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At least 325 records · Page 18

A detailed treatment of two-dimensional, starved lubrication in the vicinity of two counter-rotating cylinders

The problem of starved lubrication in the inlet region for the case of line contact between two nondeforming, equal radii cylinders rotating in opposite directions with equal surface speeds is considered. The lubricant is assumed to be a constant density, isoviscous, Newtonian fluid. The usual approach, which involves the use of Reynolds equation everywhere, is not followed. Instead, the situation is restricted to one in which the lubricant enters the contact region in thin films which adhere to the cylinders. Using Reynolds equation only at the line of centers and a suitable thin film approximation far from that point, the intervening region is treated as a general creeping flow region. Solutions, incorporating complete free surface boundary conditions, are obtained numerically. The hitherto unobtained results due to this approach include the existence of a unique free surface location for a fixed set of operating conditions.

Medrow, R. A.↗

The Boundary Layers in Fluids with Little Friction

The vortices forming in flowing water behind solid bodies are not represented correctly by the solution of the potential theory nor by Helmholtz's jets. Potential theory is unable to satisfy the condition that the water adheres at the wetted bodies, and its solutions of the fundamental hydrodynamic equations are at variance with the observation that the flow separates from the body at a certain point and sends forth a highly turbulent boundary layer into the free flow. Helmholtz's theory attempts to imitate the latter effect in such a way that it joins two potential flows, jet and still water, nonanalytical along a stream curve. The admissibility of this method is based on the fact that, at zero pressure, which is to prevail at the cited stream curve, the connection of the fluid, and with it the effect of adjacent parts on each other, is canceled. In reality, however, the pressure at these boundaries is definitely not zero, but can even be varied arbitrarily. Besides, Helmholtz's theory with its potential flows does not satisfy the condition of adherence nor explain the origin of the vortices, for in all of these problems, the friction must be taken into account on principle, according to the vortex theorem.

Blasius, H.↗

Particle acceleration at shocks - A Monte Carlo method

A Monte Carlo method is presented for the problem of acceleration of test particles at relativistic shocks. The particles are assumed to diffuse in pitch angle as a result of scattering off magnetic irregularities frozen into the fluid. Several tests are performed using the analytic results available for both relativistic and nonrelativistic shock speeds. The acceleration at relativistic shocks under the influence of radiation losses is investigated, including the effects of a momentum dependence in the diffusion coefficient. The results demonstrate the usefulness of the technique in those situations in which the diffusion approximation cannot be employed, such as when relativistic bulk motion is considered, when particles are permitted to escape at the boundaries, and when the effects of the finite length of the particle mean free path are important.

Kirk, J. G.↗

Aeromechanics Analysis of a Distortion-Tolerant Fan with Boundary Layer Ingestion

A propulsion system with Boundary Layer Ingestion (BLI) has the potential to significantly reduce aircraft engine fuel burn. But a critical challenge is to design a fan that can operate continuously with a persistent BLI distortion without aeromechanical failure -- flutter or high cycle fatigue due to forced response. High-fidelity computational aeromechanics analysis can be very valuable to support the design of a fan that has satisfactory aeromechanic characteristics and good aerodynamic performance and operability. Detailed aeromechanics analyses together with careful monitoring of the test article is necessary to avoid unexpected problems or failures during testing. In the present work, an aeromechanics analysis based on a three-dimensional, time-accurate, Reynolds-averaged Navier-Stokes computational fluid dynamics code is used to study the performance and aeromechanical characteristics of the fan in both circumferentially-uniform and circumferentially-varying distorted flows. Pre-test aeromechanics analyses are used to prepare for the wind tunnel test and comparisons are made with measured blade vibration data after the test. The analysis shows that the fan has low levels of aerodynamic damping at various operating conditions examined. In the test, the fan remained free of flutter except at one near-stall operating condition. Analysis could not be performed at this low mass flow rate operating condition since it fell beyond the limit of numerical stability of the analysis code. The measured resonant forced response at a specific low-response crossing indicated that the analysis under-predicted this response and work is in progress to understand possible sources of differences and to analyze other larger resonant responses. Follow-on work is also planned with a coupled inlet-fan aeromechanics analysis that will more accurately represent the interactions between the fan and BLI distortion.

Propulsion Aeroelasticity↗

Reynolds number influences in aeronautics

Reynolds number, a measure of the ratio of inertia to viscous forces, is a fundamental similarity parameter for fluid flows and therefore, would be expected to have a major influence in aerodynamics and aeronautics. Reynolds number influences are generally large, but monatomic, for attached laminar (continuum) flow; however, laminar flows are easily separated, inducing even stronger, non-monatomic, Reynolds number sensitivities. Probably the strongest Reynolds number influences occur in connection with transitional flow behavior. Transition can take place over a tremendous Reynolds number range, from the order of 20 x 10(exp 3) for 2-D free shear layers up to the order of 100 x 10(exp 6) for hypersonic boundary layers. This variability in transition behavior is especially important for complex configurations where various vehicle and flow field elements can undergo transition at various Reynolds numbers, causing often surprising changes in aerodynamics characteristics over wide ranges in Reynolds number. This is further compounded by the vast parameterization associated with transition, in that any parameter which influences mean viscous flow development (e.g., pressure gradient, flow curvature, wall temperature, Mach number, sweep, roughness, flow chemistry, shock interactions, etc.), and incident disturbance fields (acoustics, vorticity, particulates, temperature spottiness, even electro static discharges) can alter transition locations to first order. The usual method of dealing with the transition problem is to trip the flow in the generally lower Reynolds number wind tunnel to simulate the flight turbulent behavior. However, this is not wholly satisfactory as it results in incorrectly scaled viscous region thicknesses and cannot be utilized at all for applications such as turbine blades and helicopter rotors, nacelles, leading edge and nose regions, and High Altitude Long Endurance and hypersonic airbreathers where the transitional flow is an innately critical portion of the problem.

Bushnell, Dennis M.↗

Higher order moments of the matter distribution in scale-free cosmological simulations with large dynamic range

We calculate reduced moments (xi bar)(sub q) of the matter density fluctuations, up to order q = 5, from counts in cells produced by particle-mesh numerical simulations with scale-free Gaussian initial conditions. We use power-law spectra P(k) proportional to k(exp n) with indices n = -3, -2, -1, 0, 1. Due to the supposed absence of characteristic times or scales in our models, all quantities are expected to depend on a single scaling variable. For each model, the moments at all times can be expressed in terms of the variance (xi bar)(sub 2), alone. We look for agreement with the hierarchical scaling ansatz, according to which ((xi bar)(sub q)) proportional to ((xi bar)(sub 2))(exp (q - 1)). For n less than or equal to -2 models, we find strong deviations from the hierarchy, which are mostly due to the presence of boundary problems in the simulations. A small, residual signal of deviation from the hierarchical scaling is however also found in n greater than or equal to -1 models. The wide range of spectra considered and the large dynamic range, with careful checks of scaling and shot-noise effects, allows us to reliably detect evolution away from the perturbation theory result.

Lucchin, Francesco↗

Multidisciplinary Optimization of Tilt Rotor Blades Using Comprehensive Composite Modeling Technique

An optimization procedure is developed for addressing the design of composite tilt rotor blades. A comprehensive technique, based on a higher-order laminate theory, is developed for the analysis of the thick composite load-carrying sections, modeled as box beams, in the blade. The theory, which is based on a refined displacement field, is a three-dimensional model which approximates the elasticity solution so that the beam cross-sectional properties are not reduced to one-dimensional beam parameters. Both inplane and out-of-plane warping are included automatically in the formulation. The model can accurately capture the transverse shear stresses through the thickness of each wall while satisfying stress free boundary conditions on the inner and outer surfaces of the beam. The aerodynamic loads on the blade are calculated using the classical blade element momentum theory. Analytical expressions for the lift and drag are obtained based on the blade planform with corrections for the high lift capability of rotor blades. The aerodynamic analysis is coupled with the structural model to formulate the complete coupled equations of motion for aeroelastic analyses. Finally, a multidisciplinary optimization procedure is developed to improve the aerodynamic, structural and aeroelastic performance of the tilt rotor aircraft. The objective functions include the figure of merit in hover and the high speed cruise propulsive efficiency. Structural, aerodynamic and aeroelastic stability criteria are imposed as constraints on the problem. The Kreisselmeier-Steinhauser function is used to formulate the multiobjective function problem. The search direction is determined by the Broyden-Fletcher-Goldfarb-Shanno algorithm. The optimum results are compared with the baseline values and show significant improvements in the overall performance of the tilt rotor blade.

Chattopadhyay, Aditi↗

Radiatively driven interactions between stratocumulus and synoptic waves

Quasi-geostrophic disturbances on a midlatitude beta-plane channel forced by radiative heating perturbations due to synoptic-scale variations of low-level stratiform cloud are considered. The longitudinal phase of the cloud is linked to that of the low-level streamfunction. Cloudiness is wavelike with cooling above cloudy areas that decreases exponentially with height. No perturbation cooling occurs above cloud-free areas. Two background flows are considered: one is constant and the other has a jet centered near the tropopause. Forced linear steady waves are found. Though infinitesimal amplitude disturbances are considered, the problem is nonlinear because of the coupling between cloud and winds. The resulting structures are sensitive to the phase shift between cloud and streamfunction with strongest coupling for cloud to the west of surface troughs. The waves have vertical scales on the order of the troposphere depth. The stationary structures capture the summertime pattern of stratocumulus off California and its linkage to the mid-Pacific ridge. When zonal-mean cloud cooling is allowed, the mean westerlies are strengthened in the northern half of the channel near the lower boundary. Synoptic-scale amplitudes respond to the mean cloud cooling by increasing (decreasing) just above the cloud in the northern (southern) part of the channel.

Clark, John H. E.↗

Direct numerical simulation of incompressible axisymmetric flows

In the present work, we propose to conduct direct numerical simulations (DNS) of incompressible turbulent axisymmetric jets and wakes. The objectives of the study are to understand the fundamental behavior of axisymmetric jets and wakes, which are perhaps the most technologically relevant free shear flows (e.g. combuster injectors, propulsion jet). Among the data to be generated are various statistical quantities of importance in turbulence modeling, like the mean velocity, turbulent stresses, and all the terms in the Reynolds-stress balance equations. In addition, we will be interested in the evolution of large-scale structures that are common in free shear flow. The axisymmetric jet or wake is also a good problem in which to try the newly developed b-spline numerical method. Using b-splines as interpolating functions in the non-periodic direction offers many advantages. B-splines have local support, which leads to sparse matrices that can be efficiently stored and solved. Also, they offer spectral-like accuracy that are C(exp O-1) continuous, where O is the order of the spline used; this means that derivatives of the velocity such as the vorticity are smoothly and accurately represented. For purposes of validation against existing results, the present code will also be able to simulate internal flows (ones that require a no-slip boundary condition). Implementation of no-slip boundary condition is trivial in the context of the b-splines.

Loulou, Patrick↗

A first-order global model of Late Cenozoic climatic change: Orbital forcing as a pacemaker of the ice ages

The development of a theory of the evolution of the climate of the earth over millions of years can be subdivided into three fundamental, nested, problems: (1) to establish by equilibrium climate models (e.g., general circulation models) the diagnostic relations, valid at any time, between the fast-response climate variables (i.e., the 'weather statistics') and both the prescribed external radiative forcing and the prescribed distribution of the slow response variables (e.g., the ice sheets and shelves, the deep ocean state, and the atmospheric CO2 concentration); (2) to construct, by an essentially inductive process, a model of the time-dependent evolution of the slow-response climatic variables over time scales longer than the damping times of these variables but shorter than the time scale of tectonic changes in the boundary conditions (e.g., altered geography and elevation of the continents, slow outgassing, and weathering) and ultra-slow astronomical changes such as in the solar radiative output; and (3) to determine the nature of these ultra-slow processes and their effects on the evolution of the equilibrium state of the climatic system about which the above time-dependent variations occur. All three problems are discussed in the context of the theory of the Quaternary climate, which will be incomplete unless it is embedded in a more general theory for the fuller Cenozoic that can accommodate the onset of the ice-age fluctuations. We construct a simple mathematical model for the Late Cenozoic climatic changes based on the hypothesis that forced and free variations of the concentration of atmospheric greenhouse gases (notably CO2), coupled with changes in the deep ocean state and ice mass, under the additional 'pacemaking' influence of earth-orbital forcing, are primary determinants of the climate state over this period. Our goal is to illustrate how a single model governing both very long term variations and higher frequency oscillatory variations in the Pleistocene can be formulated with relatively few adjustable parameters.

Saltzman, Barry↗

Towards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shape

Several practical materials processes, e.g., welding, float-zone purification, and Czochralski crystal growth, involve a pool of molten metal with a free surface, with strong temperature gradients along the surface. In some cases, the resulting thermocapillary flow is vigorous enough to convect heat toward the edges of the pool, increasing the driving force in a sort of positive feedback. In this work we examine this mechanism and its effect on the solid-liquid interface through a model problem: a half space of pure substance with concentrated axisymmetric surface heating, where surface tension is strong enough to keep the liquid free surface flat. The numerical method proposed for this problem utilizes a finite volume element (FVE) discretization in cylindrical coordinates. Because of the axisymmetric nature of the model problem, the control volumes used are torroidal prisms, formed by taking a polygonal cross-section in the (r, z) plane and sweeping it completely around the z-axis. Conservation of energy (in the solid), and conservation of energy, momentum, and mass (in the liquid) are enforced globally by integrating these quantities and enforcing conservation over each control volume. Judicious application of the Divergence Theorem and Stokes' Theorem, combined with a Crank-Nicolson time-stepping scheme leads to an implicit algebraic system to be solved at each time step. It is known that near the boundary of the pool, that is, near the solid-liquid interface, the full conduction-convection solution will require extremely fine length scales to resolve the physical behavior of the system. Furthermore, this boundary moves as a function of time. Accordingly, we develop the foundation of an adaptive refinement scheme based on the principles of Fast Adaptive Composite Grid methods (FAC). Implementation of the method and numerical results will appear in a later report.

Canright, David↗

Evaluation of Stereology for Snow Microstructure Measurement and Microwave Emission Modeling: A Case Study

Reliable microstructure measurement of snow is a requirement for microwave radiative transfer model validation. Snow specific surface area (SSA) can be measured using stereological methods, in which snow samples are cast in the field and photographed in the laboratory. Processing stereology photographs manually by counting intersections of test cycloids with air–ice boundaries reduces the problems in binary segmentation. This paper is a case study to evaluate the repeatability of the manually stereology interpretation by two independent research groups. We further assessed how uncertainty in snow SSA influences simulated brightness temperature(TB) driven by the Microwave Emission Model of Layered Snowpacks (MEMLS), and how stereology compares to Near Infrared (NIR) camera and hand lens. Data was obtained from two alpine snow profiles from Steamboat Springs, Colorado. Results showed that stereological SSA values measured by two groups are highly consistent, and the ground radiometer measured TBat 19 and 37 GHz was successfully predicted (RMSE<3.8 K);simulations using NIR SSA and hand-lens geometric grain size (Dg)measurements have larger errors. This conclusion was not sensitive to uncertainty in the free parameters of TB modeling.

Microwave radiometry↗

Aerodynamic Design Optimization for Natural Laminar Flow Airfoils

Natural laminar flow technology is a passive laminar flow control (LFC) strategy that seeks to delay the onset of boundary-layer transition (BLT) through shape optimization to reduce the drag of the aerodynamic vehicle. Adjoint-based design optimization for LFC is proposed in an integrated multidisciplinary framework, which includes the computational fluid dynamics (CFD), geometry and grid deformation, and linear stability analysis (LSA) for transition prediction. In particular, the BLT location is predicted using the dual N-factor method that is based on a linear stability theory (LST) eigenvalue problem. The dual N-factor criterion accounts for the amplification of planar Tollmien-Schlichting (TS) and stationary crossflow (CF) boundary-layer instabilities to predict the transition location in three-dimensional boundary-layer flows. The adjoint-based shape optimization procedure is based on an iteratively coupled CFD and LSA methodology to converge the transition location and flow solutions, as well as to calculate the sensitivities of the aerodynamic metrics of interest with respect to the flow and shape design parameters. The RAE 2822 airfoil at 0 and 30 degrees yaw angles, an angle of attack of 0.72 degrees, and subsonic conditions (M∞ = 0.19, Rec = 5.6 × 106 ) are used as baseline configurations for design optimization. The angle of attack and the vertical displacement of free-form-deformation control points are used as design variables to reduce the drag coefficient while reaching a specified lift coefficient. The optimized unswept airfoil designs achieve a 30% drag reduction accompanied by a downstream shift of the transition locations over both suction and pressure sides of the airfoil. The initial design iterations for the swept case also show a favorable trend in the drag reduction with transition delay over both sides.

Transition↗

A numerical study of shock wave/boundary layer interaction in nonequilibrium chemically reacting air - The effects of catalytic walls

This paper presents a numerical study that investigate the effects of nonequilibrium chemistry, and in particular, wall catalycity on the separated flow region generated by an oblique shock wave impinging upon a flat plate boundary layer. To obtain a solution to this problem, the full two dimensional Navier-Stokes equations were solved using MacCormack's predictor-corrector time dependent technique on a rectangular grid. Nonequilibrium chemistry was included by utilizing the 5 species, 17 reaction modified Dunn-Kang chemical kinetics model. Separate results were obtained for: calorically perfect, chemically reacting - noncatalytic wall, and chemically reacting - fully catalytic wall cases, for a given set of flow conditions. A direct comparison of all three cases revealed a slight decrease in the peak heat transfer for the noncatalytic wall case, as compared to the calorically perfect case. On the other hand, the fully catalytic wall case had a tremendous increase in the peak surface heat transfer. It is concluded that, for the particular conditons treated here (nearly frozen flow in the free stream), the effects of the nonequilibrium chemically reacting flow on the shock-wave/boundary-layer interaction depend critically on the catalycity of the wall, having virtually no effect for the case of a noncatalytic wall, and exerting a tremendous effect for a fully catalytic wall.

Grumet, Adam A.↗

Elliptic Grid Generation of Spiral-Bevel Pinion Gear Typical of OH-58 Helicopter Transmission

This paper discusses the source term treatment in the numerical solution of elliptic partial differential equations for an interior grid generation problem in generalized curvilinear coordinates. The geometry considered is that of a planar cross-section of a generic spiral-bevel gear tooth typical of a pinion in the OH-58 helicopter transmission. The source terms used are appropriate for an interior grid domain where all the boundaries are prescribed via a combination of Dirichlet and Neumann boundary conditions. New constraints based on the Green's Theorem are derived which uniquely determine the coefficients in the source terms. These constraints are designed for boundary clustered grids where gradients in physical quantities need to be resolved adequately. However, it is seen that the present formulation works satisfactorily for mild clustering also. Thus, a fully automated elliptic grid generation technique is made possible where there is no need for a parametric study of these parameters since the new relations fix these free parameters uniquely.

Kaul, Upender K.↗

Compressible laminar boundary layer with real gas effects for flight conditions to M(e) = 8 and T(o) = 2500 K

One of the problems for the hypersonic flights is the lack of accurate methods for predicting the boundary layer parameters at high Mach numbers and temperatures. At high Mach numbers and temperatures, the real gas effects should be included in calculations of the compressible laminar and turbulent boundary layers. By introducing the Mangler-Levy-Lees transformation, the compressible laminar boundary layer equations were transformed into two ordinary differential equations. To solve these ordinary differential equations for the flow over a flat plate, the Runge-Kutta method of order 5 and 6 was used with a secant method of solving the simultaneous nonlinear equations for the boundary layer conditions. Instead of using the perfect gas assumptions, the properties of air in the temperature range of 100 to 2500 K at M(e) = 8 were used for the calculations. The calculations were carried out for free flight conditions. The real gas effects were significant for the conditions of high freestream Mach numbers, and the boundary layer parameters from the real gas solutions were quite different from the existing formulas and solutions.

Nagamatsu, H. T.↗

Analysis of Aircraft Clusters to Measure Sector-Independent Airspace Congestion

The Distributed Air/Ground Traffic Management (DAG-TM) concept of operations* permits appropriately equipped aircraft to conduct Free Maneuvering operations. These independent aircraft have the freedom to optimize their trajectories in real time according to user preferences; however, they also take on the responsibility to separate themselves from other aircraft while conforming to any local Traffic Flow Management (TFM) constraints imposed by the air traffic service provider (ATSP). Examples of local-TFM constraints include temporal constraints such as a required time of arrival (RTA), as well as spatial constraints such as regions of convective weather, special use airspace, and congested airspace. Under current operations, congested airspace typically refers to a sector(s) that cannot accept additional aircraft due to controller workload limitations; hence Dynamic Density (a metric that is indicative of controller workload) can be used to quantify airspace congestion. However, for Free Maneuvering operations under DAG-TM, an additional metric is needed to quantify the airspace congestion problem from the perspective of independent aircraft. Such a metric would enable the ATSP to prevent independent aircraft from entering any local areas of congestion in which the flight deck based systems and procedures may not be able to ensure separation. This new metric, called Gaggle Density, offers the ATSP a mode of control to regulate normal operations and to ensure safety and stability during rare-normal or off-normal situations (e.g., system failures). It may be difficult to certify Free Maneuvering systems for unrestricted operations, but it may be easier to certify systems and procedures for specified levels of Gaggle Density that could be monitored by the ATSP, and maintained through relatively minor flow-rate (RTA type) restrictions. Since flight deck based separation assurance is airspace independent, the challenge is to measure congestion independent of sector boundaries. Figure 1 , reproduced from Ref. 1, depicts an example traffic situation. When the situation is analyzed by sector boundaries (left side of figure), a Dynamic Density metric would identify excessive congestion in the central sector. When the same traffic situation is analyzed independent of sector boundaries (right side of figure), a Gaggle Density metric would identify congestion in two dynamically defined areas covering portions of several sectors. The first step towards measuring airspace-independent congestion is to identify aircraft clusters, i.e., groups of closely spaced aircraft. The objective of this work is to develop techniques to detect and classify clusters of aircraft.

Bilimoria, Karl D.↗

Numerical solution of flow problems using body-fitted coordinate systems

The paper deals with numerically generated boundary-fitted coordinate systems. This procedure eliminates the shape of the boundaries as a complicating factor and allows the flow about arbitrary boundaries to be treated essentially as easily as that about simple boundaries. The technique of boundary-fitted coordinate systems is based on a method of automatic numerical generation of a general curvilinear coordinate system having a coordinate line coincident with each boundary of a general multiconnected region involving any number of arbitrarily shaped boundaries. Once the curvilinear coordinate system is generated, any partial differential system of interest may be solved on the coordinate system by transforming the equations and solving the resulting system in finite-difference approximation on the rectangular transformed plane. Attention is given to the types of boundary-fitted coordinate systems, coordinate system control, operation of the coordinate codes, solution of partial differential equations, application to free-surface flow, and other applications of interest.

Thompson, J. F.↗