Wolfgang Schröder

An efficient conservative cut-cell method for rigid bodies interacting with viscous compressible flows

A Cartesian cut-cell method for viscous flows interacting with freely moving boundaries is presented. The method enables a sharp resolution of the embedded boundaries and strictly conserves mass, momentum, and energy. A new explicit Runge-Kutta scheme (PC-RK) is introduced by which the overall computational time is reduced by a factor of up to 2.5. The new scheme is a predictor-corrector type reformulation of a popular class of Runge-Kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy. The structural motion is computed by an implicit scheme with good stability properties due to a strong-coupling strategy and the conservative discretization of the flow solver at the material interfaces. A new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted Taylor-series approach solved via singular-value decomposition. The efficiency and the accuracy of the new method are demonstrated for several three-dimensional cases of laminar and turbulent particulate flow. It is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid-solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed. The results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes. An efficient Cartesian cut-cell method for freely moving solid boundaries is presented.The new predictor-corrector Runge-Kutta scheme (PC-RK) enables simulation speedups of up to 2.5.Mass, momentum, and energy are strictly conserved at the sharply resolved solid-fluid interfaces.The method exhibits very good stability and accuracy properties even for large displacements of the boundaries.Spurious force oscillations inherent to this class of methods are suppressed.

Analysis of acoustic and entropy disturbances in a hypersonic wind tunnel

The tunnel noise in a Mach 5.9 Ludwieg tube is determined by two methods, a newly developed cone-probe-DNS method and a reliable hot-wire-Pitot-probe method. The new method combines pressure and heat flux measurements using a cone probe and direct numerical simulation (DNS). The modal analysis is based on transfer functions obtained by the DNS to link the measured quantities to the tunnel noise. The measurements are performed for several unit-Reynolds numbers in the range of 5 ⋅ 106 ≤ Re/m ≤ 16 ⋅ 106 and probe positions to identify the sensitivities of tunnel noise. The DNS solutions show similar response mechanisms of the cone probe to incident acoustic and entropy waves which leads to high condition numbers of the transfer matrix such that a unique relationship between response and source mechanism can be only determined by neglecting the contribution of the non-acoustic modes to the pressure and heat flux fluctuations. The results of the cone-probe-DNS method are compared to a modal analysis based on t...

Hydrodynamic instability and shear layer effects in turbulent premixed combustion

A turbulent premixed plane jet flame is analyzed by large-eddy simulations. The analysis shows that the flame front wrinkling is strongly influenced by the shear layer effect when the gas expansion effects are small leading to larger flame front amplitudes at the flame base than at high gas expansion ratios. However, the hydrodynamicinstabilityeffect induces a continuously increasing flame front amplitude which yields an enhanced flame pocket generation at the flame tip. Both phenomena influence the magnitude of the turbulent burning area and burning area rate response through the flame front deflections which are determined by the contribution coefficient. This coefficient represents the mutual interaction between the flame and the flow. At low gas expansion ratios, the total heat release rate spectra of the turbulentflame are wider in terms of dominant modes at Strouhal numbers which are linked to the mean flame height oscillations. Thus, at low gas expansion ratios, the vortex-flame interaction is less damped by the flame in the sense that vortices can perturb the flame front stronger. The total heat release rate trend of St−2.2 previously found for a round jet flame is also determined for the current slot jet at realistic gas expansion ratios indicating a general tendency to transfer energy from large to small flame structures. At high gas expansion ratios, an increasing Markstein length leads to an energy transfer between neighboring dominant modes in the low frequency range 1 < St < 10 and the burning area rate response becomes more important for the total heat release rate spectra of the turbulent slot flames which agrees with recent findings for a laminar premixed plane flame.

Impact of transversal traveling surface waves in a non-zero pressure gradient turbulent boundary layer flow

The impact of non-zero pressure gradient flow in a turbulent boundary layer flow over a surface undergoing spanwise transversal traveling waves is investigated via large-eddy simulations. While it is known that in zero-pressure gradient flow spanwise surface waves can lead to drag reduction, this question still remains open for non-zero pressure gradient flows. In the present analysis, the effect of a linear pressure gradient is investigated and compared to the zero-pressure gradient flow at a momentum thickness based Reynolds number R e ? = 2000 for a constant surface wave, i.e., the wave length is λ + = 500 , the amplitude A + = 50 , and the wave speed is c + = 6.25 . The results show a drag reduction of about 10% for the zero-pressure gradient flow, 6% for the adverse-pressure gradient, and a drag increase of 4% for the favorable-pressure gradient flow. The analysis of the velocity profiles shows a reduced gradient at the trough region for all actuated setups. At the crest, an increased gradient is obtained. Furthermore, the viscous sublayer is extended. The streamwise turbulent intensity is reduced for all configurations compared to the non-actuated reference case at the crest. At the trough, the shift off the wall is only present for the zero-pressure gradient flow and the adverse pressure gradient flow. The hypothesis based on numerous zero-pressure gradient flow investigations of a reduced wall-normal vorticity component at the crest and trough indicating drag reduction is corroborated. That is, for the adverse-pressure gradient flow the wall-normal component distribution is lowered and for the favorable pressure gradient flow, which possesses a drag increase, the distribution at the trough is similar to that of the reference non-actuated case.

Experimental analysis of particle sizes for PIV measurements

The right choice of seeding particles strongly influences the outcome of a particle-image velocimetry (PIV) measurement. Particles have to scatter enough light to be seen by cameras and follow the flow faithfully. As the flow following behavior depends on the inertia and therefore the size of the particle, smaller particles are desirable. Unfortunately, larger particles possess better light scattering behavior, which is especially important for volumetric PIV measurements. In this paper, the particle response of two exemplary solid particles to an oscillatory air flow created by a piston movement is analyzed and compared to analytic results by Hjelmfelt and Mockros (1966 Appl. Sci. Res. 16 149–61) concerning phase lag and amplitude ratio between particle movement and flow field. To achieve realistic experimental boundary conditions, polydispersed particles are used for the analysis. The analytic results show a strong dependence on the diameter. That is, using the volumetric mean diameter an overestimation of the phase lag of the particles is determined, whereas an underestimation of phase lag is computed for the number mean diameter. Hence, for polydispersed particles a more general analysis than that based on the particle mean diameter is required to determine in detail the particle following behavior.

A numerical analysis to evaluate Betz's Law for vertical axis wind turbines

The upper limit for the energy conversion rate of horizontal axis wind turbines (HAWT) is known as the Betz limit. Often this limit is also applied to vertical axis wind turbines (VAWT). However, a literature review reveals that early analytical and recent numerical approaches predicted values for the maximum power output of VAWTs close to or even higher than the Betz limit. Thus, it can be questioned whether the application of Betzs Law to VAWTs is justified. To answer this question, the current approach combines a free vortex model with a 2D inviscid panel code to represent the flow field of a generic VAWT. To ensure the validity of the model, an active blade pitch control system is used to avoid flow separation. An optimal pitch curve avoiding flow separation is determined for one specific turbine configuration by applying an evolutionary algorithm. The analysis yields a net power output that is slightly (≈6%) above the Betz limit. Besides the numerical result of an increased energy conversion rate, especially the identification of two physical power increasing mechanisms shows, that the application of Betzs Law to VAWTs is not justified.

Aeroacoustic Simulations of Ducted Axial Fan and Helicopter Engine Nozzle Flows

The flow and the acoustic field of an axial fan and a helicopter engine jet are computed by a hybrid fluid dynamics – computational aeroacoustics method. For the predictions of the flow field a high-fidelity, parallelized solver for compressible flow is used in the first step. In the second step, the acoustic field is determined by solving the acoustic perturbation equations. The axial fan is investigated at a Reynolds number of Re = 9. 36 × 105 for two tip-gap sizes, i.e., s∕D o = 0. 001 and s∕D o = 0. 01 at a fixed flow rate coefficient Φ = 0. 195. A comparison of the numerical results of the pressure spectrum and its directivity with measurements show a good agreement which confirms the correct identification of the sound sources and the accurate prediction of the acoustic duct propagation. Furthermore, the results show in agreement with the experimental data a higher broadband noise level for the larger tip-gap size. In the second application, jets from three different helicopter engine nozzles at a Reynolds number of Re = 7. 5 × 105 are investigated, showing an important dependence of the jet acoustic near field on the presence of the nozzle built-in components. The presence of the centerbody increases the OASPL compared to the clean nozzle, where the inclusion of struts reduces the OASPL compared to the centerbody nozzle owing to the increased turbulent mixing caused by the struts which lesses the length and time scales of the turbulent structures shed from the centerbody.

Large-Eddy Simulation of the Flow Field in a Rotating Axial Fan

Large-eddy simulation (LES) results of the turbulent flow field in a \(72^{\circ }\) segment of a rotating axial fan are discussed. A newly developed finite-volume flow solver which is based on non-boundary-fitted Cartesian grids is used to solve the three-dimensional flow equations for viscous compressible fluids. Computations are performed for two operating points at a constant Reynolds number of \(9.36 \times 10^5\) based on the outer casing wall diameter. The capability of the method to accurately resolve the main flow phenomena including the unsteady turbulent tip-gap vortices is demonstrated.