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This paper investigates the flow past two variants of root section profile cascades for a last stage rotor considering three-dimensional flow structures in the near-wall region. Analyses were drawn based on RANS numerical simulations of both variants and on the experimental data obtained by the 3D traversing in the exit flow field of one of the variants. Extent of 3D structures at two different regimes and its influence on aerodynamic characteristics of the blade cascades was assessed. The distributions of Mach number along the profiles were compared with 2D optical measurements and its distortion due to the presence of the sidewall was explored. The interaction between main vortical structures was described and its influence on the loading of the blades, mechanical energy losses and exit flow angle was discussed. The results showed that for a front loaded blade the vortical structures appeared earlier and at a larger extent than for an aft loaded variant. However, due to different Mach number distribution, contribution of end wall flow to the energy losses was lower in the case of the aft loaded variant. The influence of the near wall flow on the loading was found to be rather weak while the deviation of the exit flow angle appeared to be comparable for both of the variants.

The contribution deals with numerical and experimental investigation of the effect of incidence angle offset in a two-dimensional section of a flat linear blade cascade in a high-speed wind tunnel. The aim of the work is to complement ongoing research of quasi-stationary approximation of aerodynamic flutter by examination of setups leading to transonic flow regimes. The numerical simulations were realized by finite-volume, in-house code developed on top of the open-source software package OpenFOAM. The experiments were conducted in correspondence with the setting of numerical simulations. The comparison of experimental and numerical data is presented on the isentropic Mach number distributions at various locations in the blade cascade. The description of transonic flow structures in the vicinity of blades is also provided.

The article deals with numerical solution of the laminar-turbulent transition. A mathematical model consists of the Reynolds-averaged Navier-Stokes equations, which are completed by the explicit algebraic Reynolds stress model (EARSM) of turbulence. The algebraic model of laminar-turbulent transition, which is integrated to the EARSM, is based on the work of Kubacki and Dick (Int. J. Heat Fluid Flow 58, 68–83, 2016) where the turbulent kinetic energy is split in to the small-scale and large-scale parts. The algebraic model is simple and does not require geometry data such as wall-normal distance and all formulas are calculated using local variables. A numerical solution is obtained by the finite volume method based on the HLLC scheme and explicit Runge-Kutta method.

The article deals with the numerical simulation of unsteady flows through the turbine part of the turbocharger. The main focus of the article is the extension of the in-house CFD finite volume solver for the case of unsteady flows in radial turbines and the coupling to an external zero-dimensional model of the inlet and outlet parts. In the second part, brief description of a simplified one-dimensional model of the turbine is given. The final part presents a comparison of the results of numerical simulations using both the 3D CFD method and the 1D simplified model with the experimental data. The comparison shows that the properly calibrated 1D model gives accurate predictions of mass flow rate and turbine performance at much less computational time than the full 3D CFD method. On the other hand, the more expensive 3D CFD method does not need any specific calibration and allows detailed inspections of the flow fields.

Measurement of the lift coefficient of the AH93-157 airfoil was performed by measuring the static pressure distribution on the wind tunnel walls along the test-section. A correlation was established between the lift coefficient value, determined by integrating the static pressure distribution on the wind tunnel walls, and the lift coefficient value, determined by integrating the static pressure distribution on the airfoil surface. This method is useful for easy and quick determination of the lift coefficient on a simple airfoil model without complicated static pressure tubing from the surface. The measurement was made within a closed test-section. The correlation relationship also eliminates the problem of the finite span and the effect of the side walls. Comparison of pressure distribution on airfoil with CFD was performed as well.

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 paper presents a numerical and experimental investigation of the effect of incindence angle offset in a two-dimensional section of a flat blade cascade in a high-speed wind tunnel. The aim of the current work is tp determine the aerodynamic excitation forces and approximation of the unsteady blade-loading function using a quasi-stationary approach. The numerical simulations were performed with an in-house finite-volume code built on the top of the OpenFOAM framework. The experimental data were acquired for regimes corresponding to the numerical setup. The comparison of the computational and experimental results is shown for the static pressure distributions on three blades and upstream and downstream of the cascade. The plot of the aerodynamic moments acting on all five blades shows that the adjacent blades are significantly influenced by the angular offset of the middle blade.

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.

This article is concerned with the new design of supersonic profile cascade, marked TR-U-8, for ultra-long bucket tip area. The profile cascade represents a geometrical variant of the ultra-long bucket tip section which was designed in Doosan Skoda Power in Pilsen. There were found out outputs of two aerodynamic regimes marked OP1 India 800 MW for higher back-pressure and OP4 Temelin 1200 MW for lower back pressure. Outputs for nominal incidence cascade angle are presented in this paper. The design of cascades by aerodynamic calculations were investigated and validation by evaluation of optical and pneumatic measurements on wind tunnel tests was done. Two dimensional cascade calculations were carried out by commercial code Ansys Fluent 16.0 in Doosan Skoda Power (DSPW) and by non-commercial software developed in Czech Technical University (CTU). An aerodynamic high speed wind tunnel is located in Institute of Thermomechanics the Czech Academy of Science (AS CR).

A numerical code for calculation of leakage flowand rotordynamic coefficients of labyrinth seals has beendeveloped. The code is based on the solution of Reynolds-averagedNavier-Stokes equations combined with a two-equation turbulencemodel. The numerical solution is achieved with finite volume methodand the rotordynamic coefficients are evaluated from severalsimulations with different rotor precessions. The solution iscompared to single control volume based bulk flow method[Williams, 1998] and to the experimental results for look-throughlabyrinth seal [Schettel, 2004].

The article deals with results of the implementation of the k-kL-ω turbulence model for compressible transitional flow into OpenFOAM. This model was firstly proposed by Walters and Leylek [2] and utilizes the approach of the laminar kinetic energy in order to predict the transition between laminar and turbulent flows. The performance of the implemented model has been tested for the case of flow over a flat plate and the flow through VKI and SE 1050 turbine cascades. The properties of the implementation of the model for compressible flow simulations into OpenFOAM are discussed.

Focus of this paper is aerodynamic investigation of tie-boss stabilization devices for extremely long rotor blades. This investigation covered measurements on multiple blade cascades and computational fluid dynamics (CFD) simulation of the flow past these cascades. Conclusions were drawn from results of the measurements and CFD and from the knowledge of prior investigation of the used blade cascade. Main focus of this paper is to describe influence of a tie-boss stabilization device on flow field in interblade channel. Tie-boss with more massive shape proved to cause lesser losses, while tie-boss with a tailored trailing edge showed lesser influence on flow turning.

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.

This paper is concerned with experimental and numerical research on 3D flow past prismatic turbine cascade SE1050 (known in QNET network as open test case SE1050). The primary goal was to assess the influence of the inlet velocity profile on the flow structures in the interblade channel and on the flow field parameters at the cascade exit and to compare these findings to results of numerical simulations. Investigations of 3D flow past the cascade with non-uniform inlet velocity profile were carried out both experimentally and numerically at subsonic (M2is = 0.8) and at transonic (M2is = 1.2) regime at design angle of incidence. Experimental data was obtained using a traversing device with a five-hole conical probe. Numerically, the 3D flow was simulated by open source code OpenFOAM and in-house code. Analyses of experimental data and CFD simulations have revealed the development of distinctive vortex structures resulting from non-uniform inlet velocity profile. Origin of these structures results in increased loss of kinetic energy and spanwise shift of kinetic energy loss coefficient distribution. Differences found between the subsonic and the transonic case confirm earlier findings available in the literature. Results of CFD and experiments agree reasonably well.

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 deals with the numerical simulation of transitional flows. The aim is to evaluate two models for turbomachinery flows. The first model is a simple algebraic model developed by Straka and Přihoda and the second one is the three-equation $$k-k_L-\omega $$ model of Walters and Cokljat. Both models were tested for shear flows over the flat plate (ERCOFTAC T3A, T3B, and T3A $$-$$ cases) for natural and bypass transition, over two airfoils in a tandem for the transition due to incoming wake and finally for the flow through a subsonic turbine blade cascade. Both models are compared to available experimental data.

The contribution deals with simulation of internal flows with the laminar/turbulent transition and heat transfer. The numerical modeling of incompressible flow on a heated flat plate was carried out partly by the k-kL-ω model of Walters and Cokljat [1] and partly by the algebraic transition model of Straka and Přihoda [2] connected with the EARSM turbulence model of Hellsten [3]. Transition models were tested by means of the skin friction and the Stanton number distribution. Used models of turbulent heat transfer were compared with the simplest model based on the constant turbulent Prandtl number. The k-kL-ω model is applied for the simulation of compressible flow through the VKI turbine blade cascade with heat transfer.

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.

The contribution deals with the application of coupled implicit solver for compressible flows to CFD analysis of a twin scroll radial turbine. The solver is based on the finite volume method, convective terms are approximated using AUSM+up scheme, viscous terms use central approximation and the time evolution is achieved with lower-upper symmetric Gauss-Seidel (LU-SGS) method. The solver allows steady simulation with the so called frozen rotor approach as well as the fully unsteady solution. Both approaches are at first validated for the case of ERCOFTAC pump [1]. Then the CFD analysis of the flow through a twin scroll radial turbine and the predictions of the efficiency and turbine power is performed and the results are compared to experimental data obtained in the framework of Josef Božek – Competence Centre for Automotive Industry.

This paper deals with a numerical solution of compressible flows. In the case of Euler equations, a numerical solver is presented on a structured quadrilateral grid. The Advection Upstream Splitting Method (AUSM) scheme is used and the spatial accuracy is improved by linear reconstruction with slope limiters. The influence of those limiters are then tested in cases of transonic flow through a channel and a blade cascade.

The aim of this article is the presentation of the numerical solution of 2D and 3D transonic flows through turbine cascades. Physical model is the inviscid compressible flow described by the system of Euler equations for rotating frame of reference. The properties of a simplified scalar hyperbolic equation with a linear source term modeling Coriolis and centrifugal forces are analyzed and we show, that TV-based numerical methods are suitable for numerical solution of such problems. Several examples of 2D and 3D transonic flow through turbine cascades are presented and the effects of the rotation are discussed.

We deal with the comparison of several finite volume TVD schemes and finite difference ENO schemes and we describe a second order finite volume WENO scheme which was developed for the case of general unstructured meshes. The proposed second order WENO reconstruction is much simpler than the original ENO scheme introduced in lHarten and Chakravarthy 1991r. Moreover, the proposed WENO method is very easily extendible for unstructured meshes in 3D. All above mentioned schemes are applied for the solution of 2D and 3D transonic flows in the turbines and channels and the numerical solution is compared to experimental results or to the results obtained by other authors.

This work describes the numerical solution of compressible turbulent flows. Turbulent flows are modeled by the system of averaged Navier-Stokes equations closed by the Explicit Algebraic Reynolds Stress Model (EARSM) of turbulence. EARSM model used in this work is based on the Kok’s TNT model equations. New set of model constants which is more suitable for conjunction with EARSM model has been derived. Recalibrated model of turbulence together with the system of averaged Navier-Stokes equations is then discretized by the finite volume method and used for the solution of some realistic problems in external and internal aerodynamics.

The paper presents a numerical method, which simulates the circumferentially averaged steady flow of a compressible fluid in a multistage turbine. The method is considered in the analytic mode with known geometry. It is intended as a fast tool to turbine designers, which provides the distribution of the flow parameters in the meridional plane, gives the information about mass flow and estimates the efficiency of turbine. The method is based on the solution of the circumferentially averaged three-dimensional Euler equations complemented by the source terms related to the turbine geometry and to the loss prediction model. The meridional plane is discretized by a structured grid. Equations are solved by a finite volume method with the AUSM type numerical flux. Examples including the transonic flow in a turbine stator and in a stage are presented.

The transition model with the algebraic equation for the intermittency coefficient proposed for the bypass transition was modified for modelling of the transition at low free-stream turbulence. Further, the three-equation k-kL-ω model and the Xfoil program were used for the comparison. All models were tested by means of the incompressible flow around the flat plate and symmetrical airfoils at moderate and very low free-stream turbulence.

This contribution deals with the modern finite volume schemes solving the Euler and Navier-Stokes equations for transonic flow problems. We will mention the TVD theory for first order schemes and some numerical examples obtained by 2D central and upwind schemes for 2D transonic flows in the GAMM channel or through the SE 1050 turbine of Skoda Plzeň. The TVD MacCormack method is extended to a 3D method for solving flows through turbine cascades. Numerical examples of unsteady transonic viscous (laminar) flows through the DCA 8% cascade are also presented for $\text{Re}=4600$. Next, a new finite volume implicit scheme is presented for the case of unstructured meshes (with both triangular and quadrilateral cells) and inviscid compressible flows through the GAMM channel as well as the SE 1050 turbine cascade.

The article deals with the 2D numerical simulation of the stratified incompressible flows behind the moving thin horizontal strip in the towing tank and over the sinusoidal hill. The mathematical model is based on the Boussinesq approximation of the Navier–Stokes equations. The resulting set of PDE’s is then solved by two different numerical methods. Different boundary conditions are tested.

The article describes the development of bulk-flow code for the prediction of rotor-dynamic coefficients of labyrinth seals. The code is based on the so-called single control volume approach by Childs and Scharrer [1] and the the forces are evaluated using the automatic differentiation technique. The resulting code is very simple and provides reasonable predictions of stiffness and damping coefficients at short computational time.

This works deals with three-dimensional numerical simulation of transonic and subsonic inviscid compressible steady and unsteady flow. The problem is solved using finite volume method, namely the so–called Modified Causon’s scheme [3] in combination with Arbitrary Lagrangian–Eulerian method [5]. This scheme is based on TVD form of classical MacCormack scheme. Although it is not TVD it retains almost the same precision as the original TVD scheme, but demands approximately 30% less computational memory and power. Both subsonic and transonic regimes of flow over oscillating wings are simulated. The subsonic case (flow over the AS28 wing) is compared with experimental data with a very good agreement. Comparison for the transonic unsteady case (flow over the ONERA M6 wing) is unfortunately not possible, but numerical results show very good properties.

The paper deals with the numerical solution of turbulent flows through a 2D turbine cascade considering heat exchange between the gas and the solid blade. The flow field is described by the Favre averaged Navier-Stokes equations, and the temperature field inside the solid blade is given by the Laplace equation. Both parts are coupled in order to achieve continuity of the temperature as well as of the heat flux along the fluid-solid boundary. The analysis of simplified model case is presented and the results obtained with two in-house codes with several two-equation turbulence models are compared to results of commercial software (Fluent).

The article deals with the numerical simulation of 2D and 3D unsteady incompressible stratified flows. Initial system of equations is the Boussinesq approximation of the Navier–Stokes equations. The flow field in the towing tank with a moving sphere is modeled for a wide range of Richardson numbers. The obstacle is modeled via penalization technique. The resulting set of partial differential equations is then solved by the fifth-order finite difference WENO scheme, or by the second-order finite volume AUSM MUSCL scheme. For the time integration, the second-order BDF method was used. Both schemes are combined with the artificial compressibility method in dual time.

The aim of this contribution is to present two modern high-order finite volume (FVM) schemes for numerical solution of unsteady transonic flows. The first one is derived from the total variation diminishing (TVD) version of the classical MacCormack scheme proposed by Causon. In our case it is used with slight modifications and hence refered to as Modified Causon’s scheme. It is no more TVD, but with no loss of accuracy to the TVD version and with a significantly lower demands on computational power and memory (cca 30% less). The second one, based on a similar approach as the WENO family schemes, is the implicit Weighted Least-Square Reconstruction scheme (WLSQR) used in combination with the AUSMPW+ numerical flux. For the turbulence modelling the Kok’s TNT turbulence model is employed. Unsteady effects (forced oscillatory motion) are simulated by Arbitrary Lagrangian–Eulerian method (ALE). As the transonic test cases the inviscid and turbulent flow around the NACA 0012 profile and inviscid flow over the ONERA M6 wing were chosen. Comparison of numerical and experimental results for inviscid flow is very good, which is unfortunately not the case of turbulent flow.

The article deals with the numerical simulation of 2D and 3D unsteady incompressible flows with stratifications. The mathematical model is based on the Boussinesq approximation of the Navier-Stokes equations. The flow field in the towing tank with a moving sphere is modelled for a wide range of Richardson numbers. The obstacle is modeled via appropriate source terms. The resulting set of partial differential equations is then solved by the fifth-order finite difference WENO scheme, or by the second-order finite volume AUSM MUSCL scheme. For the time integration, the second-order BDF method was used. Both schemes are combined with the artificial compressibility method in dual time.

The work deals with the development of a high order finite volume scheme for Euler and Navier–Stokes equations. The accuracy of the scheme is improved by a piecewise quadratic interpolation of cell averaged data. The interpolation procedure uses the weighted least square approach similar to the weighted ENO scheme [2]. The resulting scheme posses extremely good convergence to steady state thanks to single stencil reconstruction with smooth weights. The truncation error for two variants of the simplified scheme for one-dimensional convection-diffusion equation is derived here. The importance of good approximation of the boundary is emphasized and an ENO-like procedure for the approximation of the boundary is described.

This study deals with the numerical solution of 2D unsteady flows of a compressible viscous fluid in two types of channels (unsymmetric, symmetric) for a 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. The numerical solution is realized by a finite volume method and an explicit predictor-corrector MacCormack scheme with Jameson artificial viscosity using a grid of quadrilateral cells. The moved grid of quadrilateral cells is considered in the form of conservation laws using an Arbitrary Lagrangian-Eulerian method. Numerical results of the unsteady flows in the channels are presented for inlet Mach number \({M_\infty \approx 10^{-2}}\), Reynolds number \({{\rm Re} \in {\rm {(5 \times 10^3, 1.1 \times 10^4)}}}\) and for a frequency of the wall motion 20 Hz and 100 Hz.

We solve the system of Euler or Navier-Stokes equations in conservative ALE formulation, possibly supplemented by a suitable turbulence model. The structural dynamics is described by the equations of anisotropic elastic continuum with large or small displacements. The problem is closed by suitable interface conditions. We present a cell centered finite volume method with linear least square reconstruction with nonlinear WENO type weights, a cell centered finite volume method with linear reconstruction and Barth’s limiter and a residual distribution scheme to solve the CFD sub-problem. To allow a large time step, all the considered methods use implicit time stepping formulated in dual time. The elastic problem and the mesh motion is solved by a simple finite element method. The whole problem is formulated in dual time and solved by a simple sub-iteration procedure. We present several numerical tests documenting the behavior of the methods. These include 2D transonic turbulent flow past a forced oscillatory pitching NACA0012 airfoil, 2D inviscid supersonic panel flutter and 3D inviscid flow past the elastic AGARD 445.6 wing.