Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q26: General Fluid Dynamics: Theory and Mathematical Methods |
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Chair: Anatoli Tumin, University of Arizona Room: Georgia World Congress Center B314 |
Tuesday, November 20, 2018 12:50PM - 1:03PM |
Q26.00001: The generic instability of relativistic fluids revisited: transverse mode fluctuations and diffussion fluxes in the Landau-Lifshitz frame Alfredo Sandoval-Villalbazo, J. Humberto Mondragón-Suárez, Alma R. Sagaceta-Mejía Stability of statistical fluctuations of relativistic fluids is a classical problem that has been addressed since the pioneering works of Hisckock and Lindblom back en 1985, who identified exponential growths of statistical fluctuations using a phenomenological approach. In the present work we critically examine the role played by the heat flux in the onset of this type of instability using the Landau-Lifschitz frame, in which the dissipative contributions to this variable are not contained in the spatial components of the energy-momentum tensor. It is shown that the generic instabilities in the transverse mode are eliminated if the corresponding constitutive equations are established within a first order in the gradients approximation kinetic theory formalism, and that purely relativistic dissipative contributions to the diffusive fluxes arise the aforementioned frame. |
Tuesday, November 20, 2018 1:03PM - 1:16PM |
Q26.00002: Solution of Basic Flows Using a Second Order Theory of Fluids Samuel Paolucci The Navier-Stokes-Fourier (NSF) equations have proved very valuable in modeling fluid flows over the last two centuries. However, there are cases in which large variations in velocity and/or thermal fields occur where it has been shown that they do not provide accurate results. Using continuum mechanics principles, second order equations were derived and shown to reproduce experimental results of the shock structure of gases over a large range of Mach numbers (Paolucci & Paolucci JFM, 486, 686-710 (2018)). Computer experiments using the direct simulation Monte Carlo (DSMC) method have shown that at small Knudsen number the pressure and temperature profiles in force-driven compressible plane Poiseuille flow exhibits different qualitative behavior from the profiles obtained by NSF equations. We compare the DSMC measurements with numerical solutions of equations resulting from the second order theory. We find that the second order equations predict the bimodal temperature profile and recover many of the other anomalous features (e.g., non-constant pressure and non-zero parallel heat flux). Comparisons of the predictions coming from the second order theory are provided in order to critically assess its validity and usefulness. |
Tuesday, November 20, 2018 1:16PM - 1:29PM |
Q26.00003: Impulse and material symmetry Harmeet Singh, James Hanna The balance of material momentum, also known as impulse or pseudomomentum, arises from material (relabeling) symmetry. We will present a brief overview of the history of this balance law of continuum mechanics, and discuss it in the context of an ideal fluid. It will be shown that Kelvin’s circulation theorem, Cauchy’s invariants, Weber’s integral, and other related quantities follow from this balance law, as do correspondences between seemingly disparate concepts such as circulation and the J-integral of fracture mechanics. |
Tuesday, November 20, 2018 1:29PM - 1:42PM |
Q26.00004: Late-time evolution of Rayleigh-Taylor instability in a domain of a finite size Annie Naveh, Snezhana I. Abarzhi We develop the theoretical analysis to systematically study the late-time evolution of Rayleigh-Taylor instability in a domain of a finite size. The nonlinear dynamics of fluids with similar and contrasting densities are considered for two-dimensional flows driven by sustained acceleration. The flows are periodic in the plane normal to the direction of acceleration and have no external mass sources. Group theory analysis is applied to accurately account for the mode coupling. Asymptotic nonlinear |
Tuesday, November 20, 2018 1:42PM - 1:55PM |
Q26.00005: Analysis of dynamics, stability and flow fields’ structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method Daniil Ilyin, Yasuhide Fukumoto, William A Goddard, Snezhana Abarzhi We develop a general matrix method to analyze from a far field the dynamics of an accelerated interface between incompressible ideal fluids of different densities with interfacial mass flux and negligible stratification. We solve the linearized boundary value problem for the dynamics conserving mass, momentum and energy in the bulk and at the interface. We find a hydrodynamic instability that develops only when the acceleration magnitude exceeds a threshold. This critical threshold value depends on the magnitudes of the steady velocities of the fluids, the ratio of their densities, and the wavelength of the initial perturbation. The flow has potential velocity fields in the fluid bulk and is shear-free at the interface. The quantitative, qualitative and formal properties of the accelerated conservative dynamics depart from those of accelerated Landau-Darrieus and Rayleigh-Taylor dynamics. New diagnostic benchmarks are identified for experiments and simulations of unstable interfaces. |
Tuesday, November 20, 2018 1:55PM - 2:08PM |
Q26.00006: Multi-Scale Turbulent Prandtl Number Model Arman Mirhashemi, Joshua Szczudlak, Scott Morris This presentation will describe a theoretical model for turbulent Prandtl number based on the intermediate mixing length concept. The model requires estimates of the streamwise velocity RMS, turbulent integral scale, and the mean velocity gradient. Experimental and numerical data obtained in a hot annular nozzle facility were used to develop this model. In order to further validate this theoretical approach, the model predictions were also compared to independent experimental measurements of turbulent Prandtl number in jet flow, flat plate boundary layer, and turbulent pipe flow. |
Tuesday, November 20, 2018 2:08PM - 2:21PM |
Q26.00007: On the symmetry properties of a random passive scalar with and without boundaries, and their connection between hot and cold states Roberto Camassa, Zeliha Kilic, Richard M McLaughlin We consider the evolution of a decaying passive scalar in the presence of a gaussian white noise fluctuating linear shear flow. We focus on deterministic initial data and establish the short, intermediate, and long time symmetry properties of the evolving point wise probability measure for the random passive scalar. We identify regions outside of which the PDF skewness is sign definite for all time, while inside these regions we observe multiple sign changes corresponding to exchanges in symmetry between hot and cold leaning states. A rapidly convergent Monte-Carlo method is developed, dubbed Direct Monte-Carlo (DMC), using the available random Green’s functions which allows for the fast construction of the PDF for single point statistics. This new method demonstrates the full evolution of the PDF from short times, to its long time, limiting and collapsing universal distribution at arbitrary points in the plane. Further, this method provides a strong benchmark for full Monte-Carlo simulations (FMC) of the associated stochastic differential equation. Armed with this benchmark, we apply the FMC to a channel with a no-flux boundary condition observe a dramatically different long time state resulting from the existence of the walls. |
Tuesday, November 20, 2018 2:21PM - 2:34PM |
Q26.00008: Semi-Extrapolated Finite Difference Schemes: Stability and Accuracy Andrew Brandon, Sheila Whitman, Mikayla Feldbauer, Brendan Drachler, Carter Alexander, Lucas Wilkins Compared to analogous explicit finite difference schemes, semi-extrapolated finite difference schemes exhibit extended stability ranges. Furthermore, because semi-extrapolated schemes are explicit, they are significantly cheaper to use than their implicit counterparts. However, semi-extrapolation can have unexpected effects on accuracy and consistency. In this presentation, the concept of semi-extrapolation will be introduced and semi-extrapolated discretizations of the Advection Equation, Heat Equation, and Advection-Diffusion Equation will be discussed. Then, the semi-extrapolated schemes’ stability constraints for the Advection Equation and Heat Equation will be compared to the corresponding stability constraints of common finite difference schemes. Following this one-dimensional stability analysis will be an overview of the effects semi-extrapolation can have on consistency and accuracy. Time permitting, preliminary stability constraints for the Advection-Diffusion Equation will be presented. |
Tuesday, November 20, 2018 2:34PM - 2:47PM |
Q26.00009: Analytical and Numerical Study of a Pulsatile Flow in a Porous Tube Qianhong Wu, Bchara Sidnawi, Srihdar Santhanam Lateral leakage is encountered in many biological and chemical applications such as renal flows and filtration processes. In this paper we report a comprehensive analytical and numerical method to examine pulsatile flow in a porous-walled tube, with leakage flow rate or leakage pressure gradient prescribed. In the first scenario, analytical results have been obtained when the leakage flow rate is small as compared to the axial flow rate. Numerical simulations using ANSYS Fluent were also performed for cases where both the pulsatile Reynolds number based on the amplitude of the mean axial velocity and the leakage ratio, were varied. The results indicate that, the analytical solution for the axial velocity had an increasing deviation from the numerical results with the pulsatile Reynolds number, and the leakage ratio. Interestingly, the analytical radial velocity almost overlapped with its numerical counterpart, for all considered cases. In the second scenario where the pressure-gradient for the leakage is prescribed, an analytical solution was obtained. Importantly, it suggests the criteria, based on the wall permeability, for the application of the analytical method developed herein. |
Tuesday, November 20, 2018 2:47PM - 3:00PM |
Q26.00010: Inviscid and viscous interaction of a line or a circular vortex filament with a solid sphere Devanayagam Palaniappan Inviscid and viscous fluid flows induced by a line vortex or a circular vortex ring in the presence of a solid sphere of radius $a$ are studied. Euler equations are used for the inviscid fluid flow model while equations of low-Reynolds number flow (Stokes flow) are employed for the viscous fluid model. The velocity potential formulation yields exact solution for the line vortex-sphere non-viscous interaction problem. Our analytic solution reveals extreme values for the radial and axial velocities indicating a strong interaction. An expression for the force on the sphere is calculated in an integral form containing a logarithmic term. The force is higher when the line vortex is closer to the sphere and is weaker when it is placed farther. Analytic solution for the corresponding viscous problem is found using a general solution representation. It is observed that the interaction in the viscous case is weaker. Closed form solutions for the axisymmetric vortex ring-sphere problem are also determined using stream function methods. The radius and location parameters have significant impact on the interaction in all cases. Our results form a basis for the investigation of the motion of vortex lines and rings in the vicinity of a spherical boundary. |
Tuesday, November 20, 2018 3:00PM - 3:13PM |
Q26.00011: Conformal Mapping to Calculate Force Induced by Attached Potential Flow around Arbitrary Unsteady Simply Connected Planar Regions Stephen Mackes, John Mansfield A current topic of interest in naval hydrodynamics is maneuvering and control of non-axisymmetric underwater vehicles; i.e. the forces and moments acting on submerged vehicles with hulls that are not bodies of revolution. One approach is conformal mapping from the flow past a cylinder, which constitutes mapping from an axisymmetric case. This approach takes cross sections of the hull and finds complex maps from the unit circle to the hull contour that are conformal outside the hull. The force on the hull can be found by integrating an unsteady version of Bernoulli’s pressure equation, which formulates the explicit dependence of the pressure on the temporal and spatial derivatives of the complex velocity potential. The force integral can be computed by Cauchy’s Integral Formula from complex analysis. The evaluation of this integral is complicated because the conformal map is kept in a general form so that the hull shape may remain unspecified. However, the integral possesses a rather beautiful derivative structure that yields a simple algebraic expression for the force due to the attached crossflow. |
Tuesday, November 20, 2018 3:13PM - 3:26PM |
Q26.00012: Analysis of Fluid-Structure Interactions using Information Theory Ben Pocock, Maurizio Porfiri, Sean D. Peterson The challenges of analyzing interactions between stochastic structures in a fluid can be ameliorated by recasting the problem as a system of information transfer. Information flow can be resolved from the time series of structure displacement or the fluid velocity, thereby circumventing the need to resolve the fluid interactions between the structures. Transfer Entropy (TE) provides a model-free method for analyzing interactions of fluid-structure interactions. The TE function is a non-symmetric measure of the reduction in uncertainty in the state of one variable due to knowledge about the state of another. Here it is employed to measure the directional Granger Causality between two structures, map the extent of fluid influenced by the structures and quantify the time lags associated with the various communication paths. The experiment consisted of a stochastically rotating cylinder, driven by a first order Markov system, with a passively pivoted airfoil located directly downstream. Laser Doppler Velocimetry (LDV) was used to measure the local fluid velocity at various points upstream of the airfoil and optical tracking was used to obtain the structure displacements. The causality of this simple system is known a priori, allowing for validation of the proposed method. |
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