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NASA NTRS1982

Shock-fitted Euler solutions to shock vortex interactions

The interaction of a planar shock wave with one or more vortexes is computed using a pseudospectral method and a finite difference method. The development of the spectral method is emphasized. In both methods the shock wave is fitted as a boundary of the computational domain. The results show good agreement between both computational methods. The spectral method is, however, restricted to smaller time steps and requires use of filtering techniques.

Salas, M. D.↗

NASA NTRS1982

Shock-fitted Euler solutions to shock-vortex interactions

Salas, M. D.↗

NASA NTRS1985

Simulation of turbulent mixing layers

A hybrid numerical scheme, combined with a scalar convection scheme, is used to compute turbulent mixing layers. The hybrid scheme is used to solve the vorticity equation by dividing the domain into two regions, applying a Lagrangian method in one region and an Eulerian method in the other. The scalar convection scheme is used to track an interface which separates a dyed fluid from a dye-free fluid, thereby distinguishing the fluid that starts on the high speed side from the fluid that starts on the low speed side. A two-dimensional mixing layer has been simulated using this new method; the roll up of a vortex sheet into structures that interact and pair is observed. The growth of the momentum thickness and the development of the mean turbulence statistics are found to be consistent with experimental observations. Forcing of the layer at moderate and low frequencies shows a dramatic effect on the growth of the momentum thickness and the entrainment ratio. Low frequency forcing enhances the growth of the layer; moderate frequency forcing inhibits the growth.

Mansour, N. N.↗

NASA NTRS1991

A design strategy for the use of vortex generators to manage inlet-engine distortion using computational fluid dynamics

A reduced Navier-Stokes solution technique was successfully used to design vortex generator installations for the purpose of minimizing engine face distortion by restructuring the development of secondary flow that is induced in typical 3-D curved inlet ducts. The results indicate that there exists an optimum axial location for this installation of corotating vortex generators, and within this configuration, there exists a maximum spacing between generator blades above which the engine face distortion increases rapidly. Installed vortex generator performance, as measured by engine face circumferential distortion descriptors, is sensitive to Reynolds number and thereby the generator scale, i.e., the ratio of generator blade height to local boundary layer thickness. Installations of corotating vortex generators work well in terms of minimizing engine face distortion within a limited range of generator scales. Hence, the design of vortex generator installations is a point design, and all other conditions are off design. In general, the loss levels associated with a properly designed vortex generator installation are very small; thus, they represent a very good method to manage engine face distortion. This study also showed that the vortex strength, generator scale, and secondary flow field structure have a complicated and interrelated influence over engine face distortion, over and above the influence of the initial arrangement of generators.

Anderson, Bernhard H.↗

NASA NTRS1991

A design strategy for the use of vortex generators to manage inlet-engine distortion using computational fluid dynamics

Anderson, Bernhard H.↗

NASA NTRS1992

Invariant two-dimensional structures of vorticity field in nonviscous fluid

It is shown that a fluid flow which are invariant under translations along their vorticity field directions can be described in terms of a formally 2D system. Its nonviscous behavior of the scalar vorticity is governed by Hamiltonian dynamics, similar to the 2D line vortex case. Applying a statistical mechanical method, the equilibrium distribution of the vorticity field for such a general 2D system is shown to obey a nonlinear partial differential equation that is a generalization of the sinh-Poisson equation derived by Montgomery and Joyce (1973, 1974). Thus, if the domain containing the fluid is finite, similar negative temperature states may occur and the distribution of the vorticity intensity may become localized in space. The results are believed to have applications in studying large-scale partial and temporal properties of flows having small but nonzero viscosity. The analysis can probably be extended to other fluid systems with curved magnetic field lines.

Chen, Hudong↗

NASA NTRS2001

High Order Difference Method for Low Mach Number Aeroacoustics

A high order finite difference method with improved accuracy and stability properties for computational aeroacoustics (CAA) at low Mach numbers is proposed. The Euler equations are split into a conservative and a symmetric non- conservative portion to allow the derivation of a generalized energy estimate. Since the symmetrization is based on entropy variables, that splitting of the flux derivatives is referred to as entropy splitting. Its discretization by high order central differences was found to need less numerical dissipation than conventional conservative schemes. Owing to the large disparity of acoustic and stagnation quantities in low Mach number aeroacoustics, the split Euler equations are formulated in perturbation form. The unknowns are the small changes of the conservative variables with respect to their large stagnation values. All nonlinearities and the conservation form of the conservative portion of the split flux derivatives can be retained, while cancellation errors are avoided with its discretization opposed to the conventional conservative form. The finite difference method is third-order accurate at the boundary and the conventional central sixth-order accurate stencil in the interior. The difference operator satisfies the summation by parts property analogous to the integration by parts in the continuous energy estimate. Thus, strict stability of the difference method follows automatically. Spurious high frequency oscillations are suppressed by a characteristic-based filter similar to but without limiter. The time derivative is approximated by a 4-stage low-storage second-order explicit Runge-Kutta method. The method has been applied to simulate vortex sound at low Mach numbers. We consider the Kirchhoff vortex, which is an elliptical patch of constant vorticity rotating with constant angular frequency in irrotational flow. The acoustic pressure generated by the Kirchhoff vortex is governed by the 2D Helmholtz equation, which can be solved analytically using separation of variables.

Mueller, B.↗

NASA NTRS1993

An adaptive multigrid model for hurricane track prediction

This paper describes a simple numerical model for hurricane track prediction which uses a multigrid method to adapt the model resolution as the vortex moves. The model is based on the modified barotropic vorticity equation, discretized in space by conservative finite differences and in time by a Runge-Kutta scheme. A multigrid method is used to solve an elliptic problem for the streamfunction at each time step. Nonuniform resolution is obtained by superimposing uniform grids of different spatial extent; these grids move with the vortex as it moves. Preliminary numerical results indicate that the local mesh refinement allows accurate prediction of the hurricane track with substantially less computer time than required on a single uniform grid.

Fulton, Scott R.↗

NASA NTRS1987

Motion and decay of vortex rings submerged in a rotational flow

The interaction between vortex rings of finite strength and an axisymmetric rotational background flow is studied by a singular perturbation method, because it is difficult to use a finite-difference method to analyze the viscous decay in the small core of a vortex ring. The analysis is carried out by combining a composite solution of a vortex ring and an unsteady Euler solution for the background rotational flow. Using the method of averaging, a numerical scheme is developed to obtain an Euler solution in which the grid and time-step sizes depend solely on the length and velocity scales of the background flow. Numerical results are presented to illustrate the interaction between the trajectories and decay rates of the vortex rings and the background rotational flow.

Ishii, K.↗

NASA NTRS1987

A full potential flow analysis with realistic wake influence for helicopter rotor airload prediction

A 3-D, quasi-steady, full potential flow solver was adapted to include realistic wake influence for the aerodynamic analysis of helicopter rotors. The method is based on a finite difference solution of the full potential equation, using an inner and outer domain procedure for the blade flowfield to accommodate wake effects. The nonlinear flow is computed in the inner domain region using a finite difference solution method. The wake is modeled by a vortex lattice using prescribed geometry techniques to allow for the inclusion of realistic rotor wakes. The key feature of the analysis is that vortices contained within the finite difference mesh (inner domain) were treated with a vortex embedding technique while the influence of the remaining portion of the wake (in the outer domain) is impressed as a boundary condition on the outer surface of the finite difference mesh. The solution procedure couples the wake influence with the inner domain solution in a consistent and efficient solution process. The method has been applied to both hover and forward flight conditions. Correlation with subsonic and transonic hover airload data is shown which demonstrates the merits of the approach.

Egolf, T. Alan↗

NASA NTRS1981

An empirical method for computing leeside centerline heating on the Space Shuttle Orbiter

An empirical method is presented for computing top centerline heating on the Space Shuttle Orbiter at simulated reentry conditions. It is shown that the Shuttle's top centerline can be thought of as being under the influence of a swept cylinder flow field. The effective geometry of the flow field, as well as top centerline heating, are directly related to oil-flow patterns on the upper surface of the fuselage. An empirical turbulent swept cylinder heating method was developed based on these considerations. The method takes into account the effects of the vortex-dominated leeside flow field without actually having to compute the detailed properties of such a complex flow. The heating method closely predicts experimental heat-transfer values on the top centerline of a Shuttle model at Mach numbers of 6 and 10 over a wide range in Reynolds number and angle of attack.

Helms, V. T., III↗

NASA NTRS1981

Computer program documentation for a subcritical wing design code using higher order far-field drag minimization

A subsonic, linearized aerodynamic theory, wing design program for one or two planforms was developed which uses a vortex lattice near field model and a higher order panel method in the far field. The theoretical development of the wake model and its implementation in the vortex lattice design code are summarized and sample results are given. Detailed program usage instructions, sample input and output data, and a program listing are presented in the Appendixes. The far field wake model assumes a wake vortex sheet whose strength varies piecewise linearly in the spanwise direction. From this model analytical expressions for lift coefficient, induced drag coefficient, pitching moment coefficient, and bending moment coefficient were developed. From these relationships a direct optimization scheme is used to determine the optimum wake vorticity distribution for minimum induced drag, subject to constraints on lift, and pitching or bending moment. Integration spanwise yields the bound circulation, which is interpolated in the near field vortex lattice to obtain the design camber surface(s).

Kuhlman, J. M.↗

NASA NTRS1987

Distortion of the vortex core during blade-vortex interaction

The effect of vortex distortion on the flow arising from the interaction of a convecting vortex and an airfoil is analyzed for two-dimensional, incompressible, inviscid flow. Significant distortion of the vortex structure, owing to interaction with the airfoil, can occur, especially during close interactions. The vorticity field is represented by multiple vortices. Vortex instability and diffusion, resulting from discretization in space and time, are discussed. An integral boundary element method is used to represent the airfoil surface. The body panels are re-distributed on the surface as the vortices are convected past to calculate the effect of the vorticity field more accurately. The method is applied to several cases to examine effects of vortex strength, distribution, initial separation position, and airfoil angle of attack. Calculations of vortex trajectory and distortion, and airfoil surface-pressure distribution, lift, drag, and circulation as functions of time are presented.

Lee, G. J.↗

NASA NTRS1987

Aerodynamic interaction between vortical wakes and lifting two-dimensional bodies

Unsteady rotor wake interactions with the empenage, tail boom, and other aerodynamic surfaces of a helicopter have a significant influence on its aerodynamic performance, the ride quality, and amount of vibration. A numerical method for computing the aerodynamic interaction between an interacting vortex wake and the viscous flow about arbitrary two-dimensional bodies has been developed to address this helicopter problem. The method solves for the flow field velocities on a body-fitted computational mesh using finite-difference techniques. The interaction of a rotor wake with the flow about a 4:1 elliptic cylinder at 45-deg incidence was calculated for a Reynolds number of 3000.

Stremel, Paul M.↗

NASA NTRS1997

Toward Understanding Wake Vortices and Atmospheric Turbulence Interactions Using Large-Eddy Simulation

The vortices produced by an aircraft in flight are a complex phenomena created from a 'sheet of vorticity' leaving the trailing edge of the aircraft surfaces. This sheet tends to roll-up into two counter-rotating vortices. After a few spans downstream of the aircraft, the roll-up process is complete and the vortex pair may be characterized in a simple manner for modeling purposes. Our research will focus on what happens to these post roll-up vortices in the vicinity of an airport terminal. As the aircraft wake vortices descend, they are transported by the air mass which they are embedded and are decayed by both internal and external processes. In the vicinity of the airport, these external influences are usually due to planetary boundary layer (PBL) turbulence. Using large-eddy simulation (LES), one may simulate a variety of PBL conditions. In the LES method, turbulence is generated in the PBL as a response to surface heat flux, horizontal pressure gradient, wind shear, and/or stratification, and may produce convective or unstably stratified, neutral, or stably stratified PBL's. Each of these PBL types can occur during a typical diurnal cycle of the PBL. Thus it is important to be able to characterize these conditions with the LES method. Once this turbulent environment has been generated, a vortex pair will be introduced and the interactions are observed. The objective is to be able to quantify the PBL turbulence vortex interaction and be able to draw some conclusions of vortex behavior from the various scale interactions. This research is ongoing, and we will focus on what has been accomplished to date and the future direction of this research. We will discuss the model being used, show results that validate its use in the PBL, and present a nested-grid method proposed to analyze the entire PBL and vortex pair simultaneously.

DeCroix, David↗

NASA NTRS1993

A time-accurate finite volume method valid at all flow velocities

A finite volume method to solve the Navier-Stokes equations at all flow velocities (e.g., incompressible, subsonic, transonic, supersonic and hypersonic flows) is presented. The numerical method is based on a finite volume method that incorporates a pressure-staggered mesh and an incremental pressure equation for the conservation of mass. Comparison of three generally accepted time-advancing schemes, i.e., Simplified Marker-and-Cell (SMAC), Pressure-Implicit-Splitting of Operators (PISO), and Iterative-Time-Advancing (ITA) scheme, are made by solving a lid-driven polar cavity flow and self-sustained oscillatory flows over circular and square cylinders. Calculated results show that the ITA is the most stable numerically and yields the most accurate results. The SMAC is the most efficient computationally and is as stable as the ITA. It is shown that the PISO is the most weakly convergent and it exhibits an undesirable strong dependence on the time-step size. The degenerated numerical results obtained using the PISO are attributed to its second corrector step that cause the numerical results to deviate further from a divergence free velocity field. The accurate numerical results obtained using the ITA is attributed to its capability to resolve the nonlinearity of the Navier-Stokes equations. The present numerical method that incorporates the ITA is used to solve an unsteady transitional flow over an oscillating airfoil and a chemically reacting flow of hydrogen in a vitiated supersonic airstream. The turbulence fields in these flow cases are described using multiple-time-scale turbulence equations. For the unsteady transitional over an oscillating airfoil, the fluid flow is described using ensemble-averaged Navier-Stokes equations defined on the Lagrangian-Eulerian coordinates. It is shown that the numerical method successfully predicts the large dynamic stall vortex (DSV) and the trailing edge vortex (TEV) that are periodically generated by the oscillating airfoil. The calculated streaklines are in very good comparison with the experimentally obtained smoke picture. The calculated turbulent viscosity contours show that the transition from laminar to turbulent state and the relaminarization occur widely in space as well as in time. The ensemble-averaged velocity profiles are also in good agreement with the measured data and the good comparison indicates that the numerical method as well as the multipletime-scale turbulence equations successfully predict the unsteady transitional turbulence field. The chemical reactions for the hydrogen in the vitiated supersonic airstream are described using 9 chemical species and 48 reaction-steps. Consider that a fast chemistry can not be used to describe the fine details (such as the instability) of chemically reacting flows while a reduced chemical kinetics can not be used confidently due to the uncertainty contained in the reaction mechanisms. However, the use of a detailed finite rate chemistry may make it difficult to obtain a fully converged solution due to the coupling between the large number of flow, turbulence, and chemical equations. The numerical results obtained in the present study are in good agreement with the measured data. The good comparison is attributed to the numerical method that can yield strongly converged results for the reacting flow and to the use of the multiple-time-scale turbulence equations that can accurately describe the mixing of the fuel and the oxidant.

Kim, S.-W.↗

NASA NTRS1987

Measurement of velocity and vorticity fields in the wake of an airfoil in periodic pitching motion

The velocity field created by the wake of an airfoil undergoing a prescribed pitching motion was sampled using hot wire anemometry. Data analysis methods concerning resolution of velocity components from cross wire data, computation of vorticity from velocity time history data, and calculation of vortex circulation from vorticity field data are discussed. These data analysis methods are applied to a flow field relevant to a two dimensional blade-vortex interaction study. Velocity time history data were differentiated to yield vorticity field data which are used to characterize the wake of the pitching airfoil. Measurement of vortex strength in sinusoidal and nonsinusoidal wakes show vortices in the sinusoidal wake have stronger circulation and more concentrated vorticity distributions than the tailored nonsinusoidal wake.

Booth, Earl R., Jr.↗

NASA NTRS1993

Reduction in size and unsteadiness of a VTOL ground vortex by ground fences

A ground vortex, produced when a jet impinges on the ground in the presence of cross flow, is encountered by V/STOL aircraft hovering near the ground and is known to be hazardous to the aircraft. The objective of this research was to identify a ground-based technique by which both the mean size and fluctuation in size of the ground vortex could be reduced. A simple passive method was identified and examined in the laboratory. Specifically, one or two fine wire mesh screens (ground fences) bent in a horseshoe shape and located on the ground in front of the jet impingement point proved to be very effective. The ground fences work by decreasing the momentum of the upstream-traveling wall jet, effectively causing a higher freestream-to-jet velocity ratio (V(sub infinity)/V(sub j)) and thus, a ground vortex smaller in size and unsteadiness. At(V(sub infinity)/V(sub j)) = 0.15, the addition of a single ground fence resulted in a 70 percent reduction in mean size of the ground vortex. With two ground fences, the mean size decreased by about 85 percent. Fluctuations in size decreased nearly in proportion to the mean size, for both the single and double fence configurations. These results were consistent over a wide range of jet Reynolds number (10(exp 4) less than Re(sub jet) less than 10(exp 5)); further development and full-scale Reynolds number testing are required, however, to determine if this technique can be made practical for the case of actual VTOL aircraft.

Cimbala, John M.↗