Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

Time-Mean Structure of Axisymmetric Synthetic Jets

Abstract: Actuators generating synthetic jets are currently receiving increased attention as very promising means for fluid flow control. Necessary for their design are methods for evaluation of time-mean spatial distributions of such quantities as velocity, fluctuation intensity, etc.. An exact analysis is extremely difficult due to the complexity of synthetic jets, which consist of mutually interacting and convoluted vortex rings surrounded by stochastic turbulence, into which they gradually decompose. In ref. [2], authors derived a successful, relatively simple model – in the form of a set of simple ordinary differential equations for similarity-transformed quantities. The solution depends on a dimensionless parameter, which must be found experimentally. In contrast to analogous situation in similarity solutions of other shear flows, the parameter instead of being a constant was found to vary along the jet. In [2], only two sets of experimental data were available for evaluating this variation. The model is corrected and made more reliable in the present paper on the basis of extensive additional experimental evidence. In particular, it is found that in synthetic jets there are two distinctly different regions, the one further downstream exhibiting turbulence structure properties similar – but not identical – to those of steady jets.

Viscous effects in a vertically propagating internal wave

Abstract: A circular cylinder is positioned horizontally in an incompressible stably stratified fluid which has a constant Brunt-Vaisala frequency. A vertical two-dimensional internal wave is produced when the cylinder is oscillated at this natural frequency. A small amplitude viscous similarity solution which explains the main features of the internal wave is presented.

Similarity solution of mixed convection over a horizontal moving plate

Abstract: Investigation to the mixed convective heat and mass transfer over a horizontal plate has been carried out. By applying transformation group theory to analysis of the governing equations of continuity, momentum, energy and diffusion, we show the existence of similarity solution for the problem provided that the temperature and concentration at the wall are proportional to x 4/(7-5n) and that the moving speed of the plate is proportional to x (3-n)/(7-5n), and further obtain a similarity representation of the problem. The similarity equations have been solved numerically by a fourth-order Runge–Kutta scheme. The numerical results obtained for Pr=0.72 and various values of the parameters Sc, K 1, K 2 and K 3 reveals the influence of the parameters on the flow, heat and mass transfer behavior.

Re-entrant corner flows of PTT fluids in the Cartesian stress basis

Abstract: We consider the planar flow of Phan-Thien–Tanner (PTT) fluids around a re-entrant corner of angle π / α where α ∈ [ 1 / 2 , 1 ) . The model is considered in the absence of a solvent viscosity and the flow situation assumes complete flow around the corner with the absence of a lip votex. The local asymptotic solution structure is similar to that for the upper convected Maxwell (UCM) model and is shown to comprise a core flow (outer) region in which the fluid behaves elastically, together with wall boundary layers (inner regions) of similar thickness as those in the UCM model. In the core flow, the stress singularity is that for UCM, namely O ( r − 2 ( 1 − α ) ) where r is the radial distance from the corner, although the stream function vanishes at the slower rate O ( r α ( 1 + α ) ) compared to O ( r α ( 3 − α ) ) for UCM—this latter feature being a consequence of the shear thinning property of the PTT model. The amplitudes of the velocity and stress fields are determined and are seen to be independent from this local analysis, any link between them appearing to require global flow information away from the corner. The analysis is performed here in the Cartesian stress formulation of the problem, allowing the description of a similarity solution for the core flow and upstream boundary layer. The analysis remains to be completed by a solution for the downstream boundary layer which requires the use of the natural stress basis.

Three-dimensional wall-bounded laminar boundary layer with span-wise cross free stream and moving boundary

Abstract: In the current work, the 3D boundary layers of wall-bounded flow configurations were extended to the situations with span-wise cross moving boundary and free stream. The unsteady boundary layer is also addressed for the Falkner-Skan wedge flow with a span-wise oscillating wall or oscillating free stream. The span-wise secondary boundary layer equation is obtained using similarity transformation technique and solved analytically in terms of the primary stream-wise boundary layer flow solutions. Different fluid motion behaviors are found for these new solutions. It is found that for the span-wise secondary boundary layer flow there is no flow separation for any wall cross moving velocity, which is different from the primary stream-wise boundary layers with a reverse flow. For the unsteady boundary layer with an oscillating wall or free stream, it is seen that the solution is different from the Stokes oscillating plate or free stream problem. The unsteady wall drag increases with the increase in the oscillating frequency and decreases with increasing the primary span-wise free stream magnitude. The velocity overshooting near the wall is also seen for an oscillating free stream for a large oscillating frequency or a lower primary stream-wise free stream magnitude.