Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session M5: Compressible Flow: General |
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Chair: Carlo Scalo, Purdue University Room: B113 |
Tuesday, November 22, 2016 8:00AM - 8:13AM |
M5.00001: Local and global stability analysis of compressible channel flow over wall impedance Iman Rahbari, Carlo Scalo The stability properties of compressible channel flow over porous walls is investigated via Local (LSA) and Global Stability Analysis (GSA) for laminar and turbulent base flows at $\mathrm{Re}_{b}=6900$ and $\mathrm{M}_{b}=0.85, 1.5, 3.5$. Linearized Navier-Stokes equations are discretized via a sixth-order fully collocated Pad\'e scheme leading to a Generalized Eigenvalue Problem (GEVP) solved using a parallel sparse eigenvalue solver based on the shift-invert Arnoldi method. The adopted discretization guarantees spectral-like spatial resolution. Fully sparsity of the system is retained via implicit calculation of the numerical derivatives ensuring computational efficiency on multi-processor platforms. The global eigen-spectrum exhibits various sets of modes grouped by streamwise wave-numbers, which are captured via LSA, as well as global acoustic modes. Consistently with the findings of C. Scalo, \emh{et al.} Phys. Fluids (2015), two unstable local modes are found for sufficiently high wall permeability: one standing-wave-like and one representing a bulk pressure mode, both generating additional Reynolds shear stresses concentrated in the viscous sublayer region. Stability properties of the flow over non-modal streamwise impedance distributions are also discussed. [Preview Abstract] |
Tuesday, November 22, 2016 8:13AM - 8:26AM |
M5.00002: A Multi-Fidelity Surrogate Model for Handling Real Gas Equations of State Frederick Ouellet, Chanyoung Park, Bertrand Rollin, S. "Bala" Balachandar The explosive dispersal of particles is an example of a complex multiphase and multi-species fluid flow problem. This problem has many engineering applications including particle-laden explosives. In these flows, the detonation products of the explosive cannot be treated as a perfect gas so a real gas equation of state is used to close the governing equations (unlike air, which uses the ideal gas equation for closure). As the products expand outward from the detonation point, they mix with ambient air and create a mixing region where both of the state equations must be satisfied. One of the more accurate, yet computationally expensive, methods to deal with this is a scheme that iterates between the two equations of state until pressure and thermal equilibrium are achieved inside of each computational cell. This work strives to create a multi-fidelity surrogate model of this process. We then study the performance of the model with respect to the iterative method by performing both gas-only and particle laden flow simulations using an Eulerian-Lagrangian approach with a finite volume code. Specifically, the model's (i) computational speed, (ii) memory requirements and (iii) computational accuracy are analyzed to show the benefits of this novel modeling approach. [Preview Abstract] |
Tuesday, November 22, 2016 8:26AM - 8:39AM |
M5.00003: Solving the Guderley Implosion Problem with a Gruneisen-Like Equation of State Jennifer Lilieholm, Emma Schmidt, Scott Ramsey, Zachary Boyd The Guderley problem is a solution to the inviscid Euler Equations which models a strong shock originating at infinity in both space and time. This shock converges to the one-dimensional symmetric origin, where the resulting in?nite pressure causes a weaker diverging shock. The solutions to the converging and diverging shocks are self-similar, and thus the results can be scaled. This scaling means that the solutions are independent of unit choice, and can then be freely transformed across time, space, and material state. However, this requirement of self-similarity limits the equations of state (EoS) that can be used with the problem, because the EoS must exhibit scaling behavior as well. The Gruneisen equation of state is one such closure model that does not feature scaling properties. The EoS describes the behavior of crystalline solids, making it desirable for use in studies of shock propagation in solid materials. Our work endeavored to find coefficients for the Virial EoS (which consists of a power series expansion about the ideal gas in density) to approximate the Gruneisen EoS. This was done because Virial EoS is inherently scalable, and thus can be used to solve the Guderley problem. With our new form of the Virial EoS, we were able to solve the Guderley problem for a material with Gruneisen-like qualities. [Preview Abstract] |
Tuesday, November 22, 2016 8:39AM - 8:52AM |
M5.00004: Symmetries of the Gas Dynamics Equations Using the Differential Form Method Joe Schmidt, Scott Ramsey, Roy Baty A brief review of the theory of exterior differential systems and isovector symmetry analysis methods is presented in the context of the one-dimensional inviscid compressible flow equations. These equations are formulated as an exterior differential system with equation of state (EOS) closure provided in terms of an adiabatic bulk modulus. The scaling symmetry generators – and corresponding EOS constraints – otherwise appearing in the existing literature are recovered through the application of and invariance under Lie derivative dragging operations. [Preview Abstract] |
Tuesday, November 22, 2016 8:52AM - 9:05AM |
M5.00005: The Radially Symmetric Euler Equations as an Exterior Differential System Roy Baty, Scott Ramsey, Joseph Schmidt This work develops the Euler equations as an exterior differential system in radially symmetric coordinates. The Euler equations are studied for unsteady, compressible, inviscid fluids in one-dimensional, converging flow fields with a general equation of state. The basic geometrical constructions (for example, the differential forms, tangent planes, jet space, and differential ideal) used to define and analyze differential equations as systems of exterior forms are reviewed and discussed for converging flows. Application of the Frobenius theorem to the question of the existence of solutions to radially symmetric converging flows is also reviewed and discussed. The exterior differential system is further applied to derive and analyze the general family of characteristic vector fields associated with the one-dimensional inviscid flow equations. [Preview Abstract] |
Tuesday, November 22, 2016 9:05AM - 9:18AM |
M5.00006: Effects of spanwise instabilities on the suppression of wake mode in flow over a long rectangular cavity Yiyang Sun, Kunihiko Taira, Louis Cattafesta, Lawrence Ukeiley Direct numerical simulation (DNS) and biglobal stability analysis are performed to examine the spanwise effects on the appearance of the so-called wake mode in the flow over long rectangular cavities. The wake mode has been reported to exhibit high-amplitude fluctuations and eject large spanwise vortices in numerical studies, despite its lack of observation in experiments, leaving its existence an open question. The present study focuses on a rectangular cavity flow with aspect ratio of $L/D=6$, free stream Mach number of $M_\infty=0.6$ and $Re_D=502$. The properties of the wake mode are revealed via 2D DNS. From the biglobal stability analysis, the wake mode can be captured with a zero spanwise wavenumber. Furthermore, 3D eigenmodes are calculated with spanwise wavelength $\lambda/D\in[0.5,2]$. With the knowledge of the features of the wake mode and the 3D eigenmodes, 3D DNS are performed with width-to-depth ratio of $W/D=1$ and $2$. We find the flow exhibits the wake mode with $W/D=1$ but presents a moderate shear-layer mode with $W/D=2$. Based on the findings, we argue that the spanwise instabilities in flows over wide cavities redistribute energy from spanwise vortices to streamwise vortical structures, which suppresses the emergence of the wake mode in the 3D cavity flows. [Preview Abstract] |
Tuesday, November 22, 2016 9:18AM - 9:31AM |
M5.00007: Effects of the Mach number on the evolution of vortex-surface fields in compressible Taylor-Green flows Naifu Peng, Yue Yang We investigate the evolution of vortex-surface fields (VSFs) in viscous compressible Taylor-Green flows. The VSF is applied to the direct numerical simulation of the Taylor-Green flows at a range of Mach numbers from $Ma = 0.6$ to $Ma = 2.2$ for characterizing the Mach-number effects on evolving vortical structures. We find that the dilatation and baroclinic force strongly influence the geometry of vortex surfaces and the energy dissipation rate in the transitional stage. The vortex tubes in compressible flows are less curved than those in incompressible flows, and the maximum dissipation rate occurs earlier in high-Mach-number flows perhaps owing to the conversion of kinetic energy into heat. Moreover, the relations between the evolutionary geometry of vortical structures and flow statistics are discussed. [Preview Abstract] |
Tuesday, November 22, 2016 9:31AM - 9:44AM |
M5.00008: Nonmodal Growth Of Kelvin-Helmholtz Instability In Compressible Flows Mona Karimi, Sharath Girimaji Kelvin-helmholtz instability (khi) is central to the vertical mixing in shear flows and is known to be suppressed in compressible flows. To understand the inhibition of mixing under the influence of compressibility, we analyze the linear growth of khi in the short-time limit using initial value analysis. The evolution of perturbations is studied from a nonmodal standpoint. As the underlying suppression mechanism can be understood by considering primarily linear physics, the effect of compressibility on khi is scrutinized by linear analysis. Then its inferences are verified against direct numerical simulations. It has been demonstrated that compressibility forces the dominance of dilatational, rather than shear, dynamics at the interface of two fluids of different velocities. Within the dilatiatonal interface layer, pressure waves cause the velocity perturbation to become oscillatory [karimi and girimaji, 2016]. Thereupon, the focus is to examine the effect of the initial perturbation wavenumber on the formation of this layer and eventually the degree of khi suppression in compressible flows. We demonstrate that the degree of suppression decreases with the increase the wavenumbers of the initial perturbation of dilatational, rather than shear, dynamics at the interface of two fluids of different velocities. Within the dilatiatonal interface layer, pressure waves cause the velocity perturbation to become oscillatory [karimi and girimaji, 2016]. Thereupon, the focus is to examine the effect of the initial perturbation wavenumber on the formation of this layer and eventually the degree of khi suppression in compressible flows. We demonstrate that the degree of suppression decreases with the increase the wavenumbers of the initial perturbation. [Preview Abstract] |
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