Characterization of Unsteadiness in an Overexpanded Planar Nozzle

Abstract

The sea-level startup of rocket engines is characterized by the nozzle experiencing a high degree of overexpansion and consequent internal flow separation with a strong unsteady shock-wave/boundary-layer interaction. In this work, a three-dimensional planar overexpanded nozzle, characterized by an internal flow separation, has been simulated by means of the delayed detached-eddy simulation (DDES) method. The unsteady pressure signals have been analyzed by the wavelet decomposition to characterize their spectral content. The results indicate that the DDES approach is able to capture the shock oscillations, and the computed characteristic frequency is close to the ones available from literature for the same test case. The fundamental frequency computed in this work is lower than the one predicted by the model of the longitudinal acoustic frequency. The self-sustained oscillation is driven by a pressure imbalance between the pressure level downstream of the recompression shock and the ambient. Different nozzle pressure ratios (NPRs) have been simulated, all showing the same qualitative behavior, even if the test case with the highest NPR seems to be heavily influenced by the presence of a large region with reversed flow.

Flow dynamics and wall-pressure signatures in a high-Reynolds-number overexpanded nozzle with free shock separation

“…The code is written in Fortran 90 and uses domain decomposition while fully exploiting the message-passing interface paradigm for the parallelism. The accuracy and reliability of the DDES flow solver were addressed in recent SWBLI studies (Martelli et al 2017(Martelli et al , 2019Memmolo et al 2018).…”

“…In fact, in the DES approach, attached boundary layers are treated in RANS mode (thus lowering the computational requirements), while the most energetic turbulent scales of the separated shear layers and turbulent recirculating zones are treated directly in LES mode. As shown by a series of recent studies (Martelli et al 2017(Martelli et al , 2019Memmolo, Bernardini & Pirozzoli 2018), the DES method has proven to be a powerful tool for investigating the flow physics of SWBLI involving massive flow separation where the dynamics is mainly characterized by the dominance of downstream effects (Clemens & Narayanaswamy 2014;Estruch-Samper & Chandola 2018). However, very few DES simulations of separated rocket nozzle flows are discussed in the open literature.…”

Numerical Analysis of Side-loads Reduction in a Sub-scale Dual-bell Rocket Nozzle

“…This objective is achieved by defining the length-scale d in (3) as where d w is the distance from the nearest wall, is the subgrid length-scale that controls the wavelengths resolved in LES mode and C DES is a calibration constant set equal to 0.65 in the original model. On the basis of previous calibration studies performed on DDES of a sub-scale rocket nozzle Martelli et al (2019Martelli et al ( , 2020 the constant C DES has been set equal to 0.20 and the function f d here employed is (1) t + ( u j )…”

“…The simulations have been performed by means of an in-house, compressible, finite-volume, structured solver, widely employed in the past to investigate the dynamics of turbulent, separated flows in transonic and supersonic rocket nozzles, involving complex shockwaves/boundary-layer interactions (Martelli et al 2017(Martelli et al , 2019(Martelli et al , 2020Memmolo et al 2018). In the flow regions away from the shock, the spatial discretization consists of a centered, second-order, energy consistent scheme, that makes the numerical method extremely robust without the addition of numerical dissipation (Pirozzoli 2011).…”

Jet resonance in truncated ideally contoured nozzles

“…While this kind of nozzle flow configuration has been widely studied with Reynolds-averaged Navier-Stokes (RANS) simulations, it is worth recalling that, until very recently, only very few unsteady simulations with hybrid approaches, similar to the one adopted in the present study, have been attempted. Such unsteady simulations have been carried out in the case of planar nozzle configuration (Martelli et al 2019) or truncated ideally contoured nozzles (Deck 2009;Shams et al 2013). The first hybrid simulations of TIC nozzle flow have more recently been reported in Goncalves, Lehnasch & Herpe (2017) and then in Martelli et al (2020).…”