摘要:

In this paper some results are presented on the statistical properties of zero crossings of turbulent velocity fluctuations in boundary layers over a wide range of Reynolds numbers. The earlier finding that the probability density function (pdf) of the intervals between successive zero crossings of the streamwise velocity fluctuationucan be approximated by two exponentials, each with its own characteristic scale, is confirmed. The cross‐stream variation of these characteristic scales is investigated. One of these scales, corresponding to the large zero‐crossing intervals, is independent of the Reynolds number, while the other for the viscous‐dominated small‐scale crossings varies with asR&lgr;−1/2, whereR&lgr;is the Reynolds number based on the Taylor microscale, &lgr;. The pdf’s for the normal velocity componentvand the fluctuating part of the Reynolds stressuvare essentially exponential over the whole range of zero‐crossing scales, and each possesses just one characteristic scale. The mean and the standard deviation of the zero‐crossing scales ofuandv, when normalized by their respective Taylor microscales, are roughly unity and essentially independent of the cross‐stream position. Similar data are also presented for the Reynolds stress fluctuations. A brief discussion of the results as well as an example of the application of the zero‐crossing pdf are given.

ISSN:0899-8213    

DOI:10.1063/1.858697

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The equations for the higher‐order moments of turbulent velocity fluctuations are considered. These are derived utilizing truncated, cumulant expansions as an approximation for the probability density distributions of the corresponding turbulence properties. By applying different degrees of truncations to these expansions, an alternative set of equations for the moments is formulated that contains only velocity correlations. From these equations, interrelations between the higher‐order moments are deduced and are experimentally verified using data available in the literature and also data measured by the authors.

ISSN:0899-8213    

DOI:10.1063/1.858698

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A procedure that combines a one‐point probability density function (pdf) and two‐point correlation functions (TPCF’s) is introduced to simulate the multispecies chemical reactions carried by a homogeneous turbulence field. In this procedure, the pdf equation and the evolution of TPCF’s are treated in parallel using time splitting. The one‐point pdf equation requires closure of only the molecular diffusion terms. At any instant the time scale for the linear mean square estimate closure is obtained from the parallel solutions of the equations for TPCF’s, using a physical‐space EDQNM (eddy damped quasinormal Markovian) closure for the advection terms and a similarity assumption for the reaction terms. With this procedure, a study of chemical reactions with four or five species is possible. The model’s predictions are in good agreement with DNS data and a fully two‐point pdf description of simpler kinetic schemes. Results for a range of Damko¨hler numbers, Schmidt numbers, and Reynolds numbers that are beyond the reach of DNS are also shown.

ISSN:0899-8213    

DOI:10.1063/1.858699

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

For small Mach numbers the Rayleigh–Plesset equations (modified to include acoustic radiation damping) provide the hydrodynamic description of a bubble’s breathing motion. Measurements are presented for the bubble radius as a function of time. They indicate that in the presence of sonoluminescence the ratio of maximum to minimum bubble radius is about 100. Scaling laws for the maximum bubble radius and the temperature and duration of the collapse are derived in this limit. Inclusion of mass diffusion enables one to calculate the ambient radius. For audible sound fields these equations yield picosecond hot spots, such as are observed experimentally. However, the analysis indicates that a detailed description of sonoluminescence requires the use of parameters for which the resulting motion reaches large Mach numbers. Therefore the next step toward explaining sonoluminescence will require the extension of bubble dynamics to include nonlinear effects such as shock waves.

ISSN:0899-8213    

DOI:10.1063/1.858700

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Computational solutions to the Rayleigh–Taylor fluid mixing problem, as modeled by the two‐fluid two‐dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a renormalization group analysis. The computations, carried out with the front tracking method on an Intel iPSC/860, are highly resolved and statistical convergence of ensemble averages is achieved. The computations are consistent with the experimentally observed growth rates for nearly incompressible flows. The dynamics of the interior portion of the mixing zone is simplified by the use of scaling variables. The size of the mixing zone suggests fixed‐point behavior. The profile of statistical quantities within the mixing zone exhibit self‐similarity under fixed‐point scaling to a limited degree. The effect of compressibility is also examined. It is found that, for even moderate compressibility, the growth rates fail to satisfy universal scaling, and moreover, increase significantly with increasing compressibility. The growth rates predicted from a renormalization group fixed‐point model are in a reasonable agreement with the results of the exact numerical simulations, even for flows outside of the incompressible limit.

ISSN:0899-8213    

DOI:10.1063/1.858701

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A three‐dimensional direct numerical simulation (using a fully spectral method) of compressible convection of an infinite Prandtl number fluid in a wide box with dimensions 5×5×1 was conducted. Depth‐dependent viscosity, thermal expansivity, and thermal conductivity have been included in order to model deep‐seated processes in the Earth’s mantle. Solutions have been obtained up to a surface Rayleigh number of 4×107. There is a remarkable contrast between the dynamics of the upper and lower boundary layers. Very few cylindrical plumes are developed at the bottom but they merge collectively to form a strong upwelling, which pulses chaotically. Viscous and adiabatic heating are found to become important at high Rayleigh numbers, larger than 107. These results have important implications on the thermal structure of early Earth, where there might have been dramatic effects from intense mechanical heating near the top boundary layer.

ISSN:0899-8213    

DOI:10.1063/1.858702

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The spatial supersonic shear layer in a rectangular channel is investigated by numerical simulation with the piecewise parabolic method, a high-order Godunov-type scheme. Both streams are supersonic with Mach number 4.5 and 1.6, respectively. A weak broadbanded noise is introduced at the inflow boundary and the growth of multiple unstable modes is observed. In order to extract detailed information from the computed data, the time-dependent flow field is Fourier transformed in time and in the spanwise direction. For a given frequency and a given spanwise wave number the complex eigenfunction and streamwise wave number can be compared to results from linear stability theory. This work aims at investigating in detail the limit of the linear development of the flow and to describe the transition to turbulence. In particular, this technique enables one to distinguish between oblique subsonic instabilities of the Kelvin–Helmholtz (KH) type and supersonic wall modes. A good agreement with linear stability theory is obtained in two and three dimensions until a characteristic streamwise distance is reached, where the flow becomes nonlinear. It is shown that it is mainly the oblique KH modes which are responsible for an increase in the spreading rate during transition and that the nonlinear regime in three dimensions is therefore essentially different from that in two dimensions. The most unstable mode in our configuration is a wall mode and the frequency spectra are largely dominated by the wall modes. However, it turns out that the transition is not governed by the wall modes, but by the oblique KH modes, which evolve into longitudinal streaks.  

ISSN:0899-8213    

DOI:10.1063/1.858703

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The one‐dimensional (1‐D) asymptotic solution of subcritical transonic nozzle flows with nonequilibrium homogeneous condensation is presented. An algorithm based on a local iterative scheme that exhibits the asymptotic solution in distinct condensation zones is developed for transonic moist air expansions under atmospheric supply conditions. Two models that characterize the state of the condensed phase as water drops or ice crystals are employed, together with the classical nucleation theory and Hertz–Knudsen droplet growth law. It is shown that the 1‐D asymptotic predictions are in good agreement with the recent static pressure measurements of moist air expansions in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops.  

ISSN:0899-8213    

DOI:10.1063/1.858704

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A detailed analysis of supercritical transonic nozzle flows with stationary normal shock waves is presented. A classification scheme based on the normal shock location is obtained using asymptotic methods, and four distinct supercritical flow regimes are distinguished. A simple shock fitting technique that determines the shock location within any desired precision is introduced. Consequently, an algorithm that exhibits the asymptotic solution in each supercritical flow regime is developed for the expansion of moist air in nozzles with atmospheric supply conditions by utilizing the classical nucleation theory and the Hertz–Knudsen droplet growth law. Good agreement with the recent static pressure measurements and visualized shock locations is achieved in relatively slender nozzles when the condensed phase is assumed to consist purely of water drops.

ISSN:0899-8213    

DOI:10.1063/1.858705

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The influence of dense gases on the curvature and the strength of a normal shock near curved walls is discussed. In classical gasdynamics there is a postshock expansion and the shock is curved upstream if the wall is convex. The transonic small disturbance theory for the problem has been derived, including the fundamental gasdynamic derivative &Ggr; and the second nonlinearity parameter &Lgr;. Special attention is drawn on flows where &Ggr; becomes either zero or negative. According to the similarity laws, change of the sign of &Ggr; changes the sign of the velocity disturbances &Jgr;xand &Jgr;yand of the wall curvature. Thus an expansion shock is followed by a compression if &Ggr;<0 and the wall is concave. Again the shock is curved upstream. A variation of the second nonlinearity parameter &Lgr; influences the strength of the shock, its curvature, and of the postshock expansion. Considering a &Ggr;≳0 flow at a convex wall, the postshock expansion and the shock curvature are weakened if &Lgr;≳0. Comparing the real gas flow with the perfect gas flow (e.g., &Ggr;=1.2 and &Lgr;=0), both the expansion behind the shock and the shock curvature increase if &Lgr; becomes negative.

ISSN:0899-8213    

DOI:10.1063/1.858706

出版商:AIP    

年代:1993

数据来源: AIP