Stability Theory Of Flows Research Articles

Effect of surface radiation on the stability of hypersonic flat plate boundary layer

Transition of hypersonic boundary layer flow is an important problem in aerodynamic research. To obtain the natural transition position using the flow stability analysis method, it is necessary to analysis the neutral curve and the perturbation growth rule. Accurate calculation of the basic flow is the basis and prerequisite for stability analysis. This paper proposes that surface radiation should be considered in the analysis of hypersonic boundary layer flow stability due to the high temperatures at the vehicle surface caused by aerodynamic heating. In order to obtain the influence of surface radiation on the flow stability, we assume that the surface satisfies the energy balance and the gas satisfies calorimetrically perfect gas properties. To simplify the analysis, gas radiation has been neglected. The boundary layer analysis of a hypersonic flat plate with and without radiation has been performed by a combination of flow stability theory and direct numerical simulation. It is found that high temperature radiation on the surface causes energy to transfer outwards. The results showed that surface temperature decreases along the streamwise direction and is no longer an adiabatic surface temperature. Instability interval decreases and the maximum growth rate increases. The range of the instability region expressed in dimensionless frequency values moves to lower frequency as the Mach number increases. Maximum growth rate shows a tendency to increase and then decrease as the Mach number increases.

Bifurcations and Attractor-Repeller Splittings of Non-Saddle Sets

This paper is devoted to the study of some aspects of the stability theory of flows. In particular, we study Morse decompositions induced by non-saddle sets, including their corresponding Morse equations, attractor-repeller splittings of non-saddle sets and bifurcations originated by implosions of the basin of attraction of asymptotically stable fixed points. We also characterize the non-saddle sets of the plane in terms of the Euler characteristic of their region of influence.

On Reynolds stress and neutral azimuthal modes in the stability problem of swirling flows with radius-dependent density

We consider the linear stability problem of inviscid, incompressible swirling flows with radius-dependent density with respect to two-dimensional disturbances. Some results of Miles on the parallel flow stability theory are extended to the swirling flow stability theory. In particular, series solutions for the stability equation for swirling flows are obtained and these solutions are used in the study of the variation of the Reynolds stress. For singular neutral modes it is shown that the Reynolds stress varies like the inverse square of the radial distance in agreement with the homogeneous flow result of Maslowe & Nigam. It is also proved that singular neutral modes do not exist whenever the value of the Richardson number at the critical layer exceeds one quarter.

Temporal Stability of Boundary-Free Shear Flows: The Effects of Diffusion

The stability of boundary-free shear flow is studied for the case of variable viscosity due to binary diffusion across the shear layer. This leads to the main difficulty of this investigation, the direct coupling of the momentum and species equations in both the base state calculations as well as the stability analysis. Linear stability analysis is used to examine the effect of a nonuniform concentration profile on the stability of the flow. It is found that for the flow to be stable for all disturbance wave numbers the Reynolds number has to be zero. This is in agreement with constant viscosity free shear flow stability theory. Increasing the magnitude of concentration gradient (increasing the Schmidt number) destabilizes the flow.

Study on flow stability margin by method of system Identification / Studie über Strömungsstabilitätsreserven unter Verwendung von Methoden zur Systemidentifikation

The main objective of the investigation is to develop a practical technology and method in engineering, based on general control theory, for distinguishing two-phase flow stability and identifying the safety margin by using the system identification method. By combining the two-phase flow stability theory in the thermo-physics field with the system stability theory and the system identification method in the field of information science, a thermo-hydraulic experiment technology with a new concept was developed. The experiment was carried out on the thermo-hydraulic test system HRTL-5 which serves as simulator to the primary circulation of the nuclear heating reactor NHR-5 and was used for investigation on its thermophysical behavior. Reverse repeat pseudo-random sequences which were added to the steady heat flux as input signal sources and measured flow rates as response function were used in the test. The two-phase flow stability and the stability margin of the natural circulation system were investigated by analyzing the system pulse response function, the decay ratio and the stability boundary under different operational conditions. The results are compared with those obtained by using conventional methods. The test method and typical results obtained are presented in this paper.

The upper branch stability of the Blasius boundary layer, including non-parallel flow effects

The stability of the Blasius boundary layer is studied theoretically, with the aim of fixing the character of the upper branch of the neutral stability curve(s) and its dependence on non-parallel flow effects. Unlike most previous studies this work has a rational basis since, throughout, we consider the linear stability structure for asymptotically large Reynolds numbers ( Re ). The structure is five-zoned and quite complicated, more so than the structure (discussed in Smith (1979 a )) governing the lower branch stability properties, but nevertheless it lends itself to the systematic determination of the neutral frequency and of the influence of non-parallelism. The four leading terms in the asymptotic expansion of the neutral frequency are determined and then the non-parallel flow effects are considered. The latter are shown to be of relative order Re -3/10 in general, much larger than the relative order Re -1/2 suggested by the parallel flow approximations used extensively in the literature. The cause of this discrepancy lies partly in the relatively large wavelength of the Tollmien-Schlichting modes but, more especially, in a ‘transmission feature’, associated with the stability structure and brought about by the major determining role played by the small curvature of the boundary layer profile at the critical layer. This transmission feature enables even quite small effects in the disturbance velocity field to produce a much more profound effect in the neutral stability criteria. The results of this study are not inconsistent overall with previous numerical work but they do tend to suggest that linear non-parallel flow stability theory may well explain most of the related experimental observations, even near the critical Reynolds number.

The influence of nonparallelism in channel flow stability

Considered below are the high Reynolds number flows of an incompressible fluid, and their nonparallel stability properties, in certain plane channels whose widths vary slowly in the streamwise direction. The first approximation to the steady-state flow is governed by the classical boundary layer equations but with the pressure unknown. Solutions, some including separation and reattachment, to this are obtained numerically for a range of the parameters involved, and the stability of the resulting flows is considered using fixed frequency disturbances and taking into account the nonparallel nature of the basic flow by use of a W.K.B. method. The calculations yield critical Reynolds numbers, below which all the disturbances decay downstream, and for various Reynolds numbers above the critical values the growths of the small disturbances are calculated. The results are specialized to a particular class of channels which are straight far upstream and far downstream but vary in between. So the predictions should be much more easily amenable to experimental investigation and comparisons than those of the more idealized, diverging channel, flow problem studied by Eagles & Weissman [1] and the only other basic flow seriously studied from the viewpoint of nonparallel flow stability theory, the Blasius boundary layer. The results also represent the first application of both quasiparallel and slightly non-parallel stability theory to channels involving slowly varying but finite changes in width.