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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Numerical simulations of small amplitude acoustic wave propagation in a converging-diverging nozzle

Numerical simulations of the small amplitude acoustic wave propagation in a converging-diverging nozzle proposed in Category 5 are performed and presented here. The quasi 1-D unsteady flow equations in conservative form are discretized by the DRP scheme with the artificial damping developed by Tam and Webb. Characteristic boundary conditions are used at both the inlet and outlet of the nozzle. The effect of different numerical implementations of the subsonic inflow boundary conditions on the convergence of the solution to the steady state is studied. In the case of a subsonic outflow in which a shock is formed in the nozzle, the interaction between acoustics and the shock is also investigated.

Dong, Thomas Z.↗
NASA NTRS1995

Pressure updating methods for the steady-state fluid equations

We consider the steady state equations for a compressible fluid. Since we wish to solve for a range of speeds we must consider the equations in conservation form. For transonic speeds these equations are of mixed type. Hence, the usual approach is to add time derivatives to the steady state equations and then march these equations in time. One then adds a time derivative of the density to the continuity equation, a derivative of the momentum to the momentum equation and a derivative of the total energy to the energy equation. This choice is dictated by the time consistent equations. However, since we are only interested in the steady state this is not necessary. Thus we shall consider the possibility of adding a time derivative of the pressure to the continuity equation and similar modifications for the energy equation. This can then be generalized to adding combinations of time derivatives to each equation since these vanish in the steady state. When using acceleration techniques such as residual smoothing, multigrid, etc. these are applied to the pressure rather than the density. Hence, the code duplicates the behavior of the incompressible equations for low speeds.

Fiterman, A.↗
NASA NTRS1996

On buffer layers as non-reflecting computational boundaries

We examine an absorbing buffer layer technique for use as a non-reflecting boundary condition in the numerical simulation of flows. One such formulation was by Ta'asan and Nark for the linearized Euler equations. They modified the flow inside the buffer zone to artificially make it supersonic in the layer. We examine how this approach can be extended to the nonlinear Euler equations. We consider both a conservative and a non-conservative form modifying the governing equations in the buffer layer. We compare this with the case that the governing equations in the layer are the same as in the interior domain. We test the effectiveness of these buffer layers by a simulation of an excited axisymmetric jet based on a nonlinear compressible Navier-Stokes equations.

Hayder, M. Ehtesham↗
NASA NTRS1994

Numerical Simulation of the Instability of an Inviscid Liquid Jet in a Coflowing Compressible Airstream

The nonlinear interfacial instability of a liquid jet in a coflowing compressible airstream is studied numerically. A high-resolution scheme which has second-order accuracy in space and time is coupled with a Lagrangian marker particle algorithm to visualize the large-scale motion of the interfaces in compressible flow. A numerical algorithm based on an approximate equation of state of a compressible liquid is developed to allow this two-fluid system to be governed by the nonlinear unsteady Euler equations in conservative form. The initial growth of small disturbances given by the simulations agrees well with linear theory. The process of jet disruption in compressible flow is demonstrated to consist of the formation of liquid spikes, interweaving of the gas and liquid and stretching and detachment of the liquid main center core.

Li, H. -S.↗
NASA NTRS1982

A Numerical Method for Solving the Equations of Compressible Viscous Flow

Although much progress has already been made In solving problems in aerodynamic design, many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely. This paper describes one such development. A new method for solving these equations has been devised that 1) is second-order accurate in space and time, 2) is unconditionally stable, 3) preserves conservation form, 4) requires no block or scalar tridiagonal inversions, 5) is simple and straightforward to program (estimated 10% modification for the update of many existing programs), 6) is more efficient than present methods, and 7) should easily adapt to current and future computer architectures. Computational results for laminar and turbulent flows at Reynolds numbers from 3 x 10(exp 5) to 3 x 10(exp 7) and at CFL numbers as high as 10(exp 3) are compared with theory and experiment.

MacCormack, R. W.↗
NASA NTRS1999

Factorizable Schemes for the Equations of Fluid Flow

We present an upwind high-resolution factorizable (UHF) discrete scheme for the compressible Euler equations that allows to distinguish between full-potential and advection factors at the discrete level. The scheme approximates equations in their general conservative form and is related to the family of genuinely multidimensional upwind schemes developed previously and demonstrated to have good shock-capturing capabilities. A unique property of this scheme is that in addition to the aforementioned features it is also factorizable, i.e., it allows to distinguish between full-potential and advection factors at the discrete level. The latter property facilitates the construction of optimally efficient multigrid solvers. This is done through a relaxation procedure that utilizes the factorizability property.

Sidilkover, David↗
NASA NTRS1998

A 2.5D Single Passage CFD Model for Centrifugal Pumps

This paper describes the single passage model based on CFD to analyze the flow in blade passages of a centrifugal pump. The model consists of the flow passage between two impeller blades and the spaces in the inlet eye as well as in the volute. The incompressible Navier-Stokes equations in the conservation form are solved by a finite difference method. The code is designed to investigate the velocity and pressure distributions and intended to investigate how the pump design affects fluid flow through the rotor as well as the pump performance. An early part of the paper investigates the behavior of the model as well as validity of the assumptions made in the model. Then, applications to a rotodynamic heart pump are presented.

Nakamura S.↗
NASA NTRS2000

Multigrid Relaxation of a Factorizable, Conservative Discretization of the Compressible Flow Equations

The second-order factorizable discretization of the compressible Euler equations developed by Sidilkover is extended to conservation form on general curvilinear body-fitted grids. The discrete equations are solved by symmetric collective Gauss-Seidel relaxation and FAS multigrid. Solutions for flow in a channel with Mach numbers ranging from 0.0001 to a supercritical Mach number are shown, demonstrating uniform convergence rates and no loss of accuracy in the incompressible limit. A solution for the flow around the leading edge of a semi-infinite parabolic body demonstrates that the scheme maintains rapid convergence for a flow containing a stagnation point.

Roberts, Thomas W.↗
NASA NTRS2000

On the Coupling of CDISC Design Method with FPX Rotor Code

A rotor section aerodynamics design package is developed by coupling Constrained Direct Iterative Surface Curvature (CDISC) design method with the FPX rotor code. The coupling between the CDISC design and the FPX flow analysis is fully automated. The CDISC design method employs a predictor-corrector procedure iteratively to determine a surface geometry which produces a target pressure distribution, where the target pressure distributions is either pre-defined or automatically generated through flow and geometry constraints. The FPX code is an eXtended Full-Potential rotor Computational Fluid Dynamics (CFD) code, which solves the three-dimensional unsteady full-potential equation in a strong conservative form using an implicit approximate factorization finite-difference scheme with entropy and viscosity corrections. Application of the CDISC design method coupled with the FPX rotor code is made for rotor blades in hovering motions. Several design examples are presented to demonstrate the capability of the new package in rotor section design.

Hu, Hong↗
NASA NTRS2001

Numerical Modeling of Liquid-Vapor Phase Change

We implemented a two- and three-dimensional finite difference/front tracking technique to solve liquid-vapor phase change problems. The mathematical and the numerical features of the method were explained in great detail in our previous reports, Briefly, we used a single formula representation which incorporated jump conditions into the governing equations. The interfacial terms were distributed as singular terms using delta functions so that the governing equations would be the same as conventional conservation equations away from the interface and in the vicinity of the interface they would provide correct jump conditions. We used a fixed staggered grid to discretize these equations and an unstructured grid to explicitly track the front. While in two dimensions the front was simply a connection of small line segments, in three dimensions it was represented by a connection of small triangular elements. The equations were written in conservative forms and during the course of computations we used regriding to control the size of the elements of the unstructured grid. Moreover, we implemented a coalescence in two dimensions which allowed the merging of different fronts or two segments of the same front when they were sufficiently close. We used our code to study thermocapillary migration of bubbles, burst of bubbles at a free surface, buoyancy-driven interactions of bubbles, evaporation of drops, rapid evaporation of an interface, planar solidification of an undercooled melt, dendritic solidification, and a host of other problems cited in the reference.

Esmaeeli, Asghar↗
NASA NTRS2001

An Implicit Characteristic Based Method for Electromagnetics

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

Beggs, John H.↗
NASA NTRS1995

Heliospheric Termination Shock Motion Due to Fluctuations in the Solar Wind Upstream Conditions: Spherically Symmetric Model

Large-scale fluctuations in the solar wind plasma upstream of the heliospheric termination shock (TS) will cause inward and outward motions of the shock. Using numerical techniques, we extend an earlier strictly one-dimensional (planar) analytic gas dynamic model to spherical symmetry to investigate the features of global behavior of shock motion. Our starting point is to establish a steady numerical solution of the gasdynamic equations describing the interaction between the solar wind and the interstellar medium. We then introduce disturbances of the solar wind dynamic pressure at an inner boundary, and follow the subsequent evolution of the system, especially the motion of the termination shock. Our model solves spherically symmetric gasdynamic equations as an initial-boundary value problem. The equations in conservative form are solved using a fully implicit Total Variation Diminishing (TVD) upwind scheme with Roe-type Riemann solver. Boundary conditions are given by the solar wind parameters on an inner spherical boundary, where they are allowed to vary with time for unsteady calculations, and by a constant pressure (roughly simulating the effect of the local interstellar medium) on an outer boundary. We find that immediately after the interaction, the shock moves with speeds given by the earlier analogous analytic models. However, as the termination shock propagates it begins to slow down, seeking a new equilibrium position. In addition, the disturbance transmitted through the TS, either a shock or rarefaction wave, will encounter the heliopause boundary and be reflected back. The reflected signal will encounter the TS, causing it to oscillate. The phenomenon may be repeated for a number of reflections, resulting in a "ringing" of the outer heliosphere.

Ratkiewicz, R.↗
NASA NTRS2002

A New Low Dissipative High Order Schemes for MHD Equations

The goal of this talk is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids.

Yee, H. C.↗
NASA NTRS2003

A Generalized Fluid Formulation for Turbomachinery Computations

A generalized formulation of the equations of motion of an arbitrary fluid are developed for the purpose of defining a common iterative algorithm for computational procedures. The method makes use of the equations of motion in conservation form with separate pseudo-time derivatives used for defining the numerical flux for a Riemann solver and the convergence algorithm. The partial differential equations are complemented by an thermodynamic and caloric equations of state of a complexity necessary for describing the fluid. Representative solutions with a new code based on this general equation formulation are provided for three turbomachinery problems. The first uses air as a working fluid while the second uses gaseous oxygen in a regime in which real gas effects are of little importance. These nearly perfect gas computations provide a basis for comparing with existing perfect gas code computations. The third case is for the flow of liquid oxygen through a turbine where real gas effects are significant. Vortex shedding predictions with the LOX formulations reduce the discrepancy between perfect gas computations and experiment by approximately an order of magnitude, thereby verifying the real gas formulation as well as providing an effective case where its capabilities are necessary.

Merkle, Charles L.↗
NASA NTRS2001

An Implicit LU/AF FDTD Method

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗
NASA NTRS2006

A Computational and Experimental Investigation of Shear Coaxial Jet Atomization

The instability and subsequent atomization of a viscous liquid jet emanated into a high-pressure gaseous surrounding is studied both computationally and experimentally. Liquid water issued into nitrogen gas at elevated pressures is used to simulate the flow conditions in a coaxial shear injector element relevant to liquid propellant rocket engines. The theoretical analysis is based on a simplified mathematical formulation of the continuity and momentum equations in their conservative form. Numerical solutions of the governing equations subject to appropriate initial and boundary conditions are obtained via a robust finite difference scheme. The computations yield real-time evolution and subsequent breakup characteristics of the liquid jet. The experimental investigation utilizes a digital imaging technique to measure resultant drop sizes. Data were collected for liquid Reynolds number between 2,500 and 25,000, aerodynamic Weber number range of 50-500 and ambient gas pressures from 150 to 1200 psia. Comparison of the model predictions and experimental data for drop sizes at gas pressures of 150 and 300 psia reveal satisfactory agreement particularly for lower values of investigated Weber number. The present model is intended as a component of a practical tool to facilitate design and optimization of coaxial shear atomizers.

Ibrahim, Essam A.↗
NASA NTRS2018

Uncertainty in Inverted Pendulum Thrust Measurements

An uncertainty analysis of a common configuration of electric propulsion thrust stand is presented. The analysis applies to inverted pendulum thrust stands operating in a null-coil configuration with in-situ calibration. Several sources of bias and precision uncertainty are discussed, propagated, and combined to form conservative estimates of the relative and absolute thrust uncertainties. A case study of the NASA Glenn Research Center Vacuum Facility 6 thrust stand is presented. For the thruster investigated, the uncertainty was estimated to be +/-6.9 mN over the entire span of thrust. This uncertainty represents a maximum instrument bias introduced by the thrust stand. The paper does not address repeatability of actual thrust measurements, as this is generally beyond the influence of the thrust stand and can be dependent on a large number of factors.

Mackey, J.↗
NASA NTRS2018

Uncertainty in Inverted Pendulum Thrust Measurements

An uncertainty analysis of a common configuration of electric propulsion thrust stand is presented. The analysis applies to inverted pendulum thrust stands operating in a null-coil configuration with in-situ calibration. Several sources of bias and precision uncertainty are discussed, propagated, and combined to form conservative estimates of the relative and absolute thrust uncertainties. A case study of the NASA Glenn Research Center Vacuum Facility 6 thrust stand is presented. For the thruster investigated, the uncertainty was estimated to be ±6.9 mN over the entire span of thrust. This uncertainty represents a maximum instrument bias introduced by the thrust stand. The paper does not address repeatability of actual thrust measurements, as this is generally beyond the influence of the thrust stand and can be dependent on a large number of factors.

Mackey, Jonathan A.↗