In this survey paper transitional turbulence modeling is approached from the point of view relevant to small unmanned aerial vehicles (span ≈ 1m), of which the flow is characterized by very low values of turbulent intensity and transition is predominantly of the separation induced kind. The physical mechanisms that are present during transition are discussed based on the experimental and numerical findings of the last five decades and their influence on high angle of attack behavior, with the appearance of abrupt stall, stall cells, low frequency oscillations and hysteresis are reviewed. Furthermore, an overview will be given of the different methodologies that exist to predict transitional flows. Emphasis will be placed on the modeling of separation bubbles within the RANS-based environment: a number of transitional turbulence models will be summarized and categorized based on their transition predicting methodologies. Four different turbulence models for low Reynolds number flow will be discussed in depth: Menter's k − ω SST model with Wilcox's low-Re modification, Menter & Langtry's (k − ω SST) γ − Re θ model, it's simplified (k − ω SST) γ model and Walters & Cokljat's k − k l − ω model.
This paper considers transition modeling for the flow over small unmanned aerial vehicles with a span of around 1 m. Such flows are characterized by very low values of turbulent intensity and the main cause for transition corresponds to flow separation. Four different turbulence models for low Reynolds number flow are compared with the experimental data for a NACA 0018 airfoil over a range of 2D as well as 3D conditions. The turbulence models under consideration are Menter's k − ω SST model with Wilcox's low-Re modification, Menter & Langtry's (k − ω SST) γ − Re θ model along with its simplified version in the form of the (k − ω SST) γ model, and Walters & Coklja's k − k l − ω model. The NACA 0018 profile is rotated in a flow with a chord-based Reynolds number of 3×10 5 at three different rotational speeds between an angle of attack (AoA) of 0 o and 25 o . Using a curve fitting methodology, an estimate of the results at an infinitesimally slow rotation can be made. Both clockwise and counterclockwise rotations are considered to allow an assessment of the model for predicting steady hysteresis. Furthermore, 3D computations for an infinite wing are performed to examine the appearance of coherent structures at high AoA, namely, stall cells or low frequency fluctuations.
In this work, robust design optimization (RDO) is treated, motivated by the increasing desire to account for variability the design phase. The problem is formulated in a multi-objective setting with the objective of simultaneously minimizing the mean of the objective and its variance due to variability of design variables and/or parameters. This allows the designer to choose its robustness level without the need to repeat the optimization as typically encountered when formulated as a single objective. To account for the computational cost that is often encountered in RDO problems, the problem is fitted in a Bayesian optimization framework. The use of surrogate modeling techniques to efficiently solve problems under uncertainty has effectively found its way in the optimization community leading to surrogate-assisted optimization-under-uncertainty schemes. The surrogates are often considered cheap-to-sample black-boxes and are sampled to obtain the desired quantities of interest. However, since the analytical formulation of the surrogates is known, an analytical treatment of the problem is available. To obtain the quantities of interest without sampling an analytical uncertainty propagation through the surrogate is presented. The multi-objective Bayesian optimization framework and the analytical uncertainty quantification are linked together through the formulation of the robust expected improvement (REI), obtaining the novel efficient robust global optimization (ERGO) scheme. The method is tested on a series of test cases to examine its behavior for varying difficulties and validated on an aerodynamic test function which proves the effectiveness of the novel scheme.
In this paper the multi-objective, multi-fidelity optimization of a wing fence on an unmanned aerial vehicle (UAV) near stall is presented. The UAV under consideration is characterized by a blended wing body (BWB), which increases its efficiency, and a tailless design, which leads to a swept wing to ensure longitudinal static stability. The consequence is a possible appearance of a nose-up moment, loss of lift initiating at the tips and reduced controllability during landing, commonly referred to as tip-stall. A possible solution to counter this phenomenon is wing fences: planes placed on top of the wing aligned with the flow and developed from the idea of stopping the transverse component of the boundary layer flow. These are optimized to obtain the design that would fence off the appearance of a pitch-up moment at high angles of attack, without a significant loss of lift and controllability. This brings forth a constrained multi-objective optimization problem. The evaluations are performed through Unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations. However, since controllability cannot be directly assessed through Computational Fluid Dynamics (CFD), surrogate-derived gra-
In this paper, we address the formulation of a novel scheme for reliabilitybased design optimization, in which the design optimization problem is characterized by constraints that must be met with a certain probability. Assessment of the aforementioned is typically referred to as reliability analysis. Conventional methods rely on sampling approaches or by reformulating the problem as a two-level optimization that requires gradient or Hessian information of the constraints to obtain a trustworthy solution. However, the computational cost of such methods makes them often impractical. To overcome the aforementioned, a surrogateassisted asymptotic reliability analysis (SARA) is presented that makes use of surrogate-derived gradient and Hessian information. The sub-optimization problem is reformulated as a set of constraints using the Karush-Kuhn-Tucker conditions and fitted in an efficient global optimization-like setting through the formulation of the reliability-based expected improvement (RBEI), obtaining the novel efficient single-loop approach (ESLA). The method is tested on a series of test cases which prove the effectiveness of the novel scheme.
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