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The analysis and modelling of the structure of turbulent flow in a circular pipe
subjected to an axial rotation is presented. Particular attention is paid to determining
the terms in various turbulence closures that generate the two main physical features
that characterize this flow: a rotationally dependent axial mean velocity and a
rotational...
Contexts in source publication
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... analyse flow in an axially rotating circular pipe of radius R, we consider the Navier-Stokes and continuity equations in a steadily rotating frame -about the axial direction -written in cylindrical coordinates (see the schematic diagram shown in figure 1). For the three-dimensional velocity field u = u r (r, θ, z, t)e r + u θ (r, θ, z, t)e θ + 4 C. G. Speziale, B. A. Younis and S. A. Berger u z (r, θ, z, t)e z , they take the form (Batchelor 1967) ...
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... large- eddy simulations, the full Navier-Stokes equations (1)-(3) are solved numerically with a subgrid-scale stress model. In figure 10a, b the axial mean velocity and mean swirl velocity relative to the inertial frame are displayed. The Reynolds stresses are not compared in detail due to the problem of defiltering that leads to uncertainties. ...
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... should be noted that the profile for τ rθ is such that the values for the Reynolds shear stress are zero except close to the wall. From (13) it is clear that in the inviscid Figure 10. Comparison of the predictions of various second-order closure models and the K-ε model for the mean velocity in the axially rotating pipe with the large-eddy simulations of Eggels et al. (1994). ...
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... τ rθ is the generator for a mean swirl velocity, we can conclude that a non-zero mean swirl velocity arises largely from near-wall effects in a high-Reynolds-number ax- ially rotating pipe flow. This is illustrated in figure 11 where the Reynolds number Re =59500 Re = 250 000 Re = 500 000 Re =1 000 000 LES (Re = 59 500) ×10 -5 Figure 11. Predictions of the SSG model for the Reynolds shear stress τ rθ in the axially rotating pipe. ...
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... τ rθ is the generator for a mean swirl velocity, we can conclude that a non-zero mean swirl velocity arises largely from near-wall effects in a high-Reynolds-number ax- ially rotating pipe flow. This is illustrated in figure 11 where the Reynolds number Re =59500 Re = 250 000 Re = 500 000 Re =1 000 000 LES (Re = 59 500) ×10 -5 Figure 11. Predictions of the SSG model for the Reynolds shear stress τ rθ in the axially rotating pipe. ...
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... from these results, τ rθ goes to zero as Re → ∞ consistent with these theoretical re- sults. Furthermore, these results demonstrate the difficulty of large-eddy simulations in accurately determinating the Reynolds stresses (notice in figure 11 the waves in the profile of the Reynolds shear stress obtained from the large-eddy simulations). ...
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... will also tend to cause the flow to laminarize, which explains why the axial velocity profiles become more laminar-like when there is a discernible rotation. This effect can be observed in figure 3 and figure 10. The development of a turbulence model that is fully consistent with the Taylor-Proudman theorem is a very challenging undertaking that has not yet been fully achieved (Speziale 1998b). ...
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... analyse flow in an axially rotating circular pipe of radius R, we consider the Navier-Stokes and continuity equations in a steadily rotating frame -about the axial direction -written in cylindrical coordinates (see the schematic diagram shown in figure 1). For the three-dimensional velocity field u = u r (r, θ, z, t)e r + u θ (r, θ, z, t)e θ + 4 C. G. Speziale, B. A. Younis and S. A. Berger u z (r, θ, z, t)e z , they take the form (Batchelor 1967) ...
Context 9
... large- eddy simulations, the full Navier-Stokes equations (1)-(3) are solved numerically with a subgrid-scale stress model. In figure 10a, b the axial mean velocity and mean swirl velocity relative to the inertial frame are displayed. The Reynolds stresses are not compared in detail due to the problem of defiltering that leads to uncertainties. ...
Context 10
... should be noted that the profile for τ rθ is such that the values for the Reynolds shear stress are zero except close to the wall. From (13) it is clear that in the inviscid Figure 10. Comparison of the predictions of various second-order closure models and the K-ε model for the mean velocity in the axially rotating pipe with the large-eddy simulations of Eggels et al. (1994). ...
Context 11
... τ rθ is the generator for a mean swirl velocity, we can conclude that a non-zero mean swirl velocity arises largely from near-wall effects in a high-Reynolds-number axially rotating pipe flow. This is illustrated in figure 11 where the Reynolds number Re =59500 Re = 250 000 Re = 500 000 Re =1 000 000 LES (Re = 59 500) ×10 -5 Figure 11. Predictions of the SSG model for the Reynolds shear stress τ rθ in the axially rotating pipe. ...
Context 12
... τ rθ is the generator for a mean swirl velocity, we can conclude that a non-zero mean swirl velocity arises largely from near-wall effects in a high-Reynolds-number axially rotating pipe flow. This is illustrated in figure 11 where the Reynolds number Re =59500 Re = 250 000 Re = 500 000 Re =1 000 000 LES (Re = 59 500) ×10 -5 Figure 11. Predictions of the SSG model for the Reynolds shear stress τ rθ in the axially rotating pipe. ...
Context 13
... from these results, τ rθ goes to zero as Re → ∞ consistent with these theoretical results. Furthermore, these results demonstrate the difficulty of large-eddy simulations in accurately determinating the Reynolds stresses (notice in figure 11 the waves in the profile of the Reynolds shear stress obtained from the large-eddy simulations). ...
Context 14
... will also tend to cause the flow to laminarize, which explains why the axial velocity profiles become more laminar-like when there is a discernible rotation. This effect can be observed in figure 3 and figure 10. The development of a turbulence model that is fully consistent with the Taylor-Proudman theorem is a very challenging undertaking that has not yet been fully achieved (Speziale 1998b). ...
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Citations
... Computationally expensive methods such as the second-order turbulence closure Reynolds stress models have been used in [19][20][21][22][23][24], among others, to model the effect of pipe rotation on turbulent flow. However, these studies have been focused mostly on high Reynolds number turbulent fluid flow and not on heat transfer. ...
Numerical investigation of laminarization of low Reynolds number turbulent flow in a heated rotating vertical pipe is carried out using a rotation-sensitized [Formula: see text] Shear Stress Transport (SST) model with modifications to include low Reynolds number flow effects. The results show that rotation accelerates laminarization in heated pipes and leads to as much as 72% deterioration in heat transfer for a typical inlet Reynolds number of 5000 and at a rotation number of 2. Rotation causes a reduction of the velocity gradients in the near-wall region. The lower gradients result in a reduction in the rate of production of turbulence kinetic energy, which causes the flow to laminarize. A laminarization map that relates the nondimensional heat flux as a function of inlet Reynolds number and rotation number is presented in this study. Correlation to predict the nondimensional wall heat flux required to laminarize the flow as a function of inlet Reynolds number and rotation number is proposed. The proposed laminarization map and the correlation which predicts the nondimensional heat flux required for laminarization to within an accuracy of ±8.1% accuracy for flow of air in a heated rotating vertical pipe would be of value to operators and designers of heat exchangers using air as a working medium to maintain a heat flux or a rotation number below the threshold value to prevent flow laminarization.
... Cubic and quartic terms (Ĉ 3 -andĈ 4related terms) are selected to complement shear and normal stresses in plane shear flow, which is one of the most typical configuration of turbulence in nature.Ĉ W -related term is introduced in order to incorporate a simplest effect of streamline curvature. 21 k is now determined from the following: ...
A new methodology of turbulence modeling is proposed by combining a statistical theory [T. Ariki, Phys. Fluids 31, 065104 (2019)] and the Reynolds-stress-root method [T. Ariki, Phys. Rev. E 92, 053010 (2015)], aiming at realizing practical turbulence model of wider applicability with the help of theoretical support. The resultant model integrates, at the same time, the following five features: coordinate covariance, realizability condition, near-wall behavior, history effect, and streamline curvature effect, which are all key ingredients to build up better turbulence model mimicking realistic behaviors. Numerical assessments of the model are conducted for homogeneous shear flow, channel flow, flow in a rotating pipe, and flow between concentric annuli, all of which show reasonable agreement with direct numerical simulations and experiments.
... A. Wall bounded rotational turbulence For high frequency rotating pipes, axial flow tends toward a parabolic Poiseuille laminar profile where U + = y + . Hence, a higher axial velocity U + is obtained per Reτ equivalent in the non-rotating pipe (Brehm et al., 2019;Davis et al., 2020;Kikuyama et al., 1983;Kitoh, 1991;Nygard and Andersson, 2010;Orlandi and Fatica, 1997;Reich and Beer, 1989;Speziale et al., 2000;and White, 1964). Either due to the relaminarization of the flow or the symmetry of the streamwise flow, the effect of axial rotation (azimuthal velocity) on streamwise turbulent flow in a pipe is insignificant or non-existent. ...
An elementary observation of a laminar cylindrical Poiseuille–Couette flow profile reveals no distinction in the parabolic streamwise profile, from one without a cross-stream flow, in whatever reference frame the observation is made. This is because the laminar flow is in solid-body rotation and there is no fluid intrinsic rotation. Hence, the main streamwise Poiseuille flow is unaffected. On the contrary, in turbulent (unsteady) cylindrical axial-Couette flow, the rotational reference frame must be considered, and any observation from an external inertial reference frame can give outright incorrect results. However, even in axial turbulent pipe flow with axial rotation, the resultant effect of azimuthal velocity on the flow profile is still usually too low. Hence, the importance of consideration in the rotational frame is often overlooked. A common misconception in the study of fluid mechanics is that the position of the observer does not matter. In this direct numerical simulation study, firstly turbulent flow in a pipe with axial rotation is established. Then turbulent flow in the concentric pipe, with inner wall rotation, is used to show how tilted wall streak direction is oriented by the rotational reference frame and not the inertial reference frame.
... Regarding the quality of the simulation, one can find in the literature that other authors generated similarly the rotating pipe profiles that we obtained in our deterministic CFD simulation. These authors also used the RSM model for the rotating pipe flow simulation [67][68][69], as this model exhibits the best performance. In addition, the experimental results reported by [17,70] were used to validate the accuracy of the CFD simulation in [9], being very interesting to observe a nearly perfect match for the axial velocity profile. ...
In Computational Fluid Dynamics (CFD) studies composed of the coupling of different simulations, the uncertainty in one stage may be propagated to the following stage and affect the accuracy of the prediction. In this paper, a framework for uncertainty quantification in the computational heat transfer by forced convection is applied to the two-step simulation of the mechanical design of a swirling jet flow generated by a rotating pipe (Simulation 1) impinging on a flat plate (Simulation 2). This is the first probabilistic uncertainty analysis on computational heat transfer by impinging jets in the literature. The conclusion drawn from the analysis of this frequent engineering application is that the simulated system does not exhibit a significant sensitivity to stochastic variations of model input parameters, over the tested uncertainty ranges. Additionally, a set of nonlinear regression models for the stochastic velocity and turbulent profiles for the pipe nozzle are created and tested, since impinging jets for heat transfer at Reynolds number of \(Re\,=\,23,000\) are very frequent in the literature, but stochastic inlet conditions have never been provided. Numerical results demonstrate a negligible difference in the predicted convective heat transfer with respect to the use of the profiles simulated via CFD. These suggested surrogate models can be directly embedded onto other engineering applications (e.g. arrays of jets, jet flows impinging on plates with different shapes, inlet piping in combustion, chemical mixing, etc.) in which a realistic swirling flow under uncertainty can be of interest.
... Thus, according to the Rayleigh stability criteria [2], the effects of rotation lead to more stability and hence a reduction in turbulence intensity when compared to the non-rotating case. This type of rotating flow has been studied using a wide range set of techniques, including experiments [1,3,4] analytical methods [5,6] turbulence closures [7,8] and largeeddy and direct numerical simulations [9][10][11]. ...
Results from large-eddy simulations, are reported for the flow and heat transfer inside a rotating cylinder with axial airflow. The objective of this work is to document the effects of destabilizing rotation on the turbulent transport of heat and momentum. The outer wall of the cylinder is set with the boundary condition of a constant temperature. Results are obtained for different rotation numbers and the Reynolds number was set at 5500 for all cases. Present predicted results of velocity and turbulence quantities are compared with others found in the literature, and present calculations of the thermal quantities are validated using experimental measurements. Calculations of the mean velocity, turbulence statistics, mean temperature and thermal statistics inside and close to the outer wall are then given.
... Some other ARSM which consider the realizability [17,19,20] are also quadraticnonlinear models. However, it was pointed out that cubic nonlinearity is essential for predicting the mean swirl or tangential velocity in an axially rotating turbulent pipe flow, which is an example of the three-dimensional flow [22]. The realizable ARSM involving cubic or higher-order nonlinearity is required to make numerically stable predictions of three-dimensional flows of high-Reynolds number. ...
... Although these models can capture the anisotropic property of the Reynolds stress in turbulent shear flows owing to the quadratic-nonlinear terms, it is almost impossible to extend these models to higher-order nonlinear ones because the freedom for the dimensional coefficients ζ 's is too large to analytically determine their form. However, Speziale et al. [22] pointed out that cubic nonlinearity is essential for predicting the mean swirl or tangential velocity in an axially rotating turbulent pipe flow, which is an example of the three-dimensional flow. Furthermore, the Reynolds stress should be affected not only by the mean velocity gradient but also the turbulent helicity [25][26][27] or the time history effect of the mean strain [21,28,29]. ...
... Third, we perform an axially rotating turbulent pipe flow as an example of the three-dimensional flow. In this flow, no quadratic-nonlinear eddy-viscosity model can predict the mean tangential or swirl velocity [22]. In contrast to the conventional realizable model, such as that given by Shih et al. [14,15], the present model involves cubic nonlinearity on the velocity gradient, as seen in Eq. (23), and thus, is able to predict the mean tangential or swirl velocity. ...
In this study, realizable algebraic Reynolds stress modeling based on the square root tensor [Phys. Rev. E 92, 053010 (2015)] is further developed for extending its applicability to more complex flows. In conventional methods, it was difficult to construct an algebraic Reynolds stress model satisfying the realizability conditions when the model involves higher-order nonlinear terms on the mean velocity gradient. Such higher-order nonlinear terms are required to predict turbulent flows with three-dimensional mean velocity. The present modeling based on the square root tensor enables us to make the model always satisfy the realizability conditions, even when it involves higher-order nonlinearity. To construct a realizable algebraic Reynolds stress model applicable to turbulent flows with three-dimensional mean velocity, a quartic-nonlinear eddy-viscosity model is proposed. The performance of the model is numerically verified in a turbulent channel flow, a homogeneous turbulent shear flow, and an axially rotating turbulent pipe flow. The present model gives a good result in each turbulent flow. Note that the mean swirl flow in an axially rotating turbulent pipe flow is reproduced because the present model involves cubic nonlinearity. Such a higher-order realizable algebraic Reynolds stress model, involving quartic nonlinearity on the mean velocity, is expected to be useful in numerically stable predictions of turbulent flows with three-dimensional mean velocity.
... The word "rotation" in turbulence is usually referred to the circular motion around a fixed axis. Its effect is found in a wide range of flows such as the isotropic turbulence [7] , the turbulent channel flow [8 , 9] , the pipe flow [10] and so on. When the rotation is imposed, all the above flows show quite different characteristics comparing to the non-rotating state, e.g. the turbulence being enhanced near one side and suppressed near another side. ...
The complex geometry of rotating machines makes the flows strongly affected by rotation and curvature, which are challenging for turbulence modeling. During the development of CFD, large amount of turbulence models appeared and hence make the user hard to de- cide which one to choose. The present paper presents a coherent review of the various approaches proposed in the recent literatures on this topic. First, the influence of the rota- tion and curvature is reviewed and concluded. Then, the basic concepts of RANS and LES are introduced to facilitate the description of the models and each method is classified into several types. A variety of models are then described and assessed either by the results in the literatures or by own results, with special concentration on the application to rotating machines. Finally, a brief introduction to the hybrid RANS/LES is made and assessed, to- gether with the recommendation for the selection of the models. The aim of the review is to provide information on the advantages and limitations of related models and make it easier for the user to choose an appropriate model.
... In the previous studies of the RANS modeling, the effects of the system rotation on inhomogeneous turbulence are mainly discussed in terms of the Reynolds stress. In these studies, the effects of the system rotation on the Reynolds stress are expressed in the form of the nonlinear eddy-viscosity models with rotation-dependent coefficients [6,7] and with helicity density (hereafter simply referred to as helicity) [8][9][10]. However, the effects of the system rotation on the turbulent energy transport were not discussed. ...
... There are some elaborate RANS models in which the effects of system rotation are incorporated. For example, the effect of the suppression of the energy cascade is considered by modifying the transport equation for ε [4,5], and the rotation-dependent model coefficient is proposed with the aid of the algebraic Reynolds stress model procedure [6,7]. Although these effects are essential for describing some effects of rotation on turbulence, they are insufficient to predict the energy transport enhanced in rotating oscillating-grid turbulence. ...
It is known that turbulent energy is rapidly transferred in the direction of the rotation axis in a rotating system, in comparison with the non-rotating case. In this study, this phenomenon is investigated as a problem of energy diffusion expressed by the Reynolds averaged Navier-Stokes (RANS) model. The conventional gradient-diffusion approximation for the turbulent energy flux cannot account for the enhanced energy transport observed in rotating inhomogeneous turbulence. In order to adequately describe the phenomenon, we propose a new model for the energy flux due to the pressure associated with the rotational motion of a fluid. The model of the energy flux is expressed to be proportional to the turbulent helicity. This property is closely related to the group velocity of inertial waves in a rapidly rotating fluid. The validity of the model is assessed using a direct numerical simulation (DNS) of inhomogeneous turbulence under rotation. It is shown that most of the turbulent energy transport enhanced by the system rotation is attributed to the pressure diffusion term. The spatial distribution of the energy flux due to the pressure related to the system rotation is similar to that of the turbulent helicity with negative coefficient. Hence, the new model which is proportional to the turbulent helicity is able to qualitatively account for the enhanced energy flux due to the system rotation. Finally, the helical Rossby number is proposed in order to estimate the relative importance of the energy flux enhanced by the turbulent helicity and the rotation, in comparison to the conventional gradient-diffusion approximation.
... For the case of the flow in a single rotating cylinder, the gradient of angular momentum is positive away from the axis of rotation and thus, according to Rayleigh's stability criteria [1], the effects of rotation are stabilizing leading to reduction in turbulence activity relative to the non-rotating case. Results for this flow have been obtained by utilizing all the tools that are available for the study of fluid-flow phenomena including analytical solutions [2,3], experiments [4,5], large-eddy and direct numerical simulations [6][7][8][9] and turbulence closures [10,11]. Collectively, these studies have served to document in detail the substantial modifications of the flow and heat transfer processes wrought by stabilizing rotation. ...
Results from large-eddy simulations are reported for the flow and heat transfer in the annular gap between two concentric cylinders with the outer cylinder stationary and the inner cylinder rotating about its longitudinal axis. The objective of the study was to document the effects of destabilizing rotation on the turbulent transport of heat and momentum. The inner cylinder was heated by applying a constant heat flux while the conditions at the outer wall were adiabatic. Results were obtained for a stationary inner cylinder to serve as baseline for isolating the effects of rotation, and for the inner cylinder rotated at two different rotation numbers viz. 0.21 and 0.86. The Reynolds number was set at 9000 for all cases. With the outer cylinder stationary and the inner cylinder rotating, the effects of rotation are to destabilize the turbulence leading to enhanced mixing and significant increase in wall shear stress and Nusselt number. Additional effects include the displacement from each other of the points where the Reynolds stresses and the corresponding rates of strain are zero, and the non-alignment of their respective directions. These and other results reported herein provide a useful contribution to the very limited literature on heated turbulent flows destabilized by rotation, and can serve as benchmark to aid in the development and validation of turbulence closures for engineering applications.
... Those data were used later by Ref. [158] in order to show that LES can reasonably well predict phenomena in rotating turbulent pipe flows. Reynolds stress models were developed by Ref. [156] and were successful in capturing the main features of turbulent swirling flow as described above. More recent DNS on turbulent swirling flow in a straight pipe [160] have shown the effect of swirl on near wall structures which appear as elongated streaks being tilted and shortened as the swirl intensity increases. ...
Curved pipes are essential components of nearly all the industrial process equipments, ranging from power production, chemical and food industries, heat exchangers, nuclear reactors, or exhaust gas ducts of engines. During the last two decades, an interest on turbulent flows in such conduits has revived, probably due to their connection to technical applications such as cooling systems of nuclear reactors (e.g., safety issues due to flowinduced fatigue) and reciprocating engines (e.g., efficiency optimization through exhaust gas treatment in pulsatile turbulent flows). The present review paper, therefore, is an account on the state-of-the-art research concerning turbulent flow in curved pipes, naturally covering mostly experimental work, while also analytical and numerical works are reviewed. This paper starts with a historical review on pipe flows in general and specifically on flows through curved conduits. In particular, research dealing with the effect of curvature on transition to turbulence, work dealing with pressure losses in curved pipes, as well as turbulence statistics are summarized. The swirl-switching phenomenon, a specific structural phenomenon occurring in turbulent curved pipe flows, which has interesting fundamental as well as practical implications, is reviewed. Additional complications, with respect to flow through bends, namely, entering swirling flow and pulsating flow, are reviewed as well. This review closes with a summary on the main literature body as well as an outlook on future work that should be performed in order to tackle open questions remaining in the field.
