Numerical Computation of Flow in Rotating Ducts
01 Mar 1977-Journal of Fluids Engineering-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 99, Iss: 1, pp 148-153
TL;DR: In this article, a finite-difference procedure is employed to predict the turbulent flaw in ducts of rectangular cross-section, rotating about an axis normal to the longitudinal direction, and the turbulence model involved the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate.
Abstract: A finite-difference procedure is employed to predict the turbulent flaw in ducts of rectangular cross-section, rotating about an axis normal to the longitudinal direction. The flows were treated as “parabolic”; and the turbulence model used involved the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. Agreement with experimental data is good for a constant-area duct at low rotation, but less satisfactory for a divergent duct at larger rotation. It is argued that a “partially-parabolic” procedure will be needed to predict the latter flow correctly.
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TL;DR: In this paper, a numerical study of the laminar flow of an incompressible viscous fluid in rotating ducts of rectangular cross-section is conducted, where the full time-dependent nonlinear equations of motion are solved by finite-difference techniques for moderate to relatively rapid rotation rates where both the convective and viscous terms play an important role.
Abstract: A numerical study of the laminar flow of an incompressible viscous fluid in rotating ducts of rectangular cross-section is conducted. The full time-dependent nonlinear equations of motion are solved by finite-difference techniques for moderate to relatively rapid rotation rates where both the convective and viscous terms play an important role. At weak to moderate rotation rates, a double-vortex secondary flow appears in the transverse planes of the duct whose structure is relatively independent of the aspect ratio of the duct. For Rossby numbers Ro c 100 this secondary flow is shown to lead to substantial distortions of the axial velocity profiles. For more rapid rotations (Ro c l), the Secondary flow (in a duct with an aspect ratio of two) is shown to split into an asymmetric configuration of four counter-rotating vortices similar to that which appears in curved ducts. It is demonstrated mathematically that this effect could result from a disparity in the symmetry of the convective and Coriolis terms in the equations of motion. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration and the axial velocity wumes a Taylor-Proudman configuration in the interior of the duct. Comparisons with existing experimental results are quite favourable.
89 citations
78 citations
TL;DR: In this article, the effect of an arbitrary change of frame on the structure of turbulence models is examined from a theoretical standpoint and it is proven that turbulence models must be form invariant under arbitrary translational accelerations of the reference frame and should only be affected by rotations through the intrinsic mean vorticity.
Abstract: The effect of an arbitrary change of frame on the structure of turbulence models is examined from a theoretical standpoint It is proven, as a rigorous consequence of the Navier-Stokes equations, that turbulence models must be form invariant under arbitrary translational accelerations of the reference frame and should only be affected by rotations through the intrinsic mean vorticity A direct application of this invariance property along with the Taylor-Proudman theorem, material frame-indifference in the limit of two-dimensional turbulence, and Rapid Distortion Theory is shown to yield powerful constraints on the allowable form of turbulence models Most of the commonly used turbulence models are demonstrated to be in violation of these constraints and consequently are inconsistent with the Navier-Stokes equations in noninertial frames Alternative models with improved noninertial properties are developed and some simple applications to rotating turbulent flows are considered
73 citations
TL;DR: In this article, the authors review current capabilities for predicting flow in the cooling passages and cavities of jet engines and show that progress is being made, particularly in respect to the flow in serpentine blade-cooling passages.
71 citations
TL;DR: In this paper, the analysis and modelling of the structure of turbulent flow in a circular pipe subjected to an axial rotation is presented, with particular attention 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 rotatedally dependent mean azimuthal or swirl velocity relative to the rotating pipe.
Abstract: 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 rotationally dependent mean azimuthal or swirl velocity relative to the rotating pipe. It is shown that the first feature is well represented by two-dimensional explicit algebraic stress models but is irreproducible by traditional two-equation models. On the other hand, three-dimensional frame-dependent models are needed to predict the presence of a mean swirl velocity. The latter is argued to be a secondary effect which arises from a cubic nonlinearity in standard algebraic models with conventional near-wall treatments. Second-order closures are shown to give a more complete description of this flow and can describe both of these features fairly well. In this regard, quadratic pressure–strain models perform the best overall when extensive comparisons are made with the results of physical and numerical experiments. The physical significance of this problem and the implications for future research in turbulence are discussed in detail.
64 citations
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TL;DR: In this paper, the authors present a review of the applicability and applicability of numerical predictions of turbulent flow, and advocate that computational economy, range of applicability, and physical realism are best served by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy k and its dissipation rate ϵ, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour.
11,866 citations
TL;DR: In this article, a general, numerical, marching procedure is presented for the calculation of the transport processes in three-dimensional flows characterised by the presence of one coordinate in which physical influences are exerted in only one direction.
5,946 citations
TL;DR: In this article, experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described, and three stability related phenomena are observed or inferred: (1) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (2) the total suppression of transition to turbulence in a stabilized layer; (3) the development of large-scale roll cells on the destabilized side of the channel by growth of a Taylor-Gortler vortex instability.
Abstract: Experiments on fully developed turbulent flow in a channel which is rotating at a steady rate about a spanwise axis are described. The Coriolis force components in the region of two-dimensional mean flow affect both local and global stability. Three stability-related phenomena were observed or inferred: (1) the reduction (increase) of the rate of wall-layer streak bursting in locally stabilized (destabilized) wall layers; (2) the total suppression of transition to turbulence in a stabilized layer; (3) the development of large-scale roll cells on the destabilized side of the channel by growth of a Taylor-Gortler vortex instability. Local effects of rotational stabilization, such as reduction of the turbulent stress in wall layers, can be related to the local Richardson number in a simple way. This paper not only investigates this effect, but also, by methods of flow visualization, exposes some of the underlying structure changes caused by rotation.-
487 citations
01 Jan 1961
TL;DR: In this paper, ausgebildeten turbulenten Flussigkeitsstromung vortragen will, ist, wie ich gleich sagen mochte, noch weit davon entfernt, etwas Abgeschlossenes darzustellen.
Abstract: M. H. Was ich Ihnen hier uber die Gesetzmasigkeiten der ausgebildeten turbulenten Flussigkeitsstromung vortragen will, ist, wie ich gleich sagen mochte, noch weit davon entfernt, etwas Abgeschlossenes darzustellen, es handelt sich vielmehr um die ersten Schritte auf einem neuen Weg, denen, wie ich hoffe, noch mancherlei Schritte folgen werden.
408 citations
TL;DR: In this paper, the authors describe the application of a recently developed numerical scheme to the computation of the flow in a curved duct, which is partially-parabolic in nature as there are significant elliptic effects, which are transmitted through the pressure field.
Abstract: The paper describes the application of a recently developed numerical scheme to the computation of the flow in a curved duct. The flow situation is partially-parabolic in nature as there are significant elliptic effects, which are transmitted through the pressure field. The turbulence model used comprises two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate. It has been observed that the predictions using the new procedure agree very satisfactorily with the experimental data. Comparisons are also made with the predictions of a fully-parabolic calculation procedure.
67 citations