Numerical simulation of two-dimensional flows with different approximation schemes for shock-wave capturing

Nicholas Dicati Pereira da Silva¹; Luciano Kiyoshi Araki¹

¹ Universidade Federal do Paraná

doi:10.20906/CPS/CILAMCE2015-0565

Resumo

Shock waves can occur inside nozzle rocket engines by different causes: relatively higher ambient pressure, nozzle geometric aspects, or even small superficial imperfections in the divergent region of the nozzle. Even if a perfect rocket nozzle could be manufactured, shock waves would appear during the transient regime, corresponding to the turning-on time interval of the rocket engine. Numerically, shock waves show a series of difficulties to be captured, since high order approximation schemes, such as the Central Differencing Scheme (CDS), can present wiggles and other numerical oscillation phenomena and low order approximation schemes, such as the Upstream Differencing Scheme (UDS), present false or numerical diffusion. In order to guarantee better numerical results for such problems, Total Variation Diminishing (TVD) schemes were developed, combining aspects of both UDS and CDS schemes. In this work, TVD, UDS and CDS schemes are compared for a two-dimensional steady flow in a rocket engine. Flow with constant properties is considered in the numerical code, implemented using the Finite Volume Method (FVM), non-starred grids, SIMPLEC pressure-velocity coupling and a suitable methodology for all speed flows. Numerical verification and validation were employed in order to certificate both the solution and the model. Richardson Repeated Extrapolations (RRE) technique were also employed as post-processing, in order to obtain more accurate numerical results. At the end of the study we conclude that (1) the model is valid and the UDS solution is verified, (2) UDS with aid of RRE had the same error magnitude as accurate schemes with shorter time, (3) this TVD procedure could not avoid completely the oscillations and (4) other analysis are needed in other improve the RRE performance with shocks.

Palavras-chave: TVD; shock-wave; Repeated Richardson Extrapolations