reliable and efficient way the corresponding property directly from the 3D geometry, which allows engineers to agilely adjust their airfoil design.

Abstract The application of Surrogate-Based Optimization (SBO) to the industrial design process for a radial compressor with two operating points is described. The design specification includes two operating points at mass flow rates differing by a factor of three, and efficiency and pressure ratio targets for each point. The base case, while roughly sized from 1D analysis, fails to achieve the pressure ratio targets. In this paper, the optimization focusses on correcting the two speed-line map of total to static pressure ratio vs. mass flow rate. “Smart parameterization”, combining independent and dependent geometric parameters, and yielding reasonable geometries for most input combinations, coupled with efficient SBO, with separate models for response surface modeling and failure prediction, yields a design achieving the targets in just 57 CFD runs. FINE/Turbo [1] is used as the CFD analysis code and FINE/Design3D [2] and MINAMO [3] as the multi-objective optimizer.

Abstract This paper provides an assessment of three different machine learning techniques for accurately reproducing a distributed temperature prediction of a high-pressure turbine airfoil. A three-dimensional Finite Element Analysis thermal model of a cooled turbine airfoil was solved repeatedly (200 instances) for various operating point settings of the corresponding gas turbine engine. The response surface created by the repeated solutions was fed into three machine learning algorithms and surrogate model representations of the FEA model’s response were generated. The machine learning algorithms investigated were a Gaussian Process, a Boosted Decision Tree, and an Artificial Neural Network. Additionally, a simple Linear Regression surrogate model was created for comparative purposes. The Artificial Neural Network model proved to be the most successful at reproducing the FEA model over the range of operating points. The mean and standard deviation differences between the FEA and the Neural Network models were 15% and 14% of a desired accuracy threshold, respectively. The Digital Thread for Design (DT4D) was used to expedite all model execution and machine learning training. A description of DT4D is also provided.

Abstract Film cooling technique has been widely applied to protect gas turbine blades from high temperature combustion gases. In this study, to improve the cooling effectiveness of fan-shaped film cooling holes, the effect of the main shape parameters on the film cooling effectiveness was investigated through numerical and experimental studies. Commercial software based on Reynolds Averaged Navier-Stokes (RANS) analysis was used in the numerical study, and the PSP (Pressure Sensitive Paint) technique was used to experimentally measure the film cooling effectiveness. The design points for the optimization were derived by the Box-Behnken method, which is one of the design of experiments (DOE). Three shape parameters of a fan-shaped hole were selected as design variables: the forward expansion angle, the lateral expansion angle, and the length of cylindrical part of the hole. The area-averaged film cooling effectiveness was selected as an objective function and the optimal hole shape of each analysis was obtained using the response surface methodology (RSM). It was confirmed that the film cooling effectiveness was affected by all three variables in both numerical and experimental results. Both analyses showed similar trends of each variable on film cooling effectiveness, but the optimal hole shape obtained by each method was different. The difference is attributed to flow separation not captured by RANS based analysis and surface roughness caused by the manufacturing process and the PSP coating in experimental analysis. Notably, the experimentally optimized hole showed better film cooling effectiveness than that of the numerically optimized hole in the comparison experiments.

Abstract Fluid film bearings for turbomachinery are designed to support the loads applied by the rotor system. Oil-lubricated bearings are widely used in high speed rotating machines. However, environmental issues and risk-averse operations have made water lubricated bearings increasingly popular. Due to different viscosity properties between oil and water, the low viscosity of water decreases film thickness significantly. Crowning and tapers are two main ways to maintain the film thickness requirements in water lubrication, but no studies about the influence of these parameters on the film thickness in water-lubricated bearings have been reported. Therefore, further understanding of the performance associated with optimizing the bearing design with different weighted performance and their relationships to bearing design variables could be invaluable to bearing design engineers. This study explores the impact of three crowning and taper design variables on the performance of one tilting pad thrust bearing using the design of experiments techniques applied to a thermoelastohydrodynamic (TEHD) bearing model. The bearing design variables analyzed in this study include the radius of the ground-in crown, taper circumferential angle offset, and the vertical taper distance at the inner and outer radii. Each of the design variables is first varied over five levels, each in central composite design. The outputs from the TEHD numerical simulations used as performance measures for each bearing design point were the minimum film thickness, the film thickness at the pivot location, maximum film pressure and power loss. Multi-objective optimization was performed. A range of weighting parameters was selected for the optimization function to find a bearing design that maintains the minimum film thickness criterion while minimizing power loss. The resulting optimum design points allowed for a comparison between the design optimization at different weightings. This study demonstrates how designers can use these approaches to view the relationships between design variables and important performance metrics to design better bearing for a wide range of applications.

Nowadays, the flow field at the compressor is more and more complex with the increasing of the aerodynamic loading. The complex flow in the endwall regions is thus key to aerodynamic blockage, loss production, and finally its performance deterioration. The design of Blended Blade and End Wall (BBEW) contouring technology had been proved to be useful in delaying, reducing, and eliminating the corner separation in the compressor. The BBEW technology can adjust the dihedral angle between the suction and the endwall in 30% of the spanwise easily, which is different with the fillet. However, the design of the BBEW always relies on the experiences of the designers, and the effective design results cannot be the optimal result. This paper presents an optimization design method for the BBEW technology, and analyses the flow mechanism of the BBEW design. Firstly, the parameters for the BBEW design is simplified as two, one is the maximum blended width, the other is the axial position of the maximum blended width. The optimal result can be obtained through the response surface method. Secondly, based on the optimization method, this paper make an optimization BBEW design at the suction side of a NACA65 linear compressor cascade with the turning angle 42 degrees. The numerical results show that the optimal BBEW design can eliminate the boundary layer separation at the corner intersection region, and reduce the suction side separation. When the incidence angle is 0 degrees, the BBEW technology can reduce the total pressure loss coefficient by 5%, and reduce the aerodynamic blockage coefficient by 14%. The aerodynamic performance of the cascade shows a more obvious improvement with the BBEW design at a larger incidence. The total pressure loss coefficient of the cascade is reduced by 20% at 15 degrees incidence. The numerical study shows that the design with the BBEW can control the axial development of the dihedral angle between the suction side and the endwall, which can eliminate the boundary layer separation at the corner intersection region. What’s more, the BBEW technology can produce a pressure gradient at the axial position of the maximum blended width, and value of the pressure gradient in proportion to the maximum blended width. This pressure gradient enhance the kinetic energy of the low energy fluid at the endwall region, which is consist of the secondary cross flow, thus elevating the capability to withstand the adverse pressure gradient, and improve the suction side separation around the trailing edge.

The blockerless cascade thrust reverser is one of the innovative thrust reverser systems, which replaces the traditionally mechanical blocker door with the aerodynamic blocker door by high-pressure secondary injection, thus significantly reduces the nacelle weight and the complexity of the actuator, and especially suitable for high-bypass-ratio turbofan engine. In order to obtain the optimum performance of a blockerless cascade thrust reverser system and provide the guidance for the design of the blockerless cascade thrust reverser system, a blockerless cascade thrust reverser system was studied in this paper based on the Response Surface Method (RSM), focusing on the effect of different geometric and aerodynamic parameters on the thrust reverser performance. Results show that the secondary injection with high pressure forms the blockage effect to the fan flow, then forces the fan flow to deflect and discharge from the cascade window, realizing the reverse thrust. The thrust reverser performance is mainly affected by fan pressure ratio (FPR), secondary flow pressure ratio (SPR), secondary injection position (X jet ), secondary injection angle (α jet ) and cascade installation angle (β), and the dominated factors are FPR, SPR and X jet . According to the obtained response equation of the thrust reverser performance, the relationship between reverse thrust efficiency and various parameters are clearly described, and performance of thrust reverser can be quickly evaluated. Significant interaction effects exist between different two factors, which must be taken into consideration in the design process of the blockerless cascade thrust reverser system, especially for the interaction effect between FPR and X jet , interaction effect between FPR and β. Optimization design with objective of maximum reverse thrust was carried out to determine the best parameter settings, and reverse thrust ratio η Trev of 60% is achieved under the constraint of the secondary flow ratio.

A fan blade is a complicated object and obviously it is subjected to geometrical uncertainties from manufacture tolerances and other production deviations. In spite of all uncertainties a fan blade should provide stable aerodynamic efficiency and strength properties. That is why it is considered to solve a multidimensional and multidisciplinary optimization task (aerodynamics, strength and flutter sensitivity) in robust statement under geometrical uncertainties. In the proposed test case geometrical uncertainties from the fan blade manufacture tolerances and deviations are considered. The probability density function (pdf) was obtained as a result of statistical operation upon the results of blade coordinate measurements. Approximately 2500 fan blades were measured by means of CMM process to reconstruct the pdf for more than 40 geometrical uncertainties (there are blade thicknesses for different airfoil locations in several cross-sections). CFD and FEM calculations were carried out in NUMECA FINE/Turbo and ANSYS software, correspondingly. The surrogate model technique (the response surface and the Monte-Carlo method implemented to RSM results) was applied for the uncertainty quantification and the robust optimization process for the task under consideration. APPROX software was used for surrogate model construction. The IOSO technology was employed as one of the robust optimization tools. This technology is also based on a widespread application of the response surface technique. As a result, robust optimal solutions (the Pareto set) for all 4 considered criteria (aerodynamic efficiency, structural properties, stall margin and flutter sensitivity) were obtained. The probabilistic criteria were assessed based on the results obtained. The robust optimization results were compared with the deterministic optimization results.

Angled ribs have been widely used in the rectangular internal cooling channel of gas turbine to enhance heat convection strength and the optimal rib parameters have been shown in the former investigations. However, the heat transfer strength of the wall near the terminal of angled ribs is less enhanced by the rib and the local Nusselt number ratio may be lower than 1, which means that the local heat transfer strength of the ribbed wall is lower than that of smooth wall. At the same time, the ribs also generate large friction loss. As a result, a part of ribs which provides little heat transfer enhancement effect are removed in order to both reduce friction loss and maintain or enhance local heat transfer strength. In order to find out the optimal geometry parameters of the removed part of the rib, the optimization study are conducted in this paper based on the ANSYS Workbench software. The channel width to height ratio is 1 and 4. The rib attack angle is 45 degrees. The length of removed part, the transverse location of the removed part and the angle between the flow direction and the incision edge are chosen as the design variables. The area-averaged Nusselt number ratio and temperature on the ribbed wall, the friction factor ratio of the channel and the thermal performance factor are chosen as the objectives. The samples are generated by Latin Hypercube Sampling method and the CFD calculation is conducted by ANSYS CFX module using SST turbulence model. The response surface is obtained by Kriging model based on the CFD results and the Pareto optimal solution of this multi-objective problem is conducted by Multi-Objective Genetic Algorithm (MOGA) in the Response Surface Optimization module of ANSYS Workbench. The results show that the removed part of rib could both maintain or slightly enhance the overall Nusselt number ratio and obviously reduce the friction factor at the same time. Furthermore, the Nusselt number ratio in the terminal region of original ribs is also largely enhanced.

Predictive lifing with probabilistic treatment of key variables represents a promising approach to realizing the digital gas turbine of the future. In this paper, we present a predictive model for creep life assessment of an uncooled turbine blade. The model development methodology draws on well-established machine learning principles to develop and validate a surrogate model for creep life from engine performance parameters. Verified creep life results, obtained from 3D non-linear thermo-mechanical finite element simulation for varying engine operating conditions are used as the basis for model development. The selection of model response surface order is studied over a range of models by evaluating normalized residual error on training and uncorrelated validation data sets. A model that is fully quadratic in the data set features is shown to have excellent predictive capability, yielding nominal creep life predictions to within ± 3% on the validation data set. This work then considers probabilistic techniques to evaluate the impact of uncertainty associated with each key factor on the predicted nominal creep life in order to achieve a mandated life target with a defined probability of failure.

Current probabilistic design methods mainly focus on single mode of failure, under the consideration on random variables including geometry, loading, and material properties. However, due to the complex structural characters and unevenly distributed temperature, turbine disks are always undergoing multiple potential failure modes, which should be effectively evaluated under a coupling scheme in reliability analysis. To this end, a collaborative response surface method involving multiple potential modes was established, aligning individual failure modes that were precisely evaluated via linear heteroscedastic regression analysis. To validate our model, reliability assessment was conducted on a turbine disk in turbo-shaft engine, where the coupling failure including low cycle fatigue and creep-fatigue was considered. This method can be an effective tool in the evaluation of reliability analysis involving multiple failure modes.

Fluid film bearings for turbomachinery are designed to support the loads applied by the rotor system, often at high speeds when power loss in the bearing becomes significant and bearing temperatures can reach levels that can be detrimental to the long-term reliability of the support system. These requirements of supportive bearings require an intimate understanding of how bearing design variables affect their overall performance. Ideal bearings minimize power loss to increase machine efficiency and maintain low operating temperatures to ensure long-term reliability while meeting other design criteria such as minimum film thickness to provide proper support and avoiding high fluid pressures that can be harmful to the bearing structure. However, real world designs are often forced to sacrifice some of these design goals in order to preserve others. Therefore, further understanding of the relative opportunity costs associated with optimizing the bearing design with differently weighted performance metrics and their relationships to bearing design variables is invaluable to design engineers. This study explores the impact of eight bearing design variables on the performance of two tilting pad journal bearings supporting an eight-stage centrifugal compressor using design of experiments techniques applied to an established thermoelastohydrodynamic (TEHD) bearing model of tilting pad bearing performance. The bearing design variables analyzed include the radial clearance, pad arc spacing, pad axial length, pivot offset, preload, working fluid viscosity and viscosity index, and the number of pads. Each of the design variables — excluding the number of pads which was realistically constrained — were first varied over five levels each in a central composite design. These central composite designs were repeated for each of three values for number of pads. The responses obtained from the TEHD numerical simulations for each bearing design point were power loss, maximum pad temperature, minimum film thickness, and maximum fluid film pressure. The results from the central composite studies were fit with a multivariate least-squares regression model and a secondary series of experimental design studies were simulated around potential optimum design points to obtain a learning set to initialize direct optimization methods. Two direct multi-objective optimization methods, a sequential quadratic programming method and a multi-island genetic algorithm, were performed using Isight, a commercial software. A range of weighting parameters were selected for the optimization functions to find bearing designs that minimized power loss and pad temperature while maintaining pressure and film thickness criteria within acceptable design ranges for fluid film bearings. The resulting optimum design points allowed for a comparison between the design optimization approaches. The various strengths and weaknesses of the different methods are discussed. This study demonstrates how designers can use these approaches to view the relationships between design variables and important performance metrics to design better bearings for a wide range of applications.

This paper presents the results of a CAD-based aerodynamic optimization study conducted on the TU Berlin TurboLab Stator benchmark test case. Two different approaches are examined and compared: a conventional gradient-free optimization process which makes use of 2D and 3D CFD results and constructs a response surface to obtain the optimum solution; and an adjoint-driven optimization workflow, where the derivatives w.r.t. the design parameters are calculated by linking the adjoint surface sensitivity map with the model’s geometric sensitivities. Both methods are applied to the turbomachinery test case, where a multi-objective multi-point problem is considered. Moreover, manufacturing constraints are incorporated in the process chain, which makes the case even more challenging. Since the optimization output is already in CAD format, there is no requirement for a back-to-CAD step and the optimum blade can be straightforwardly manufactured.

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

This paper presents a procedure for experimentally optimizing a multistage axial compressor. Due to the usual proprietary nature of such tests, a mean-line model of a nine-stage compressor with three rows of variable geometry is used instead of a real machine as a testbed for explaining the optimization method. The compressor is optimized to achieve design-intent corrected flow and pressure ratio while achieving acceptable efficiency and stage matching. The optimization is performed using a response surface methodology that leverages a full factorial design of experiments approach. The resulting empirical models of compressor performance are of high quality, with coefficients of determination exceeding 0.99. An important finding of the work is that stage interactions are important for modeling both efficiency and stage matching, much more than for corrected flow and pressure ratio. Additionally the empirical equations resulting from the design of experiments analysis provide sensitivities due to changes in the variable geometry. These sensitivities can be applied to understanding the impact of uncertainties related to rigging the variable geometry and for assessing potential new or upgraded compressor designs.

In recent years, development of new manufacturing technologies like additive manufacturing has made it possible to make complex cooling structures to improve the efficiency of jet impingement. Present paper considers hybrid-linked jet impingement cooling channels which involve both parallel linked jets and serial linked jets. Systematic analysis was conducted with the aid of Computational Fluid Dynamics and Response Surface Methodology, focusing on the influence of topology on performance. An optimization platform was established with aid of the regressed database and the Genetic Algorithm. Of particular interest is the influence of optimization strategies on results. Results obtained indicates that the topology number developed in this study works well with the Response Surface Methodology. Topology can be considered to be a new degree of freedom of jet impingement design. Among the tested topologies, serial linked jet impingement has significantly higher heat transfer and pressure drop than the traditional parallel linked jet impingement. In the first optimization strategy, mass flow rate was used as the objective function while heat transfer and pressure drop were constrained. Optimized results under this strategy show consistent parameters and purely serial linked topology for all cases, due to the high cooling efficiency of serial linked jets. In the second optimization strategy, pressure drop was minimized while heat transfer and mass flow rate were constrained. Contrast with the first strategy, optimal results of this strategy have different topologies under different constraint conditions, which is caused by the complex influence of geometric parameters on pressure drop. Such results indicate the capability of hybrid-linked jet impingement to fit a wide various requirement by changing topology.

During engine operation fan casing abradable liners are worn by the blade tip, resulting in the formation of trenches. This paper investigates the influence of these trenches on the fan blade tip aerodynamics. A detailed understanding of the tip flow features for the fan blade under investigation is developed. A parametric model is then used to model trenches in the casing above the blade tip. It is shown that increasing clearance via a trench reduces performance by less than increasing clearance through cropping the blade tip. A response surface method is then used to generate a model that can predict fan efficiency for a given set of clearance and trench parameters. It is shown that the efficiency sensitivity to clearance is greater for cropped tips than trenches, and is biased towards the leading edge for cropped tips, and the trailing edge for trenches.

This paper proposes an effective method for sensitivity analysis of forced response of bladed discs to blade mistuning. The numerical studies of forced response of a turbine bladed disc vibrating in the frequency ranges corresponding to resonances with higher modes are also presented. The blade mistuning is modelled by specially defined mistuning matrices used for simulating experimentally measured scatter of blade natural frequencies. Based on this method, the sensitivity of forced response amplitude levels are studied for displacements and stress levels for a realistic model of a bladed disc. The effective response surface techniques are developed for explicit representation of the mistuned forced response as a function of blade mistuning elements.

In this paper, a multi-objective optimization of a transonic axial fan to enhance aerodynamic stability has been conducted using three-dimensional Reynolds-Averaged Navier-Stokes equations, surrogate modeling and multi-objective genetic algorithm (MOGA). Hub radius and first rotor chord length of the axial fan were chosen as design variables for the optimization. Peak adiabatic efficiency of the axial fan and stall margin at 60% of the designed rotational speed, were used as objective functions. Latin Hypercube Sampling (LHS) method was used to select design points in the design space. The objective functions were formulated using the response surface approximation (RSA) model. Three LHS samples with different distributions of twelve design points were tested to study their effects on prediction accuracy of the RSA model and optimization results. MOGA with the RSA models based on the best LHS sample, was used to obtain the Pareto-optimal front. As a result of optimization, an improvement of 17.2% in the stall margin at 60% of the designed rotational speed and 2.96% in peak adiabatic efficiency were obtained compared to the reference design. It was also found that distribution of the design points generated by LHS affects the effectiveness of the surrogate-based optimization.