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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

The dimension of attractors underlying periodic turbulent Poiseuille flow

A lower bound on the Liapunov dimenison, D-lambda, of the attractor underlying turbulent, periodic Poiseuille flow at a pressure-gradient Reynolds number of 3200 is calculated, on the basis of a coarse-grained (16x33x8) numerical solution, to be approximately 352. Comparison of Liapunov exponent spectra from this and a higher-resolution (16x33x16) simulation on the same spatial domain shows these spectra to have a universal shape when properly scaled. On the basis of these scaling properties, and a partial exponent spectrum from a still higher-resolution (32x33x32) simulation, it is argued that the actual dimension of the attractor underlying motion of the given computational domain is approximately 780. It is suggested that this periodic turbulent shear flow is deterministic chaos, and that a strange attractor does underly solutions to the Navier-Stokes equations in such flows.

Keefe, Laurence↗
NASA NTRS1989

On the secondary instability in plane Poiseuille flow

Numerical experiments were performed to clarify apparent differences between experimental observations and a theoretical prediction of the secondary instability in plane Poiseuille flow. It is shown that subharmonic breakdown is unlikely in natural transition as a result of the initial growth of what we call the 'minus' modes and consequent forcing of Orr-Sommerfeld modes present in the background noise. Subharmonic breakdown was achieved only when these minus modes were continuously suppressed.

Kim, John↗
NASA NTRS1987

Wave-growth associated with turbulent spot in plane Poiseuille flow

A kinematic wave theory is used to investigate the cause of the rapid growth of waves observed at the wingtip of turbulent spot in plane Poiseuille flow. It is found that the qualitative behavior of the wave motions is well described by Landahl's breakdown criterion as the wave selection procedure. The predicted wave number, wave angle, and phase velocity are in agreement with those values obtained in a direct simulation.

Henningson, D. S.↗
NASA NTRS1988

Migration arising from gradients in shear stress: Particle distributions in Poiseuille flow

Experimental evidence for the existence of shear induced migration processes is reviewed and the mechanism by Leighton and Acrivos (1987b) is described in detail. The proposed mechanism is shown to lead to the existence of an additional shear induced migration in the presence of gradients in shear stress such as would be found in Poiseuille flow, and which may be used to predict the amplitude of the observed short-term viscosity increase. The concentration and velocity profiles which result from such a migration are discussed in detail and are compared to the experimental observations of Karnis, Goldsmith and Mason (1966).

Leighton, D. T., Jr.↗
NASA NTRS1988

Turbulence characteristics inside a turbulent spot in plane Poiseuille flow

In wall-bounded shear flows the transition to turbulence through localized disturbances goes through a pattern starting with a development of shear layers. The localized normal velocity fluctuations induce normal vorticity through the lift-up effect. These shear layers become unstable to secondary disturbances, and if the amplitudes of the disturbances are large enough, a turbulent spot develops. Investigations of the spot in boundary layers has shown that the turbulent part of the spot is very similar to a fully developed boundary layer. Wygnanski et al. (1976) showed that the mean profile at the center-symmetry plane has a logarithmic region and Johansson et al. (1987) showed that both the higher-order statistics and flow structures in the spot were the same as in the corresponding fully developed flow. In what respects the turbulence inside the Poiseuille spot is similar to fully developed turbulent channel flow is studied. The numerically simulated spot is used, where the characteristics inside the spot are compared to those of the wave packet in the wingtip area. A recent experimental investigation of the velocity field associated with the Poiseuille spot by Klingmann et al. is used for comparison.

Henningson, D. S.↗
DOE OSTI2021

Pulsating Poiseuille flow of a cement slurry

In this paper, we investigate the pulsatile flow of a cement slurry in a pipe. The constitutive relation for the viscous stress tensor is based on the power-law model, where the shear viscosity not only depends on the shear rate but also the volume fraction of the cement particles. To solve for the volume fraction field, a convection-diffusion equation is used. The dimensionless form of the governing equations and the boundary conditions are solved numerically at different pulsatile cycles. Further, a parametric study is conducted to study the effect of different dimensionless numbers at different cycles on the velocity and the volume fraction profiles.

36 MATERIALS SCIENCE↗
NASA NTRS1990

Two-dimensional convection and radiation with scattering from a Poiseuille flow

Two-dimensional combined convection and radiation heat transfer from a gray scattering fluid in a reflecting channel is considered. The model, represented by a set of simultaneous nonlinear integro-partial differential equations, is solved numerically. The effects of aspect ratio, conduction-radiation parameter, scattering albedo, and wall emissivity, are systematically investigated. It is found that these parameters have a significant influence on the temperature field and alter the radiative and convective fluxes at the hot and cold walls. In particular, when radiation effects are considerable, the heat-transfer characteristics of the fluid at the hot and cold walls are very different.

Kassemi, M.↗
NASA NTRS1991

Numerical investigation of instability and transition in rotating plane Poiseuille flow

Direct numerical simulations with initial small-amplitude random disturbances are used to investigate instability and transition in plane Pouseuille flow with spanwise system rotation, employing a large computational domain to facilitate the selection of the dominant spanwise wavelength of the observed streamwise vortices as well as the streamwise wavelength of the dominant secondary modes due to streamwise vortices. In all cases studied, the unstable primary three-dimensional waves persist in the nonlinear stage. Where there is primary three-dimensional wave decay, the finite-amplitude streamwise vortices can become unstable to two different three-dimensional secondary instability modes, depending on the Reynolds and the rotation numbers.

Yang, Kyung-Soo↗
NASA NTRS2015

Direct Numerical Simulation of Turbulent Couette-Poiseuille Flow With Zero Skin Friction

The near-wall scaling of mean velocity U(yw) is addressed for the case of zero skin friction on one wall of a fully turbulent channel flow. The present DNS results can be added to the evidence in support of the conjecture that U is proportional to the square root of yw in the region just above the wall at which the mean shear dU=dy = 0.

Coleman, Gary N.↗
NASA NTRS1982

Thresholds for the onset of fluid and magnetofluid turbulence

Linear stability calculations conducted in plasma physics are based on the theory of hydrodynamic stability of neutral fluids. The present investigation is concerned with the validity of procedures based on linear stability analysis in six much-studied situations. All have the property that the fluid goes from laminar to turbulent at critical values of some dimensionless number, such as the Reynolds number or the Rayleigh number. The question is, at what threshold values of the dimensionless number do the unstable motions set in, and can these thresholds be predicted by a linear analysis of the stability of the laminar state as the threshold is approached from the stable side. In three cases linear stability analysis clearly seems to fail. These cases include Plane Poiseuille Flow, Plane Couette Flow, and Cylindrical Pipe Flow (Hagen-Poiseuille Flow). Situations in which predictions provided by linear stability analysis are correct are related to Rotating Couette Flow, Thermally-Driven Convection, and Instability of Laminar Boundary Layers.

Montgomery, D.↗
NASA NTRS1986

Structure parameters in rotating Couette-Poiseuille channel flow

It is well-known that a number of steady state problems in fluid mechanics involving systems of nonlinear partial differential equations can be reduced to the problem of solving a single operator equation of the form: v + lambda Av + lambda B(v) = 0, v is the summation of H, lambda is the summation of one-dimensional Euclid space, where H is an appropriate (real or complex) Hilbert space. Here lambda is a typical load parameter, e.g., the Reynolds number, A is a linear operator, and B is a quadratic operator generated by a bilinear form. In this setting many bifurcation and stability results for problems were obtained. A rotating Couette-Poiseuille channel flow was studied, and it showed that, in general, the superposition of a Poiseuille flow on a rotating Couette channel flow is destabilizing.

Knightly, George H.↗
NASA NTRS1983

Secondary instability of wall-bounded shear flows

The present analysis of a secondary instability in a wide class of wall-bounded parallel shear flows indicates that two-dimensional, finite amplitude waves are exponentially unstable to infinitessimal three-dimensional disturbances. The instability appears to be the prototype of transitional instability in such flows as Poiseuille flow, Couette flow, and flat plate boundary layers, in that it has the convective time scales observed in the typical transitions. The energetics and vorticity dynamics of the instability are discussed, and it is shown that the two-dimensional perturbation without directly providing energy to the disturbance. The three-dimensional instability requires that a threshold two-dimensional amplitude be achieved. It is found possible to identify experimental features of transitional spot structure with aspects of the nonlinear two-dimensional/linear three-dimensional instability.

Orszag, S. A.↗
NASA NTRS1985

Simplex finite element analysis of viscous incompressible flow with penalty function formulation

Viscous flow calculations are important for the determination of separated flows, recirculating flows, secondary flows and so on. This paper presents a penalty function approach for the finite element analysis of steady incompressible viscous flow. A simplex element is used with linear velocity and constant pressure in contrast to other works which usually employ higher order elements. Simplex elements yield analytical expressions for the element matrices which in turn lead to efficient solutions. Earlier works have partially indicated how constraint and lock-up problems might be avoided for simplex elements. This paper extends the earlier works by indicating the approach in detail and verifying that it is successful for several applications not discussed in the literature so far. Solution times and accuracy considerations are discussed for Couette flow, plane Poiseuille flow, a driven cavity problem, and laminar and turbulent flow over a step.

Allaire, P. E.↗
NASA NTRS2003

Measurements of Shear Lift Force on a Bubble in Channel Flow in Microgravity

Under microgravity conditions, the shear lift force acting on bubbles, droplets or solid particles in multiphase flows becomes important because under normal gravity, this hydrodynamic force is masked by buoyancy. This force plays an important role in furnishing the detachment process of bubbles in a setting where a bubble suspension is needed in microgravity. In this work, measurements of the shear lift force acting on a bubble in channel flow are performed. The shear lift force is deduced from the bubble kinematics using scaling and then compared with predictions from models in literature that address different asymptotic and numerical solutions. Basic trajectory calculations are then performed and the results are compared with experimental data of position of the bubble in the channel. A direct comparison of the lateral velocity of the bubbles is also made with the lateral velocity prediction from investigators, whose work addressed the shear lift on a sphere in different two-dimensional shear flows including Poiseuille flow.

Nahra, Henry K.↗
NASA NTRS1976

The eigenvalue spectrum of the Orr-Sommerfeld problem

A numerical investigation of the temporal eigenvalue spectrum of the ORR-Sommerfeld equation is presented. Two flow profiles are studied, the plane Poiseuille flow profile and the Blasius boundary layer (parallel): flow profile. In both cases a portion of the complex c-plane bounded by 0 less than or equal to CR sub r 1 and -1 less than or equal to ci sub i 0 is searched and the eigenvalues within it are identified. The spectra for the plane Poiseuille flow at alpha = 1.0 and R = 100, 1000, 6000, and 10000 are determined and compared with existing results where possible. The spectrum for the Blasius boundary layer flow at alpha = 0.308 and R = 998 was found to be infinite and discrete. Other spectra for the Blasius boundary layer at various Reynolds numbers seem to confirm this result. The eigenmodes belonging to these spectra were located and discussed.

Antar, B. N.↗
NASA NTRS1993

On the cross-stream spectral method for the Orr-Sommerfeld equation

Cross-stream models are defined as solutions to the Orr-Sommerfeld equation which are propagating normal to the flow direction. These models are utilized as a basis for a Hilbert space to approximate the spectrum of the Orr-Sommerfeld equation with plane Poiseuille flow. The cross-stream basis leads to a standard eigenvalue problem for the frequencies of Poiseuille flow instability waves. The coefficient matrix in the eigenvalue problem is shown to be the sum of a real matrix and a negative-imaginary diagonal matrix which represents the frequencies of the cross-stream modes. The real coefficient matrix is shown to approach a Toeplitz matrix when the row and column indices are large. The Toeplitz matrix is diagonally dominant, and the diagonal elements vary inversely in magnitude with diagonal position. The Poiseuille flow eigenvalues are shown to lie within Gersgorin disks with radii bounded by the product of the average flow speed and the axial wavenumber. It is shown that the eigenvalues approach the Gersgorin disk centers when the mode index is large, so that the method may be used to compute spectra with an essentially unlimited number of elements. When the mode index is large, the real part of the eigenvalue is the product of the axial wavenumber and the average flow speed, and the imaginary part of the eigen value is identical to the corresponding cross-stream mode frequency. The cross-stream method is numerically well-conditioned in comparison to Chebyshev based methods, providing equivalent accuracy for small mode indices and superior accuracy for large indices.

Zorumski, William E.↗