Numerical Simulation Of Transonic Flow Research Articles

Numerical simulations of transonic flows with non-unique solutions

Inviscid, compressible flows are described by a first-order system of hyperbolic partial differential equations in conservation form, and are solved numerically with simple schemes. These schemes show the ability to reproduce well-known solutions and benchmarks for the two-dimensional Euler equations. Finally, the schemes are used to explore the anomaly of non-unique solutions in the transonic regime. Furthermore, numerical solutions for the isentropic Euler equations with γ = 2, which are analogous to the shallow water equations, also exhibit non-uniqueness. In the appendix, results computed with OVERFLOW also exhibit non-unique solutions for the same geometries considered in the text.

Study on the Numerical Model of Transonic Wind Tunnel Test Section

The authors consider numerical simulations of transonic flows through various turbine cascades in a confined channel which approximates boundaries of real wind tunnel. The boundaries of the wind tunnel are impermeable or there can be permeable tailboards to diminish shock wave reflections. The mathematical model is based on Favre-averaged Navier-Stokes equations closed by a turbulence model and model of transition to turbulence. The mathematical model is solved by an implicit finite volume method with multi-block grids. Several types of turbine blade cascades with subsonic or supersonic inlet are presented. The results are compared with optical measurements and simulations of periodic cascades. The validity of experimental reference flow parameters in relation to computed flow patterns is discussed.

Mean flow compressibility effects in transonic turbulence modeling

The mean flow compressibility effects greatly influence the behavior of turbulent flows, as long as the flow is compressible. The fact is even though Favre average has taken into account the variation of the density, less accurate CFD results are always obtained when the flow is compressible. Thus, many compressibility corrections are made for high Mach number flows. As for the transonic turbulence flow, the mean flow compressibility effects are not mentioned. In this paper, it is demonstrated that the mean flow compressibility effects are not ignorable in transonic flows on some flow features. The mean flow compressibility effects are taken into account by introducing a characteristic turbulence length scale. The key is a new definition of vorticity by the curl of momentum. A compressible von Kármán length scale is introduced to obtain a new turbulence model CKDO (Compressible Kinetic Dependent Only) for complex compressible flows on the basis of the KDO. The only two empirical coefficients in the KDO model are not changed, which were calibrated by a slice of the incompressible flat plate boundary layer flow. Numerical simulations of transonic flows around RAE2822 airfoil, axisymmetric bump pipe and ONERA-M6 wing show that compressibility is non-negligible, and the new length scale definition can improve the prediction accuracies of aerodynamic features, such as the onset locations of shock waves, skin friction and pressure coefficients.

Simulation of transonic flows through a turbine blade cascade with various prescription of outlet boundary conditions

The contribution deals with the numerical simulation of transonic flows through a linear turbine blade cascade. Numerical simulations were carried partly for the standard computational domain with various outlet boundary conditions by the algebraic transition model of Straka and Příhoda [1] connected with the EARSM turbulence model of Hellsten [2] and partly for the computational domain corresponding to the geometrical arrangement in the wind tunnel by the γ-ζ transition model of Dick et al. [3] with the SST turbulence model. Numerical results were compared with experimental data. The agreement of numerical results with experimental results is acceptable through a complicated experimental configuration.

凝縮を伴う超臨界二酸化炭素の遷音速流動シミュレーション

凝縮を伴う超臨界二酸化炭素の遷音速流動シミュレーション

Transonic Shock Wave Patterns Over an Airfoil in an Accelerated Flow

It is well known that in a high subsonic flow over an airfoil, there exists a local supersonic pocket and similarly in a supersonic flow over the same, there exists a local subsonic pocket. But, how the transonic shock wave pattern over the airfoil changes when the freestream flow accelerates uniformly from high subsonic to supersonic - i.e. how a subsonic flow with a supersonic pocket changes into a supersonic flow with a subsonic pocket- is not reported so far. This study is an attempt to explore the above phenomena. In order to study the accelerated flow, Navier-Stokes equations are extended to acceleration frame of reference. Using these equations, numerical simulation of transonic flow over NACA0012 airfoil is carried out with freestream acceleration. The influence of acceleration on the flow field is studied with different levels of acceleration and retardation. This study revealed that both acceleration and retardation do influence the movement of transonic shock movement, and it is more pronounced in high levels of retardation. But, the shock wave pattern during the change from high subsonic to supersonic remains the same for various levels of acceleration. The continuous change of shock wave pattern over the airfoil is visualized in a single simulation and the underlying physical phenomena are investigated.

1608 超臨界二酸化炭素の二次元翼列遷音速流動シミュレーション

1608 超臨界二酸化炭素の二次元翼列遷音速流動シミュレーション

Numerical simulation of transonic flow of wet steam in nozzles and turbines

The paper presents several modifications of the flow model published in Stastný and Sejna (Proceedings of the 12th international conference of the properties of water and steam, Begel House, pp 711–719, 1995). Modifications related to the droplet growth model and the equation of state and their implementation into numerical code are described. The effect of droplet size spectra of incoming wet steam is also discussed. Numerical results of three-dimensional flow of wet steam in a turbine cascade show the effect of surface tension correction.

Numerical Simulation of Transonic Flow of Gas Water Separation Process

Numerical Simulation of Transonic Flow of Gas Water Separation Process

Implicit numerical simulation of transonic flow through turbine cascades on unstructured grids

Numerical simulation of the compressible flow through a turbine cascade is studied in the present paper. The numerical solution is performed on self-adaptive unstructured meshes by an implicit method. Computational codes have been developed for solving Euler as well as Navier-Stokes equations with various turbulence modelling. The Euler and Navier-Stokes codes have been applied on a standard turbine cascade, and the computed results are compared with experimental results. A hybrid scheme is used for spatial discretization, where the inviscid fluxes are discretized using a finite volume method while the viscous fluxes are calculated by central differences. A MUSCL-type approach is used for achieving higher-order accuracy. The effects of the turbulent stress terms in the Reynolds-averaged Navier-Stokes equations have been studied with two different models: an algebraic turbulence model (Baldwin-Lomax model) and a two-equation turbulence model ( k-ɛ model). The system of linear equations is solved by a Gauss-Seidel algorithm at each step of time integration. A new treatment of the non-reflection boundary condition is applied in the present study to make it consistent with the finite volume flux calculation and the implicit time discretization.

Numerical Simulation of Transonic Flow over Wing-Mounted Twin-Engine Transport Aircraft

A numerical method has been developed for computing the e owe eld around advanced transport aircraft with wing-mounted nacelles. The method is based on a multiblock point-matched grid-generation approach combined with zonal solving strategy for complex e owe eld. In this study the e owe eld is divided into a number of nonoverlapped blocks by a cutout technique. H-type grids are generated independently in each block using an elliptic grid-generation method, in which the control of the grid quality is accomplished by the forcing-function technique of Hilgenstock. The e owe eld is simulated by solving the Euler equations. An explicit three-stage Runge ‐Kutta algorithm based on the Jameson’ s e nite volume scheme for the Euler equations has been developed that is applied to the multiregion H-type grids. The present method has been applied to isolated powered engine nacelles and complex transport aircrafts consisting of low-wing/fuselage with wing-mounted pylon/nacelles. On the wing surfaces the viscous effects are simulated by the employment of the viscous/inviscid interaction (VII) technique of two-dimensional strip boundary layer. In this study the boundary-layer program uses an integral method to calculate turbulent boundary layers. With the concept of an equivalent inviscid e ow, the model of blowing velocity is employed in the VII technique. The effect of the boundary layeron the outer inviscid e ow is represented through a transpiration boundaryconditionderived from theboundary-layerparameters.Themain benee tofthistreatment isthatthegridisgeneratedonlyonceinoverallcomputingprocedure.Computationalresultsandcomparisonswith experimental data are presented. The good agreement indicates that the present method is effective in predicting the e ows about powered engine nacelles and/or complex transport aircrafts.

Domain decomposition methods for nonlinear problems in fluid dynamics

The numerical solution of finite element approximations of complicated two- and three-dimensional nonlinear problems can be a most formidable task. In order to overcome this difficulty related to dimensionality, domain-splitting methods can be very effective, particularly in view of obtaining a fast and economical conjugate gradient solver, which can be used to precondition the solution of nonlinear problems by optimization methods via nonlinear least squares or weighted residual formulations. A new technique of this type will be introduced and analysed and its efficiency will be discussed from numerical experiments concerning the numerical simulation of transonic flows for compressible inviscid fluids and incompressible viscous flows modelled by the Navier-Stokes equations.