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Fundamental equations encountered in computational fluid dynamics (CFD), and analyses used for internal flow are introduced. Irrotational flow; Euler equations; boundary layers; parabolized Navier-Stokes equations; and time averaged Navier-Stokes equations are treated. Assumptions made and solution methods are outlined, with examples. The overall status of CFD in propulsion is indicated.
Analyses useful to problems of computing mathematical functions
Spectral and real time computation for acoustic absorbers with nonlinear material characteristics
The computing equipment in the engineering systems simulation laboratory of the Houston University Cullen College of Engineering is described and its advantages are summarized. The application of computer techniques in aerospace-related research psychology and in chemical, civil, electrical, industrial, and mechanical engineering is described in abstracts of 84 individual projects and in reprints of published reports. Research supports programs in acoustics, energy technology, systems engineering, and environment management as well as aerospace engineering.
Conservative dissipative difference schemes for computing one dimensional flow are introduced, and the recognition and representation of flow discontinuities are discussed. Multidimensional methods are outlined. Second order finite volume schemes are introduced. Conversion of difference schemes for a single linear convection equation into schemes for the hyperbolic system of the nonlinear conservation laws of ideal compressible flow is explained. Approximate Riemann solvers are presented. Monotone initial value interpolation; and limiters, switches, and artificial dissipation are considered.
Powerful computational fluid dynamics (CFD) tools have emerged that appear to offer significant benefits as an adjunct to the experimental methods used by the stability and control community to predict aerodynamic parameters. The decreasing costs for and increasing availability of computing hours are making these applications increasingly viable as time goes on and the cost of computing continues to drop. This paper summarizes the efforts of four organizations to utilize high-end computational fluid dynamics (CFD) tools to address the challenges of the stability and control arena. General motivation and the backdrop for these efforts will be summarized as well as examples of current applications.
Algorithm for fast digital computer recursive estimation of mean of random variable
An assessment of several three-dimensional computer codes used at the NASA Lewis Research Center is presented. Four flow situations are examined, for which both experimental data and computational results are available. The four flows form a basis for the evaluation of the computational procedures. It is concluded that transonic rotor flow at peak efficiency conditions may be calculated with a reasonable degree of accuracy, whereas, off-design conditions are not accurately determined. Duct flows and turbine cascade flows may also be computed with reasonable accuracy whereas radial inflow turbine flow remains a challenging problem.
An assessment of several three-dimensional computer codes used at the NASA Lewis Research Center is presented. Four flow situations are examined, for which both experimental data and computational results are available. The four flows form a basis for the evaluation of the computational procedures. It is concluded that transonic rotor flow at peak efficiency conditions may be calculated with a reasonable degree of accuracy, whereas, off-design conditions are not accurately determined. Duct flows and turbine cascade flows may also be computed with reasonable accuracy whereas radial inflow turbine flow remains a challenging problem.
The paper uses finite-difference algorithms called 'fast direct elliptic solvers' within an iteration scheme for the rapid solution of the equations of inviscid transonic aerodynamics. The methods are called 'direct' (or semidirect) because the entire computational field is solved at once rather than in successive traverses over the field. These semidirect iterative methods have been limited here to the investigation of two-dimensional steady inviscid flow over airfoils in subsonic free stream.
A program aimed at facilitating the use of computational fluid dynamics (CFD) simulations by the controls discipline is presented. The objective is to reduce the development time and cost for propulsion system controls by using CFD simulations to obtain high-fidelity system models for control design and as numerical test beds for control system testing and validation. An interdisciplinary team has been formed to develop analytical and computational tools in three discipline areas: controls, CFD, and computational technology. The controls effort has focused on specifying requirements for an interface between the controls specialist and CFD simulations and a new method for extracting linear, reduced-order control models from CFD simulations. Existing CFD codes are being modified to permit time accurate execution and provide realistic boundary conditions for controls studies. Parallel processing and distributed computing techniques, along with existing system integration software, are being used to reduce CFD execution times and to support the development of an integrated analysis/design system. This paper describes: the initial application for the technology being developed, the high speed civil transport (HSCT) inlet control problem; activities being pursued in each discipline area; and a prototype analysis/design system in place for interactive operation and visualization of a time-accurate HSCT-inlet simulation.
Complicated mission design problems require innovative computational solutions. As spacecraft depart from a proposed Gateway in a Near Rectilinear Halo Orbit (NRHO), recontact analysis is required to avoid risk of collision and ensure safe operations. Escape dynamics from NRHOs are governed by multiple gravitational bodies, yielding a trajectory design space that is exhaustively large. This paper summarizes the recontact analysis for departure from the NRHO and describes how the Deep Space Trajectory Explorer (DSTE) trajectory design software incorporates high performance cloud computing to compute and visualize the orbit design space. Recent focus on exploration missions to cislunar space has kindled accelerated interest in multibody orbit solutions. Trajectory analysis in the presence of multiple gravity fields is complex, and innovative computational tools are needed to simplify complicated design spaces, to generate large quantities of data quickly, and to visualize the output for user accessibility. The Gateway mission is a prime example. The Gateway1 is proposed as a human outpost in deep space. The current baseline orbit for the Gateway is a Near Rectilinear Halo Orbit (NRHO) near the Moon.2 The NRHO exists in a regime that experiences the gravitational effects of the Earth and the Moon simultaneously, complicating orbit analysis. The mission design process benefits greatly from updated computational tools for multibody missions like the Gateway. As an example, consider the problem of assessing the risk of collision in an NRHO. As a staging location to missions to the lunar surface and beyond the Earth-Moon system, the Gateway will experience spacecraft and other objects regularly arriving and departing. Departing objects potentially include spent logistics modules, visiting crew vehicles, debris objects, wastewater particles, and cubesats. Each departure is governed by the dynamics of the Gateway orbit and the surrounding dynamical environment. Over time, any unmaintained object in such an orbit eventually departs due to the small instabilities associated with the NRHOs. A separation maneuver speeds the departure from the NRHO, but the effects of the maneuver on the spacecraft behavior depend on the location, magnitude, and direction of the burn. Escape dynamics from the NRHO with regard to these maneuver options open up an enormous potential trajectory design space where subtle changes in input can produce dramatically large changes in the results. Any departing object must avoid recontacting the Gateway as it leaves the lunar vicinity, and a recontact analysis thus involves a significant number of computations and extensive output data. To explore the dynamics of this extensive design space, the Deep Space Trajectory Explorer3 (DSTE) trajectory design software incorporates new High Performance Computing (HPC) services and novel interactive visualizations. This paper details the HPC and cloud infrastructure techniques that are implemented in the DSTE, applying the new capabilities to analysis of recontact risk with the Gateway in NRHO. NEAR RECTILINEAR HALO ORBITS The Gateway is planned to fly in a lunar NRHO as its baseline orbit. The NRHO families of orbits are subsets of the larger halo families, which originate from planar orbits near the L1 and L2 libration points; the Earth-Moon L2 halo family appears in Figure 1. Each halo orbit is perfectly periodic in the Circular Restricted 3-Body Problem (CR3BP) and becomes a quasi-periodic orbit in a higher fidelity ephemeris force model. The NRHOs are defined as those members of the halo family with bounded stability properties;2 they pass near the Moon at perilune and are nearly polar. Families exist with apolunes located both above the lunar north pole and above the lunar south pole; the Gateway is planned to reside in a southern L2 NRHO in a 9:2 resonance with the lunar synodic period. The 9:2 NRHO is characterized by a period of about 6.5 days, a perilune radius of about 3,500 km, and an apolune radius of about 71,000 km; it is strongly affected by the gravity of both the Earth and the Moon simultaneously. This NRHO offers extended communications with assets on the south pole of the Moon,4 as well as low-cost orbit maintenance and attitude control,5 favorable eclipse avoidance properties,6 and inexpensive transfers from Earth and to other destinations.5,7 The NRHO portion of the southern L2 halo family is highlighted in black in Figure 1, and the 9:2 NRHO appears in blue.
Topics addressed include: transient dynamics; transient finite element method; transient analysis in impact and crash dynamic studies; multibody computer codes; dynamic analysis of space structures; multibody mechanics and manipulators; spatial and coplanar linkage systems; flexible body simulation; multibody dynamics; dynamical systems; and nonlinear characteristics of joints.
Computational algorithm to mechanize theory of optimal time-invariant output-feedback controllers - Vol. 3
Integral methods are used to model subsonic flow in planar diffusers operating with or without stall. Turbulent boundary layers are computed with a lag-entrainment method employing new correlations for shape factor and skin friction, which are based on a Coles-Van Driest velocity profile. The inviscid flow is modeled as one dimensional and is easily coupled with the boundary layer method to yield equations that can be solved by integrating in the downstream direction. Analysis of the equations describing flow in a diffuser shows that the boundary layer separation singularity may not be eliminated by viscous-inviscid interaction; a modified interaction scheme is used to guarantee a non-singular equation set. The nature of this singularity offers an explanation for the apparent universality of asymmetric stall in planar diffusers. Results for several flows demonstrate the accuracy and range of applicability of the method.
A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.
A computational procedure is presented for the solution of frictional contact problems for aircraft tires. A Space Shuttle nose-gear tire is modeled using a two-dimensional laminated anisotropic shell theory which includes the effects of variations in material and geometric parameters, transverse-shear deformation, and geometric nonlinearities. Contact conditions are incorporated into the formulation by using a perturbed Lagrangian approach with the fundamental unknowns consisting of the stress resultants, the generalized displacements, and the Lagrange multipliers associated with both contact and friction conditions. The contact-friction algorithm is based on a modified Coulomb friction law. A modified two-field, mixed-variational principle is used to obtain elemental arrays. This modification consists of augmenting the functional of that principle by two terms: the Lagrange multiplier vector associated with normal and tangential node contact-load intensities and a regularization term that is quadratic in the Lagrange multiplier vector. These capabilities and computational features are incorporated into an in-house computer code. Experimental measurements were taken to define the response of the Space Shuttle nose-gear tire to inflation-pressure loads and to inflation-pressure loads combined with normal static loads against a rigid flat plate. These experimental results describe the meridional growth of the tire cross section caused by inflation loading, the static load-deflection characteristics of the tire, the geometry of the tire footprint under static loading conditions, and the normal and tangential load-intensity distributions in the tire footprint for the various static vertical loading conditions. Numerical results were obtained for the Space Shuttle nose-gear tire subjected to inflation pressure loads and combined inflation pressure and contact loads against a rigid flat plate. The experimental measurements and the numerical results are compared.
The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.