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The calculation of flow fields past aircraft configuration at flight Reynolds numbers is considered. Progress in devising accurate and efficient numerical methods, in understanding and modeling the physics of turbulence, and in developing reliable and powerful computer hardware is discussed. Emphasis is placed on efficient solutions to the Navier-Stokes equations.
The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectra method with up to about 10 to the 7th power grid points. Periodic spanwise and stream-wise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is examined and compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.
The computer code ALGAE (algorithms for the gas equations) treats incompressible, thermally expandable, or locally compressible flows in complicated two-dimensional flow regions. The solution method, finite differencing schemes, and basic modeling of the field equations in ALGAE are applicable to engineering design settings of the type found in Stirling cycle engines. The use of ALGAE to model multiple components of the space power research engine (SPRE) is reported. Videotape computer simulations of the transient behavior of the working gas (helium) in the heater-regenerator-cooler complex of the SPRE demonstrate the usefulness of such a program in providing information on thermal and hydraulic phenomena in multiple component sections of the SPRE.
Shape and inner flow of a tridimensional spark are studied. The spark is created by focusing a laser beam in a gas. A second order fully non-linear equation is derived for the radial velocity on the axis of symmetry in the neighborhood of the origin. Solutions to that equation display the existence of a forbidden region near the focus, thus indicating the limits of applicability of a small perturbation solution.
A three-dimensional potential analysis has been formulated and applied to the inviscid flow over a turbofan forced mixer. The method uses a unique small disturbance formulation to analytically uncouple the circumferential flow from the radial and axial flow problem, thereby reducing the analysis to the solution of a series of axisymmetric problems. These equations are discretized using a flux volume formulation along a Cartesian grid. The method extends earlier applications of the Cartesian method to complex cambered geometries. The effects of power addition are also included within the potential formulation. Good agreement is obtained with an alternate small disturbance analysis for a symmetric mixer in a planar duct. In addition calculations showing pressure distributions and induced secondary vorticity fields are presented for practical turbofan mixer configurations, and where possible, comparison has been made with available experimental data.
A three-dimensional potential analysis (FLOMIX) was formulated and applied to the inviscid flow over a turbofan foced mixer. The method uses a small disturbance formulation to analytically uncouple the circumferential flow from the radial and axial flow problem, thereby reducing the analysis to the solution of a series of axisymmetric problems. These equations are discretized using a flux volume formulation along a Cartesian grid. The method extends earlier applications of the Cartesian method to complex cambered geometries. The effects of power addition are also included within the potential formulation. Good agreement is obtained with an alternate small disturbance analysis for a high penetration symmetric mixer in a planar duct. In addition, calculations showing pressure distributions and induced secondary vorticity fields are presented for practical trubofan mixer configurations, and where possible, comparison was made with available experimental data. A detailed description of the required data input and coordinate definition is presented along with a sample data set for a practical forced mixer configuration. A brief description of the program structure and subroutines is also provided.
This document describes progress in the development of finite element codes for the prediction of near and far field acoustic radiation from the inlet and aft fan ducts of turbofan engines. The report consists of nine papers which have appeared in archival journals and conference proceedings, or are presently in review for publication. Topics included are: 1. Aft Fan Duct Acoustic Radiation; 2. Mapped Infinite Wave Envelope Elements for Acoustic Radiation in a Uniformly Moving Medium; 3. A Reflection Free Boundary Condition for Propagation in Uniform Flow Using Mapped Infinite Wave Envelope Elements; 4. A Numerical Comparison Between Multiple-Scales and FEM Solution for Sound Propagation in Lined Flow Ducts; 5. Acoustic Propagation at High Frequencies in Ducts; 6. The Boundary Condition at an Impedance Wall in a Nonuniform Duct with Potential Flow; 7. A Reverse Flow Theorem and Acoustic Reciprocity in Compressible Potential Flows; 8. Reciprocity and Acoustics Power in One Dimensional Compressible Potential Flows; and 9. Numerical Experiments on Acoustic Reciprocity in Compressible Potential Flows.
This paper develops the mathematical relations for the Virtual Kinetic Model as an improvement over the vectorial model developed earlier. The model solution described provides the most energy efficient means of cooling gears, i.e., it requires the least pressure or pumping power to distribute the coolant onto the tooth surface. Further, this nozzle orientation allows impingement to the root of the tooth if needed and provides the most cooling control when compared to into-mesh and out-of-mesh cooling.
This paper develops the mathematical relations for the Virtual Kinetic Model as an improvement over the vectorial model developed earlier. The model solution described provides the most energy efficient means of cooling gears, i.e., it requires the least pressure or pumping power to distribute the coolant onto the tooth surface. Further, this nozzle orientation allows impingement to the root of the tooth if needed and provides the most cooling control when compared to into-mesh and out-of-mesh cooling.
The flow inside a model exhaust configuration was studied using both experimental and computational techniques. The hardware was tested at the NASA Lewis Research Center's Powered Lift Facility at tailpipe total pressure to ambient static pressure ratios ranging from 1.0 to 5.0. The flow simulations were obtained using the two 3-D Navier-Stokes CFD codes run on the Lewis Cray Y-MP computer. Both codes produced oscillatory solutions due to the inflow boundary condition reflecting acoustic waves. The CFD solutions correctly predicted the flow separation along the inside elbow of the takeoff and also along the walls of the ventral duct. Mass flow rates were overpredicted due to underprediction of the turbulent energy dissipation and subsequent total pressure loss.
In order to have confidence in a numerical method, the verification of its reproduction of known benchmark analytic solutions for simple model problems is of great importance. Attention is presently given to a novel benchmarking procedure for numerical models of high speed, reactive 2D flows. The procedure is illustrated by comparing asymptotic and numerical solutions for oblique detonations in which an attached oblique shock is followed by an exothermic reaction with a thick reaction zone.
Low-frequency, unsteady, lifting-line theory is used to characterize the energetics and optimum motion of an unswept rigid wing oscillating harmonically in an inviscid, incompressible flow. The energetics calculations account for the leading edge suction force, the power absorbed in the wing oscillations, and the energy loss rate produced by vortex shedding. Optimization is achieved by minimizing the average energy loss rate in relation to a given thrust, and a unique solution is found in the three dimensional case for low, reduced frequencies. The two-dimensional solution is nonunique, a condition which is examined in terms of the normal modes of the energy loss rate matrix. An invisible mode with a hydrodynamic efficiency of 100 pct is obtained in the two-dimensional case, causing the nonuniqueness of the solution by yielding no fixed positive thrust through perfect unsteady feathering.
Computational fluid dynamics (CFD) has matured to the point where it is becoming ubiquitous in the design and analysis of aerospace vehicles and their propulsion systems. The current state-of-the-art of CFD in hypersonic propulsion design and analysis as well as a historical perspective of its development over the last 50 years is presented. The current state-of-the-art for the design of finite rate chemically reacting turbulent hypersonic flow is shown to currently be Reynolds averaged simulations (RAS) where the Reynolds averaged Navier-Stokes (RAS) equations are solved to obtain steady state solutions. An overview of the physical modeling techniques employed by RAS for the simulation of hypersonic chemically reacting flow are presented. However, scale resolving simulation techniques, such as detached eddy simulation (DES), large eddy simulations (LES), hybrid RAS/LES and direct numerical simulations (DNS), are becoming becoming powerful tools for point design analysis. One example of such a scale resolving technique, hybrid RAS/LES, will be briefly described as well as how it can be used to help address model form uncertainties in RAS.
This paper describes the effort by the Texas Engineering Experiment Station (TEES) and Honeywell for NASA to design and test a pre-flight prototype pump for use in the Extra-vehicular activity (EVA) portable life support subsystem (PLSS). Major design decisions were driven by the need to reduce the pump s mass, power, and volume compared to the existing PLSS pump. In addition, the pump must accommodate a much wider range of abnormal conditions than the existing pump, including vapor/gas bubbles and increased pressure drop when employed to cool two suits simultaneously. A positive displacement, external gear type pump was selected because it offers the most compact and highest efficiency solution over the required range of flow rates and pressure drops. An additional benefit of selecting a gear pump design is that it is self priming and capable of ingesting non-condensable gas without becoming air locked. The chosen pump design consists of a 28 V DC, brushless, sealless, permanent magnet motor driven, external gear pump that utilizes a Honeywell development that eliminates the need for magnetic coupling. Although the planned flight unit will use a sensorless motor with custom designed controller, the pre-flight prototype to be provided for this project incorporates Hall effect sensors, allowing an interface with a readily available commercial motor controller. This design approach reduced the cost of this project and gives NASA more flexibility in future PLSS laboratory testing. The pump design was based on existing Honeywell designs, but incorporated features specifically for the PLSS application, including all of the key features of the flight pump. Testing at TEES verified that the pump meets the design requirements for range of flow rates, pressure drop, power consumption, working fluid temperature, operating time, gas ingestion , and restart capability under both ambient and vacuum conditions. The pump operated between 40 and 240 lbm/hr flowrate, 35 to 100 F pump temperature range, and 5 to 10 psid pressure rise. Power consumption of the pump controller at the nominal operating point in both ambient and vacuum conditions was 9.5 W, which was less than the 12 W predicted. Gas ingestion capabilities were tested by injecting 100 cc of air into the fluid line; the pump operated normally throughout this test. The test results contained a number of anomalies, specifically power increases and a few flow stoppages, that prompted TEES and Honeywell to disassemble and inspect the pump. Inspection indicated contamination in the pump and fit issues may have played roles in the observed anomalies. Testing following reassembly indicated that the performance of the pump 1) matched both the predicted performance values, 2) the performance values measured prior to disassembly, and 3) was free of the anomalies noted in the pre-disassembly testing.
The Charney problem for baroclinic instability involves the quasi-geostrophic instability of a zonal flow on a beta plane where the zonal flow is characterized by a constant vertical shear. The atmosphere is non-Boussinesq and continuous. The solution of this problem involves confluent hypergeometric functions, and the mathematical difficulty of the problem has precluded extracting simple results of generality. It is shown that there exists very simple, powerful approximate result for the growth rate of the most rapidly growing instability, viz., that this growth rate is linearly proportional to the surface meridional temperature gradient. The coefficient of proportionality is also easily determined. The result extends to substantially more general profiles than those in the Charney problem.
In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.
Two major episodes of heliospheric VLF emissions near 3 kHz have been observed by the Voyager spacecraft in 1983/84 and 1992/3. This higher-frequency component is apparently triggered by solar wind transients with sufficiently large spatial extents and energies to continue to propagate as shocks in the heliosheath. Entrainment of previously unshocked material and changed flow conditions in the heliosheath both tend to slow the shock propagation. The shock evolution is not self-similar. Rather, it is intermediate to two blast-wave similarity solutions in the moving solar wind frame. In one solution the shock moves as time to the 2/3 power and in the other as time to the 4/5 power. Using these models, the shock/Forbush decrease observed at Voyager 2 in September, 1991 and the turn-on of the 1992 emission is consistent with an emission region distance of approximately 130 AU (assuming no additional slowing of the shock in the heliosheath). If the termination shock was at approximately 70 AU when the transient shock collided with it, the true distance to the source region was probably closer to approximately 115 AU.
Two major episodes of heliospheric VLF emissions near 3 kHz have been observed by the Voyager spacecraft in 1983-1984 and 1992-1993. This higher-frequency component is apparently triggered by solar wind transients with sufficiently large spatial extents and energies to continue to propagate as shocks in the heliosheath. Entrainment of previously unshocked material and changed flow conditions in the heliosheath both tend to slow the shock propagation. The shock evolution is not self-similar. Rather, it is intermediate to two blast-wave similarity solutions in the moving solar wind frame. In one solution the shock moves as time to the 2/3 power and in the other as time to the 4/5 power. Using these models, the shock/Forbush decrease observed at Voyager 2 in September, 1991 and the turn-on of the 1992 emission is consistent with an emission region distance of approx. 130 AU (assuming no additional slowing of the shock in the heliosheath). If the termination shock was at approx. 70 AU when the transient shock collided with it, the true distance to the source region was probably closer to approx. 115 AU.