Renato Paciorri

Numerical analysis of three-dimensional flow of supercritical fluid in asymmetrically heated channels

The knowledge of the flow behavior inside asymmetrically heated channels is of great importance to improve design and performance of regeneratively cooled rocket engines. The modeling of the coolant flow is a challenging task because of its particular features, such as the high wall temperature gradient, the high Reynolds number, the three-dimensional geometry of the passages, and the possible supercritical conditions of the fluid. In the present work, a numerical approach to study the turbulent flow of supercritical fluids is presented and validated by comparison with experimental data. Solutions of the supercritical nitrogen flowfield in an asymmetrically heated three-dimensional channel with a high-aspect ratio (channel height-to-width ratio) are presented and discussed. Emphasis is given to the analysis of the peculiar behavior and cooling performance of the supercritical fluid as compared with perfect gas. In particular, a long channel is considered, such that entrance effects are negligible, to analyze in detail wall heat-flux evolution throughout the channel.

Compressibility Correction for the Spalart-Allmaras Model in Free-Shear Flows

A correction of the Spalart-Allmaras turbulence model to account for the compressibility effects in mixing-layer flows is presented. Unlike other corrections proposed for the K-e model, the present correction does not need the knowledge of the turbulent Mach number and, therefore, can be applied to those turbulence models, like the Spalart-Allmaras one, which do not integrate directly the turbulent kinetic energy equation. To explore the validity of the proposed correction, four mixing-layer flows and four supersonic backward-facing step flows, covering a wide range of flow conditions, were selected and computed using both the standard and the corrected Spalart-Allmaras model. The analysis of the numerical results and their comparison with the experimental data show that the proposed correction produces a significant improvement of the numerical predictions.

Exploring the Validity of the Spalart-Allmaras Turbulence Model for Hypersonic Flows

The Spalart‐ Allmaras turbulence model has been implemented in a e nite volume code using an implicit e nite difference technique. First, the implementation was validated on e at plate turbulent boundary-layer e ows under various e ow conditions. Then, three high-speed e ow applications characterized by different turbulent phenomena were considered to investigate the behavior of the Spalart‐ Allmaras model in the hypersonicregime, namely, a hypersonicwind-tunnel e ow, a Mach 5 e owovera hollow-cylinder e are, and aMach 6.8 e ow overa hyperboloid e are. Numerical results were found in excellent agreement with experimental data for the attached nozzle e ow and the hyperboloid e ow involving laminar separation and turbulent reattachment. For the hollow-cylinder e are cone guration,whichinvolvesturbulentseparation,themagnitudesofsurfacepressureandofheattransferpeakswerecorrectly predicted,whereastheirpositionswereslightly incorrectdueto theunderprediction of theseparationbubble size. Nomenclature bdest = destruction term, m 2 s i2 bprod = production term, m 2 s i2 btrip = trip term, m 2 s i2

Shock interaction computations on unstructured, two-dimensional grids using a shock-fitting technique

A new shock-fitting technique has been recently proposed and implemented by the authors in conjunction with an unstructured shock-capturing solver. In the present paper, the attention is addressed towards the computation of shock-shock and shock-wall interactions by means of this novel computational technique.

Convergence Analysis of Shock-Capturing and Shock-Fitting Solutions on Unstructured Grids

A new shock-fitting technique for unstructured two- and three-dimensional meshes has been recently proposed and developed by the authors. In the present paper, both global and local a posteriori grid-convergence analysis is used to quantitatively measure the discretization error and order of convergence of the numerical solutions obtained using this new unstructured shock-fitting technique. Specifically, the analysis has considered the numerical solutions of two different flows characterized by the presence of strong shocks: a transonic source flow and an hypersonic flow past a circular cylinder. It is shown that the shock-fitting technique allows to compute numerical solutions that converge, both pointwise and in a global sense, with an observed order of accuracy that is very close to the design order of the spatial discretization scheme and with very small discretization errors.

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.

Three Dimensional Features of Clustered Plug Nozzle Flows

The plug nozzle is one of the concepts proposed to improve the overall performance of large liquid rocket engines for launcher first stages. One of the aspects to be investigated is the three dimensional flow field generated by partitioning of the primary nozzle in modules. Three configurations with different size of the gap between two adjacent primary nozzles are selected and numerically simulated. Specific three-dimensional flow structures that take place on the plug are identified comparing the numerical solutions. The relationship between these structure and the skin friction distribution along the plug surface is also investigated. Finally, a performance analysis of the selected test cases based on the thrust coefficient evaluation is presented.

An unstructured shock-fitting solver for hypersonic plasma flows in chemical non-equilibrium

Abstract A CFD solver, using Residual Distribution Schemes on unstructured grids, has been extended to deal with inviscid chemical non-equilibrium flows. The conservative equations have been coupled with a kinetic model for argon plasma which includes the argon metastable state as independent species, taking into account electron–atom and atom–atom processes. Results in the case of an hypersonic flow around an infinite cylinder, obtained by using both shock-capturing and shock-fitting approaches, show higher accuracy of the shock-fitting approach.

A mass-matrix formulation of unsteady fluctuation splitting schemes consistent with Roe’s parameter vector

A mass-matrix formulation of the fluctuation splitting schemes for solving compressible, unsteady flows is proposed. This formulation is consistent with the conservative linearisation based on parameter vector and allows to extend to unsteady flows the ‘invariance under similarity transformations’ property that had been shown to hold for the steady version of the schemes. Second-order time accuracy is achieved using a Petrov–Galerkin finite element interpretation of the fluctuation splitting schemes. The approach may however be readily applicable to all other time-accurate fluctuation splitting formulations that have been so far proposed in the literature. Applications of the proposed methodology to two- and three-dimensional, inviscid and viscous compressible flows are reported and discussed in the paper.

Transition between open and closed wake in 3D linear aerospike nozzles

Linear aerospike nozzles are envisaged as a possible device able to improve launcher engine performance. One of the most interesting properties of these nozzles is the possibility of a good integration with the vehicle. To improve the knowledge of the flow-field and performance of aerospike nozzles, they are studied numerically, with particular attention to the dierences between the basic two-dimensional nozzle, usually considered in the design phase, and the more realistic three-dimensional nozzle. The study considers dierent plug lengths and ambient pressures to assess the role of the linear plug side truncation on the base pressure behavior. Numerical tests are carried out at supersonic flight Mach number.