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At least 109 records · Page 6

A weakly nonlinear theory based explanation for wave interactions in rotating channel flow

A weakly nonlinear wave-interaction theory is used to explain the decay of linearly unstable oblique waves in rotating channel flow at low Reynolds number. At the low Reynolds number studied, the waves tend to stabilize each other and therefore when no waves are preferentially excited, the linearly most unstable mode reaches a nonlinear amplitude first and causes the stabilization of all competing modes.

Singer, Bart A.↗

Modeling the dissipation rate in rotating turbulent flows

A variety of modifications to the modeled dissipation rate transport equation that have been proposed during the past two decades to account for rotational strains are examined. The models are subjected to two crucial test cases: the decay of isotropic turbulence in a rotating frame and homogeneous shear flow in a rotating frame. It is demonstrated that these modifications do not yield substantially improved predictions for these two test cases and in many instances give rise to unphysical behavior. An alternative proposal, based on the use of the tensor dissipation rate, is made for the development of improved models.

Speziale, Charles G.↗

Modeling the dissipation rate in rotating turbulent flows

A variety of modifications to the modeled dissipation rate transport equation that have been proposed during the past two decades to account for rotational strains are examined. The models are subjected to two crucial test cases: the decay of isotropic turbulence in a rotating frame and homogeneous shear flow in a rotating frame. It is demonstrated that these modifications do not yield substantially improved predictions for these two test cases and in many instances give rise to unphysical behavior. An alternative proposal, based on the use of the tensor dissipation rate, is made for the development of improved models.

Speziale, Charles G.↗

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

Hall, Philip↗

PLIF Temperature and Velocity Distributions in Laminar Hypersonic Flat-plate Flow

Rotational temperature and velocity distributions have been measured across a hypersonic laminar flat-plate boundary layer, using planar laser-induced fluorescence. The measurements are compared to a finite-volume computation and a first-order boundary layer computation, assuming local similarity. Both computations produced similar temperature distributions and nearly identical velocity distributions. The disagreement between calculations is ascribed to the similarity solution not accounting for leading-edge displacement effects. The velocity measurements agreed to within the measurement uncertainty of 2 % with both calculated distributions. The peak measured temperature was 200 K lower than the computed values. This discrepancy is tentatively ascribed to vibrational relaxation in the boundary layer.

OByrne, S.↗

Secondary instability in rotating-disk flow

Primary instability of the 3D boundary layer on a rotating disk introduces periodic modulation of the mean flow in the form of stationary crossflow vortices. We study the stability of this modulated mean flow with respect to secondary disturbances. Both fundamental and subharmonic resonance cases are considered, and their corresponding results indicate that the growth rate and the frequency of the secondary instability are insensitive to the exact nature of the resonance condition. The threshold primary stationary crossflow vortex amplitude for secondary instability found in this 3D incompressible boundary layer is significantly larger than that for a 2D boundary layer which is subjected to Tollmien-Schlichting instability. The secondary instability results in a pair of travelling counter-rotating vortices, tilted up and oriented at an angle to the primary stationary crossflow vortices.

Balachandar, S.↗

The analysis sensitivity to tropical winds from the Global Weather Experiment

The global scale divergent and rotational flow components of the Global Weather Experiment (GWE) are diagnosed from three different analyses of the data. The rotational flow shows closer agreement between the analyses than does the divergent flow. Although the major outflow and inflow centers are similarly placed in all analyses, the global kinetic energy of the divergent wind varies by about a factor of 2 between different analyses while the global kinetic energy of the rotational wind varies by only about 10 percent between the analyses. A series of real data assimilation experiments has been performed with the GLA general circulation model using different amounts of tropical wind data during the First Special Observing Period of the Global Weather Experiment. In exeriment 1, all available tropical wind data were used; in the second experiment, tropical wind data were suppressed; while, in the third and fourth experiments, only tropical wind data with westerly and easterly components, respectively, were assimilated. The rotational wind appears to be more sensitive to the presence or absence of tropical wind data than the divergent wind. It appears that the model, given only extratropical observations, generates excessively strong upper tropospheric westerlies. These biases are sufficiently pronounced to amplify the globally integrated rotational flow kinetic energy by about 10 percent and the global divergent flow kinetic energy by about a factor of 2. Including only easterly wind data in the tropics is more effective in controlling the model error than including only westerly wind data. This conclusion is especially noteworthy because approximately twice as many upper tropospheric westerly winds were available in these cases as easterly winds.

Paegle, J.↗

Viscous flows in rotating pipes with internal cavities and related vortex breakdowns

The problem of predicting vortex breakdown, which is characterized by a drastic change in core size and trajectory, is still basically unsolved. In the present paper, viscous flow in a long rotating pipe is analyzed, as a model for the type of breakdown observed in wake vortices. The full Navier-Stokes equations are shown to simplify to a set of unlinked partial differential equations. These equations allow for two separate solutions, for both full pipe flows (the classic rotating Hagen-Poiseuille flow) and cavity flows, in which a central area, with no net mass flux or viscous dissipation, is produced. Conditions permitting switching from one type of flow to the other, with no change in the mass flux or velocities at the pipe surface, are found. It is then argued that these conditions indicate when vortex breakdown will occur.

Weihs, D.↗

Nonlinear interactions between convection, rotation and flows with vertical shear

The effects of a mean flow with vertical shear on the convective motions in a rotating layer are examined using a three-dimensional and time-dependent numerical model. In the absence of rotation, the convective motions are shown to be dominated by the shear flow when the Richardson number becomes greater than about -1.0. Both heat and momentum are carried down their respective gradients. For rotating cases with vertical rotation vectors, the Coriolis force turns the flow induced by the convection to produce a more complicated shear that changes direction with height. For rotating cases with tilted rotation vectors, the results depend on the direction of the shear. When the imposed flow is in the opposite direction, the convection motions are less energetic and are even suppressed entirely when the shear is strong. When the imposed flow is in the same direction, as that produced by the rotation, the convective motions are enhanced and a countergradient flux of momentum can be produced.

Hathaway, D. H.↗

Study Of Disturbances In Rotating Plane Poisseuille Flow

Report describes computer-simulation of instability and transition to turbulence in plane Poisseuille flow in rotating channel. Motions of fluid governed by Navier-Stokes equations of incompressible flow, using periodic boundary conditions in streamwise and spanwise directions. Principal parameters affecting flow are Reynolds and rotation numbers.

Kim, John↗

Secondary instability in rotating disk flow

Primary instability of the three-dimensional boundary layer on a rotating disk introduces periodic modulation of the mean flow in the form of cross-flow vortices. The stability of this modulated base flow to secondary disturbances is studied. In a three-dimensional boundary layer the threshold primary amplitude for secondary instability is larger than that for a two-dimensional boundary layer. The secondary instability results in a pair of traveling counter-rotating vortices, tilted up and oriented at an angle to the primary cross-flow vortices.

Balachandar, S.↗

The role of zonally asymmetric heating in the vertical and temporal structure of the global scale flow fields during FGGE SOP-1

By examining the vertical structure of the low order spherical harmonics of the divergence and vorticity fields, the relative contribution of tropical and monsoonal circulations upon the global wind fields was estimated. This indicates that the overall flow over North America and the Pacific between January and February is quite distinct both in the lower and upper troposphere. In these longitudes there is a stronger tropical overturning and subtropical jet stream in January than February. The divergent flow reversed between 850 and 200 mb. Poleward rotational flow at upper levels is associated with an equatorward rotational flow at low levels. This suggests that the monsoon and other tropical circulations project more amplitude upon low order (global scale) representations of the flow than do the typical midlatitude circulations and that their structures show conspicuous changes on a time scale of a week or less.

Paegle, J.↗

A note on secondary flow in rotating radial channels

A general vector differential equation for the vorticity component parallel to a streamline is derived for steady, nonviscous, and incompressible flow in a rotating system. This equation is then simplified by restricting it to rotating radial channels and by making further simplifying assumptions. The simplified equation is used to solve for the secondary vorticity, the vorticity component parallel to the streamline, in three special cases involving different streamtube geometries; the results are presented in a series of figures. The secondary vorticity is shown to decrease with decreased absolute angular velocity of the fluid, decreased inlet total-pressure gradient, decreased length of relative flow path, and increased relative velocity.

Kramer, James J↗

Identification of complex flows in Taylor-Couette counter-rotating cavities

The transition in confined rotating flows is a topical problem with many industrial and fundamental applications. The purpose of this study is to investigate the Taylor-Couette flow in a finite-length cavity with counter-rotating walls, for two aspect ratios L=5 or L=6. Two complex regimes of wavy vortex and spirals are emphasized for the first time via direct numerical simulation, by using a three-dimensional spectral method. The spatio-temporal behavior of the solutions is analyzed and compared to the few data actually available. c2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.

Non-NASA Center↗

Monte Carlo calculations of diatomic molecule gas flows including rotational mode excitation

The direct simulation Monte Carlo method was used to solve the Boltzmann equation for flows of an internally excited nonequilibrium gas, namely, of rotationally excited homonuclear diatomic nitrogen. The semi-classical transition probability model of Itikawa was investigated for its ability to simulate flow fields far from equilibrium. The behavior of diatomic nitrogen was examined for several different nonequilibrium initial states that are subjected to uniform mean flow without boundary interactions. A sample of 1000 model molecules was observed as the gas relaxed to a steady state starting from three specified initial states. The initial states considered are: (1) complete equilibrium, (2) nonequilibrium, equipartition (all rotational energy states are assigned the mean energy level obtained at equilibrium with a Boltzmann distribution at the translational temperature), and (3) nonequipartition (the mean rotational energy is different from the equilibrium mean value with respect to the translational energy states). In all cases investigated the present model satisfactorily simulated the principal features of the relaxation effects in nonequilibrium flow of diatomic molecules.

Yoshikawa, K. K.↗