Engineering topics

Pruett, C. David

Publications and source records attributed to Pruett, C. David.

11 records

NASA NTRS1999

On Taylor-Series Approximations of Residual Stress

Although subgrid-scale models of similarity type are insufficiently dissipative for practical applications to large-eddy simulation, in recently published a priori analyses, they perform remarkably well in the sense of correlating highly against exact residual stresses. Here, Taylor-series expansions of residual stress are exploited to explain the observed behavior and "success" of similarity models. Until very recently, little attention has been given to issues related to the convergence of such expansions. Here, we re-express the convergence criterion of Vasilyev [J. Comput. Phys., 146 (1998)] in terms of the transfer function and the wavenumber cutoff of the grid filter.

Pruett, C. David↗

NASA NTRS1999

Large-Eddy Simulation of Aeroacoustic Applications

This report summarizes work accomplished under a one-year NASA grant from NASA Langley Research Center (LaRC). The effort culminates three years of NASA-supported research under three consecutive one-year grants. The period of support was April 6, 1998, through April 5, 1999. By request, the grant period was extended at no-cost until October 6, 1999. Its predecessors have been directed toward adapting the numerical tool of large-eddy simulation (LES) to aeroacoustic applications, with particular focus on noise suppression in subsonic round jets. In LES, the filtered Navier-Stokes equations are solved numerically on a relatively coarse computational grid. Residual stresses, generated by scales of motion too small to be resolved on the coarse grid, are modeled. Although most LES incorporate spatial filtering, time-domain filtering affords certain conceptual and computational advantages, particularly for aeroacoustic applications. Consequently, this work has focused on the development of subgrid-scale (SGS) models that incorporate time-domain filters.

Pruett, C. David↗

NASA NTRS1998

A Priori Analyses of Three Subgrid-Scale Models for One-Parameter Families of Filters

The decay of isotropic turbulence a compressible flow is examined by direct numerical simulation (DNS). A priori analyses of the DNS data are then performed to evaluate three subgrid-scale (SGS) models for large-eddy simulation (LES): a generalized Smagorinsky model (M1), a stress-similarity model (M2), and a gradient model (M3). The models exploit one-parameter second- or fourth-order filters of Pade type, which permit the cutoff wavenumber k(sub c) to be tuned independently of the grid increment (delta)x. The modeled (M) and exact (E) SGS-stresses are compared component-wise by correlation coefficients of the form C(E,M) computed over the entire three-dimensional fields. In general, M1 correlates poorly against exact stresses (C < 0.2), M3 correlates moderately well (C approx. 0.6), and M2 correlates remarkably well (0.8 < C < 1.0). Specifically, correlations C(E, M2) are high provided the grid and test filters are of the same order. Moreover, the highest correlations (C approx.= 1.0) result whenever the grid and test filters are identical (in both order and cutoff). Finally, present results reveal the exact SGS stresses obtained by grid filters of differing orders to be only moderately well correlated. Thus, in LES the model should not be specified independently of the filter.

Pruett, C. David↗

NASA NTRS1997

Computational Investigations of Noise Suppression in Subsonic Round Jets

NASA Grant NAG1-1802, originally submitted in June 1996 as a two-year proposal, was awarded one-year's funding by NASA LaRC for the period 5 Oct., 1996, through 4 Oct., 1997. Because of the inavailability (from IT at NASA ARC) of sufficient supercomputer time in fiscal 1998 to complete the computational goals of the second year of the original proposal (estimated to be at least 400 Cray C-90 CPU hours), those goals have been appropriately amended, and a new proposal has been submitted to LaRC as a follow-on to NAG1-1802. The current report documents the activities and accomplishments on NAG1-1802 during the one-year period from 5 Oct., 1996, through 4 Oct., 1997. NASA Grant NAG1-1802, and its predecessor, NAG1-1772, have been directed toward adapting the numerical tool of Large-Eddy Simulation (LES) to aeroacoustic applications, with particular focus on noise suppression in subsonic round jets. In LES, the filtered Navier-Stokes equations are solved numerically on a relatively coarse computational grid. Residual stresses, generated by scales of motion too small to be resolved on the coarse grid, are modeled. Although most LES incorporate spatial filtering, time-domain filtering affords certain conceptual and computational advantages, particularly for aeroacoustic applications. Consequently, this work has focused on the development of SubGrid-Scale (SGS) models that incorporate time- domain filters. The author is unaware of any previous attempt at purely time-filtered LES; however, Aldama and Dakhoul and Bedford have considered approaches that combine both spatial and temporal filtering. In our view, filtering in both space and time is redundant, because removal of high frequencies effects the removal of small spatial scales and vice versa.

Pruett, C. David↗

NASA NTRS1997

Toward Simplification of Dynamic Subgrid-Scale Models

We examine the relationship between the filter and the subgrid-scale (SGS) model for large-eddy simulations, in general, and for those with dynamic SGS models, in particular. From a review of the literature, it would appear that many practitioners of LES consider the link between the filter and the model more or less as a formality of little practical effect. In contrast, we will show that the filter and the model are intimately linked, that the Smagorinsky SGS model is appropriate only for filters of first- or second-order, and that the Smagorinsky model is inconsistent with spectral filters. Moreover, the Germano identity is shown to be both problematic and unnecessary for the development of dynamic SGS models. Its use obscures the following fundamental realization: For a suitably chosen filter, the computible resolved turbulent stresses, property scaled, closely approximate the SGS stresses.

Pruett, C. David↗

NASA NTRS1997

Eulerian Time-Domain Filtering for Spatial LES

Eulerian time-domain filtering seems to be appropriate for LES (large eddy simulation) of flows whose large coherent structures convect approximately at a common characteristic velocity; e.g., mixing layers, jets, and wakes. For these flows, we develop an approach to LES based on an explicit second-order digital Butterworth filter, which is applied in,the time domain in an Eulerian context. The approach is validated through a priori and a posteriori analyses of the simulated flow of a heated, subsonic, axisymmetric jet.

Pruett, C. David↗

NASA NTRS1997

Time-Domain Filtering for Spatial Large-Eddy Simulation

An approach to large-eddy simulation (LES) is developed whose subgrid-scale model incorporates filtering in the time domain, in contrast to conventional approaches, which exploit spatial filtering. The method is demonstrated in the simulation of a heated, compressible, axisymmetric jet, and results are compared with those obtained from fully resolved direct numerical simulation. The present approach was, in fact, motivated by the jet-flow problem and the desire to manipulate the flow by localized (point) sources for the purposes of noise suppression. Time-domain filtering appears to be more consistent with the modeling of point sources; moreover, time-domain filtering may resolve some fundamental inconsistencies associated with conventional space-filtered LES approaches.

Pruett, C. David↗

NASA NTRS1995

Simulation of crossflow instability on a supersonic highly swept wing

A direct numerical simulation (DNS) algorithm has been developed and validated for use in the investigation of crossflow instability on supersonic swept wings, an application of potential relevance to the design of the High-Speed Civil Transport (HSCT). The algorithm is applied to the investigation of stationary crossflow instability on an infinitely long 77-degree swept wing in Mach 3.5 flow. The results of the DNS are compared with the predictions of linear parabolized stability equation (PSE) methodology. In-general, the DNS and PSE results agree closely in terms of modal growth rate, structure, and orientation angle. Although further validation is needed for large-amplitude (nonlinear) disturbances, the close agreement between independently derived methods offers preliminary validation of both DNS and PSE approaches.

Pruett, C. David↗

NASA NTRS1994

A spectrally accurate boundary-layer code for infinite swept wings

This report documents the development, validation, and application of a spectrally accurate boundary-layer code, WINGBL2, which has been designed specifically for use in stability analyses of swept-wing configurations. Currently, we consider only the quasi-three-dimensional case of an infinitely long wing of constant cross section. The effects of streamwise curvature, streamwise pressure gradient, and wall suction and/or blowing are taken into account in the governing equations and boundary conditions. The boundary-layer equations are formulated both for the attachment-line flow and for the evolving boundary layer. The boundary-layer equations are solved by marching in the direction perpendicular to the leading edge, for which high-order (up to fifth) backward differencing techniques are used. In the wall-normal direction, a spectral collocation method, based upon Chebyshev polynomial approximations, is exploited. The accuracy, efficiency, and user-friendliness of WINGBL2 make it well suited for applications to linear stability theory, parabolized stability equation methodology, direct numerical simulation, and large-eddy simulation. The method is validated against existing schemes for three test cases, including incompressible swept Hiemenz flow and Mach 2.4 flow over an airfoil swept at 70 deg to the free stream.

Pruett, C. David↗

NASA NTRS1991

On the wall-normal velocity of the compressible boundary-layer equations

Numerical methods for the compressible boundary-layer equations are facilitated by transformation from the physical (x,y) plane to a computational (xi,eta) plane in which the evolution of the flow is 'slow' in the time-like xi direction. The commonly used Levy-Lees transformation results in a computationally well-behaved problem for a wide class of non-similar boundary-layer flows, but it complicates interpretation of the solution in physical space. Specifically, the transformation is inherently nonlinear, and the physical wall-normal velocity is transformed out of the problem and is not readily recovered. In light of recent research which shows mean-flow non-parallelism to significantly influence the stability of high-speed compressible flows, the contribution of the wall-normal velocity in the analysis of stability should not be routinely neglected. Conventional methods extract the wall-normal velocity in physical space from the continuity equation, using finite-difference techniques and interpolation procedures. The present spectrally-accurate method extracts the wall-normal velocity directly from the transformation itself, without interpolation, leaving the continuity equation free as a check on the quality of the solution. The present method for recovering wall-normal velocity, when used in conjunction with a highly-accurate spectral collocation method for solving the compressible boundary-layer equations, results in a discrete solution which is extraordinarily smooth and accurate, and which satisfies the continuity equation nearly to machine precision. These qualities make the method well suited to the computation of the non-parallel mean flows needed by spatial direct numerical simulations (DNS) and parabolized stability equation (PSE) approaches to the analysis of stability.

Pruett, C. David↗

NASA NTRS1991

On the nonlinear stability of a high-speed, axisymmetric boundary layer

The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer.

Pruett, C. David↗