Martin Wörner

Direct numerical and large eddy simulations in nuclear applications

Direct numerical and large eddy simulations are powerful tools for analyses of turbulent flows at low and large Reynolds or Rayleigh numbers in fundamental research. The current status of both methods and recent extensions are compiled. The progress achieved with subgrid scale models and numerics makes the method attractive for investigations in nuclear research and engineering. Applications of both methods of realistic technical flows are discussed. Open problems are mainly related to more general subgrid scale models for large complex containers, to the wall and inlet conditions for high Reynolds number and buoyant flows, and to discretisation schemes for local refinement of spatial resolution. As a classical example for the use of direct simulations, results are presented for a turbulent internally heated horizontal fluid layer. The analysis of the closure terms in the transport equation of the kinetic energy demonstrates major difficulties of the conventional statistical modelling for partially stably stratified convection.

Numerical investigation of the stability of bubble train flow in a square minichannel

The stability of a train of equally sized and variably spaced gas bubbles that move within a continuous wetting liquid phase through a straight square minichannel is investigated numerically by a volume-of-fluid method. The flow is laminar and cocurrent upward and driven by a pressure gradient and buoyancy. The simulations start from fluid at rest with two identical bubbles placed on the axis of the computational domain, the size of the bubbles being comparable to that of the channel. In vertical direction, periodic boundary conditions are used. These result in two liquid slugs of variable length, depending on the initial bubble-to-bubble distance. The time evolution of the length of both liquid slugs during the simulation indicates if the bubble train flow is “stable” (equal terminal length of both liquid slugs) or “unstable” (contact of both bubbles). Several cases are considered, which differ with respect to bubble size, domain size, initial bubble shape, and separation. All cases lead to axisymmetric ...

Analysis and modelling of the temperature variance equation in turbulent natural convection for low-Prandtl-number fluids

Results of direct numerical simulation (DNS) for Rayleigh-Benard convection for the Prandtl number Pr=0.025 are used to show some peculiarities of turbulent natural convection for low-Prandtl-number fluids. Simulations for this flow at sufficiently large Rayleigh numbers became feasible only recently because this flow requires the resolution of very small velocity scales and the recording of long-wave structures for the slow changes in the convective temperature field

Direct numerical simulation of turbulence in an internally heated convective fluid layer and implications for statistical modelling

Direct numerical simulations (DNS) are reported for the convection in an internally heated convective fluid layer which is bounded by rigid isothermal horizontal walls at equal temperature. The simulations for a fluid Prandtl number of seven cover seven distinct internal Rayleigh numbers in the range 105 ≤ RaI ≤ 109. From the numerical database the changes of convective patterns and dynamics for increasing RaI , i.e. increasing turbulence intensity, are analysed. To support the development and improvement of statistical turbulence models for this special type of convection, turbulence data for mean and fluctuating temperature and velocities are provided. For the simulation with RaI = 108 budgets of turbulence kinetic energy k and vertical turbulent heat flux are presented. In addition, closure assumptions commonly used in statistical turbulence models are tested against the DNS data. It is found that the turbulent diffusive transport of k and is strongly underestimated by standard models. The modelling of...

Pressure transport in direct numerical simulations of turbulent natural convection in horizontal fluid layers

Abstract Direct numerical simulation (DNS) data of two types of turbulent natural convection in horizontal fluid layers are used to compute turbulent diffusive transport terms for turbulence kinetic energy and vertical turbulent heat flux. For both quantities turbulent diffusive transport is represented by a pressure correlation and a triple correlation. While for Rayleigh–Benard convection in air the pressure correlation dominates the triple correlation, for the convection in an internally heated layer the opposite behaviour is observed. The dominance of pressure transport in the Rayleigh–Benard convection and its minor importance in the internally heated layer is explained by the coherent structures and dynamics of the respective flow. The coherent structures are intermittent; they exist only for limited time intervals. Thus, conventional closure relations for turbulent diffusive transport, which are used in statistical turbulence models basing on long-time averaged quantities, may not be appropriate for the flows under consideration.

Numerical and experimental analysis of local flow phenomena in laminar Taylor flow in a square mini-channel

The vertically upward Taylor flow in a small square channel (side length 2 mm) is one of the guiding measures within the priority program “Transport Processes at Fluidic Interfaces” (SPP 1506) of the German Research Foundation (DFG). This paper presents the results of coordinated experiments and three-dimensional numerical simulations (with three different academic computer codes) for typical local flow parameters (bubble shape, thickness of the liquid film, and velocity profiles) in different cutting planes (lateral and diagonal) for a specific co-current Taylor flow. For most quantities, the differences between the three simulation results and also between the numerical and experimental results are below a few percent. The experimental and computational results consistently show interesting three-dimensional flow effects in the rear part of the liquid film. There, a local back flow of liquid occurs in the fixed frame of reference which leads to a temporary reversal of the direction of the wall shear stress during the passage of a Taylor bubble. Notably, the axial positions of the region with local backflow and those of the minimum vertical velocity differ in the lateral and the diagonal liquid films. By a thorough analysis of the fully resolved simulation results, this previously unknown phenomenon is explained in detail and, moreover, approximate criteria for its occurrence in practical applications are given. It is the different magnitude of the velocity in the lateral film and in the corner region which leads to azimuthal pressure differences in the lateral and diagonal liquid films and causes a slight deviation of the bubble from the rotational symmetry. This deviation is opposite in the front and rear parts of the bubble and has the mentioned significant effects on the local flow field in the rear part of the liquid film.

Balance of Liquid-phase Turbulence Kinetic Energy Equation for Bubble-train Flow

In this paper the investigation of bubble-induced turbulence using direct numerical simulation (DNS) of bubbly two-phase flow is reported. DNS computations are performed for a bubble-driven liquid motion induced by a regular train of ellipsoidal bubbles rising through an initially stagnant liquid within a plane vertical channel. DNS data are used to evaluate balance terms in the balance equation for the liquid phase turbulence kinetic energy. The evaluation comprises single-phase-like terms (diffusion, dissipation and production) as well as the interfacial term. Special emphasis is placed on the procedure for evaluation of interfacial quantities. Quantitative analysis of the balance equation for the liquid phase turbulence kinetic energy shows the importance of the interfacial term which is the only source term. The DNS results are further used to validate closure assumptions employed in modelling of the liquid phase turbulence kinetic energy transport in gas-liquid bubbly flows. In this context, the performance of respective closure relations in the transport equation for liquid turbulence kinetic energy within the two-phase k—epsilon and the two-phase k—l model is evaluated.

Shock structure near a wall in pure inert gas and in binary inert-gas mixtures

The shock-wave structure close to a wall in pure argon and binary mixtures of noble gases (argon–helium, xenon–helium) is investigated experimentally and numerically in the shock-wave Mach-number range 2·24 ≤ M s ≤ 9.21. Measured and calculated density profiles are compared, and some conclusions are drawn about the accommodation at the wall and the intermolecular force potential. For binary gas mixtures only a few results are presented. Weak argon signals of the electron-beam-luminescence method on the experimental side and the computer time needed for the numerical simulation allowed the treatment of a few parameter combinations only.

Consistent modelling of fluctuating temperature-gradient-velocity-gradient correlations for natural convection

A model is proposed for the buoyant production term in the dissipation rate equation of turbulence kinetic energy and the molecular sink term in the turbulent heat flux equation. Based on an analytical decomposition by a two-point correlation technique, the model consists of an inhomogeneous and a homogeneous part. The inhomogeneous part involves the Laplacian operator of the turbulent heat flux and needs no further modeling. For the homogeneous part of the model is derived that incorporates Pr/R as key parameter, where Pr is the Prandtl number and R is the ratio of thermal to mechanical turbulent time scales. The model is shown to obey the correct wall-limiting behaviour without further wall corrections. Comparisons with (DNS) data for Rayleigh Benard convection in air and sodium, and for convection in an internally heated fluid layer confirm its excellent near-wall performance for a wide range of Prandtl numbers. Utilizing these DNS data, the performance of the model in the bulk region is improved by slightly modifying the homogeneous part of the model.

Analysis of Semi-Implicit Time Integration Schemes For Direct Numerical Simulation of Turbulent Convection in Liquid Metals

Fully explicit time integration schemes are very inefficient for numerical simulation of diffusion dominated problems. In case of natural convection flow in liquid metals an implicit treatment of the thermal diffusion terms allows for the use of substantially increased time steps without involving loss of physically relevant information. Two suitable semi-implicit time integration schemes are investigated analytically by a Von Neumann stability analysis and a spectral analysis of the numerical error. Numerical solutions by the semi-implicit schemes are compared to the exact solution of a 1D linear test problem. The results show the crucial influence of the discretization ratio X = At/Ax on the accuracy of the numerical solutions. First 3D time dependent numerical simulations of natural convection in liquid metals with the semi-implicit time integration schemes confirm the theoretically estimated gain in the time step width and result in CPU-time savings up to a factor of 50 compared to the fully explicit scheme.