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NASA NTRS1986

Wall reflection of a viscous vortex ring

The behavior of a viscous axisymmetric vortex ring being reflected from a wall is investigated. The incompressible Navier-Stokes equations formulated in terms of the vorticity function and vector potential are numerically integrated by implicit finite difference methods. To specify the vector potential at a far boundary from the wall, the existing integral method used so far only for an unbounded domain is modified by a kind of image method. The trajectory of the vortex ring calcualted as a result closely resembles that observable from the experiment.

Sa, J. Y.↗

NASA NTRS1989

A multi-domain spectral computation of three-dimensional laminar horseshoe vortex flow using incompressible Navier-Stokes equations

Multidomain spectral methods are presently used to numerically simulate a strut-wall intersection's laminar horseshoe vortex flow through direct solution of the three-dimensional, incompressible, time-dependent Navier-Stokes equations. Direct expansion in Chebyshev polynomials and spectral element method spatial discretization of flow dependence are used to achieve high-order accuracy, and minimal dispersion errors. Low and moderate Reynolds number results are presented to illustrate the method application.

Tan, C. S.↗

NASA NTRS1995

Flow Over Swept Flaps and Flap Tips

Preliminary measurements have been made of the flow over the tip of an unswept wing flap. To achieve an acceptable Reynolds number based on flap chord, the flap chord was chosen equal to the chord of the main airfoil (c = 19 in. approx. 0.48 m). The model was mounted in a 30 in. x 30 in. wind tunnel running at up to 100 ft/sec. (30 m/s): severe wind-tunnel interference was accepted, and any computations would be done using the tunnel walls as the boundaries of the computational domain. Maximum Reynolds number based on flap chord and tunnel speed was about 1.O x lO(exp 6). The grant ended before a full set of measurements could be made, but the work done so far yields a useful picture of the flow. The vortex originates at about mid-chord on the flap and rises rapidly above the chord line. It has a concentrated core, with total pressure lower than the ambient static pressure, and there is no evidence of large-scale wandering. A simple method of model construction, giving light weight and excellent surface finish, was developed.

Bradshaw, Peter↗

NASA NTRS1994

Three Dimensional Compressible Turbulent Flow Computations for a Diffusing S-Duct With/Without Vortex Generators

Numerical investigations on a diffusing S-duct with/without vortex generators and a straight duct with vortex generators are presented. The investigation consists of solving the full three-dimensional unsteady compressible mass averaged Navier-Stokes equations. An implicit finite volume lower-upper time marching code (RPLUS3D) has been employed and modified. A three-dimensional Baldwin-Lomax turbulence model has been modified in conjunction with the flow physics. A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vortical structure for modeling the shed vortex is used as a source term in the computation domain. The injected vortex paths in the straight duct are compared with the analysis by two kinds of prediction models. The flow structure by the vortex generators are investigated along the duct. Computed results of the flow in a circular diffusing S-duct provide an understanding of the flow structure within a typical engine inlet system. These are compared with the experimental wall static-pressure, static- and total-pressure field, and secondary velocity profiles. Additionally, boundary layer thickness, skin friction values, and velocity profiles in wall coordinates are presented. In order to investigate the effect of vortex generators, various vortex strengths are examined in this study. The total-pressure recovery and distortion coefficients are obtained at the exit of the S-duct. The numerical results clearly depict the interaction between the low velocity flow by the flow separation and the injected vortices.

Cho, Soo-Yong↗

NASA NTRS1989

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Yen, Guan-Wei↗

NASA NTRS2003

Mechanisms of Rotating Instability in Axial Compressors Investigated

Rotating instability is a phenomenon that occurs in the tip flow region of axial compressor stages during stable operation. It can be observed in highly staggered rotors with significant tip clearance and is strongest at high-load operating points where the characteristic levels off. In this condition, the single-stage fan under investigation radiates an audible, whistling tone, and wall pressure spectra in the vicinity of the rotor disk exhibit nonrotational components. The graph shows the spectrum of static pressure at a point on the endwall near the leading edge. A hump appears at roughly half of the blade passing frequency (BPF) and is characteristic of rotating instability. A computational model was developed at the NASA Glenn Research Center to investigate the mechanism behind this phenomenon. A three-dimensional steady Navier-Stokes code that has been successfully tested for a wide range of turbomachinery flows was modified to execute a time-accurate simulation of the full annulus of the compressor. At the inlet of the computational domain, the total pressure, total temperature, and two velocity components are specified. Since no unsteady measurements of static pressure or other flow variables were available downstream of the rotor, circumferentially averaged static pressure was specified on the shroud at the outlet of the computational domain. A three-dimensional view of the vortex from the numerical model is shown. Particle traces released near the leading edge tip have rolled up to illustrate the tip clearance vortex. Flow near the trailing edge is pushed forward by the axially reversed flow. It then interacts with the tip clearance flow and the incoming flow and results in the rotating instability vortex, the core of which is illustrated by total pressure shading on planes located successively downstream. The rotating instability vortex is formed periodically midway between the blades and moves toward the pressure side of the passage. The unsteady behavior of this vortex structure is the main mechanism of the rotating instability is shown. The numerical model can be used to detect any possible occurrence of rotating instability when the tip clearance increases during engine service.

Hah, Chunill↗

NASA NTRS2002

Sensitivities of Modeled Tropical Cyclones to Surface Friction and the Coriolis Parameter

In this investigation the sensitivities of a 2-D tropical cyclone (TC) model to surface frictional coefficient and the Coriolis parameter are studied and their implication is discussed. The model used is an axisymmetric version of the latest version of the Goddard cloud ensemble model. The model has stretched vertical grids with 33 levels varying from 30 m near the bottom to 1140 m near the top. The vertical domain is about 21 km. The horizontal domain covers a radius of 962 km (770 grids) with a grid size of 1.25 km. The time step is 10 seconds. An open lateral boundary condition is used. The sea surface temperature is specified at 29C. Unless specified otherwise, the Coriolis parameter is set at its value at 15 deg N. The Newtonian cooling is used with a time scale of 12 hours. The reference vertical temperature profile used in the Newtonian cooling is that of Jordan. The Newtonian cooling models not only the effect of radiative processes but also the effect of processes with scale larger than that of TC. Our experiments showed that if the Newtonian cooling is replaced by a radiation package, the simulated TC is much weaker. The initial condition has a temperature uniform in the radial direction and its vertical profile is that of Jordan. The initial winds are a weak Rankin vortex in the tangential winds superimposed on a resting atmosphere. The initial sea level pressure is set at 1015 hPa everywhere. Since there is no surface pressure perturbation, the initial condition is not in gradient balance. This initial condition is enough to lead to cyclogenesis, but the initial stage (say, the first 24 hrs) is not considered to resemble anything observed. The control experiment reaches quasi-equilibration after about 10 days with an eye wall extending from 15 to 25 km radius, reasonable comparing with the observations. The maximum surface wind of more than 70 m/s is located at about 18 km radius. The minimum sea level pressure on day 10 is about 886 hPa. Thus the overall simulation is considered successful and the model is considered adequate for our investigation.

Chao, Winston C.↗

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↗