Rotating Pipe Flow Research Articles

Role of cubic turbulence model in an axially rotating pipe flow

Role of cubic turbulence model in an axially rotating pipe flow

Large eddy simulation of turbulent axially rotating pipe and swirling jet flows

Fully-developed, turbulent rotating pipe flow and swirling jet flow, emitted from the pipe, into open quiescent ambient are investigated numerically using large eddy simulation. Simulations are performed at various rotation rates and Reynolds numbers. Time-averaged large eddy simulation results are compared to experimental and simulation data from previous studies. Pipe flow results show deformation of the turbulent mean axial velocity profile towards the laminar-type Poiseuille profile, with increased rotation. The Reynolds stress anisotropy tensor experiences a component-level redistribution due to pipe rotation. Turbulent energy is transferred from the axial component to the tangential component as rotation is increased. The Reynolds stress anisotropy invariant map also shows a movement away from the one-component limit in the buffer layer, with increased rotation. Exit conditions for the pipe flow simulation are utilized as inlet conditions for the jet flow simulation. Jet flow without swirl and at a swirl rate of S = 0.5 are investigated. Swirl is observed to change the characteristics of the jet flow field, leading to increased jet spread and velocity decay, and a corresponding decrease in the length of the jet potential core. The Reynolds stress anisotropy invariant map shows that the turbulent stress field, with or without rotation straddles the axi-symmetric limit.

Hydrodynamic instabilities in the developing region of an axially rotating pipe flow

We conduct experiments in a rotating Hagen–Poiseuille flow (RHPF) through flow visualizations when the flow becomes convectively and absolutely unstable at low-to-moderate Reynolds numbers, Re. We characterize periodic patterns at a very high swirl parameter, L, when the flow overcomes the absolutely unstable region. These non-steady helical filaments wrapped around the axis appear in the developing region of the pipe. Experimentally, we compute the onset of these oscillations in the (L, Re)-plane finding that the rotation rate decreases as the Reynolds number increases in the process of achieving the time-dependent state. Additionally, we report information regarding frequencies and wavelengths that appear downstream of the rotating pipe for convectively and absolutely unstable flows, even for very high swirl parameters at which the flow becomes time-dependent in the developing region. We do not observe variations in the trends of these parameters, so these hydrodynamic instabilities in the developing region do not affect the unstable travelling waves downstream of the pipe.

Experimental study of rotating Hagen-Poiseuille flow discharging into a 1:8 sudden expansion

In this paper, we present experimental evidence for the five different states that result from rotating Hagen-Poiseuille flow when it discharges into a 1:8 sudden expansion, namely: stable, convectively unstable, unstable shear layer, stable and unstable vortex breakdowns. Sanmiguel-Rojas et al. [“Three-dimensional structure of confined swirling jets at moderately large Reynolds numbers,” Phys. Fluids 20, 044104 (2008)] numerically predicted four of these five states and mapped the transition from one state to another. Our main objective is to study the onset of instabilities and vortex breakdown in these states experimentally. For this purpose, we visualize the flow at the inlet of the expansion for several values of moderately large Reynolds numbers, Re, and of swirl parameters, S. We analyze the inner region of the state that corresponds to the unstable shear layer in the sudden expansion and find two different states that share the same character, although they have different non-dimensional frequencies. The first relates to an oscillating structure near the axis, which arises at a small value of the swirl parameter, as well as to a generation of vortices that move downstream. The second shows, for greater values of the swirl parameter, vortices interacting with the boundary layer located on the wall of the static container that is perpendicular to the flow direction. In addition, we find a transition from stable to unstable vortex breakdown when perturbations become absolutely unstable inside the rotating pipe flow. Therefore, the most remarkable experimental finding is a new state, namely, unstable or transient vortex breakdown that takes place for the same pair of values (Rea, Sa) at which the onset of the absolute instability curve appears and intersects the region of stable vortex breakdown.

The Effect of a Pressure-Containing Correlation Model on Near-Wall Flow Simulations with RST Models.

It is accustomed to think that turbulence models based on solving the Reynolds-Averaged Navier-Stokes equations require empirical functions to accurately reproduce the behavior of flow characteristics of interest, particularly near a wall. The current paper analyzes how choosing a model for pressure-strain correlations in second-order closures affects the need for introducing empirical functions in model equations to reproduce the flow behavior near a wall correctly. An axially-rotating pipe flow is used as a test flow for the analysis. Results of simulations demonstrate that by using more physics-based models to represent pressure-strain correlations, one can eliminate wall functions associated with such models. The higher the Reynolds number or the strength of imposed rotation on a flow, the less need there is for empirical functions regardless of the choice of a pressure-strain correlation model.

Turbulent pipe flow downstream a 90° pipe bend with and without superimposed swirl

In the present work, the turbulent flow downstream a 90° pipe bend is investigated by means of stereoscopic particle image velocimetry. In particular, the three dimensional flow field at the exit of the curved pipe is documented for non-swirling and swirling flow conditions, with the latter being generated through a unique axially rotating pipe flow facility. The non-swirling flow was examined through snapshot proper orthogonal decomposition (POD) with the aim to reveal the unsteady behaviour of the Dean vortices under turbulent flow conditions, the so-called “swirl-switching” phenomenon. In respect to the swirling turbulent pipe flow, covering a wide range of swirl strengths, POD has been employed to study the effect of varying strength of swirl on the Dean vortices as well as the interplay of swirling motion and Dean cells. Furthermore, the visualised large scale structures in turbulent swirling flows through the bend are found to incline and tear up with increasing swirl intensity. The present time-resolved, three component, experimental velocity field data will provide a unique and useful database for future studies; in particular for the CFD community.

Experimental evidence of convective and absolute instabilities in rotating Hagen–Poiseuille flow

AbstractExperimental results for instabilities present in a rotating Hagen–Poiseuille flow are reported in this study through fluid flow visualization. First, we found a very good agreement between the experimental and the theoretical predictions for the onset of convective hydrodynamic instabilities. Our analysis in a space–time domain is able to obtain quantitative data, so the wavelengths and the frequencies are also estimated. The comparison of the predicted theoretical frequencies with the experimental ones shows the suitability of the parallel, spatial and linear stability analysis, even though the problem is spatially developing. Special attention is focused on the transition from convective to absolute instabilities, where we observe that the entire pipe presents wavy patterns, and the experimental frequencies collapse with the theoretical results for the absolute frequencies. Thus, we provide experimental evidence of absolute instabilities in a pipe flow, confirming that the rotating pipe flow may be absolutely unstable for moderate values of Reynolds numbers and low values of the swirl parameter.

On the minimal representation of non-linear eddy-viscosity models

This study attempts to provide a minimal explicit non-linear relationship between the Reynolds stresses and the mean strain rate and vorticity. Such relationship is also referred to as the nonlinear eddy-viscosity model (EVM) of the Reynolds stresses. Based on the observation of the independent terms in the Reynolds stress anisotropy tensor, it is proposed here that the explicit Reynolds stress closure can be formulated in a compact vorticity tensor to form a minimal representation. With the application of the generalized Cayley–Hamilton theory, it is shown that the explicit algebraic stress model with 10 integrity bases can be transformed into a five-term model expression. Thus, the present work provides a framework for the development of the explicit Reynolds stress closure in the compact form. Indeed, a cubic EVM is developed here that is capable of revealing the quadratic behaviour of the tangential velocity with respect to the radial distance in the fully developed turbulent rotating pipe flow. This model, hence, removed some major defects in the lower-order EVMs, while the model complexity is kept at minimum.

Near-field dynamics of a turbulent round jet with moderate swirl

The near-field characteristics of a turbulent jet with moderate swirl generated by a fully developed, axially rotating pipe flow are investigated with LDV, time-resolved stereoscopic PIV measurements, as well as with large-eddy simulations. Large-scale vortical structures in either double, triple or even quadruple-helix configuration are found at the pipe exit but rapidly break down or amalgamate after two jet diameters. Further downstream, the swirling jet is dominated by large-scale sweeping motions not present at such a scale and strength in the non-swirling case. Of special interest is the recently discovered counter-rotating core (in the mean) which develops about six jet diameters downstream the jet exit. Data for all six Reynolds stresses is reported at this position and it is argued that the counter-rotation is the result of the transport of angular momentum radially outward by the radial–azimuthal Reynolds shear stress. The mechanisms behind this transport are discussed by qualitative analysis of the time-resolved PIV and LES data and comparisons with the non-swirling case are made.

Direct numerical simulation of the motion of particles in rotating pipe flow

In this paper the motion of particles in rotating pipe flow is studied for various flow cases by means of direct numerical simulation. Compared to flow in a non-rotating pipe, the Navier–Stokes equation contains as only extra term the Coriolis force when the equation is considered in a rotating frame of reference. Particles in the flow also experience a centrifugal force, which drives them to one side of the wall of the pipe. The flow is characterized by two Reynolds numbers for the mean axial velocity and the rotation rate, respectively. Among the cases studied are one in which the flow without rotation would be laminar and rotation leads to turbulence and another one for which Poiseuille flow is unstable but instead of transition to a turbulent state, a time-dependent laminar flow results. In all cases studied a counter-rotating vortex is present. The simulation results are used to calculate the collection efficiency of the rotational phase separator (RPS) under turbulent flow conditions. The RPS is a device to separate liquid or solid particles from a lighter or heavier fluid by means of centrifugation in a bundle of channels which rotate around a common axis. The results show that, compared to Poiseuille flow, the collection efficiency for larger particles decreases due to the combined action of the vortex and turbulent velocity fluctuations, while it is unchanged for smaller particles.

An Experimental Study of the Near-Field Mixing Characteristics of a Swirling Jet

The present experimental investigation is devoted to the mixing characteristics of a passive scalar in the near-field region of a moderately swirling jet issuing from a fully developed axially rotating pipe flow. Instantaneous streamwise and azimuthal velocity components as well as the temperature were simultaneously accessed by means of a combined X-wire and cold-wire probe. The results indicate a modification of the turbulence structures to that effect that the swirling jet spreads, mixes and evolves faster compared to its non-swirling counterpart. The high correlation between streamwise velocity and temperature fluctuations as well as the streamwise passive scalar flux are even more enhanced due to the addition of swirl, which in turn shortens the distance and hence time needed to mix the jet with the ambient air.

축을 중심으로 회전하는 관유동에서 난류열전달의 모형화

축을 중심으로 회전하는 관유동에서 난류열전달의 모형화

A study of swirling turbulent pipe and jet flows

Axially rotating turbulent pipe flow is an example in which the rotation strongly affects the turbulence, which then also influences the mean flow properties. For instance, in the fully developed flow as well, the fluid is not in solid body rotation due to the influence of the cross-stream Reynolds stress. The present paper reports new measurements from a rotating pipe flow and the streamwise mean velocity distribution is compared with recent scaling ideas of Oberlack [J. Fluid Mech. 379, 1 (1999)] and good agreement is found. A second part of the paper deals with the initial stages when the flow leaves the pipe and forms a swirling jet. The measurements in the jet show that at some distance downstream (approximately five jet diameters) the central part of the jet actually rotates in the opposite direction as compared to the rotation of the pipe. This effect is explained by the influence of the cross-stream Reynolds shear stress.

Techniques for deriving explicit algebraic Reynolds stress models based on incomplete sets of basis tensors and predictions of fully developed rotating pipe flow

Different techniques for deriving explicit algebraic Reynolds stress models (EARSMs) using incomplete sets of basis tensors are discussed. The first is the Galerkin method which has been used by several authors. The second alternative technique, proposed here, is based on the least-squares method. The idea behind the latter method is to minimize the error induced in the implicit relation, i.e., the algebraic Reynolds stress model (ARSM) equation, due to the use of incomplete sets of basis tensors. It is argued that since the system matrix of the ARSM equation is not symmetric and positive definite, the Galerkin method does not give EARSMs that are optimal in the strict classical sense. The possible singular behavior depending on the choice of the basis tensors has also been investigated. It is demonstrated that many of the EARSMs based on incomplete tensor bases, expressed in general three-dimensional mean flows, have singularity problems in some flows, such as general two-dimensional (2D) mean flows or more specifically, strain- and/or rotation-free 2D mean flows. The different EARSMs emanating from the two derivation methods are investigated by computing fully developed rotating pipe flow. The results indicate that the EARSMs derived with the least-squares method capture the behavior of the complete EARSMs significantly better than those derived with the Galerkin method. Furthermore, by using mean flow data from the complete EARSMs to evaluate the square error of the incomplete EARSMs it is demonstrated that the least-squares based EARSMs have square errors significantly smaller than the Galerkin EARSMs, very close to minimum.

An explicit algebraic Reynolds stress model based on a nonlinear pressure strain rate model

The use of a pressure strain rate model including terms nonlinear in the mean strain and rotation rate tensors in an explicit algebraic Reynolds stress model (EARSM) is considered. For 2D mean flows the nonlinear contributions can be fully accounted for in the EARSM formulation. This is not the case for 3D mean flows and a suggestion of how to modify the nonlinear terms to make the EARSM formulation in 3D mean flows consistent with its 2D counterpart is given. The corresponding EARSM is derived in conjunction with the use of streamline curvature corrections emanating from the advection of the Reynolds stress anisotropy. The proposed model is tested for rotating homogeneous shear flow, rotating channel flow and rotating pipe flow and the nonlinear contributions are shown to have a significant effect on the predicted flow characteristics. In cases where the 3D effects are strong, the approximations of the production to dissipation ratio made in the EARSM formulation for 3D mean flows must be made carefully and a 3D mean flow correction is considered. For the rotating pipe flow at the highest rotation rate investigated, the standard formulation even prevented convergence, while inclusion of the 3D correction gives reasonable results.

Observations on the predictions of fully developed rotating pipe flow using differential and explicit algebraic Reynolds stress models

The differences between two differential Reynolds stress models (DRSM) and their corresponding explicit algebraic Reynolds stress models (EARSM) are investigated by studying fully developed axially rotating turbulent pipe flow. The mean flow and the turbulence quantities are strongly influenced by the imposed rotation, and is well captured by the differential models as well as their algebraic truncations. All the tested models give mean velocity profiles that are in good qualitative agreement with the experimental data. It is demonstrated that the predicted turbulence kinetic energy levels vary dramatically depending on the diffusion model used, and that this is closely related to the model for the evolution of the length-scale determining quantity. Furthermore, the effect of the weak equilibrium assumption, underlying the EARSMs, and the approximation imposed for 3D mean flows on the turbulence levels are investigated. In general the predictions obtained with the EARSMs rather closely follow those of the corresponding DRSMs.

Turbulence Statistics in a Fully Developed Rotating Pipe Flow

This paper presents Direct Numerical Simulations (DNS) of fully developed turbulent flows in axially rotating pipes. The study is aimed at investigation of the effects of the Reynolds number and of the rotation number on turbulent flow characteristics. The mean velocity profiles and the statistics are compared to numerical and experimental data available in the literature, and reasonably good agreement is obtained. In particular, the results show that the axial velocity profile gradually approaches a laminar shape when increasing the rotation rate, due to the stability effect caused by the centrifugal force. Consequently, the friction factor decreases. To have a better understanding of the behavior of this kind of complex flows and to investigate the effects of higher Reynolds numbers, we have also carried out Large Eddy Simulations (LES).

Optimal Disturbances in Swirling Flows

The mechanism of optimal disturbances, which are composed of both growing and decaying modes, in swirling flows (with an axial velocity component) is explored. Two characterizing cases are considered: stationary disturbances in rotating pipe flow and temporal disturbances in a trailing vortex

The counter-rotating core of a swirling turbulent jet issued from a rotating pipe flow

Axially rotating turbulent pipe flow is an example where rotation strongly affects the turbulence and thereby the Reynolds stresses and mean flow properties. The present Letter reports new measurements where a rotating pipe flow is used to establish a swirling jet. The measurements in the jet show that at some distance downstream (approximately 6 nozzle diameters) the central part of the jet starts to rotate in the opposite direction as compared to the rotation of the pipe. This effect is explained by the influence of the cross flow Reynolds stress originating in the pipe flow.

Computation of strongly swirling confined flows with cubic eddy‐viscosity turbulence models

AbstractAn investigation on the predictive performance of four cubic eddy‐viscosity turbulence models for two strongly swirling confined flows is presented. Comparisons of the prediction with the experiments show clearly the superiority of cubic models over the linear k–εmodel. The linear k–εmodel does not contain any mechanism to describe the stabilizing effects of swirling motion and as a consequence it performs poorly. Cubic models return a lower level of Reynolds stresses and the combined forced‐free vortex profiles of tangential velocity close to the measurements in response to the interaction between swirl‐induced curvature and stresses. However, a fully developed rotating pipe flow is too simple to contain enough flow physics, so the calibration of cubic terms is still a topic of investigation. It is shown that explicit algebraic stress models require fewer calibrations and contain more flow physics. Copyright © 2003 John Wiley & Sons, Ltd.