Time-accurate Solver Research Articles

Unsteady RANS-based DMD analysis of airfoil NACA0015 with Gurney flap

The present investigation summarizes the numerical prediction and DMD analysis of the flow in the vicinity of a Gurney flap set on an airfoil NACA0015 at Re = 10,300 tested in a water tunnel with time-resolved Particle Image Velocimetry. A series of two-dimensional U-RANS simulations has been accomplished using an incompressible, time-accurate solver of OpenFOAM. A purely data-based DMD analysis has followed to extract the spatio-temporal coherent structures from the time-evolving flowfields, to mimic the experiments. It is stressed that this work focuses on the analysis of this kind of flap by applying DMD to datasets generated with numerical simulations, which has not been previously investigated, but using experimental datasets. Under this approach, the comparison of the numerics with the experimental counterpart shows a remarkable agreement for both the structures and major frequencies, which stresses the suitability of the incompresible U-RANS approach in this class of studies. Special attention has been focused on the modelling of the experimental facility, and a quantification of the prediction accuracy is provided by assessing the deviation of the spectral content. The simulations clearly show the key role of having a good characterization of the water tunnel to be successful at capturing the spectrum and flow unsteadiness. Furthermore, they reveal quite promising for those industrial oriented simulations, which deal with lift-enhancement devices and lift-to-drag ratio optimization of airfoils since they permit an accurate prediction.

Coupled Newton–Krylov Time-Spectral Solver for Flutter and Limit Cycle Oscillation Prediction

Flutter and limit cycle oscillation (LCO) are important phenomena that need to be considered in aircraft design. Previous harmonic-balance-based flutter and LCO prediction methods either have low linear convergence rates or require expensive Newton steps to achieve quadratic convergence. In this paper, we propose a preconditioned, Jacobian-free, coupled Newton–Krylov (CNK) method for the time-spectral aeroelastic equations. By solving the coupled system directly, the method reduces the computational cost of each Newton step, making quadratic convergence affordable. The proposed Jacobian-free method is easier to implement and requires less memory relative to previous methods. We demonstrate the capability of the CNK solver by verifying the results against a time-accurate solver and by comparing them to other harmonic-balance-based results reported in the literature. We observe that the proposed method is more efficient than the time-accurate method in LCO response simulations. And the LCO velocities and frequencies predicted by the proposed method and the time-accurate method are within 1% of relative difference when the same mesh is used. This method can be potentially used in aircraft design.

Time-Linearized and Time-Accurate 3D RANS Methods for Aeroelastic Analysis in Turbomachinery

A computational method for performing aeroelastic analysis using either a time-linearized or an unsteady time-accurate solver for the compressible Reynolds averaged Navier--Stokes (RANS) equations is described. The time-linearized solver employs the assumption of small time-harmonic perturbations and is implemented via finite differences of the nonlinear flux routines of the time-accurate solver. The resulting linear system is solved using a parallelized generalized minimal residual (GMRES) method with block-local preconditioning. The time accurate solver uses a dual time stepping algorithm for the solution of the unsteady RANS equations on a periodically moving computational grid. For either solver, and both flutter and forced response problems, a mapping algorithm has been developed to map structural eigenmodes, obtained from finite element structural analysis, from the surface mesh of the finite element structural solver to the surface mesh of the finite volume flow solver. Using the surface displacement data an elliptic mesh deformation algorithm, based on linear elasticity theory, is then used to compute the grid deformation vector field. The developed methods are validated first using standard configuration 10. Finally, for an ultra-high bypass ratio fan, the results of the time-linearized and the unsteady module are compared. The gain in prediction time using the linearized methods is highlighted.

Vortical gust boundary condition for realistic rotor wake/stator interaction noise prediction using computational aeroacoustics

In this work, the NASA Glenn Research Center Broadband Aeroacoustic Stator Simulation (BASS) code is extended for use in the prediction of noise produced by realistic three-dimensional rotor wakes impinging on a downstream stator row. In order to accurately simulate such a flow using a nonlinear time-accurate solver, the inflow and outflow boundary conditions must simultaneously maintain the desired mean flow, allow outgoing vortical, entropic, and acoustic waves to cleanly exit the domain, and accurately impose the desired incoming flow disturbances. This work validates a new method for the acoustics-free imposition of three-dimensional vortical disturbances using benchmark test cases.

Reprint of: Towards the Prediction of Noise from Realistic Rotor Wake/Stator Interaction Using CAA

In this work, the NASA Glenn Research Center Broadband Aeroacoustic Stator Simulation (BASS) code is extended for use in the prediction of noise produced by realistic three dimensional rotor wakes impinging on a downstream stator row. In order to accurately simulate such a flow using a nonlinear time-accurate solver, the inflow and outflow boundary conditions must simultaneously maintain the desired mean flow, allow outgoing vortical, entropic, and acoustic waves to cleanly exit the domain, and accurately impose the desired incoming flow disturbances. This work validates a new method for the acoustics-free imposition of three-dimensional vortical disturbances using a benchmark test case.

Towards the prediction of noise from realistic rotor wake/stator interaction using CAA

In this work, the NASA Glenn Research Center Broadband Aeroacoustic Stator Simulation (BASS) code is extended for use in the prediction of noise produced by realistic three dimensional rotor wakes impinging on a downstream stator row. In order to accurately simulate such a flow using a nonlinear time-accurate solver, the inflow and outflow boundary conditions must simultaneously maintain the desired mean flow, allow outgoing vortical, entropic, and acoustic waves to cleanly exit the domain, and accurately impose the desired incoming flow disturbances. This work validates a new method for the acoustics-free imposition of three-dimensional vortical disturbances using a benchmark test case.

Comparative Study of Coupled-Mode Flutter-Analysis Methods for Fan Configurations

A comparative computational study of current e utter-analysis methods, for fan geometry in subsonic e ow, is carried out to evaluate the relative advantage of the methods. The e utter characteristics are computed using the followingthreemethods:timedomain, workpercycle, andtheeigenvalueanalysis.Theeigenvalueanalysisisbased on a pulse method in combination with the ine uence coefe cient method. The aeroelastic analyses are performed using a time-accurate solver based on Euler equations. The aeroelastic characteristics of the fan are obtained by coupling the unsteady Euler equation solution with a normal-mode analysis of elastic blades. For the coupledmodee utteranalyzed,thetime-domainmethod indicated stability orinstability fasterthan theeigenvaluemethod, whereas the work-per-cycle method failed to predict the e utter. The eigenvalue method provided the results in the form of aerodynamic damping and e utter frequency for each interblade phase angle analyzed. However, it was more expensive than the time-domain method, and it was better suited for analysis with a fewer number of modes.

Analysis of Fluid-Structure Interaction by Means of Dynamic Unstructured Meshes

This paper presents a computational analysis on forced vibration and fluid-structure interaction in compressible flow regimes. A so-called staggered approach is pursued where the fluid and structure are integrated in time by distinct solvers. Their interaction is then taken into account by a coupling algorithm. The unsteady fluid motion is simulated by means of an explicit time-accurate solver. For the fluid-structure interaction problems which are considered here the effects due to the viscosity can be neglected. The fluid is hence modeled by the Euler equations for compressible inviscid flow. Unstructured grids are used to discretise the fluid domain. These grids are particularly suited to simulate unsteady flows over complex geometries by their capacity of being dynamically refined and unrefined. Dynamic mesh adaptation is used to enhance the computational precision with minimal CPU and memory constraints. Fluid-structure interaction involves moving boundaries. Therefore the Arbitrary Lagrange Euler method (ALE-method) is adopted to solve the Euler equations on a moving domain. The deformation of the mesh is controlled by means of a spring analogy in conjunction with a boundary correction to circumvent the principle of Saint Venant. To take advantage of the differences between fluid and structure time scales, the fluid calculation is subcycled within the structural time step. Numerical results are presented for large rotation, pitching oscillation and aeroelastic motion of the NACA0012 airfoil. The boundary deformation is validated by comparing the numerical solution for a flat plate under supersonic flow with the analytical solution.

Multigrid Computations of Unsteady Rotor-Stator Interaction Using the Navier-Stokes Equations

A Navier-Stokes time-accurate solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. A four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. Those accelerating strategies include local time stepping, residual smoothing, and multigrid. Direct interpolation of the conservative variables is used to handle the interfaces between blade rows. Two-dimensional viscous calculations of unsteady rotor-stator interaction in a modern gas turbine stage are presented to check for the capability of the procedure.