A data assimilation methodology for reconstructing turbulent flows around aircraft

Katô, Hiroshi; Yoshizawa, Atsushi; Ueno, G.; Obayashi, Shigeru

doi:10.1016/j.jcp.2014.12.013

Cited by 106 publications

(44 citation statements)

References 11 publications

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“…The EnKF consists of serial propagation equations that are difficult to obtain explicitly in turbulent flows. This leads to a statistical data-driving approach for the determination of the Kalman gain, and the variance using a large ensemble that is computationally expensive for highdimension systems, 14 or the inclusion of reduced-order models but with the introduction of extra model uncertainties. 15 The adjoint-based method is typically implemented in the discrete form, within which the system is discretized before the need of adjoint equation derivation.…”

Section: Introductionmentioning

confidence: 99%

A data assimilation model for turbulent flows using continuous adjoint formulation

Liu

Gan

2018

Physics of Fluids

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A generalized data assimilation model for turbulent flows using the continuous adjoint formulation is proposed. Within this formulation, the Spalart-Allmaras turbulence model is modified by adding a correction function β as a spatially varying coefficient to the turbulence production term. The model-form error is thus corrected by optimizing the β distribution, using the adjoint equations and the corresponding boundary conditions, to minimize the discrepancy between the predictions and observations. In addition, a constraint is applied to drive β toward a large value to avoid the flow unsteadiness owing to the low eddy viscosity. The present adjoint-based data assimilation (ABDA) model is expected to be applicable to various flow conditions unsolvable by the simple optimization of the model constant. This model is fully equation-driven and is thus computationally cheaper than the discretized adjoint method, as well as convenient to be implemented in the existing computational fluid dynamics codes. The flow over a cylinder with synthetic observations, the free round jet, the flow over a hump, and the three-dimensional flow over a wall-mounted cube, all of which are challenging for original Reynolds-averaged Navier-Stokes simulations, are employed to successfully demonstrate the reliability and capacity of the present ABDA model. The first-order scheme applied to the adjoint equations exhibits little effects on the final assimilation results, but improves the robustness significantly, and drives β to another solution that can also minimize the cost function. The present ABDA model is efficient in the heavy assimilation work of different types of shear and separated flows.

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Section: Introductionmentioning

confidence: 99%

A data assimilation model for turbulent flows using continuous adjoint formulation

Liu

Gan

2018

Physics of Fluids

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“…In order to minimise the cost function (5), one iteration of Newton CG method is performed with (6) and (7). The obtained β is used to update the state vector α according to (1).…”

Section: Ensemble-based Variational Schemementioning

confidence: 99%

“…Kato and Obayashi [5] applied EnKF to infer the optimal parameters in the Spalart-Allmaras turbulence model for zero-pressure gradient flat plate boundary layer at Mach number of 0.2 and Reynolds number of 5 × 10 6 . They [6] also used the Ensemble Transform Kalman Filter to integrate the CFD and experimental fluid dynamics (EFD) to replicate the transonic turbulent flows over RAE 2822 airfoil and ONERA M6 wing through estimating the proper angle of attack, Mach number, and turbulent viscosity. Heng et al [7] introduced uncertainty in Reynolds stress directly and adopted an iterative ensemble Kalman method to reduce the model-form uncertainty in k − model for the flow over periodic hills and the flow in a square duct by assimilating very sparse observations.…”

Section: Introductionmentioning

confidence: 99%

Bayesian optimisation of RANS simulation with ensemble-based variational method in convergent-divergent channel

Zhang

Gomez

Coutier-Delgosha

2019

Journal of Turbulence

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This paper investigates the applicability of a hybrid data assimilation approach, namely ensemble-based variational method (EnVar), to optimise Reynolds Averaged Navier-Stokes (RANS) simulations in convergent-divergent channel from the perspective of Bayesian inference. Concretely, the ensemble-based variational method is applied to infer the inlet velocity and turbulence model corrections by assimilating Direct Numerical Simulation (DNS) results or limited experimental data. The approach is first adopted to infer the inlet velocity profile for the WallTurb Bump and Venturi geometry. The improvement can be achieved near the inlet region for the bump, but for Venturi in light of the view field limited in adverse pressure gradient region, the observation space is not sensitive to the perturbation of inlet condition. In a second step, the model corrections in k − ω SST model are investigated by assimilating the limited sparse experimental data. With the inferred model corrections, the predictions on both velocity and turbulent kinetic energy (TKE) get improved. The results indicate that the ensemble-based variational method is efficient in inferring unknown quantities of both low dimension (D = 20) and high dimension (D = 2400) with small ensemble size robustly and non-intrusively. This approach could prove very useful for Bayesian inference or optimisation in CFD problems.

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“…Kikuchi et al [13] compared the performance of an EnKF and a particle filter applied to the POD-Galerkin model of the problem of the flow past a cylinder. Kato et al [14] used a variation of the EnKF to achieve synchronization between a Reynolds-averaged Navier-Stokes/Spalart-Allmaras numerical simulation of a steady transonic flow past airfoils and pressure experimental data. Mons et al [15] use a Kalman smoother and other variational methods to reconstruct freestream perturbation history based on measurements taken on and around a circular cylinder subjected to it.…”

Section: Introductionmentioning

confidence: 99%

Ensemble-Based State Estimator for Aerodynamic Flows

Silva

Colonius

2018

AIAA Journal

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Regardless of the plant model, robust flow estimation based on limited measurements remains a major challenge in successful flow control applications. Aiming to combine the robustness of a high-dimensional representation of the dynamics with the cost efficiency of a low-order approximation of the state covariance matrix, a flow state estimator based on the ensemble Kalman filter is applied to two-dimensional flow past a cylinder and an airfoil at high angle of attack and low Reynolds number. For development purposes, the numerical algorithm is used as both the estimator and as a surrogate for the measurements. Estimation is successful using a reduced number of either pressure sensors on the surface of the body or sparsely placed velocity probes in the wake. Because the most relevant features of these flows are restricted to a low-dimensional manifold of the state space, asymptotic behavior of the estimator is shown to be achieved with a small ensemble size. The relative importance of each sensor location is evaluated by analyzing how they influence the estimated flowfield, and optimal locations for pressure sensors are determined. Covariance inflation is used to enhance the estimator performance in the presence of unmodeled freestream perturbations. A combination of parametric modeling and augmented state methodology is used to successfully estimate the forces on immersed bodies subjected to deterministic and random gusts.

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A data assimilation methodology for reconstructing turbulent flows around aircraft

Cited by 106 publications

References 11 publications

A data assimilation model for turbulent flows using continuous adjoint formulation

A data assimilation model for turbulent flows using continuous adjoint formulation

Bayesian optimisation of RANS simulation with ensemble-based variational method in convergent-divergent channel

Ensemble-Based State Estimator for Aerodynamic Flows

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