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The paper deals with the development of the lower-upper symmetric Gauss–Seidel (LU-SGS) matrix-free finite volume solver for the simulation of compressible flows within the framework of the OpenFOAM package. The solver evaluates the convective fluxes using approximate Riemann solvers with limited piece-wise linear reconstructions whereas the viscous fluxes are approximated using a central scheme. The time evolution is realised through the backward differentiation formula of first or second order. The system of non-linear equations is then solved with the help of the matrix-free LU-SGS method. The developed solver is used to solve several flow problems and compared to a pressure-based segregated solver. Our numerical experiments indicate that the LU-SGS solver is more efficient for flows with higher Mach numbers and provides better resolution of shock waves. Moreover the LU-SGS solver benefits from the low memory footprint and does not use any problem specific setup.

The paper deals with the numerical simulation of the flow field in a turbine cascade, which corresponds to the tip section of a last low-pressure steam turbine rotor. Considered cascade consists of very thin profiles with high stagger angle. The resulting flow field is complex with interactions of strong shock waves, shear layers and shock reflections. The paper proposes a proper numerical approximation of boundary conditions suitable for cases with supersonic inlet and outlet flow velocities and compares the flow field for two cascade configurations: the first one corresponding to real experiment (cascade with finite number of blades located in the wind tunnel test section) and the second one corresponding to annular cascade. The experimental configuration includes the complicated geometry of wind tunnel. The annular configuration leads to blade to blade periodicity, which is not guaranteed for the experimental configuration. Numerical simulations are based on the Favre-averaged Navier–Stokes equations with SST k – ω turbulence model and the in-house implicit finite volume solver with AUSM-type discretization. This method considers structured multi-block grid. Results are compared with experimental data.

This paper describes a pressure-based solver based on the finite volume approach for the simulation of high-speed wet steam flows with non-equilibrium condensation. The governing mathematical model consists of the system of Navier–Stokes equations for common mixture density, velocity, and enthalpy equipped with an appropriate nonlinear equation of state based on IAPWS formulation and with additional equations for liquid mass fraction and droplet radius distribution. The proposed method has been implemented into open-source package OpenFOAM and validated using available experimental data for nozzle flows. Finally, it was used for simulations of flows in turbine cascades.

The article deals with the numerical simulation of flows with laminar to turbulent transition due to the separation of boundary layer. Mathematical model consists of the Reynolds averaged Navier–Stokes equations which are completed by the explicit algebraic Reynolds stress model (EARSM) of turbulence. The EARSM model is enhanced with algebraic model of bypass transition which is further modified by the additional source term for prediction of laminar boundary layer separation induced transition. Numerical solution is obtained by the finite volume method based on the second order HLLC scheme and explicit Runge–Kutta method. The proposed method is then tested on several cases of low-Reynolds subsonic transitional flows including flows over the SD 7003 airfoil with various angles of attack and flow past the NACA 0012 airfoil.

The paper refers about the development of a fast computational code, which should be able to provide an approximate information about the three-dimensional flow field in a multistage turbine. The code is based upon the solution of circumferentially averaged Euler equations coupled with the thermodynamic, geometry and loss prediction models. The computational domain is the meridional cut of a turbine. The Euler equations are solved by a finite volume solver with the AUSM type flux. Initial tests showed, that developed solver is able to predict well radial distributions of flow parameters upstream and downstream considered blade cascades at a fraction of CPU time compared to fully three-dimensional simulations.

The work deals with the numerical simulation of turbulent flow through turbine cascades including heat exchange between fluid and blades. The numerical algorithm couples an implicit AUSM finite volume solver for fluid flow and a finite element solver for heat conduction inside the blade. Several [email protected] turbulence models are applied. The eddy diffusivity assumption is used for turbulent heat flux computation. The influence of inlet boundary conditions for turbulence models is discussed. A case of failure of eddy diffusivity turbulent heat flux with common value of turbulent Prandtl number Pr"t=0.91 is presented, where remedy is achieved by lowering the magnitude of Pr"t.

The article is devoted to numerical simulation of stratified flows described by the Navier-Stokes equations in Boussinesq approximation. The equations are solved by two high order schemes. The first one using the fifth-order WENO scheme combined with spectral projection to solenoidal field, the second one being based on the second-order AUSM MUSCL scheme with artificial compressibility in dual time. The schemes are used to model a flow around an obstacle moving through the stratified fluid. The setup of the computational case corresponds to the experiment of Chaschechkin and Mitkin [23] . Mutual comparison of results obtained by both schemes as well as of the experimental data is presented.

This paper describes the implicit MacCormack scheme [1] in finite volume formulation. Unsteady flows with moving boundaries are considered using arbitrary Lagrangian–Eulerian approach. The scheme is unconditionally stable and does not require solution of large systems of linear equations. Moreover, the upgrade from explicit MacCormack scheme to implicit one is very simple and straightforward. Several computational results for 2D and 3D flows over profiles and wings are presented for the case of inviscid and viscous flows.

This study deals with a numerical solution of a 2D unsteady flow of a compressible viscous fluid in a channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall with large amplitudes, nearly closing the channel during oscillations. The channel is a simplified model of the glottal space in the human vocal tract and the flow can represent a model of airflow coming from the trachea, through the glottal region with periodically vibrating vocal folds, and to the human vocal tract. The flow is described by a system of Navier-Stokes equations for laminar flows. The numerical solution is implemented using the finite volume method (FVM) and the predictor-corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. Due to the unsteadiness of the grid (motion of the grid), the basic system of conservation laws is considered in a changed form using the Arbitrary Lagrangian-Eulerian (ALE) method. The numerical solution has been carried out for a symmetric and a non-symmetric flow field in two computational domains. The numerical results for unsteady flows in the channel are presented for inlet Mach number M"~=0.012, Reynolds number Re=5x10^3 and wall motion frequency 100Hz. The authors present the numerical solution and simulations of flow fields in the channel, acquired from a program that has been developed exclusively for this purpose. The reason for using a numerical simulation was the lack of data from experimental results of flows through the glottal region, and the capability of such simulation to model the problem.