Bernardo Favini

A Second Order Godunov-Type Scheme for Naval Hydrodynamics

A second order Godunov-type scheme for the simulation of free surface turbulent incompressible flows is presented. The scheme is applied to the RANSE written in pseudo-compressible formulation, whose asymptotic solution is computed by means of a Runge-Kutta time integration coupled with a multigrid algorithm. Examples of application of this scheme to the computation of the flow in a driven-cavity and past a surface-piercing hull are reported and, for the latter, compared with towing tank experiments carried out at INSEAN. Convergence properties when halving the grid size are also shown.

Fractal modelling of turbulent combustion

In a previous paper we proposed a new model for turbulent flows, called the fractal model (FM), which is applicable both to RANS and LES formulations. Here, the model is extended to the reactive case with the goal of simulating turbulent flames, both premixed and non-premixed. FM is a subgrid model that describes the physics of the small scales of turbulence building on the phenomenological concept of vortex cascade and on fractal theory. The physics of the small scales is summarized by a turbulent ‘viscosity’ μ t , to be added to the molecular one. μ t is zero where the flow is laminar and, in particular, goes to zero at solid walls. The fundamental assumption in treating combustion in this work is that chemical reactions take place only at the dissipative scales of turbulence, i.e. near the so-called ‘fine structures’ (the eddy dissipation concept). FM predicts the growth of dissipative scales due to heat release; therefore, it enables a local DNS in the hot regions of the flow where the dissipative scale may grow up to the cell dimension. FM can also estimate the volume fraction γ* occupied by the ‘fine structures’; this quantity is critical for modelling the reaction rate, and therefore the source terms in the energy and species equations. FM can also estimate the local surface of the reactive ‘fine structures’, that is, the local flame front area. It also takes into account, although in approximate manner, the formation of islands of unburnt mixture. In this paper, the model (in the isotropic formulation (IFM)) is used in conjunction with a time-dependent LES (but with the limitations of an isotropic model) approach and is validated through a three-dimensional axisymmetric diffusion flame studied experimentally by Correa and Gulati and numerically by many researchers. The time-dependent results obtained are in good agreement with the experiments. Moreover, the IFM solution offers a possible explanation for the stabilization process of this flame, which undergoes local stretching of the order of 46 000 s−1.

Fractal modelling of turbulent mixing

The aim of this work is to propose a new model for turbulent flows, called the fractal model (FM), applicable both in a Reynolds averaged Navier–Stokes (RANS) and a large-eddy simulation (LES) formulation, with the ultimate goal of applying it to simulate turbulent combustion irrelevant of its mode (premixed or non-premixed). The model is able to turn itself off in the laminar zones of the flow, and in particular near walls. It is based on the fractal theory. It describes the physics of the smaller spatial scales and therefore represents a small-scales model. FM describes the physics of the small scales of turbulence based on the phenomenological concept of vortex cascade and on the self-similar behaviour of turbulence in the inertial range. Such a model is used in each cell of a numerical calculation. A characteristic length Δ is associated to each cell, and the local energy u 3 Δ/Δ is distributed over a certain number of eddies, which depends on the local Reynolds number Re Δ. Each vortex of the cascade...

Ignition Transient Pressure Oscillations in Solid Rocket Motors

In the static fire test of Zefiro 16, a solid rocket motor with a finocyl region in the rear, pressure oscillations have been detected during the first phase of the ignition transient. By analysing the results of the numerical simulations performed with an unsteady quasi-one-dimensional model, called SPIT, a possible explanation about the origin of these pressure fluctuations has been proposed. By means of the same simulation model, a parametric analysis of the motor behaviour, by changing some of its design parameters, has been also performed. This analysis seems to confirm the hypothesis about the concurring events that generate the pressure oscillations. In fact, on the contrary of what it could be expected, some design modification have no significant effects on these fluctuations. On the contrary, a simple solution, with a low impact on both design and operative procedures, is proposed and numerically tested for eliminating the pressure oscillations. The internal flow field of the motor has been simulated also with an inviscid axisymmetric model, called ALIAS, in order to validate the previous quasi-1D results. The results obtained by these two simulation models are in good agreement and, notwithstanding the increasing complexity of a multidimensional flowfield analysis, the same phenomena evidenced by the quasi-1D analysis can be qualitatively recognized in the axisymmetric numerical simulations.

SRM Internal Ballistic Numerical Simulation by SPINBALL Model

In the design and development of solid propellant rocket motors (SRMs), the use of numerical tools able to simulate, predict and reconstruct the behavior of a given motor, in all its operative conditions, is particularly important in order to decrease all the planning times and costs. This paper is devoted to propose and present an approach to the numerical simulation of SRM internal ballistics, during the entire combustion time, by means of dierent own made models. The core of this procedure is represented by the SPINBALL model and numerical code. SPINBALL considers a Q1D unsteady modeling of the SRM internal ballistics, with many dierent sub-models able to represents all the driving phenomena that characterize the bore chamber oweld conditions during the SRM timelife, from the motor start-up to burn-out. In particular, the grain burning surface evolution is accomplished by means of a 3D numerical grain regression model, named GREG. This model is based on a full matrix level set approach, on rectangular or cylindrical structured grids. GREG gives to the SPINBALL gasdynamical model the evolution in time of the port area, wet perimeter and burn perimeter along the motor axis and, in case, within the submergence zone. The nal objective is, hence, to develop an analysis/simulation capability of SRM internal ballistics, for the entire combustion time, with simplied physical models, in order to reduce the computational cost required, but ensuring, in the meanwhile, an accuracy of the simulation greater than the one usually given by 0D quasi steady models, during quasi steady state and tail o. Notwithstanding, a 0D quasi steady model of SRM internal ballistic has been developed to reconstruct the experimental data coming from static ring tests (SFTs), in order to evaluate non-ideal behaviour parameters, like combustion eciency, hump law and nozzle eciency and the nozzle throat area evolution. These parameters are used in the SPINBALL model as inputs. The results of the internal ballistics numerical simulation, from motor start-up to burnout yielded with the SPINBALL model, will be shown for Zero23, second solid rocket motor stage developed in the ESA (European Space Agency) project of the new European small launcher Vega.

RANS simulations of a junction flow

The ERCOFTAC junction flow is numerically simulated with both a structured and an unstructured RANS solver for incompressible flows. The structured code adopts a finite volume, cell-centered formulation while the unstructured code uses residual distribution schemes and a vertex centered storage of the unknowns. Two differential eddy viscosity models, based on local quantities, are considered in the computations: the one-equation Spalart–Allmaras model and the two equations model proposed by Lam and Bremhorst. The grid dependence of the numerical solutions is evaluated by means of a convergence analysis based on computation of the GCI and a code-to-code comparison. The numerical results provided by both turbulence models are compared with the experimental measurements of the pressure and velocity fields.

Internal Ballistics Simulation of a NAWC Tactical SRM

In the design and development of solid propellant rocket motors, the use of numerical tools able to predict the behavior of a given motor is particularly important in order to decrease the planning times and costs. This paper is devoted to present the results of the internal ballistics numerical simulation of the NAWC tactical motor n. 6, from ignition to burn-out, by means of a quasi-one-dimensional unsteady numerical simulation model, SPINBALL, coupled with a three-dimensional grain burnback model, GREG. In particular, the attention is focused on the effects on the SRM behavior of the erosive burning, total pressure drops and the cause of the pressure overpeak occurring during the last part of the ignition transient. The final objective is to develop an analysis/simulation capability of SRM internal ballistics for the entire combustion time with simplified physical models, in order to have reduced the computational costs, but ensuring an accuracy greater than the one usually given by zero-dimensional models. The results of the simulations indicate a very good agreement with the experimental data, as no attempt of submodels calibration is made, enforcing the ability of the proposed approach to predict the SRMs internal flow-field conditions. The numerical simulations show that NAWC n. 6 internal ballistics is completely led by the erosive burning, that is the root cause of the pressure peak occurring immediately after the SRM start-up.

Numerical simulations of acoustic resonance of Solid Rocket Motor

Low amplitude but sustained pressure and thrust oscillations can characterize the quasisteady condition of solid rocket motor; notwithstanding they are not threatening for motor life, coupling to the structural modes, they can damage the payload. These oscillations are due to uid dynamics instabilities and acoustic coupling. To correctly predict the oscillatory level, a numerical model has to include ad hoc model for: two-phase

On the numerical integration of multi-dimensional, initial boundary value problems for the Euler equations in quasi-linear form

A matricial formalism to solve multi-dimensional initial boundary values problems for hyperbolic equations written in quasi-linear based on the λ scheme approach is presented. The derivation is carried out for nonorthogonal, moving systems of curvilinear coordinates. A uniform treatment of the integration at the boundaries, when the boundary conditions can be expressed in terms of combinations of time or space derivatives of the primitive variables, is also presented. The methodology is validated against a two-dimensional test case, the supercritical flow through the Hobson cascade n.2, and in three-dimensional test cases such as the supersonic flow about a sphere and the flow through a plug nozzle.

About the numerical modelling of multidimensional unsteady compressible flow

Abstract The paper concerns the analysis of finite difference methods for describing the unsteady motion of a compressible inviscid fluid with emphasis for the modelling of the wave propagation phenomena. The main questions addressed are how the multidimensional nature of the flow is retained by the numerical process and how the treatment of boundaries is affected by the choice of the numerical formulations.