Sub-Alfvenic duct flow with a nonuniform magnetic field.
Nonuniformity of magnetic field effect on steady flow of incompressible inviscid electrically conducting fluid in duct, considering Reynolds and Alfven numbers
Peyret, R.↗
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The evolution of cooling flows. II - Galaxies and galaxy formation
Self-similar solutions are presented for the idealized case of a spherical galaxy with a singular isothermal gravitational potential where the ISM is built up from mass loss by stars or by accretion of external gas. For the former case, where a galaxy initially devoid of gas obtains gas from stellar evolution, steady flow only is obtained inside the cooling radius. Several possibilities occur and are discussed for flow outside the cooling radius. For the case involving infall of external gas, the nature of the flow depends on the initial density of the infalling gas. At high density, only a cold, unshocked flow is possible. At low density, the flow is accelerated inward, is heated in a shock front, approaches a hydrostatic state, passes through the cooling radius and enters a steady subsonic cooling flow, and finally passes through a sonic point. The effects of radiative cooling are discussed.
Chevalier, Roger A.↗
Flow and arrest in stressed granular materials
Flowing granular materials often abruptly arrest if not driven by sufficient applied stresses. Such abrupt cessation of motion can be economically expensive in industrial materials handling and processing, and is significantly consequential in intermittent geophysical phenomena such as landslides and earthquakes. Using discrete element simulations, we calculate states of steady flow and arrest for granular materials under the conditions of constant applied pressure and shear stress, which are also most relevant in practice. Here the material can dilate or compact, and flow or arrest, in response to the applied stress. Our simulations highlight that under external stress, the intrinsic response of granular materials is characterized by uniquely-defined steady states of flow or arrest, which are highly sensitive to interparticle friction. While the flowing states can be equivalently characterized by volume fraction, coordination number or internal stress ratio, to characterize the states of shear arrest, one needs to also consider the structural anisotropy in the contact network. Here, we highlight the role of dilation in the flow-arrest transition, and discuss our findings in the context of rheological transitions in granular materials.
36 MATERIALS SCIENCE↗
Value contamination avoidance devices
Mechanical redesign methods were used to minimize contamination damage of conventional fluid components and a contamination separator device was developed for long term reusable space vehicles. These were incorporated into an existing 50.8 mm poppet valve and tested for damage tolerance in a full size open loop flow system with gaseous and liquid nitrogen. Cyclic and steady flow conditions were tested with particles of 125 to 420 micrometers aluminum oxide dispersed in the test fluids. Nonflow life tests (100,000 cycles) were made with two valve configurations in gaseous hydrogen. The redesigned valve had an acceptable cycle life and improved tolerance to contamination damage when the primary sealing surfaces were coated with thin coatings of hard plastic (Teflon S and Kynar). Analytical studies and flow testing were completed of four different versions of the separator. overall separation efficiencies in the 55-90% range were measured with these non-optimum configurations.
Endicott, D. L.↗
Evolution of shock-induced pressure on a flat-face/flat-base body and afterbody flow separation
The time-dependent, compressible Reynolds-averaged, Navier-Stokes equations are applied to solve an axisymmetric supersonic flow around a flat-face/flat-base body with and without a sting support. Important transient phenomena, not yet well understood, are investigated, and the significance of the present solution to the phenomena is discussed. The phenomena, described in detail, are as follows: the transient formation of the bow and recompression shock waves; the evolution of a pressure buildup due to diffraction of the incident shock wave in the forebody and afterbody regions, including the luminosity accompanying the pressure buildup; the separation of the flow as influenced by pressure buildup; the location of the separation and the reattachment points; and the transient period of the shock-induced base flow. The important influence of the nonsteady (transient) and steady flow on the aerodynamic characteristics, radiative heat transfer, and, thus, on the survivability or safeguard problems for an aircraft fuselage, missile, or planetary entry probe at very high flight speeds is described.
Yoshikawa, K. K.↗
Application of a linearized unsteady aerodynamic analysis to standard cascade configurations
A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the linearized unsteady aerodynamic response to prescribed blade motions, has been applied to five cascade configurations. These include the first, fifth, eighth and ninth standard configurations proposed as a result of the Second International Symposium on Aeroelasticity in Turbomachines and a NASA Lewis flutter cascade. Selected results from this study, including comparisons between analytical predictions and the experimental measurements submitted for three of the foregoing configurations, are described. The correlation between theory and experiment for the first standard configuration (a compressor cascade operating at low Mach number and frequency) is quite good. Moreover, the predictions and measurements for the NASA Lewis cascade of symmetric biconvex airfoils show good qualitative agreement. However, wide discrepancies exist between the theoretical predictions and the experimental measurements for the fifth standard configuration (a subsonic transonic fan tip cascade). These can be partially attributed to conditions being imposed in the experiment which differ from those commonly used in unsteady aerodynamic analyses.
Verdon, J. M.↗
On the application of a linearized unsteady potential-flow analysis to fan-tip cascades
A linearized potential flow analysis, which accounts for the effects of nonuniform steady flow phenomena on the unsteady response to prescribed blade motions, has been applied to five two-dimensional cascade configurations. These include a flat-plate cascade and three cascades which are representative of the tip sections of current fan designs. Here the blades are closely spaced, highly staggered, and operate at low mean incidence. The fifth configuration is a NASA Lewis cascade of symmetric biconvex airfoils for which experimental measurements are available. Numerical solutions are presented that clearly illustrate the effects and importance of blade geometry and mean blade loading on the linearized unsteady response at high subsonic inlet Mach number and high blade-vibrational frequency. In addition, a good qualitative agreement is shown between the analytical predictions and experimental measurements for the cascade of symmetric biconvex airfoils. Finally, recommendations on the research needed to extend the range of application of linearized unsteady aerodynamic analyses are provided.
Usab, W. J., Jr.↗
Visualizing Time-Varying Phenomena In Numerical Simulations Of Unsteady Flows
Streamlines, contour lines, vector plots, and volume slices (cutting planes) are commonly used for flow visualization. These techniques are sometimes referred to as instantaneous flow visualization techniques because calculations are based on an instant of the flowfield in time. Although instantaneous flow visualization techniques are effective for depicting phenomena in steady flows,they sometimes do not adequately depict time-varying phenomena in unsteady flows. Streaklines and timelines are effective visualization techniques for depicting vortex shedding, vortex breakdown, and shock waves in unsteady flows. These techniques are examples of time-dependent flow visualization techniques, which are based on many instants of the flowfields in time. This paper describes the algorithms for computing streaklines and timelines. Using numerically simulated unsteady flows, streaklines and timelines are compared with streamlines, contour lines, and vector plots. It is shown that streaklines and timelines reveal vortex shedding and vortex breakdown more clearly than instantaneous flow visualization techniques.
Lane, David A.↗
Nonisentropic unsteady three dimensional small disturbance potential theory
Nonisentropic modifications to the three-dimensional transonic small disturbance (TSD) theory, which allows for more accurate modeling of transonic flow fields, are described. The modified flux equation and entropy corrections are presented; the Engquist-Osher differencing (1980) is added to the solution algorithm in order to eliminate the velocity overshoots upstream of shocks. The modified theory is tested in the XTRAN3S finite difference computer code. Steady flows over a rectangular NACA 0012 wing with an aspect ratio of 12 are calculated and compared to Euler equation solutions; good correlation is observed between the data and the modified TSD theory provides more accurate data, particularly for the lift curve slope. The nonisentropic theory is evaluated on an RAE tailplane model for steady and unsteady flows and the modified theory results agree well with the experimental data.
Gibbons, M. D.↗
Linearized Aeroelastic Solver Applied to the Flutter Prediction of Real Configurations
A fast-running unsteady aerodynamics code, LINFLUX, was previously developed for predicting turbomachinery flutter. This linearized code, based on a frequency domain method, models the effects of steady blade loading through a nonlinear steady flow field. The LINFLUX code, which is 6 to 7 times faster than the corresponding nonlinear time domain code, is suitable for use in the initial design phase. Earlier, this code was verified through application to a research fan, and it was shown that the predictions of work per cycle and flutter compared well with those from a nonlinear time-marching aeroelastic code, TURBO-AE. Now, the LINFLUX code has been applied to real configurations: fans developed under the Energy Efficient Engine (E-cubed) Program and the Quiet Aircraft Technology (QAT) project. The LINFLUX code starts with a steady nonlinear aerodynamic flow field and solves the unsteady linearized Euler equations to calculate the unsteady aerodynamic forces on the turbomachinery blades. First, a steady aerodynamic solution is computed for given operating conditions using the nonlinear unsteady aerodynamic code TURBO-AE. A blade vibration analysis is done to determine the frequencies and mode shapes of the vibrating blades, and an interface code is used to convert the steady aerodynamic solution to a form required by LINFLUX. A preprocessor is used to interpolate the mode shapes from the structural dynamics mesh onto the computational fluid dynamics mesh. Then, LINFLUX is used to calculate the unsteady aerodynamic pressure distribution for a given vibration mode, frequency, and interblade phase angle. Finally, a post-processor uses the unsteady pressures to calculate the generalized aerodynamic forces, eigenvalues, an esponse amplitudes. The eigenvalues determine the flutter frequency and damping. Results of flutter calculations from the LINFLUX code are presented for (1) the E-cubed fan developed under the E-cubed program and (2) the Quiet High Speed Fan (QHSF) developed under the Quiet Aircraft Technology project. The results are compared with those obtained from the TURBO-AE code. A graph of the work done per vibration cycle for the first vibration mode of the E-cubed fan is shown. It can be seen that the LINFLUX results show a very good comparison with TURBO-AE results over the entire range of interblade phase angle. The work done per vibration cycle for the first vibration mode of the QHSF fan is shown. Once again, the LINFLUX results compare very well with the results from the TURBOAE code.
Reddy, Tondapu S.↗
Steady incompressible potential flow around lifting bodies immersed in a fluid
The refinement was investigated of a method for evaluating the pressure distribution on a body surface of arbitrary shape in incompressible flow. The solution was obtained in terms of the velocity potential, through numerical approximations which require the use of a high speed digital computer. The box method and the modal method are described in detail, and were applied to a very thin, rectangular wing in incompressible, steady flow. The box method is found to be more practical as it is applicable to more general geometries (the modal method requires a new set of functions for each geometry), and requires less computer time (fifty percent of that required by the modal method for the same problem).
Chiuchiolo, E. A.↗
Supersonic Stall Flutter of High Speed Fans
An analytical model is developed for predicting the onset of supersonic stall bending flutter in axial flow compressors. The analysis is based on a modified two dimensional, compressible, unsteady actuator disk theory. It is applied to a rotor blade row by considering a cascade of airfoils whose geometry and dynamic response coincide with those of a rotor blade element at 85 percent of the span height (measured from the hub). The rotor blades are assumed to be unshrouded (i.e., free standing) and to vibrate in their first flexural mode. The effects of shock waves and flow separation are included in the model through quasi-steady, empirical, rotor total-pressure-loss and deviation-angle correlations. The actuator disk model predicts the unsteady aerodynamic force acting on the cascade blading as a function of the steady flow field entering the cascade and the geometry and dynamic response of the cascade. Calculations show that the present model predicts the existence of a bending flutter mode at supersonic inlet Mach numbers. This flutter mode is suppressed by increasing the reduced frequency of the system or by reducing the steady state aerodynamic loading on the cascade. The validity of the model for predicting flutter is demonstrated by correlating the measured flutter boundary of a high speed fan stage with its predicted boundary. This correlation uses a level of damping for the blade row (i.e., the log decrement of the rotor system) that is estimated from the experimental flutter data. The predicted flutter boundary is shown to be in good agreement with the measured boundary.
Adamczyk, J. J.↗
Unsteady transonic small disturbance theory with strong shock waves
A theory to correct the transonic small disturbance (TSD) equation to treat strong shock waves in unsteady flow is developed. The technique involves the addition of higher order terms, which are formally of negligible magnitude, to the low frequency TSD equation. These terms are then chosen such that any shock waves in the flow have strengths approximately equal to the appropriate Rankine-Hugoniot shock strength. Two correcting approaches are investigated. The first is to derive a correction for the mean steady flow and then simply use this corrected form for oscillatory flows. The second is to derive a correction for both steady and oscillatory parts of the flow. This second development is the most satisfactory and comparisons of the present results with Euler equation results are generally favorable, particularly regarding shock location, although there are some discrepancies in the pressure distribution in the leading edge region.
Kerlick, G. D.↗
A Comparison of Linear Solvers for Resolving Flow in Three-Dimensional Discrete Fracture Networks
We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.
58 GEOSCIENCES↗
Total pressure averaging in pulsating flows
A number of total-pressure tubes were tested in a non-steady flow generator in which the fraction of period that pressure is a maximum is approximately 0.8, thereby simulating turbomachine-type flow conditions. Most of the tubes indicated a pressure which was higher than the true average. Organ-pipe resonance which further increased the indicated pressure was encountered within the tubes at discrete frequencies. There was no obvious combination of tube diameter, length, and/or geometry variation used in the tests which resulted in negligible averaging error. A pneumatic-type probe was found to measure true average pressure, and is suggested as a comparison instrument to determine whether nonlinear averaging effects are serious in unknown pulsation profiles. The experiments were performed at a pressure level of 1 bar, for Mach number up to near 1, and frequencies up to 3 kHz.
Krause, L. N.↗
Computational analysis of flow in 3D propulsive transition ducts
A numerical analysis of fully three dimensional, statistically steady flows in propulsive transition ducts being considered for use in future aircraft of higher maneuverability is investigated. The purpose of the transition duct is to convert axisymmetric flow from conventional propulsion systems to that of a rectangular geometry of high aspect ratio. In an optimal design, the transition duct would be of minimal length in order to reduce the weight penalty, while the geometrical change would be gradual enough to avoid detrimental flow perturbations. Recent experiments conducted at the Propulsion Aerodynamics Branch have indicated that thrust losses in ducts of superelliptic cross-section can be surprisingly low, even if flow separation occurs near the divergent walls. In order to address the objective of developing a rational design procedure for optimal transition ducts, it is necessary to have available a reliable computational tool for the analysis of flows achieved in a sequence of configurations. Current CFD efforts involving complicated geometries usually must contend with two separate but interactive aspects: namely, grid generation and flow solution. The first two avenues of the present investigation were comprised of suitable grid generation for a class of transition ducts of superelliptic cross-section, and the subsequent application of the flow solver PAB3D to this geometry. The code, PAB3D, was developed as a comprehensive tool for the solution of both internal and external high speed flows. The third avenue of investigation has involved analytical formulations to aid in the understanding of the nature of duct flows, and also to provide a basis of comparison for subsequent numerical solutions. Numerical results to date include the generation of two preliminary grid systems for duct flows, and the initial application of PAB3D to the corresponding geometries, which are of the class tested experimentally.
Sepri, Paavo↗
Pressure sensitive gas flow meter
Regulator, which increases flow area in discrete steps as upstream pressure falls, maintains steady flow rate of gas as the supply pressure from storage system decreases.
Hallum, C. E.↗
Computation of subsonic and transonic flow about lifting rotor blades
An inviscid, nonconservative, three-dimensional potential flow code has been developed for computing the quasi-steady flow about an isolated lifting rotor blade. Calculations from the code were compared with chordwise pressure measurements obtained in a wind tunnel on a nonlifting rotor at transonic tip speeds at advance ratios from 0.40 to 0.55. The overall agreement between theoretical calculations and experiment was good. To illustrate the early capability of the program, the flow about a hypothetical lifting rotor blade having twist, airfoil thickness taper, and a 20 deg sweptback tip was analyzed at azimuthal positions of 60, 90, and 120 deg for an advance ratio of 0.342. A typical run on a CDC 7600 computer required about 5 min for one rotor position at transonic tip speeds.
Arieli, R.↗