摘要:

Steady convection rolls in a horizontal fluid layer heated from below are described numerically with a Galerkin method. A rigid lower and stress‐free upper boundary are assumed, while the temperature is fixed at both boundaries. The stability of the steady solutions with respect to arbitrary three‐dimensional infinitesimal disturbances is analyzed and the stability boundaries in the Rayleigh number–wave‐number plane are determined for selected Prandtl numbers. It is found that results of the analysis correspond more closely to the case of two rigid boundaries than to the case of two stress‐free boundaries. The domains of stability in the case of asymmetric boundaries are larger at high Prandtl numbers than in the case of two rigid boundaries, but smaller for low Prandtl numbers. Some of the asymmetric properties of convection rolls are discussed.

ISSN:0899-8213    

DOI:10.1063/1.858793

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Linear‐stability theory has been applied to a basic state of thermocapillary convection in a model half‐zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half‐zone is of finite,O(1) aspect ratio with two‐dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities are nonseparablepartialdifferential equations. The disturbance equations are treated by a staggered‐grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases; they complement recent calculations of the corresponding energy‐stability limits.    

ISSN:0899-8213    

DOI:10.1063/1.858796

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Turbulence structure in an open‐channel flow with a zero‐shear gas–liquid interface was numerically investigated by a three‐dimensional direct numerical simulation (DNS) based on a fifth‐order finite‐difference formulation, and the relationship between scalar transfer across a zero‐shear gas–liquid interface and organized motion near the interface was discussed. The numerical predictions of turbulence quantities were also compared with the measurements by means of a two‐color laser Doppler velocimeter. The results by the DNS show that the vertical motion is restrained in the interfacial region and there the turbulence energy is redistributed from the vertical direction to the streamwise and spanwise directions through the pressure fluctuation. The large‐scale eddies are generated by bursting phenomena in the wall region and they are lifted up toward the interfacial region. Then, the eddies renew the interface and promote the scalar transfer across the gas–liquid interface. Both the damping effect and the generation process of the surface‐renewal motions predicted by the DNS explain well the experimental results deduced in previously published studies. Furthermore, the predicted bursting frequency and mass transfer coefficient are in good agreement with the measurements.  

ISSN:0899-8213    

DOI:10.1063/1.858797

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The strained‐spiral vortex model of turbulent fines scales given by Lundgren [Phys. Fluids25, 2193 (1982)] is used to calculate vorticity and velocity‐derivative moments for homogeneous isotropic turbulence. A specific form of the relaxing spiral vortex is proposed modeled by a rolling‐up vortex layer embedded in a background containing opposite signed vorticity and with zero total circulation at infinity. The numerical values of two dimensionless groups are fixed in order to give a Kolmogorov constant and skewness which are within the range of experiment. This gives the result that the ratio of the ensemble average hyperskewnessS2p+1≡ (∂u/∂x)2p+1/[(∂u/∂x)2](2p+1)/2to the hyperflatnessF2p≡(∂u/∂x)2p/[(∂u/∂x)2] p,p=2,3,..., is constant independent of Taylor–Reynolds numberR&lgr;, as is the ratio of the 2pth moment of one component of the vorticity &OHgr;2p≡&ohgr;2px/(&ohgr;2x)ptoF2p. A cutoff in a relevant time integration is then used to eliminate vortex‐sheet‐induced divergences in the integrals corresponding to &ohgr;2px,p=2,3,..., and an assumption is made that the lateral scale of the spiral vortex in the model is the geometric mean of the Taylor and the Kolmogorov microscales. This gives &OHgr;2p=&OHgr;ˆ2pR&lgr;p/2−3/4,F2p=Fˆ2pR&lgr;p/2−3/4andS2p+1=Sˆ2p+1R&lgr;p/2−3/4,p=2,3,..., with explicit calculation of the numbers &OHgr;ˆ2p,Fˆ2p, andSˆ2p+1. The results of the model are compared with experimental compilation of Van Atta and Antonia [Phys. Fluids23, 252 (1980)] forF4and with the isotropic turbulence calculations of Kerr [J. Fluid Mech.153, 31 (1985)] and of Vincent and Meneguzzi [J. Fluid Mech.225, 1 (1991)].  

ISSN:0899-8213    

DOI:10.1063/1.858798

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The limitations of the commonly used Smagorinsky subgrid‐scale (SGS) eddy viscosity model in large eddy simulation (LES) of turbulent flows are that the model’s eddy viscosity constant must be optimized in different flows, and also that a damping function must be used to account for near‐wall effects. A new SGS model which mitigates these drawbacks is proposed, i.e., a more proper eddy viscosity velocity scale was determined by utilizing the third‐order terms in an anisotropic representation model of the Reynolds stresses [K. Horiuti, Phys. Fluids A2, 1708 (1990)]. This method utilizes the direct numerical simulation (DNS) database for fully developed turbulent channel flow to show these drawbacks to be inherent in the use of an improper velocity scale, i.e., the total SGS energy component adopted in the Smagorinsky model. As a result, the SGS normal shear stress was alternatively employed as the velocity scale, thereby significantly improving the correlation with DNS data. Methods to correlate the SGS normal shear stress to the grid scale quantities are proposed and compared, and the resultant high accuracy of the scale‐similarity model to represent the SGS turbulence fluctuations is shown. The proposed SGS model was also tested in actual LES computations of turbulent channel flow, where it was found that the SGS eddy viscosity in the near‐wall region similarly acted as the conventionally used Van Driest damping function. This result is consistent with previous reports which assert that in the Reynolds averaged models, the rapid reduction of the Reynolds shear stress as the wall is approached is due to the preferential damping of the normal shear stress. It is shown that three eddy viscosity parameters contained in the proposed SGS model can be practically reduced to a single parameter, which is subsequently shown to be more universal and independent of the flow field than the Smagorinsky model constant. A qualitative interpretation for the variance of the Smagorinsky model constant in different flows is also provided via a correlation with the anisotropy of SGS turbulence intensities.

ISSN:0899-8213    

DOI:10.1063/1.858800

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Questions about applicability of multiplicative cascade models for turbulent small‐scale intermittency (such as lognormal, random curdling, &bgr;, &agr;,pmodels, etc.) are addressed by using the multifractal formalism to predict new properties of two‐point moments. These predictions are compared with experimental data. Measurements are performed in the wake of a cylinder and grid turbulence. Data at high Reynolds number in the atmospheric surface layer are also considered. The autocorrelation function of the local singularity strength &agr;(x), as well as mixed moments of the form <&egr;r(x)q&egr;r(x+s)−q≳ are computed from the kinetic energy dissipation obtained from single‐component, single‐probe measurements using Taylor’s hypothesis. For flows at high‐enough Reynolds number, the &agr;(x) autocorrelation function exhibits logarithmic decay with distance, as predicted from a random multiplicative cascade process. Some discrepancies exist in the quantitative details, implying enhanced randomization. The mixed moments are found to exhibit a scaling transition, also in agreement with the multiplicative models. The results illustrate the usefulness of the two‐point multifractal formalism in characterizing intermittency and, as far as two‐point statistics is concerned, lend further (qualified) support to the multiplicative cascade models.

ISSN:0899-8213    

DOI:10.1063/1.858801

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A new computational method extending the contour dynamics/surgery (CS) algorithm is announced which gives typical speed‐up factors of two orders of magnitude in calculations of flows involving many interacting vortices. The method makes use of an alternative expression for the velocity field in the exterior of a vortex that takes the form of a rapidly convergent series. Each term in this series can be expressed as a complex coefficient divided by the complex distancex+iyfrom the vortex center. The complex coefficient, or moment, is a real number pair that describes shape characteristics of the vortex (e.g., circulation, eccentricity, etc.). In numerical calculations, where accuracy is necessarily limited, it is frequently sufficient to retain only the leading‐order terms in this series, particularly for a gas of well‐separated vortices. The real computational gain is made, however, by reexpanding the series of all vortices that are sufficiently separated from a given vortex as asingle, truncated series in positive powers of the complex distance from this vortex’s center. The coefficients of this series involve only the moments of the other vortices and their centroid separation from the given vortex. The leading‐order truncation, for instance, simply gives point vortex dynamics,exceptthat self‐ or close‐range interactions are computed using the full contour integral expression of contour dynamics (hence, all vortices retain nontrivial spatial structure, vital to a proper dynamical description of close‐range interactions). In general, the optimal truncation depends on a dynamic balance between the cost of all moment computations and the cost of all contour integrations. This method, called ‘‘moment‐accelerated contour surgery,’’ which is briefly outlined above for the planar case, has a direct analog in spherical geometry. There are also extensions to generalized two‐dimensional (2‐D) flows having more general linear operator relationships between streamfunction and vorticity. Details are provided for quasigeostrophic flow.

ISSN:0899-8213    

DOI:10.1063/1.858802

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Pitot pressure measurements and flow visualizations were used to investigate streamwise vortices previously observed in underexpanded jets. A simple model was developed, which gives reasonable agreement with the pressure measurements. A converging nozzle and converging–diverging nozzle of design Mach number 1.5 were used to generate jet flows of equivalent Mach numbers up to 2.5 (stagnation to ambient pressure ratios up to 17.1). By operating the nozzles fully expanded, overexpanded, and underexpanded, insight was gained into both the occurrence and cause for formation of the vortices. Spatially stationary streamwise vortices were found to exist in the near‐field region around the circumference of underexpanded jets in the vicinity of the jet boundary. Short exposure visualizations show the vortices persist much farther downstream with a loss of spatial organization. Visualizations suggest adjacent vortices have streamwise vorticity of opposite sign, so the action of adjacent vortices is to either pump jet fluid radially outward or entrain ambient fluid radially inward toward the jet. The downstream extent, strength, and number of vortices around the jet circumference increase with degree of underexpansion. A large number of vortices is found near the nozzle exit. Fewer vortices of larger scale are found farther downstream, indicative of a merging process. The absence of the vortices in fully expanded and overexpanded jets suggests the vortices are a consequence of a Taylor–Goertler‐type instability.

ISSN:0899-8213    

DOI:10.1063/1.858803

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The flow arising from two, closely spaced turbulent jets flowing counter to one another is analyzed for both two‐dimensional and axisymmetric configurations. By closely spaced it is indicated that the diameter of the jets is large compared to their separation distance. Two parameters, one a measure of the integral scale of the turbulence compared with half the separation distance of the jets, and a second, a measure of the intensity of the turbulence issuing from the jets, are assumed small and form the basis of an asymptotic analysis. As a consequence, the mean velocity components are given by the mean Euler equations, except in a thin layer that is centered about the plane containing either the stagnation line or point and within which discontinuities in the flow from each jet are adjusted. Thus, outside of this layer, the turbulence characteristics in a known mean velocity field are determined, in the present study, in terms of a Reynolds stress description. The rate of strain field associated with the stagnating flow results in anisotropy of the turbulence as the plane containing the stagnation line or point is approached. Differences in the mean velocities in two‐dimensional and axisymmetric configurations result in significant differences in the evolution of the gradient of the Reynolds shear stress from the exit planes of the jets and thus in the thin layer at the stagnation plane. For two‐dimensional flows, the velocity characteristics in the thin layer satisfy to lowest order in an expansion parameter the requisite symmetry conditions, whereas this is not the case for axisymmetric flows. The temperature in the two streams is assumed to be slightly different but uniform so that there is also a thermal layer at the stagnation plane. Comparison is made with the applicable experimental data for the mean velocity and the turbulence intensities with good and reasonable agreement, respectively.

ISSN:0899-8213    

DOI:10.1063/1.858776

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The structure of normal shock waves is investigated on the basis of the standard Boltzmann equation for hard‐sphere molecules. This fundamental nonlinear problem in rarefied gas dynamics is analyzed numerically by a newly developed finite‐difference method, where the Boltzmann collision integral is computed directly without using the Monte Carlo method. The velocity distribution function, as well as the macroscopic quantities, is accurately obtained. The numerical results are compared with the Mott‐Smith and the direct simulation Monte Carlo results in detail. The analytical solution for a weak shock wave based on the standard Boltzmann equation is also presented up to the second order of the shock strength together with its explicit numerical data for hard‐sphere molecules.  

ISSN:0899-8213    

DOI:10.1063/1.858777

出版商:AIP    

年代:1993

数据来源: AIP