Matthias Meinke

A comparison of second- and sixth-order methods for large-eddy simulations

Abstract Large-eddy simulations of spatially developing planar turbulent jets are performed using a compact finite-difference scheme of sixth-order and an advective upstream splitting method-based method of second-order accuracy. The applicability of these solution schemes with different subgrid scale models and their performance for realistic turbulent flow problems are investigated. Solutions of the turbulent channel flow are used as an inflow condition for the turbulent jets. The results compare well with each other and with analytical and experimental data. For both solution schemes, however, the influence of the subgrid scale model on the time averaged turbulence statistics is small. This is known to be the case for upwind schemes with a dissipative truncation error, but here it is also observed for the high-order compact scheme. The reason is found to be the application of a compact high-frequency filter, which has to be used with strongly stretched computational grids to suppress high-frequency oscillations. The comparison of the results of the two schemes shows hardly any difference in the quality of the solutions. The second-order scheme, however, is computationally more efficient.

Large-eddy simulation of low frequency oscillations of the Dean vortices in turbulent pipe bend flows

Large-eddy simulations are performed to investigate turbulent flows through 90° pipe bends that feature unsteady flow separation, unstable shear layers, and an oscillation of the Dean vortices. Single bends with curvature radii of one- and three-pipe diameters are considered at the Reynolds number range 5000–27 000. The numerically computed distributions of the time-averaged velocities, Reynolds stress components, and power spectra of the velocities are validated by comparison with particle image velocimetry measurements. The power spectra of the overall forces onto the pipe walls are determined. The spectra exhibit a distinct peak in the high frequency range that is ascribed to vortex shedding at the inner side of the bends and shear layer instability. At the largest Reynolds number the spectra also exhibit an oscillation at a frequency much lower than that commonly observed at vortex shedding from separation. It turns out that the associated flow pattern is similar to the swirl switching phenomenon earl...

An accurate moving boundary formulation in cut-cell methods

A cut-cell method for Cartesian meshes to simulate viscous compressible flows with moving boundaries is presented. We focus on eliminating unphysical oscillations occurring in Cartesian grid methods extended to moving-boundary problems. In these methods, cells either lie completely in the fluid or solid region or are intersected by the boundary. For the latter cells, the time dependent volume fraction lying in the fluid region can be so small that explicit time-integration schemes become unstable and a special treatment of these cells is necessary. When the boundary moves, a fluid cell may become a cut cell or a solid cell may become a small cell at the next time level. This causes an abrupt change in the discretization operator and a suddenly modified truncation error of the numerical scheme. This temporally discontinuous alteration is shown to act like an unphysical source term, which deteriorates the numerical solution, i.e., it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary. We develop an accurate moving boundary formulation based on the varying discretization operators yielding a cut-cell method which avoids these discontinuities. Results for canonical two- and three-dimensional test cases evidence the accuracy and robustness of the newly developed scheme.

The constrained reinitialization equation for level set methods

Based on the constrained reinitialization scheme [D. Hartmann, M. Meinke, W. Schroder, Differential equation based constrained reinitialization for level set methods, J. Comput. Phys. 227 (2008) 6821-6845] a new constrained reinitialization equation incorporating a forcing term is introduced. Two formulations for high-order constrained reinitialization (HCR) are presented combining the simplicity and generality of the original reinitialization equation [M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146-159] in terms of high-order standard discretization and the accuracy of the constrained reinitialization scheme in terms of interface displacement. The novel HCR schemes represent simple extensions of standard implementations of the original reinitialization equation. The results evidence the significantly increased accuracy and robustness of the novel schemes.

Numerical simulation of the flow field in a model of the nasal cavity

Abstract Results of a numerical simulation of the flow in a model of the human nasal cavity using an AUSM-based method of second-order accuracy on a multi-block structured grid are presented and compared with experimental data. Computations are performed for inspiration and expiration at rest with Reynolds numbers Re =1560 and Re =1230 at the nostril, respectively. The comparison shows good agreement with experimental findings.

Differential equation based constrained reinitialization for level set methods

A partial differential equation based reinitialization method is presented in the framework of a localized level set method. Two formulations of the new reinitialization scheme are derived. These formulations are modifications of the partial differential equation introduced by Sussman et al. [M. Sussman, P. Smereka, S. Osher, A level set approach for computing solutions to incompressible two-phase flow, J. Comput. Phys. 114 (1994) 146-159] and, in particular, improvements of the second-order accurate modification proposed by Russo and Smereka [G. Russo, P. Smereka, A remark on computing distance functions, J. Comput. Phys. 163 (2000) 51-67]. The first formulation uses the least-squares method to explicitly minimize the displacement of the zero level set within the reinitialization. The overdetermined problem, which is solved in the first formulation of the new reinitialization scheme, is reduced to a determined problem in another formulation such that the location of the interface is locally preserved within the reinitialization. The second formulation is derived by systematically minimizing the number of constraints imposed on the reinitialization scheme. For both systems, the resulting algorithms are formulated in a three-dimensional frame of reference and are remarkably simple and efficient. The new formulations are second-order accurate at the interface when the reinitialization equation is solved with a first-order upwind scheme and do not diminish the accuracy of high-order discretizations of the level set equation. The computational work required for all components of the localized level set method scales with O(N). Detailed analyses of numerical solutions obtained with different discretization schemes evidence the enhanced accuracy and the stability of the proposed method, which can be used for localized and global level set methods.

On the assumption of steadiness of nasal cavity flow

The unsteady flow through a model of the human nasal cavity is analyzed at a Strouhal number of Sr=0.791 for the complete respiration cycle. A comparison of the essential flow structures in the model geometry and a real nasal cavity shows the relevance of the model data. The analysis of the steady and unsteady solutions indicate that at Reynolds numbers Re> or =1500 the differences of the solutions of the unsteady and steady flow field can be neglected. To be more precise, the comparison of the total pressure loss distribution as a function of mass flux for the steady state and unsteady solutions shows the major differences to occur at increasing mass flux. At transition from inspiration to expiration the unsteady results differ the most from the steady state solutions. At high mass fluxes the total pressure loss of the nasal cavity flow almost matches that of the steady state solutions. The comparison with rhinomanometry measurements confirms the present numerical findings.

Drag reduction by spanwise transversal surface waves

A numerical simulation of a spatially evolving turbulent boundary layer impacted by a spanwise traveling transversal sinusoidal wall oscillation is performed. Compared to boundary layer flow over a non-oscillating surface, i.e a standard flat plate boundary layer, a reduction of friction drag of more than 6% is found. A detailed discussion of the near-wall flow reveals similar effects as observed by other excitation methods, such as additionally implemented volume forces or longitudinal sinusoidal wall oscillation. Secondary flow structures induced by the moving wall and a controlled formation of streamwise vorticity close to the wall are identified. The wall-normal vorticity fluctuations are found to be damped such that streak instability and formation of new streaks are reduced yielding an evidently decreased friction drag.

Large-eddy simulations of 90° pipe bend flows

Oscillatory phenomena in separated turbulent flows through 90° pipe bends are numerically investigated using large-eddy simulations. Curvature ratios of one and three pipe diameters are considered and the Reynolds numbers range from 5000 up to 27 000. The analysis of the simulations shows that the results are in good agreement with the experimental data. Spectra of the overall forces exhibit a distinct peak in the high-frequency range, related to vortex shedding at the inner side of the bends, and show a low-frequency oscillation at higher Reynolds numbers, which is due to an alternating domination of one of the Dean vortices. The Strouhal number of the low-frequency oscillation matches the so-called swirl switching frequency earlier found in experimental measurements. This article was chosen from selected Proceedings of the Eighth European Turbulence Conference (Advances in Turbulence VIII (Barcelona, 27-30 June 2000) (Barcelona: CIMNE) ed C Dopazo. ISBN: 84-89925-65-8).

Cut-cell method based large-eddy simulation of tip-leakage flow

The turbulent low Mach number flow through an axial fan at a Reynolds number of 9.36 × 105 based on the outer casing diameter is investigated by large-eddy simulation. A finite-volume flow solver in an unstructured hierarchical Cartesian setup for the compressible Navier-Stokes equations is used. To account for sharp edges, a fully conservative cut-cell approach is applied. A newly developed rotational periodic boundary condition for Cartesian meshes is introduced such that the simulations are performed just for a 72° segment, i.e., the flow field over one out of five axial blades is resolved. The focus of this numerical analysis is on the development of the vortical flow structures in the tip-gap region. A detailed grid convergence study is performed on four computational grids with 50 × 106, 250 × 106, 1 × 109, and 1.6 × 109 cells. Results of the instantaneous and the mean fan flow field are thoroughly analyzed based on the solution with 1 × 109 cells. High levels of turbulent kinetic energy and pressure fluctuations are generated by a tip-gap vortex upstream of the blade, the separating vortices inside the tip gap, and a counter-rotating vortex on the outer casing wall. An intermittent interaction of the turbulent wake, generated by the tip-gap vortex, with the downstream blade, leads to a cyclic transition with high pressure fluctuations on the suction side of the blade and a decay of the tip-gap vortex. The disturbance of the tip-gap vortex results in an unsteady behavior of the turbulent wake causing the intermittent interaction. For this interaction and the cyclic transition, two dominant frequencies are identified which perfectly match with the characteristic frequencies in the experimental sound power level and therefore explain their physical origin.