Numerical Design Of Experiments Research Articles

Characterization of internal thermohydraulic flow and heat transfer improvement in a three‐dimensional circular corrugated tube surfaces based on numerical simulation and design of experiment

AbstractTo meet the requirements of development in heat exchangers design, the effect of different tubes geometrical parameters on its flow field analysis and thermal heat transfer performance are investigated in the current research work. The hydraulic thermal fluid coupling with computational simulations is applied. The numerical results are solving used flow transport and heat transfer equations, then these results are validated with available experimental data. The behavior of hydraulic and thermal flow in the corrugated tube is discussed with different geometrical parameters' position and shape. Turbulent flow in the tube is calculated in three‐dimensional numerical simulations with optimization of a multiobjective algorithm are analyzed. The influences of various design parameters, for instance, the number of corrugated rings around the tube, distance between each corrugated ring, the diameter of the ring, and pitch of ring are investigated firstly in the flow field and then optimized by using the design of experiment (DOE). The influence of flow structural modifications such as static pressure, dynamic pressure, and pressure drop is taken into consideration as analyzed performance parameters. The DOE method is investigated based on implements and variances the L16 orthogonal arrays are chosen as the experimental strategy. Furthermore, the optimization results found that the maximum value of pressure difference was for corrugated diameter. The numerical method using DOE has enhanced heat transfer rate as compared to the smooth pipe. Moreover, the minimum Tout is for Case 11 (296.49°C) and the maximum Tout is for (303.10°C) hence the value of Nu number for both cases is 32.9 and 42, respectively. That means using this type of passive device can improve the heat transfer in the pipe. The outcomes illustrate that the performance evaluation factor (PEF) ratio of the corrugated pipe with different geometrical configurations is changed and increased as the corrugated pipe geometrically changed and the value of PEF is more than 1.3.

Digital Twin-driven framework for fatigue lifecycle management of steel bridges

This paper presents a Digital Twin-driven framework for fatigue lifecycle management of steel bridges. A probabilistic multi-scale fatigue deterioration model is proposed to predict the entire fatigue process of steel bridges. Bayesian inference of the deterioration parameters realizes the real-time updating of the predicted lifecycle fatigue evolution process, which provides a good basis for lifecycle optimization. To avoid an empirically predefined repair crack size for maintenance, an optimization process for maintenance strategies is included. The relationship of the extended lifetime and the design repair crack size is constructed by numerical experimental design and surrogate modeling. The solution for optimum repair crack size is obtained while maximizing the extended fatigue life and minimizing the maintenance costs. Based on the occurrence time distribution of the optimum repair crack size, the inspection/monitoring planning is determined from a probabilistic optimization process based on the minimization of the expected damage detection delay and the lifecycle costs. The uncertainties associated with the damage occurrence and detection ability are considered during the formulation of the expected damage detection delay by decision tree analysis. Based on Digital Twin concept, the predicted deterioration process, derived maintenance, and inspection/monitoring planning are timely updated until a defined stopping rule is met.

Simultaneous extraction of the elastic-plastic properties of a thin film and its substrate from an identifiability-based design of depth-sensing nanoindentation testing

This work presents an approach to simultaneously identify reliable elasto-plastic properties of a 100 nm amorphous alumina film and plastic properties of its silicon substrate by the Finite Element Model Updating (FEMU) method, using exclusively nanoindentation P−h curves. A 2D axisymmetric finite element model simulates the nanoindentation tests, and the Young's modulus E, the initial yield stress σy and the hardening modulus Hp of the thin film, as well as the yield stress of silicon σys are the parameters to identify. This work relies on a numerical design of experiments carried prior to the identification process. It uses the sensitivity of the nanoindentation force to a variation of the parameters to define an identifiability indicator (I-index) based on the conditioning of the inverse problem. It reflects the stability of the potential solution of the inverse problem. I-index minimisation below a certain value allows to ensure a reliable identification by designing the best combination of experiments in terms of relevant information. I-index analyses values demonstrate that combining Berkovich and cube corner nanoindentation tests at two different indentation depths brings sufficient information to well-conditioned the inverse problem. Indeed, the increased penetration and the varied indenter tip shape induce differentiating factors which activates the substrate effect, or anvil effect, and allow the dissociation of the thin film plasticity from that of the substrate, and thus its identification. The identification procedure of the four parameters carried out with the designed dual nanoindentation test from several starting points reveals that the FEMU method converged to a unique solution. Lastly, the identified parameters are validated by confronting experimental and numerical (i) P−h curves of a Berkovich test on a bulk silicon sample and (ii) residual topographies using a 3D FEM of a Berkovich test on the composite system thin film – substrate.

Geometric parameters optimization of a two-dimensional phoxonic crystal with dual forbidden band characteristics

In this paper, a novel phoxonic crystal (PxC) structure composed of silicon, with optimal dual phononic band gap (PNBG) and photonic band gap (PTBG), is presented. Using the finite element analysis method, both the transmission characteristics and dispersion relation of PNBG and PTBG are calculated, and the existence of dual BGs is demonstrated by the means of the analysis of transmission for the PxC structure. The influences of structural parameters on the dual forbidden band characteristics are further explored, the sensitive structure parameters can be determined: the width of elastic beams, the length of square silicon, and the length of square hole. Using the orthogonal test, 25 experimental runs based on 3-factor and 5-level experiment are performed to finish the numerical experimental design and analysis. Four functional relationships can be acquired between the three sensitive parameters and dual BGs. Finally, the unified objective function method is employed to perform the construction of the single objective optimization model for the purpose of obtaining the optimal dual BGs and the corresponding optimal parameter combinations of the PxC structure. Such scheme can be used as the potential optimization way, which may find wide application in the development and design of PxCs.

Optimization scheme for piezoelectric energy harvesting in line-defect for 2D starlike hole-type phononic crystals considering waveguides

Enhancement of elastic wave energy harvesting by utilizing a phononic crystal (PnC) is a hot topic in electroelastic systems. Piezoelectric energy harvesting (PEH) is implemented herein due to attaching a piezoelectric transducer (PZT) disk on a 2D starlike hole-type PnC with a line-defect. Waveguide and energy localization will lead to the amplification of harvestable mechanical energy using the opened complete bandgaps of the PnC. For a given line-defect PnC structure, two geometric parameters (diameter and thickness of the PZT disk) of the PEH device are found to be key factors to influence the energy harvesting performance. Therefore, the finite element method is used to obtain the optimal diameter and thickness of the PZT disk through the design of numerical experiments. Using the two optimal geometric parameters, the electric power amplification ratio of the present PEH device will be 26.7 times over that of the PEH device using a thin plate with the same outer dimensions.

Proof-of-Concept of a Thermal Barrier Coated Titanium Cooling Layer for an Inside-Out Ceramic Turbine

Abstract Increasing turbine inlet temperature (TIT) of recuperated gas turbines would lead to simultaneously high efficiency and power density, making them prime candidates for low-emission aeronautics applications, such as hybrid-electric aircraft. The inside-out ceramic turbine (ICT) architecture achieves high TIT by using compression-loaded monolithic ceramics. To resist inertial forces due to blade tip speed exceeding 450 m/s, the shroud of the ICT is made of carbon-polymer composite, wound around a metallic cooling ring. This paper demonstrates that it is beneficial to use a titanium alloy cooling ring with a thermal barrier coating (TBC), rather than nickel superalloys, for the interstitial cooling ring protecting the carbon-polymer from the hot combustion gases. A numerical design of experiments (DOE) analysis shows the design tradeoffs between the minimum safety factor and the required cooling power for multiple geometries. An optimized high-pressure first turbine stage of a 500 kW microturbine concept using ceramic blades and a titanium cooling ring in an ICT configuration is presented. Its structural performance (minimum safety factor of 1.4), as well as its cooling losses, (2% of turbine stage power) are evaluated. Finally, a 20 kW-scale prototype is tested at 300 m/s and a TIT of 1375 K during 4 h to demonstrate the viability of the concept. Experiments show that the polymer composite was kept below its maximum safe operating temperature and components show no early signs of degradation.

Effect of infill and density pattern on the mechanical behaviour of ABS parts manufactured by FDM using Taguchi and ANOVA approach

Purpose: The present work aims to investigate the effect of many infill patterns (rectilinear, line, grid, triangles, cubic, concentric, honeycomb, 3D honeycomb) and the infill density on the mechanical tensile strength of an Acrylonitrile Butadiene Styrene (ABS) test specimen manufactured numerically by FDM. Design/methodology/approach: Computer-Aided Design (CAD) software has been used to model the geometry and the mesostructure of the test specimens in a fully automatic manner from a G-code file by using a script. Then, a Numerical Design of Experiments (NDoE) has been carried out by using Taguchi method and the Analysis of Variance (ANOVA). The tensile behaviour of these numerical test specimens has been studied by the Finite Element Analysis (FEA). Findings: The FEA results showed that a maximal Ultimate Tensile Strength (UTS) was reached by using the ‘concentric’ infill pattern combined with an infill density of 30%. The results also show that the infill pattern and the infill density are significant factors. Research limitations/implications: The low infill densities of 20% and 30% that have already been used in many previous studies, we have also applied it in order to reduce the time of the simulations. Indeed, with high infill density, the simulations take a very excessive time. In an ongoing study, we predicted higher percentages. Practical implications: This study provided an important modelling tool for the design and manufacture of functional parts and helps the FDM practitioners and engineers to manufacture strong and lightweight FDM parts by choosing the optimal process parameters. Originality/value: This study elucidated the effect of various infill patterns on the tensile properties of the test specimens and applied for the first time a NDoE using numerical test specimens created by the mesostructured approach, which considerably minimized the cost of the experiments while obtaining an error of 6.8% between the numerical and the experimental values of the UTS.

Sensitivity analysis of the uncertainties of the mechanical design parameters: Stochastic study performed via a numerical design of experiment

As the GDL (Gas diffusion layer) is the most sensitive component in the fuel cell, any change in its structure causes a change in its porosity, which strongly influences the contact between the components of the fuel cell. Note that the state of contact depends on the applied clamping pressure, the thickness and the porosity of the GDL, and the geometry of the rib (bending radius) of the BPP (Bipolar plates). These components can be subject to variations coming from very high compression, so it is necessary to consider the reliability of their dimension via modeling/simulation by the integration of uncertainties. In this article, we will study the influence on the contact pressure of the uncertainties of the mechanical design parameters. A probabilistic approach (Gauss's law) is applied to evaluate the effect of the mechanical uncertainties parameter on the contact pressure between GDL/MEA and GDL/BPP.

Влияние рецептурных факторов на прочностные свойства тяжелых сталефибробетонов

Today, steel fibre is one of the most promising components used to produce fibre reinforced con-crete. To improve the mechanical properties of heavyweight steel fibre reinforced concrete, the influ-ence of recipe factors, namely the percentage of fibre reinforcement and the fibre length, on these properties was studied. 18 series of reference samples of a standard size were manufactured and tested: 27 cubes with dimensions of 100x100x100 mm for compression tests and 27 prisms with di-mensions of 100x100x400 mm for bending under tension test. We calculated mechanical strength characteristics depending on the recipe factor. The calculations were performed using a numerical ex-perimental design (full factorial experiment 2k). Based on the obtained results, it can be concluded that the utilisation of steel fibre with a fibre length of 30 mm or the percentage of three-dimensional rein-forcement of 1.5% is the most effective.

FLUID FLOW BODIES FOR THE PULP AND PAPER INDUSTRY

The question of the use of vortex flowmeters with different versions of the flow body (TO) under operating conditions on the technological lines of pulp and paper production is considered.
 It is shown that when using different TO in vortex flowmeters, an error occurs in the working range of speeds (flow rates). The observed error arises due to a change in the Strouhal number (Sh) and is associated with the measurement method. In this case, the Strouhal number begins to depend not only on the TO used as a vortex generator, but also on the flow velocity and the concentration of the fibrous suspension. As the main comparative factor for the investigated TOs, the force action on the sensitive element (flexible electrode) located inside the TO was taken.
 The study was carried out in several stages using numerical modeling and experimental design method. According to the results of a numerical study, the dependence of the Strouhal number (Sh) on the flow rate (V) and the concentration of the suspension (c) is presented.
 In a comparative analysis of the deviation of the Strouhal number from the average values, it was revealed that MOT No. 1 has a minimal effect on the concentration of the suspension in the working range of flow rates (± 0.5%). This circumstance makes it possible to verify and test flow meters with such maintenance in conventional pouring installations.
 The analysis of the maintenance with respect to the signal-to-noise ratio shows that the purest signal is generated by the cylindrical maintenance (maintenance No. 3), and maintenance No. 2 and No. 1 have noticeably large noise. The differences are explained by the absence on the surface of a cylindrical TO of extra protrusions, faces, which leads to a smoother flow of a suspension around its surface, as well as to a decrease in internal spurious noise.

Revealing the modulation of boundary conditions and governing processes on ozone formation over northern China in June 2017

Abstract In this study, ozonesonde data were used to evaluate the impact of different boundary conditions on the vertical distribution of ozone over urban Beijing. The comparison shows that the clean and static boundary conditions, referred to as PROFILE, apparently underestimate the ozone concentration over the upper troposphere and stratosphere, whereas the global chemical transport model (CTM) provides much more reasonable performance. Further investigation reveals that the boundary conditions exert larger impacts over areas with high altitudes and close distances to boundaries, such as the Tibetan Plateau, while they yield weak impacts on regions relatively far from the boundary, such as the North China Plain (NCP). Process analysis was conducted to investigate the modulation of physical and chemical processes on ozone formation in June 2017, illustrating that during the daytime of the high-O3 period, the photochemical reactions within the planetary boundary layer (PBL) almost become the only source favorable to ozone accumulation. Motivated by this phenomenon, we constructed a linear regression and found that the maximum daily 8-hr ozone (MDA8) ozone concentration was highly correlated with the surface ozone change rate and chemical reactions in the PBL during the pollution period, with MDA8 ozone exceeding 70 ppbv over NCP. Based on this relationship as well as the design of numerical experiments, we propose a strategy of dynamic emission control. Firstly, the emission reduction during the peak ozone formation period may weaken the fast chemical reactions in the PBL and subsequent surface ozone concentration. Secondly, emission reduction one or two days prior to an episode might achieve larger ozone reduction through the accumulation effect. Lastly, emission control outside of the NCP may surpass the local impact under favorable meteorological conditions. Therefore, the efficacy of dynamic emission control was striking when both the accumulation and transport effect were taken into consideration.

An effective finite element modeling approach for prediction of the behaviour of a jute fibre-reinforced composite tube under axial impact

The focus of the work reported here is on the prediction of the behaviour of a hollow cylindrical jute– polyester composite tube under axial impact using the explicit finite element analysis code, LS-DYNA. An efficient finite element modelling approach using a single shell element through the thickness of a thin-walled structural part has been chosen. Effective orthotropic material properties of a laminate which can be determined through standard ASTM tests have been used as input data for a popular constitutive model titled ‘Enhanced Composite Damage’ with the option of specifying either the Chang–Chang criteria or the Tsai–Wu criterion for failure. A unique feature of the current approach is to verify the modeling procedure initially for coupon-level tensile, compressive and flexural tests through a numerical design of experiments involving a set of physically meaningful fibre and matrix failure strain parameters, and then extend the same toward successfully predicting the mechanical behaviour of a jute composite tube subject to axial drop-weight impact. Theoretical predictions of peak responses for flexural and tube impact tests are also presented.

Toward new methods for optimization study in automotive industry including recent reduction techniques

In the last years, the automotive engineering industry has been deeply influenced by the use of «machine learning» techniques for new design and innovation purposes. However, some specific engineering aspects like numerical optimization study still require the development of suitable high-performance machine learning approaches involving parametrized Finite Elements (FE) structural dynamics simulation data. Weight reduction on a car body is a crucial matter that improves the environmental impact and the cost of the product. The actual optimization process at Renault SA uses numerical Design of Experiments (DOE) to find the right thicknesses and materials for each part of the vehicle that guarantees a reduced weight while keeping a good behavior of the car body, identified by criteria or sensors on the body (maximum displacements, upper bounds of instantaneous acceleration …). The usual DOE methodology generally uses between 3 and 10 times the numbers of parameters of the study (which means, for a 30-parameters study, at least 90 simulations, with typically 10 h per run on a 140-core computer). During the last 2 years, Renault’s teams strived to develop a disruptive methodology to conduct optimization study. By ‘disruptive’, we mean to find a methodology that cuts the cost of computational effort by several orders of magnitude. It is acknowledged that standard DoEs need a number of simulations which is at least proportional to the dimension of the parameter space, leading generally to hundreds of fine simulations for real applications. Comparatively, a disruptive method should require about 10 fine evaluations only. This can be achieved by means of a combination of massive data knowledge extraction of FE crash simulation results and the help of parallel high-performance computing (HPC). For instance, in the recent study presented by Assou et al. (A car crash reduced order model with random forest. In: 4th International workshop on reduced basis, POD and PGD Model Reduction Techniques—MORTech 2017. 2017), it took 10 runs to find a solution of a 34-parameter problem that fulfils the specifications. In order to improve this method, we must extract more knowledge from the simulation results (correlations, spatio-temporal features, explanatory variables) and process them in order to find efficient ways to describe the car crash dynamics and link criteria/quantities of interest with some explanatory variables. One of the improvements made in the last months is the use of the so-called Empirical Interpolation Method (EIM, [Barrault et al.]) to identify the few time instants and spatial nodes of the FE-mesh (referred to as magic points) that “explain” the behavior of the body during the crash, within a dimensionality reduction approach. The EIM method replaces a former K-Means algorithm (Davies et al. in IEEE Trans Pattern Anal Mach Intell, 1(2):224–227, 1979) which was processed online, for each ROM. Instead, the computation of EIM method is done offline, once for all, for each simulation. This new method allows us to compute a ROM quite faster, and to reduce the number of features that we use for the regression step (~ 100). The nonlinear regression step is achieved by a standard Random Forest (RF, [Breiman. Mach Learn 45:5–32, 2001]) algorithm. Another improvement of the method is the characterization of numerical features describing the shape of the body, at a nodal scale. The characteristics of orientation of the elements surrounding a mesh node must be taken into account to describe the behavior of the node during the crash. The actual method integrates some numerical features, computed from the orientation of the elements around each node, to explain the node behavior. The paper is organized as follows: The introduction states the scientific and industrial context of the research. Then, the ReCUR Method is detailed, and the recent improvements are highlighted. Results are presented and discussed before having some concluding remarks on this piece of work.

Numerical modeling of the effects hydration and number of hydrogen bonds on the mechanical properties of the tropocollagen molecule.

Bone aging involves structural and molecular modifications, especially at the level of type I tropocollagen. This macromolecule shows two main age-related alterations, which are the decrease of both molecular diameter (due to the loss of hydration) and number of hydrogen bonds. In this work, it is proposed to investigate the influence of these two parameters (molecular diameter and number of hydrogen bonds) on the mechanical behavior of tropocollagen using finite element method. To this end, a novel three-dimensional finite element model of collagen molecule accounting for hydrogen bonds was developed. Then, a numerical design of experiments for the diameter of tropocollagen and variations in the number of hydrogen bonds has been established. The mechanical properties ("load-strain" curve and apparent Young's modulus) of the collagen molecule were obtained by employing the proposed model to uniaxial tensile tests. The parametric study demonstrates that the mechanical properties of tropocollagen are slightly affected by the rate of hydration but considerably affected by variation of the number of hydrogen bonds. Finally, a fitted analytical function was deduced from the above results showing effects of the two parameters (hydration rate and hydrogen bonds) on the apparent Young's modulus of tropocollagen. This study could be useful to understand the influence of structural age modifications of tropocollagen on the macroscopic mechanical properties of bone.

The Mars Regional Atmospheric Modeling System (MRAMS): Current Status and Future Directions

The Mars Regional Atmospheric Modeling System (MRAMS) is closing in on two decades of use as a tool to investigate mesoscale and microscale circulations and dynamics in the atmosphere of Mars. Over this period of time, there have been numerous improvements and additions to the model dynamical core, physical parameterizations, and framework. At the same time, the application of the model to Mars (and related code for other planets) has taught many lessons about limitations and cautions that should be exercised. The current state of MRAMS is described along with a review of prior studies and findings utilizing the model. Where appropriate, lessons learned are provided to help guide future users and aid in the design and interpretation of numerical experiments. The paper concludes with a discussion of future MRAMS development plans.

Micromechanical Modeling of Fatigue Crack Nucleation around Non-Metallic Inclusions in Martensitic High-Strength Steels

Martensitic high-strength steels are prone to exhibit premature fatigue failure due to fatigue crack nucleation at non-metallic inclusions and other microstructural defects. This study investigates the fatigue crack nucleation behavior of the martensitic steel SAE 4150 at different microstructural defects by means of micromechanical simulations. Inclusion statistics based on experimental data serve as a reference for the identification of failure-relevant inclusions and defects for the material of interest. A comprehensive numerical design of experiment was performed to systematically assess the influencing parameters of the microstructural defects with respect to their fatigue crack nucleation potential. In particular, the effects of defect type, inclusion–matrix interface configuration, defect size, defect shape and defect alignment to loading axis on fatigue damage behavior were studied and discussed in detail. To account for the evolution of residual stresses around inclusions due to previous heat treatments of the material, an elasto-plastic extension of the micromechanical model is proposed. The non-local Fatemi–Socie parameter was used in this study to quantify the fatigue crack nucleation potential. The numerical results of the study exhibit a loading level-dependent damage potential of the different inclusion–matrix configurations and a fundamental influence of the alignment of specific defect types to the loading axis. These results illustrate that the micromechanical model can quantitatively evaluate the different defects, which can make a valuable contribution to the comparison of different material grades in the future.

A model based predictive tool for fire safety intumescent coatings design

In order to improve structures survivability, intumescent paints provide an attractive alternative to insulating materials. Such protective coatings provide an efficient thermal protection due to their swelling properties when exposed to thermal aggressions. The key-goal for safety aspects is to determine which initial paint thickness has to be applied in order to satisfy thermal safety requirements. Thus, if all the thermo physical properties of the intumescent paint are accurately known, the development of a numerical predictive tool could offer a solution for safety recommendations. A numerical design of experiment is proposed. Response surfaces are determined and optimal initial paint thickness can be found using D-optimum design. The optimal thickness is validated in simulated specific accidental configurations using a Solar Furnace.

High Throughput Co-culture Assays for the Investigation of Microbial Interactions.

The study of interactions between microorganisms has led to numerous discoveries, from novel antimicrobials to insights in microbial ecology. Many approaches used for the study of microbial interactions require specialized equipment and are expensive and time intensive. This paper presents a protocol for co-culture interaction assays that are inexpensive, scalable to large sample numbers, and easily adaptable to numerous experimental designs. Microorganisms are cultured together, with each well representing one pairwise combination of microorganisms. A test organism is cultured on one side of each well and first incubated in monoculture. Subsequently, target organisms are simultaneously inoculated onto the opposite side of each well using a 3D-printed inoculation stamp. After co-culture, the completed assays are scored for visual phenotypes, such as growth or inhibition. These assays can be used to confirm phenotypes or identify patterns among isolates of interest. Using this simple and effective method, users can analyze combinations of microorganisms rapidly and efficiently. This co-culture approach is applicable to antibiotic discovery as well as culture-based microbiome research and has already been successfully applied to both applications.

Stress-Based Model for Lifetime Estimation of Bond Wire Contacts Using Power Cycling Tests and Finite-Element Modeling

In this paper, a lifetime model for bond wire contacts of insulated gate bipolar transistors (IGBT) power modules is reported. This model is based on power cycling tests obtained under accelerated conditions, and a finite-element model taking into account the electrical, thermal, and mechanical coupling. It allows us to estimate the bond wire lifetime for a large scale of junction temperature swing amplitudes (ΔT <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> ) and stress durations (t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> ). To build it, a numerical design of experiment was performed in both high and low stress values (ΔT <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> ). Then, a strain-life curve has been constructed where the average strain values on a defined volume around the contact areas between top-metallization and the most exposed bond wires to fatigue and liftoff have been used. As a result, it has been shown that the total strain is linearly dependent with ΔT <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> and power law dependent with t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> . The combination of the strain-life relation and the strain dependency with stress parameters leads to the lifetime relationship. The obtained lifetime model has been satisfactorily validated with some additional experimental points obtained from literature and with a large range of values for t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ON</sub> . This methodology can be easily replicated to other structures and is quite generic.

Parametric exploration on the airfoil design space by numerical design of experiment methodology and multiple regression model

Robust airfoil design is crucial to efficient, stable, and safe operation for modern wind turbines. However, even for deterministic wind turbine airfoil design, the problem is complex regarding to aerodynamic, acoustic, and structural requirements of wind turbine blades. Therefore, this study aims to assess the design variable impact, identify significant variables, and obtain the correlation with the airfoil responses, to reduce the cost of the airfoil robust optimization. In this paper, the optimal hypercube design method was applied to an airfoil designed by the National Advisory Committee for Aeronautics, NACA 63-421, which is commonly employed in the outboard modern wind turbine blade, to perform the numerical design of experiments. Then, a parametric exploration on the characteristics of airfoil design space by the multiple regression model and statistical analysis method were conducted. It was identified that in regular design space, the variations of aerodynamic and structural parameters are dominated by the airfoil camber and radius of leading edge. Meanwhile, the chord-wise position of the maximum thickness also has strong impacts on the airfoil performance. In further, the overall design spaces are explored to be highly nonlinear in aerodynamic and acoustic responses because of the nonlinear effects of the airfoil chord-wise position of the maximum camber and radius of leading edge. Strong but undesirable correlations were demonstrated between the maximum lift-to-drag ratio and the total sound pressure level. These findings could serve as a valuable guidance for wind turbine airfoil robust design to screen the stochastic design variables, simplify the design space, and reduce the cost.