A majority of the eddy viscosity models for supersonic turbulent flow are based on linear relationship between Reynolds stresses and mean strain rate. The validity of these models can be improved by introducing non-linearity in relation as RANS models offer advantages in terms of reduced turnaround times typical of industry applications. With these benefits, the present work utilizes quadratic constitutive relation (QCR) with Menter’s k omega SST model to characterize the flowfield of rectangular jets. The sensitivity of this model with QCR, weighted towards diffusion, dissipation, and a combination of both, is addressed. Viscous large eddy simulations (LES) with WALE subgrid scale models are employed for qualitative comparisons using a commercial solver. Massively parallel LES are enabled by the new in-house 1088-core computing cluster at the University of Cincinnati and are also used for benchmarking. The nearfield results are validated with available experimental data and show good agreement in both fidelities. Flow characteristics, including the shear layer profiles, Reynolds stresses, and turbulence kinetic energy (TKE) and its production are compared. LES reveal higher TKE production in the regions with highest Reynolds stresses. It is comparatively lower in QCR RANS. As a special case of TKE analysis in jets, a preliminary investigation of retropropulsion is outlined for rectangular nozzles for the first time. Improved flow behavior by implementation of a non-linear relationship between Reynolds stresses and mean strain rate is demonstrated.

The aim of this work is to highlight the significance of Fluid-Thermal-Structural Interaction (FTSI) as a diagnosis of existing designs, and as a means of preliminary investigation to ensure the feasibility of new designs before conducting experimental and field tests. The novelty of this work lies in the multi-physics simulations, which are, for the first time, performed on rectangular nozzles. An existing experimental supersonic rectangular converging/diverging nozzle geometry is considered for multi-physics 3D simulations. A design that has been improved by eliminating the sharp throat is further investigated to evaluate its structural integrity at design Nozzle Pressure Ratio (NPR 3.67) and off-design (NPR 4.5) conditions. Static structural analysis is performed by unidirectional coupling of pressure loads from steady 3D Computational Fluid Dynamics (CFD) and thermal loads from steady thermal conduction simulations, such that the simulations represent the experimental set up. Structural deformation in the existing design is far less than the boundary layer thickness, because the impact of Shock wave Boundary Layer Interaction (SBLI) is not as severe. FTSI demonstrates that the discharge coefficient of the improved design is 0.99, and its structural integrity remains intact at off-design conditions. This proves the feasibility of the improved design. Although FTSI influence is shown for a nozzle, the approach can be applied to any product design cycle, or as a prelude to building prototypes.

This work attempts to connect internal flow to the exit flow and supersonic jet mixing in rectangular nozzles with low to high aspect ratios (AR). A series of low and high aspect ratio rectangular nozzles (design Mach number = 1.5) with sharp throats are numerically investigated using steady state Reynolds-averaged Navier−Stokes (RANS) computational fluid dynamics (CFD) with k-omega shear stress transport (SST) turbulence model. The numerical shadowgraph reveals stronger shocks at low ARs which become weaker with increasing AR due to less flow turning at the throat. Stronger shocks cause more aggressive gradients in the boundary layer resulting in higher wall shear stresses at the throat for low ARs. The boundary layer becomes thick at low ARs creating more aerodynamic blockage. The boundary layer exiting the nozzle transforms into a shear layer and grows thicker in the high AR nozzle with a smaller potential core length. The variation in the boundary layer growth on the minor and major axis is explained and its growth downstream the throat has a significant role in nozzle exit flow characteristics. The loss mechanism throughout the flow is shown as the entropy generated due to viscous dissipation and accounts for supersonic jet mixing. Axis switching phenomenon is also addressed by analyzing the streamwise vorticity fields at various locations downstream from the nozzle exit.

Turbulence is governed by various mechanisms, such as production, dissipation, diffusion, dilatation and convection, which lead to its evolution and decay. In high-speed flows, turbulence becomes complicated due to compressibility effects. Therefore, the goal of the current work is to characterize these mechanisms in rectangular supersonic jets by directly evaluating their contributions in turbulent kinetic energy (TKE) budget equation. The budgets are obtained using high-fidelity Large Eddy Simulations that employ WALE subgrid-scale model. Jet nearfield data are validated with PIV experimental measurements, available from the literature, which include mean flow and second-order statistics. To ensure spatial resolution and temporal convergence of higher-order statistics, qualitative performance metrics are presented. The results indicate that TKE production is the major source term, while pressure-dilatation term acts as a sink throughout the development of the jet. The diffusion term has the highest contribution from triple-velocity correlations, followed by pressure diffusion and molecular diffusion. Subgrid-scale diffusion and dissipation are also evaluated and their contributions are minimal. Each term is presented on both minor and major axis plane and reveals asymmetry in the statistics. A detailed explanation of budget contributions is provided, leading to the mechanisms responsible for the anisotropy of TKE.

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