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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 NTRS1993

Effect of rotation rate on the forces of a rotating cylinder: Simulation and control

In this paper we present numerical solutions to several optimal control problems for an unsteady viscous flow. The main thrust of this work is devoted to simulation and control of an unsteady flow generated by a circular cylinder undergoing rotary motion. By treating the rotation rate as a control variable, we can formulate two optimal control problems and use a central difference/pseudospectral transform method to numerically compute the optimal control rates. Several types of rotations are considered as potential controls, and we show that a proper synchronization of forcing frequency with the natural vortex shedding frequency can greatly influence the flow. The results here indicate that using moving boundary controls for such systems may provide a feasible mechanism for flow control.

Burns, John A.↗

NASA NTRS1991

Probabilistic load simulation: Code development status

The objective of the Composite Load Spectra (CLS) project is to develop generic load models to simulate the composite load spectra that are included in space propulsion system components. The probabilistic loads thus generated are part of the probabilistic design analysis (PDA) of a space propulsion system that also includes probabilistic structural analyses, reliability, and risk evaluations. Probabilistic load simulation for space propulsion systems demands sophisticated probabilistic methodology and requires large amounts of load information and engineering data. The CLS approach is to implement a knowledge based system coupled with a probabilistic load simulation module. The knowledge base manages and furnishes load information and expertise and sets up the simulation runs. The load simulation module performs the numerical computation to generate the probabilistic loads with load information supplied from the CLS knowledge base.

Newell, J. F.↗

NASA NTRS1992

Dilatation-dissipation corrections for advanced turbulence models

This paper analyzes dilatation-dissipation based compressibility corrections for advanced turbulence models. Numerical computations verify that the dilatation-dissipation corrections devised by Sarkar and Zeman greatly improve both the k-omega and k-epsilon model predicted effect of Mach number on spreading rate. However, computations with the k-gamma model also show that the Sarkar/Zeman terms cause an undesired reduction in skin friction for the compressible flat-plate boundary layer. A perturbation solution for the compressible wall layer shows that the Sarkar and Zeman terms reduce the effective von Karman constant in the law of the wall. This is the source of the inaccurate k-gamma model skin-friction predictions for the flat-plate boundary layer. The perturbation solution also shows that the k-epsilon model has an inherent flaw for compressible boundary layers that is not compensated for by the dilatation-dissipation corrections. A compressibility modification for k-gamma and k-epsilon models is proposed that is similar to those of Sarkar and Zeman. The new compressibility term permits accurate predictions for the compressible mixing layer, flat-plate boundary layer, and a shock separated flow with the same values for all closure coefficients.

Wilcox, David C.↗

NASA NTRS1992

On the coupling between a supersonic boundary layer and a flexible surface

The coupling between a two-dimensional, supersonic, laminar boundary layer and a flexible surface is studied using direct numerical computations of the Navier-Stokes equations coupled with the plate equation. The flexible surface is forced to vibrate by plane acoustic waves at normal incidence emanated by a sound source located on the side of the flexible surface opposite to the boundary layer. The effect of the source excitation frequency on the surface vibration and boundary layer stability is analyzed. We find that, for frequencies near the fifth natural frequency of the surface or lower, large disturbances are introduced in the boundary layer which may alter its stability characteristics. The interaction between a stable two-dimensional disturbance of Tollmien-Schlichting (TS) type with the vibrating surface is also studied. We find that the disturbance level is higher over the vrating flexible surface than that obtained when the surface is rig id, which indicates a strong coupling between flow and structure. However, in the absence of the sound source the disturbance level over the rigid and flexible surfaces are identical. This result is due to the high frequency of the TS disturbance which does not couple with the flexible surface.

Frendi, Abdelkader↗

NASA NTRS1993

An instability associated with a magnetosphere-disk interaction

The evolution of a thin accretion disk surrounding a rapidly rotating magnetosphere is considered. By taking account of the variations of the magnetospheric boundary in response to the conditions at the inner edge of the disk, we find from linear analysis and numerical computation that the accretion disk can become unstable. Mass can be accreted by the central object in a cyclic fashion, with the cycle involving the storage and release of mass in the inner parts of the disk. The physical origin of the instability is associated with the variations of the magnetospheric boundary about corotation. The recurrence time scale of the cycle can vary by several orders of magnitude depending on the details of the conditions at the magnotosphere. The possible applicability of this instability process to the 'rapid burster' MXB 1730-335 is briefly discussed.

Spruit, H. C.↗

NASA NTRS1993

Further development towards a new virtual-pulse time integral methodology for general nonlinear transient thermal analysis

New developments describing the theoretical basis towards an effective virtual-pulse time integral procedure are presented for general nonlinear transient heat transfer problems. To validate the proposed methodology of computation, numerical test examples are given and comparisons are drawn with the implicit second-order accurate Crank-Nicolson technique. The proposed method shows superior or improved accuracy and stability characteristics for the models tested.

Tamma, K. K.↗

NASA NTRS1993

Centrifuge in space fluid flow visualization experiment

A prototype flow visualization system is constructed to examine buoyancy driven flows during centrifugation in space. An axial density gradient is formed by imposing a thermal gradient between the two ends of the test cell. Numerical computations for this geometry showed that the Prandtl number plays a limited part in determining the flow.

Arnold, William A.↗

NASA NTRS1992

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, thin-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption have been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5-deg semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers have been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5-deg circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.

Liu, C. H.↗

NASA NTRS1993

Neptune's magnetic field - Calculation of field geometric invariants derived from the I8E1 GSFC/BRI model

L shell values along the Voyager 2 encounter trajectory and those associated with the N1 through N6 moons and N1R through N6R rings of Neptune are computed numerically on the basis of a simplified description of the Neptunian magnetic field derived from the Goddard Space Flight Center/Bartol Research Institute I8E1 model, which includes internal terms up to and including the octupole (but no external terms). Like Uranus, the large tilt between the dipole term and the rotation axis causes the moons and rings to sweep a very large range of L shells. Their orbital motion introduces additional periodicities, causing the maxima and minima in L space to vary systematically with time.

Acuna, M. H.↗

NASA NTRS1993

Experimental and numerical investigation of supersonic turbulent flow in an annular duct

Experimental and numerical results are presented for developing supersonic turbulent flow in an annular duct formed by a circular centerbody and outer shroud. The experimental results are based on data taken in a new flow facility that was designed to generate a shock-free, supersonic annular flow. Numerical computations were performed using the Baldwin-Lomax turbulence model for comparison with experimentally measured profiles. The results demonstrate that computed and measured profiles are in excellent agreement, so that studies can now be conducted of shock wave/boundary layer interaction phenomena within the duct, such as those induced by changes in downstream duct geometry or by the placement of struts between the duct walls.

Williams, K. E.↗

NASA NTRS1993

Coronal heating by the resonant absorption of Alfven waves - Importance of the global mode and scaling laws

Numerical simulations of the MHD equations for a fully compressible, low-beta, resistive plasma are used to study the resonance absorption process for the heating of coronal active region loops. Comparisons with more approximate analytic models show that the major predictions of the analytic theories are, to a large extent, confirmed by the numerical computations. The simulations demonstrate that the dissipation occurs primarily in a thin resonance layer. Some of the analytically predicted features verified by the simulations are (a) the position of the resonance layer within the initial inhomogeneity; (b) the importance of the global mode for a large range of loop densities; (c) the dependence of the resonance layer thickness and the steady-state heating rate on the dissipation coefficient; and (d) the time required for the resonance layer to form. In contrast with some previous analytic and simulation results, the time for the loop to reach a steady state is found to be the phase-mixing time rather than a dissipation time. This disagreement is shown to result from neglect of the existence of the global mode in some of the earlier analyses. The resonant absorption process is also shown to behave similar to a classical driven harmonic oscillator.

Steinolfson, Richard S.↗

NASA NTRS1924

Some tables of the factor of apparent additional mass

This note, prepared for publication by the National Advisory Committee for Aeronautics, is a collection of the tables of the factor of apparent mass that have been published up to now. The theory of the motion of solids in a perfect fluid is of the greatest value for the study of most aerodynamic problems, and the additional apparent mass of an immersed solid is the most important characteristic for such theoretical numerical computations. It will therefore be helpful to have the most important values of the apparent mass - for some elementary cases - collected in a convenient form.

Munk, Max M↗

NASA NTRS1938

A study of the torque equilibrium of an autogiro rotor

Two improvements have been made in the method developed in NACA Reports nos. 487 and 591 for the estimation of the inflow velocity required to overcome a given decelerating torque in an autogiro rotor. At low tip-speed ratios, where the assumptions necessary for the analytical integrations of the earlier papers are valid, the expressions therein derived are greatly simplified by combining and eliminating terms with a view of minimizing the numerical computations required. At high tip-speed ratios, by means of charts based on graphical integrations, errors inherent in the assumptions associated with the analytical method are largely eliminated. The suggested method of estimating the inflow velocity presupposes a knowledge of the decelerating torque acting on the rotor; all available full-scale experimental information on this subject is included.

Bailey, F J , Jr↗

NASA NTRS1947

Isolated and cascade airfoils with prescribed velocity distribution

An exact solution of the problem of designing an airfoil with a prescribed velocity distribution on the suction surface in a given uniform flow of an incompressible perfect fluid is obtained by replacing the boundary of the airfoil by vortices. By this device, a method of solution is developed that is applicable both to isolated airfoils and to airfoils in cascade. The conformal transformation of the designed airfoil into a circle can then be obtained and the velocity distribution at any angle of attack computed. Numerical illustrations of the method are given for the airfoil in cascade.

Goldstein, Arthur W↗

NASA NTRS1952

An empirically derived basis for calculating the area, rate, and distribution of water-drop impingement on airfoils

An empirically derived basis for predicting the area, rate, and distribution of water-drop impingement on airfoils of arbitrary section is presented. The concepts involved represent an initial step toward the development of a calculation technique which is generally applicable to the design of thermal ice-prevention equipment for airplane wing and tail surfaces. It is shown that sufficiently accurate estimates, for the purpose of heated-wing design, can be obtained by a few numerical computations once the velocity distribution over the airfoil has been determined. The calculation technique presented is based on results of extensive water-drop trajectory computations for five airfoil cases which consisted of 15-percent-thick airfoils encompassing a moderate lift-coefficient range. The differential equations pertaining to the paths of the drops were solved by a differential analyzer.

Bergrun, Norman R↗

NASA NTRS1990

An alternative formulation of the global sensitivity equations

To optimize the performance of any system, the sensitivity derivatives of the system's output variables with respect to its input variables must be readily available. It is also desirable that these derivatives be inexpensive to calculate as the optimization process requires many evaluations of the output variables and their derivatives. Optimization methods that have been developed for use in automated structural design programs may not be extended for use in integrated multidisciplinary design programs until adequate means of calculating accurate sensitivity derivatives of complex, internally coupled systems have been developed. Until the development of the Global Sensitivity Equations (GSE), the only method of determining the sensitivity derivatives of coupled systems has been by using finite differences. Analytical or semi-analytical derivatives do not exist as there is no analytical solution to the coupled problem. Also, difficulties arise because the finite difference method is expensive as the system has to iterate to a converged solution for each incremental input variable. The method may not be accurate, and the choice of the input variable increment may cause the difference in the output variable to be insignificant compared to computer numerical error if the choice is too small, or the process may not predict the true value of the output variable if the increment is too large. The GSE allow the system's sensitivity derivatives to be calculated as functions of the component subsystem's (local) sensitivity derivatives. These local sensitivity derivatives are calculated from specifically decoupled subsystems, whereas the GSE account for total system coupling. Since the subsystems are decoupled, it may be possible for the local derivatives to be calculated by analytical or semi-analytical methods, which generally reduce cost and improve accuracy. Several academic problems have been solved using GSE and have demonstrated encouraging results.

James, Benjamin B.↗

NASA NTRS1993

Sloshing dynamics on rotating helium dewar tank

The generalized mathematical formulation of sloshing dynamics for partially filled liquid of cryogenic superfluid helium II in dewar containers driven by both the gravity gradient and jitter accelerations applicable to scientific spacecraft which is eligible to carry out spinning motion and/or slew motion for the purpose to perform scientific observation during the normal spacecraft operation are investigated. An example is given with Gravity Probe-B (GP-B) spacecraft which is responsible for the sloshing dynamics. The jitter accelerations include slew motion, spinning motion, atmospheric drag on the spacecraft, spacecraft attitude motions arising from machinery vibrations, thruster firing, pointing control of spacecraft, crew motion, etc. Explicit mathematical expressions to cover these forces acting on the spacecraft fluid systems are derived. The numerical computation of sloshing dynamics were based on the non-inertia frame spacecraft bound coordinate, and solve time dependent, three-dimensional formulations of partial differential equations subject to initial and boundary conditions. The explicit mathematical expressions of boundary conditions to cover capillary force effect on the liquid vapor interface in microgravity environments are also derived. The formulations of fluid moment and angular moment fluctuations in fluid profiles induced by the sloshing dynamics, together with fluid stress and moment fluctuations exerted on the spacecraft dewar containers were derived. Results were widely published in the open journals.

Hung, R. J.↗