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Lodato G.,Stanford University | Lodato G.,Center for Turbulence Research | Ham F.,Stanford University | Ham F.,Center for Turbulence Research | And 2 more authors.
AIAA Journal | Year: 2012

The inclusion of transverse effects in designing characteristic boundary conditions for the Euler and Navier-Stokes equations was discussed by different authors and has proved to give some improvement in the perspective of reducing numerical perturbations generated at open boundaries. Based on the most general characteristic formulation using nonorthogonal and rotated reference frames, ananalysis of the different terms involved in such an approach is carried out in the present work. To achieve the best performance for the numerical behavior of the boundary condition, it is then shown that different transverse terms need to be treated differently when included in the definition of the incoming wave amplitude variations. The analysis is supported by a series of numerical tests involving aninviscid vortex convected atanangle or a purely acoustic wave propagating radially. It is concluded that the optimal behavior in terms of acoustic reflection by outgoing vorticity can be achieved by minimizing the contribution of the transverse terms related to the material derivatives along the bicharacteristics, either by properly relaxing them or by selecting a characteristic direction which is not necessarily orthogonal to the boundary. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.

Seshadri P.,Stanford University | Seshadri P.,Center for Turbulence Research | Constantine P.,Stanford University | Constantine P.,Colorado School of Mines | And 2 more authors.
16th AIAA Non-Deterministic Approaches Conference | Year: 2014

This paper presents a novel approach for design under uncertainty-aggressive design. For a given objective, aggressive design seeks to minimize the distance between a designs' PDF under uncertainty and a given target. This target is the probability distribution of the quantity of interest given uncertainty in the model inputs. The objective of aggressive design is to find a design whose PDF most closely resembles the target PDF. The frame- work outlined here is designed to be computationally cheaper than robust, multi-objective optimization. To evaluate the efficacy of this approach, detailed numerical experiments are carried out on the the Gaussian and beta families of PDFs-both for smooth and discrete PDFs. Finally the approach is applied to the design of an airfoil under Mach number uncertainty and compared with results obtained using robust design.

Pecnik R.,Stanford University | Pecnik R.,Center for Turbulence Research | Pecnik R.,Technical University of Delft | Terrapon V.E.,Stanford University | And 9 more authors.
AIAA Journal | Year: 2012

The internal flow in the HyShot II scramjet is investigated through numerical simulations. A computational infrastructure to solve the compressible Reynolds-averaged Navier-Stokes equations on unstructured meshes is introduced. A combustion model based on tabulated chemistry is considered to incorporate detailed chemical-kinetics mechanics while retaining a low computational cost. Both nonreactive and reactive simulations have been performed, and results are compared with ground test measurements obtained at DLR, German Aerospace Center. Different turbulence models were tested, and the dependence on the mesh is assessed through grid refinement. The comparison with experimental data shows good agreement, although the computed heat fluxes at the wall are higher than measurements for the reactive case.Asensitivity analysis on the turbulent Schmidt and Prandtl numbers shows that the choice of these parameters has a strong influence on the results. In particular, variations of the turbulent Prandtl number lead to large changes in the heat flux at the walls. Finally, the inception of thermal choking is investigated by increasing the equivalence ratio, whereby a normal shock is created locally and moves upstream, leading to a large increase in the maximum pressure. Nevertheless, a large portion of the flow is still supersonic. Copyright. © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Terashima H.,Japan Aerospace Exploration Agency | Terashima H.,University of Tokyo | Kawai S.,Stanford University | Kawai S.,Center for Turbulence Research | And 2 more authors.
AIAA Journal | Year: 2011

A high-resolution methodology using a high-order compact differencing scheme with localized artificial diffusivity is introduced with the aim of simulating jet mixing under supercritical pressure environments. The nonlinear localized artificial diffusivity provides the stability to capture different types of discontinuity, such as shock wave, contact surface, and material interface, whereas the high-order compact difference scheme resolves broadband scales in the rest of the domain. The present method is tested on several one-dimensional discontinuity-related problems under super/transcritical conditions and a comparatively more illustrative two-dimensional lowtemperature planar jet problem under a supercritical pressure condition. The localized artificial diffusivity, especially artificial thermal conductivity for temperature gradients, effectively suppresses numerical wiggles near the interfaces. The effects of the artificial thermal conductivity on numerical stability and accuracy are examined. Comparisons between the present method and a conventional low-order scheme demonstrate the superior performance of the present method for resolving a wide range of flow scales while successfully capturing large density/temperature variations at interfaces. Copyright © 2011 by the American Institute of Aeronautics and Astronautics, Inc.

Congedo P.M.,French Institute for Research in Computer Science and Automation | Witteveen J.,Stanford University | Witteveen J.,Center for Turbulence Research | Iaccarino G.,Stanford University
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference 2012 | Year: 2012

The Simplex Stochastic Collocation (SSC) method has been recently proposed in order to handle aleatory uncertainty quantification (UQ), i.e. irreducible variabilities inherent in nature. In this work, we present an extension of this method for treating epistemic uncertainty in the context of interval analysis approach. This numerical method is based on a Simplex space representation, high-order polynomial interpolation and adaptive refinements, permitting to treat mixed aleatory-epistemic uncertainties. This method displays good properties in terms of accuracy and computational cost. Several numerical examples are presented to demonstrate the properties of the proposed method. © 2012 by Pietro Marco Congedo. Published by the American Institute of Aeronautics and Astronautics, Inc.

Morgan B.,Stanford University | Kawai S.,Stanford University | Kawai S.,Center for Turbulence Research | Lele S.K.,Stanford University
40th AIAA Fluid Dynamics Conference | Year: 2010

Large-eddy simulation (LES) of an oblique shock impinging on a supersonic turbulent boundary layer is carried out with a high-order compact differencing scheme using localized artificial diffusivity (LAD) for shock capturing. Flow conditions attempt to match those of the tomographic particle image velocimetry (PIV) experiments conducted at the Delft University of Technology (M ∞ = 2.05 and φ = 8°). However, due to computational cost, the Reynolds number is taken to be Reδ = 20,000 (1/30th of the experimental Reynolds number), and an attempt is made to geometrically match the interaction parameters. Inflow conditions are generated by an improved recycling/rescaling method to eliminate the non-physical "tones" associated with standard recycling/rescaling. The numerical scheme is first validated by simulating a two-dimensional laminar shock wave / boundary layer interaction (SWBLI). Next, a three-dimensional simulation with progressive mesh refinement is conducted to investigate flow physics and establish confidence in the ability of the computational method to accurately and efficiently simulate complex supersonic flow phenomena. Mean and fluctuating profiles of velocity, pressure, and skin friction provide good indication of grid convergence between the two highest levels of refinement. Instantaneous data fields are analyzed, and observations are made regarding "flapping" motion caused by boundary layer turbulence and spanwise variation in shock location. Additionally, the range of spatial and temporal scales captured by the present work is quantified by analyzing spanwise wavenumber and frequency spectra at various locations in the flow. Through analysis of the frequency spectra of the wall pressure signal, low-frequency motion of the separation bubble with a time scale ∼O(100δ/u ∞) is observed and described. Through direct comparison, we additionally observe that standard recycling/rescaling inflow conditions may result in different low-frequency behavior. © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Khalighi Y.,Cascade Technologies, Inc. | Nichols J.W.,Stanford University | Nichols J.W.,Center for Turbulence Research | Lele S.K.,Stanford University | And 2 more authors.
17th AIAA/CEAS Aeroacoustics Conference 2011 (32nd AIAA Aeroacoustics Conference) | Year: 2011

A novel numerical scheme for unstructured compressible large eddy simulation (LES) is developed. This method is low-dissipative and less sensitive to the quality of the computa-tional grid and is targeted for performing large-scale, high-fidelity simulations of turbulent flows in complex configurations. The objective of this work is to introduce this method, present a rigorous validation study, and demonstrate the application to a variety of jet configurations. This technique is validated by predicting the flow and noise emitted from a single-stream pressure-matched hot supersonic jet. Nearfield ow as well as farfield noise computed using an acoustic projection method is studied and compared to experimental measurements obtained by Dr. James Bridges at NASA Glenn. Mesh refinement studies and sensitivity study on selecting the acoustic projection surface are provided. To test the method's performance in a variety of jet noise configurations, it is applied to a high bypass ratio dual-stream jet at sonic conditions, a vertical supersonic jet impinging on the ground, and a horizontal supersonic jet impinging on an angled jet blast deflector. © 2011 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc.

Kawai S.,Stanford University | Kawai S.,Center for Turbulence Research | Lele S.K.,Stanford University
AIAA Journal | Year: 2010

Large-eddy simulation of an underexpanded sonic jet injection into supersonic crossflows is performed to obtain insights into key physics of the jet mixing. A high-order compact differencing scheme with a recently developed localized artificial diffusivity scheme for discontinuity-capturing is used. Progressive mesh refinement study is conducted to quantify the broadband range of scales of turbulence that are resolved in the simulations. The simulations aim to reproduce the flow conditions reported in the experiments of Santiago and Dutton [Santiago, J. G., and Dutton, J. C, "Velocity Measurements of a Jet Injected into a Supersonic Crossflow," Journal of Propulsion and Power, Vol. 132, 1997, pp. 264-273] and elucidate the physics of the jet mixing. A detailed comparison with these data is shown. Statistics obtained by the large-eddy simulation with turbulent crossflow show good agreement with the experiment, and a series of mesh refinement studies shows reasonable grid convergence in the predicted mean and turbulent flow quantities. The present large-eddy simulation reproduces the large-scale dynamics of the flow and jet fluid entrainment into the boundary-layer separation regions upstream and downstream of the jet injection reported in previous experiments, but the richness of data provided by the large-eddy simulation allows a much deeper exploration of the flow physics. Key physics of the jet mixing in supersonic crossflows are highlighted by exploring the underlying unsteady phenomena. The effect of the approaching turbulent boundary layer on the jet mixing is investigated by comparing the results of jet injection into supersonic crossflows with turbulent and laminar crossflows. Copyright © 2010.

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