Chien Model Research Articles

Performance of turbulence models to predict supersonic boundary layer flows

Abstract The aim of this paper is to analyze the compressibility effect and to evaluate the performance of the turbulence models to predict the near-wall compressible flows. For this reason the k - e models without any compressibility correction and the k - ω 2 of the Wilcox-Rubesin model, derived for compressible flows are chosen. Another interest for this paper is the anisotropy phenomenon, which characterizes the wall-bounded flows. In order to seek the behaviour of this feature, the second order model is selected. The calculation has been performed for the supersonic flat-plate boundary layer. The results presented for this simple test case show that all the tested models gave approximately good results. The second order model and the Wilcox-Rubesin model perform better than the other first order models. The incompressible Chien and Launder-Sharma models underestimate the turbulent kinetic energy production. To improve the prediction of this quantity for compressible flows, we choose the Chien model and introduce the correction suggested by Nichols. The results present better agreement with the available data. Moreover, to emphasize the anisotropy given by the second order model, we use the compressibility corrections suggested by Vandromme. The comparison with the first calculations obtained by the non-modified model show some ameliorations in the results.

Comparison of turbulence models for the natural convection boundary layer along a heated vertical plate

With a numerical code for solving the boundary-layer equations, the performance of different turbulence models for the natural convection boundary layer for air along a heated vertical plate is tested. The algebraic Cebeci-Smith model, the standard k- ε model with wall functions for k and ε and different low-Reynolds number k- ε models are tested. The Cebeci-Smith model calculates a too low wall-heat transfer and turbulent viscosity. The standard k- ε model with wall functions gives a too high wall-heat transfer, but the velocity and temperature profiles agree reasonably with experiments. Accurate wall-heat transfer results require the use of low-Reynolds number k- ε models; the models of Lam and Bremhorst, Chien, and Jones and Launder perform best up to a Grashof number of 10 11. For larger Grashof numbers the Jones and Launder model is best. A sensitivity study shows that the wall-heat transfer with the standard k- ε model largely depends on the choice of the wall functions for k and ε. Replacing these wall functions by zero wall conditions for k and ε and adding the functions D and ƒ μ of the Chien model to the standard k- ε model gives a simple, but accurate low-Reynolds number k- ε model for the natural convection boundary layer.

Diagnosis Without Repair for Hybrid Fault Situations

For a new class of fault situations called hybrid fault situations, we consider the fault diagnosing capabilities of systems which for testing/monitoring purposes can be viewed as being composed of independent units. The classical Preparata, Metze, and Chien model (PMC model) is used to specify the various testing assignments among the units. Hybrid fault situations are described as explicitly bounded combinations of permanently and intermittently faulty units. This new concept of a hybrid fault situation includes as special cases the all permanent fault case and the unrestricted intermittent fault case which have both been previously considered with PMC models. A general characterization of the so-called connection assignment of a PMC model is established for a diagnosing capability which is referred to as hybrid fault diagnosability without repair. This diagnosing capability is compatible with the well-known permanent fault diagnosability without repair concept, and the quality of this diagnosing capability is shown to be correct, but sometimes an incomplete diagnosis where the incompleteness is solely a consequence of intermittently faulty units. The characterization for hybrid fault diagnosability without repair is seen to encompass as extreme cases the previously known special characterizations for permanent and unrestricted intermittent diagnosability without repair. Fundamental interrelationships are determined among parameter bounds used to describe the hybrid fault cases which can be diagnosed for a given PMC model.