Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session A13: Compressible Flows: General 
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Chair: Kenneth Granlund, North Carolina State University Room: 143C 
Sunday, November 19, 2023 8:00AM  8:13AM 
A13.00001: Shock Interaction and the Formation of a Contact Discontinuity Roy S Baty In this work the classical problem of the interaction of two shock waves traveling in opposite directions is analyzed using modern methods of infinitesimal analysis. Two shock waves, a rightrunning shock and a leftrunning shock, are modeled as traveling waves in a onedimensional, inviscid, ideal gas. The shock waves are represented by nonstandard Heaviside jump functions and are defined using infinitesimal analysis. It is shown that the interaction of the two shocks admits a solution that may be expressed using a third nonstandard Heaviside function which combines the two shocks downstream of the interaction and demonstrates that in general a contact discontinuity must exist between the two shock waves. Nonstandard analysis is applied to describe the jump functions and their derivatives. Nonstandard analysis is an area of modern mathematics that studies extensions of the real number system to number systems that contain both infinitesimal numbers and infinitely large numbers and provides a rigorous framework for infinitesimal analysis. It is assumed that the shock wave thicknesses occur on idealized infinitesimal intervals and that the nonstandard jump functions in the thermodynamic and kinematic parameters vary smoothly across these shock layers. The equations of motion are cast in nonconservative form and applied to derive unambiguous relationships between the nonstandard jump functions and their products for the flow parameters in the regions behind the two shock waves. 
Sunday, November 19, 2023 8:13AM  8:26AM 
A13.00002: Asymptotically entropy conservative and kineticenergy and pressureequilibrium preserving schemes based on economical algebraic fluxes Gennaro Coppola, Carlo De Michele In the context of Direct and Large Eddy Simulations of (lowMach) turbulent compressible flows, an important topic is the design of robust and accurate numerical methods, which can efficiently handle high Reynolds number and/or under resolved simulations by keeping under control the aliasing errors coming from spatial discretization. To this aim modern numerical methods are usually required to satisfy some physicscompatible constraints, which typically amount to the discrete enforcement of the induced balance of suitably selected secondary quantities. Kinetic Energy Preserving (KEP) schemes are the most used among them, and in recent years various KEP formulations have been proposed. Their use for the spatial discretization of the mass and momentum equations is now considered a necessity for a reliable simulation. Entropy Conservative (EC) methods have also been explored. As they guarantee a correct discrete balance of entropy, they provide an important additional property for both the reliability and robustness of the overall procedure. Finally, Pressure Equilibrium Preserving (PEP) schemes guarantee the correct discrete evolution of density waves. 
Sunday, November 19, 2023 8:26AM  8:39AM 
A13.00003: A Geometric Interpretation of the Euler Equations Jesse F Giron, Scott D Ramsey, Roy S Baty The purpose of this work is to explore the notion of generalized similarity in the context of the Euler equations written in twodimensional axisymmetric coordinates. Leveraging previous work done by Coggeshall for the radiation hydrodynamics equations featuring an ideal gas equation of state, we show that the Euler equations are invariant under an optimal system of transformations including translations in time, translations in the azimuthal direction, and concurrent scaling in time and mass density. This symmetry algebra may be leveraged to construct a change of variables through which the Euler equations are reducible to a set of four coupled ordinary differential equations (ODEs), any solution of which possesses the same symmetries. After further constraining the ODEs using a physically motivated assumption on the velocity field, we obtain associated solutions for the density, pressure, specific internal energy, and entropy variables. These novel, closedform solutions exemplify the generalization of classical similarity as encountered in geometry or intermediate asymptotics within the setting of the Euler equations interpreted as an 18dimensional surface invariant under Lie point symmetries. 
Sunday, November 19, 2023 8:39AM  8:52AM 
A13.00004: Vorticity and the Entropy Jump Across a Shock Wave Scott D Ramsey, Roy S Baty This work studies the relationship between vorticity and entropy in threedimensional, compressible, inviscid flow fields. The Crocco equation is applied to analyze flows with shock waves by expressing the entropy gradient in terms of the cross product of the velocity and vorticity. Shock waves are modeled as twodimensional curved surfaces embedded in threedimensional flow fields. The relationship between the entropy jump condition and the kinematic jump conditions across a shock surface is derived using singular generalized functions cast as generalized derivatives concentrated on moving surfaces. For the perfect gas case, the entropy jump condition across a shock wave, which satisfies both the Crocco equation and the second law of thermodynamics, is shown to be a nonlinear generalized jump function of pressure and specific volume. It is also shown that the vorticity jump conditions do not change the functional form of the entropy jump function across a shock wave; this results because the vorticity jump conditions are purely kinematic relationships that depend only on the curl of velocity and the conservation of mass and momentum. 
Sunday, November 19, 2023 8:52AM  9:05AM 
A13.00005: The Piston Problem:sonic and supersonic velocities David R Kassoy, Adam Norris Kevorkian and Cole, (Perturbation Methods in Applied Mathematics; Springer Verlag,1985), formulate a mathematical model for the acoustic response of a gas at rest in a semiinfinite space to an imposed subsonic piston velocity. The model combines classical linear acoustic analysis with asymptotic methods to develop solutions for the induced fluid motion and the accompanying thermodynamics. 
Sunday, November 19, 2023 9:05AM  9:18AM 
A13.00006: Entropy Balance of Steady, QuasiOneDimensional, Internal Compressible Flow with Area Change, Heat Addition, and Friction (edited) Andrew A Oliva, Joshua D Szczudlak, Aleksandar Jemcov, Scott C Morris The quasionedimensional entropy transport equation is derived for flow with an arbitrary combination of area change, heat transfer, and friction. Irreversibilities are identified using the ClausiusDuhem inequality, which is found to be satisfied in a weak sense. Irreversibility arises due to the difference between a "thermal work" term and reversible work. A closedform equation is derived in order to calculate the contributions of the individual components to the overall entropy change. Further, a new mechanism is identified, which explains the ability of a discontinuity to generate entropy (e.g., shockwaves in an inviscid and nonthermally conducting fluid). These entropy generation mechanisms are then examined for the "classical" compressible flows: isentropic flow, Rayleigh flow, Fanno flow, and flow across a normal shock. Further, these mechanisms are also used to show entropy generation for sudden expansion, sudden contraction, simultaneous area change with friction and simultaneous heat transfer with friction. 
Sunday, November 19, 2023 9:18AM  9:31AM 
A13.00007: Effect of streamline curvature on flow nonuniformity in WindTunnel contractions and nozzles O N Ramesh, Dhirendu Somani

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