Evaluation and application of the Baldwin-Lomax turbulence model in two-dimensional, unsteady, compressible boundary layers with and without separation in engine inlets

There is a practical need to model high speed flows that exist in jet engine inlets. The boundary layers that form in these inlets may be turbulent or laminar and either separated or attached. Also, unsteady supersonic inlets may be subject to frequent changes in operating conditions. Some changes in the operating conditions of the inlets may include varying the inlet geometry, bleeds and bypasses, and rotating or translating the centerbody. In addition, the inlet may be either started or unstarted. Therefore, a CFD code, used to model these inlets, may have to run for several different cases. Also, since the flow conditions through an unsteady inlet may be continually fluctuating, the CFD code which models these flows may have to be run over many time steps. Therefore, it would be beneficial that the code run quickly. Many turbulence models, however, are cumbersome to implement and require a lot of computer time to run, since they add to the number of differential equations to be solved to model a flow. The Baldwin-Lomax turbulence model is a popular model. It is an algebraic, eddy viscosity model. The Baldwin-Lomax model is used in many CFD codes because it is quick and easy to implement. In this paper, we will discuss implementing the Baldwin-Lomax turbulence model for both steady and unsteady compressible flows. In addition, these flows may be either separated or attached. In order to apply this turbulence model to flows which may be subjected to these conditions, certain modifications should be made to the original Baldwin-Lomax model. We will discuss these modifications and determine whether the Baldwin-Lomax model is a viable turbulence model that produces reasonably accurate results for high speed flows that can be found in engine inlets

Statistical Analysis of a Semilinear Hyperbolic System Advected by a White in Time Random Velocity Field

We study a system of semilinear hyperbolic equations passively advected by smooth white noise in time random velocity fields. Such a system arises in modeling non-premixed isothermal turbulent flames under single-step kinetics of fuel and oxidizer. We derive closed equations for one-point and multi-point probability distribution functions (PDFs) and closed form analytical formulas for the one point PDF function, as well as the two-point PDF function under homogeneity and isotropy. Exact solution formulas allows us to analyze the ensemble averaged fuel/oxidizer concentrations and the motion of their level curves. We recover the empirical formulas of combustion in the thin reaction zone limit and show that these approximate formulas can either underestimate or overestimate average concentrations when reaction zone is not tending to zero. We show that the averaged reaction rate slows down locally in space due to random advection induced diffusion; and that the level curves of ensemble averaged concentration undergo diffusion about mean locations.Comment: 18 page

A New Extension of Wray-Agarwal Wall Distance Free Turbulence Model to Rough Wall Flows

This paper provides a roughness correction to the latest version of Wall-Distance-Free Wray-Agarwal (WA) one equation turbulence model (WA2018). The results from WA 2018 rough wall model are compared to Spalart-Allmaras model and the previous version of WA roughness model (WA2017). The results from WA2018-Rough model for flow over a flat plate show substantial improvement from the previous version WA2017-Rough and a good agreement with a semi-empirical formula based on experimental results. For flow past a S809 airfoil with surface roughness, WA2018-Rough model performs quite well compared to SA-Rough model

Lagrangian statistics of light particles in turbulence

We study the Lagrangian velocity and acceleration statistics of light particles (micro-bubbles in water) in homogeneous isotropic turbulence. Micro-bubbles with a diameter of 340 microns and Stokes number from 0.02 to 0.09 are dispersed in a turbulent water tunnel operated at Taylor-Reynolds numbers (Re) ranging from 160 to 265. We reconstruct the bubble trajectories by employing three-dimensional particle tracking velocimetry (PTV). It is found that the probability density functions (PDFs) of the micro-bubble acceleration show a highly non-Gaussian behavior with flatness values in the range 23-30. The acceleration flatness values show an increasing trend with Re, consistent with previous experiments (Voth et al., JFM, 2002) and numerics (Ishihara et al., JFM, 2007). These acceleration PDFs show a higher intermittency compared to tracers (Ayyalasomayajula et al., Phys. Fluids, 2008) and heavy particles (Ayyalasomayajula et al., Phys. Rev. Lett., 2006) in wind tunnel experiments. In addition, the micro-bubble acceleration autocorrelation function decorrelates slower with increasing Re. We also compare our results with experiments in von Karman flows and point-particle direct numerical simulations with periodic boundary conditions.Comment: 13 pages, 9 figures, revised manuscrip

Application of Quadratic Constitutive Relation to One- Equation k-kL Turbulence Model

This paper analyzes the accuracy of the recently developed one-equation k-kL turbulence model with Quadratic Constitutive Relation (QCR) compared to the linear Boussinesq relation and Algebraic Reynolds Stress Model (ARSM). The computational results in several benchmark cases from NASA TMR are compared to other widely used one equation turbulence models with QCR, such as Spalart-Allmaras model (SA), Wray-Agarwal model (WA) and SST k-ω model. In particular, one-equation k-kL-QCR model shows good accuracy with experimental data for supersonic flow in a square duct where the effect of QCR is clearly visible in capturing the secondary flow vortices which is not feasible with the any standard model without QCR. In addition, both one-equation k-kL and one-equation k- kL-QCR models show better accuracy for subsonic separated flow in 3D NASA Glenn S- duct compared to other one-equation models. Other test cases show little difference in the results obtained without and with QCR

Numerical Investigation of Wind Turbine Airfoils under Clean and Dusty Air Conditions

This paper focuses on the simulation of the airflow around wind turbine airfoils (S809 and S814) under both clean and dusty air conditions by using Computational Fluid Dynamics (CFD). The physical geometries of the airfoils and the meshing processes are completed in the ANSYS Mesh package ICEM. The simulation is done by ANSYS FLUENT. For clean air condition, Spalart– Allmaras (SA) model and realizable k-ε model are used. The results are compared with the experimental data to test which model agrees better. For dusty air condition, simulation of the two-phase flow is operated by realizable k-ε model and discrete phase model (DPM) in different concentration of dust particles (1% and 10% in volume). The results are compared with the data of clean air to illustrate the effect of dust contamination on the lift and drag characteristics of the airfoil

Bending modes and transition criteria for a flexible fiber in viscous flows

The present paper follows our previous work in which a coupling approach of smoothed particle hydrodynamics (SPH) and element bending group (EBG) was developed for modeling the interaction of viscous incompressible flows with flexible fibers. It was also shown that a flexible object may experience drag reduction because of its reconfiguration due to fluid force on it. However, the reconfiguration of deformable bodies does not always result in drag reduction as different deformation patterns can result in different drag scales. In the present work, we studied the bending modes of a flexible fiber in viscous flows using the presented SPH and EBG coupling approach. The flexible fiber is immersed in a fluid and is tethered at its center point, while the two ends of the fiber are free to move. We showed that the fiber undergoes four different bending modes: stable U-shape, slight swing, violent flapping, and stable closure modes. We found there is a transition criterion for the flexible fiber from slight swing, suddenly to violent flapping. We defined a bending number to characterize the bending dynamics of the interaction of flexible fiber with viscous fluid and revealed that this bending number is relevant to the non-dimensional fiber length. We also identified the critical bending number from slight swing mode to violent flapping mode