Theory of optimum shapes in free-surface flows. Part 2. Minimum drag profiles in infinite cavity flow

The problem considered here is to determine the shape of a symmetric two-dimensional plate so that the drag of this plate in infinite cavity flow is a minimum. With the flow assumed steady and irrotational, and the effects due to gravity ignored, the drag of the plate is minimized under the constraints that the frontal width and wetted arc-length of the plate are fixed. The extremization process yields, by analogy with the classical Euler differential equation, a pair of coupled nonlinear singular integral equations. Although analytical and numerical attempts to solve these equations prove to be unsuccessful, it is shown that the optimal plate shapes must have blunt noses. This problem is next formulated by a method using finite Fourier series expansions, and optimal shapes are obtained for various ratios of plate arc-length to plate width

Unsteady, Free Surface Flows; Solutions Employing the Lagrangian Description of the Motion

Numerical techniques for the solution of unsteady free surface flows are briefly reviewed and consideration is given to the feasibility of methods involving parametric planes where the position and shape of the free surface are known in advance. A method for inviscid flows which uses the Lagrangian description of the motion is developed. This exploits the flexibility in the choice of Lagrangian reference coordinates and is readily adapted to include terms due to inhomogeneity of the fluid. Numerical results are compared in two cases of irrotational flow of a homogeneous fluid for which Lagrangian linearized solutions can be constructed. Some examples of wave run-up on a beach and a shelf are then computed

Theory of optimum shapes in free-surface flows. Part 1. Optimum profile of sprayless planing surface

This paper attempts to determine the optimum profile of a two-dimensional plate that produces the maximum hydrodynamic lift while planing on a water surface, under the condition of no spray formation and no gravitational effect, the latter assumption serving as a good approximation for operations at large Froude numbers. The lift of the sprayless planing surface is maximized under the isoperimetric constraints of fixed chord length and fixed wetted arc-length of the plate. Consideration of the extremization yields, as the Euler equation, a pair of coupled nonlinear singular integral equations of the Cauchy type. These equations are subsequently linearized to facilitate further analysis. The analytical solution of the linearized problem has a branch-type singularity, in both pressure and flow angle, at the two ends of plate. In a special limit, this singularity changes its type, emerging into a logarithmic one, which is the weakest type possible. Guided by this analytic solution of the linearized problem, approximate solutions have been calculated for the nonlinear problem using the Rayleigh-Ritz method and the numerical results compared with the linearized theory

Cavity-flow wall effects and correction rules

This paper is intended to evaluate the wall effects in the pure-drag case of plane cavity flow past an arbitrary body held in a closed tunnel, and to establish an accurate correction rule. The three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant-jet models, are employed to provide solutions in the form of some functional equations. From these theoretical solutions several different rules for the correction of wall effects are derived for symmetric wedges. These simple correction rules are found to be accurate, as compared with their corresponding exact numerical solutions, for all wedge angles and for small to moderate 'tunnel-spacing ratio' (the ratio of body frontal width to tunnel spacing). According to these correction rules, conversion of a drag coefficient, measured experimentally in a closed tunnel, to the corresponding unbounded flow case requires only the data of the conventional cavitation number and the tunnel-spacing ratio if based on the open-wake model, though using the Riabouchinsky model it requires an additional measurement of the minimum pressure along the tunnel wall. The numerical results for symmetric wedges show that the wall effects invariably result in a lower drag coefficient than in an unbounded flow at the same cavitation number, and that this percentage drag reduction increases with decreasing wedge angle and/or with decreasing tunnel spacing relative to the body frontal width. This indicates that the wall effects are generally more significant for thinner bodies in cavity flows, and they become exceedingly small for sufficiently blunt bodies. Physical explanations for these remarkable features of cavity-flow wall effects are sought; they are supported by the present experimental investigation of the pressure distribution on the wetted body surface as the flow parameters are varied. It is also found that the theoretical drag coefficient based on the Riabouchinsky model is smaller than that predicted by the open-wake model, all the flow parameters being equal, except when the flow approaches the choked state (with the cavity becoming infinitely long in a closed tunnel), which is the limiting case common to all theoretical models. This difference between the two flow models becomes especially pronounced for smaller wedge angles, shorter cavities, and with tunnel walls farther apart. In order to gauge the degree of accuracy of these theoretical models in approximating the real flows, and to ascertain the validity of the correction rules, a series of definitive experiments was carefully designed to complement the theory, and then carried out in a high-speed water tunnel. The measurements on a series of fully cavitating wedges at zero incidence suggest that, of the theoretical models, that due to Riabouchinsky is superior throughout the range tested. The accuracy of the correction rule based on that model has also been firmly established. Although the experimental investigation has been limited to symmetric wedges only, this correction rule (equations (85), (86) of the text) is expected to possess a general validity, at least for symmetric bodies without too large curvatures, since the geometry of the body profile is only implicitly involved in the correction formula. This experimental study is perhaps one of a very few with the particular objective of scrutinizing various theoretical cavity-flow models

Experimental Verification of Cavity-Flow Wall Effects and Correction Rules

This report is intended as a companion to Report No. E-111A.5, "Wall Efects in Cavity Flows", by Wu, Whitney and Lin. Some simple rules for the correction of wall effect are derived from that theoretical study. Experiments designed to complement the theory and to inspect the validity of the correction rules were then carried out in the high-speed water tunnel of the Hydrodynamics Laboratory, California Institute of Technology. The measurements on a series of fully cavitating wedges at zero angle of attack suggested that of the theoretical models that due to Riabouchinsky is superior. They also confirmed the accuracy of the correction rule derived using that model and based on a measurement of the minimum pressure along the tunnel wall

Final Report: Wall Effects in Cavity Flows

The wall effects in cavity flows past an arbitrary two-dimensional body is investigated for both pure-drag and lifting cases based on an inviscid nonlinear flow theory. The over-all features of various theoretical flow models for inviscid cavity flows under the wall effects are discussed from the general momentum consideration in comparison with typical viscous, incompressible wake flows in a channel. In the case of pure drag cavity flows, three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant jet models, are applied to evaluate the solution. Methods of numerical computation are discussed for bodies of arbitrary shape, and are carried out in detail for wedges of all angles. The final numerical results are compared between the different flow models, and the differences pointed out. Further analysis of the results has led to development of several useful formulas for correcting the wall effect. In the lifting flow case, the wall effect on the pressure and hydrodynamic forces acting on arbitrary body is formulated for the choked cavity flow in a closed water tunnel of arbitrary shape, and computed for the flat plate with a finite cavity in a straight tunnel

Inhibition of 5-lipoxygenase activity in mice during cuprizone-induced demyelination attenuates neuroinflammation, motor dysfunction and axonal damage

Multiple sclerosis (MS) is a chronic inflammatory demyelinating disease of the central nervous system (CNS). Increased expression of 5-lipoxygenase (5-LO), a key enzyme in the biosynthesis of leukotrienes (LTs), has been reported in MS lesions and LT levels are elevated in the cerebrospinal fluid of MS patients. To determine whether pharmacological inhibition of 5-LO attenuates demyelination, MK886, a 5-LO inhibitor, was given to mice fed with cuprizone. Gene and protein expression of 5-LO were increased at the peak of cuprizone-induced demyelination. Although MK886 did not attenuate cuprizone-induced demyelination in the corpus callosum or in the cortex, it attenuated cuprizone-induced axonal damage and motor deficits and reduced microglial activation and IL-6 production. These data suggest that during cuprizone-induced demyelination, the 5-LO pathway contributes to microglial activation and neuroinflammation and to axonal damage resulting in motor dysfunction. Thus, 5-LO inhibition may be a useful therapeutic treatment in demyelinating diseases of the CNS

2020 American College of Rheumatology Guideline for the Management of Reproductive Health in Rheumatic and Musculoskeletal Diseases

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154675/1/art41191.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154675/2/art41191_am.pd

Genes implicated in multiple sclerosis pathogenesis from consilience of genotyping and expression profiles in relapse and remission

<p>Abstract</p> <p>Background</p> <p>Multiple sclerosis (MS) is an inflammatory demyelinating disease of the central nervous system (CNS). Although the pathogenesis of MS remains unknown, it is widely regarded as an autoimmune disease mediated by T-lymphocytes directed against myelin proteins and/or other oligodendrocyte epitopes.</p> <p>Methods</p> <p>In this study we investigated the gene expression profiles of peripheral blood cells from patients with RRMS during the relapse and the remission phases utilizing gene microarray technology. Dysregulated genes encoded in regions associated with MS susceptibility from genomic screens or previous trancriptomic studies were identified. The proximal promoter region polymorphisms of two genes were tested for association with disease and expression level.</p> <p>Results</p> <p>Distinct sets of dysregulated genes during the relapse and remission phases were identified including genes involved in apoptosis and inflammation. Three of these dysregulated genes have been previously implicated with MS susceptibility in genomic screens: TGFβ1, CD58 and DBC1. TGFβ1 has one common SNP in the proximal promoter: -508 T>C (rs1800469). Genotyping two Australian trio sets (total 620 families) found a trend for over-transmission of the T allele in MS in females (p < 0.13). Upregulation of CD58 and DBC1 in remission is consistent with their putative roles in promoting regulatory T cells and reducing cell proliferation, respectively. A fourth gene, ALOX5, is consistently found over-expressed in MS. Two common genetic variants were confirmed in the ALOX5 putatve promoter: -557 T>C (rs12762303) and a 6 bp tandem repeat polymorphism (GGGCGG) between position -147 and -176; but no evidence for transmission distortion found.</p> <p>Conclusion</p> <p>The dysregulation of these genes tags their metabolic pathways for further investigation for potential therapeutic intervention.</p