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At least 685 records · Page 38

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NASA NTRS1985

A mathematical formulation of the Scole control problem, part 1

A mathematical formulation of the SCOLE control problem in terms of a continuous model described by partial differential equations with delta functions on the boundary is presented along with three techniques of solution. The abstract wave equation approach leads immediately to a linear feedback law that can ensure (strong) stability. The boundary control approach yields an explicit solution, albeit in a simple case.

Balakrishnan, A. V.↗

NASA NTRS1985

The response of turbulent boundary layers to sudden pertubations

The processes present in a turbulent boundary layer (BL) which experiences a sudden change in the surface roughness are discussed in terms of numerical models in comparison with empirical data. Consideration is limited to flow perturbations which preserve the BL approximation. Generalized continuity, momentum and turbulent energy transport equations are reviewed. The perturbed BL has two regions: one with large velocity gradients and an outer zone with smaller gradients. Expressions are defined for the velocity and temperature profiles and the roughness length after a step change in surface roughness, which causes the disturbance. A pertrurbation could also arise from a heat flux input of a pressure gradient. The effects of the shape of the perturbing step and the presence of several disturbing edges are explored. Finally, it is shown that closure forms and constants for self-preserving flows are worthy of further development because of their demonstrable abilities to describe simple perturbed flows.

Smits, A. J.↗

NASA NTRS1986

A spline-based parameter estimation technique for static models of elastic structures

The problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem is considered. Under appropriate conditions this problem can be treated as a first order hyperbolic equation in the unknown coefficient. Some continuous dependence results are developed for this problem and a spline-based technique is proposed for approximating the unknown coefficient, based on these results. The convergence of the numerical scheme is established and error estimates obtained.

Dutt, P.↗

NASA NTRS1987

A two-fluid model for solar wind fluid with higher order moments

A spherically symmetric two-fluid model for the solar wind with higher-order moments is presented. In this model, continuity, momentum, temperature and heat flux equations for two components (electrons and protrons) in steady solar wind states are simultaneously solved by using a time-dependent method. This work is used to compare solutions of the steady-state solar wind with and without higher order moments, and to study the effects of thermal conduction. The coupling between electrons and protrons is also given special attention. The numerical solutions of the steady-state solar wind in both subsonic and supersonic regions between the Sun and 1 AU are obtained and graphically illustrated.

Wang, Jingfang↗

NASA NTRS1989

A spline-based parameter estimation technique for static models of elastic structures

Dutt, P.↗

NASA NTRS1990

Simulated dynamic response of a servovalve controlled hydraulic actuator

A general purpose math model of a servovalve controlled hydraulic actuator system is derived. The system consists of a linear actuator with unequal piston areas, a single stage servovalve, a gas charged hydraulic accumulator, and the interconnecting piping. The state equations are integrated using the Advanced Continuous Simulation Language (ACSL) for determining the system's dynamic response characteristics. Using this generalized hydraulic actuator system model, response characteristics were determined for various servovalve commands.

Babcock, Dale A.↗

NASA NTRS1992

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomas devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1 - X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Papell, S. Stephen↗

NASA NTRS1992

Liquid hydrogen mass flow through a multiple orifice Joule-Thomson device

Liquid hydrogen mass flow rate, pressure drop, and temperature drop data were obtained for a number of multiple orifice Joule-Thomson devices known as visco jets. The present investigation continues a study to develop an equation for predicting two phase flow of cryogens through these devices. The test apparatus design allowed isenthalpic expansion of the cryogen through the visco jets. The data covered a range of inlet and outlet operating conditions. The mass flow rate range single phase or two phase was 0.015 to 0.98 lbm/hr. The manufacturer's equation was found to overpredict the single phase hydrogen data by 10 percent and the two phase data by as much as 27 percent. Two modifications of the equation resulted in a data correlation that predicts both the single and two phase flow across the visco jet. The first modification was of a theoretical nature, and the second strictly empirical. The former reduced the spread in the two phase data. It was a multiplication factor of 1-X applied to the manufacturer's equation. The parameter X is the flow quality downstream of the visco jet based on isenthalpic expansion across the device. The latter modification was a 10 percent correction term that correlated 90 percent of the single and two phase data to within +/- 10 percent scatter band.

Papell, S. S.↗

NASA NTRS1992

Transient scattering from two-dimensional dielectric cylinders of arbitrary shape

In this work, the problem of transient scattering by arbitrary shaped two-dimensional dielectric cylinders is solved using the marching-on-in-time (MOT) technique. The dielectric problem is approached via the surface equivalence principle. A pair of coupled integral equations are derived by enforcing the continuity of the electric and magnetic fields which are solved by using the method of moments. Numerical results are presented for two cross sections, viz. a circle and a square, and compared with inverse discrete Fourier transform (IDFT) techniques. In each case, good agreement is obtained with the IDFT solution.

Vechinski, Douglas A.↗

NASA NTRS1999

Aerosol Transport Over Equatorial Africa

Long-range and inter-hemispheric transport of atmospheric aerosols over equatorial Africa has received little attention so far. Most aerosol studies in the region have focussed on emissions from rain forest and savanna (both natural and biomass burning) and were carried out in the framework of programs such as DECAFE (Dynamique et Chimie Atmospherique en Foret Equatoriale) and FOS (Fires of Savanna). Considering the importance of this topic, aerosols samples were measured in different seasons at 4420 meters on Mt Kenya and on the equator. The study is based on continuous aerosol sampling on a two stage (fine and coarse) streaker sampler and elemental analysis by Particle Induced X-ray Emission. Continuous samples were collected for two seasons coinciding with late austral winter and early austral spring of 1997 and austral summer of 1998. Source area identification is by trajectory analysis and sources types by statistical techniques. Major meridional transports of material are observed with fine-fraction silicon (31 to 68 %) in aeolian dust and anthropogenic sulfur (9 to 18 %) being the major constituents of the total aerosol loading for the two seasons. Marine aerosol chlorine (4 to 6 %), potassium (3 to 5 %) and iron (1 to 2 %) make up the important components of the total material transport over Kenya. Minimum sulfur fluxes are associated with recirculation of sulfur-free air over equatorial Africa, while maximum sulfur concentrations are observed following passage over the industrial heartland of South Africa or transport over the Zambian/Congo Copperbelt. Chlorine is advected from the ocean and is accompanied by aeolian dust recirculating back to land from mid-oceanic regions. Biomass burning products are transported from the horn of Africa. Mineral dust from the Sahara is transported towards the Far East and then transported back within equatorial easterlies to Mt Kenya. This was observed during austral summer and coincided with the dying phase of 1997/98 El Nino.

Gatebe, C. K.↗

NASA NTRS2000

Two-Dimensional Array Beam Scanning Via Externally and Mutually Injection Locked Coupled Oscillators

Some years ago, Stephan proposed an approach to one dimensional (linear) phased array beam steering which requires only a single phase shifter. This involves the use of a linear array of voltage-controlled electronic oscillators coupled to nearest neighbors. The oscillators are mutually injection locked by controlling their coupling and tuning appropriately. Stephan's approach consists of deriving two signals from a master oscillator, one signal phase shifted with respect to the other by means of a single phase shifter. These two signals are injected into the end oscillators of the array. The result is a linear phase progression across the oscillator array. Thus, if radiating elements are connected to each oscillator and spaced uniformly along a line, they will radiate a beam at an angle to that line determined by the phase gradient which is, in turn, determined by the phase difference between the injection signals.The beam direction is therefore controlled by adjusting this phase difference. Recently, Pogorzelski and York presented a formulation which facilitates theoretical analysis of the above beam steering technique. This was subsequently applied by Pogorzelski in analysis of two dimensional beam steering using perimeter detuning of a coupled oscillator array. The formulation is based on a continuum model in which the oscillator phases are represented by a continuous function satisfying a partial differential equation of diffusion type. This equation can be solved via the Laplace transform and the resulting solution exhibits the dynamic behavior of the array as the beam is steered. Stephan's beam steering technique can be similarly generalized to two-dimensional arrays in which the beam control signals are applied to the oscillators on the perimeter of the array. In this paper the continuum model for this two-dimensional case is developed and the dynamic solution for the corresponding aperture phase function is obtained. The corresponding behavior of the resulting far-zone radiation pattern is displayed as well.

Pogorzelski, Ronald J.↗

NASA NTRS2022

Continuum Covariance Propagation for Understanding Variance Loss in Advective Systems

Motivated by the spurious variance loss encountered during covariance propagation in atmospheric and other large-scale data assimilation systems, we consider the problem for state dynamics governed by the continuity and related hyperbolic partial differential equations. This loss of variance has been attributed to reduced-rank representations of the covariance matrix, as in ensemble methods for example, or else to the use of dissipative numerical methods. Through a combination of analytical work and numerical experiments, we demonstrate that significant variance loss, as well as gain, typically occurs during covariance propagation, even at full rank. The cause of this unusual behavior is a discontinuous change in the continuum covariance dynamics as correlation lengths become small, for instance in the vicinity of sharp gradients in the velocity field. This discontinuity in the covariance dynamics arises from hyperbolicity: the diagonal of the kernel of the covariance operator is a characteristic surface for advective dynamics. Our numerical experiments demonstrate that standard numerical methods for evolving the state are not adequate for propagating the covariance, because16they do not capture the discontinuity in the continuum covariance dynamics as correlations lengths tend to zero. Our analytical and numerical results show that this leads to significant, spurious variance loss in certain regions, and gain in others. The results suggest that developing local covariance propagation methods designed specifically to capture covariance evolution near the diagonal may prove a useful alternative to current methods of covariance propagation.

covariance propagation↗

NASA NTRS1986

An embedding method for the steady Euler equations

Certain difficulties arise in connection with the numerical solution of a direct finite difference representation of the steady Euler equations. Johnson (1979, 1981, 1982) has, therefore, proposed a surrogate-equation technique, in which the first-order steady Euler equations are embedded in a certain second-order system of equations. The present paper is concerned with the theoretical justification for such an embedding approach. For the numerical solution of the two-dimensional steady Euler equations, it is shown that, under a continuity restriction, it is possible to solve a second-order embedded system together with appropriate additional boundary conditions. The result indicates that a more direct and potentially more efficient approach to the steady solutions exists than the alternative of solving the unsteady equations.

Chang, S.-H.↗

NASA NTRS2004

Adjoint Formulation for an Embedded-Boundary Cartesian Method

Many problems in aerodynamic design can be characterized by smooth and convex objective functions. This motivates the use of gradient-based algorithms, particularly for problems with a large number of design variables, to efficiently determine optimal shapes and configurations that maximize aerodynamic performance. Accurate and efficient computation of the gradient, however, remains a challenging task. In optimization problems where the number of design variables dominates the number of objectives and flow- dependent constraints, the cost of gradient computations can be significantly reduced by the use of the adjoint method. The problem of aerodynamic optimization using the adjoint method has been analyzed and validated for both structured and unstructured grids. The method has been applied to design problems governed by the potential, Euler, and Navier-Stokes equations and can be subdivided into the continuous and discrete formulations. Giles and Pierce provide a detailed review of both approaches. Most implementations rely on grid-perturbation or mapping procedures during the gradient computation that explicitly couple changes in the surface shape to the volume grid. The solution of the adjoint equation is usually accomplished using the same scheme that solves the governing flow equations. Examples of such code reuse include multistage Runge-Kutta schemes coupled with multigrid, approximate-factorization, line-implicit Gauss-Seidel, and also preconditioned GMRES. The development of the adjoint method for aerodynamic optimization problems on Cartesian grids has been limited. In contrast to implementations on structured and unstructured grids, Cartesian grid methods decouple the surface discretization from the volume grid. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin e t al. developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation.

Nemec, Marian↗

NASA NTRS1993

Preconditioning and the limit to the incompressible flow equations

The use of preconditioning methods to accelerate the convergence to a steady state for both the incompressible and compressible fluid dynamic equations are considered. The relation between them for both the continuous problem and the finite difference approximation is also considered. The analysis relies on the inviscid equations. The preconditioning consists of a matrix multiplying the time derivatives. Hence, the steady state of the preconditioned system is the same as the steady state of the original system. For finite difference methods the preconditioning can change and improve the steady state solutions. An application to flow around an airfoil is presented.

Turkel, E.↗

NASA NTRS1989

Full potential unsteady computations including aeroelastic effects

A unified formulation is presented based on the full potential framework coupled with an appropriate structural model to compute steady and unsteady flows over rigid and flexible configurations across the Mach number range. The unsteady form of the full potential equation in conservation form is solved using an implicit scheme maintaining time accuracy through internal Newton iterations. A flux biasing procedure based on the unsteady sonic reference conditions is implemented to compute hyperbolic regions with moving sonic and shock surfaces. The wake behind a trailing edge is modeled using a mathematical cut across which the pressure is satisfied to be continuous by solving an appropriate vorticity convection equation. An aeroelastic model based on the generalized modal deflection approach interacts with the nonlinear aerodynamics and includes both static as well as dynamic structural analyses capability. Results are presented for rigid and flexible configurations at different Mach numbers ranging from subsonic to supersonic conditions. The dynamic response of a flexible wing below and above its flutter point is demonstrated.

Shankar, Vijaya↗

DOE OSTI2024

Neural lumped parameter differential equations with application in friction-stir processing

Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a “lumped” element representative of the physical scales of the modeled system. For systems where the definition of a lumped element or its associated physics may be unknown, modeling tasks may be restricted to full-fidelity physics simulations. Here, in this work, we consider data-driven modeling tasks with limited point-wise measurements of otherwise continuous systems. We build upon the notion of the Universal Differential Equation (UDE) to construct data-driven models for reducing dynamics to that of a lumped parameter and inferring its properties. The flexibility of UDEs allow for composing various known physical priors suitable for application-specific modeling tasks, including lumped parameter methods. The motivating example for this work is the plunge and dwell stages for friction-stir welding; specifically, (i) mapping power input into the tool to a point-measurement of temperature and (ii) using this learned mapping for process control.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

Stochastic differential equations and turbulent dispersion

Aspects of the theory of continuous stochastic processes that seem to contribute to an understanding of turbulent dispersion are introduced and the theory and philosophy of modelling turbulent transport is emphasized. Examples of eddy diffusion examined include shear dispersion, the surface layer, and channel flow. Modeling dispersion with finite-time scale is considered including the Langevin model for homogeneous turbulence, dispersion in nonhomogeneous turbulence, and the asymptotic behavior of the Langevin model for nonhomogeneous turbulence.

Durbin, P. A.↗