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Non-linear threshold analysis enabled discovery of a highly soluble (1.3 M) bipyrimidine anolyte. Stable cycling in a full flow battery cell for 75 cycles.
Analysis of flutter of flat rectangular panels at low supersonic mach numbers using air forces from exact linearized potential-flow theory
A combination of linear, weakly nonlinear, and secondary stability theories has been used to study the transition process in rotating channel flow. Results for parts of the theory have been confirmed by direct numerical simulations. Preliminary results indicate that the theory can help explain some experimental observations regarding the evolution of streamwise vortices.
The upper-branch linear and nonlinear stability of compressible boundary layer flows is studied using the approach of Smith and Bodonyi (1982) for a similar incompressible problem. Both pressure gradient boundary layers and Blasius flow are considered with and without heat transfer, and the neutral eigenrelations incorporating compressibility effects are obtained explicitly. The compressible nonlinear viscous critical layer equations are derived and solved numerically and the results indicate some solutions with positive phase shift across the critical layer. Various limiting cases are investigated including the case of much larger disturbance amplitudes and this indicates the structure for the strongly nonlinear critical layer of the Benney-Bergeon (1969) type. It is also shown how a match with the inviscid neutral inflexional modes arising from the generalized inflexion point criterion, is achieved.
A general method of design is developed for two-dimensional unbranched channels with prescribed velocities as a function of arc length along the channel walls. The method is developed for both compressible and incompressible, irrotational, nonviscous flow and applies to the design of elbows, diffusers, nozzles, and so forth. In part I solutions are obtained by relaxation methods; in part II solutions are obtained by a Green's function. Five numerical examples are given in part I including three elbow designs with the same prescribed velocity as a function of arc length along the channel walls but with incompressible, linearized compressible, and compressible flow. One numerical example is presented in part II for an accelerating elbow with linearized compressible flow, and the time required for the solution by a Green's function in part II was considerably less than the time required for the same solution by relaxation methods in part I.
The surface integral terms in Green's third identity are often used to solve the Prandtl-Glauert (linear potential-flow) equation with panel methods. This can be done, as in the PAN AIR code, for either subsonic or supersonic flow about complete aircraft. The extension to transonic flow is suggested by the volume integral terms of Green's third identity. The mathematical basis for this extension, without the use of body-fitted grids, is presented. Supercritical transonic results computed from a two-dimensional transonic PAN AIR research code demonstrate the method.
The propagation of sound in a converging-diverging duct containing a quasi-one-dimensional steady flow with a high subsonic throat Mach number is studied. The behavior of linearized acoustic theory at the throat of the duct is shown to be singular, and the explicit form of the singularity is determined for two special types of area variation. Numerically computed results showing the development of the singularity are presented. The singularity implies that linearized acoustic theory is invalid for sound propagating through a throat carrying a near-sonic flow.
The cylindrical slab was the first and simplest model of intrinsically unstable microturbulence. The Helimak is an experimental realization of this model. Although finite, it is sufficiently large to escape boundary effects, with dimensionless parameters similar to those of a tokamak edge or scrape off layer. The essential drive is interchange-like, a pressure gradient with unfavorable magnetic curvature, leading to a non-linearly saturated state of large-amplitude turbulence, Δn{sub rms}/n ∼ 0.5. The nonlinear processes governing this saturation are unique, unlike any of those posited for the much weaker turbulence typical of confined plasma, e.g., in a tokamak. Neither linear stability theory, quasi-linear theory, zonal flows, nor flow shear stabilization is consistent with the observations. The mechanisms determining the non-linearly saturated state constitute an important challenge to our understanding of strongly nonlinear systems.
A method for solving the linear integral equations of incompressible potential flow in three dimensions is presented. Both analysis (Neumann) and design (Dirichlet) boundary conditions are treated in a unified approach to the general flow problem. The method is an influence coefficient scheme which employs source and doublet panels as boundary surfaces. Curved panels possessing singularity strengths, which vary as polynomials are used, and all influence coefficients are derived in closed form. These and other features combine to produce an efficient scheme which is not only versatile but eminently suited to the practical realities of a user-oriented environment. A wide variety of numerical results demonstrating the method is presented.
A technique for estimating the additive forces and moments associated with supersonic, external compression inlets as a function of mass flow ratio has been developed. The technique makes use of a low order supersonic paneling method for calculating minimum additive forces at maximum mass flow conditions. A linear relationship between the minimum additive forces and the maximum values for fully blocked flow is employed to obtain the additive forces at a specified mass flow ratio. The method is applicable to two-dimensional inlets at zero or nonzero angle of attack, and to axisymmetric inlets at zero angle of attack. Comparisons with limited available additive drag data indicate fair to good agreement.
The linear stability of an incompressible laminar flow in the blending boundary layer between the boundary layer in a 90 deg streamwise corner and a Blasius boundary layer well away from the corner is examined using a locally parallel flow approximation. It is shown that the influence of the outer boundary conditions associated with oblique modes of disturbances which are anti-symmetric about the bisector plane have a profound effect on the stability of the flow. As a result, in good agreement with observation, the critical streamwise Reynolds number, associated with a spanwise location is significantly reduced as the corner is approached, being R(sub Cr) = 60 approximately for spanwise distance of z* = 6x*R(sup -1) from the corner compared with R(sub Cr) = 322 approximately for z* = 20x*R(sup -1), where x* measures downstream distance from the leading edges. At R = 600, the growth rate of the most amplified mode of disturbance at the former location is over six times greater than that at the latter; the corresponding wave angle at the two locations is respectively 44 deg and 5 deg, approximately.
Theoretical analyses and computer codes are being developed for predicting compressible unsteady inviscid and viscous flows through blade rows of axial-flow turbomachines. Such analyses are needed to determine the impact of unsteady flow phenomena on the structural durability and noise generation characteristics of the blading. The emphasis has been placed on developing analyses based on asymptotic representations of unsteady flow phenomena. Thus, high Reynolds number flows driven by small amplitude unsteady excitations have been considered. The resulting analyses should apply in many practical situations and lead to a better understanding of the relevant flow physics. In addition, they will be efficient computationally, and therefore, appropriate for use in aeroelastic and aeroacoustic design studies. Under the present effort, inviscid interaction and linearized inviscid unsteady flow models have been formulated, and inviscid and viscid prediction capabilities for subsonic steady and unsteady cascade flows have been developed. In this report, we describe the linearized inviscid unsteady analysis, LINFLO, the steady inviscid/viscid interaction analysis, SFLOW-IVI, and the unsteady viscous layer analysis, UNSVIS. These analyses are demonstrated via application to unsteady flows through compressor and turbine cascades that are excited by prescribed vortical and acoustic excitations and by prescribed blade vibrations. Recommendations are also given for the future research needed for extending and improving the foregoing asymptotic analyses, and to meet the goal of providing efficient inviscid/viscid interaction capabilities for subsonic and transonic unsteady cascade flows.
In a time-dependent flow, nonlinear harmonics can be excited by coupling between linear waves and flow-induced harmonic waves. Examining the dispersion relations and selection rules for the coupling, we investigate nonlinearly coupled harmonics for waves propagating along the magnetic field line in a magnetized plasma, as well as waves in an unmagnetized plasma. The coupled harmonics in a plasma flow are described by analytic dispersion relations and selection rules. This nonlinear coupling is corroborated by the particle-in-cell simulation. Here, the coupled-harmonics model describes a mechanism for the excitation of nonlinear harmonics from linear waves in a time-dependent flow. The spectral analysis of the dispersion relation provides a useful way to evaluate the spatiotemporal behavior of a plasma flow.
The requirements placed on an unsteady aerodynamic theory intended for turbomachinery aeroelastic applications are discussed along with a brief description of the various theoretical models that are available to address these requirements. The main emphasis is placed on the description of a linearized inviscid theory which fully accounts for the effects of a nonuniform mean or steady flow on unsteady aerodynamic response. Although this theory has been developed primarily for blade flutter prediction, more general equations are presented which account for unsteady excitations due to incident external aerodynamic disturbances as well as those due to blade motions. The resulting equations consist of a system of three field equations along with conditions imposed at blade, wake and shock surfaces and in the far field. These equations can be solved to determine the fluctuations in all fluid dynamic properties throughout the required solution domain. Example solutions are presented to demonstrate several effects associated with nonuniform steady flows on the linearized unsteady aerodynamic response to prescribed blade motions.
Hydrologic alteration continues to affect aquatic biodiversity asknowledge of the spawning requirements of fishes, especially keystone or foundation species, becomes more critical for conservation and management. Our objectives are to quantify the spawning micro- and mesohabitat use of river chub Nocomis micropogon, a gravel mound nesting minnow, in a hydrologically regulated river in North Carolina, USA. At the microhabitat scale, substrate sizes on nests were compared with pebble counts in 1-m2 adjacent quadrats. Average depths and current velocities at nests were compared with measurements from paired transects. At the mesohabitat scale, generalised linear mixed models (GLMMs) were used to identify the importance of average bed slope, average depth and percentages of rock outcrops (a measure of flow heterogeneity and velocity shelters) for predicting nest presence and abundance. To relate nesting activities to hydrologic alteration from dam operation, nest dimensions were measured before and after a scheduled discharge event approximately six times that of base flow. In addition, linear regression was used to predict changes in the use of flow refugia and overhead cover with increased fluvial distance from the dam. Microhabitats in which nests were placed had, on average, slower current velocities and shallower depths. Gravel diameters of nests were significantly smaller than substrate particles adjacent to nests. GLMMs revealed that mesohabitats with nests were shallower, had more moderate slopes and greater proportions of rock outcrops than mesohabitats without nests. Finally, the scheduled discharge event significantly flattened nests. Near the dam, nests were built in close proximity ( 2 m) to velocity shelters; this relationship diminished with distance from the dam. River chubs are spawning habitat specialists. Because multiple species rely on river chub nests for reproduction and food, the needs of this species should be considered when managing instream flows.
A two-dimensional, linear stability analysis of a thin nonplanar liquid sheet flow in vacuum is carried out. A sheet flow created by a narrow slit of W and tau attains a nonplanar cross section as a consequence of cylinders forming on the sheet edge under the influence of surface tension forces. The region where these edge cylinders join the sheet is one of high curvature, and this is found to be the location where instability is most likely to occur. The sheet flow is found to be unstable, but with low growth rates for symmetric wave disturbances and high growth rates for antisymmetric disturbances. By combining the symmetric and antisymmetric disturbance modes, a wide range of stability characteristics is obtained. The product of unstable growth rate and flow time is proportional to the width-to-thickness ratio of the sift generating the sheet Three-dimensional effects can alter these results, particularly when the sheet length-to-width ratio is not much greater than unity.
Conventional semi-infinite analytical solutions of correlation diffusion equation may lead to errors when calculating blood flow index (BFI) from diffuse correlation spectroscopy (DCS) measurements in tissues with irregular geometries. Very recently, we created an algorithm integrating a Nth-order linear model of autocorrelation function with the Monte Carlo simulation of photon migrations in homogenous tissues with arbitrary geometries for extraction of BFI (i.e., αD{sub B}). The purpose of this study is to extend the capability of the Nth-order linear algorithm for extracting BFI in heterogeneous tissues with arbitrary geometries. The previous linear algorithm was modified to extract BFIs in different types of tissues simultaneously through utilizing DCS data at multiple source-detector separations. We compared the proposed linear algorithm with the semi-infinite homogenous solution in a computer model of adult head with heterogeneous tissue layers of scalp, skull, cerebrospinal fluid, and brain. To test the capability of the linear algorithm for extracting relative changes of cerebral blood flow (rCBF) in deep brain, we assigned ten levels of αD{sub B} in the brain layer with a step decrement of 10% while maintaining αD{sub B} values constant in other layers. Simulation results demonstrate the accuracy (errors < 3%) of high-order (N ≥ 5) linear algorithm in extracting BFIs in different tissue layers and rCBF in deep brain. By contrast, the semi-infinite homogenous solution resulted in substantial errors in rCBF (34.5% ≤ errors ≤ 60.2%) and BFIs in different layers. The Nth-order linear model simplifies data analysis, thus allowing for online data processing and displaying. Future study will test this linear algorithm in heterogeneous tissues with different levels of blood flow variations and noises.
Power distribution systems are more prone to disruptions and cause most power system outages. We propose a service restoration technique to recover the system service (electricity delivery) following an extreme event-triggered substation outage. The proposed technique considers the problem of controlling distributed energy resources (DERs) of a distribution system with the objective of achieving maximum load pick up while satisfying network flow and voltage constraints. The problem is formulated as a model predictive control (MPC), where a linearized optimal power flow (OPF) model is employed to describe the network. The formulation is augmented with a ramping (up) reserve product for the DERs to ensure an upward monotonic load restoration as time evolves. We perform simulations considering the IEEE 13-bus test feeder integrated with wind, solar, microturbine, and energy storage devices. We demonstrate the efficacy of the devised technique in restoring the system loads monotonically, without shedding previously restored loads. We also show the benefit of co-optimization of power and reserve products for DERs on service restoration. In addition, the capability of the technique in regulating nodal voltages and reducing renewable power curtailment is demonstrated.