Numerical study of flow between rotating cylinders
Numerical analysis of flow between rotating cylinders
NUMERICAL ANALYSIS↗
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Turbulent Flow Between Rotating Cylinders
The turbulent air flow between rotating cylinders was investigated. The distributions of mean speed and of turbulence were measured in the gap between a rotating inner and a stationary outer cylinder. The measurements led to the conclusion that the turbulent flow in the gap cannot be considered two dimensional, but that a particular type of secondary motion takes place. It is shown that the experimentally found velocity distribution can be fully understood under the assumption that this secondary motion consists of three-dimensional ring-shape vortices. The vortices occur only in pairs, and their number and size depend on the speed of the rotating cylinder; the number was found to decrease with increasing speed. The secondary motion has an essential part in the transmission of the moment of momentum. In regions where the secondary motion is negligible, the momentum transfer follows the laws known for homologous turbulence. Ring-shape vortices are known to occur in the laminar flow between rotating cylinders, but it was hitherto unknown that they exist even at speeds that are several hundred times the critical limit.
Shih-I, Pai↗
The computation of inviscid rotational gasdynamic flows using an alternate velocity decompositon
The present investigation has the objective to present a method which can be considered to be a modification of existing potential flow algorithms. The method can be employed for the accurate and efficient solution of rotational gasdynamic flows. The general approach to computing inviscid rotational flows considered makes use of a velocity decomposition discussed by Clebsch (1859). Recent applications of the Clebsch representation in inviscid flows have involved the convection of an externally generated vorticity. Attention is given to the case of a steady, inviscid flow of a perfect gas with a uniform incoming stream. The developed procedure makes it possible to obtain a rapid solution to inviscid, compressible, rotational flows with solution algorithms which are a modification of existing potential flow codes. An application of the procedure to supersonic rotational conical flow is discussed.
Grossman, B.↗
Rotating stratified flow over finite isolated topography
Inviscid, steady, stratified rotating flow over a finite, isolated topographic feature is critically analyzed. The formulation is based on approximating the horizontal momentum by the geostrophic momentum. A boundary value problem governs the perturbation pressure field. The solution is an anticyclonic, topographically-bound vortex whose characteristics are independent of the upstream velocity but do depend on stratification, rotation, and the nature of the topography. The vortex is baroclinic in the vicinity of the mountain but barotropic in the far field. The velocity field is a combination of the bound vortex and an upstream velocity interacting with the perturbation pressure field. The effects of stratification, upstream velocity and the nature of the topography are investigated, and fluid trajectories are plotted.
Merkine, L.-O.↗
Thermal convection in a rotating shear flow
The dynamics of thermal convection in a rotating shear flow was studied using a three-dimensional time-dependent numerical model of the flow. The model assumes a sheared zonal wind in the form of an atmospheric jet stream and considers convective motions imbedded in this flow. It was found that rotation plays a vital role in the dynamics. Without rotation, the convective motions extract energy and momentum from the mean zonal flow. With rotation, the convective motions feed the energy and momentum into the mean flow. The results show how the small-scale convection might influence the large-scale dynamics of rotating stars and planets.
Hathaway, David H.↗
Flow Surfaces in Rotating Axial-flow Passages
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Stanitz, John D↗
An electron beam study of vibrational and rotational relaxing flows of nitrogen and air.
Vibrational and rotational nonequilibrium flow effects in hypersonic conical nozzle expansion of nitrogen flows and airflows
OSCILLATING FLOW↗
Instability and transition in rotating disk flow
The stability of three dimensional rotating disk flow and the effects of Coriolis forces and streamline curvature were investigated. It was shown that this analysis gives better growth rates than Orr-Sommerfeld equation. Results support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number.
Malik, M. R.↗
Instability and transition in rotating disk flow
The stability of three-dimensional rotating disk flow is investigated, including the effects of Coriolis forces and streamline curvature. The numerical results show that the critical Reynolds number for establishment of stationary vortex flow is 287. These vortices spiral outward at an angle of about 11.2 deg, and transition to turbulence occurs when their total amplification is about e to the 11th. New experimental results are also reported on the spatial growth rates of the stationary vortices. It is shown that the analysis gives growth rates that compare much better with the experimental results than do results obtained using the Orr-Sommerfeld equation. The experimental results tend to support the numerical prediction that the number of stationary vortices varies directly with the Reynolds number. The calculations also indicate the existence of weakly unstable propagating (type II) modes at low Reynolds numbers (Critical Reynolds Number being approximately equal to 49).
Malik, M. R.↗
Penalty function finite element analysis of steady viscous incompressible flow in rotating coordinates
Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuile flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimenal measurements.
Rosen, M. C.↗
Second-order closure models for rotating turbulent flows
The physical properties of the commonly used second-order closure models are examined theoretically for rotating turbulent flows. Comparisons are made with results which are a rigorous consequence of the Navier-Stokes equations for the problem of a fully-developed turbulent channel flow in a rapidly rotating framework. It is demonstrated that all existing second-order closures yield spurious physical results for this test problem of rotating channel flow. In fact, the results obtained are shown to be substantially more unphysical than those obtained from the simpler K-epsilon and K-l models. Modifications in the basic structure of these second-order closure models are proposed which can alleviate this problem.
Speziale, C. G.↗
Second-order closure models for rotating turbulent flows
The physical properties of the commonly used second-order closure models are examined theoretically for rotating turbulent flows. Comparisons are made with results which are a rigorous consequence of the Navier-Stokes equations for the problem of fully-developed turbulent channel flow in a rapidly rotating framework. It is demonstrated that all existing second-order closures yield spurious physical results for this test problem of rotating channel flow. In fact, the results obtained are shown to be substantially more unphysical than those obtained from the simpler k-epsilon and k-l models. Modifications in the basic structure of these second-order closure models are proposed which can alleviate this problem.
Speziale, Charles G.↗
Interaction of a decaying vortex ring with a rotational background flow bounded by a solid wall
The interaction between a vortex ring of finite strength and an axisymmetric rotational background flow bounded by a solid wall is studied by a singular perturbation method. The analysis is carried out by combining a composite solution of a vortex ring and an unsteady Navier-Stokes solution for the background rotational flow. Using the method of averaging, numerical scheme is developed to obtain a Navier-Stokes solution in which the grid and time-step sizes depend solely on the length and velocity scales of the background flow. Numerical results are presented to illustrate the separation of the boundary layer on a solid wall and its interaction with the vortex ring.
Ishii, K.↗
Minimization of jet and core noise by rotation of flow
Jet and core noise can be reduced and flame lengths may be significantly decreased when exhaust gases are caused to rotate or swirl about longitudinal axis of exhaust. Combustion in rotating flows is steady and quiet, and is not accompanied by pulsations or violent fluctuations.
Schwartz, I. R.↗
On the receptivity and non-parallel stability of travelling disturbances in rotating disk flow
The generation and evolution of small amplitude wavelength traveling disturbances in rotating disk flow is discussed. The steady rotational speed of the disk is perturbed so as to introduce high frequency oscillations in the flow field. Secondly, surface imperfections are introduced on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations that are solved numerically. For the class of disturbances considered (wavelength on the order of Reynolds number), it is found that eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are excited the most. The width of these roughness elements in the radial direction is about .1 r(sub 0) where r(sub 0) is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wavenumber than for a positive one. Typical wave angles found for these disturbances are about -26 degrees.
Balakumar, P.↗
Laboratory vortices in rotating, sheared flow.
By placing a small convective source (electrical heater) in a rotating, vertically sheared, stratified flow in a rotating annulus, a well-organized vortex flow is generated. A qualitative description of the flow is given. The flow is always cyclonic below the heater and anticyclonic above, and is quite persistent in the sheared flow.
Kaiser, J. A. C.↗
Axisymmetric supersonic flow in rotating impellers
General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.
Goldstein, Arthur W↗
On the receptivity and nonparallel stability of traveling disturbances in rotating-disk flow
The generation and evolution of small amplitude long wavelength traveling disturbances in rotating-disk flow are discussed. The steady rotational speed of the disk is perturbed so as to introduce high-frequency oscillations in the flow field. Secondly, surface imperfections on the disk such as roughness elements are introduced. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations which are solved numerically. It is found that, for the class of disturbances considered here (wavelength on the order of Reynolds number), eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are preferentially excited.
Balakumar, P.↗