On the Stability of Oscillatory Pipe Flows

The linear stability of pure oscillatory pipe flow is investigated by solving the linearized disturbance equations as an initial value problem. The importance of the initial conditions on transient dynamics of the flow is analyzed. It is shown that transient growth can play an important role in the development of flow instability. The accuracy of the quasi-steady assumption is assessed. It is shown that the growth rates obtained with this assumption deviate considerably from the results obtained with a direct numerical solution of the linearized initial value problem

Transient viscous flow in an annulus

The method of matched asymptotic expansions is used in the present paper to derive an approximate solution for transient flow of a viscous incompressible fluid in an annulus. The transient is caused by a sudden reduction of flow rate to zero. The laminar flow before deceleration can be either steady or unsteady but unidirectional. The solution is valid for short time intervals after sudden deceleration. Pereinamasis klampusis tekėjimas žiede Santrauka Išnagrinetas klampiojo nespudaus skysčio vienas atvejis, kai procesas modeliuojamas antrosios eiles dierencialine lygtimi su mažu parametru. Sukonstruotas uždavinio su pradine, kraštinemis bei su nelokaliaja salygomis formalusis asimptotinis sprendinys. First Published Online: 14 Oct 201

Spatial and temporal instability of slightly curved particle-laden shallow mixing layers

In the present paper we present linear and weakly nonlinear models for the analysis of stability of particle-laden slightly curved shallow mixing layers. The corresponding linear stability problem is solved using spatial stability analysis. Growth rates of the most unstable mode are calculated for different values of the parameters of the problem. The accuracy of Gaster’s transformation away from the marginal stability curve is analyzed. Two weakly nonlinear methods are suggested in order to analyze the development of instability analytically above the threshold. One method uses parallel flow assumption. If a bed-friction number is slightly smaller than the critical value then it is shown that the evolution of the most unstable mode is governed by the complex Ginzburg-Landau equation. The second method assumes that the base flow is slightly changing downstream. Applying the WKB method we derive the first-order amplitude evolution equation for the amplitude

Stability analysis of velocity profiles in water-hammer flows

This paper performs linear stability analysis of base flow velocity profiles for laminar and turbulent water-hammer flows. These base flow velocity profiles are determined analytically, where the transient is generated by an instantaneous reduction in flow rate at the downstream end of a simple pipe system. The presence of inflection points in the base flow velocity profile and the large velocity gradient near the pipe wall are the sources of flow instability. The main parameters that govern the stability behavior of transient flows are the Reynolds number and dimensionless timescale. The stability of the base flow velocity profiles with respect to axisymmetric and asymmetric modes is studied and its results are plotted in the Reynolds number/timescale parameter space. It is found that the asymmetric mode with azimuthal wave number 1 is the least stable. In addition, the results indicate that the decrease of the velocity gradient at the inflection point with time is a stabilizing mechanism whereas the migration of the inflection point from the pipe wall with time is a destabilizing mechanism. Moreover, it is shown that a higher reduction in flow rate, which results in a larger velocity gradient at the inflection point, promotes flow instability. Furthermore, it is found that the stability results of the laminar and the turbulent velocity profiles are consistent with published experimental data and successfully explain controversial conclusions in the literature. The consistency between stability analysis and experiments provide further confirmation that (I) water-hammer flows can become unstable; (2) the instability is asymmetric; (3) instabilities develop in a short (water-hammer) timescale; and (4) the Reynolds number and the wave timescale are important in the characterization of the stability of water-hammer flows. Physically, flow instabilities change the structure and strength of the turbulence in a pipe, result in strong flow asymmetry, and induce significant fluctuations in wall shear stress. These effects of flow instability are not represented in existing water-hammer models