Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session H30: Compressible Flows I: DNS |
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Chair: Todd Oliver, University of Texas at Austin Room: 408 |
Monday, November 25, 2013 10:30AM - 10:43AM |
H30.00001: The convergence of DNS results to the LIA solution in canonical shock-turbulence interaction Jaiyoung Ryu, Daniel Livescu The interaction between isotropic turbulence and a normal shock wave is studied using Direct Numerical Simulations, with all flow scales (including the shock width) accurately solved. The simulation domain is open-ended, in a reference frame where the shock is stationary and turbulence is fed through the inlet. Realistic turbulence is generated in separate stationary isotropic simulations, with background velocity matching the shock speed, to avoid the use of the Taylor hypothesis. The shock Mach numbers range from 1.1 to 2.2 and the microscale Reynolds numbers range from 10 to 50. The vortical mode dominates upstream of the shock and the simulations cover the parameter space from linear inviscid, close to the Linear Interaction Analysis (LIA) limit, to regimes dominated by nonlinear and/or viscous effects. This comprehensive coverage of the parameter space shows, for the first time, that turbulence quantities from DNS converge to the LIA solutions as the shock width becomes thinner than the turbulence scales. In this regime, the shock Mach number becomes the dominant parameter, consistent to the LIA prediction. [Preview Abstract] |
Monday, November 25, 2013 10:43AM - 10:56AM |
H30.00002: Reynolds Stress Anisotropy and Vortex Structures in Compressible Homogeneous Turbulent Shear Flow Vaibhav Bhutoria, Gregory Blaisdell, Mukul Rao Direct numerical simulations of compressible homogeneous shear flow using natural initial conditions are performed for a range of gradient and turbulent Mach numbers. A pseudo-spectral Fourier collocation method is used to perform the simulations. Compressibility effects result in a reduced growth rate of turbulent kinetic energy, predominantly through a reduced production rate. This is found to be parameterized better by the gradient Mach number than by the turbulent Mach number. From the Reynolds stress anisotropy tensor it is found that the reduced production rate is due to lower energy in the velocity fluctuations in the direction of the mean velocity gradient. Lumley's tensor invariant map shows that more compressible flows tend towards the 1-component turbulence state. High speed and low speed streaks associated with corrugated vortex sheets are found in these simulations. The mechanism of formation of the corrugated vortex sheets is investigated. [Preview Abstract] |
Monday, November 25, 2013 10:56AM - 11:09AM |
H30.00003: High-speed laminar-turbulent boundary layer transition induced by a discrete roughness element Prahladh Iyer, Krishnan Mahesh Direct numerical simulation (DNS) is used to study laminar to turbulent transition induced by a discrete hemispherical roughness element in a high-speed laminar boundary layer. The simulations are performed under conditions matching the experiments of Danehy {\it et al.} ({\it AIAA Paper 2009--394, 2009}) for free-stream Mach numbers of 3.37, 5.26 and 8.23. It is observed that the Mach 8.23 flow remains laminar downstream of the roughness, while the lower Mach numbers undergo transition. The Mach 3.37 flow undergoes transition closer to the bump when compared with Mach 5.26, in agreement with experimental observations. Transition is accompanied by an increase in $C_f$ and $C_h$ (Stanton number). Even for the case that did not undergo transition (Mach 8.23), streamwise vortices induced by the roughness cause a significant rise in $C_f$ until 20$D$ downstream. The mean van Driest transformed velocity and Reynolds stress for Mach 3.37 and 5.26 show good agreement with available data. A local Reynolds number based on the wall properties is seen to correlate with the onset of transition for the cases considered. [Preview Abstract] |
Monday, November 25, 2013 11:09AM - 11:22AM |
H30.00004: The role of compressions and expansions in stationary compressible isotropic turbulence Shriram Jagannathan, Diego Donzis A characteristic of turbulence that is unique to compressible flows is the presence of compressing and expanding fluid regions that correspond to negative and positive values of dilatation respectively. While considerable attention has been given to studying the role of compressions, the effect of expansions has not been investigated in any detail. We employ a large database of Direct Numerical Simulation of stationary compressible isotropic turbulence at Taylor Reynolds numbers up to $450$ and a range of Mach numbers ($M_t \approx 0.1-0.6$) to examine the impact of compressions and expansions on the statistics of thermodynamic variables. Our results indicate that expansions affect the flow thermodynamics more significantly than equally strong compressions. While at low $M_t$ thermodynamic variables are less likely to be affected by compressions and expansions, they tend to be altered significantly by expansions at high $M_t$. Expansions are less likely to appear as compared to compressions, but tend to produce an increase in the correlation between density and temperature at high $M_t$, which, as will be shown, affects the pressure fluctuations. The differences in flow statistics in regions of intense fluctuations for low and high $M_t$ will also be discussed. [Preview Abstract] |
Monday, November 25, 2013 11:22AM - 11:35AM |
H30.00005: Predictive Inner-Outer Wall Model for Hypersonic Turbulent Boundary Layers Pino Martin, Clara Helm The inner-outer predictive wall model of Mathis et al. (JFM 2011) is modified for hypersonic turbulent boundary layers. The model is based on a modulation of the energized motions in the inner layer by large scale momentum fluctuations in the logarithmic layer. Using direct numerical simulation (DNS) data of Mach 3 and Mach 7 turbulent boundary layers it is shown that this modulating effect exists in compressible conditions and at low Reynolds number. The model is extended to include also spanwise and wall-normal velocity fluctuations and is generalized for compressible flow through Morkovin scaling. Temperature fluctuations are modeled using an appropriate Reynolds Analogy. Density fluctuations are calculated from the temperature fluctuations using an equation of state and a linear scaling with Mach number. DNS data are used to obtain the universal signal and parameters. The model is tested by using the universal signal to reproduce the flow conditions of Mach 3 and Mach 7 turbulent boundary layer DNS data and comparing turbulence statistics between the modeled flow and the DNS data. This work is supported by the Air Force Office of Scientific Research under grant AF/9550-10-1-0164. [Preview Abstract] |
Monday, November 25, 2013 11:35AM - 11:48AM |
H30.00006: A Semi-Implicit, Fourier-Galerkin/B-Spline Collocation Approach for DNS of Compressible, Reacting, Wall-Bounded Flow Todd Oliver, Rhys Ulerich, Victor Topalian, Nick Malaya, Robert Moser A discretization of the Navier-Stokes equations appropriate for efficient DNS of compressible, reacting, wall-bounded flows is developed and applied. The spatial discretization uses a Fourier-Galerkin/B-spline collocation approach. Because of the algebraic complexity of the constitutive models involved, a flux-based approach is used where the viscous terms are evaluated using repeated application of the first derivative operator. In such an approach, a filter is required to achieve appropriate dissipation at high wavenumbers. We formulate a new filter source operator based on the viscous operator. Temporal discretization is achieved using the SMR91 hybrid implicit/explicit scheme. The linear implicit operator is chosen to eliminate wall-normal acoustics from the CFL constraint while also decoupling the species equations from the remaining flow equations, which minimizes the cost of the required linear algebra. Results will be shown for a mildly supersonic, multispecies boundary layer case inspired by the flow over the ablating surface of a space capsule entering Earth's atmosphere. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615]. [Preview Abstract] |
Monday, November 25, 2013 11:48AM - 12:01PM |
H30.00007: Direct Numerical Simulation of a Compressible Reacting Boundary Layer using a Temporal Slow Growth Homogenization Victor Topalian, Todd Oliver, Rhys Ulerich, Robert Moser A DNS of a compressible, reacting boundary layer flow at $\mbox{Re}_\theta\approx{}430$ was performed using a temporal slow-growth homogenization, for a multispecies flow model of air at supersonic regime. The overall scenario parameters are related to those of the flow over an ablating surface of a space capsule upon Earth's atmospheric re-entry. The simulation algorithm features Fourier spatial discretization in the streamwise and spanwise directions, B-splines in the wall normal direction, and is marched semi-implicitly in time using the SMR91 scheme. Flow statistics will be presented for relevant flow quantities, in particular those related with RANS modeling. Since analogous slow growth computations can be performed using RANS to predict the flow mean profiles, the use of data gathered from this type of simulation as a vehicle for the calibration and uncertainty quantification of RANS models will be discussed. This work is supported by the Department of Energy [National Nuclear Security Administration] under Award Number [DE-FC52-08NA28615]. [Preview Abstract] |
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