Cavity and Wake Flows

The phenomenon of wake formation behind a body moving through a fluid, and the associated resistance of fluids, must have been one of the oldest experiences of man. From an analytical point of view, it is also one of the most difficult problems in fluid mechanics. Rayleigh, in his 1876 paper, observed that "there is no part of hydrodynamics more perplexing to the student than that which treats of the resistance of fluids." This insight of Rayleigh is so penetrating that the march of time has virtually left no mark on its validity even today, and likely still for some time to come. The first major step concerning the resistance of fluids was made over a century ago when Kirchhoff (1869) introduced an idealized inviscid-flow model with free streamlines (or surfaces of discontinuity) and employed (for steady, plane flows) the ingenious conformal-mapping technique that had been invented a short time earlier by Helmholtz (1868) for treating two-dimensional jets formed by free streamlines. This pioneering work offered an alternative to the classical paradox of D’Alembert (or the absence of resistance) and laid the foundation of the free-streamline theory. We appreciate the profound insight of these celebrated works even more when we consider that their basic idea about wakes and jets, based on a construction with surfaces of discontinuity, was formed decades before laminar and turbulent flows were distinguished by Reynolds (1883), and long before the fundamental concepts of boundary-layer theory and flow separation were established by Prandtl (1904a). However, there have been some questions raised in the past, and still today, about the validity of the Kirchhoff flow for the approximate calculation of resistance. Historically there is little doubt that in constructing the flow model Kirchhoff was thinking of the wake in a single-phase fluid, and not at all of the vapor-gas cavity in a liquid; hence the arguments, both for and against the Kirchhoff flow, should be viewed in this light. On this basis, an important observation was made by Sir William Thomson, later Lord Kelvin (see Rayleigh 1876) "that motions involving a surface of separation are unstable" (we infer that instability here includes the viscous effect). Regarding this comment Rayleigh asked "whether the calculations of resistance are materially affected by this circumstance as the pressures experienced must be nearly independent of what happens at some distance in the rear of the obstacle, where the instability would first begin to manifest itself." This discussion undoubtedly widened the original scope, brought the wake analysis closer to reality, and hence should influence the course of further developments. An expanded discussion essentially along these lines was given by Levi-Civita (1907) and was included in the survey by Goldstein (1969). Another point of fundamental importance is whether the Kirchhoff flow is the only correct Euler (or outer) limit of the Navier-Stokes solution to steady flow at high Reynolds numbers. If so, then a second difficulty arises, a consequence of the following argument: We know that the width of the Kirchhoff wake grows parabolically with the downstream distance x, at a rate independent of the (kinematic) viscosity u. If Prandtl’s boundary-layer theory is then applied to smooth out the discontinuity (i.e. the vortex sheet) between the wake and the potential flow, one obtains a laminar shear layer whose thickness grows like (ux/U)^-1/2 in a free stream of velocity U. Hence, for sufficiently small u/U the shear layers do not meet, so that the wake bubble remains infinitely long at a finite Reynolds number, a result not supported by experience. (For more details see Lagerstrom 1964, before p. 106, 131; Kaplun 1967, Part II.) The weaknesses in the above argument appear to lie in the two primary suppositions that, first, the free shear layer enveloping the wake would remain stable indefinitely, and second (perhaps a less serious one), the boundary-layer approximation would be valid along the infinitely long wake boundary. Reattachment of two turbulent shear layers, for instance, is possible since their thickness grows linearly with x. By and large, various criticisms, of the Kirchhoff flow model have led to constructive refinements of the free-streamline theory rather than to a weakening of the foundation of the theory as a valuable idealization. The major development in this direction has been based on the observation that the wake bubble is finite in size at high Reynolds numbers. (The wake bubble, or the near-wake, means, in the ordinary physical sense, the region of closed streamlines behind the body as characterized by a constant or nearly constant pressure.) To facilitate the mathematical analysis of flows with a finite wake bubble, a number of potential-flow models have been introduced to give the near-wake a definite configuration as an approximation to the inviscid outer flow. These theoretical models will be discussed explicitly later. It suffices to note here that all these models, even though artificial to various degrees, are aimed at admitting the near-wake pressure coefficient as a single free parameter of the flow, thus providing a satisfactory solution to the state of motion in the near part of the wake attached to the body. On the whole, their utility is established by their capability of bringing the results of potential theory of inviscid flows into better agreement with experimental measurements in fluids of small viscosity. The cavity flow also has a long, active history. Already in 1754, Euler, in connection with his study of turbines, realized that vapor cavitation may likely occur in a water stream at high speeds. In investigating the cause of the racing of a ship propeller, Reynolds (1873) observed the phenomenon of cavitation at the propeller blades. After the turn of this century, numerous investigations of cavitation and cavity flows were stimulated by studies of ship propellers, turbomachinery, hydrofoils, and other engineering developments. Important concepts in this subject began to appear about fifty years ago. In an extensive study of the cavitation of water turbines, Thoma (1926) introduced the cavitation number (the underpressure coefficient of the vapor phase) as the principal similarity parameter, which has ever since played a central role in small-bubble cavitation as well as in well-developed cavity flows. Applications of free-streamline theory to finite-cavity flows have attracted much mathematical interest and also provided valuable information for engineering purposes. Although the wake interpretation of the flow models used to be standard, experimental verifications generally indicate that the theoretical predictions by these finite-wake models are satisfactory to the same degree for both wake and cavity flows. This fact, however, has not been widely recognized and some confusion still exists. As a possible explanation, it is quite plausible that even for the wake in a single-phase flow, the kinetic energy of the viscous flow within the wake bubble is small, thus keeping the pressure almost unchanged throughout. Although this review gives more emphasis to cavity flows, several basic aspects of cavity and wake flows can be effectively discussed together since they are found to have many important features in common, or in close analogy. This is in spite of relatively minor differences that arise from new physical effects, such as gravity, surface tension, thermodynamics of phase transition, density ratio and viscosity ratio of the two phases, etc., that are intrinsic only to cavity flows. Based on this approach, attempts will be made to give a brief survey of the physical background, a general discussion of the free-streamline theory, some comments on the problems and issues of current interest, and to point out some basic problems yet to be resolved. In view of the vast scope of this subject and the voluminous literature, efforts will not be aimed at completeness, but rather on selective interests. Extensive review of the literature up to the 1960s may be found in recent expositions by Birkhoff & Zarantonello (1957), Gilbarg (1960), Gurevich (1961), Wehausen (1965), Sedov (1966), Wu (1968), Robertson & Wislicenus (1969), and (1961)

Bio-medical application on predicting systolic blood pressure using neural networks

This paper presents a new study based on artificial neural network, which is a typical technique for processing big data, for the prediction of systolic blood pressure by correlated factors (gender, serum cholesterol, fasting blood sugar and electrocardiography signal). Two neural network algorithms, back-propagation neural network and radial basis function network, are used to construct and validate the bio-medical prediction system. The database of raw data is divided into two parts: 80% for training the neural network and the remaining 20% for testing the performance. The experimental result shows that artificial neural networks are suitable for modeling and predicting systolic blood pressure. This novel method of predicting systolic blood pressure contributes to giving early warnings to adults who may not take regular blood pressure measurements. Also, as it is known that an isolated blood pressure measurement is sometimes not very accurate due to the daily fluctuation, our predictor can provide another reference value to the medical staff.published_or_final_versio

Decision support and data mining for direct consumer-to-consumer trading

This paper describes a decision support system that integrates a hybrid neighborhood search algorithm for determining the price of sale item when it is placed for trading in the Internet. The seller would provide the condition and number of years of usage of the used item, and the intelligent system would provide real-time search on related items in the marketplace and suggest a price for trading. Data mining techniques are explored for efficient processing of a vast amount of information in the database tables. In addition, the trading system would also have the intelligence of recommending items or products to a potential buyer given the previous purchase patterns. Related items to a recently purchased item would also be suggested with an aim of providing friendly reminders and recommendations so that the user of the website would obtain a pleasant trading experience. © 2014 Infonomics Society.published_or_final_versio

Predicting systolic blood pressure using machine learning

In this paper, a new study based on machine learning technique, specifically artificial neural network, is investigated to predict the systolic blood pressure by correlated variables (BMI, age, exercise, alcohol, smoke level etc.). The raw data are split into two parts, 80% for training the machine and the remaining 20% for testing the performance. Two neural network algorithms, back-propagation neural network and radial basis function network, are used to construct and validate the prediction system. Based on a database with 498 people, the probabilities of the absolute difference between the measured and predicted value of systolic blood pressure under 10mm Hg are 51.9% for men and 52.5% for women using the back-propagation neural network With the same input variables and network status, the corresponding results based on the radial basis function network are 51.8% and 49.9% for men and women respectively. This novel method of predicting systolic blood pressure contributes to giving early warnings to young and middle-aged people who may not take regular blood pressure measurements. Also, as it is known an isolated blood pressure measurement is sometimes not very accurate due to the daily fluctuation, our predictor can provide another reference value to the medical staff. Our experimental result shows that artificial neural networks are suitable for modeling and predicting systolic blood pressure. © 2014 IEEE.published_or_final_versio

Design intelligence of web application for internet direct consumer-to-consumer trading

An online web application called Student-Trade has been developed. It is a state-of-the-art platform for direct consumer-to-consumer trading in the Internet. The platform is targeted for direct consumer-to-consumer trading among university students. The items for trading include books, household items, electronics, housing rental, sports equipment and tutoring services. This paper is on the design intelligence of the Student-Trade web application. One objective is to help the user to decide on the selling price of his item when the item is being posted in the web application. The system integrates a hybrid neighborhood search algorithm for determining the price of sale item when it is placed for trading in the Internet. Data mining techniques are explored for efficient processing of a vast amount of information in the database tables. In addition, the trading system would also have the intelligence of recommending items or products to a potential buyer given the previous purchase patterns. The aim is to provide a pleasant trading experience for the user. © 2015 IEEE.published_or_final_versio

Inclinations and black hole masses of Seyfert 1 galaxies

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An optimization model for a battery swapping station in Hong Kong

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Remnant Fermi surface in the presence of an underlying instability in layered 1T-TaS_2

We report high resolution angle-scanned photoemission and Fermi surface (FS) mapping experiments on the layered transition-metal dichalcogenide 1T-TaS_2 in the quasi commensurate (QC) and the commensurate (C) charge-density-wave (CDW) phase. Instead of a nesting induced partially removed FS in the CDW phase we find a pseudogap over large portions of the FS. This remnant FS exhibits the symmetry of the one-particle normal state FS even when passing from the QC-phase to the C-phase. Possibly, this Mott localization induced transition represents the underlying instability responsible for the pseudogapped FS

Spectroscopic Properties of QSOs Selected from Ultraluminous Infrared Galaxy Samples

We performed spectroscopic observations for a large infrared QSO sample with a total of 25 objects. The sample was compiled from the QDOT redshift survey, the 1 Jy ULIRGs survey and a sample obtained by a cross-correlation study of the IRAS Point Source Catalogue with the ROSAT All Sky Survey Catalogue. Statistical analyses of the optical spectra show that the vast majority of infrared QSOs have narrow permitted emission lines (with FWHM of Hbeta less than 4000 km/s) and more than 60% of them are luminous narrow line Seyfert 1 galaxies. Two of the infrared QSOs are also classified as low ionization BAL QSOs. More than 70% of infrared QSOs are moderately or extremely strong Fe II emitters. This is the highest percentage of strong Fe II emitters in all subclasses of QSO/Seyfert 1 samples. We found that the Fe II to Hbeta, line ratio is significantly correlated with the [OIII]5007 peak and Hbeta blueshift. Soft X-ray weak infrared QSOs tend to have large blueshifts in permitted emission lines and significant Fe II48,49 (5100--5400 A) residuals relative to the Boroson & Green Fe II template. If the blueshifts in permitted lines are caused by outflows, then they appear to be common in infrared QSOs. As the infrared-selected QSO sample includes both luminous narrow line Seyfert 1 galaxies and low ionization BAL QSOs, it could be a useful laboratory to investigate the evolutionary connection among these objects.Comment: 35 pages,14 figures, 4 tables, accepted for publication in A

Does gravitational wave propagate in the five dimensional space-time with Kaluza-Klein monopole?

The behavior of small perturbations around the Kaluza-Klein monopole in the five dimensional space-time is investigated. The fact that the odd parity gravitational wave does not propagate in the five dimensional space-time with Kaluza-Klein monopole is found provided that the gravitational wave is constant in the fifth direction.Comment: 10 @ages, LATE