摘要:

Viscous fingering in a wedge-shaped Hele-Shaw cell is analyzed. The shape of a self-dilating viscous finger is shown to obey a time-independent nonlinear integrodifferential equation that is solved numerically. The results show that there is a continuum of zero-surface-tension solutions for any wedge angle between 0 and &pgr;/2. When surface tension is taken into account only a discrete set of solutions exist. In contrast to the classical case, different branches merge for finite values of the surface tension parameters.

ISSN:0899-8213    

DOI:10.1063/1.858222

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The linear stability of the inertialess, pressure-driven Poiseuille flow of an Oldroyd-B fluid through a slightly curved channel is considered. The flow is shown to be unstable in certain flow parameter regimes. The critical conditions and the structure of the vortex flow at the onset of instability are presented. These results reveal that there is a purely elastic, instability in the flow, and the instability is a stationary mode in contrast to the elastic, oscillatory instability that occurs in Taylor-Couette flow [see Larson, Shaqfeh, and Muller, J. Fluid Mech.218, 573 (1990)]. In addition, the mechanism of the instability is investigated through an examination of the disturbande-energy equation.

ISSN:0899-8213    

DOI:10.1063/1.858223

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The rate of convergence of the Karhunen–Loe`ve expansion of an inhomogeneous, instantaneous random field is compared with that of Fourier expansion in relation to the Reynolds number. The model turbulence is generated by solving the Burgers’ equation with random forcing. The coefficients of the Fourier expansion are determined by a Galerkin solution scheme. The results show obvious superiority of the Karhunen–Loe`ve expansion, especially for high Reynolds number flows.

ISSN:0899-8213    

DOI:10.1063/1.857948

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

High‐resolution measurements of the mean temperature gradient field of a fluid undergoing thermal convection in a vertical slot were made. The detection method employs schlieren optics with a linear photodiode array detector. With proper calibration the schlieren signals permit quantitative reconstruction of the varying temperature field along one dimension in the fluid, with a relative temperature resolution of ±0.02 K. The critical applied temperature difference, &Dgr;Tb,c, is determined by extrapolation of the measured convection pattern amplitudes. The measurements permit detailed monitoring of the wave number distribution and its development in time as well as harmonic analysis of the temperature waveform. The stability limits of convective patterns are investigated as a function of forcing and wave number and the observed limits are compared to theoretical predictions. The details of the transitions from conduction to convection and from one convective spatial pattern to another are observed and analyzed as the degree of forcing is varied. The creation and destruction of convective roll cells is observed as is the propagation of convective flow across the slot.

ISSN:0899-8213    

DOI:10.1063/1.857949

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

Steady two‐dimensional jets of an inviscid and incompressible fluid emerging from a nozzle and falling under gravity are calculated numerically by series truncation. The nozzle is aimed at an angle &bgr; above the horizontal. It is shown that there are flows for all values of &bgr; between 0° and 90° and for all values of the Froude numberF. Local solutions are constructed to describe the limiting behavior of the flows asF→0 and asF→∞. The problem of a uniform free stream hitting a vertical wall, rising, and forming a jet that falls back upon the oncoming stream is also solved. It is shown that solutions exist only for Froude numbers greater than 2.96.

ISSN:0899-8213    

DOI:10.1063/1.857950

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The linear stability of unidirectional flow sinusoidal both in a transverse direction and in time is considered. The problem reduces to an infinite algebraic eigenvalue problem. By using continued fractions, it is proved rigorously that the time‐independent flow is unstable to perturbation modes which do not have the periodicity of the basic flow in the transverse direction. Also, instability is proved for the inviscid case, for which the proofs known before do not work even when perturbation modes have the same periodicity as the basic flow. In the case of time‐dependent inviscid flow, exact solutions of a generalized Orr–Sommerfeld equation are found by the separation of continuous variables. Comparison with Galerkin solutions of the eigenvalue problem obtained by the separation of a discrete ‘‘time’’ variable leads to insights into reliability of the Galerkin results for the original, two‐dimensional eigenvalue problem.

ISSN:0899-8213    

DOI:10.1063/1.857951

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The upward dispersion of heavy particles in suspension in turbulent flow was studied using a numerical model. The interaction between the turbulence and the particle diffusion leads to the formation of a horizontal front (or a ‘‘lutocline’’), across which the diffusion of particles and the propagation of turbulent energy are inhibited. However, as the settling velocity of the particles becomes larger, or as the particle concentration becomes smaller, the interaction weakens, thus suppressing the front formation. One‐dimensional model equations for the problem are solved numerically to calculate the evolution of the particle concentration. A criterion for the formation of the front is proposed and the steady depth of the suspension layer is determined.

ISSN:0899-8213    

DOI:10.1063/1.857952

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

The dynamics of the flow in the separated region and near wake of a vertical flat plate was analyzed with the phase‐locked laser‐Doppler technique at Reynolds number Re=2.8×104. The flow exhibits an intense quasiperiodic component at a Strouhal frequency of St=0.14. The vortex shedding process was resolved into six phases, resulting in a time difference between consecutive phases of &Dgr;t=0.02 sec. Interactions between the free shear layers, emanating from the model edges, lead to nonlinear dynamics of the flow. The distributions of the Reynolds stresses indicate that maximal amplitudes in the normal stresses ⟨u’2⟩ and ⟨v’2⟩ as well as in the shear stress term ⟨u’v’⟩ are provoked by positive pressure gradients in the shear layer flows upstream of saddle points. Saddles are quasiperiodically formed by interactions between the two free shear layers. Regions with enhanced Reynolds stresses and saddles are convectively transported within the flow field.

ISSN:0899-8213    

DOI:10.1063/1.857953

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

A two‐dimensional time‐dependent numerical study of separating and reattaching flow over a blunt plate is described. Four Reynolds numbers, Re=150, 250, 300, and 1000, are studied. The first three are in the steady flow regime and calculated values of reattachment lengths compare well with experimental data. For Re=1000, the separated shear layer becomes unsteady with the formation of spanwise vortices. These vortices coalesce and are shed periodically from the reattachment region. Although the resulting flow field is known to be three dimensional, the current two‐dimensional calculation is able to predict important flow properties. Calculated time‐dependent properties such as vortex shedding frequency and convection velocities compare well with experimental data. The present study is a precursor to a three‐dimensional simulation.

ISSN:0899-8213    

DOI:10.1063/1.857954

出版商:AIP    

年代:1991

数据来源: AIP

摘要:

One major drawback of the eddy viscosity subgrid‐scale stress models used in large‐eddy simulations is their inability to represent correctly with a single universal constant different turbulent fields in rotating or sheared flows, near solid walls, or in transitional regimes. In the present work a new eddy viscosity model is presented which alleviates many of these drawbacks. The model coefficient is computed dynamically as the calculation progresses rather than inputapriori. The model is based on an algebraic identity between the subgrid‐scale stresses at two different filtered levels and the resolved turbulent stresses. The subgrid‐scale stresses obtained using the proposed model vanish in laminar flow and at a solid boundary, and have the correct asymptotic behavior in the near‐wall region of a turbulent boundary layer. The results of large‐eddy simulations of transitional and turbulent channel flow that use the proposed model are in good agreement with the direct simulation data.

ISSN:0899-8213    

DOI:10.1063/1.857955

出版商:AIP    

年代:1991

数据来源: AIP