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A numerical model of viscous transonic swirling flow in axisymmetric nozzles is developed. MacCormack's implicit Gauss-Seidel method is applied to the thin-layer Navier-Stokes equations in transformed coordinates. Numerical results are compared with experimental data to validate the method. The effect of swirl and viscosity on nozzle performance are demonstrated by examining wall pressures, Mach contours, and integral parameters.
Thermal stratification and self-pressurization of partially filled liquid hydrogen (LH2) storage tanks under microgravity condition is studied theoretically. A spherical tank is subjected to a uniform and constant wall heat flux. It is assumed that a vapor bubble is located in the tank center such that the liquid-vapor interface and tank wall form two concentric spheres. This vapor bubble represents an idealized configuration of a wetting fluid in microgravity conditions. Dimensionless mass and energy conservation equations for both vapor and liquid regions are numerically solved. Coordinate transformation is used to capture the interface location which changes due to liquid thermal expansion, vapor compression, and mass transfer at liquid-vapor interface. The effects of tank size, liquid fill level, and wall heat flux on the pressure rise and thermal stratification are studied. Liquid thermal expansion tends to cause vapor condensation and wall heat flux tends to cause liquid evaporation at the interface. The combined effects determine the direction of mass transfer at the interface. Liquid superheat increases with increasing wall heat flux and liquid fill level and approaches an asymptotic value.
Piloting difficulties associated with conducting aircraft maneuvers in hypersonic flight are caused in part by the nonintuitive nature of the aircraft response and the stringent constraints anticipated on allowable angle of attack and dynamic pressure variations. An approach is documented that provides precise, coordinated maneuver control during excursions from a hypersonic cruise flight path and the necessary flight condition constraints. The approach is to achieve specified guidance commands by resolving altitude and cross range errors into a load factor and bank angle command by using a coordinate transformation that acts as an interface between outer and inner loop flight controls. This interface, referred to as a 'resolver', applies constraints on angle of attack and dynamic pressure perturbations while prioritizing altitude regulation over cross range. An unpiloted test simulation, in which the resolver was used to drive inner loop flight controls, produced time histories of responses to guidance commands and atmospheric disturbances at Mach numbers of 6, 10, 15, and 20. Angle of attack and throttle perturbation constraints, combined with high speed flight effects and the desire to maintain constant dynamic pressure, significantly impact the maneuver envelope for a hypersonic vehicle.
The continuous-time regularization scheme for defining phase-space path integrals is briefly reviewed as a method to define a quantization procedure that is completely covariant under all smooth canonical coordinate transformations. As an illustration of this method, a limited set of transformations is discussed that have an image in the set of the usual squeezed states. It is noteworthy that even this limited set of transformations offers new possibilities for stationary phase approximations to quantum mechanical propagators.
This paper describes the design, fabrication, test, and operation of a unique six axis force/torque dynamometer The specimen table used to hold components under test is supported in a full six axis kinematic mount. Support struts fabricated from high strength steel with special integral two axis flexures link the specimen table to the load cell transducers. Realtime force/torque coordinate transform, root mean squared calculation, and data averaging, and color six axis display with controllable scaling are provided by a specially programmed desktop computer. The extensive structural analysis and design optimization required to obtain a stiff, well damped, lightweight structure is described in detail. Geometric optimization of the kinematic mount and fabrication details of the struts are also described.
A fault tolerant processor (FTP) plays a key role in many high performance, safety-critical control system applications. Realistic modeling of an FTP is crucial to gaining a high degree of confidence in the reliability and safety analysis of such a system. While fidelity is clearly a major consideration, a practical model must also be kept to a moderate size to allow its incorporation into the overall system model. This paper presents a systematic reduction technique that starts from a complex, detailed model of a triple, redundant FTP and produces a low order approximation of very high accuracy. The existence of two distinct time scales represents the key to the success of the technique. No eigenvalue solution or coordinate transformation are needed. The reduced model captures all the important features of the detailed model, is amenable to an analytical solution and provides insight into the reconfiguration behavior of an FTP.
This research investigates an approach to provide precise, coordinated maneuver control during excursions from a hypersonic cruise flight path while observing the necessary flight condition constraints. The approach achieves specified guidance commands by resolving altitude and cross-range errors into a load factor and bank angle command through a coordinate transformation which acts as an interface between outer loop guidance controls and inner loop flight controls. This interface, referred to as a 'resolver', applies constraints on angle-of-attack and dynamic pressure perturbations while prioritizing altitude regulation over crossrange. An unpiloted test simulation, in which the resolver was used to drive inner-loop flight controls, produced time histories of responses to guidance commands at Mach numbers of 6, 10, 15, and 20. It is shown that angle-of-attack and throttle perturbation constraints, combined with high-speed flight effects and the desire to maintain constant dynamic pressure, significantly impact the maneuver envelope for a hypersonic vehicle. Turn rate, climb rate, and descent rate limits are expressed in terms of these constraints.
The Navier-Stokes-Boussinesq equations governing the transport of momentum, mass and heat in a nonisothermal liquid bridge with a temperature-dependent surface tension are solved using a vorticity-stream-function formulation together with a nonorthogonal coordinate transformation. The equations are discretized using a pseudo-unsteady semi-implicit finite difference scheme and are solved by the ADI method. A Picard-type iteration is adopted which consists of inner and outer iterative processes. The outer iteration is used to update the shape of the free surface. Two schemes have been used for the outer iteration; both use the force balance normal to the free surface as the distinguished boundary condition. The first scheme involves successive approximation by the direct solution of the distinguished boundary condition. The second scheme uses the artificial force imbalance between the fluid pressure, viscous and capillary forces at the free surface which arises when the boundary condition for force balance normal to the surface is not satisfied. This artificial imbalance is then used to change the surface shape until the distinguished boundary condition is satisfied. These schemes have been used to examine a variety of model liquid bridge situations including purely thermocapillary-driven flow situations and mixed thermocapillary- and bouyancy-driven flow.
Dexterous dual-arm manipulations are feasible with the system described and illustrated in the paper. The structure is based on an extensible host arm that carries the dual-arm robot which comprises two 7-DOF arms each of which includes a hand with a thumb and three fingers with 4 DOF each. Joint compliance can be stiffened to any level, and the operator uses arm harnesses and gloves to utilize the robotics in an anthropomorphic fashion. The configuration eliminates coordinate-transformation computations, and the system is found to achieve a control-frequency rate of 1000 Hz for its direct man/machine interfaces based on fiber-optic cables. The electronics control for the system utilizes a sensory system consisting of force, position, and compliance sensors. The robotics system is expected to be a user-friendly device that permits assembly, repair, tethering, and other complex mechanical operations.
Thermal stratification and self-pressurization of partially filled liquid hydrogen (LH2) storage tanks under microgravity condition is studied theoretically. A spherical tank is subjected to a uniform and constant wall heat flux. It is assumed that a vapor bubble is located in the tank center such that the liquid-vapor interface and tank wall form two concentric spheres. This vapor bubble represents an idealized configuration of a wetting fluid in microgravity conditions. Dimensionless mass and energy conservation equations for both vapor and liquid regions are numerically solved. Coordinate transformation is used to capture the interface location which changes due to liquid thermal expansion, vapor compression, and mass transfer at liquid-vapor interface. The effects of tank size, liquid fill level, and wall heat flux on the pressure rise and thermal stratification are studied. Liquid thermal expansion tends to cause vapor condensation and wall heat flux tends to cause liquid evaporation at the interface. The combined effects determine the direction of mass transfer at the interface. Liquid superheat increases with increasing wall heat flux and liquid fill level and approaches an asymptotic value.
Partly-digital, partly-optical 'hybrid' image processing attempts to use the properties of each domain to synergistic advantage: while Fourier optics furnishes speed, digital processing allows the use of much greater algorithmic complexity. The video-rate image-coordinate transformation used is a critical technology for real-time hybrid image-pattern recognition. Attention is given to the separation of pose variables, image registration, and both single- and multiple-frame registration.
The first order doubly averaged potential due to third-body gravity is derived in any arbitrary coordinates. The equations of motion are nonsingular at zero eccentricity. The derivation uses a recursive method which allows easy expansion to higher order terms. Instead of using analytical quadrature to obtain the doubly averaged potential, the method presented in this paper simply eliminates the mean anomaly of the perturbed and perturbing bodies by inspection of the recursive formulation. The derivatives of the orbital elements can be numerically integrated rapidly. When a planet equator coordinate system is used, they can be added directly to the derivatives due to gravity harmonics without any coordinate transformation. The method is applied to various high altitude missions. The results are compared with a high precision numerical integration method and are found to provide excellent agreement.
An improved computational technique for calculating the electromagnetic force field, the power absorption and the deformation of an electromagnetically levitated metal sample is described. The technique is based on the volume integral method, but represents a substantial refinement; the coordinate transformation employed allows the efficient treatment of a broad class of rotationally symmetrical bodies. Computed results are presented to represent the behavior of levitation melted metal samples in a multi-coil, multi-frequency levitation unit to be used in microgravity experiments. The theoretical predictions are compared with both analytical solutions and with the results of previous computational efforts for the spherical samples and the agreement has been very good. The treatment of problems involving deformed surfaces and actually predicting the deformed shape of the specimens breaks new ground and should be the major usefulness of the proposed method.
Arcjet thrusters are being actively considered for use in Earth orbit maneuvering applications. Experimental studies are currently the chief means of determining an optimal thruster configuration. Earlier numerical studies have failed to include all of the effects found in typical arcjets including complex geometries, viscosity, and swirling flow. Arcjet geometries are large area ratio converging nozzles with centerbodies in the subsonic portion of the nozzle. The nozzle walls serve as the anode while the centerbody functions as the cathode. Viscous effects are important because the Reynolds number, based on the throat radius, is typically less than 1,000. Experimental studies have shown that a swirl or circumferential velocity component stabilizes a constricted arc. This dissertation describes the equations governing flow through a constricted arcjet thruster. An assumption that the flowfield is in local thermodynamic equilibrium leads to a single fluid plasma temperature model. An order of magnitude analysis reveals the governing fluid mechanics equations are uncoupled from the electromagnetic field equations. A numerical method is developed to solve the governing fluid mechanics equations, the Thin Layer Navier-Stokes equations. A coordinate transformation is employed in deriving the governing equations to simplify the application of boundary conditions in complex geometries. An axisymmetric formulation is employed to include the swirl velocity component as well as the axial and radial velocity components. The numerical method is an implicit finite-volume technique and allows for large time steps to reach a converged steady-state solution. The inviscid fluxes are flux-split, and Gauss-Seidel line relaxation is used to accelerate convergence. Converging-diverging nozzles with exit-to-throat area ratios up to 100:1 and annular nozzles were examined. Quantities examined included Mach number and static wall pressure distributions, and oblique shock structures. As the level of swirl and viscosity in the flowfield increased the mass flow rate and thrust decreased. The technique was used to predict the flow through a typical arcjet thruster geometry. Results indicate swirl and viscosity play an important role in the complex geometry of an arcjet.
The basic governing equations for the second-order three-dimensional hypersonic thermal and chemical nonequilibrium boundary layer are derived by means of an order-of-magnitude analysis. A two-temperature concept is implemented into the system of boundary-layer equations by simplifying the rather complicated general three-temperature thermal gas model. The equations are written in a surface-oriented non-orthogonal curvilinear coordinate system, where two curvilinear coordinates are non-orthogonial and a third coordinate is normal to the surface. The equations are described with minimum use of tensor expressions arising from the coordinate transformation, to avoid unnecessary confusion for readers. The set of equations obtained will be suitable for the development of a three-dimensional nonequilibrium boundary-layer code. Such a code could be used to determine economically the aerodynamic/aerothermodynamic loads to the surfaces of hypersonic vehicles with general configurations. In addition, the basic equations for three-dimensional stagnation flow, of which solution is required as an initial value for space-marching integration of the boundary-layer equations, are given along with the boundary conditions, the boundary-layer parameters, and the inner-outer layer matching procedure. Expressions for the chemical reaction rates and the thermodynamic and transport properties in the thermal nonequilibrium environment are explicitly given.
We propose to develop an interactive environment for the analysis of large Earth science observation and model data sets. We will use a standard scientific data storage format and a large capacity (greater than 20 GB) optical disk system for data management; develop libraries for coordinate transformation and regridding of data sets; modify the NCSA X Image and X Data Slice software for typical Earth observation data sets by including map transformations and missing data handling; develop analysis tools for common mathematical and statistical operations; integrate the components described above into a system for the analysis and comparison of observations and model results; and distribute software and documentation to the scientific community.
A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.
A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.