Takuji Kurotaki

Generalized characteristic interface conditions for high-order multi-block computation

In practical fluid computation with structured grids around complex geometries, singular points with metric discontinuity can frequently be found. Generally, the grid singularities may cause numerical oscillations when some high-order finite difference scheme is applied. Recently, an excellent theory has been proposed which solves the above singular problem by block decomposition along the singular surface and by imposition of the characteristic interface conditions (CIC) on the block interface. However, the original theory has constraints on the mathematical treatment of the block interface, and therefore prevents numerical flexibility from a practical point of view. In this article, in order to extend the functions of the original CIC, we propose the generalized characteristic interface conditions (GCIC). Proper numerical test analysis is conducted to validate the performance of the GCIC, and as a practical application, multi-block computation is performed with the GCIC applied to complex geometry.

Interface Conditions of Finite Difference Compact Schemes for Computational Aeroacoustics

The interface condition provides flexibility to handle complex geometries on a set of structured grids. However, when used with a compact scheme to apply in computational aeroacoustics, its accuracy and stability may be degraded seriously by the boundary treatment that arises at a grid interface. To minimize this effect, a modified characteristic condition is incorporated in the finite difference compact scheme by using an explicit difference form at the boundary. The extension of this approach is naturally attained through the coordinate transformation of convective terms across an interface in multidimensions. The validity of current development is demonstrated through a simulation of trailing-edge noise generation from an airfoil at a low Mach number.

Numerical Simulation around Airfoil with Natural Transition in High Reynolds Numbers

A new approach for the analysis of subsonic flow is proposed and the capability of capturing the detail flow properties is investigated. Especially, the natural transition phenomenon is focused on. The flows around two-dimensional aerofoil of the NACA0012 under relatively high Reynolds number conditions (Re ≃ 10 6 ) are analyzed. The development of so called T-S wave and the laminar-turbulent transition are clearly captured. Locations of transition points are compared with the experiments and agreements are excellent. The detail comparison with the linear stability analysis indicates that the most unstable disturbance in the linear unstable region is captured quantitatively by taking care of grid resolution in the chord direction. The disturbance distribution inside the boundary layer in the transitional region is examined and the phase jump is also captured.

Generalized Characteristic Interface Conditions for Accurate Multi-block Computation

In a practical computation with a structured grid around a complex body, singular points can be frequently found where an abrupt grid change exists. The grid singularity poses a troublesome problem when some finite difference scheme with high accuracy and resolution is applied. An excellent theory has been proposed, which solve the above singular problem by decomposing a computational domain into two blocks along a line or a surface which contains the singular points and by imposing accurate characteristic-based interface conditions at the block interface. However, the original theory has a limitation on the combination between the adjacent computational coordinate definitions. Concretely, these two coordinates have to be the same direction on the block interface. For a flexible coordinate arrangement without the restriction, the original characteristic-based interface treatment is extended and generalized. Consequently, the coincidence of the computational coordinate definitions becomes unnecessary, and a more flexible multi-block computation can be realized successfully. Numerical test analysis of vortex convection is performed for validation of the new theory, and excellent performance is confirmed as a result.

Practical Multi-block Computation with Generalized Characteristic Interface Conditions around Complex Geometry

In practical fluid computation with structured grid around complex geometry, singular points with metric discontinuity can be frequently found. Generally, the grid singularities may cause severe numerical oscillations when some high-order finite difference method (FDM) is employed. Recently, in order to solve this problem, high-order multi-block computation technique with characteristic interface conditions (CIC) were proposed. In the previous study, the authors extended the functions of the CIC, and newly derived the generalized characteristic interface conditions (GCIC). Resultantly, numerical flexibility and robustness of the multi-block interface treatment can be further improved from a practical point of view. In this article, as a preliminary study, the GCIC are applied to multi-block large eddy simulation (LES) around complex geometry, and their practical extensibility is shown and discussed.

Numerical Simulation Around Airfoil with High Resolution in High Reynolds Numbers

A new approach for the analysis of subsonic flow is proposed and the capability of capturing the detail flow properties is validated both qualitatively and quantitatively. Especially, the natural transition phenomenon is focused on. The flows around twodimensional aerofoil of the NACA0012 under relatively high Reynolds number conditions ( Re ≃ 10 ) are analyzed. The development of so called T-S wave and the laminar-turbulent transition are clearly captured. Locations of transition points are compared with the experiments and agreements are excellent. The same peak spectrum as in the experiment is also obtained. The detail comparison with the linear stability analysis indicates that the most unstable disturbance in the linear unstable region is still slightly underestimated. The acoustic field around the airfoil is also captured and some discussions are given.

Evaluation of Surface Catalytic Effect on TPS in 110kW ICP-heated wind tunnel

New 110kW inductively coupled plasma (ICP)-heated wind tunnel in JAXA-ISTA was constructed and some performance evaluations have been conducted to simulate atmospheric reentry environment. Using this wind tunnel, initial heating tests for catalytic effect research were carried out, and new materials were tested to evaluate its characteristics including catalysis, emissivity, and so on. SiC coating samples showed comparatively low temperature, but high catalytic coating showed higher temperature. The difference was about 100 ~ 200 C, and it corresponded to 0.3 ~ 0.4MW/m 2 of heat flux. The difference of heat flux due to effect of catalytic effect was reasonable to compare with former CFD results for arc-heated wind tunnel tests. Ultra high temperature ceramic (UHTC) material was also tested, and its characteristics changed from low catalytic region to high catalytic region as the temperature increased. It was caused by changing catalytic effect and emmisivity due to oxidization.

Interpolated characteristic interface conditions for zonal grid refinement of high-order multi-block computations

When numerically calculating fluid flows around complex geometries using the high-order finite-difference method on structured grids, grid singularities are frequently observed, even if the grids are carefully generated. In multi-block computations with the generalised characteristic interface conditions (GCIC), decomposed subdomains (blocks) do not overlap but are connected by the inviscid characteristic relations. In the original theory of the GCIC, discontinuity of the metrics on the interface can be accurately treated; however, discontinuity of the grid lines on the interface is not allowed. This article proposes a theoretical extension to the GCIC by incorporating high-order interpolation methods; this extension is called GCIC with interpolation (GCIC + I). The basic concept and solution procedure of the multi-block computation with the GCIC + I are presented in detail, and two benchmark tests are conducted to validate the proposed theory.

Numerical Analysis of Experimental Results on the Surface Catalycity in HIEST

Experimental results of a catalytic model in a free-piston driven shock tunnel (HIEST) was analyzed using a non-equilibrium CFD code. Results showed that almost all oxygen molecules were dissociated behind the bow shock and that about 80% of the dissociated oxygen reached the model surface in a typical HIEST flow condition, in the case of noncatalytic wall assumption. In addition to the condition to use air as the test gas, conditions with various oxygen fractions were also tested and compared with numerical analysis. The influence of oxygen fraction in the test gas to the shock-standoff distance agrees well between experiment and numerical analysis. However, the heat flux to the model surface was different between experiment and numerical analysis, especially in the conditions with low oxygen fractions.

CFD Evaluation of Pressure Effects on Surface Catalysis of SiO 2 -Based TPS

Effects of pressure on the surface catalysis of SiO2-based materials are investigated. The stagnation aerodynamic heat is measured in JAXA 750kW arc-heated wind tunnel under several flow conditions with the various pressure levels. Results are evaluated by comparing with CFD results with a reaction model describing heterogeneous finite rate catalysis. Four kinds of the testing conditions are chosen. Operating parameters for the arc-heated wind tunnel are adjusted to get each stagnation pressures ranging from 1.67 to 4.04 kPa. Agreements between CFD and experimental results are good for all four heating conditions within the error of less than 10%. Two kinds of definitions of catalytic efficiencies according to the difference of NO formation on the surface are estimated. For both ones, the influence of partial pressure of dissociating gases on the surface catalysis is clearly recognized. From this study, it is concluded that the dominant mechanism of recombination process should be the Langmuir- Hinshelwood type.