Abstract: Numerical modeling of fluid flows, whether compressible or incompressible, laminar or turbulent presents a considerable contribution in the scientific and industrial fields. However, the development of an approximate model of a supersonic flow requires the introduction of specific and more precise techniques and methods. For this purpose, the object of this paper is modeling a supersonic flow of inviscid fluid around a dihedral airfoil. Based on the thin airfoils theory and the non-dimensional stationary Steichen equation of a two-dimensional supersonic flow in isentropic evolution, we obtained a solution for the downstream velocity potential of the oblique shock at the second order of relative thickness that characterizes a perturbation parameter. This result has been dealt with by the asymptotic analysis and characteristics method. In order to validate our model, the results are discussed in comparison with theoretical and experimental results. Indeed, firstly, the comparison of the results of our model has shown that they are quantitatively acceptable compared to the existing theoretical results. Finally, an experimental study was conducted using the AF300 supersonic wind tunnel. In this experiment, we have considered the incident upstream Mach number over a symmetrical dihedral airfoil wing. The comparison of the different Mach number downstream results of our model with those of the existing theoretical data (relative margin between 0.07% and 4%) and with experimental results (concordance for a deflection angle between 1° and 11°) support the validation of our model with accuracy.
Abstract: The complex oblique shock phenomenon can be simply assumed as a normal shock at the constant area section to simulate a sharp pressure increase and velocity decrease in 1-D thermodynamic models. The assumed normal shock location is one of the greatest sources of error in ejector thermodynamic models. Most researchers consider an arbitrary location without justifying it. Our study compares the effect of normal shock place on ejector dimensions in 1-D models. To this aim, two different ejector experimental test benches, a constant area-mixing ejector (CAM) and a constant pressure-mixing (CPM) are considered, with different known geometries, operating conditions and working fluids (R245fa, R141b). In the first step, in order to evaluate the real value of the efficiencies in the different ejector parts and critical back pressure, a CFD model was built and validated by experimental data for two types of ejectors. These reference data are then used as input to the 1D model to calculate the lengths and the diameters of the ejectors. Afterwards, the design output geometry calculated by the 1D model is compared directly with the corresponding experimental geometry. It was found that there is a good agreement between the ejector dimensions obtained by the 1D model, for both CAM and CPM, with experimental ejector data. Furthermore, it is shown that normal shock place affects only the constant area length as it is proven that the inlet normal shock assumption results in more accurate length. Taking into account previous 1D models, the results suggest the use of the assumed normal shock location at the inlet of the constant area duct to design the supersonic ejectors.
Abstract: There is an evident trend to elevate pressure ratio of a
single stage of a turbo compressors - axial compressors in particular.
Whilst there was an opinion recently that a pressure ratio 1,9 was a
reasonable limit, later appeared information on successful modeling
tested of stages with pressure ratio up to 2,8. The authors recon that
lack of information on high pressure stages makes actual a study of
rational choice of design parameters before high supersonic flow
problems solving. The computer program of an engineering type was
developed. Below is presented a sample of its application to study
possible parameters of the impeller of the stage with pressure ratio
3,0. Influence of two main design parameters on expected efficiency,
periphery blade speed and flow structure is demonstrated. The results
had lead to choose a variant for further analysis and improvement by
CFD methods.
Abstract: In this work, we try to find the best setting
of Computational Fluid Dynamic solver available for the problems in
the field of supersonic internal flows. We used the supersonic air-toair
ejector to represent the typical problem in focus. There are
multiple oblique shock waves, shear layers, boundary layers
and normal shock interacting in the supersonic ejector making this
device typical in field of supersonic inner flows. Modeling of shocks
in general is demanding on the physical model of fluid, because
ordinary conservation equation does not conform to real conditions in
the near-shock region as found in many works. From these reasons,
we decided to take special care about solver setting in this article by
means of experimental approach of color Schlieren pictures and
pneumatic measurement. Fast pressure transducers were used to
measure unsteady static pressure in regimes with normal shock in
mixing chamber. Physical behavior of ejector in several regimes is
discussed. Best choice of eddy-viscosity setting is discussed on the
theoretical base. The final verification of the k-ω SST is done on the
base of comparison between experiment and numerical results.