Machine learning and automatized routines for parameter optimization have experienced a surge in development in the past years, mostly caused by the increasing availability of computing capacity. Gradient-free optimization can avoid cumbersome theoretical studies as input parameters are purely adapted based on output data. As no knowledge about the objective function is provided to the algorithms, this approach might reveal unconventional solutions to complex problems that were out of scope of classical solution strategies. In this study, the potential of these optimization methods on thermoacoustic problems is examined. The optimization algorithms are applied to a generic low-order thermoacoustic can-combustor model with several fuel injectors at different locations. We use three optimization algorithms — the well established Downhill Simplex Method, the recently proposed Explorative Gradient Method, and an evolutionary algorithm — to find optimal fuel distributions across the fuel lines while maintaining the amount of consumed fuel constant. The objective is to have minimal pulsation amplitudes. We compare the results and efficiency of the gradient-free algorithms. Additionally, we employ model-based linear stability analysis to calculate the growth rates of the dominant thermoacoustic modes. This allows us to highlight general and thermoacoustic-specific features of the optimization methods and results. The findings of this study show the potential of gradient-free optimization methods on combustor design for tackling thermoacoustic problems, and motivate further research in this direction.

Adaptive modelling (AM) based Gas Path Analysis (GPA) is a powerful diagnostic and prognostic technique for turbofan engine maintenance. This involves the assessment of turbofan component condition using thermodynamic models that can iteratively adapt to measurements values in the gas path by changing component condition parameters. The problem with this approach is that newer turbofan engines such as the General Electric GEnx-1B have fewer gas path sensors installed causing the AM equation systems to become underdetermined. To overcome this problem, a novel approach has been developed that combines the AM model with an Evolutionary Algorithm (EA) optimization scheme and applies it to multiple operating points. Additionally, these newer turbofan engines provide performance data continuously during flight. Information on variable geometry and bleed valve position, active clearance control state and power off-take is included and can be accounted for to further enhance AM model accuracy. A procedure is proposed where the selection of operating points is based on steady-state stability requirements, cycle model operating point uncertainty and parameter outlier filtering. The Gas turbine Simulation Program (GSP) is used as the non-linear GPA modelling environment. A Multiple Operating Point Analysis (MOPA) is chosen to overcome the problem of underdetermination by utilizing multiple data sets at different operating points. The EA finds the best fit of health parameter deviations by minimizing the multi-point objective function using the GSP AM model. A sub-form of the EA class named Differential Evolution (DE) has been chosen as the optimizer. Like all EAs, DE is a parallel direct search method in which a population of parameter vectors evolves following genetic operations towards an optimum output candidate. The resulting hybrid GPA tool has been verified by solving for different simulated deterioration cases of a GSP model. The tool can identify the direction and magnitude of condition deviation of 10 health parameters using 6 gas path sensors. It has subsequently been validated using historical in-flight data of the GEnx-1B engine. It has demonstrated successful tracking of engine component condition for all 10 health parameters and identification of events such as turbine blade failure and water washes. The authors conclude that the tool has proven significant potential to enhance turbofan engine condition monitoring accuracy for minimizing maintenance costs and increasing safety and reliability.

Throughflow design of multi-stage axial flow compressor still takes the upmost importance throughout the compressor whole design procedure as it generally fixes 80%∼90% of the final design. The incorporation of multi-objective evolutionary algorithms (MOEA) into throughflow design has been proven effective. In the existing works, the MOEA commonly uses thousands of objective evaluations to obtain a representative approximation of the complete Pareto front (PF), which usually consists of tens and hundreds of solutions. Once the representative PF is obtained, several typical solutions on the PF (especially the extreme ones and/or compromised ones) will be chosen and then examined by the decision-makers. But the remained considerable solutions on the PF are left behind, leading to a significant waste of computational resources. The preference-inspired MOEA has been suggested to resolve this problem as its focus on obtaining solutions in the region of interests only. In this work, a preference-inspired multi-objective axial flow compressor throughflow design optimization approach is developed through integrating the preference-inspired reference vector guided evolutionary algorithm and the open-source axial flow compressor axisymmetric throughflow design code of T-AXI. In terms of the objective definition for the multi-objective throughflow design, efficiency, stall margin, and blade counts are taken as the focuses. Specifically, the equivalent relative velocity ratio is adopted to form an operability parameter to assess designs with better or worse stall margin of the whole compressor. The developed method is used in the design of a 6-stage axial flow compressor at the throughflow level, which is a 3-objective problem with 58 variables. Preference-inspired and non-preference optimization are compared to verify the cost-saving benefit of incorporating the preferences into multi-objective optimization. Designs in the preferred target regions are obtained which demonstrates the practical ability of the proposed preference-inspired throughflow optimization design method for multi-stage axial flow compressors.

Variable cycle engine (VCE) is considered as one of the best options for advanced military or commercial supersonic propulsion system. Variable geometries enable the engine to adjust performance over the entire the flight envelope but add complexity to the engine. Evolutionary algorithms (EAs) have been widely used in the design of VCE. The initial guesses of the engine model are generally set using design point information during evolutionary optimization. However, the design point information is not suitable for all situations. Without suitable initial guesses, the Newton-Raphson solver will not be able to reach the solution quickly, or even get a convergent solution. In this paper, a new method is proposed to obtain suitable initial guesses of VCE model during evolutionary optimization. Differential evolution (DE) algorithm is used to verify our method through a series of optimization cases of a double bypass VCE. The result indicates that the method can significantly reduce the VCE model call number during evolutionary optimization, which means a dramatic reduction in terms of evolution time. And the robustness of the optimization is not affected by the method. The method can also be used in the evolutionary optimization of other engines.

This paper presents a constrained multipoint optimization of the LS89 turbine cascade. The objective of the optimization consists in minimizing the entropy losses generated inside the cascade over a predefined operating range. The operating range is bounded by two operating points respectively characterized by a downstream isentropic Mach number of 0.9 and 1.01. During the optimization, 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 turbine. The second constraint limits the mass-flow passing through the optimized cascade. The optimization is performed using a hybrid algorithm which combines efficiently a classical evolutionary algorithm with a gradient-based method. The hybridization process between both methods is based on the Lamarckian approach which consists in incorporating directly the gradient method inside the loop of the evolutionary algorithm. In this methodology, the evolutionary method allows to globally explore the overall design space while the gradient-based method locally improves certain designs located in the most promising regions of the search space. First, the better performance of the proposed hybrid method compared to the performance of a classical evolutionary algorithm is demonstrated on two benchmark problems. Then, the methodology is applied on a turbomachinery application in order to minimize the losses in the linear LS89 cascade. The optimization process allows to find a new blade 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.

Fans used in tunnel ventilation operate for decades in an atmosphere that carries dust, soot, and other solid particles. The formation of deposit on the rotor blades, considering a so long time of exposition to this particle-laden flow, is highly probable. A not negligible quantity of deposited material can produce damages on the performance of the fan, but also mass unbalancing, which is potentially dangerous for the structural integrity of the fan components. We applied our simulation tool to study a case of deposition on a large axial fan blade, used for tunnel ventilation. The outcome of the study is a parametric map of fouled blade geometries, obtained by simulating the deposition process over the increasing quantity of ingested particles mixture. The final map correlates the level and shape of deposit to the overall amount of particle ingested by the fan in its operating life. The same map can be easily used to predict the time needed in a specific application to reach any specific deposit thickness. The evolution algorithm and simulation tools developed in the past years by the authors was applied to predict the modified geometry of eroded rotor blades. Here the same framework is updated to simulate the deposit problem. We use an integrated multiphase solver, coupled with a geometry update method. The solver can iteratively simulate the flow field, compute the particle tracking, dispersion and deposit processes, and modify the geometry (and mesh) according to the predicted deposit shape and rate.

The optimization of the turbine rotor tip geometry remains a vital opportunity to create more efficient and durable engines. Balancing the aerodynamic and thermal aspects, while maintaining the mechanical integrity is key to reshape one of the most vulnerable and life determining parts of the entire turbine. The ever-increasing turbine gas temperatures, combined with the difficulty of cooling the tip and the aerodynamically penalizing nature of the overtip leakage vortex, makes the design of the tip a truly multi-disciplinary challenge. While many earlier efforts focused on uncooled geometries, or studied the aerothermal impact with a fixed cooling configuration, the current paper presents the outcome of a multi-objective optimization where both the squealer rim geometry as well as the cooling injection pattern was allowed to vary simultaneously. This study explores a significantly wider design space, seeking a further synergistic aerothermal benefit through the combination of a quasi-fully arbitrary cooling arrangement, with mutating squealer rim structures. Specifically, the current manuscript presents the results of over 330 cooled and uncooled squealer tip geometries. The high pressure turbine tip was automatically altered using a novel parametrization strategy adopting a maximum of 40 design variables to vary the squealer rim structures, as well as the size and location of the various cooling holes. The aerodynamic and thermal characteristics of every design were evaluated through Reynolds-Averaged Navier-Stokes CFD simulations with the k-ω SST model for the turbulence closure, adopting an unstructured hexahedral grid typically containing more than 8 million cells. A multi-objective differential evolution algorithm was used to obtain a Pareto front of designs which maximize the aerodynamic efficiency, while minimizing the overtip thermal loads. Eventually, a detailed investigation and robustness study was performed on a set of prime squealer geometries, to further investigate the aerodynamic flow topology, and the effect of various cooling injection schemes on the heat transfer patterns.

This paper presents a single point optimization of the LS89 turbine vane cascade for a downstream isentropic Mach number of 0.9. The objective of the optimization is to minimize the entropy generation through the cascade while maintaining the flow turning of the baseline geometry. The optimization is performed using a hybrid optimization algorithm which combines two main families of optimization methods, namely an evolutionary algorithm and a gradient-based method. The combination of these two methods aims to correct their respective main disadvantage which are the poor convergence performance of the evolutionary and the trend to get trapped in local minima of the gradient-based method. The hybrid algorithm implemented in this work is based on the Lamarckian evolution and consists in incorporating directly the gradient-based method inside the loop of the evolutionary algorithm. In this approach, the evolutionary algorithm performs a global exploration of the design space while the gradient-based method improves the convergence rate of the evolutionary algorithm. The better performance of the developed hybrid method, compared to a classical evolutionary algorithm, is first demonstrated on two analitycal functions used as benchmark problems. Subsequently, the hybrid algorithm is used to optimize LS89 turbine vane, resulting in a new design with about 20 percent lower entropy production compared to baseline geometry. A thorough flow analysis shows that the improvements are largely due to a significant decrease in trailing edge losses, which is characterized by a higher base pressure. A previous optimization of the LS89 cascade has been already realized using a classical gradient-based method. This optimization converged towards a new design which reduces the entropy rise by a factor of 11 percent. Therefore, the comparison between this optimum and the one found using the proposed method demonstrates that the hybrid algorithm allows to locate a better minimum by performing a global exploration of the design space.

High performance of the last stage long blade plays an important role on the aerodynamic performance of low pressure cylinder for steam turbines. Aerodynamic optimization design of the last stage long blade for the maximization total-total isentropic efficiency with constraints of mass flow rate and leaving velocity using self-adaptive differential evolution algorithm is presented in this work. The aerodynamic performance of last stage is evaluated using three-dimensional Reynolds-Averaged Navier-Stokes (RANS) computations. Six two-dimensional airfoils along the span and three controlling points for the radial foil of blade using B-Spline functions are used to parameterize the three-dimensional profiles of the stator and rotor blade of the last stage, respectively. Self-adaptive differential evolution algorithms is developed to optimize the maximization total-total isentropic efficiency of last stage. The results show that the total-total isentropic efficiency of the optimized last stage is higher 1.68% than that of the referenced design. Furthermore, the aerodynamic performance of the five stages low pressure cylinder with three extractions coupled with the optimized last stage and referenced design is analyzed and compared. The detailed flow field and aerodynamic parameters of the optimized last stage are also illustrated.

Due to the recent developments of the engine industry, turbine internal channel cooling is a need. In fact, in order to supply more power efficiently, the fluid temperature at turbine inlet approaches to 2000 K when common turbine materials cannot resist temperature values higher than 1500 K. The crucial point is that the engine cycle efficiency and thrust highly depend on the turbine inlet temperature and, so, such a thermal problem needs to be overcome by cooling. Coolant air of the internal channel cooling systems is mostly taken from valuable compressor bleed that makes it to circulate through the serpentine internal passages. The coolant air flow is commonly fully turbulent, incompressible and with 3D characteristics because of the complex shape of the cooling passage. Considering this latter aspect, the pressure drop also plays a relevant role because, in order to minimize the cooling mass flow, it needs to be reduced. In this study, rib cross-section shape optimization of a ribbed internal cooling channel is conducted to assess the trade-off between two conflicting objectives: heat transfer performance and pressure drop. For this purpose, a novel mesh morphing based optimization tool is developed which uses radial basis functions (RBF) for morphing and meta-model assisted evolutionary algorithms (EA) for optimization. Experimental tests characterized by Reynolds number of 20000 are performed to validate such an optimization tool. The local Nusselt number is calculated using hydraulic diameter of channel and air thermal conductivity corresponding to bulk temperature. The cooling effectiveness of the channel is quantified using the ratio of the Nusselt number of the ribbed case to the Nusselt number of the smooth case. With the gained optimized geometry, the heat transfer shows better results than initial case with a pressure loss improvement of 8%.

The scope of this work is to perform a single-objective optimization of the high-lift and aft-loaded T2 low pressure turbine blade profile previously designed at the von Karman Institute for Fluid Dynamics (VKI). At correct engine Mach and Reynolds numbers and for a uniform inflow at low turbulence level, a laminar separation bubble occurs in the decelerating part of the suction side. The main goal of the optimization is to obtain a high-lift and aft-loaded blade characterized by lower aerodynamic losses with respect to the original profile. The optimization uses a metamodel-assisted Differential Evolution algorithm, with an Ordinary Kriging metamodel performing the low-fidelity evaluations and Numeca FINE/Turbo for the high-fidelity ones. The numerical results relative to the optimized profile are compared with those obtained for the baseline profile, in order to highlight the improvements on the blade aerodynamic performance coming from the optimization process.

The present contribution proposes a Reduced Order Model based multi-fidelity optimization methodology for the design of highly loaded blades in low pressure compressors. Environmental, as well as, economical limitations applied to engine manufacturers make the design of modern turbofans an extremely complex task. A smart compromise has to be found to guarantee both a high efficiency and a high average stage loading imposed for mass reduction constraints, while satisfying stability requirements. The design of compressor blades, usually involves at the same time a dedicated parametrization set-up in highdimensional space and high-fidelity simulations capturing, at least, efficiency and stability as most impacting phenomena. Despite recent advances in the high-performance computing area, introducing high-fidelity simulations into automated optimization, or even surrogate assisted optimization, loops still stands as a endeavor for engineers. In this framework, the proposed methodology is based on multi-fidelity surrogate models capable of representing the physics at hand in reduced spaces inferred from both precise, albeit costly, high-fidelity simulations and abundant, yet less accurate lower-fidelity data. Finally, we investigate the coupling of the proposed hierarchised multi-fidelity non-intrusive Proper Orthogonal Decomposition based surrogates with an evolutionary algorithm to reduce the number of high-fidelity simulation calls towards the targeted optimum.

Classical RANS turbulence models have known deficiencies when applied to jets in crossflow. Identifying the linear Boussinesq stress-strain hypothesis as a major contribution to erroneous prediction, we consider and contrast two machine learning frameworks for turbulence model development. Gene Expression Programming, an evolutionary algorithm that employs a survival of the fittest analogy, and a Deep Neural Network, based on neurological processing, add non-linear terms to the stress-strain relationship. The results are Explicit Algebraic Stress Model-like closures. High fidelity data from an inline jet in crossflow study is used to regress new closures. These models are then tested on a skewed jet to ascertain their predictive efficacy. For both methodologies, a vast improvement over the linear relationship is observed.

The use of multi-stage centrifugal compressors carries out a leading role in oil and gas process applications. Green operation and market competitiveness require the use of low-cost reliable compression units with high efficiencies and wide operating range. A methodology is presented for the design optimization of multi-stage centrifugal compressors with prediction of the compressor map and estimation of the uncertainty limits. A one-dimensional (1D) design tool has been developed that automatically generates a multi-stage radial compressor satisfying the target machine requirements based on a few input parameters. The compressor performance map is then assessed using the method proposed by Casey-Robinson [1], and the approach developed by Al-Busaidi-Pilidis [2]. The off-design performance method relies on empirical correlations calibrated on the performance maps of many single-stage centrifugal compressors. An uncertainty quantification study on the predicted performance maps was conducted using Monte Carlo method (MCM) and generalized Polynomial Chaos Expansion (gPCE). Finally, the design procedure has been coupled to an in-house optimizer based on evolutionary algorithms. The complete design procedure has been applied to a multi-stage industrial compressor test case. A multi-objective optimization of a multi-stage industrial compressor has been performed targeting maximum compressor efficiency and flow range. The results of the optimization show the existence of optimum compressor architectures and how the Pareto fronts evolve depending on the number of stages and shafts.

The design of turbomachinery cascades is a typical high dimensional and computationally expensive problem, a metamodel-based global optimization and data mining method is proposed to solve it. A modified Efficient Global Optimization (EGO) algorithm named Multi-Point Search based Efficient Global Optimization (MSEGO) is proposed, which is characterized by adding multiple samples at per iteration. By testing on typical mathematical functions, MSEGO outperforms EGO in accuracy and convergence rate. MSEGO is used for the optimization of a turbine vane with non-axisymmetric endwall contouring (NEC), the total pressure coefficient of the optimal vane is increased by 0.499%. Under the same settings, another two optimization processes are conducted by using the EGO and an Adaptive Range Differential Evolution algorithm (ARDE), respectively. The optimal solution of MSEGO is far better than EGO. While achieving similar optimal solutions, the cost of MSEGO is only 3% of ARDE. Further, data mining techniques are used to extract information of design space and analyze the influence of variables on design performance. Through the analysis of variance (ANOVA), the variables of section profile are found to have most significant effects on cascade loss performance. However, the NEC seems not so important through the ANOVA analysis. This is due to the fact the performance difference between different NEC designs is very small in our prescribed space. However, the designs with NEC are always much better than the reference design as shown by parallel axis, i.e., the NEC would significantly influence the cascade performance. Further, it indicates that the ensemble learning by combing results of ANOVA and parallel axis is very useful to gain full knowledge from the design space.

The multidisciplinary design optimization of high temperature blades is a typical high dimensional, computational expensive and black box problem, since too many design variables are involved and large amounts of CFD evaluations are usually demanded to ensure the convergence of global algorithms like GAs. By integrating the technique of analysis of variance (ANOVA), Self-adaptive Multi-objective Differential Evolution algorithm (SMODE), Conjugate Heat Transfer analysis and 3D parameterization method for both blade and the cooling holes, a knowledge-based aero-thermal multidisciplinary design optimization of a high temperature blade is carried out. Through the ANOVA analysis, an insight into the relation between significant design variables and the blade aero-thermal performance is obtained. By eliminating the variables which have small effects on the blade aero-thermal performance, the number of design variables for the optimization process is decreased from 36 to 15, which is verified by the numerical simulations. After optimization, 9 optimal Pareto solutions are achieved. Detailed aero-thermal analysis of typical optimal Pareto solutions indicates that the performance of optimal designs is significantly better than the reference design. Therefore, the effectiveness of the developed knowledge-based multidisciplinary design method for high temperature blades is demonstrated.

The validity of the Boussinesq approximation in the wake behind a high-pressure turbine blade is explored. We probe the mathematical assumptions of such a relationship by employing a least-squares technique. Next, we use an evolutionary algorithm to modify the anisotropy tensor a priori using highly resolved LES data. In the latter case we build a non-linear stress-strain relationship. Results show that the standard eddy-viscosity assumption underpredicts turbulent diffusion and is theoretically invalid. By increasing the coefficient of the linear term, the farwake prediction shows minor improvement. By using additional non-linear terms in the stress-strain coupling relationship, created by the evolutionary algorithm, the near-wake can also be improved upon. Terms created by the algorithm are scrutinized and the discussion is closed by suggesting a tentative non-linear expression for the Reynolds stress, suitable for the wake behind a high-pressure turbine blade.

An automated multidisciplinary optimization system for multi-objective design of the long blade turbine stage for steam turbines is developed in this paper. The Self-adaptive Multi-objective Differential Evolution (SMODE) algorithm, cubic non-uniform B-Spline curves based on surface modeling technology for three-dimensional turbine blade parameterization method, aerodynamic and mechanical performance of long blade turbine stage evaluation approach are coupled in the presented multidisciplinary optimization system. The aerodynamic performance of long blade turbine stage design candidates is evaluated using three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solutions. The mechanical performance of the designed long rotor blade is analyzed using Finite Element Analysis (FEA) method based on the software ANSYS. Multi-objective design of long blade turbine stage is conducted using the developed multidisciplinary optimization methodology for the maximization of specific power and minimization of maximum Von Mises Stress with constraints on mass flow rate. The design variables are specified by the stator and rotor blade parameterization method. The Pareto solutions of the multidisciplinary optimization design for the long blade turbine stage are obtained. The aerodynamic and strength performance of obtained Pareto solutions improves obviously by comparison of the referenced design. The dynamic frequency with pre-stress of the referenced and optimized long rotor blade is also calculated in order to avoid resonance. The availability of the presented multidisciplinary optimization system for multi-objective design of long blade turbine stage for steam turbines is also demonstrated.

A method of tandem airfoil geometry generation and an algorithm of master-slave parallel differential evolution are first developed for the later optimization. An initial tandem cascade is roughly designed and significantly outperforms the original conventional cascade. Based on the parallel differential evolution algorithm and a Navier-Stokes solver, five configuration variables of the initial tandem cascade are then numerically optimized at an inlet Mach number of 0.7 and an approximately minimum-loss incidence of 1.9°. The result shows that the total pressure loss coefficient of the optimum design decreases by 8.67%. The history data of the optimization is statistically analyzed, which reveals the influence levels of the five configuration variables on tandem performance. The performances of the initial and optimum designs at a range of incidence angles are then numerically calculated, showing that the optimum design outperforms the initial design at small or negative incidence angles and performs more poorly at high incidence angles. It is proposed and verified that the different front-rear distributions of camber and chord leads to this phenomenon. Finally, a new-defined variable is proposed to measure the distribution above.

In this paper, an optimization design approach to recirculation flow type casing treatment for centrifugal compressors of turbochargers has been performed. The optimization code is a global exploring system based on a metamodel assisted evolutionary algorithm. In this study, the objective functions of the optimization are adiabatic efficiency at design flow rate and near surge flow rate condition. Several optimized shapes on a “Pareto front” are selected in order to discuss the effect of casing treatment at the point of view of suppression of flow separation and a reduction of leading edge flow separation. The influence of optimized recirculation flow rate on the optimization output is also discussed. Increase in adiabatic efficiency of optimized casing treatment at near surge flow rate is discussed by the streamwise relative velocity distribution, reversed flow zone, static entropy distribution and flow incidence at impeller inlet. Detailed sensitivity of design variables on the adiabatic efficiency at design and off-design conditions was carried out.