Turbulent secondary flows in channels with no-slip and shear-free boundaries

Nikitin, N.

doi:10.1017/jfm.2021.306

Cited by 10 publications

(20 citation statements)

References 38 publications

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“…If the pressure changes along the wall, then a secondary flow must certainly arise, directed from higher pressure to a lower one. The secondary flow along the pipe wall is directed from the points of the local The examples considered in Nikitin (2021) confirm the presence of a local mean-pressure maximum at the internal corners, which is consistent with the qualitative explanation given above. However, the pressure distribution in the vicinity of the external corner turns out to be more complex.…”

Section: Introductionsupporting

confidence: 85%

“…For comparison, figure 25(b) shows the distributions of all terms of (3.9) and (3.10) along the line θ = 0 in a pipe with internal apex angle α = π/2 at Re H = 2800. Some results of simulating the turbulent flow in such a pipe are given in figure 26, which shows the mean velocity field, the pressure field, and streamlines of the secondary flow (see also Nikitin 2021;Nikitin et al 2021). In accordance with the qualitative mechanism for the formation of secondary flows in the internal corners (figure 2a), an increase in pressure occurs in each of the three corner points.…”

Section: Formation Of Secondary Flowsmentioning

confidence: 73%

“…In Nikitin (2021) it is noted that the shape of the secondary flow near a solid wall is consistent with the distribution of the mean wall pressure. If the pressure changes along the wall, then a secondary flow must certainly arise, directed from higher pressure to a lower one.…”

Section: Introductionmentioning

confidence: 74%

“…In this work, considerable attention is paid to the study of the features of the formation of secondary flows. In general, the emerging secondary flows fit into the qualitative mechanism formulated in Nikitin (2021) and Nikitin et al (2021). According to this mechanism, the main driving element that generates secondary flows is the centrifugal force arising from a transverse fluctuating flow around a corner in a turbulent flow.…”

Section: Discussionmentioning

confidence: 99%

“…Many experimental, theoretical and computational works are devoted to the estimation of the source term and the relative importance of its two components: the normal stress difference term , and the shear stress term (see references and discussion in Nikitin 2021; Nikitin et al. 2021).…”

Section: Introductionmentioning

confidence: 99%

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Turbulent flows along a streamwise external corner

Nikitin

Krasnopolsky

2022

J. Fluid Mech.

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A numerical investigation of turbulent flows in straight pipes with a cross-section in the form of a circular sector at different values of the apex angle ${\alpha }$ is carried out. Main attention is paid to the cases ${\alpha }>{\rm \pi}$ when the cross-section boundary contains a convex external corner. An analytical solution to the problem of laminar flow in the geometry under consideration is given. The law of resistance is determined, and velocity distributions over the pipe cross-section are obtained. The singularity of wall shear stress $\tau _w\sim r^{{\rm \pi} /{\alpha }-1}$ at ${\alpha }>{\rm \pi}$ is shown which persists in turbulent flows as well. Turbulent flows are simulated at $Re=2000$ and four apex-angle values ${\alpha }=5{\rm \pi} /4$ , $3{\rm \pi} /2$ , $7{\rm \pi} /4$ and $2{\rm \pi}$ , as well as at a larger $Re=4000$ and ${\alpha }=3{\rm \pi} /2$ . The characteristic features of the mean-velocity distributions are outlined, and their relationship with secondary flows is shown. The velocity of the secondary flow in the vicinity of the external corner reaches the value $6.3\,\%$ of the bulk flow velocity at the maximum ${\alpha }=2{\rm \pi}$ . A characteristic feature of the considered flows is the presence of intense transverse velocity fluctuations in the region above the apex corner. It is hypothesized that the cause of these fluctuations may be the linear instability of the mean flow field. The studies of linear stability confirm this hypothesis. Considerable attention is paid to the study of secondary flows in the vicinity of the external corner. In general, the formation of these flows fits into the scheme proposed earlier (Nikitin, J. Fluid Mech., vol. 917, 2021, A24; Nikitin et al., Fluid Dyn., vol. 56, issue 4, 2021, pp. 513–538), according to which the main mechanism is the centrifugal force arising from the fluctuating flow over the corner in the transverse plane. It is shown that the shape of secondary flows is reproduced to a certain extent by the vortical part of the Reynolds-stress force field. The latter may be found from the Helmholtz decomposition. The features of the mean pressure distribution associated with the secondary flow and with the presence of a region of concentrated fluctuations above the external corner are explained.

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Section: Introductionsupporting

confidence: 85%

Section: Formation Of Secondary Flowsmentioning

confidence: 73%

Section: Introductionmentioning

confidence: 74%

Section: Discussionmentioning

confidence: 99%