# CTR Seminars Archive 2006

Date: December 8, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Andrea Lamorgese, Ph.D.

Title: Direct Simulation of Phase Transition in Liquid Mixtures

Abstract: We investigate phase transition of a liquid binary mixture that is instantaneously brought from the one- to the two-phase region of its phase diagram (or vice-versa). Our theoretical approach follows the diffuse interface model, where convection and diffusion are coupled via a non-equilibrium (Korteweg) force, expressing the tendency of the demixing system to minimize its free energy. In liquid mixtures, this driving force induces a material flux which is much larger than that due to pure molecular diffusion, thereby accelerating phase separation but effectively slowing down mixing, since the larger domains that result from enhanced drop coalescence, eventually, must dissolve by diffusion. Therefore, when all other convective fluxes can be neglected and the mixture is macroscopically quiescent, the mixing process is faster for very viscous mixtures, unlike phase separation, which is faster for very fluid mixtures. We show that heat transfer in regular binary mixtures at low Reynolds number is enhanced by induced convection during phase separation. Predictably, considering that convection is within the creeping flow regime, the Nusselt number is always of O(10).

Date: November 3, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Thierry Magin, Stanford University

Title: A model for inductive plasma wind-tunnels

Abstract: One of the main design parameters for spacecraft is the wall heat flux over the trajectory of reentry on Earth or entry on alien planets. The convective heat flux strongly depends on the surface catalytic properties of the vehicle thermal protection materials. These properties can be determined by performing tests in inductive plasma wind tunnels (Plasmatrons). A model was developed to describe tests carried out at the von Karman Institute for both Earth and Mars entries. The contribution of the radiative heat flux was a crucial issue during the entry of the Huygens probe into the atmosphere of Titan. An electronic collisional-radiative model was also proposed to predict the nonequilibrium populations and the radiation of the excited electronic states of the CN radicals produced in the shock layer.

Date: October 20, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Johan Larrson

Title: Issues in hybrid LES/RANS: the artificial buffer layer and the effects of forcing

Abstract: The computational cost of large eddy simulations (LES) increases rapidly with the Reynolds number for boundary layer flows. Several approaches to avoid this high cost through modeling of the near wall region have been proposed, several of which fall in the category of hybrid LES/RANS. Most models in this category suffer from similar problems, namely an artificial buffer layer around the modeling interface. Some authors have proposed the use of forcing as a means to remove this artificial buffer layer, typically with favorable results. The present study investigates some of these issues in hybrid LES/RANS, for example: Apart from yielding better mean velocity profiles, how does the forcing affect the dynamics in the near wall region? Can better results be achieved by using more physically sound forcing models? What are the inherent limitations of LES/RANS? How sensitive are the results to the parameters in the forcing models?

Date: October 6, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Olaf Marxen, Department of Mechanical Engineering, Royal Institute of Technology, Sweden

Title: Direct Numerical Simulations of Laminar Separation Bubbles

Abstract: Various phenomena occurring during laminar-turbulent transition in laminar separation bubbles are investigated using direct numerical simulations. Such separation bubbles can originate if a laminar boundary layer is subject to a sufficiently strong adverse pressure gradient. Laminar separation bubbles can be observed on laminar wing profiles or on high-lift devices. Occurrence of such bubbles can often be related to a loss of lift or stall. Transition is a direct consequence of an instability of the separated shear layer with respect to small perturbations and follows a number of consecutive stages. The earlier of these stages are linear if low turbulence-level environments are considered. Only controlled transition scenarios are treated, characterized by an explicit disturbance excitation. The underlying configuration is given by a flat-plate boundary layer subjected to a streamwise pressure gradient. This pressure gradient is suppositionally caused by putting a displacement body into the flow at some distance from the wall. Transition occurs in the detached shear-layer, which can lead to immediate mean reattachment, thus forming a closed, short bubble. However, in some cases an increased mixing induced by transition is not sufficient to reattach the flow. As a result, an initially short separation bubble will not remain short but will continue to grow to very large sizes towards a long-bubble state. This process is denoted as bubble bursting. Large-scale simulations are required to capture this process.

Date: September 22, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Asghar Afshari, Michigan State University

Title: Large-Scale Simulations of Turbulent Reacting Flows

Abstract: A high-order density-based, multi-block, computational model has been developed for large eddy simulation (LES) of reacting and nonreacting, compressible turbulent flows in generalized coordinate system. All spatial derivatives are approximated by a high-order compact differencing scheme and time derivatives are modeled via a third-order, Runge-Kutta method. The nonreacting results for isotropic, jet, and axisymmetric sudden expansion turbulent flows are found to be in good agreement with those obtained via validated numerical methods and with the available experimental data. The simulated results indicate that the high-order compact differencing scheme is an appropriate numerical method for LES while the multi-block capability of the scheme enables its application to complex geometries. Simulations of reacting flows are also considered. For this, a generalized Lagrangian/Eulerian, theoretical/numerical methodology is developed in which the subgrid mixing and reaction is obtained by the filtered mass density function (FMDF) methodology. The new Lagrangian FMDF flow solver is coupled with the high-order multi-block flow solver. This allows LES/FMDF to be applied to relatively complex geometries and general coordinate systems. The consistency, convergence, and accuracy of the FMDF and the Monte Carlo solution of its equivalent, stochastic differential equations are assessed for different flows. The consistency between Eulerian and Lagrangian fields is established for non-reacting isothermal and non-isothermal flows as well as reacting flows in an axisymmetric, dump-combustor. It has been found that the conventional LES and FMDF methods and their numerical solvers are fully consistent in both nonreacting and reacting cases. The results obtained for turbulent reacting flows in a premixed propane-air dump-combustor show favorable agreement with laboratory data.

Date: August 18, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Juan Carlos del Alamo, University of California San Diego

Title: Linear Energy Amplification in Turbulent Channels

Abstract: We study the temporal stability of the Orr-Sommerfeld and Squire equations in channels with turbulent mean velocity profiles and turbulent eddy viscosities. Friction Reynolds numbers up to Re_x = 2x10^4 are considered. All the eigensolutions of the problem are damped, but initial perturbations with wavelengths λ_x > λ_z can grow temporarily before decaying. Comparison with recent DNS data reveals that the most amplified solutions reproduce the organization of turbulent structures in actual channels, including their self-similar spreading in the logarithmic region. The typical widths of the near-wall streaks and of the large-scale structures of the outer layer, λ_z^{+} = 100 and λ_z = 3h are well predicted. The dynamics of the most amplified solutions is roughly the same regardless of the wavelength of the perturbations and of the Reynolds number. They start with a wall-normal v event which does not grow but which forces streamwise velocity fluctuations by stirring the mean shear u*v < 0. The resulting u fluctuations appear upstream and beneath the transverse motions that cause them. They grow significantly and last longer than the v ones, containing nearly all the kinetic energy at the instant of maximum amplification.

Date: June 30, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. Jan Nordstrom

Title: Error Bounded Schemes for Time-dependent Hyperbolic Problems

Abstract: problems on first order form. The energy method is used to study when a linear error growth or a fixed error bound is obtained. It is shown that the choice of boundary procedure is a crucial point. Numerical experiments corroborate the theoretical findings.

Date: June 23, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Ali Jafari, University of Toronto

Title: Numerical Simulations of Turbulent Interfacial Flows

Abstract: An overview of strategies for numerical investigation of turbulent interfacial flows involving liquid breakup is presented. Both RANS and LES formalisms are considered. In the RANS part, some RANS closures for the interfacial transport terms are developed. The results show that these closures may have significant effects on the interface evolution. In the LES part, the Eulerian LES- Interface capturing Technique (ELIT) is developed to simulate the disintegration of a liquid jet into atomized mass and subsequent droplet formation. To tackle complex turbulent flows involving liquid-gas interfaces with minimum empiricism, a combination of an LES model and a stable interface capturing method along with accurate spatial and temporal numerical schemes is used. The focus has been on characterizing the effects of turbulent nozzle flow on the deformation and disintegration of the liquid jet. A number of test cases and examples of liquid primary breakup are presented.

Date: June 16, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. Jan Nordstrom

Title: Boundary Conditions for a Divergence Free Velocity-Pressure Formulation of the Navier-Stokes Equations

Abstract: New sets of boundary conditions for the velocity-pressure formulation of the incompressible Navier-Stokes equations are derived. The boundary conditions have the same form on both inflow and outflow boundaries and lead to a divergence free solution. Moreover, the specific form of the boundary condition makes it possible derive a symmetric positive definite equation system for the internal pressure. Numerical experiments support the theoretical conclusions.

Date: June 2, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: M. Pino Martin, Assistant Professor, Princeton University

Title: Turbulent Hypersonic Flows: Physics and Simulation

Abstract: We are using direct and large-eddy simulations to study hypersonic turbulent flows with the goal of understanding the interaction of turbulence with shock waves, finite-rate reactions, surface catalysis and ablation, and radiation. To do this we have developed numerical methods for low-dissipation, high-bandwidth and shock capturing, as well as implicit time integration methods, initialization procedures, and methodologies to prescribe continuous inflow conditions. We are now applying these methods to problems of interest to atmospheric hypersonic flight, supersonic combustion and access to space. Some of the flows that we have simulated include shock wave-turbulent boundary layer interactions. The resulting data are being validated against experiments that are designed for this purpose. So far, we have obtained remarkable agreement between the simulation and experiments in mean flow variables, turbulence amplification, structure angle, and the size of the separation zone. Currently, we are studying the unsteady motion of the shock and its effect on the wall-pressure fluctuations and heat transfer. Another aspect that we are investigating is the characterization of turbulent structures, which is relevant to aspects of flow control. We find that increasing the freestream Mach number results in structures that are shorter and inclined at higher angles. This is due to the higher number density of shocklets that are found with increasing freestream Mach number. We are using simulation data to study various other problems including the coupling of finite-rate reactions and surface chemistry with turbulence.

Date: April 28, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. James E. Broadwell

Title: Shock Wave Structure in a Lattice Gas

Abstract: The motion and structure of shock and expansion waves in a simple particle system, a lattice gas and cellular automaton, are determined in an exact computation. Shock wave solutions, also exact, of a continuum description, a model Boltzmann equation, are compared with the lattice results. The comparison demonstrates that, as proved by Caprino et al, only when the lattice processes are stochastic is the model Boltzmann description accurate. In the strongest shock wave the velocity distribution function is the bimodal function proposed by Mott-Smith.

Date: April 21, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Mingjiu Ni, UCLA

Title: Development of Incompressible Solver for MHD with Low Magnetic Reynolds Number

Abstract: A general second-order projection method is developed for the calculation of incompressible Navier-Stokes equation with Lorentz force included. The relationship between classical second-order projection methods and SIMPLE-type methods has been discussed. SIMPLE-type methods have been proven to own second-order temporal accuracy for unsteady flows. A bridge between SIMPLE-type methods and projection methods has been built up. A consistent and conservative scheme has been designed to solve electrical potential equation for low magnetic Reynolds number and high-Hartmann number MHD flows on a finite-volume structured collocated grid. In this grid, velocity u, pressure p, and electrical potential are located in the grid center, while current flux is located on the cell face. We will show that both "conservative" and "consistent" are very important properties of the scheme to get the accurate results for high Hartmann number MHD with a very nonuniform mesh employed to resolve the Hartmann layer and side layers of Hunt's conductive wall and Shercliff's insulator wall.

Date: April 7, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Sangeeta Gupta

Title: Linear and nonlinear evolution of pressure driven MHD Instabilities

Abstract: Ideal Magnetohydrodynamics (MHD) is very successful for defining the equilibrium and stable operational regimes for magnetic fusion devices like Tokamak and Stellarator, which confine high temperature plasmas using magnetic field configurations. Ideal MHD also provide the criterion for maximum b parameter (defined as the ratio of plasma kinetic pressure to the magnetic field pressure), which governs the energy economics of a fusion device. This limit, derived from marginal stability condition of pressure driven instabilities, is known as Suydam criterion in cylindrical geometry or Mercier criterion in toroidal geometry. In last decade, innovative methods has facilitated operations of some fusion devices near or even above their b limit without showing any degradation in confined plasma. This talk will address the issue of why violation of stability criterion does not limit the fusion plasma operation. Linear and nonlinear analysis of pressure driven ideal MHD instabilities, showing their benign character well above (> twice) the stability criterion, will be presented. The instability growth rate is calculated analytically and verified numerically. The nonlinear equations are solved numerically and their final nonlinear state comprises modified magnetic field with current sheets. The modified magnetic field supports steep pressure gradient in the current sheet region, which is contrary to usual pressure flattening saturation mechanism.

Date: March 17, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Bertil Gustafsson, Uppsala University, CTR Senior Fellow

Title: Compact difference methods for scalar transport problems

Abstract: We consider scalar transport problems for incompressible flow. We shall describe two classes of compact approximations that are norm conserving and unconditionally stable. The first one is the well known box scheme. If u and v do not change sign within the computational domain, it requires no more work per time-step than an explicit scheme. To overcome the restriction on the velocity, we suggest a modified method called the shifted box scheme, which has the same stability properties as the original scheme, without requiring much extra work. It is also easily adapted to non-uniform grids. This part of the talk is based on joint work with Yaser Khalighi. The other type of method uses compact Pade' type fourth order accurate difference operators. It is an implicit one-step scheme, and it is fourth order accurate also in time. This is preliminary work, but we will demonstrate for some simple 1-D model problems, that it is an effective scheme compared to standard second order ones.

Date: January 27, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Tom Lundgren, Professor Emeritus, University of Minnesota and Senior Fellow, CTR

Title: Asymptotic Analysis of the Constant Pressure Turbulent Boundary Layer

Abstract: The Navier-Stokes equations are expanded in a asymptotic power series in a small parameter which is determined as a function of Reynolds number by an asymptotic matching procedure. The present matched asymptotic expansion analysis differs form the more traditional approach by employing the unsteady Navier-Stokes equations instead of the unclosed Reynolds-averaged equations. It is therefore not necessary to expand the Reynolds stress separately in the small parameter. The analysis is simpler and requires fewer assumptions. The main result is an instantaneous log-law in the overlap region.

Date: January 13, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Prof. Snezhana Abarzhi

Title: Turbulence and turbulent mixing in accelerated flows

Abstract: Whenever fluids of different densities are accelerated against the density gradient, we observe the development of the Rayleigh-Taylor instability (RTI). The instability causes with time extensive interfacial mixing of the fluids. The mixing plays a key role in preventing the formation of hot spot in inertial confinement fusion, providing proper conditions for the synthesis of heavy mass elements in supernovae, controlling the non-equilibrium heat transfer induced by ultra-fast laser pulses in solids, mantle-lithosphere tectonics, oil production, and many other phenomena. We present phenomenological model describing the Rayleigh-Taylor turbulent mixing, which accounts for the multi-scale character of the interface dynamics as well as the effects of turbulent diffusion and stratification. In the accelerated mixing flow, the rate of momentum loss is the flow invariant, whereas the energy dissipation rate is not, and the fundamental invariant, scaling and spectral properties of the accelerated flow differ from those of the classical Kolmogorov turbulence. We account for the random character of the mixing process and show that the ratio between the rates of momentum loss and gain is statistically steady and is the flow characteristics, for either sustained or time-dependent accelerations. Possible applications of the model are discussed.

Date: January 6, 2006

Time: 4:00pm

Location: CTR Conference Room

Speaker: Dr. Piotr Boronski

Title: (Magneto-) Hydrodynamics in a Finite Cylinder

Abstract: This work is motivated by the recent international effort to create an experimentally self-sustained dynamo. The dynamo effect, whose existence was proposed by Larmor at the beginning of the 20th century, is believed to be the explanation for the magnetic field of Earth and other celestial bodies due to the flow of a conducting fluid. In order to numerically study the von Kármán flow, which models the configuration of the dynamo experiment implemented at Cadarache, we have developed a new numerical approach for solving the equations of magnetohydrodynamic equations in potential formulation in a finite cylindrical geometry. The poloidal-toroidal decomposition has been used to ensure the solenoidal character of the velocity and magnetic fields. We use the influence matrix technique to impose the boundary conditions for the velocity and the continuity between the internal and external magnetic fields. The computational power of the code, which is the result of the MPI-based parallelization, enabled us to investigate two problems concerning turbulence in cylindrical geometry: axisymmetric turbulence and a recently discovered turbulent bifurcation.