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Integral Velocity Sampling for Unsteady Rotor Models on Cartesian Meshes

An unsteady body-force rotor model utilizing integral velocity sampling is developed for Cartesian meshes with a focus on accurate performance predictions. In this approach, the rotors are modeled as body-force source terms, and integral sampling is used to define the local freestream velocity vector. The method is verified in two dimensions for airfoils, providing accurate angle of attack and freestream Mach number estimates even on relatively coarse meshes, and demonstrating excellent mesh convergence across a variety of source region thicknesses. Extensions of the model to three dimensions for both fixed and rotating wings are considered, with numerical experiments demonstrating the need for a spanwise-continuous representation of the induced velocity or angle of attack. The model provides reasonable spanwise lift distributions without any explicit tip-loss model. Comparisons to high-fidelity simulations and experimental data show excellent agreement for predictions of an isolated DJI Phantom 3 propeller in hover. Finally, simulations of the full aircraft in edgewise forward flight also compare well with wind tunnel data across a variety of pitch angles and propeller speeds.

ARMD↗

NASA NTRS1995

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

Krishnamoorthy, S.↗

NASA NTRS1989

Time-dependent viscous incompressible Navier-Stokes equations - The finite difference Galerkin formulation and streamfunction algorithms

Numerical techniques are developed to solve the Navier-Stokes equations for unsteady incompressible flow. The extension of the finite-difference Galerkin (FDG) method of Stephens et al. (1984) to the continuous-time case in two or three space dimensions is explained, and the numerical implementation of the method is discussed with particular attention to the staggered-MAC-grid primitive-variable discretization, the application of discrete mass balance to avoid problems inherent in FDG schemes, the direct interpretation of the FDG expansion variables as a discrete streamfunction, and a mass-balance approach to two-dimensional problems with throughflow or obstacles. Numerical results are presented graphically for the evolution of asymptotic steady flow in a driven cavity at Reynolds number 400, 1000, or 3200; good agreement with published experimental data is demonstrated, with accurate predictions of secondary-vortex formation from wall bubble recirculations at Reynolds number 1000.

Goodrich, John W.↗

NASA NTRS1983

Numerical investigation of unsteady flow development in a nozzle-duct configuration

A computational approach has been used to resolve the transient phenomena caused by a rocket engine starting up and exhausting into a short duct. The results are obtained from the finite-difference Navier-Stokes, continuity, and energy equations for a single component gas. Using a recently developed numerical technique to account for the time-varying boundary conditions at the nozzle throat and the duct openings, the numerical simulation of the idealized ignition flow model has yielded some insight into the complex interactions between the wave patterns and the vortical flow. The present findings verify the hypothesis that a lateral expansion of the jetstream outside the nozzle will generate an over-pressure pulse on the duct wall if the jetstream is restricted within the nozzle by flow separation. The numerical simulations of this complex flow problem should be useful for improving simple correlation techniques used for engineering purposes.

Li, C. P.↗

NASA NTRS1993

Structure of confined laminar spray diffusion flames: Numerical investigation

The structure of confined laminar spray diffusion flames is investigated numerically by solving the gas-phase conservation equations for mass species, continuity, momentum, and energy and the liquid-phase equations for droplet position, velocity, size, and temperature. A one-step global reaction scheme along with six equilibrium reactions are employed to model the flame chemistry. Monodisperse as well as polydisperse sprays are considered. The numerical results demonstrate that liquid spray flames substantially differ from gaseous flames in their structure, i.e., temperature, concentration, and velocity fields, shape, and dimensions under the same conditions. Spray flames are predicted to be taller and narrower than their counterpart gaseous ones and their shapes are almost cylindrical. This is in agreement with experimental observations. The numerical computations also show that the use of the equilibrium reactions with the one-step reaction scheme decreases the flame temperature compared to the one-step reaction scheme without the equilibrium reactions and more importantly increases the surface area of the flame zone due to a phenomenon termed 'equilibrium broadening.' The spray flames also possess a finite thickness with minimal overlap of the fuel and oxygen species. A case for which a fuel-mixture consisting of 20 to 80 percent gas-liquid by mass is introduced into the combustor is also investigated and compared with predictions using only gaseous or liquid fuel.

Mawid, M. A.↗

NASA NTRS2016

Voyager Interstellar Mission: Challenges of Flying a Very Old Spacecraft on a Very Long Mission

Two Voyager spacecraft were launched in 1977. After the successful flybys of Jupiter and Saturn by both Voyagers and Uranus and Neptune by Voyager 2, the mission has been extended for another 30 years in search of the transition region between the dominance of the solar energy and interstellar energy. The Voyager Interstellar Mission (VIM) started on January 1, 1990. It can be characterized by several factors including extremely long communication distances, aging hardware, reduced staffing levels and difficulty in obtaining Deep Space Network (DSN) resources necessitated by the increasing distance between the spacecraft and Earth. The mission was redesigned to compensate for such factors while maximizing the science return. After 25 years of VIM and several significant science discoveries, both Voyager spacecraft are still functioning well and the Voyager flight team is preparing for an even longer mission - until the year 2025 and beyond. In order to work around the challenges and to continue the mission even further, the team has been implementing numerous changes, mainly through flight software modifications and hardware reconfiguration. The major drivers for the changes are two-fold: resource constraints (such as decreasing power output and difficulty in obtaining the necessary DSN coverage) and anomalies due to the aging hardware. The majority of changes occur through flight software modifications so the state of the on-board responses is appropriate for the changing space environment and mission phase, and the flight software is compatible in allowing the maximum data gathering. The on-board flight software routines such as baseline sequence, fault protection routines, the High Gain Antenna POINTing to Earth (HPOINT) table, and long-term events table need to be maintained through flight software updates. The changes also occur through hardware reconfiguration such as selecting the backup Hybrid Buffer Interface Circuits (HYBIC) or attitude propulsion thrusters. This paper will describe the challenges of VIM and what has been done to overcome or mitigate those challenges. The primary focus will be the major flight software changes made during VIM and the changes that are in store for the near future in preparation for continuing the extended mission, from the originally projected year of 2020 out to the year 2025 and possibly beyond.

Matsumoto, Sun Kang↗

NASA NTRS1994

A Numerical Investigation of Turbulent Flow in Noncircular Ducts

Since turbulent duct flows play an important role in engineering, continuous efforts to investigate this problem have been made. Until recently, these investigations were limited mostly to experiments and various semi-analytic methods. Owing to the improvement of turbulence modeling, the prevailing method of prediction is now mainly numerical. The majority of these studies deals, however, with turbulent flows in circular or square ducts and only limited information is available for straight noncircular ducts. In view of this situation, we propose to conduct a numerical investigation of turbulent flow in a class of ducts, whose cross sections vary from a circle to a near square. Turbulent flow in a noncircular duct is characterized by the presence of secondary flow for which a more refined turbulence model than the k-epsilon equations is required. In order to show that the calculated results are credible, various modes of verification were used to examine the results for a selected configuration, including an accuracy check by a scaling law and observing the decay of secondary flow as the cross section changes from a noncircular shape to a circle. After this was done, computations were performed for other configurations and with different Reynolds numbers from which wall shear stresses and friction factors are plotted.

Kao, Hsiao C.↗

NASA NTRS1995

On the application of Chimera/unstructured hybrid grids for conjugate heat transfer

A hybrid grid system that combines the Chimera overset grid scheme and an unstructured grid method is developed to study fluid flow and heat transfer problems. With the proposed method, the solid structural region, in which only the heat conduction is considered, can be easily represented using an unstructured grid method. As for the fluid flow region external to the solid material, the Chimera overset grid scheme has been shown to be very flexible and efficient in resolving complex configurations. The numerical analyses require the flow field solution and material thermal response to be obtained simultaneously. A continuous transfer of temperature and heat flux is specified at the interface, which connects the solid structure and the fluid flow as an integral system. Numerical results are compared with analytical and experimental data for a flat plate and a C3X cooled turbine cascade. A simplified drum-disk system is also simulated to show the effectiveness of this hybrid grid system.

Kao, Kai-Hsiung↗

NASA NTRS1971

Comparison of a discrete steepest ascent method with the continuous steepest ascent method for optimal programing

A discrete steepest ascent method which allows controls which are not piecewise constant (for example, it allows all continuous piecewise linear controls) was derived for the solution of optimal programming problems. This method is based on the continuous steepest ascent method of Bryson and Denham and new concepts introduced by Kelley and Denham in their development of compatible adjoints for taking into account the effects of numerical integration. The method is a generalization of the algorithm suggested by Canon, Cullum, and Polak with the details of the gradient computation given. The discrete method was compared with the continuous method for an aerodynamics problem for which an analytic solution is given by Pontryagin's maximum principle, and numerical results are presented. The discrete method converges more rapidly than the continuous method at first, but then for some undetermined reason, loses its exponential convergence rate. A comparsion was also made for the algorithm of Canon, Cullum, and Polak using piecewise constant controls. This algorithm is very competitive with the continuous algorithm.

Childs, A. G.↗

NASA NTRS1975

ORACLS - A modern control theory design package

A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.

Armstrong, E. S.↗

NASA NTRS1979

A viscous flow analysis for the tip vortex generation process

A three dimensional, forward-marching, viscous flow analysis is applied to the tip vortex generation problem. The equations include a streamwise momentum equation, a streamwise vorticity equation, a continuity equation, and a secondary flow stream function equation. The numerical method used combines a consistently split linearized scheme for parabolic equations with a scalar iterative ADI scheme for elliptic equations. The analysis is used to identify the source of the tip vortex generation process, as well as to obtain detailed flow results for a rectangular planform wing immersed in a high Reynolds number free stream at 6 degree incidence.

Shamroth, S. J.↗

NASA NTRS1980

On the numerical solution of time-dependent viscous incompressible fluid flows involving solid boundaries

An inherent numerical problem associated with the fully explicit pseudospectral numerical simulation of the incompressible Navier-Stokes equation for viscous flows with no-slip walls is described. A semi-implicit scheme which circumvents this numerical difficulty is presented. In this algorithm the equation of continuity rather than the Poisson equation for pressure is solved directly. Pseudospectral formulation of the channel flow problem using Fourier series and Chebyshev polynomials expansions is given for this scheme. An example demonstrating the applicability of the method is given.

Moin, P.↗

NASA NTRS1983

Flare loop radiative hydrodynamics. I - Basic methods

The study presented here has two goals. The first is to examine the role of energy transport mechanisms in flare dynamics, for instance, thermal cone conduction in the corona and radiative transfer in the chromosphere. The second is to provide diagnostics of flare energization processes by predicting the evolutionary behavior of concurrent emissions from all regions of the flaring atmosphere. To attain these ends, a numerical method is developed for the simultaneous solution of thy continuity, momentum, and energy equations; the time-dependent atomic rate equations describing ionization and excitation; and the radiative transfer equations. With the physical model and computational methods used here, all components of the plasma move as a single fluid and in the initial studies are assumed to have a common kinetic temperature. The plasma is constrained to move in one dimension along the axis of a loop of nonuniform cross section, the geometry of which is defined by a sufficiently strong magnetic field.

Mcclymont, A. N.↗

NASA NTRS1982

A penalty finite element algorithm for parabolic flow problems

The thin-layer simplification of the two-dimensional Navier-Stokes equations for steady viscous flow are developed using an order of magnitude analysis. A space marching finite element solution algorithm is developed, wherein the first order continuity effects are enforced as a penalty function differential constraint. Numerical results are presented to document accuracy and convergence features of the numerical solution algorithm.

Baker, A. J.↗

NASA NTRS1983

Comments on some problems in computational penetration mechanics

Three problem areas in the computer simulation of large-scale penetration mechanics problems are briefly discussed. These are numerical instabilities due to incomplete integration of the momentum or continuity equations, constitutive modelling, and friction effects.

Oden, J. T.↗

NASA NTRS1986

Using PCDS to study the influence of UV flux variation on the middle atmosphere

The value of the Pilot Climate Data System (PCDS) in examining the influences of short-period solar flux variations on the middle atmosphere was demonstrated. Several Nimbus satellite data sets proposed for the study exist in the PCDS. Planned for retrieval through the PCDS are ozone mixing ratios and cumulative ozone profiles available from the Backscatter Ultraviolet Spectrophotometer on Nimbus-4. Also to be accessed are Nimbus-7 data sets that will provide ozone and nitrogen dioxide mixing ratios, temperature profiles from the Limb Infrared Monitor of the Stratosphere, and ozone mixing ratio profiles from the Solar Backscatter Ultraviolet Spectrophotometer. Bypassing the time-consuming process of reading raw data tapes, the researchers plan to transfer the PCDS processed data to an IBM PC at Iowa State University. The IBM PC will serve as an intermediate vehicle for transferring the data to the NOAA CYBER 840 at Boulder, Colorado, where research will continue on both an eight-layer radiative-photochemical numerical model and on a nonlinear dynamical model. in this research are the FGGE and ERB data sets. These relevant data sets also reside in the PCDS. Problems associated with remote access to the PCDS were discussed in regard to all the PCDS data sets.

Heilman, W.↗

NASA NTRS1989

Aerodynamic stability and heating analyses for the aeroassist flight experiment vehicle

Since ground based flow simulations are presently unable to model flight conditions expected for AOTVs (Aeroassist Orbital Transfer Vehicle) and other hypersonic space vehicles, computer codes are being developed to provide design parameters necessary for structure, guidance, and control aspects. Over the past four years, VRFLO (Viscous Reactive Flow) has been written to model finite-rate chemistry and viscous effects for a variety of aerobrake bodies. VRFLO includes a number of unique features that are summarized as follows: (1) Grid generation is an integral part of the code for several aerobrake configurations which includes the wake flow region; (2) The formulation is valid for three air chemical models; (3) An ADI central difference technique is used to solve the Navier-Stokes and species continuity equations in split groups; and (4) Grid density and numerical damping are minimized by shock-fitting and conformal mapping of body points.

Mcgary, J.↗

NASA NTRS1991

A continuous mixing model for pdf simulations and its applications to combusting shear flows

The problem of time discontinuity (or jump condition) in the coalescence/dispersion (C/D) mixing model is addressed in this work. A C/D mixing model continuous in time is introduced. With the continuous mixing model, the process of chemical reaction can be fully coupled with mixing. In the case of homogeneous turbulence decay, the new model predicts a pdf very close to a Gaussian distribution, with finite higher moments also close to that of a Gaussian distribution. Results from the continuous mixing model are compared with both experimental data and numerical results from conventional C/D models.

Hsu, A. T.↗