Two-dimensional unsteady aerodynamics analysis based on a multiphase perspective. (English) Zbl 1271.76247
Summary: Compressible aerodynamics is analyzed by the CIP/CCUP (constraint interpolation profile/CIP-combined unified procedure) method. The CIP method is feasible for an analysis of various phase change problems, those associated with compressible and incompressible flow areas. For aeroelastic problems based on CFD (computational fluid dynamics), the use of Lagrangian body-fitted grids is problematic because these grids increase the skewness of a mesh, or can be broken – even during structural motions. Therefore, a method embedding a physical boundary in a fixed Eulerian grid is appropriate compared to Lagrangian grids. In this paper, the CCUP method based on a pressure-based algorithm in which the pressure Poisson equation is modified to deal with compressible flows. A collocated grid system with the velocity components on the cell face obtained from the CIP interpolations is applied. Boundary condition for arbitrary surfaces are newly derived using a simple algebraic relationship based on the immersed boundary method. Far-field boundary condition is replaced with sponge layers. Several numerical benchmarking problems, in this case a wedge or a bump under transonic and supersonic flows, are tested to verify the code. Unsteady motions are directly applied to embedded solid areas. Finally, the steady and unsteady aerodynamics of airfoil sections are calculated and compared to reference data to validate the proposed method.
MSC:
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76N15 | Gas dynamics (general theory) |
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
References:
| [1] | Garcia, J. A., Numerical investigation of nonlinear aeroelastic effects on flexible high-aspect-ratio wings, J. Aircraft, 42, 4, 1025-1036 (2005) |
| [2] | Harlow, F. H.; Welch, J. E., Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface, Phys Fluids, 8, 12, 2182-2189 (1965) · Zbl 1180.76043 |
| [3] | Unverdi, S. O.; Tryggvason, G., Computations of multi-fluid flows, Physica D, 60, 70-83 (1992) · Zbl 0779.76101 |
| [4] | Sussman, M.; Smereka, P.; Osher, S., A level set approach for computing solutions to incompressible two-phase flow, J Comput Phys, 114, 146-159 (1994) · Zbl 0808.76077 |
| [5] | Hirt, C. W.; Nichols, B. D., Volume of fluid (VOF) method for the dynamics of free boundaries, J Comput Phys, 39, 1, 201-225 (1981) · Zbl 0462.76020 |
| [6] | Yabe, T., Challenge of CIP as a universal solver for solid, liquid and gas, Int J Numer Method Fluid, 47, 655-676 (2005) · Zbl 1134.76436 |
| [7] | Takewaki, H.; Nishiguchi, A.; Yabe, T., Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations, J Comput Phys, 61, 2, 261-268 (1985) · Zbl 0607.65055 |
| [8] | Yabe, T.; Xiao, F.; Utsumi, T., The constrained interpolation profile method for multiphase analysis, J Comput Phys, 169, 556-593 (2001) · Zbl 1047.76104 |
| [9] | Tanaka, R.; Nakamura, T.; Yabe, T., Constructing exactly conservative scheme in a non-conservative form, Comput Phys Commun, 126, 232-243 (2000) · Zbl 0959.65097 |
| [10] | Yabe, T.; Xiao, F., A method to trace sharp interface of two fluids in calculations involving shocks, Shock Waves, 4, 101-108 (1994) · Zbl 0820.76063 |
| [11] | Yabe, T.; Aoki, T., A universal solver for hyperbolic equations by cubic-polynomial interpolation I. one-dimensional solver, Comput Phys Commun, 66, 219-232 (1991) · Zbl 0991.65521 |
| [12] | Yabe, T., A universal solver for hyperbolic equations by cubic-polynomial interpolation II. Two- and three-dimensional solvers, Comput Phys Commun, 66, 233-242 (1991) · Zbl 0991.65522 |
| [13] | Yoon, S. Y.; Yabe, T., The unified simulation for incompressible and compressible flow by the predictor-corrector scheme based on the CIP method, Comput Phys Commun, 119, 149-158 (1999) · Zbl 1175.76119 |
| [14] | Ida, M., An improved unified solver for compressible and incompressible fluids involving free surfaces. Part I. Convection, Comput Phys Commun, 132, 44-65 (2000) · Zbl 0994.76079 |
| [15] | Ida, M., An improved unified solver for compressible and incompressible fluids involving free surfaces. Part II. Multi-time-step integration and applications, Comput Phys Commun, 150, 300-322 (2003) · Zbl 1196.76053 |
| [16] | Takizawa, K., Computation of free-surface flows and fluid-object interactions with the CIP method based on adaptive meshless Soroban grids, Comput Mech, 40, 167-183 (2007) · Zbl 1177.76300 |
| [17] | Rhie, C. M.; Chow, W. L., Numerical study of the turbulent flow past an airfoil with trailing edge separation, AIAA J, 21, 11, 1525-1532 (1983) · Zbl 0528.76044 |
| [18] | Aoki, T., Interpolated differential operator (IDO) scheme for solving partial differential equations, Comput Phys Commun, 102, 132-146 (1997) |
| [19] | Xiao, F.; Ikebata, A.; Hasegawa, T., Numerical simulations of free-interface fluids by a multi-integrated moment method, Comput Struct, 83, 409-423 (2005) |
| [20] | Yabe, T.; Wang, P. Y., Unified numerical procedure for compressible and incompressible fluid, J Phys Soc Jpn, 60, 7, 2105-2108 (1991) |
| [21] | Nakamura, T., Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique, J Comput Phys, 174, 171-207 (2001) · Zbl 0995.65094 |
| [22] | Hu, C.; Kashiwagi, M., A CIP-based method for numerical simulations of violent free-surface flows, J Mar Sci Technol - Japan, 9, 4, 143-157 (2004) |
| [23] | Hagstrom T, Appelö D. Experiments with hermite methods for simulating compressible flows: Runge-Kutta time-stepping and absorbing layers. AIAA-2007-3505.; Hagstrom T, Appelö D. Experiments with hermite methods for simulating compressible flows: Runge-Kutta time-stepping and absorbing layers. AIAA-2007-3505. |
| [24] | Ogata, Y.; Yabe, T., Shock capturing with improved numerical viscosity in primitive Euler representation, Comput Phys Commun, 119, 179-193 (1999) · Zbl 1175.76112 |
| [25] | Chandar DDJ, Rao SVR, Deshpande SM. A one point shock capturing kinetic scheme for hyperbolic conservation laws. In: The third international conference on computational fluid dynamics, ICCFD3; 2004.; Chandar DDJ, Rao SVR, Deshpande SM. A one point shock capturing kinetic scheme for hyperbolic conservation laws. In: The third international conference on computational fluid dynamics, ICCFD3; 2004. |
| [26] | Ni, R. H., A multiple grid scheme for solving the Euler equations, AIAA J, 20, 1565-1571 (1982) · Zbl 0496.76014 |
| [27] | Moukalled, F.; Darwish, M., A high-resolution pressure-based algorithm for fluid flow at all speeds, J Comput Phys, 168, 101-133 (2001) · Zbl 0991.76047 |
| [28] | Eidelman, S.; Colella, P.; Shreeve, R. P., Application of the Godunov method and its second-order extension to cascade flow modeling, AIAA J, 22, 11, 1609-1615 (1984) · Zbl 0555.76016 |
| [29] | Taghaddosi, F., An adaptive least-squares method for the compressible Euler equations, Int J Numer Method Fluid, 31, 1121-1139 (1999) · Zbl 0964.76046 |
| [30] | Yoshihara H, Sacher P. Test cases for inviscid flow field methods. AGARD AR-211; 1986.; Yoshihara H, Sacher P. Test cases for inviscid flow field methods. AGARD AR-211; 1986. |
| [31] | Report of the fluid dynamics panel working group 04. Experimental data base for computer program assessment. AGARD AR-138; 1979.; Report of the fluid dynamics panel working group 04. Experimental data base for computer program assessment. AGARD AR-138; 1979. |
| [32] | Robinson BA, Batina JT, Yang HTY. Aeroelastic analysis of wings using the Euler equations with a deforming mesh. AIAA-90-1032-CP:1510-18.; Robinson BA, Batina JT, Yang HTY. Aeroelastic analysis of wings using the Euler equations with a deforming mesh. AIAA-90-1032-CP:1510-18. |
| [33] | Pullian, T., Artificial dissipation models for Euler equations, AIAA J, 24, 12, 1931-1940 (1986) · Zbl 0611.76075 |
| [34] | Howlett J. Calculation of viscous effects on transonic flow for oscillating airfoils and comparisons with experiments. NASA-TP 2731; 1987.; Howlett J. Calculation of viscous effects on transonic flow for oscillating airfoils and comparisons with experiments. NASA-TP 2731; 1987. |
| [35] | Chen, Z. B.; Bradshawt, P., Calculations of viscous transonic flow over airfoils, AIAA J, 22, 2, 201-205 (1984) · Zbl 0541.76081 |
| [36] | Kirshman, D. J.; Liu, F., Flutter prediction by an Euler method on non-moving Cartesian grids with gridless boundary conditions, Comput Fluids, 35, 571-586 (2006) · Zbl 1160.76379 |
| [37] | Chyu, W. J.; Davis, S. S.; Chang, K. S., Calculation of unsteady transonic flow over an airfoil, AIAA J, 19, 6, 684-690 (1981) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
