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At least 217 records · Page 12

A method for calculating turbulent boundary layers and losses in the flow channels of turbomachines

An interactive inviscid core flow-boundary layer method is presented for the calculation of turbomachine channel flows. For this method, a one-dimensional inviscid core flow is assumed. The end-wall and blade surface boundary layers are calculated using an integral entrainment method. The boundary layers are assumed to be collateral and thus are two-dimensional. The boundary layer equations are written in a streamline coordinate system. The streamwise velocity profiles are approximated by power law profiles. Compressibility is accounted for in the streamwise direction but not in the normal direction. Equations are derived for the special cases of conical and two-dimensional rectangular diffusers. For these cases, the assumptions of a one-dimensional core flow and collateral boundary layers are valid. Results using the method are compared with experiment and good quantitative agreement is obtained.

Schumann, Lawrence F.↗

Long range frequency chirping of Alfvén eigenmodes

In this work, a theoretical framework has been developed for an NBI scenario to model the hard non-linear evolution of global Alfvén eigenmodes (GAEs) where the adiabatic motion of phase-space structures (holes and clumps), associated with frequency chirping, occurs in generalized phase-space of slowing down energetic particles. The radial profile of the GAE is expanded using finite elements, which allows an update of the mode structure as the mode frequency chirps. Constants of motion are introduced to track the dynamics of energetic particles during frequency chirping by implementing proper action-angle variables and canonical transformations which reduce the dynamics essentially to 1D. Consequently, we specify whether the particles are drifting inward/outward as the frequency deviates from the initial MHD eigenfrequency. Using the principle of least action, we have derived the non-linear equation describing the evolution of the radial profile by varying the total Lagrangian of the system with respect to the weights of the finite elements. For the choice of parameters in this work, it is shown that the peak of the radial profile is shifted and also broadens due to frequency chirping. The time rate of frequency change is also calculated using the energy balance and we show that the adiabatic condition remains valid once it is satisfied. This model clearly illustrates the theoretical treatment to study the long-range adiabatic frequency sweeping events observed for Alfvén gap modes in real experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗

Calculations of Laminar Heat Transfer Around Cylinders of Arbitrary Cross Section and Transpiration-Cooled Walls with Application to Turbine Blade Cooling

An approximate method for development of flow and thermal boundary layers in laminar regime on cylinders with arbitrary cross section and transpiration-cooled walls is obtained by use of Karman's integrated momentum equation and an analogous heat-flow equation. Incompressible flow with constant property values throughout boundary layer is assumed. Shape parameters for approximated velocity and temperature profiles and functions necessary for solution of boundary-layer equations are presented as charts, reducing calculations to a minimum. The method is applied to determine local heat-transfer coefficients and surface temperature-cooled turbine blades for a given flow rate. Coolant flow distributions necessary for maintaining uniform blade temperatures are also determined.

TURBINE COOLING↗

Equatorial wave-mean flow interaction - A numerical study of the role of latitudinal shear

A time-dependent primitive equation model for an equatorial channel is used to assess the interaction of equatorial Kelvin and mixed Rossby-gravity waves with the mean flow. The proposed model involves a semiimplicit time-differencing scheme and a finite-difference grid in the meridional plane. It is shown that forced equatorial waves interact with mean flow to produce equatorial jets characterized by downward-moving westerly (Kelvin wave forcing) and easterly (mixed Rossby-gravity wave forcing) shear zones, respectively. For parameters characteristic of the observed waves in the equatorial stratosphere, the wave-mean flow interaction process always reduces the amplitude of any initial cross-equatorial mean wind shear. The mean flow profile tends to become symmetric about the equator as the interaction process continues.

Holton, J. R.↗

Unravelling the orbits of cluster galaxy populations according to their dominant gas ionization source

ABSTRACT We investigate the kinematical and dynamical properties of cluster galaxy populations classified according to their dominant source of gas ionization, namely: star-forming (SF) galaxies, optical active galactic nuclei (AGNs), mixed SF plus AGN ionization (transition objects, T), and quiescent (Q) galaxies. We stack 8892 member galaxies from 336 relaxed galaxy clusters to build an ensemble cluster and estimate the observed projected profiles of numerical density and velocity dispersion, $\sigma _P(R)$, of each galaxy population. The MAMPOSSt code and the Jeans equations inversion technique are used to constrain the velocity anisotropy profiles of the galaxy populations in both parametric and non-parametric ways. We find that Q (SF) galaxies display the lowest (highest) typical cluster-centric distances and velocity dispersion values. Transition galaxies are more concentrated and tend to exhibit lower velocity dispersion values than SF galaxies. Galaxies that host an optical AGN are as concentrated as Q galaxies but display velocity dispersion values similar to those of the SF population. MAMPOSSt is able to find equilibrium solutions that successfully recover the observed $\sigma _P(R)$ profile only for the Q, T, and AGN populations. We find that the orbits of all populations are consistent with isotropy in the inner regions, becoming increasingly radial with the distance from the cluster centre. These results suggest that Q galaxies are in equilibrium within their clusters, while SF galaxies have more recently arrived in the cluster environment. Finally, the T and AGN populations appear to be in an intermediate dynamical state between those of the SF and Q populations.

Valk, Greique A. (ORCID:0009000827731299)↗

The behavior of surface tension on steady-state rotating fluids in the low gravity environments

The effect of surface tension on steady-state rotating fluids in a low gravity environment is studied. All the values of the physical parameters used in these calculations, except in the low gravity environments, are based on the measurements carried out by Leslie (1985) in the low gravity environment of a free-falling aircraft. The profile of the interface of two fluids is derived from Laplace's equation relating the pressure drop across an interface to the radii of curvature which has been applied to a low gravity rotating bubble that contacts the container boundary. The interface shape depends on the ratio of gravity to surface tension forces, the ratio of centrifugal to surface tension forces, the contact radius of the interface to the boundary, and the contact angle. The shape of the bubble is symmetric about its equator in a zero-gravity environment. This symmetry disappears and gradually shifts to parabolic profiles as the gravity environment becomes non-zero. The location of the maximum radius of the bubble moves upward from the center of the depth toward the top boundary of the cylinder as gravity increases. The contact radius of interface to the boundary r0 at the top side of cylinder increases and r0 at the bottom side of the cylinder decreases as the gravity environment increases from zero to 1 g.

Hung, R. J.↗

Analysis and control of supersonic vortex breakdown flows

Analysis and computation of steady, compressible, quasi-axisymmetric flow of an isolated, slender vortex are considered. The compressible, Navier-Stokes equations are reduced to a simpler set by using the slenderness and quasi-axisymmetry assumptions. The resulting set along with a compatibility equation are transformed from the diverging physical domain to a rectangular computational domain. Solving for a compatible set of initial profiles and specifying a compatible set of boundary conditions, the equations are solved using a type-differencing scheme. Vortex breakdown locations are detected by the failure of the scheme to converge. Computational examples include isolated vortex flows at different Mach numbers, external axial-pressure gradients and swirl ratios.

Kandil, Osama A.↗

A numerical simulation to verify the stress-free growth of silicon crystal ribbon

Thermal stresses developed during the growth of silicon crystal ribbon have been shown to be negligible, thus eliminating residual stresses and dislocations, if the temperature profile satisfies a second-order partial differential equation inside the ribbon. This has been numerically verified through a finite element model, an outline of which is presented here. This model shows that, for homogeneous isotropic material with temperature independent thermal expansion coefficients, thermal stresses will vanish if the temperature profile satisfies the Laplacian. A comparison of stresses due to uniform and nonuniform temperature gradients in the plane of the ribbon is also presented. The strategies employed to control the round-off error and to validate the computer model are discussed.

Ray, Sujit K.↗

A Generalized Dual-Frequency Ratio (DFR) Approach for Rain Retrievals

The dual-frequency ratio of radar reflectivity factors (DFR) has been shown to be a useful quantity as it is independent of the number concentration of the particle size distribution and primarily a function of the mass-weighted particle diameter, Dm. A drawback of DFR-related methods for rain estimation, however, is the non-unique relationship between Dm and DFR. At Ku- and Ka-band frequencies, two solutions for Dm exist when DFR is less than zero. This ambiguity generates multiple solutions for the range profiles of the particle size parameters. We investigate characteristics of these solutions for both the initial-value (forward) and final-value (backward) forms of the equations. To choose one of among many possible range profiles of Dm, number concentration and rain rate, R, independently measured path attenuations are used. For the backward approach the possibility exists of dispensing with externally measured path attenuations by achieving consistency between the input and output path attenuations. The methods are tested by means of a simulation based on disdrometer-measured raindrop size distributions and the results are compared with a simplified version of the operational R-Dm method.

Robert Meneghini↗

Improving the Physical Basis for Updraft Dynamics in Deep Convection Parameterizations

This article presents a new deep convective parameterization that determines cloud characteristics based on a specified cloud size distribution. The vertical profiles of cloud properties are determined by analytic equations, which formulate entrainment with an inverse relationship to cloud width. In line with recent studies of large eddy simulations (LES), cloud widths are assumed to be constant with height and vertical mass flux (M) characteristics of the clouds are therefore regulated by the vertical velocity profile. The parameterization is configured to work with existing cloud base M closure formulations, with the closure predicting the total cloud area rather than the cloud base M directly. Analytic formula are also used to connect the vertical wind shear magnitude to the cloud size distribution, wherein larger shear magnitudes result in more numerous large updrafts than weaker shear magnitudes, which is in line with recent research results. The parameterization is compared against 10 deep convective LES with varying thermodynamic and vertical wind shear profiles. Results show dramatic improvements in the prediction of normalized M, detrainment, and the properties of detrained air over the existing Zhang and McFarlane (1995) scheme. In particular, the new model is able to correctly portray the transition from a bottom-heavy M profile in weakly sheared environments, to a top-heavy M profile in strongly sheared environments.

54 ENVIRONMENTAL SCIENCES↗

A prediction method for velocity and temperature profiles in a two-dimensional nominally steady turbulent boundary layer

This paper describes a recently developed boundary-layer prediction method for a variable property compressible flow, in which heat transfer takes place primarily by forced convection and for which the mainstream Mach number is small. The leading order terms, in asymptotic expansions for large Reynolds numbers, are obtained for the mean velocity and temperature distribution in both the inner and outer layer of the turbulent boundary layer. Closure in the inner layer is achieved using an analytical model for the mean profiles which is based on the observed coherent structure of the time-dependent inner layer flow. For the outer layer, simple eddy viscosity and conductivity models are developed without recourse to the Reynolds analogy. In the prediction method a numerical solution of the outer layer equations is matched to the analytical inner layer profiles as the computation procedes downstream. Calculations are presented for a range of adverse and favorable pressure gradient flows and the predicted results compare well with existing data.

Weigand, G. G.↗

Radial diffusion in the Uranian radiatian belts - Inferences from satellite absorption loss models

Low-energy charged particle (LECP) phase space density profiles available from the Voyager/1986 Uranus encounter are analyzed, using solutions of the time-averaged radial diffusion equation for charged particle transport in a dipolar planetary magnetic field. Profiles for lower-energy protons and electrons are first analyzed to infer radial diffusion rate as a function of L, assuming that satellite absorption is the dominant loss process and local sources for these particles are negligible. Satellite macrosignatures present in the experimentally derived profiles are approximately reproduced in several cases, lending credence to the loss model and indicating that magnetospheric distributed losses are not as rapid as satellite absorption near the minimum satellite L shells for the particles. Diffusion rates and L dependences are found to be similar to those previously inferred in the inner Jovian magnetosphere (Thomsen et al., 1977) and for the inner Saturnian magnetosphere (Hood, 1985). Profiles for higher energy electrons and protons are also analyzed using solutions that allow for the existence of significant particle sources as well as sinks. Possible implications for radial diffusion mechanisms in the Uranian radiation belts are discussed.

Hood, L. L.↗

Performance characteristics of STIS detectors

We report quantum efficiency measurements of back-illuminated, ion-implanted, laser-annealed charge coupled devices (CCD's) in the wavelength range 13-10,000 A. The equivalent quantum efficiency (EQE = effective photons detected per incident photon) ranges from a minimum of 5 percent as 1216 A to a maximum of 87 percent at 135 A. Using a simple relationship for the charge collection efficiency of the CCD pixels as a function of depth, we present a semi-empirical model with few parameters which reproduces our measurements with a fair degree of accuracy. The advantage of this model is that is can be used to predict CCD QE performance for shallow backside implanted devices without detailed solution of a system of differential equations, as in conventional approaches, and yields a simple analytic form for the charge collection efficiency which is adequate for detector calibration purposes. Making detailed assumptions about the dopant profile, we also solve the carrier density and continuity equations in order to relate our semi-empirical model parameters to surface and bulk device properties. The latter procedure helps to better establish device processing parameters for a given level of CCD QE performance.

Stern, Robert A.↗

A study to determine the characteristic shapes of helicopter visual approach profiles

On previous helicopter instrument approach studies, pilot comments frequently indicated that the deceleration profiles were characterized by 'unnatural cues', and it was found that the pilots were comparing the motion and attitude cues with those obtained during visual approaches. Prior to this study, the characteristic shape of visual approach profiles had not been formally documented. Over 200 visual approaches were flown using different helicopter types, test subjects, and initial conditions, and the altitude and groundspeed profiles were measured by a precision tracking radar. The data from each approach were then processed, and the characteristic shape of the altitude, groundspeed, and deceleration profiles was determined for each set of initial conditions. These flight data were processed further using graphical analysis techniques and parameterization, which, in turn, led to developing closed-form equations that accurately describe the characteristic groundspeed and deceleration profiles. Results from this study can be used to select instrument approach profiles, to develop instrument approach control laws, and to define the corresponding hardware requirements.

Moen, G. C.↗

The Smoke-Trail Method for Obtaining Detailed Measurements of the Vertical Wind Profile for Application to Missile-Dynamic-Response Problems

Detailed measurements of the vertical profile of the wind are urgently needed f o r studies of the response of rising missiles, but conventional wind-measuring systems cannot provide the accuracy and detail required over the necessary range of altitudes. A method is presented for obtaining a detailed, accurate profile over a large altitude range. The method utilizes photogrammetric measurement of successive positions of the t rail of an ascending rocket. Construction of a rocketborne smoke generator is discussed and the photography, film reading, and data-reduction procedures are described. The accuracy of the method i s examined and error equations are derived. Finally, some examples of wind profiles measured by this method are shown, and their implications for missile response are indicated.

Henry, Robert M.↗

Convergent laser beam shapes: Unveiling the dynamics of Laser-induced elastic waves in composite materials

Overcoming the low signal-to-noise ratio (SNR) in laser ultrasonic testing of composite materials remains a significant challenge. Current efforts focus on enhancing SNR by inserting more energy into the material through temporal and/or spatial modulation of the laser beam. However, potential SNR improvements through wave convergence and wave energy manipulation have been overlooked. This paper addresses this gap by demonstrating the convergence of different wave types to a designated point and by showing the feasibility of directing absorbed laser energy into a specific wave type through spatial modulation of the laser beam. To achieve this, mathematical expressions for the convergent laser beams are derived. Various laser beam profiles are then introduced to the thermoelastic equations and solved using the finite element method. The sample under investigation is a transversely isotropic unidirectional carbon fiber reinforced plastic, characterized by anisotropic thermal expansion coefficients and thermal conductivities. Results reveal pronounced convergence of the intended wave type at the center due to laser beam shaping. This study showcases the ability to direct absorbed laser energy toward a specific wave type through spatial modulation of the laser beam and highlights the role of material anisotropy in energy focusing.

composite materials↗

Paradigm for global gyrokinetic turbulence

Using a novel wave-number-advection algorithm, we describe a method to add global profile curvature terms to the local gyrokinetic equations. This approach enables a high-precision global simulation capability without sacrificing the efficiency and spectral accuracy of local simulations. Preliminary numerical results suggest that there are two distinct types of global correction to the local result: (1) a trivial shift of the local result in radius, (2) a non-trivial decorrelation that is roughly equivalent to the well-known E×B shear effect. This interpretation provides a new, intuitive framework for understanding global gyrokinetic simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗