Analytical investigation of boundary layer growth and swirl intensity decay rate in a pipe

Abstract

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed that the free vortex velocity profile can better predict the boundary layer parameters in the entrance region than in the forced one. Also, effects of pressure gradient inside the boundary layer is investigated and showed that if pressure gradient is ignored inside the boundary layer, results deviate greatly from the experimental data.

Turbulent flow in converging nozzles, part one: boundary layer solution

“…Then, the obtained differential equations are solved with the fourth-order Adams predictorcorrector method [27] . It must be mentioned that this study is the continuation of the previous study done by [26] on swirling flows.…”

“…In most of the previous studies on the boundary layer such as [11] and [12], although a constant pressure gradient is considered due to the small thickness of the boundary layer, due to the high rotational velocity, the variation of the pressure inside the boundary layer has an important effect on the growth of the boundary layer [26] . To predict the pressure gradient, u θ inside the boundary layer is ignored.…”

“…Therefore, an empirical expression for the wall shear stress in turbulent flows is used [29] . Considering the velocity profiles near the wall, the wall shear stress can be decomposed into the axial and tangential directions [12,[25][26] . It should be mentioned that the obtained results in [12,[25][26] showed the validity of the following equations Turbulent flow in converging nozzles 653 in predicting the wall shear stress of turbulent swirling flows:…”

“…Najafi et al [25] used the boundary layer integral method to predict the boundary layer parameters of a swirling flow in a pipe, and introduced the analytical solution to boundary layer equations for large Rossby numbers. Maddahian et al [26] investigated the development of turbulent swirling flows at the entrance region of a pipe using the integral method. The general tangential velocity profile was applied to consider both free and forced vortex velocity profiles.…”

“…Within a flow with a high swirl intensity, the structure of the swirling flow is unstable, and multi recirculation zones are formed [19][20] . Noticing the importance of the swirl intensity, numerous investigations focused on the prediction of the swirl intensity and its decay rate in relevant applications [21][22][23][24][25][26] .…”