摘要:

This paper is concerned with the stability of two‐dimensional incompressible mixing layers with small transversal velocity gradients. Using the approach of slight flow divergence, a boundary layer type of approximation of solutions to the steady mixing layer flow is obtained. We derive in the limit of small velocity gradients a velocity profile of an error function type. To gain an insight into the problem of the spatial instability of this flow we apply a model involving perturbations with only a single frequency component. A generalized approach, however, is outlined in the Appendix. There the interaction of a fundamental mode with its subharmonic, oscillating at one‐third the frequency, is analyzed. First numerical results show that under certain conditions the subharmonic can represent the dominant disturbance. A multiple scales expansion of the disturbance streamfunction is constructed with variables chosen to derive a Landau‐type equation with cubic nonlinearities governing an amplitude functionA. Scaling spatial and temporal variables and the Reynolds number we obtain in leading order a generalized Rayleigh equation. We solve the associated eigenvalue problem for spatially growing modes, whereas the calculation of damped modes is beyond the scope of our approach. The solution to this equation can be separated into a shape function and the amplitudeA. An investigation of the second‐order terms yields a rederivation of the boundary layer approximation of the steady flow, an equation governing second harmonics of the disturbance and an equation determining the mean flow correction. At third order we have to apply a resonance condition, which demands small linear spatial growth rates. This restriction is consistent with the limit of small velocity gradients and we can thus derive a cubic amplitude equation governing the space–time evolution ofA. This equation can be cast into a separated first‐order ODE. The numerical results show that the combined effect of nonlinearity and flow divergence strongly influences the amplitudes such that they reach a maximum and decay farther downstream. The study is based on an essentially inviscid approach. The regime of amplitude decay is therefore restricted and the integrations have to be terminated when the limit of neutral growth is reached. Comparison with experimental data is difficult because the latter are taken for higher values of the velocity gradients. Yet typical experimental trends are predicted by the findings of the present study. We found in particular in the numerical study of vortex contours structural instabilities in terms of breakup of sinusoidal lines to create vortex patches and the phenomenon of cut‐and‐connect of vortices near ‘‘saddle points.’’ ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869175

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The effect of vortex generators in the form of tabs on the penetration and spreading of a jet in a cross‐flow has been studied experimentally. It is found that the tab has very little effect when placed on the leeward side, i.e., on the downstream edge of the jet nozzle relative to the free‐stream flow. A study of the static pressure distribution reveals significantly lower pressures on the leeward side. Thus, when placed on that side the tab does not produce a ‘‘pressure hill’’ of sufficient magnitude that is the primary source of streamwise vorticity in the flow field over the tab. This qualitatively explains the ineffectiveness. In comparison, there is a significant effect on the flow field when the tab is placed on the windward side. The sense of vorticity generated by the tab in the latter configuration is opposite to that of the bound vortex pair that otherwise characterizes the flow. Thus, the strength of the bound vortex pair is diminished and the jet penetration is reduced. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869154

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A horizontal jet emerging continuously from a small round nozzle (concentrated source of momentum) in a rotaing stratified fluid is investigated using laboratory experiments. The jet either (i) deflects from the direction of injection, forming an anticyclonic spiral monopole (monopole regime), or (ii) propagates along the injection direction, forming a dipolar structure (dipole regime). Which of these characteristic flows occurs depends on the system parameters, the Reynolds number Re, and the buoyancy frequency to Coriolis parameter ratioN/f; a flow regime diagram is developed for the parameter ranges 40≲ Re≲200 and 0≲N/f≲35, respectively. A theoretical analysis is advanced to explain the conditions under which the monopole and dipole regimes occur, including the transition curve between the two regimes. The theory is supported by laboratory experiments. Some geophysical examples of the considered flows are discussed. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869155

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The collapse of a gas bubble near a solid wall is studied numerically by assuming the liquid to be incompressible and the Mach number of the gas flow to be small. The liquid motion is simulated by a boundary integral method and the gas thermo‐fluid dynamics by finite differences on a boundary‐fitted grid. With the physical properties of a liquid monopropellant, it is found that the liquid heating is essentially localized in the microjet, but is probably not sufficient to cause spontaneous ignition. The reasons for this conclusion — that, while being in general agreement with available experimental evidence, is at variance with deductions from previous spherical collapse calculations — are elucidated. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869153

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The renormalization group (RNG) theory of turbulence is often used for the forced Navier–Stokes equation in order to investigate turbulence models in Fourier space. The strong point of this kind of theory is the ability to construct turbulence models with the aid of the Kolmogorov −5/3 power law for the energy spectrum. In this paper, we have made use of an iterative averaging method proposed by McComb (1990), which does not have the misleading &egr;‐expansion technique developed by Yakhot and Orszag (1986), then applied this method to the derivation of an eddy‐viscosity type turbulence model. Using the exact Navier–Stokes equation excluding artificial external forces, we have obtained the eddy‐viscosity type turbulence model which is equivalent to the Boussinesq postulate, and its model constantC&mgr;is determined from only a Kolmogorov constant &agr;. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869156

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Probability density function (pdf) methods are extended to include modeling of wall‐bounded turbulent flows. A pdf near‐wall model is developed in which the generalized Langevin model is combined with an exact model for viscous transport. Then the method of elliptic relaxation is used to incorporate the wall effects without the use of wall functions or damping functions. Information about the proximity of the wall is provided only in the boundary conditions so that the model can be implemented withoutadhocassumptions about the geometry of the flow. A Reynolds‐stress closure is derived from this pdf model, and its predictions are compared with DNS and experimental results for fully developed turbulent channel flow. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869157

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A numerical study of the long‐time evolution of incompressible Navier‐Stokes turbulence forced at a single long‐wavelength Fourier mode, i.e., a Kolmogorov flow, has been completed. The boundary conditions are periodic in three dimensions and the forcing is effected by imposing a steady, two‐dimensional, sinusoidal shear velocity which is directed along thex‐direction and varies along thez‐direction. A comparison with experimental data shows agreement with measured cross‐correlations of the turbulent velocity components which lie in the mean‐flow plane. A statistical analysis reveals that the shear‐driven turbulence studied here has significant spectral anisotropy which increases with wave number. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869159

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Direct numerical simulations of decaying two‐dimensional turbulence in a fluid of large extent are performed primarily to ascertain the asymptotic decay laws of the energy and enstrophy. It is determined that a critical Reynolds numberRcexists such that for initial Reynolds numbers withR(0)<Rcfinal period of decay solutions result, whereas forR(0)>Rcthe flow field evolves with increasing Reynolds number. Exactly atR(0)=Rc, the turbulence evolves with constant Reynolds number and the energy decays ast−1and the enstrophy ast−2. At−2decay law for the enstrophy was originally predicted by Batchelor for large Reynolds numbers [Phys. Fluids Suppl. II,12, 233 (1969)]. Numerical simulations are then performed for a wide range of initial Reynolds numbers withR(0)>Rcto study whether a universal power‐law decay for the energy and enstrophy exist ast→∞. Different scaling laws are observed forR(0) moderately larger thanRc. WhenR(0) becomes sufficiently large so that the energy remains essentially constant, the enstrophy decays at large times as approximatelyt−0.8. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869169

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Recent studies of a passive scalar diffusing in a rapidly fluctuating Gaussian distributed linear shear layer have demonstrated intermittency in the form of broad tails and non‐symmetric limiting probability distribution functions. In this paper the authors explore similar issues within the context of a large class of rapidly fluctuating bounded periodic shear layers. We compute the evolution of the moments by analogy to anNdimensional quantum mechanics problem. By direct comparison of an appropriate system of interacting and non‐interacting quantum particles, we illustrate that the role of interaction is to induce a lowering of the ground state energy, which implies that the scalar PDF will havebroaderthanGaussiantailsfor all large, but finite times. We demonstrate for the case of Gaussian random wave initial data involving a zero spatial mean, that the effect of this energy shift is to induce diverging normalized flatness factors indicative of very broad tails. For the more general case with Gaussian random initial data involving a non‐zero spatial mean, the distribution must approach that of a Gaussian at infinite times, as required by homogenization theory, but we show that the approach is highly non‐uniform. In particular our calculation shows that the time required for the system to approach Gaussian statistics grows like the square of the moment number. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869161

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Nonequilibrium real‐gas effects on surface heating rates, skin friction, and flow field unsteadiness of two‐dimensional hypersonic shock‐wave/boundary‐layer interaction were studied by numerical simulations. The unsteady Navier–Stokes equations with nonequilibrium vibrational and chemical models for five‐species air were solved by a finite‐volume second‐order TVD scheme together with a third‐order semi‐implicit Runge–Kutta scheme. Two cases of high‐enthalpy shock/boundary layer interaction problems were studied in this paper. The freestream enthalpy was high enough to produce vibrational excitation and dissociation/recombination chemistry behind the shock. The first case was a steady two‐dimensional shock/boundary layer interaction on a flat plate with a mixture of N2and O2in the freestream. It was found that the real gas effects reduce the size of the shock induced separation bubble and the magnitude of the surface heating rates. The second case was a self‐sustained unsteady type IV shock–shock interference heating of a pure N2flow over a cylinder. The results showed that type IV shock–shock interference heating flows with real‐gas effects are inherently unsteady. Vortices are generated and shed off near the jet impingement point. This periodic shedding of the vortices contributes to the self‐sustained oscillations of both the jet and other parts of the flow fields. In addition, the real‐gas effects reduce the level of peak surface heating and peak surface pressure due to endothermic real‐gas effects. ©1997 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869162

出版商:AIP    

年代:1997

数据来源: AIP