Merging Patterns Research Articles

A model for seasonal and annual cooling tower impacts

The Argonne National Laboratory/University of Illinois Seasonal/Annual Cooling Tower Impacts model provides predictions of seasonal, monthly, and annual cooling tower impacts from any number of mechanical- or natural-draft cooling towers. The model typically requires five years of hourly surface meteorological data and concurrent twice-daily mixing heights in addition to basic data on the thermal performance of the cooling tower. The model predicts average plume length, rise, drift deposition, fogging, icing, and shadowing. The model uses a category scheme in which the five years of hourly surface data are placed into about 100 categories based on a special plume-scalling relationship. With this reduced number of cases to be run for long-term impact evaluations, advanced state-of-the-art models for plume impacts are then applied. For multiple plumes, the methodology includes variation of the merging patterns and of the wake effects from tower housings for different wind directions. The main advantage to this model over previous models is its advanced theoretical development and extensive model validation with experimental data for its component submodels. From studies in the United States of America and Europe, an extensive database on cooling tower plumes and drift was accumulated and analysed to assist in the identification of superior theoretical assumptions. Other data, not used in model development, provided for independent model verification. The validation of each submodel is presented, and typical results are given for a representative natural-draft cooling tower installation and for a typical linear mechanical-draft cooling tower arrangement.

Acoustic-vortex interactions and low-frequency oscillations in axisymmetric combustors

Time-dependent, compressible numerical simulations have been performed to study the flowfields in an idealized ramjet consisting of an axisymmetric inlet and a combustor. The simulations indicate strong coupling between the flowfield and the acoustics of both the inlet and the combustor. For the cases studied, forcing at the first longitudinal acoustic mode of the combustor induces vortex rollup near the entrance to the combustor at the forcing frequency. A low-frequency oscillation is also observed in all of the simulations. Pressure fluctuations in the inlet indicate that the low frequency corresponds to a quarter-wave mode in the inlet. Changing the length of the inlet appropriately changes the observed low frequency. The merging pattern of the vortices in the combustor is modified significantly when either the acoustics of the combustor or that of the inlet are changed. These merging patterns are explained on the basis of an interaction between the vortex-rollup frequency and the acoustic modes of the inlet and combustor.

Numerical simulations of acoustic-vortex interactions in a central-dump ramjet combustor

A potentially important source of large pressure oscillations in compact ramjets is a combustion instability induced by the interaction of large-scale vortex structures with the acoustic modes of the ramjet. These interactions have been studied using time-dependent, compressible numerical simulations of cold flow in an idealized ramjet consisting of an axisymmetric inlet and combustor. The simulations indicate a strong coupling between the flowfield and the acoustics of both the inlet and the combustor. Vortex rollup is observed near the entrance to the combustor at the first longitudinal acoustic mode of the combustor. A low-frequency mode is also observed in the simulations. This mode is determined by the acoustics of the inlet and causes major changes in the merging pattern of the vortices.

The effect of phase-difference on the spreading rate of a jet

The role of initial phase-difference between fundamental and subharmonic instability waves on the spreading rate of a circular jet under bimodal excitation is investigated theoretically. For all Strouhal numbers considered, the initial growth rate of the subharmonic was found to be a maximum when the two waves are initially in-phase. The effect of phase-differe nce on the subharmonic's peak is dependent on Strouhal number. Development of the momentum thickness along the jet is characterized by regions of stepwise growth. The momentum thickness first increases as the fundamental amplifies. This growth region is followed by a region where the decay of the fun- damental and the growth of the subharmonic result in a constant momentum thickness. Once the fundamental has fully decayed, the momentum thickness grows again as a result of the subharmonic's amplification. The growth rate is dependent on the initial phase-difference, and is maximum when the subharmonic suffers max- imum amplification. UMERICAL simulation of vortex-pairin g interactions in two-dimensional mixing layers1'2 has shown that the pair- ing process is dependent on the phase-difference between the fundamental and subharmonic instability waves. The smaller the initial phase-difference between the two modes, the faster the coalescence of the two vortices. In the limiting case where the two components are antiphase, the numerical results of Patnaik et al. 1 showed that the vortex-pairing interaction is actually suppressed and replaced by shredding interactions. In the experiment of Zhang et al. 3 of a two-dimensional shear layer under bimodal excitation, significantly different merging patterns were observed as a result of changing the in- itial phase-difference between the fundamental and sub- harmonic. Monkewitz4 modified Kelly's5 temporal stability analysis of a spatially periodic mixing layer to include an ar- bitrary phase-difference between the fundamental and sub- harmonic instability waves. The initial growth rate was found to vary continuously from maximum when both waves are in- phase, to a minimum when they are out of phase. These in- vestigations indicate the importance of the phase-difference on the fundamental-subharmonic interaction. In the plane shear-layer case, Ho and Huang6 have shown that the spreading rates can be greatly manipulated by con- trolling the vortex-pairing process. Since this pairing process is dependent on the phase-difference between the fundamen- tal and subharmonic instabilities,15 one would expect the spreading rate to be dependent on this phase-difference. The present work is concerned with the technologically important problem of a round jet where the spreading rate can be manipulated via bimodal excitation at fundamental and sub- harmonic frequencies. In the present analysis, the energy equations for each flow component are used to study the ef- fect of initial phase-differencing between the two excitation components on their spatial developments and on the spreading rate. In the jet mixing region, the vortex-pairing process results in the growth of the subharmonic. The loca- tion of pairing and, thus, of the subharmonic's amplification depends on the random initial fluctuations at the jet exit and, hence, on the initial phase-difference. The question arises as to how much energy is carried by the subharmonic

Rotational distribution of para-H2 in He shock wave

The rotational distribution and collision number Zr of para-H2 in the He shock wave are studied using the master equation and the quantum mechanical rate constant obtained by Rabitz and Zarur. For high Mach number, at the initial stage, the rotational distribution indicates a merging pattern of two Boltzmann distributions at the lower and higher rotational levels corresponding to the pre-shock temperature T1 and the reduced temperature T2Tc/(T2+Tc), where T2 and Tc are the post-shock and rate-constant temperatures, respectively. The rotational distribution at the final stage indicates a non-Boltzmann distribution with underpopulation at the higher levels, which is also observed for low Mach number. The rotational collision number Zr over the period of the rotational relaxation is found to show a step pattern with the plateaus corresponding to the rotational collision number Zjj′ of the two-level systems (jj′) = (02), (24), (46),....

Rotational distribution of N2 in Ar shock wave

The rotational distribution of N2 in the Ar shock wave is quantitatively studied using the rotational transition cross sections of the exponential gap and power laws. The relaxation of the rotational distribution in the shock wave is described by the master equation, where the velocity distributions are taken as the local Maxwell distribution at a low Mach number and the Mott–Smith bimodal distribution at a high Mach number. The rotational distribution indicates a near Boltzmann distribution at a low Mach number. At a high Mach number a merging pattern of the Boltzmann distributions at the lower and higher rotational levels corresponding to temperatures before and after the shock wave, respectively, is obtained at the fore part of the shock wave, where the rapid increase in the populations of the higher levels is caused by the accumulation of the fluxes from the lower levels. The merging pattern is well established by the existence of hot molecules in the Mott–Smith bimodal velocity distribution. The rotational temperature profile precedes the density profile both at low and high Mach numbers. The fact that the pattern of the rotational distribution in the N2–Ar system is in qualitative agreement with the measured pattern in the pure N2 system may indicate that the rotation–rotation transition does not play an important role in the pattern of the rotational distribution of N2 in the shock wave.

On V-Optimal Trees

The problem of determining minimal cost trees when the cost function is a linear combination of degree path length and external path length arises in the study of optimal disk merge patterns, as first pointed out by Knuth. This paper considers the special case when internal nodes of degrees two and three only are permitted. The notion of the V-cost of a tree is introduced, and the properties of trees of minimal V-cost are found, with particular emphasis on the case when the external weights are all equal. Some algorithms are presented which generate trees of minimal V-cost under certain restrictive conditions.

Measured Wake-Vortex Characteristics of Aircraft in Ground Effect

In support of the NASA wake vortex alleviation program, measurements were made of the influences of a ground plane on vortex trajectories and velocity profiles within lift-generated wakes. The wakes were generated by towing 0. 61-m (2-ft) span models of a B-747 and DC-10-30 under water in a ship model basin. The models were configured with landing flaps and flight spoilers to investigate the wake characteristics of these aircraft in ground effect at simulated full-scale distances of 19-116 m (62-380 ft) above the ground. The ground plane caused modifications in the vortex trajectories but did not alter vortex interactions and merging patterns in these multiple vortex wakes. Some distortions in vortex vertical (tangential) velocity profiles were recorded as a result of vortex lateral motions and vortex interactions with the viscous boundary layer on the ground plane; however, maximum tangential velocities remained unchanged.

A method for finding plasmasphere statistics from solar wind measurements

This paper gives the results of a calculation of the characteristic size of the plasmasphere based on a specific formulation of the prevailing view that its size is determined by a dynamic equilibrium between two essentially independent processes: depletion by magnetospheric convection and refill by flux from the ionosphere. The first of these processes exhibits a time behavior best described as being stochastic. The characteristic size of the plasmasphere is therefore also stochastic. The formulation given here combines simple models of dayside magnetic merging, corotation and convection patterns, and the refill process. It predicts statistical characteristics of the plasmasphere size from measurements of the solar wind convection electric field. From Mariner 5 measurements the method predicts the median value of the characteristic size of the plasmasphere to be 4.8 R/sub E/ with a 50% central range of 3.8--5.2 R/sub E/, values entirely compatible with observations. Although the method gives no information about the shape of the plasmapause, it has the advantage that it can be applied to geophysical situations different from those that exist at present. This is illustrated by applying it to a case in which the dipole strength is double the present value.

Optimal disk merge patterns

Our purpose is to study the optimal way to merge n initially sorted runs, stored on a disk like device, into a unique sorted file. This problem is equivalent to finding a tree with n leaves which minimizes a certain cost function (see Knuth [1]). We shall study some properties of those optimal trees, in the hope of finding efficient ways for constructing them. In particular, if all the initial runs have the same length, an algorithm for constructing the best merge pattern is described ; its running time is proportional to n 2 and it requires space proportional to n. A special case is also analyzed in which the problem is solved in time and space proportional to n, and which provides some insight into the asymptotic behaviour of optimal merge trees.

Effects of Handling and Salinity on Oxygen Requirements of the Striped Bass, Morone saxatilis

Oxygen requirements of striped bass, Morone saxatilis, were studied at 0 and 10‰ salinity using combinations of handling and constantly decreasing oxygen concentrations. Effects of handling and salinity on oxygen requirements were negligible or absent. Successive and merging patterns of behavior at low oxygen concentrations were: restlessness, spasmodic swimming, surfacing, inactivity, equilibrium loss, and death. Mean oxygen levels with 99% confidence limits at restlessness, inactivity, equilibrium loss, and death were 1.81 ±.10, 1.28 ±.10, 0.95 ±.06, and 0.72 ±.04 mg/liter. Virtually no fish exhibited these behavior patterns until oxygen declined to 3.12, 2.19, 1.44, and 1.04 mg/liter, respectively; nearly all fish did at 0.91, 0.66, 0.62, and 0.50 mg/liter, respectively. Size of fish did not affect oxygen levels at death and equilibrium loss.Ventilation rate was maximum at 2.0–3.0 mg/liter and declined at lower concentrations. Amplitude was maximum at the beginning of inactivity then declined. Because short-term respiratory failure occurred at equilibrium loss, this behavior probably represents oxygen levels that would cause an abrupt fish-kill. Long-term respiratory failure at inactivity indicated that death would follow a period of resistance.There is no sharp distinction between suitable and unsuitable oxygen concentrations, because duration of exposure determines the intensity of the result even at lethal levels. Onset of restlessness (about 3 mg/liter at 16–19 C) probably represents the minimum permissible oxygen level for normal existence. Even this may be insufficient to maintain optimum populations of striped bass.

A tape file merge pattern generator

A routine is presented which specifies the sequence of merge cycles to effect the merging of sorted tape files. The routine is designed to minimize elapsed computer time by varying the power of the merge cycles, so as to use all the available tape drives, with its characteristic of assigning one drive to a single-eel file and two drives to each multiple-reel file.