Fulvio Stella

Onset of natural convection in a cube

The problem of transient natural convection in a cube-shaped cavity is investigated ex- perimentally and numerically. The motion is driven by a sudden temperature difference ap- plied to two opposite side walls of the vessel. The experiments are performed at a Rayleigh number of 1:66 10 5 and a Prandtl number of 1109, inside a 5 5 5cm 3 cavity made of plexiglas, with two isothermal copper walls kept at a prescribed temperature. Numeri- cal simulation has been performed using a nite difference vorticity-velocity model of the Navier-Stokes equation with the Boussinesq approximation. The theoretical predictions are found to be in a good agreement with the experimental results.

Melting of a pure metal on a vertical wall : Numerical simulation

Melting of pure gallium in a bidimensional rectangular cavity with aspect ratio 1.4 is presented. The paper is focused on pattern formation in the fluid phase during the process of melting. The formation of a multiple cells structure has been found during the first stage of the transient, while a merging of the small recirculating cells into larger ones is observed during the following stage of the transient, generating a quite complex evolution of the flow pattern. To ensure the validity of the flow pattern evolution found, a deep meshsensitivity analysis has beenperformed and repeated during the different phases of flow evolution. Three different meshes have been tested, the finest of those, assuming as unity the shorter vertical dimension, with a Delta x = 1/640 and a Delta y = 1/320. To optimize computational resources requests, an optimal solution strategy has been adopted, using different meshes during the various phases of the transient, depending on the size of the melted zone. Because of the large request of CPU time only one test case is presented and compared with available results at Ra = 7 x 10 5 , Pr = 0.0216, and Ste = 4.6 x 10 - 2. Results show that only the use of a fine mesh allows the observation of the multicellular flow structure described.

Rayleigh-Benard convection in limited domains. Part 1: Oscillatory flow

Transition from the steady state to an oscillatory regime in three-dimensional limited aspect ratio boxes, filled with an incompressible fluid and heated from below, has been examined by direct numerical simulation. Two different physical problems have been considered: the first is related to a domain 3.5 x 1 x 2.1 filled with water at 70 degrees C (Prandtl number 2.5); the second considers a domain 2.4 x 1 x 1.2 filled with water at 33 degrees C (Prandtl number 5). The Rayleigh number has been varied from 20,000 to 80,000. A new procedure based on a statistical approach for evaluation of the critical Rayleigh number for transition from steady state to oscillatory flow (RaII) has been introduced in order to reduce numerical errors and estimate the error bars. A systematic study for the determination of RaII has been conducted as a function of the geometries considered and the different flow structures observed.

RAYLEIGH-BENARD CONVECTION IN LIMITED DOMAINS: PART 2 - TRANSITION TO CHAOS

Transitions to chaos in three-dimensional limited aspect ratio boxes, filled with an incompressible fluid and heated from below, have been examined by direct numerical simulation as the Rayleigh number is varied. Two different problems have been considered: the first is related to a domain 3.5 x 1 x 2.1 filled with water at 70 degrees C (Prandtl number 2.5); the second is related to a domain 2.4 x 1 x 1.2 filled with water at 33 degrees C (Prandtl number 5). The Rayleigh number has been varied from 45,000 up to 300,000. Three different bifurcation sequences have been detected, but only two individual mechanisms for the transition to the nonperiodic motion have been identified: the subharmonic cascade and the quasi-periodicity with three incommensurate frequencies. Effects of different regimes and flow structures on heat transfer have been discussed.

A NUMERICAL STUDY OF SOLIDIFICATION IN THE PRESENCE OF A FREE SURFACE UNDER MICROGRAVITY CONDITIONS

A numerical study of the relative importance of Marangoni effects under microgravity conditions is presented. The mathematical formulation adopted is based on the enthalpy porosity method. One of the advantages of the fixed grid method is that a unique set of equations and boundary conditions is used for the whole domain, including both solid and liquid phases. The governing equations written in a vorticity-velocity formulation are discretized using a finite volume technique on a staggered grid. A fully implicit method has been adopted for the mass and momentum equations, while the temperature field is solved separately in order to evaluate the variation in the local liquid mass fraction. The resulting algebraic system of equations is solved using a preconditioned BI-CGStab method. Numerical results modelling the free surface, including the effects on it of Marangoni convection, are presented. The influence of the presence of argon in the gap above the free surface is investigated. During the numerical simulations presented in this paper 161 2 41 and 641 2 161 uniform meshes on the whole computational domain for values of Marangoni number ( Ma ) up to 16,120 and Rayleigh number ( Ra ) of 5 have been used.

A Comparison of Velocity-Vorticity and Stream Function-Vorticity Formulations for Pr=0

A comparison is made of solutions obtained by the velocity-vorticity and stream function-vorticity formulations of the governing equations for the case of a rigid-rigid cavity with Pr = 0. A uniform mesh of 41 × 161 was used in both formulations. The velocity-vorticity method predicts more accurate velocity components but at a higher computational cost.

Linearized Aeroelastic Gust Response Analysis of a Launch Vehicle

Amethodology for aeroelastic gust response of launch vehicles inflight is developedbyusing apreviously validated aeroelastic stability analysis. The effects on the aeroelastic vibrations of a launch vehicle encountering a wind gust while operating at a particular supersonic flight condition are determined. A linearized dynamic aeroelastic analysis of the launch vehicles is performed using the previously developed procedure, but this time in supersonic flow. Then, the pressure on the moving launcher surface resulting from the combined motion induced by each elastic mode is obtained from the solution of the Euler equation. These effects are superimposed to determine the combined aerodynamic effects of all themodes. Thus, a generalized aerodynamic forcematrix of the aerodynamic loads caused by themotion of the launch vehicles (rigid body, aswell as elastic deformations) and the effect of a gust encountered in the flight is constructed. Finally, a generalized (iterative) eigenvalue analysis is performed to evaluate the aeroelastic stability of the linearizedmodel of the launch vehicles, operating at the prescribedflowconditions,when it encounters a gust. This approach, along with the use the matched-filter theory on the resulting frequency response function, allows one to evaluate the effects of the worst-case excitation on the launch vehicle’s aeroelastic response. The methodology has been applied to predict successfully the aeroelastic stability of LYRA launch vehicles when it flies through transverse gusts.

Sensitivity Analysis for the Dynamic Aeroelasticity of a Launch Vehicle

launcherintermsofthe firstnonzeronaturalfrequenciesandmodesofvibrationiscarriedout.Moreover,areducedorder model for the unsteady transonic aerodynamics is obtained, performing several prescribed modal transient boundary conditions by laminar-based computational fluid dynamics. Thus, a modal input/output system identification for the aerodynamics, performed in the frequency domain, allows one to identify the linearized unsteady aerodynamic operator in the neighborhood of the specific transonic flight condition. Both the structural andaerodynamic modelsare finally employedin the aeroelastic coupledmodel given bythe generalized Lagrangian equations of motion. An eigenanalysis, in terms of aeroelastic-system poles and complex eigenvectors on the linearized model, is performed to check the local dynamic stability of the launch vehicle. Finally, the proposed approach also allows one to give an evaluation of the uncertainty in the obtained stability scenario in terms of perturbing flight parameters like angle of attack, Mach number, flight speed, and air density.

Numerical Simulation of Re-Entry Flow: Heat Flux Evaluation

A method for the study of the flow field around a re-entry vehicle is discussed. Flow field at re-entry is characterized by high energy with the presence of dissociative effects. To take into account such dissociative effects, a simplified model based on the use of a modified specific heat has been adopted and discussed. A numerical method has been validated by means of a comparison with available data of Riley and De Jarnette [1]. Numerical results are also presented for a YES-2 re-entry capsule in the correspondence of three of the most critical flight conditions.

Parallel polynomial preconditioners for the analysis of chaotic flows in Rayleigh - Benard convection

In recent years, the development of robust fully implicit solvers allowed the study of complex unsteady flows and the analysis of the transition to chaotic and fully developed turbulent regime by means of direct numerical simulations. However, it is well known that implicit methods require high computational resources, in terms of memory and CPU time, especially when a chaotic flow is considered. In this case, a very fine computational grid must be used, in order to capture all the significant scales of the flow, from the largest (related to the dimensions of the geometry) to the smallest (determined by the viscosity). Therefore, the use of a multiprocessor machine is strongly recommended. In this work a parallel fully implicit flow solver for incompressible Navier-Stokes equations, written in terms of vorticity and velocity, has been used for the study of Rayleigh - Benard convection in chaotic regime. The Bi-CGSTAB algorithm has been adopted for the resolution of the linear systems arising from discretization. Parallel polynomial preconditioners are considered; they are compared with the classical ILU preconditioner and with its parallel implementation (B-ILU).