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Skin-friction measurements in incompressible flow

Description: Report presenting experiments conducted to measure in incompressible flow the local surface-shear stress and average skin-friction coefficient for a turbulent boundary layer on a smooth, flat plate with zero pressure gradient. Local velocity measurements and local surface-shear measurements were taken and a sensitive manometer was used.
Date: March 1958
Creator: Smith, Donald W. & Walker, John H.
Partner: UNT Libraries Government Documents Department

A General Integral Form of the Boundary-Layer Equation for Incompressible Flow With an Application to the Calculation of the Separation Point of Turbulent Boundary Layers

Description: Note presenting a general integral form of the boundary-layer equation that is derived from the Prandtl partial-differential boundary-layer equation. The general integral equation, valid for either laminar or turbulent incompressible boundary-layer flow, contains the Von Karman momentum equation, the kinetic-energy equation, and the Loitsianskii equation as special cases.
Date: August 1950
Creator: Tetervin, Neal & Lin, Chia Chiao
Partner: UNT Libraries Government Documents Department

Method of estimating the incompressible-flow pressure distribution of compressor blade sections at design angle of attack

Description: A method was devised for estimating the incompressible-flow pressure distribution over compressor blade sections at design angle of attack. The theoretical incremental velocities due to camber and thickness of the section as an isolated airfoil are assumed proportional to the average passage velocity and are modified by empirically determined interference factors. Comparisons were made between estimated and test pressure distributions of NACA 65-series sections for typical conditions. Good agreement was obtained.
Date: December 9, 1953
Creator: Erwin, John R. & Yacobi, Laura A.
Partner: UNT Libraries Government Documents Department

Inf-sup estimates for the Stokes problem in a periodic channel

Description: We derive estimates of the Babuska-Brezzi inf-sup constant {beta} for two-dimensional incompressible flow in a periodic channel with one flat boundary and the other given by a periodic, Lipschitz continuous function h. If h is a constant function (so the domain is rectangular), we show that periodicity in one direction but not the other leads to an interesting connection between {beta} and the unitary operator mapping the Fourier sine coefficients of a function to its Fourier cosine coefficients. We exploit this connection to determine the dependence of {beta} on the aspect ratio of the rectangle. We then show how to transfer this result to the case that h is C{sup 1,1} or even C{sup 0,1} by a change of variables. We avoid non-constructive theorems of functional analysis in order to explicitly exhibit the dependence of {beta} on features of the geometry such as the aspect ratio, the maximum slope, and the minimum gap thickness (if h passes near the substrate). We give an example to show that our estimates are optimal in their dependence on the minimum gap thickness in the C{sup 1,1} case, and nearly optimal in the Lipschitz case.
Date: December 10, 2008
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

Inf-sup estimates for the Stokes problem in a periodic channel

Description: We derive estimates of the Babuska-Brezzi inf-sup constant {beta} for two-dimensional incompressible flow in a periodic channel with one flat boundary and the other given by a periodic, Lipschitz continuous function h. If h is a constant function (so the domain is rectangular), we show that periodicity in one direction but not the other leads to an interesting connection between {beta} and the unitary operator mapping the Fourier sine coefficients of a function to its Fourier cosine coefficients. We exploit this connection to determine the dependence of {beta} on the aspect ratio of the rectangle. We then show how to transfer this result to the case that h is C{sup 1,1} or even C{sup 0,1} by a change of variables. We avoid non-constructive theorems of functional analysis in order to explicitly exhibit the dependence of {beta} on features of the geometry such as the aspect ratio, the maximum slope, and the minimum gap thickness (if h passes near the substrate). We give an example to show that our estimates are optimal in their dependence on the minimum gap thickness in the C{sup 1,1} case, and nearly optimal in the Lipschitz case.
Date: June 27, 2007
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department

Multi-material incompressible flow simulation using the moment-of-fluid method

Description: The Moment-of-Fluid interface reconstruction technique is implemented in a second order accurate, unstructured finite element variable density incompressible Navier-Stokes solver. For flows with multiple materials, MOF significantly outperforms existing first and second order interface reconstruction techniques. For two material flows, the performance of MOF is similar to other interface reconstruction techniques. For strongly driven bouyant flows, the errors in the flow solution dominate and all the interface reconstruction techniques perform similarly.
Date: January 1, 2009
Creator: Garimella, R V; Schofield, S P; Lowrie, R B; Swartz, B K; Christon, M A & Dyadechko, V
Partner: UNT Libraries Government Documents Department

An Imcompressible Rayleigh-Taylor Problem in KULL

Description: The goal of the EZturb mix model in KULL is to predict the turbulent mixing process as it evolves from Rayleigh-Taylor, Richtmyer-Meshkov, or Kelvin-Helmholtz instabilities. In this report we focus on a simple example of the Rayleigh-Taylor instability (which occurs when a heavy fluid lies above a light fluid, and we perturb the interface separating them). It is well known that the late time asymptotic, fully self-similar form for the growth of the mixing zone scales quadratically with time.
Date: September 22, 2005
Creator: Ulitsky, M
Partner: UNT Libraries Government Documents Department

A Cell-Centered Adaptive Projection Method for the IncompressibleNavier-Stokes Equations in Three Dimensions

Description: We present a method for computing incompressible viscousflows in three dimensions using block-structured local refinement in bothspace and time. This method uses a projection formulation based on acell-centered approximate projection, combined with the systematic use ofmultilevel elliptic solvers to compute increments in the solutiongenerated at boundaries between refinement levels due to refinement intime. We use an L_0-stable second-order semi-implicit scheme to evaluatethe viscous terms. Results are presentedto demonstrate the accuracy andeffectiveness of this approach.
Date: September 25, 2007
Creator: Martin, D.F.; Colella, P. & Graves, D.T.
Partner: UNT Libraries Government Documents Department

An Incompressible Navier-Stokes with Particles Algorithm andParallel Implementation

Description: We present a variation of an adaptive projection method forcomputing solutions to the incompressible Navier-Stokes equations withsuspended particles. To compute the divergence-free component of themomentum forcing due to the particle drag, we employ an approach whichexploits the locality and smoothness of the Laplacian of the projectionoperator applied to the discretized particle drag force. We presentconvergence and performance results to demonstrate the effectiveness ofthis approach.
Date: November 28, 2006
Creator: Martin, Daniel F.; Colella, Phillip & Keen, Noel D.
Partner: UNT Libraries Government Documents Department

Tera-scalable Algorithms for Variable-Density Elliptic Hydrodynamics with Spectral Accuracy

Description: A hybrid spectral/compact solver for variable-density viscous incompressible flow is described. Parallelization strategies for the FFTs and band-diagonal matrices are discussed and compared. Transpose methods are found to be highly competitive with direct block parallel methods when the problem is scaled to tens of thousands of processors. Various mapping strategies for the IBM BlueGene/L torus configuration of processors are explored. By optimizing the communication, we have achieved virtually perfect scaling to 32768 nodes. Furthermore, communication rates come very close to the theoretical peak speed of the BlueGene/L network with sustained computation in the TeraFLOPS range.
Date: April 13, 2005
Creator: Cook, A W; Cabot, W H; Welcome, M L; Williams, P L; Miller, B J; de Supinski, B R et al.
Partner: UNT Libraries Government Documents Department

Crenulative Turbulence in a Converging Nonhomogeneous Material

Description: Crenulative turbulence is a nonlinear extension of the Bell-Plesset instability, usually observed in a converging system in which there is a nonhomogeneous response of stress to strain and/or strain rate. In general, crenelation occurs in any circumstance in which the mean flow streamlines converge the material more strongly than the compressibility can accommodate. Elements of the material slip past each other, resulting in local fluctuations in velocity from that of the mean flow, producing a type of turbulence that is more kinematic than inertial. For a homogeneous material, crenelation occurs at the atomic or molecular scale. With nonhomogeneous stress response at larger scales, the crenulative process can also occur at those larger scales. The results are manifested by a decrease in the rate of dissipation to heat, and by the configurationally-irreversible mixing of nonhomogeneities across any mean-flow-transported interface. We obtain a mathematical description of the crenulative process by means of Reynolds decomposition of the appropriate variables, and the derivation of transport equations for the second-order moments that arise in the mean-flow momentum and energy equations. The theory is illustrated by application to the spherical convergence of an incompressible fluid with nonhomogeneous distribution of kinematic viscosity.
Date: January 1, 1999
Creator: Romero, C.A.
Partner: UNT Libraries Government Documents Department

2D Numerical Simulation of the Resistive Reconnection Layer

Description: In this paper we present a two-dimensional numerical simulation of a reconnection current layer in incompressible resistive magnetohydrodynamics with uniform resistivity in the limit of very large Lundquist numbers. We use realistic boundary conditions derived consistently from the outside magnetic field, and we also take into account the effect of the back pressure from flow into the separatrix region. We find that within a few Alfvén times the system reaches a steady state consistent with the Sweet-Parker model, even if the initial state is Petschek-like.
Date: March 1, 1999
Creator: Kulsrud, R. M. & Uzdensky, D. A.
Partner: UNT Libraries Government Documents Department

An adaptive level set approach for incompressible two-phase flows

Description: In Sussman, Smereka and Osher, a numerical method using the level set approach was formulated for solving incompressible two-phase flow with surface tension. In the level set approach, the interface is represented as the zero level set of a smooth function; this has the effect of replacing the advection of density, which has steep gradients at the interface, with the advection of the level set function, which is smooth. In addition, the interface can merge or break up with no special treatment. The authors maintain the level set function as the signed distance from the interface in order to robustly compute flows with high density ratios and stiff surface tension effects. In this work, they couple the level set scheme to an adaptive projection method for the incompressible Navier-Stokes equations, in order to achieve higher resolution of the interface with a minimum of additional expense. They present two-dimensional axisymmetric and fully three-dimensional results of air bubble and water drop computations.
Date: April 1, 1997
Creator: Sussman, M.; Almgren, A. S. & Bell, J. B.
Partner: UNT Libraries Government Documents Department

A general closure relation for incompressible mixing layers induced by interface instabilities

Description: The authors describe a generalization of a recently-proposed two-phase flow model for the statistical evolution of an incompressible mixing layer. This model, which was originally developed for application to Rayleigh-Taylor mixing, predicts the distribution of volume fractions and fluid velocities across the mixing layer in terms of the trajectories of the edges. The previous analysis of this model is extended to flows that are not self-similar.
Date: October 1, 1997
Creator: Glimm, J.; Saltz, D. & Sharp, D.H.
Partner: UNT Libraries Government Documents Department

PDM performance Test Results and Preliminary Analysis: Incompressible and Compressible Fluids

Description: Three, small diameter, Moineau, positive displacement (drilling) motors (PDMs) were dynamometer tested using water, air-water mist, air-water foam, and aerated water. The motors included (1) a 1.5-inch OD, single-lobe mud motor; (2) a 1.69-inch OD, 5:6 multi-lobe mud motor; and (3) a 1.75-inch OD, 5:6 multi-lobe air motor. This paper describes the test apparatus, procedures, data analysis, and results. Incompressible and compressible fluid performance are compared; linear performance, predicted by a positive displacement motor model, is identified where it occurs. Preliminary results and conclusions are (1) the performance of all three motors is accurately modeled using a two-variable, linear model for incompressible fluid and (2) the model was not successfully adapted to model compressible fluid performance.
Date: February 1, 1999
Creator: Dreesen, D.S.; Gruenhagan, E.; Cohen, J.C. & Moran, D.W.
Partner: UNT Libraries Government Documents Department

Dynamical modeling of surface tension

Description: In a recent review it is said that free-surface flows ``represent some of the difficult remaining challenges in computational fluid dynamics``. There has been progress with the development of new approaches to treating interfaces, such as the level-set method and the improvement of older methods such as the VOF method. A common theme of many of the new developments has been the regularization of discontinuities at the interface. One example of this approach is the continuum surface force (CSF) formulation for surface tension, which replaces the surface stress given by Laplace`s equation by an equivalent volume force. Here, we describe how CSF might be made more useful. Specifically, we consider a derivation of the CSF equations from a minimization of surface energy as outlined by Jacqmin. This reformulation suggests that if one eliminates the computation of curvature in terms of a unit normal vector, parasitic currents may be eliminated For this reformulation to work, it is necessary that transition region thickness be controlled. Various means for this, in addition to the one discussed by Jacqmin are discussed.
Date: August 1, 1996
Creator: Brackbill, J.U. & Kothe, D.B.
Partner: UNT Libraries Government Documents Department

High-performance spectral element algorithms and implementations.

Description: We describe the development and implementation of a spectral element code for multimillion gridpoint simulations of incompressible flows in general two- and three-dimensional domains. Parallel performance is present on up to 2048 nodes of the Intel ASCI-Red machine at Sandia.
Date: August 28, 1999
Creator: Fischer, P. F. & Tufo, H. M.
Partner: UNT Libraries Government Documents Department

Newton-Krylov-Schwarz methods for aerodynamics problems : compressible and incompressible flows on unstructured grids.

Description: We review and extend to the compressible regime an earlier parallelization of an implicit incompressible unstructured Euler code [9], and solve for flow over an M6 wing in subsonic, transonic, and supersonic regimes. While the parallelization philosophy of the compressible case is identical to the incompressible, we focus here on the nonlinear and linear convergence rates, which vary in different physical regimes, and on comparing the performance of currently important computational platforms. Multiple-scale problems should be marched out at desired accuracy limits, and not held hostage to often more stringent explicit stability limits. In the context of inviscid aerodynamics, this means evolving transient computations on the scale of the convective transit time, rather than the acoustic transit time, or solving steady-state problems with local CFL numbers approaching infinity. Whether time-accurate or steady, we employ Newton's method on each (pseudo-) timestep. The coupling of analysis with design in aerodynamic practice is another motivation for implicitness. Design processes that make use of sensitivity derivatives and the Hessian matrix require operations with the Jacobian matrix of the state constraints (i.e., of the governing PDE system); if the Jacobian is available for design, it may be employed with advantage in a nonlinearly implicit analysis, as well.
Date: February 24, 1999
Creator: Kaushik, D. K.; Keyes, D. E. & Smith, B. F.
Partner: UNT Libraries Government Documents Department

Compressible turbulence transport equations for generalized second order closure

Description: Progress on the theory of second order closure in turbulence models of various types requires knowledge of the transport equations for various turbulence correlations. This report documents a procedure that provides such equations for a wide variety of turbulence averages for compressible flows of a multicomponent fluid. Generalizing some work by Germano for incompressible flows, we introduce an appropriate extension of his generalized second order correlations and use a generalized mass-weighted averaging procedure to derive transport equations for the correlations. The averaging procedure includes all of the commonly used averages as special cases. The resulting equations provide an internally consistent starting point for future work in developing single-point statistical turbulence transport models for fluid flows. The form invariance of the in-compressible equations also holds for the compressible case, and we discuss some of the closure issues and frequently ignored complications of statistical turbulence models of compressible flows.
Date: May 1999
Creator: Cloutman, Lawrence D.
Partner: UNT Libraries Government Documents Department

An Experimental Study of the Turbulent Development of Rayleigh-Taylor and Richtmyer-Meshkov Instabilities

Description: The objective of this three-year research program is to study the development of turbulence in Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities. Incompressible RT and RM instabilities are studied in an apparatus in which a box containing two unequal density liquids is accelerated on a linear rail system either impulsively (by bouncing it off of a spring) to produce RM instability, or at a constant downward rate (using a weight and pulley system) to produce RT instability. These experiments are distinguished from others in the field in that they are initialized with well defined, measurable initial perturbations and are well visualized utilizing planar laser induced fluorescence imaging. New experiments are proposed aimed at generating fully turbulent RM and RT instabilities and quantifying the turbulent development once fully turbulent flows are achieved. The proposed experiments focus on the development and the subsequent application of techniques to accelerate the production of fully turbulent instabilities and the quantification of the turbulent instabilities once they are achieved. The proposed tasks include: the development of RM and RT experiments utilizing fluid combinations having larger density ratios than those previously used; the development of RM experiments with larger acceleration impulse than that previously used; and the investigation of the multi-mode and three-dimensional instabilities by the development of new techniques for generating short wavelength initial perturbations. Progress towards fulfilling these goals is currently well on track. Recent results have been obtained on experiments that utilize Faraday resonance for the production of a nearly single-mode three-dimensional perturbation with a short enough wavelength to yield a self-similar instability at late-times. Last year we reported that we can reliably generate Faraday internal waves on the interface in our experimental apparatus by oscillating the tank containing the two fluids in the vertical direction at the proper frequency. This past year we have ...
Date: October 30, 2006
Creator: Jacobs, Jeffrey, W.
Partner: UNT Libraries Government Documents Department