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16:15   Numerical Methods and Data Analysis 4 16:15 15 mins #31 AERO-OPTICAL INVESTIGATION ON TURBULENT MIXING FLOW BY HIGH-ORDER ALGORITHM Sun Xi Wan, Liu Wei, Li Da Li, Wang Dong Fang Abstract: When imaging guidance vehicle experiences high-speed flight in atmosphere, severe distortion due to light propagation through the disturbed freestream around optical dome would result in image aberration, jitter, intensity attenuation, and ultimately, profound reduction of guidance precision [1] (see Figure 1). Such physical phenomenon is termed as aero-optical effect and considered as a multidisciplinary field. From the perspective of intersection between fluid dynamics and optical engineering, aero-optical research focuses on the effects of mixing layer, wall-bounded turbulent flow or turret-induced vortices on light distortion and optical wavefront. With the recent advances of high-fidelity computational method and computing power, numerical investigation has evolved as an irreplaceable technique in this field, especially in resolving turbulent structures. However, few attempts focusing on method validation are reported despite the widely existing simulative studies. Due to its urgent demand, we authors conduct a rigorous discussion on the effectiveness of combinational WCNS-E-5 and ray-tracing method in aero-optical simulation. Firstly, the in-house numerical software based on fifth-order weighted compact nonlinear scheme (WCNS-E-5) is introduced, as well as the ray-tracing method via an application in oblique shock-wave flowfield. The convective derivatives are dealt using a sixth-order central differential formula, and Roe's difference scheme is used to solve the numerical flux, with fifth-order nonlinear weighted interpolation implemented for efficient shock capture. In order to fulfill the geometric conservation law (SCL) in high-order finite difference scheme, the symmetric conservative metric method is applied for structured grid derivatives used in coordinate transformation. Aero-optical postprocessing is conducted via tracing virtual light particles (see Figure 2) [2]. Further, film cooling is often adopted on supersonic optical dome, and complex vortex structures generating from commingling between injection and freestream extremely resembles turbulent mixing layer flow. Therefore, mixing flow is an important research objective, and grid sensitivity analysis on a 3-D supersonic turbulent mixing layer (from Ref.[2], Reup≈2.3×107/m and Redown≈1.8×107/m) is conducted with regards to aero-optical effects. Based on the efficient Reynolds stress results, smaller difference of aero-optical parameters between denser grid systems implies the existence of grid independent character for aero-optical parameters just like other flow variables. Additionally, specifying the tiny density fluctuations of such rarefied flows is extremely difficult in wind tunnel, while in contrast, this implementation in subsonic commingling is much easier as well as aero-optical measurement. A back-to-back 2-D verification is conducted by our WCNS-E-5 and ray-tracing scheme for academic mechanism research. In order to eliminate the inevitable numerical noise like the wind-tunnel data (experiment from Ref.[3]) and make the results comparable, filter is also considered in the current study (see Figure 3). The relative deviation between simulated and measured data could be controlled within 10% under a reasonably prescribed inlet profile. The current study focuses on resolving turbulent mixing flow by high order scheme, and such attempts possess reference value towards numerical simulation of aero-optical investigation on turbulent flow. 16:30 15 mins #406 Parallel 2D and 3D numerical simulations of melting with convection Ionut Danaila, Corentin Lothode, Francky Luddens, Aina Rakotondrandisa, Georges Sadaka, Pierre-Henri Tournier Abstract: We present high-accuracy numerical simulations of thermal convection with melting using adaptive Galerkin finite elements. We use P2 finite elements for the velocity and P1 for the pressure and temperature to discretize a single-domain model based on the Navier-Stokes-Boussinesq equations. An enthalpy transformation model is used for the energy equation and a Carman-Kozeny penalty model to bring the velocity to zero inside the solid region. The mesh is dynamically adapted to accurately capture the interface between solid and liquid phases. The numerical method was reformulated to use domain-decomposition methods. This enables efficient parallel computations for 3D configurations or highly-resolved 2D geometries. The basic simulated configuration is a heated cavity filled with a pure phase-change material and we consider both lateral and basal heating. The two configurations are compared in detail by computing the time evolution of the average Nusselt number at the interface, the accumulated heat input and the liquid fraction. Three-dimensional simulations of the same cases will also be presented. 16:45 15 mins #122 SLOSHING DYNAMICS USING FREE ENERGY BASED LATTICE BOLTZMANN METHOD Sita Sundar, Sumesh P. Thampi, T. Jaychandran, A. Sameen Abstract: Lattice Boltzmann Method (LBM) has gained popularity for the study of a wide gamut of research and industrial problems encompassing multi-phase flows in porous media, dynamics of complex fluids, multi-component systems, dynamic phase separation, acoustics, turbulence etc. We present, for the first time, the successful implementation of free energy based Lattice Boltzmann method [1, 2, 3, 5, 6] for the investigation of physics underlying sloshing dynamics. The unsteady incompressible Navier Stokes equations are solved with lattice Boltzmann method while the Cahn-Hilliard equation is solved using two different methods (i) method of lines with spatial gradients discretised using central difference (ii) lattice Boltzmann algorithm [4]. Validation and verification of the code are discussed by comparing the numerical results with standard examples of a binary fluid interface evolution under constant lateral and transverse accelerations. Further, the effect of sinusoidal forcing on the interface has been analyzed. For small forcing, when the interface evolves in phase with forcing, numerical results are compared with approximate analytical solutions [7] Based on the strength of the lateral acceleration and the corresponding deviation of the fluid from its initial configuration, sloshing is characterized in three different regimes demarcating the responses as linear, weakly non-linear, and nonlinear. In the linear regime, numerical and analytical results compare well. Nonlinear regime manifests a multitude of inter- esting features including non-linear oscillations, interface break-up, and drop and bubble formations thus illustrating the benefit of the method to study a wide range of problems in sloshing. Moreover, the dependence of sloshing on various physical parameters i.e. sinusoidal oscillation frequency, viscosity, gravity, surface tension, and aspect-ratio is discussed. The potential of the diffused interface model combined with lattice Boltzmann algorithm is promising. Compared to the traditional interface tracking algorithm, in this method the governing equations for interface evolution is based on thermodynamics. It doesn’t need to track the interface explicitly and it shows a stable evolution of the interface. References [1] D. M. Anderson, G. B. McFadden, and A. A. Wheeler. Diffuse-interface methods in fluid mechanics. Annual Review of Fluid Mechanics, 30(1):139–165, 1998. [2] Abbas Fakhari and Diogo Bolster. Diffuse interface modeling of three-phase contact line dynamics on curved boundaries: A lattice boltzmann model for large density and viscosity ratios. Journal of Computational Physics, 334:620 – 638, 2017. [3] T. Inamuro, T. Ogata, S. Tajima, and N. Konishi. A lattice boltzmann method for incompressible two-phase flows with large density differences. Journal of Computational Physics, 198(2):628 – 644, 2004. [4] T. Krueger, H. Kusumaatmaja, A. Kuzmin, O. Shardt, G. Silva, and E.M. Viggen. Multiphase and multicomponent flows. in: The lattice boltzmann method. graduate texts in physics. springer, cham. Springer, Cham, 2017. [5] C. M. Pooley and K. Furtado. Eliminating spurious velocities in the free-energy lattice boltzmann method. Phys. Rev. E, 77:046702, Apr 2008. [6] C. M. Pooley, H. Kusumaatmaja, and J. M. Yeomans. Contact line dynamics in binary lattice boltzmann simulations. Phys. Rev. E, 78:056709, Nov 2008. [7] A. Sauret, F. Boulogne, J. Cappello, E. Dressaire, and H. A. Stone. Damping of liquid sloshing by foams. Physics of Fluids, 27(2):022103, 2015 17:00 15 mins #388 A NEW ALTERNATING DIRECTION FORCING IMMERSED BOUNDARY METHOD FOR HIGH-FIDELITY SIMULATIONS OF A MOVING OBJECT IN A FLUID Athanasios Giannenas, Sylvain Laizet Abstract: Performing high-fidelity simulations of a moving object in a fluid remains a major challenge due to the great computational cost associated with the reconstruction of a body-fitted mesh to map the moving object. An appealing alternative is based on Immersed Boundary Methods (IBMs) which rely on a fixed and structured Eulerian mesh via the imposition of no-slip or Neumann boundary conditions thanks to an extra forcing term in the Navier-Stokes equations. IBMs based on a sharp boundary interface representation abruptly impose an artificial value for the velocity inside the object to satisfy the required boundary conditions at the fluid/object interface. The resulting velocity discontinuities can introduce spurious numerical errors which in turn contaminate the flow solution. A new Alternating Direction Forcing IBM (ADF-IBM) for moving objects is presented in the present work. It employs a one-dimensional (1D) cubic spline reconstruction to interpolate an artificial velocity inside the object while ensuring the correct boundary condition at the fluid/object interface and a continuous velocity field. Hence, by removing the velocity discontinuities, spurious numerical errors can be drastically reduced. The proposed ADF-IBM is implemented in the high-order flow solver Incompact3d which is based on a Cartesian mesh and implicit finite-difference schemes [2]. It is compatible with the 2D domain decomposition used in Incompact3d, allowing simulations with a very large number of degrees of freedom. In order to demonstrate the capability of the new ADF-IBM, simulations are performed for the well-known flow around a cylinder at Re = 40 (based on the diameter D of the cylinder and the streamwise velocity u ∞ ), for a square computational domain 20D × 20D discretised with N x × N y = 513 × 513 mesh nodes. Comparisons can be made with a more conventional IBM (‘Old IBM’) with no reconstruction (with a discontinuity on the velocity field). Normalised streamwise velocity profiles along the normal direction are presented in Figure 1(Left). An excellent agreement with the reference data from Gautier [1], obtained for a fixed cylinder with spectral methods, can be observed for both IBMs, with no obvious differences. The advantage of the ADF-IBM, however, can be quantified by examining the L 2 norm of the velocity field which is reduced by 2.3 by comparison to the Old IBM. The development of the vortex shedding in the wake of a moving cylinder with the ADF-IBM for Re = 300 is presented in Figure 1(Right). 17:15 15 mins #531 NUMERICAL SCHEME FOR A LAGRANGIAN STOCHASTIC MODEL DESCRIBING RODS ORIENTATION Lorenzo Campana, Mireille Bossy, Jean Pierre Minier Abstract: Suspension of anisotropic particles can be found in various applications, e.g. industrial manufacturing processes or natural phenomena (micro-organism locomotion, ice crystal formation in clouds). Microscopic ellipsoidal bodies suspended in a turbulent fluid flow rotate in response to the velocity gradient of the flow. Understanding their orientation is important since it can affect the optical or rheological properties of the suspension (e.g. polymeric fluids). The equations of motion for the orientation of microscopic ellipsoidal particles was obtained by Jeffery [2]. But so far this description has been always investigated in the framework of direct numerical simulations (DNS) [1, 7] and experimental measurements [6]. In this work, the orientation dynamics of rod-like tracer particles, i.e. long ellipsoidal particles (in the limit of infinity the aspect-ratio) is studied. The size of the rod is assumed smaller than the Kolmogorov length scale but sufficiently large that its Brownian motion need not be considered. As a result, the local flow around a particle can be considered as inertia- freeandStokesflowsolutionscanbeusedtorelateparticlerotationaldynamicstothelocalvelocitygradienttensorAij = ∂ui/∂xj [3]. The orientation of rod can be described as the normalized solution of the linear ordinary differential equation for the separation vector ⃗r12 between two fluid tracers. Separation evolves under the action of the velocity gradient tensor. Simultaneously, a re-normalization procedure ⃗r12/||⃗r12|| is introduced to obtain the unit-vector p⃗ aligned with the rod. In this frame, the rod orientation is described by a Lagrangian stochastic model, assuming that cumulative effect of the velocity gradient tensor on the observation time interval fluctuate with a Gaussian distribution. Indeed, cumulative velocity gradient fluctuations are here represented by a white-noise tensor such that it preserves the incompressibility condition. Large observation timescale (objective of the work) justifies the Gaussian distribution hypotheses, with a decorrelation timescale equal to the Kolmogorov one τη . The model involves three time-scales: the Kolmogorov timescale τη, the Lagrangian integral timescale of the fluid TL and the integration timescale ∆t. The first two timescales are physical characteristic timescales. The third one, ∆t, represents the ’observation’ time-scale. When ∆t becomes smaller with respect to the Kolmogorov inner time scale τη the model for the orientation is no longer valid. This constraint reflects the argument that on a large enough observation time scale (meaning precisely ∆t ≫ τη ), the stochastic model for the orientation is coherent with the physical description of the Lagrangian stochastic model. In particular, it should be stressed that there is a strong interplay between the physical aspects of the model (which leads to a formulation in terms of stochastic differential equation SDE) and the numerical aspects of the practical simulations [5]. Besides, the development of a suitable numerical scheme for a large integration time steps for the SDE is a difficult task to address for the separation equation, and in this context the focus on the orientation information only is a crucial point. The purpose of this study is to describe a numerical integration scheme of the SDE involved for a large time step. A splitting algorithm, based on the decomposition into skew- and symmetric part of the process dynamics is presented. In this way, it is possible to identify, in the separation’s dynamics, two different contributions: a rotating part and a pure stretching one. To be more precise, for the rotating part, the key ingredient is to perform a semi-exact simulation algorithm for the increments of Brownian motion (BM) on a sphere, based on [4]. Often, such kinds of algorithms for BM on a sphere are constructed using tangent plane methods (or projection methods), which are accurate only for small time steps, making the algorithms computationally expensive or physically meaningless (as in this case of study). Whereas, for the stretching part, a specific SDE is simulated to control its exponential growth, so that the process can be simulated over longer time steps. Finally, the new methodology is tested in the case of homogeneous isotropic turbulence. 17:30 15 mins #515 Direct Simulation of Turbulent Plumes in a Crossflow Owen Jordan, Maarten van Reeuwijk, Ben Devenish, Gabriel Rooney Abstract: We consider direct numerical simulations (DNS) of buoyant plumes from a circular source released into a neutrally buoyant environment with a uniform crossflow. Four simulations of differing crossflow velocities are presented. We investigate the coherent structures of the plumes, with particular consideration given to the influence that these structures may have on the rate of entrainment of ambient fluid into the plumes. We present a systematic comparison of the DNS results with the mathematical theory of plumes in a crossflow. The DNS results show that while some of the assumptions made during the derivation of the classical plume equations are appropriate, others are violated. In particular, the horizontal momentum deficit flux which is predicted to be conserved is found to vary significantly. Through systematic analysis of the budget of the horizontal momentum deficit, we identify the process responsible for this behaviour. We model this process, and thus extend the classical plume equations to better match our DNS results. 17:45 15 mins #572 Flow reconstruction using thermal wall imprints Md Rakib Hossain, John Craske, Maarten Van Reeuwijk Abstract: We present results from a reconstruction of plane Couette flow using thermal wall imprints. The data set was generated using the DNS code SPARKLE and a passive scalar field was added with a constant flux at the bottom wall and a fixed temperature on the top wall. The temperature on the bottom wall is the thermal imprint. We use proper orthogonal decomposition (POD) reconstruction techniques for gappy data to reconstruct the flow. As in any other flow reconstruction technique using thermal wall imprints, e.g. thermal image velocimetry (TIV), thermal wall imprints are assumed to be the footprints of a turbulent flow near a wall. We train a set of POD modes using DNS results which are modulated with varying temporal amplitudes that can be inferred from thermal wall imprints. The evaluation of temporal amplitudes leads to an optimisation problem. The optimisation problem is ill-conditioned, because the available information is sparse in comparison with the information to be reconstructed. We regularise the ill-conditioned problem with a LASSO regularisation scheme which produces the reconstructed field shown in figure alongside actual field. We also develop a set of subdomain-POD modes which are obtained as POD modes within a spatial subdomain of the entire physical domain. Subdomain-POD modes are different from standard POD modes because subdomain-POD modes are local and require comparably less computational cost. The subdomain-POD modes were tested for reconstruction using the 1D Kuramoto-Sivashinsky system, before being applied to flow reconstruction using thermal wall imprints. 18:00 15 mins #255 Dynamic Bridging Modeling for Coarse Grained Simulations of Shock Driven Turbulent Mixing Fernando Grinstein, Juan Saenz, Rick Rauenzahn, Massimo Germano Abstract: Simulations of unsteady shock-driven turbulent mixing are required to capture late-time states of complex convectively driven multi-physics in many applications of interest, such as inertial confinement fusion (ICF) capsule implosions. The three-dimensional (3D) hydrodynamics depends on initial conditions (IC) and involves transition to turbulence nonequilibrium turbulence development and decay. Such flow physics can be captured with a coarse-grained simulation (CGS) strategy [1], presuming small-scale flow-dynamics enslaved to dynamics of the largest scales, and using mixing transition criteria and effective turbulence Reynolds numbers (Re) for macroscopic convergence metrics [2]. In practice, CGS combines classical large-eddy simulation (LES) based on explicit sub-grid scale (SGS) models and implicit LES (ILES) relying on SGS modeling provided by physics-capturing numerics. Turbulent mixing of material scalars can be usefully characterized by the length scales of the fluid physics involved: 1) large-scale entrainment in which advection brings relatively large regions of the pure materials together, 2) an intermediate length scale associated with the convective stirring due to velocity gradient fluctuations, and, 3) much smaller scale interpenetration resulting from molecular diffusion. Large-scale vortices and their interactions play a crucial role in controlling transitional mixing growth and entrainment at moderately high Re – when convective time scales are much smaller than those associated with molecular diffusion. By combining shock and turbulence emulation capabilities capable of capturing high-Re-dominating convectively driven mixing, ILES is typically the strategy of choice for practical full-scale under-resolved shock driven turbulent mixing studies. As late-time shock-driven turbulent-mixing predictability depends on IC characterization and modeling [3,4], ensemble averaging deterministic CGS over a suitably complete set of realizations covering the relevant IC variability (for the question of interest) is typically required. Bridging approaches blending CGS and Reynolds-Averaged Navier-Stokes (RANS) approaches [5,6] are attractive in offering computationally feasible methods to represent ensemble averaging while being capable of addressing effects of additional degrees of freedom associated with small-scale dynamics and multiple-shock driven transitional flow physics – not capturable with single-point-closure RANS [3]. We focus on a variable-density version of the flow simulation methodology [6], locally blending a high-resolution computational strategy (ILES) with RANS. [1] Grinstein, F.F., Coarse Grained Simulation and Turbulent Mixing, Cambridge, 2016. [2} Zhou, Y., Grinstein, F.F., Wachtor, A.J. and Haines, B.M., Estimating the effective Reynolds number …, Phys. Rev. E, 89, 013303, 2014. [3] George, W.K. and Davidson, L., Role of Initial Conditions in Establishing Asymptotic Flow Behavior, AIAA Journal, 42, 438-446 (2004) [4] Ristorcelli, J. R., Gowardhan, A.A. and Grinstein, F.F., Two classes of Richtmyer-Meshkov Instabilities; …, Physics of Fluids, 25, 044106, 2013. [5] Frolich J & von Terzi, D.A., Hybrid LES/RANS methods for the simulation of turbulent Flows, Progress in Aerospace Sciences, 44, 349-77, 2008. [6] Speziale, C.G., 1998, J. Sci. Comput., 13, pp. 253—274; Fasel, H.F., von Terzi, D.A. & Sandberg, R.D., J. Appl. Mech., 73, 405-412, 2006.