Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session M28: Turbulence: Theory III |
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Chair: Rene Pecnik, Delft University of Technology Room: 2011 |
Tuesday, November 25, 2014 8:00AM - 8:13AM |
M28.00001: Numerical experiments of variable property turbulent channel flow Ashish Patel, Jurriaan Peeters, Bendiks Boersma, Rene Pecnik We perform numerical experiments of turbulent channel flows with varying density and viscosity to investigate the validity of semi-local scaling as proposed by Huang, Coleman and Bradshaw (1995, J. Fluid Mech). Direct numerical simulations of the low Mach number approximation of the Navier-Stokes equations are used, whereby the fluid is internally heated and the temperature at the walls is set to constant. A pseudo-spectral discretization in the periodic directions and a 6th order compact finite difference in wall normal direction is used. The friction Reynolds number based on half channel height and wall friction velocity is $Re_\tau = 395$. Different relations for density and viscosity as a function of temperature are studied. A variable property case has been identified with turbulent statistics that are quasi-similar to constant property turbulence. This case corresponds to the condition when the semi-local scaling is equal to the classical scaling. For cases wherein the semi-local scaling differs from classical scaling in the channel core, we show that the near-wall turbulence deviates towards a state of increased/decreased anisotropy as compared to constant property turbulence. The above results show not only the validity but also the usefulness of the semi-local scaling. [Preview Abstract] |
Tuesday, November 25, 2014 8:13AM - 8:26AM |
M28.00002: Energy transfer and dissipation in forced isotropic turbulence Moritz Linkmann, W. David McComb, Arjun Berera, Samuel Yoffe A model for the Reynolds number dependence of the dimensionless dissipation rate $C_{\varepsilon}$ is derived from the dimensionless K\'{a}rm\'{a}n-Howarth equation, resulting in $C_{\varepsilon}=C_{\varepsilon, \infty} + C/R_L$, where $R_L$ is the integral scale Reynolds number. The coefficients $C$ and $C_{\varepsilon,\infty}$ arise from asymptotic expansions of the dimensionless second- and third-order structure functions. The model equation is fitted to data from direct numerical simulations (DNS) of forced isotropic turbulence for integral scale Reynolds numbers up to $R_L=5875$ ($R_{\lambda}=435$), which results in an asymptote for $C_\varepsilon$ in the infinite Reynolds number limit $C_{\varepsilon,\infty} = 0.47 \pm 0.01$. Since the coefficients in the model equation are scale-dependent while the dimensionless dissipation rate is not, we modelled the scale dependences of the coefficients by an \emph{ad hoc} profile function such that they cancel out, leaving the model equation scale-independent, as it must be. The profile function was compared to DNS data to very good agreement, provided we restrict the comparison to scales small enough to be well resolved in our simulations. [Preview Abstract] |
Tuesday, November 25, 2014 8:26AM - 8:39AM |
M28.00003: On the distribution of local dissipation scales in turbulent flows Ian May, Khandakar Morshed, Karan Venayagamoorthy, Lakshmi Dasi Universality of dissipation scales in turbulence relies on self-similar scaling and large scale independence. We show that the probability density function of dissipation scales, $Q(\eta)$, is analytically defined by the two-point correlation function, and the Reynolds number (Re). We also present a new analytical form for the two-point correlation function for the dissipation scales through a generalized definition of a directional Taylor microscale. Comparison of $Q(\eta)$ predicted within this framework and published DNS data shows excellent agreement. It is shown that for finite Re no single similarity law exists even for the case of homogeneous isotropic turbulence. Instead a family of scaling is presented, defined by Re and a dimensionless local inhomogeneity parameter based on the spatial gradient of the rms velocity. For moderate Re inhomogeneous flows, we note a strong directional dependence of $Q(\eta)$ dictated by the principal Reynolds stresses. It is shown that the mode of the distribution $Q(\eta)$ significantly shifts to sub-Kolmogorov scales along the inhomogeneous directions, as in wall bounded turbulence. This work extends the classical Kolmogorov's theory to finite Re homogeneous isotropic turbulence as well as the case of inhomogeneous anisotropic turbulence. [Preview Abstract] |
Tuesday, November 25, 2014 8:39AM - 8:52AM |
M28.00004: Symmetry-plane model of 3D Euler flows: Mapping to regular systems and numerical solutions of blowup Rachel M. Mulungye, Dan Lucas, Miguel D. Bustamante We introduce a family of 2D models describing the dynamics on the so-called symmetry plane of the full 3D Euler fluid equations. These models depend on a free real parameter and can be solved analytically. For selected representative values of the free parameter, we apply the method introduced in [M.D. Bustamante, Physica D: Nonlinear Phenomena, 240:1092-1099 (2011)] to map the fluid equations bijectively to globally regular systems. By comparing the analytical solutions with the results of numerical simulations, we establish that the numerical simulations of the mapped regular systems are far more accurate than the numerical simulations of the original systems, at the same spatial resolution and CPU time. In particular, the numerical integrations of the mapped regular systems produce robust estimates for the growth exponent and singularity time of the main blowup quantity (vorticity stretching rate), converging well to the analytically-predicted values even beyond the time at which the flow becomes under-resolved (i.e. the reliability time). In contrast, direct numerical integrations of the original systems develop unstable oscillations near the reliability time. We discuss the reasons for this improvement in accuracy, and explain how to extend the analysis to the full 3D case. [Preview Abstract] |
Tuesday, November 25, 2014 8:52AM - 9:05AM |
M28.00005: Large-$Re$ asymptotics of the stream-wise normal stress in the ZPG turbulent boundary layer Peter A. Monkewitz, Hassan M. Nagib Models for the stream-wise normal stress $\langle uu \rangle^+$ in wall-bounded turbulent flows have been proposed that lead to a log-law in the classical overlap layer (and part of the outer layer). Matching to the wall-layer immediately leads to $\langle uu \rangle^+_{\mathrm{inner}}\sim\ln(Re)$, i.e. to a mixed scaling in the inner layer. While this appears compatible with the observed $Re-\,$dependence of the inner peak, it is shown, in the case of the ZPG TBL, to be incompatible with DNS data and the Reynolds-averaged momentum equation. Matching inner and outer expansions of $\langle uu \rangle^+$ in terms of $1/U^+_{\infty}$ will be presented which are consistent with experimental data and DNS, and allow extrapolation to infinite Reynolds number. [Preview Abstract] |
Tuesday, November 25, 2014 9:05AM - 9:18AM |
M28.00006: Similarity of Turbulent Energy Scale Budget Equation of a Round Turbulent Jet Hamed Sadeghi, Philippe Lavoie, Andrew Pollard A novel extension to the similarity-based form of the transport equation for the second-order velocity structure function of $\langle (\delta q)^2 \rangle$ along the jet centreline (see Danaila et al., 2004) has been obtained. This new self-similar equation has the desirable benefit of requiring less extensive measurements to calculate the inhomogeneous (decay and production) terms of the transport equation. According to this equation, the normalized third-order structure function can be uniquely determined when the normalized second-order structure function, the power-law exponent of $\langle q^2 \rangle$ and the decay rate constants of $\langle u^2 \rangle$ and $\langle v^2 \rangle$ are available. In addition, on the basis of the current similarity analysis, the similarity assumptions in combination with power-law decay of mean velocity ($ U\propto(x-x_0)^{-1}$) are strong enough to imply power-law decay of fluctuations ($\langle q^2 \rangle \propto(x-x_0)^m$). The similarity solutions are then tested against new experimental data, which were taken along the centreline of a round jet at $Re_D = 50,000$. For the present set of initial conditions, $\langle q^2 \rangle$ exhibits a power-law behaviour with $m=-1.83$. [Preview Abstract] |
Tuesday, November 25, 2014 9:18AM - 9:31AM |
M28.00007: ABSTRACT WITHDRAWN |
Tuesday, November 25, 2014 9:31AM - 9:44AM |
M28.00008: Turbulent Flow past High Temperature Surfaces Igbal Mehmedagic, Siva Thangam, Pasquale Carlucci, Liam Buckley, Donald Carlucci Flow over high-temperature surfaces subject to wall heating is analyzed with applications to projectile design. In this study, computations are performed using an anisotropic Reynolds-stress model to study flow past surfaces that are subject to radiative flux. The model utilizes a phenomenological treatment of the energy spectrum and diffusivities of momentum and heat to include the effects of wall heat transfer and radiative exchange. The radiative transport is modeled using Eddington approximation including the weighted effect of nongrayness of the fluid. The time-averaged equations of motion and energy are solved using the modeled form of transport equations for the turbulence kinetic energy and the scalar form of turbulence dissipation with an efficient finite-volume algorithm. The model is applied for available test cases to validate its predictive capabilities for capturing the effects of wall heat transfer. Computational results are compared with experimental data available in the literature. Applications involving the design of projectiles are summarized. [Preview Abstract] |
Tuesday, November 25, 2014 9:44AM - 9:57AM |
M28.00009: Long-range ordering of turbulent stresses in the 2D inverse energy cascade Yang Liao, Nicholas Ouellette We report measurements of the spatial structure of the turbulent stress that couples motion on different length scales in a quasi-two-dimensional laboratory flow. We show that the range of scales over which we find net energy transfer to large scales---the inverse energy cascade---is associated with the appearance of long-range, system-spanning spatial order of the turbulent stress. Although the overall degree of order fluctuates in time, the form of the approach to ordering does not. Our results provide an unexpected example of turbulence-induced ordering, and suggest new pathways for modeling turbulence using geometric alignment. [Preview Abstract] |
Tuesday, November 25, 2014 9:57AM - 10:10AM |
M28.00010: Filtering on the Sphere Hussein Aluie, Matthew Hecht, Geoffrey Vallis The filtering approach has become an indispensable framework to analyzing and modeling turbulence, especially in the subject of Large-Eddy Simulation. However, applications have been mostly limited to flows in Euclidean spaces and generalizations to curvilinear domains suffer from several shortcomings, such as: dependence on the choice of coordinate system, commutation errors, or not preserving volume. Motivated by geophysical applications, we define a new generalized filtering operation for vector fields on the Sphere which is free from the aforementioned problems. We prove that our filter commutes with spatial derivatives, yielding simple and exact coarse-grained equations for flow on the Sphere. We demonstrate these tools with a-priori tests on flows from high-resolution Ocean simulations. [Preview Abstract] |
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