Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F30: Compressible Flow: Analytical TheoryCompressible

Hide Abstracts 
Chair: Joseph Olles, Sandia National Laboratories Room: 110 
Monday, November 20, 2017 8:00AM  8:13AM 
F30.00001: The Scaling Group of the 1D Invisicid Euler Equations Emma Schmidt, Scott Ramsey, Zachary Boyd, Roy Baty The one dimensional (1D) compressible Euler equations in nonideal media support scale invariant solutions under a variety of initial conditions. Famous scale invariant solutions include the Noh, Sedov, Guderley, and collapsing cavity hydrodynamic test problems. We unify many classical scale invariant solutions under a single scaling group analysis. The scaling symmetry group generator provides a framework for determining all scale invariant solutions emitted by the 1D Euler equations for arbitrary geometry, initial conditions, and equation of state. We approach the Euler equations from a geometric standpoint, and conduct scaling analyses for a broad class of materials. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F30.00002: Converging Shock Flows in a MieGruneisen Material Scott Ramsey, Emma Schmidt, Zachary Boyd, Jennifer Lilieholm, Roy Baty Previous work has shown that the onedimensional (1D) inviscid Euler equations admit a variety of scaleinvariant solutions when the included equation of state (EOS) closure model assumes a certain scaleinvariant form. However, this scaleinvariant EOS class does not include even simple models used for shock compression of crystalline solids, including many broadly applicable representations of MieGruneisen EOS. This incompatibility naturally arises from the presence of multiple dimensional scales in the MieGruneisen EOS. The current work uses a scaleinvariant EOS model to approximate a MieGruneisen EOS form. To this end, the adiabatic bulk modulus for the MieGruneisen EOS is constructed, and its key features are used to motivate the selection of a scaleinvariant approximation form. The approximate adiabatic bulk modulus is used in conjunction with the 1D inviscid Euler equations to calculate a semianalytical, Guderleylike imploding shock solution in a metal sphere, and to determine if and when the solution may be valid for the underlying MieGruneisen EOS. [Preview Abstract] 
Monday, November 20, 2017 8:26AM  8:39AM 
F30.00003: Hydrodynamics with strength: scalinginvariant solutions for elasticplastic cavity expansion models Jason Albright, Scott Ramsey, Roy Baty Spherical cavity expansion (SCE) models are used to describe idealized detonation and highvelocity impact in a variety of materials. The common theme in SCE models is the presence of a pressuredriven cavity or void within a domain comprised of plastic and elastic response subregions. In past work, the yield criterion characterizing material strength in the plastic subregion is usually taken for granted and assumed to take a known functional form restrictive to certain classes of materials, e.g. ductile metals or brittle geologic materials. Our objective is to systematically determine a general functional form for the yield criterion under the additional requirement that the SCE admits a similarity solution. Solutions determined under this additional requirement have immediate implications toward development of new compressible flow algorithm verification test problems. However, more importantly, these results also provide novel insight into modeling the yield criteria from the perspective of hydrodynamic scaling. [Preview Abstract] 
Monday, November 20, 2017 8:39AM  8:52AM 
F30.00004: Spontaneous shockshock and singularity formation on perturbed planar shock waves W. Mostert, D.I. Pullin, R. Samtaney, V. Wheatley We discuss the evolution of perturbed planar gasdynamic and magnetohydrodynamics shock waves. An asymptotic closed form solution of the equations of geometrical shock dynamics (GSD) based on spectral analysis is described that predicts a time to loss of analyticity in the profile of a plane propagating shock wave subject to a smooth, spatiallyperiodic shape and Mach number perturbation of arbitrarily small magnitude. The shock shape remains analytic only up to a finite, critical time that is found to be inversely proportional to a measure of the initial perturbation amplitude. It is also shown that this analysis can also be applied to strong, fast MHD shocks in the presence of an external magnetic field whose field lines are parallel to the unperturbed shock. The relation between this critical time and the numerical detection of the time to formation of shockshocks (Mostert et al., JFM. 2017) will be discussed. [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F30.00005: Modern Infinitesimals and the Entropy Jump Condition for an Inviscid Shock Wave Roy Baty, Len Margolin This presentation applies nonstandard analysis to derive jump function solutions for energy and entropy across onedimensional shock waves in a compressible, inviscid, perfect gas. Nonstandard analysis is an area of modern mathematics that studies number systems containing both infinitely small and infinitely large numbers. In the current work, it is assumed that the shock wave thickness occurs on an infinitesimal interval and the jump functions associated with energy and entropy vary smoothly across the shock layer. The classical jump functions for the equilibrium thermodynamic energy and entropy are reviewed with emphasis on the entropy peak in the shock layer. Jump functions are then constructed and analyzed for a functional form of nonequilibrium entropy that has been shown by Margolin et al. to remove the entropy peak and closely estimate the gas kinetic nonequilibrium entropy found across a shock wave with realistic statistical mechanics properties. [Preview Abstract] 
Monday, November 20, 2017 9:05AM  9:18AM 
F30.00006: Normal Shocks with High Upstream Pressure William Sirignano A normal compressive shockwave with supercritical upstream thermodynamic conditions is analyzed using SoaveRedlichKwong equation of state for realgas density, enthalpy, and entropy relations for argon, nitrogen, oxygen, and carbon dioxide. Upstream pressure and temperature varying from 10 to 500 bar and 160 to 800 K. At high pressures, the flow does not follow the caloricallyperfectgas behavior. For the perfect gas, the enthalpy and ratio of pressuretodensity are directly proportional to the square of the sound speed, allowing its direct substitution in the conservation equations. A new thermodynamic function is identified for the sound speed which is shown to remain as the proper characteristic speed. Although the sound speed does not emerge directly from the conservation equations as it does for a perfect gas, the shock speed goes to this limiting value as shock strength goes to zero. For the realgas, modifications are obtained for Prandtl's relation and the RankineHugoniot relation. The modified realgas Riemann invariants are constructed and discussed for application to weak shocks. A foundation is presented for use with other cubic equations of state, multicomponent flows, and / or for more complex flow configurations. [Preview Abstract] 
Monday, November 20, 2017 9:18AM  9:31AM 
F30.00007: Analysis of highspeed rotating flow inside gas centrifuge casing Dr. Sahadev Pradhan The generalized analytical model for the radial boundary layer inside the gas centrifuge casing in which the inner cylinder is rotating at a constant angular velocity $\Omega $\textit{\textunderscore i} while the outer one is stationary, is formulated for studying the secondary gas flow field due to wall thermal forcing, inflow/outflow of light gas along the boundaries, as well as due to the combination of the above two external forcing. The analytical model includes the sixth order differential equation for the radial boundary layer at the cylindrical curved surface in terms of master potential ($\chi )$, which is derived from the equations of motion in an axisymmetric $(r  z)$ plane. The linearization approximation is used, where the equations of motion are truncated at linear order in the velocity and pressure disturbances to the base flow, which is a solidbody rotation. Additional approximations in the analytical model include constant temperature in the base state (isothermal compressible Couette flow), high aspect ratio (length is large compared to the annular gap), high Reynolds number, but there is no limitation on the Mach number. The discrete eigenvalues and eigenfunctions of the linear operators (sixthorder in the radial direction for the generalized analytical equation) are obtained. The solutions for the secondary flow is determined in terms of these eigenvalues and eigenfunctions. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations and found excellent agreement (with a difference of less than 15{\%}) between the predictions of the analytical model and the DSMC simulations, provided the boundary conditions in the analytical model are accurately specified. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F30.00008: Pressure fluctuation caused by moderate acceleration Yoshiyuki Tagawa, Chihiro Kurihara, Akihito Kiyama Pressure fluctuation caused by acceleration of a liquid column is observed in various important technologies, e.g. waterhammer in a pipeline. The magnitude of fluctuation can be estimated by two different approaches: When the duration time of acceleration is much shorter than the propagation time for a pressure wave to travel the length of the liquid column, e.g. sudden valve closure for a long pipe, Joukowsky equation is applied. In contrast, if the acceleration duration is much longer, the liquid is modeled as a rigid column, ignoring compressibility of the fluid. However, many of practical cases exist between these two extremes. In this study we propose a model describing pressure fluctuation when the duration of acceleration is in the same order of the propagation time for a pressure wave, i.e. under moderate acceleration. The novel model considers both temporal and spatial evolutions of pressure propagation as well as gradual pressure rise during the acceleration. We conduct experiments in which we impose acceleration to a liquid with varying the length of the liquid column, acceleration duration, and properties of liquids. The ratio between the acceleration duration and the propagation time is in the range of 0.02  2. The model agrees well with measurement results. [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F30.00009: Sensitivity of boundarylayer stability to basestate distortions at high Mach numbers Junho Park, Tamer Zaki The stability diagram of highspeed boundary layers has been established by evaluating the linear instability modes of the similarity profile, over wide ranges of Reynolds and Mach numbers. In real flows, however, the base state can deviate from the similarity profile. Both the base velocity and temperature can be distorted, for example due to roughness and thermal wall treatments. We review the stability problem of highspeed boundary layer, and derive a new formulation of the sensitivity to basestate distortion using forward and adjoint parabolized stability equations. The new formulation provides qualitative and quantitative interpretations on change in growth rate due to modifications of meanflow and meantemperature in heated highspeed boundary layers, and establishes the foundation for future control strategies. [Preview Abstract] 
Monday, November 20, 2017 9:57AM  10:10AM 
F30.00010: Linear evolution of compressible G\"{o}rtler instability triggered by freestream vortical disturbances Samuele Viaro, Pierre Ricco The linear development of unsteady compressible G\"{o}rtler vortices is investigated theoretically and numerically. A rigorous initial boundary value framework (IBV) is derived from the full compressible NavierStokes equations, supplemented with initial and outer boundary conditions that synthesize the forcing of the oncoming freestream vortical disturbances (FSVD). A simplified eigenvalue framework (EV) is then derived by neglecting the interactions with FSVD. Agreement with IBV is found sufficiently downstream where FSVD are fully decayed. The matching occurs only between the normalized IBV and EV profiles due to the lack of information from the initial conditions in the EV problem. Accuracy of the EV solution is improved when nonparallel effects are considered. Incompressible steady vortices are most unstable and evolve in a wall layer that shrinks as the streamwise coordinate increases. As the Mach number and frequency increase the flow stabilizes and vortices move toward the edge of the boundary layer. In addition, the streamwise wavelength of the perturbation approaches the freestream value when stability increases. Finally, an asymptotical analysis is developed to show the different stages in which the linear vortices develop. [Preview Abstract] 
Follow Us 
Engage
Become an APS Member 
My APS
Renew Membership 
Information for 
About APSThe American Physical Society (APS) is a nonprofit membership organization working to advance the knowledge of physics. 
© 2024 American Physical Society
 All rights reserved  Terms of Use
 Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 207403844
(301) 2093200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 5914000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 200452001
(202) 6628700