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NASA NTRS1990

Incompressible spatially-developing free-shear flows

The first goal of this research is to understand the dynamics of three dimensional vortical structures, especially the interaction of the ribs and two dimensional rollers. Because of vortex stretching effects, this requires accurate and well resolved simulations. Another goal is to distinguish temporally- and spatially-growing shear layers in terms of the dynamics and observed vortical structures. This is important since the former is much easier to compute, but the error incurred in using temporal results for certain applications is unknown. The third goal is to investigate the effects of asymmetry on passive scalar mixing and fast-chemistry product formation. In this report a brief summary of a new numerical method is presented, followed by results for mixing layers and wake flows.

Buell, J. C.↗

NASA NTRS1992

Computation of high resolution unsteady airloads using a constant vorticity contour free wake model

Recent work in the study of helicopter aerodynamic loading for acoustics applications has involved research on the development of an exceptionally efficient simulation of the velocity field induced by the rotor's vortex wake. This paper summarizes the work to date on the development of this analysis, which builds on the refined constant vorticity contour (CVC) free wake model recently developed for application to the study of vibratory loading. The particular focus of this paper is on demonstrations of a reconstruction approach that efficiently computes both the flow fields and airloads induced by CVC wakes on lifting rotor blades. Results of recent calculations on both main rotor and tail rotors are presented. These calculations show that by employing flow field reconstruction it is possible to apply the CVC wake analysis with temporal and spatial resolution suitable for acoustics applications while reducing the computation time required by one to two orders of magnitude relative to the direct calculations used in traditional methods.

Quackenbush, T. R.↗

NASA NTRS1998

Numerical Experiment with Time and Spatial Accuracy of Navier-Stokes Computation For Helicopter Problems

Helicopter flowfields are highly unsteady, nonlinear and three-dimensional. In forward flight and in hover, the rotor blades interact with the tip vortex and wake sheet developed by either itself or the other blades. This interaction, known as blade-vortex interactions (BVI), results in unsteady loading of the blades and can cause a distinctive acoustic signature. Accurate and cost-effective computational fluid dynamic solutions that capture blade-vortex interactions can help rotor designers and engineers to predict rotor performance and to develop designs for low acoustic signature. Such a predictive method must preserve a blade's shed vortex for several blade revolutions before being dissipated. A number of researchers have explored the requirements for this task. This paper will outline some new capabilities that have been added to the NASA Ames' OVERFLOW code to improve its overall accuracy for both vortex capturing and unsteady flows. To highlight these improvements, a number of case studies will be presented. These case studies consist of free convection of a 2-dimensional vortex, dynamically pitching 2-D airfoil including light-stall, and a full 3-D unsteady viscous solution of a helicopter rotor in forward flight In this study both central and upwind difference schemes are modified to be more accurate. Central difference scheme is chosen for this simulation because the flowfield is not dominated by strong shocks. The feature of shock-vortex interaction in such a flow is less important than the dominant blade-vortex interaction. The scheme is second-order accurate in time and solves the thin-layer Navier-Stokes equations in fully-implicit manner at each time-step. The spatial accuracy is either second and fourth-order central difference or third-order upwind difference using Roe-flux and MUSCLE scheme. This paper will highlight and demonstrate the methods for several sample cases and for a helicopter rotor. Preliminary computations on a rotor were performed by using this method and are in the process of documentation.

Ahmad, Jasim↗

NASA NTRS1992

Direct numerical simulations of a spatially developing plane wake

In the present paper, direct numerical methods by which to simulate the spatially developing free shear flows in the transitional region are described and the numerical results of a spatially developing plane wake are presented. The incompressible time-dependent Navier-Stokes equations were solved using Pade finite difference approximations in the streamwise direction, a mapped pseudospectral Fourier method in the cross-stream direction, and a third-order compact Runge-Kutta scheme for time advancement. The unstable modes of the Orr-Sommerfeld equations were used to perturb the inlet of the wake. Statistical analyses were performed and some numerical results were compared with experimental measurements. When only the fundamental mode is forced, the energy spectra show amplification of the fundamental and its higher harmonics. In this case, unperturbed alternate vortices develop in the saturation region of the wake. The phase jitter around the fundamental frequency plays a critical role in generating vortices of random shape and spacing. Large- and small-scale distortions of the fundamental structure are observed. Pairing of vortices of the same sign is observed, as well as vortex coupling of vortices of the opposite sign.

Maekawa, Hiroshi↗

NASA NTRS1988

A numerical study of viscous vortex rings using a spectral method

Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass.

Stanaway, S. K.↗

NASA NTRS2004

Interaction of a Boundary Layer with a Turbulent Wake

The objective of this grant was to study the transition mechanisms on a flat-plate boundary layer interacting with the wake of a bluff body. This is a simplified configuration presented and designed to exemplify the phenomena that occur in multi-element airfoils, in which the wake of an upstream element impinges on a downstream one. Some experimental data is available for this configuration at various Reynolds numbers. The first task carried out was the implementation and validation of the immersed-boundary method. This was achieved by performing calculations of the flow over a cylinder at low and moderate Reynolds numbers. The low-Reynolds number results are discussed, which is enclosed as Appendix A. The high-Reynolds number results are presented in a paper in preparation for the Journal of Fluid Mechanics. We performed calculations of the wake-boundary-layer interaction at two Reynolds numbers, Re approximately equal to 385 and 1155. The first case is discussed and a comparison of the two calculations is reported. The simulations indicate that at the lower Reynolds number the boundary layer is buffeted by the unsteady Karman vortex street shed by the cylinder. This is shown: long streaky structures appear in the boundary layer in correspondence of the three-dimensionalities in the rollers. The fluctuations, however, cannot be self-sustained due to the low Reynolds-number, and the flow does not reach a turbulent state within the computational domain. In contrast, in the higher Reynolds-number case, boundary-layer fluctuations persist after the wake has decayed (due, in part, to the higher values of the local Reynolds number Re achieved in this case); some evidence could be observed that a self-sustaining turbulence generation cycle was beginning to be established. A third simulation was subsequently carried out at a higher Reynolds number, Re=3900. This calculation gave results similar to those of the Re=l155 case. Turbulence was established at fairly low Reynolds number, as a consequence of the high level of the free-stream perturbation. An instantaneous flow visualization for that case is shown. A detailed examination of flow statistics in the transitional and turbulent regions, including the evolution of the turbulent kinetic energy (TKE) budget and frequency spectra showed the formation and evolution of turbulent spots characteristic of the bypass transition mechanism. It was also observed that the turbulent eddies achieved an equilibrium, fully developed turbulent states first, as evidenced by the early agreement achieved by the terms in the TKE budget with those observed in turbulent flows. Once a turbulent Reynolds stress profile had been established, the velocity profile began to resemble a turbulent one, first in the inner region and later in the outer region of the wall layer. An extensive comparison of the three cases, including budgets, mean velocity and Reynolds stress profiles and flow visualization, is included. The results obtained are also presented.

Piomelli, Ugo↗

NASA NTRS2015

Unsteady Loss in the Stator Due to the Incoming Rotor Wake in a Highly-Loaded Transonic Compressor

The present paper reports an investigation of unsteady loss generation in the stator due to the incoming rotor wake in an advanced GE transonic compressor design with a high-fidelity numerical method. This advanced compressor with high reaction and high stage loading has been investigated both experimentally and analytically in the past. The measured efficiency in this advanced compressor is significantly lower than the design intention/goal. The general understanding is that the current generation of compressor design/analysis tools miss some important flow physics in this modern compressor design. To pinpoint the source of the efficiency miss, an advanced test with a detailed flow traverse was performed for the front one and a half stage at the NASA Glenn Research Center. Detailed data-match analysis by GE identified an unexpected high loss generation in the pressure side of the stator passage. Higher total temperature and lower total pressure are measured near the pressure side of the stator. Various analyses based on the RANS and URANS of the compressor stage do not calculate the measured higher total temperature and lower total pressure on the pressure side of the stator. In the present paper, a Large Eddy Simulation (LES) is applied to find the fundamental mechanism of this unsteady loss generation in the stator due to the incoming rotor wake. The results from the LES were first compared with the NASA test results and the GE interpretation of the test data. LES calculates lower total pressure and higher total temperature on the pressure side of the stator, as the measured data showed, resulting in large loss generation on the pressure side of the stator. Detailed examination of the unsteady flow field from LES shows that the rotor wake, which has higher total temperature and higher total pressure relative to the free stream, interacts quite differently with the pressure side of the blade compared to the suction side of the blade. The higher temperature in the wake remains high as the wake passes through the pressure side of the blade. On the other hand, the total temperature diffuses as it passes through near the suction surface. For the presently investigated compressor, the classical intra-stator wake transport to the pressure side of the blade by the slip velocity in the wake seems to be minor. The main causes of this phenomenon are three-dimensional unsteady vortex interactions near the blade surface. The stabilizing effect of the concave curvature on the suction side keeps the rotor wake thin. On the other hand, the destabilizing effect of the convex curvature of the pressure side makes the rotor wake thicker, which results in a higher total temperature measurement at the stator exit. Additionally, wake stretching through the stator seems to contribute to the redistribution of the total temperature and the loss generation.

Efficiency↗