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At least 343 records · Page 19

Computation of unsteady transonic flows through rotating and stationary cascades. 3: Acoustic far-field analysis

A small perturbation type analysis has been developed for the acoustic far field in an infinite duct extending upstream and downstream of an axial turbomachinery stage. The analysis is designed to interface with a numerical solution of the near field of the blade rows and, thereby, to provide the necessary closure condition to complete the statement of infinite duct boundary conditions for the subject problem. The present analysis differs from conventional inlet duct analyses in that a simple harmonic time dependence was not assumed, since a transient signal is generated by the numerical near-field solution and periodicity is attained only asymptotically. A description of the computer code developed to carry out the necessary convolutions numerically is included, as well as the results of a sample application using an impulsively initiated harmonic signal.

Slutsky, S.↗

Internal corner flow fields

A computational procedure has been developed to predict the inviscid super/hypersonic flow field of conical internal corners. The prediction of internal corner flow fields can be important in the design of supersonic 'box' type inlets. The computational procedure utilizes a second order finite difference marching technique to asymptote to the conical corner flow solution of Euler's equations. These flow fields are dominated by complex shock interactions. All discontinuities, shocks and slip surfaces are fitted with the appropriate jump conditions. The 'triple' points (the interaction of two shocks and a slip surface) are also computed exactly. Computed results are compared with experimental data and the computational results of other investigators. In addition, the sensitivity of these flow fields to a number of geometric parameters is studied, and the impact of these flows on inlet performance is assessed.

Marconi, F.↗

Thermocapillary migration of bubbles and droplets

A discussion is presented concerning the motion of droplets in a surrounding fluid induced by a temperature gradient. Such 'thermocapillary migration' may be characterized as the tangential stress at the interface that is induced by the temperature gradient's variation of interfacial tension, causing motion in the neighboring fluid both inside and outside the droplet. As a result, the droplet moves in the direction of the pole with the lower interfacial tension. An analysis is conducted in the creeping flow limit, for the case of small Marangoni number values. The method of matched asymptotic expansions is used for the solution of the field equations.

Subramanian, R. S.↗

The disturbance flow field produced by an evolving vortex

The flow field of a vortex in a viscous shear flow is found by constructing a uniformly valid asymptotic expansion consisting of an inner solution field represented, to lowest order, by a two dimensional, nonliner, inviscid Stuart vortex and an outer solution field represented, to lowest order, by either a two dimensional parallel or self similar viscous flow. The technique involves scaling both the transverse and streamwise coordinates in the vicinity of the vortex as well as allowing for a slow variation of the outer viscous flow. Criteria are established for both the size of the vortical structure and proximity to the boundary surfaces. The composite solution is a consistent mathematical picture of the flow field at a fixed streamwise location as the vortical structure evolves past this point. Such a formulation is also useful in the specification of boundary or initial conditions in numerical fluid dynamic calculations, where an inconsistent setting of these conditions leads to spurious results for rather long computation times.

Gatski, T. B.↗

Satellite rainfall retrieval by logistic regression

The potential use of logistic regression in rainfall estimation from satellite measurements is investigated. Satellite measurements provide covariate information in terms of radiances from different remote sensors.The logistic regression technique can effectively accommodate many covariates and test their significance in the estimation. The outcome from the logistical model is the probability that the rainrate of a satellite pixel is above a certain threshold. By varying the thresholds, a rainrate histogram can be obtained, from which the mean and the variant can be estimated. A logistical model is developed and applied to rainfall data collected during GATE, using as covariates the fractional rain area and a radiance measurement which is deduced from a microwave temperature-rainrate relation. It is demonstrated that the fractional rain area is an important covariate in the model, consistent with the use of the so-called Area Time Integral in estimating total rain volume in other studies. To calibrate the logistical model, simulated rain fields generated by rainfield models with prescribed parameters are needed. A stringent test of the logistical model is its ability to recover the prescribed parameters of simulated rain fields. A rain field simulation model which preserves the fractional rain area and lognormality of rainrates as found in GATE is developed. A stochastic regression model of branching and immigration whose solutions are lognormally distributed in some asymptotic limits has also been developed.

Chiu, Long S.↗

Three-dimensional atmospheric entry problem using method of matched asymptotic expansions

The analysis of a three-dimensional atmospheric entry problem using the method of matched asymptotic expansions is considered. A composite solution is formed in terms of an outer solution, an inner solution and a common solution. The outer solution is obtained from the gravitationally dominant region, whereas the aerodynamically dominant region contributes to the inner solution. The common solution accounts for the overlap between the outer and inner regions. In comparison to previous work, this simplified methodology yields explicit analytical expressions for various components of the composite solution without resorting to any type of transcendental equations to be solved only by numerical methods.

Naidu, D. S.↗

Ignition and structure of a laminar diffusion flame in the field of a vortex

The distortion of flames in flows with vortical motion is examined via asymptotic analysis and numerical simulation. The model consists of a constant density, one step, irreversible Arrhenius reaction between initially unmixed species occupying adjacent half-planes which are then allowed to mix and react in the presence of a vortex. The evolution in time of the temperature and mass fraction fields is followed. Emphasis is placed on the ignition time and location as a function of vortex Reynolds number and initial temperature differences of the reacting species. The study brings out the influence of the vortex on the chemical reaction. In all phases, good agreement is observed between asymptotic analysis and the full numerical solution of the model equations.

Macaraeg, Michele G.↗

Interface conditions for domain decomposition with radical grid refinement

Interface conditions for coupling the domains in a physically motivated domain decomposition method are discussed. The domain decomposition is based on an asymptotic-induced method for the numerical solution of hyperbolic conservation laws with small viscosity. The method consists of multiple stages. The first stage is to obtain a first approximation using a first-order method, such as the Godunov scheme. Subsequent stages of the method involve solving internal-layer problem via a domain decomposition. The method is derived and justified via singular perturbation techniques.

Scroggs, Jeffrey S.↗

Boundary layer transition studies

A small-scale wind tunnel previously used for turbulent boundary layer experiments was modified for two sets of boundary layer transition studies. The first study concerns a laminar separation/turbulent reattachment. The pressure gradient and unit Reynolds number are the same as the fully turbulent flow of Spalart and Watmuff. Without the trip wire, a laminar layer asymptotes to a Falkner & Skan similarity solution in the FPG. Application of the APG causes the layer to separate and a highly turbulent and approximately 2D mean flow reattachment occurs downstream. In an effort to gain some physical insight into the flow processes a small impulsive disturbance was introduced at the C(sub p) minimum. The facility is totally automated and phase-averaged data are measured on a point-by-point basis using unprecedently large grids. The evolution of the disturbance has been tracked all the way into the reattachment region and beyond into the fully turbulent boundary layer. At first, the amplitude decays exponentially with streamwise distance in the APG region, where the layer remains attached, i.e. the layer is viscously stable. After separation, the rate of decay slows, and a point of minimum amplitude is reached where the contours of the wave packet exhibit dispersive characteristics. From this point, exponential growth of the amplitude of the disturbance is observed in the detached shear layer, i.e. the dominant instability mechanism is inviscid. A group of large-scale 3D vortex loops emerges in the vicinity of the reattachment. Remarkably, the second loop retains its identify far downstream in the turbulent boundary layer. The results provide a level of detail usually associated with CFD. Substantial modifications were made to the facility for the second study concerning disturbances generated by Suction Holes for laminar flow Control (LFC). The test section incorporates suction through interchangeable porous test surfaces. Detailed studies have been made using isolated holes in the impervious test plate that used to establish the Blasius base flow. The suction is perturbed harmonically and data are averaged on the basis of the phase of the disturbance, for conditions corresponding to strong suction and without suction. The technique was enhanced by using up to nine multiple probes to reduce the experimental run-time. In both cases, 3D contour surfaces in the vicinity of the hole show highly 3D TS waves which fan out in the spanwise direction forming bow-shaped waves downstream. The case without suction has proved useful for evaluating calculation methods. With suction, the perturbations on the centerline are much stronger and decay less rapidly, while the TS waves in the far field are similar to the case without suction. Downstream, the contour surfaces of the TS waves develop spanwise irregularities which eventually form into clumps. The spanwise clumping is evidence of a secondary instability that could be associated with suction vortices. Designers of porous surfaces use Goldsmith's Criterion to minimize cross-stream interactions. It is shown that partial TS wave cancellation is possible, depending on the hole spacing, disturbance frequency and free-stream velocity. New high-performance Constant Temperature Hot-Wire Anemometers were designed and built, based on a linear system theory analysis that can be extended to arbitrary order. The motivation was to achieve the highest possible frequency reponse while ensuring overall system stability. The performance is equal to or superior to commercially available instruments at about 10% of the cost. Details, such as fabrication drawings and a parts list, have been published to enable the instrument to be construced by others.

Watmuff, Jonathan H.↗

Exact-Output Tracking Theory for Systems with Parameter Jumps

In this paper we consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to nonminimum-phase systems and obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exo-system, then we develop an exact-tracking controller in a feedback form. As in standard regulator theory, we obtain a linear map from the states of the exo-system to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

Devasia, Santosh↗

Exact-Output Tracking Theory for Systems with Parameter Jumps

We consider the exact output tracking problem for systems with parameter jumps. Necessary and sufficient conditions are derived for the elimination of switching-introduced output transient. Previous works have studied this problem by developing a regulator that maintains exact tracking through parameter jumps (switches). Such techniques are, however, only applicable to minimum-phase systems. In contrast, our approach is applicable to non-minimum-phase systems and it obtains bounded but possibly non-causal solutions. If the reference trajectories are generated by an exosystem, then we develop an exact-tracking controller in a feed-back form. As in standard regulator theory, we obtain a linear map from the states of the exosystem to the desired system state which is defined via a matrix differential equation. The constant solution of this differential equation provides asymptotic tracking, and coincides with the feedback law used in standard regulator theory. The obtained results are applied to a simple flexible manipulator with jumps in the pay-load mass.

Devasia, Santosh↗

Study of Magnetic Damping Effect on Convection and Solidification Under G-Jitter Conditions

As shown by NASA resources dedicated to measuring residual gravity (SAMS and OARE systems), g-jitter is a critical issue affecting space experiments on solidification processing of materials. This study aims to provide, through extensive numerical simulations and ground based experiments, an assessment of the use of magnetic fields in combination with microgravity to reduce the g-jitter induced convective flows in space processing systems. We have so far completed asymptotic analyses based on the analytical solutions for g-jitter driven flow and magnetic field damping effects for a simple one-dimensional parallel plate configuration, and developed both 2-D and 3-D numerical models for g-jitter driven flows in simple solidification systems with and without presence of an applied magnetic field. Numerical models have been checked with the analytical solutions and have been applied to simulate the convective flows and mass transfer using both synthetic g-jitter functions and the g-jitter data taken from space flight. Some useful findings have been obtained from the analyses and the modeling results. Some key points may be summarized as follows: (1) the amplitude of the oscillating velocity decreases at a rate inversely proportional to the g-jitter frequency and with an increase in the applied magnetic field; (2) the induced flow approximately oscillates at the same frequency as the affecting g-jitter, but out of a phase angle; (3) the phase angle is a complicated function of geometry, applied magnetic field, temperature gradient and frequency; (4) g-jitter driven flows exhibit a complex fluid flow pattern evolving in time; (5) the damping effect is more effective for low frequency flows; and (6) the applied magnetic field helps to reduce the variation of solutal distribution along the solid-liquid interface. Work in progress includes numerical simulations and ground-based measurements. Both 2-D and 3-D numerical simulations are being continued to obtain further information on g-jitter driven flows and magnetic field effects. A physical model for ground-based measurements is completed and some measurements of the oscillating convection are being taken on the physical model. The comparison of the measurements with numerical simulations is in progress. Additional work planned in the project will also involve extending the 2-D numerical model to include the solidification phenomena with the presence of both g-jitter and magnetic fields.

Li, Ben Q.↗

3-D composite velocity solutions for subsonic/transonic flow over afterbodies

A composite velocity procedure for the three-dimensional reduced Navier-Stokes equations is developed. The velocity components are written as a combined multiplicative and additive composite of viscous like velocities and pseudo-potential or inviscid velocities. The solution procedure is then consistent with both asymptotic inviscid flow and boundary layer theory. For transonic flow cases, the Enquist-Osher flux biasing scheme developed for the full potential equation is used. A quasi-conservation form of the governing equations is used in the shock region to capture the correct rotational behavior. The composite velocity procedure is applied for the solution of three-dimensional afterbody problems.

Gornier, Raymond E.↗

Summary of the Fourth AIAA CFD Drag Prediction Workshop

Results from the Fourth AIAA Drag Prediction Workshop (DPW-IV) are summarized. The workshop focused on the prediction of both absolute and differential drag levels for wing-body and wing-body-horizontal-tail configurations that are representative of transonic transport air- craft. Numerical calculations are performed using industry-relevant test cases that include lift- specific flight conditions, trimmed drag polars, downwash variations, dragrises and Reynolds- number effects. Drag, lift and pitching moment predictions from numerous Reynolds-Averaged Navier-Stokes computational fluid dynamics methods are presented. Solutions are performed on structured, unstructured and hybrid grid systems. The structured-grid sets include point- matched multi-block meshes and over-set grid systems. The unstructured and hybrid grid sets are comprised of tetrahedral, pyramid, prismatic, and hexahedral elements. Effort is made to provide a high-quality and parametrically consistent family of grids for each grid type about each configuration under study. The wing-body-horizontal families are comprised of a coarse, medium and fine grid; an optional extra-fine grid augments several of the grid families. These mesh sequences are utilized to determine asymptotic grid-convergence characteristics of the solution sets, and to estimate grid-converged absolute drag levels of the wing-body-horizontal configuration using Richardson extrapolation.

Vassberg, John C.↗

Stability of Long's vortex at large flow force

Long's self-similar vortex is known to have two solutions for each supercritical value of the flow force. Each of those solutions is shown to have a double structure if the flow force is large. The inertial instabilities of one of those large-flow-force limit solutions are investigated, showing that they are related to the instabilities of the Bickley jet in one regime. However, the swirl in the vortex becomes important for long waves, very strongly modifying the sinuous and varicose, Bickley modes. The asymptotic results obtained agree well with the numerical solutions for the sinuous mode, but not for the varicose mode, the difficulty in the latter case being apparently due to mode jumping.

Foster, M. R.↗

Effect of transverse shear and material orthotropy in a cracked spherical cap

The elastostatic problem for a relatively thin-walled spherical cap containing a through crack is considered. The problem is formulated for a specially orthotropic material within the confines of a linearized, shallow shell theory. The theory used is equivalent to Reissner's theory of flat plates and hence permits the consideration of all five physical conditions on the shell boundaries separately. The solution of the problem is reduced to that of a pair of singular integral equations and the asymptotic stress state around the crack tips is investigated. The numerical solution of the problem is given for an isotropic shell and for two specially orthotropic shells. The results indicate that the material orthotropy as well as the shell curvature and thickness may have a considerable effect on the stress intensity factors at the crack tips.

Delale, F.↗