Two new two-equation eddy-viscosity turbulence models will be presented. They combine different elements of existing models that are considered superior to their alternatives. The first model, referred to as the baseline (BSL) model, utilizes the original k-ω model of Wilcox in the inner region of the boundary layer and switches to the standard k-e model in the outer region and in free shear flows. It has a performance similar to the Wilcox model, but avoids that model's strong freestream sensitivity

/pdf/two-equation-eddy-viscosity-turbulence-models-for-54j7shl2v6.pdf

Two-equation eddy-viscosity turbulence models for engineering applications

Two new versions of the k - w two-equation turbulence model will be presented. The new Baseline (BSL) model is designed to give results similar to those of the original k - w model of Wilcox. but without its strong dependency on arbitrary freestream values. The BSL model is identical to the Wilcox model in the inner SOC7£; of the boundary-layer but changes gradually to the standard k - f. model (in a k - w fonnulation) towards the boundary-layer edge. The new model is also virtually identical to the k - f. model for free shear layers. The second version of the model is called Shear-Stress Transport (SSn model. It is a variation of the BSL model with the additional ability to account for the transport of the principal turbulent shear stress in adverse pressure gradient boundary-layers. The model is based on Bradshaw's assumption that the principal shear-stress is pro­ portional to the turbulent kinetic energy, which is introduced into the definition of the eddy-viscosity. Both models are tested for a large number of different fiowfields. The results of the BSL model are similar to those of the original k - w model, but without the undesirable free stream dependency. The predictions of the SST model are also independent of the freestrearn values but show better agreement with exper­ imental data for adverse pressure gradient boundary-layer flows.

ZONAL TWO EQUATION k-w TURBULENCE MODELS FOR AERODYNAMIC FLOWS

A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities

Computational Fluid Dynamics: Principles and Applications, Third Edition presents students, engineers, and scientists with all they need to gain a solid understanding of the numerical methods and principles underlying modern computation techniques in fluid dynamics By providing complete coverage of the essential knowledge required in order to write codes or understand commercial codes, the book gives the reader an overview of fundamentals and solution strategies in the early chapters before moving on to cover the details of different solution techniques

	This updated edition includes new worked programming examples, expanded coverage and recent literature regarding incompressible flows, the Discontinuous Galerkin Method, the Lattice Boltzmann Method, higher-order spatial schemes, implicit Runge-Kutta methods and parallelization

	An accompanying companion website contains the sources of 1-D and 2-D Euler and Navier-Stokes flow solvers (structured and unstructured) and grid generators, along with tools for Von Neumann stability analysis of 1-D model equations and examples of various parallelization techniques



	
		Will provide you with the knowledge required to develop and understand modern flow simulation codes
	
		Features new worked programming examples and expanded coverage of incompressible flows, implicit Runge-Kutta methods and code parallelization, among other topics
	
		Includes accompanying companion website that contains the sources of 1-D and 2-D flow solvers as well as grid generators and examples of parallelization techniques

Computational Fluid Dynamics: Principles and Applications Ed. 3

Detached eddy simulation of massively separated flows

The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner, using the method of pseudocompres sibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme, based on flux-difference splitting, is used to compute the convective terms. The upwind differencing is biased, based on the sign of the local eigenvalue of the Jacobian matrix of the convective fluxes. Both third-order and fifth-order differencing schemes are used on the convective fluxes throughout the grid's interior. The equations are solved using an implicit line relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudo-time, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, and good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at —90° angle of attack is computed.

Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a third-order flux-difference splitting technique for the convective terms and the second-order central difference for the viscous terms. The accuracy is obtained in the numerical solutions by subiterating the equations in pseudotime for each physical time step. The equations are solved with a line-relaxation scheme that allows the use of very large pseudotime steps leading to fast convergence for steady-state problems as well as for the subiterations of time-dependent problems. The steady-state solution of flow through a square duct with a 90-deg bend is computed, and the results are compared with experimental data. Good agreement is observed. Computations of unsteady flow over a circular cylinder are presented and compared to other experimental and computational results. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.

Steady and unsteady solutions of the incompressible Navier-Stokes equations

https://ntrs.nasa.gov/api/citations/19900012441/downloads/19900012441.pdf

An upwind differencing scheme for the incompressible Navier-Stokes equations

The two-dimensional incompressible Navier-Stokes equations are solved in a time-accurate manner in using the method of pseudocompressibility. Using this method, subiterations in pseudotime are required to satisfy the continuity equation at each time step. An upwind differencing scheme based on flux-difference splitting is used to compute the convective terms. The upwind differencing is biased based on the sign of the local eigenvalue of the Jacobian matrix. Third-order or fifth-order spatial accuracy is maintained throughout the interior grid points. The equations are solved using an implicit line-relaxation scheme. This solution scheme is stable and is capable of running at large time steps in pseudotime, leading to fast convergence for each physical time step. A variety of computed results are presented to validate the present scheme. Results for the flow over an oscillating plate are compared with the exact analytic solution, good agreement is seen. Excellent comparison is obtained between the computed solution and the analytical results for inviscid channel flow with an oscillating back pressure. Flow solutions over a circular cylinder with vortex shedding are also presented. Finally, the flow past an airfoil at -90 deg angle-of-attack is also computed.

An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

An all new, automated version of the PEGASUS software has been developed and tested. PEGASUS provides the hole-cutting and connectivity information between overlapping grids and is used as the final part of the grid-generation process for overset-grid computational fluid dynamics approaches. The new PEGASUS code (Version 5) has many new features: automated hole cutting, a projection scheme for fixing small discretization errors in overset surfaces, more efficient interpolation search methods using an alternating digital tree and a stencil-jumping scheme, hole-size optimization based on adding additional layers of fringe points, and an automatic restart capability. The new code has also been parallelized using the message-passing interface standard. The parallelization performance provides efficient speedup of the execution time by an order of magnitude, and up to a factor of 30 for very large problems. The results of two example cases are presented: a three-element high-lift airfoil and a complete Boeing 777-200 aircraft in a high-lift landing configuration

Stuart E. Rogers

Papers

Upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

Steady and unsteady solutions of the incompressible Navier-Stokes equations

An upwind differencing scheme for the incompressible Navier-Stokes equations

An upwind differencing scheme for the time-accurate incompressible Navier-Stokes equations

PEGASUS 5: An Automated Preprocessor for Overset-Grid Computational Fluid Dynamics