Efficient Generation of Initial- and Inflow-Conditions for Transient Turbulent Flows in Arbitrary Geometries

A method is presented to artificially generate initial conditions and transient inflow-conditions for DNS and LES. It creates velocity fields that satisfy a given Reynolds-stress-tensor and length-scale. Compared to existing approaches, the new method features greater flexibility, efficiency and applicability. It is well suited for the complex geometries and for the arbitrary grids that occur in technical applications. This is demonstrated in connection with the generation of initial data for an internal combustion engine. To assess the accuracy and efficiency of the new approach, it is applied to the test-case of a non-premixed jet-flame, which is known to be sensitive to transient inflow-data.     

Generation of inflow data for inhomogeneous turbulence

Inflow boundary conditions for turbulent plane channel flow are generated by solving evolution equations only for the most energetic eddies. The dynamical systems are derived by Galerkin projecting the Navier-Stokes equations onto the subspaces spanned by various sets of the most energetic modes from a proper orthogonal decomposition (POD) of the same flow. Low-energy small-scale POD-modes are added randomly in order to impose some energy in the high wave number range. This is found to be crucial in order to more rapidly establish the correct level of dissipation and achieve a more realistic distribution of energy between the velocity components. The method is tested on a DNS of R_*=180 and a LES of R_*=400. Statistics such as mean velocity, rms-profiles, turbulent shear-stress and energy spectra become close to the fully developed state within 1500 wall units downstream the inlet. PACS 47.27.Eq     

On the role of the smallest scales of a passive scalar field in a near-wall turbulent flow

Role of the smallest diffusive scales of a passive scalar field in the near-wall turbulent flow was examined with pseudo-spectral numerical simulations. Temperature fields were analyzed at friction Reynolds number Re _τ=171 and at Prandtl numbers, Pr=1 and Pr=5.4. Results of direct numerical simulations (DNS) were compared with the under-resolved simulations where the velocity field was still resolved with the DNS accuracy, while a coarser grid was used to describe the temperature fields. Since the smallest temperature scales remained unresolved in these simulations, an appropriate spectral turbulent thermal diffusivity was applied to avoid pile-up at the higher wave numbers. In spite of coarser numerical grids, the temperature fields are still highly correlated with the DNS results, including instantaneous temperature fields. Results point to practically negligible role of the diffusive temperature scales on the macroscopic behavior of the turbulent heat transfer.     

Modeling of Liquid Fuel Injection, Evaporation and Mixing in a Gas Turbine Burner Using Large Eddy Simulations

The interaction of turbulence, temperature fluctuation, liquid fuel transport, mixing and evaporation is studied by using Large Eddy Simulations (LES). To assess the accuracy of the different components of the methods we consider first isothermal, single phase flow in a straight duct. The results using different numerical methods incorporating dynamic Sub-Grid-Scale (SGS) models are compared with DNS and experimental data. The effects of the interactions among turbulence, temperature fluctuation, spray transport, evaporation and mixing of the gaseous fuel are studied by using different assumptions on the temperature field. It has been found that there are strong non-linear interactions among temperature-fluctuation, evaporation and turbulent mixing which require additional modeling if not full LES is used. The developed models and methods have been applied to a gas turbine burner into which liquid fuel is injected. The dispersion of the droplets in the burner is described. This revised version was published online in July 2006 with corrections to the Cover Date.     

A scaling analysis for point–particle approaches to turbulent multiphase flows

Simple dimensional arguments are used in establishing three different regimes of particle time scale, where explicit expression for particle Reynolds number and Stokes number are obtained as a function of nondimensional particle size (d/η)$(d/\eta )$ and density ratio. From a comparative analysis of the different computational approaches available for turbulent multiphase flows it is argued that the point–particle approach is uniquely suited to address turbulent multiphase flows where the Stokes number, defined as the ratio of particle time scale to Kolmogorov time scale (_τp/_τk)$({\tau }_p/{\tau }_k)$, is greater than 1. The Stokes number estimate has been used to establish parameter range where point–particle approach is ideally suited. The point–particle approach can be extended to handle “finite-sized” particles whose diameter approach that of the smallest resolved eddies. However, new challenges arise in the implementation of Lagrangian–Eulerian coupling between the particles and the carrier phase. An approach where the inter-phase momentum and energy coupling can be separated into a deterministic and a stochastic contribution has been suggested.     

DNS of Mixing and Reaction of Two Species in a Turbulent Channel Flow: A Validation of the Conditional Moment Closure

We consider the chemical reaction in a turbulent flow for the case that the time scale of turbulence and the time scale of the reaction are comparable. This process is complicated by the fact that the reaction takes place intermittently at those locations where the species are adequately mixed. This is known as spatial segregation. Several turbulence models have been proposed to take the effect of spatial segregation into account. Examples are the probability density function (PDF) and the conditional moment closure (CMC) models. The main advantage of these models is that they are able to parameterize the effects of turbulent mixing on the chemical reaction rate. As a price several new unknown terms appear in these models for which closure hypothesis must be supplied. Examples are the conditional dissipation 〈 χ ∣ φ 〉, the conditional diffusion 〈 κ ∇² φ ∣ u, φ 〉 and the conditional velocity 〈 u ∣ φ 〉. In the present study we investigate these unknown terms that appear in the PDF and CMC model by means of a direct numerical simulation (DNS) of a fully developed turbulent flow in a channel geometry. We present the results of two simulations in which a scalar is released from a continuous line source. In the first we consider turbulent mixing without chemical reaction and in the second we add a binary reaction. The results of our simulations agree very well with experimental data for the quantities on which information is available. Several closure hypotheses that have been proposed in the literature, are considered and validated with help of our simulation results. This revised version was published online in July 2006 with corrections to the Cover Date.     

Direct Numerical Simulation of Self-Similar Turbulent Boundary Layers in Adverse Pressure Gradients

Direct numerical simulations of the Navier–Stokes equations have been carried out with the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results can be compared with earlier experiments and simulations. This type of turbulent boundary layers also permits an analysis of the equation of motion to predict separation. The linear analysis based on the assumption of asymptotically high Reynolds number gives results that are not applicable to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the development of an outer peak in the turbulent energy in agreement with experiment. The turbulent flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with the direct simulations and low Reynolds number effects are investigated.     

Joint RANS/LES Approach to Premixed Flame Modelling in the Context of the TFC Combustion Model

We present an original timesaving joint RANS/LES approach to simulate turbulent premixed combustion. It is intended mainly for industrial applications where LES may not be practical. It is based on successive RANS/LES numerical modelling, where turbulent characteristics determined from RANS simulations are used in LES equations for estimation of the subgrid chemical source and viscosity. This approach has been developed using our TFC premixed combustion model, which is based on a generalization of the Kolmogorov’s ideas. We assume existence of small-scale statistically equilibrium structures not only of turbulence but also of the reaction zones. At the same time, non-equilibrium large-scale structures of reaction sheets and turbulent eddies are described statistically by model combustion and turbulence equations in RANS simulations or follow directly without modelling in LES. Assumption of small-scale equilibrium gives an opportunity to express the mean combustion rate (controlled by small-scale coupling of turbulence and chemistry) in the RANS and LES sub-problems in terms of integral or subgrid parameters of turbulence and the chemical time, i.e. the definition of the reaction rate is similar to that of the mean dissipation rate in turbulence models where it is expressed in terms of integral or subgrid turbulent parameters. Our approach therefore renders compatible the combustion and turbulent parts of the RANS and LES sub-problems and yields reasonable agreement between the RANS and averaged LES results. Combining RANS simulations of averaged fields with LES method (and especially coupled and acoustic codes) for simulation of corresponding nonstationary process (and unsteady combustion regimes) is a promising strategy for industrial applications. In this work we present results of simulations carried out employing the joint RANS/LES approach for three examples: High velocity premixed combustion in a channel, combustion in the shear flow behind an obstacle and the impinging flame (a premixed flame attached to an obstacle).     

The near wake structure of a square cylinder

The near wake structure of a square cross section cylinder in flow perpendicular to its length was investigated experimentally over a Reynolds number (based on cylinder width) range of 6700–43,000. The wake structure and the characteristics of the instability wave, scaling on θ at separation, were strongly dependent on the incidence angle () of the freestream velocity. The nondimensional frequency (St_θ) of the instability wave varied within the range predicted for laminar instability frequencies for flat plate wakes, jets and shear layers. For = 22.5°, the freestream velocity was accelerated over the side walls and the deflection of the streamlines (from both sides of the cylinder) towards the center line was higher compared to the streamlines for = 0°. This caused the vortices from both sides of the cylinder to merge by x/d 2, giving the mean velocity distribution typical of a wake profile. For = 0°, the vortices shed from both sides of the cylinder did not merge until x/d 4.5. The separation boundary layer for all cases was either transitional or turbulent, yet the results showed good qualitative, and for some cases even quantitative, agreement with linearized stability results for small amplitude disturbances waves in laminar separation layers.     

DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow

The Lie group, or symmetry approach, developed by Oberlack (see e.g. Oberlack [26] and references therein) is used to derive new scaling laws for various quantities of a zero pressure gradient turbulent boundary layer flow. The approach unifies and extends the work done by Oberlack for the mean velocity of stationary parallel turbulent shear flows. From the two-point correlation (TPC) equations the knowledge of the symmetries allows us to derive a variety of invariant solutions (scaling laws) for turbulent flows, one of which is the new exponential mean velocity profile that is found in the mid-wake region of flat-plate boundary layers. Further, a third scaling group was found in the TPC equations for the one-dimensional turbulent boundary layer. This is in contrast to the Navier–Stokes and Euler equations, which have one and two scaling groups, respectively. The present focus is on the exponential law in the outer region of turbulent boundary layer corresponding new scaling laws for one- and two-point correlation functions. A direct numerical simulation (DNS) of a flat plate turbulent boundary layer with zero pressure gradient was performed at two different Reynolds numbers Re=750,2240. The Navier–Stokes equations were numerically solved using a spectral method with up to 140 million grid points. The results of the numerical simulations are compared with the new scaling laws. TPC functions are presented. The numerical simulation shows good agreement with the theoretical results, however only for a limited range of applicability. PACS 02.20.-a, 47.11.+j, 47.27.Nz, 47.27.Eq     

Analysis of DNS and LES of Flow in a Low Pressure Turbine Cascade with Incoming Wakes and Comparison with Experiments

The flow around a low-pressure turbine rotor blade with incoming periodic wakes is computed by means of DNS and LES. The latter adopts a dynamic sub-grid-scale model. The computed results are compared with time-averaged and instantaneous measured quantities. The simulation sreveal the presence of elongated flow structures, stemming from the incoming wake vorticity, which interact with the pressure side boundary layer. As the wake approaches the upstream half of the suction side, its vortical structures are stretched and align with the main flow, resulting in an impingement at virtually zero angle of attack. Periodically, in the absence of impinging wakes, the laminar suction side boundary layer separates in the adverse pressure gradient region. Flow in the laminar separation bubble is found to undergo transition via a Kelvin–Helmholtz instability. Subsequent impingement of the wake inhibits separation and thus promotes boundary layer reattachment. LES provides a fair reproduction of the DNS results both in terms of instantaneous, phase-averaged, and time-averaged flow fields with a considerable reduction in computational effort. This revised version was published online in July 2006 with corrections to the Cover Date.