Cord-Christian Rossow

The MEGAFLOW project

Within the framework of the German aerospace research program, the CFD project MEGAFLOW was initiated. Its goal is the development and validation of a dependable and efficient numerical tool for the aerodynamic simulation of complete aircraft in cruise as well as in take-off and landing configurations. In order to meet the requirements for industrial implementation, a concentrated cooperative effort involving the aircraft industry, the DLR and several universities has been set up. This paper gives an overview of the goals and the major achievements of the project. It is concluded with an outlook towards future developments.

Efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central-difference approximations and Runge-Kutta time stepping, is described. By using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method, and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques,which are important for convergence on meshes with high-aspect-ratio cells, are discussed. Emphasis is placed on the analysis of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

Convergence acceleration of Runge-Kutta schemes for solving the Navier-Stokes equations

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7x10^6 and 100x10^6. It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between 4 and 10.

Efficient computation of compressible and incompressible flows

The combination of explicit Runge-Kutta time integration with the solution of an implicit system of equations, which in earlier work demonstrated increased efficiency in computing compressible flow on highly stretched meshes, is extended toward conditions where the free stream Mach number approaches zero. Expressing the inviscid flux Jacobians in terms of Mach number, an artificial speed of sound as in low Mach number preconditioning is introduced into the Jacobians, leading to a consistent formulation of the implicit and explicit parts of the discrete equations. Besides extension to low Mach number flows, the augmented Runge-Kutta/Implicit method allowed the admissible Courant-Friedrichs-Lewy number to be increased from O(100) to O(1000). The implicit step introduced into the Runge-Kutta framework acts as a preconditioner which now addresses both, the stiffness in the discrete equations associated with highly stretched meshes, and the stiffness in the analytical equations associated with the disparity in the eigenvalues of the inviscid flux Jacobians. Integrated into a multigrid algorithm, the method is applied to efficiently compute different cases of inviscid flow around airfoils at various Mach numbers, and viscous turbulent airfoil flow with varying Mach and Reynolds number. Compared to well tuned conventional methods, computation times are reduced by half an order of magnitude.

Convergence Acceleration for Solving the Compressible Navier-Stokes Equations

A fully implicit operator for implicit smoothing of residuals in the framework of explicit Runge-Kutta time stepping and multigrid acceleration is developed. To avoid memory overhead associated with storing the complete flux Jacobians, the Jacobians are expressed in terms of Mach number to enable economic computation of all flux Jacobians during iteration. The implicit operator allows increasing Courant-Friedrichs-Lewy numbers of the basic explicit scheme to the order of 100, and it properly addresses the stiffness in the discrete equations associated with highly stretched meshes. The proposed method was applied to different cases of viscous, turbulent airfoil flow, and convergence rates ranging from 0.8 to 0.87 were achieved. Comparing the present scheme to well-tuned state-of-the-art methods using common implicit residual smoothing techniques, CPU time is better than halved.

The MEGAFLOW Project — Numerical Flow Simulation for Aircraft

Some years ago the national CFD project MEGAFLOW was initiated in Germany, which combined many of the CFD development activities from DLR, universities and aircraft industry. Its goal was the development and validation of a dependable and efficient numerical tool for the aerodynamic simulation of complete aircraft which met the requirements of industrial implementations. The MEGAFLOW software system includes the block-structured Navier-Stokes code FLOWer and the unstructured Navier-Stokes code TAU. Both codes have reached a high level of maturity and they are intensively used by DLR and the German aerospace industry in the design process of new aircraft. Recently, the follow-on project MEGADESIGN was set up which focuses on the development and enhancement of efficient numerical methods for shape design and optimization. This paper highlights recent improvements and enhancements of the software. Its capability to predict viscous flows around complex industrial applications for transport aircraft design is demonstrated. First results concerning shape optimization are presented.

Numerical Simulation of Engine Airframe Integration for High-Bypass Engines

Abstract Due to a trend towards very high-bypass ratio engines and a corresponding close coupling of engine and airframe, the minimization of adverse interference effects is an important aspect in aircraft design. Investigations of engine/airframe integration have been carried out within a long-term collaborative European research initiative, starting in 1990 with the programs DUPRIN I, DUPRIN II to the current ENIFAIR and AIRDATA projects. Based on some selected results the contribution highlights major outcomes of the numerical activities accompanying the experimental studies in the aforementioned programs. After a brief introduction to the basic aerodynamic phenomena of engine/airframe interference and the numerical methods in use, the capabilities of the theoretical approach are demonstrated for three aspects: The influence of increasing engine size on the aerodynamic interference is outlined by simulating turbine powered engine simulators (TPS) of different bypass ratio on the ALVAST narrow body wing/fuselage model. Second, the influence of position variations is demonstrated for different engine concepts, representing the major design parameter for influencing engine/airframe interference. Finally, the jet influence is stressed by comparing numerical results for different thrust conditions. The investigations show, that the lift loss, caused by the mounting of engines, is proportional to the engine size. An upstream movement of the engine position alleviates the lift loss, whereas a vertical movement does not have a significant influence. Especially for the VHBR and UHBR concepts the incorporation of the engine jet is essential to assess the aerodynamic interference. In general validated numerical methods are capable to simulate the dominant features of engine/airframe integration.

Extension of a Compressible Code Toward the Incompressible Limit

Pressure is used as a dependent variable for consistent extension toward incompressible flows. The proposed method exploits the fact that the divergence-free constraint on the velocity field for incompressible flow derives from the energy equation. In the compressible regime the implicit elliptic pressure equation transforms into an explicit hyperbolic equation, leading to the common formulation used in explicit compressible codes. The method strictly respects the strong conservation form, and reliable shock capturing is established by the use of a proven approximate Riemann solver for flux computation

Numerical Aerodynamics at DLR

Abstract Some years ago the national CFD project MEGAFLOW was initiated in Germany to combine many of the CFD development activities from DLR, universities and aircraft industry. Its goal was the development and validation of a dependable and efficient numerical tool for the aerodynamic simulation of complete aircraft which met the requirements of industrial implementations. The MEGAFLOW software system includes the block-structured Navier-Stokes code FLOWer and the unstructured Navier-Stokes code TAU. Both codes have reached a high level of maturity and they are intensively used by DLR and the German aerospace industry in the design process of new aircraft. Recently, the follow-on project MEGADESIGN and MEGAOPT were set up which focus on the development and enhancement of efficient numerical methods for shape design and optimization. This article highlights recent improvements of the software and its capability to predict viscous flows for complex industrial aircraft applications.

Numerical Simulation ??? Complementing Theory and Experiment as the Third Pillar in Aerodynamics

Numerical flow simulation has matured to a point where it is widely accepted as analysis and design tool complementary to theoretical considerations and experimental investigations. Methods to solve the Navier-Stokes equations have developed from specialized research techniques to practical engineering tools being used on a routine basis in the industrial design process. Examples for the development path followed in the DLR Institute of Aerodynamics and Flow Technology to mature Computational Fluid Dynamics are presented, and the level reached today is illustrated by examples of flow computations for civil transport aircraft, military aircraft, and helicopter. Finally, the major challenges for future development are outlined and perspectives for the coming years are given.