Characteristic boundary conditions for simulations of compressible reacting flows with multi-dimensional,viscous and reaction effects

A generalized formulation of the characteristic boundary conditions for compressible reacting flows is proposed. The new and improved approach resolves a number of lingering issues of spurious solution behaviour encountered in turbulent reacting flow simulations in the past. This is accomplished (a) by accounting for all the relevant terms in the determination of the characteristic wave amplitudes and (b) by accommodating a relaxation treatment for the transverse gradient terms with the relaxation coefficient properly determined by the low Mach number asymptotic expansion. The new boundary conditions are applied to a comprehensive set of test problems including: vortex-convection; turbulent inflow; ignition front propagation; non-reacting and reacting Poiseuille flows; and counterflow cases. It is demonstrated that the improved boundary conditions perform consistently superior to existing approaches, and result in robust and accurate solutions with minimal acoustic wave interactions at the boundary in hostile turbulent combustion simulation conditions.     

Low- and high-temperature study of n-heptane combustion chemistry

n-Heptane has been used extensively in various fundamental combustion experiments as a prototypical hydrocarbon fuel. While the formation of polycyclic aromatic hydrocarbon (PAH) in n-heptane combustion has been studied preferably in premixed flames, this study aims to investigate the combustion chemistry of n-heptane in less-studied diffusion flame and highly rich high-temperature homogeneous oxidation configurations by using a counterflow burner and a flow reactor, respectively. This work addresses the formation of higher-molecular species in the mass range up to about 160 u in both configurations. Samples are analyzed by time-of-flight (TOF) molecular beam mass spectrometry (MBMS) using electron-impact (EI) and single-photon ionization (PI). Highly resolved speciation data are reported. Laminar flow reactor experiments cover a wide temperature range. Especially the measurements at low temperatures provide speciation data of large oxygenates produced in the low-temperature oxidation of n-heptane, which are scarce in the literature. Important precursor molecules for PAH and soot formation, such as C₉H₈, C₁₀H₈, C₁₁H_10, and C₁₂H₈, are formed during the high-temperature combustion process in the counterflow flame, while oxygenated growth species are observed under low-temperature conditions, even at the fuel-rich equivalence ratio of ?=4.00.Numerical modeling for both conditions is performed by using a newly developed kinetic model of n-heptane, which includes the n-heptane and PAH formation chemistry with state-of-the-art kinetic knowledge. Good agreement between model predictions and experimental data of counterflow flame and flow reactor is observed for the major species and some intermediates of n-heptane oxidation. While the concentrations of benzene and toluene measured in the counterflow burner are well-reproduced, the numerical results for flow reactor data are not satisfactory. Differences are found between the formation pathways of fulvene, from whose isomerization benzene is produced in diffusion flame and flow reactor.     

On mean flow universality of turbulent wall flows. I. High Reynolds number flow analysis

ABSTRACT

The universality and mathematical physical structure of wall-bounded turbulent flows is a topic of discussions over many decades. There is no agreement about questions like what is the physical mean flow structure, how universal is it, and how universal are theoretical concepts for local and global flow variations. These questions are addressed by using latest direct numerical simulation (DNS) data at moderate Reynolds numbers Re and experimental data up to extreme Re. The mean flow structure is explained by analytical models for three canonical wall-bounded turbulent flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Thorough comparisons with DNS and experimental data provide support for the validity of models. Criteria for veritable physics derived from observations are suggested. It is shown that the models presented satisfy these criteria. A probabilistic interpretation of the mean flow structure shows that the physical constraints of equal entropies and equally likely mean velocity values in a region unaffected by boundary effects impose a universal log-law structure. The structure of wall-bounded turbulent flows is much more universal than previously expected. There is no discrepancy between local logarithmic velocity variations and global friction law and bulk velocity variations. Flow effects are limited to the minimum: the difference of having a bounded or unbounded domain, and the variation range of mean velocity values allowed by the geometry.     

Verified predictions of shape sensitivities in wall-bounded turbulent flows by an adaptive finite-element method

A Continuous Sensitivity Equation (CSE) method is presented for shape parameters in turbulent wall-bounded flows modeled with the standard k–? turbulence model with wall functions. Differentiation of boundary conditions and their complex dependencies on shape parameters, including the two-velocity scale wall functions, is presented in details along with the appropriate methodology required for the CSE method. To ensure accuracy, grid convergence and to reduce computational time, an adaptive finite-element method driven by asymptotically exact error estimations is used. The adaptive process is controlled by error estimates on both flow and sensitivity solutions. Firstly, the proposed approach is applied on a problem with a closed-form solution, derived using the Method of the Manufactured Solution to perform Code Verification. Results from adaptive grid refinement studies show Verification of flow and sensitivity solvers, error estimators and the adaptive strategy. Secondly, we consider turbulent flows around a square cross-section cylinder in proximity of a solid wall. We examine the quality of the numerical solutions by performing Solution Verification and Validation. Then, Sensitivity Analysis of these turbulent flows is performed to investigate the ability of the method to deal with non-trivial geometrical changes. Sensitivity information is used to estimate uncertainties in the flow solution caused by uncertainties in the shape parameter and to perform fast evaluation of flows on nearby configurations.     

Direct numerical simulation of the flow around a wall-mounted square cylinder under various inflow conditions

The flow around a wall-mounted square cylinder of side d is investigated by means of direct numerical simulation (DNS). The effect of inflow conditions is assessed by considering two different cases with matching momentum-thickness Reynolds numbers Re_θ ? 1000 at the obstacle: the first case is a fullyturbulent zero pressure gradient boundary layer, and the second one is a laminar boundary layer with prescribed Blasius inflow profile further upstream. An auxiliary simulation carried out with the pseudo-spectral Fourier–Chebyshev code SIMSON is used to obtain the turbulent time-dependent inflow conditions which are then fed into the main simulation where the actual flow around the cylinder is computed. This main simulation is performed, for both laminar and turbulent-inflows, with the spectral-element method code Nek5000. In both cases the wake is completely turbulent, and we find the same Strouhal number St ? 0.1, although the two wakes exhibit structural differences for x > 3d downstream of the cylinder. Transition to turbulence is observed in the laminar-inflow case, induced by the recirculation bubble produced upstream of the obstacle, and in the turbulent-inflow simulation the streamwise fluctuations modulate the horseshoe vortex. The wake obtained in our laminar-inflow case is in closer agreement with reference particle image velocimetry measurements of the same geometry, revealing that the experimental boundary layer was not fully turbulent in that dataset, and highlighting the usefulness of DNS to assess the quality of experimental inflow conditions.     

Sooting turbulent jet flame: characterization and quantitative soot measurements

Computational fluid dynamics (CFD) modelers require high-quality experimental data sets for validation of their numerical tools. Preferred features for numerical simulations of a sooting, turbulent test case flame are simplicity (no pilot flame), well-defined boundary conditions, and sufficient soot production. This paper proposes a non-premixed C₂H₄/air turbulent jet flame to fill this role and presents an extensive database for soot model validation.     

Characterisation of backflow events over a wing section

Rare backflow (negative wall-shear stress) events have recently been found and quantified in the near-wall region of canonical wall-bounded turbulent flows. Although their existence and correlation with large-scale events have been established beyond numerical and measurement technique uncertainties, their occurrence at numerically high Reynolds numbers is still rare (less than 1 per thousand and 1 per million at the wall and beyond the viscous sublayer, respectively). To better quantify these rare events, the turbulent boundary layer developing over the suction side of a wing section, experiencing an increasing adverse pressure gradient (APG) without separation along its chord c, is considered in the present work. We find that the backflow level of 0.06% documented in turbulent channels and zero-pressure-gradient (ZPG) turbulent boundary layers is already exceeded on the suction side for x/c > 0.3, at friction Reynolds numbers three times lower, while close to the trailing edge the backflow level reaches 30%. Conditional analysis of extreme events indicates that for increasing Clauser pressure-gradient parameters (reaching β ? 35), the flow reaches a state in which the extreme events are more likely aligned with or against the freestream, and that the otherwise strong spanwise component of the wall-shear stress reduces towards the vicinity of the trailing edge. Backflow events subjected to moderate up to strong APG conditions (0.6 < β < 4.1) exhibit an average width of Δz⁺ ? 20, and an average lifetime of Δt⁺ ? 2. This directly connects with the findings by Lenaers et al., and implies that there is a connection between high-Re ZPG and strong APG conditions.     

Direct numerical simulation of transitional flow in a finite length curved pipe

Transition to turbulent flow in a curved pipe has been well studied through experiments and numerical simulations. Numerical simulations often use a helical pipe with an infinite length such that the inlet and outlet boundary conditions can be modelled as periodic which greatly reduces computational time. In this study, we examined a finite length curved pipe with Poiseuille flow imposed at the inlet and a stress-free boundary condition at the outlet. Direct numerical simulation of the Navier-Stokes equations for rigid walls and a Newtonian fluid was performed using nek5000. Straight extensions were added to the inlet and outlet such to diminish the impact of boundary conditions on the flow field in the region with curvature. The examined model has a pipe radius of curvature that is three times the pipe radius. The model has ～355 million nodes and required an order of magnitude greater computational time when compared with an infinite length curved pipe. Results show that the critical Reynolds number, the lowest value with instabilities present in the flow, is much greater than that of a straight pipe and occurs near Re=5000–5200. This is larger than the critical Reynolds number typically reported for an infinite length curved pipe (Re=4200–4300).     

Numerical and experimental investigations on the mach 2 pseudo-shock wave in a square duct

This paper describes numerical and experimental investigations for the multiple shock wave/turbulent boundary layer interaction in a Mach 2 supersonic square duct. The numerical simulation is carried out with the Harten-Yee second-order accuracy TVD scheme and the Baldwin-Lomax turbulence model. The flow conditions are a free-stream Mach number ofM _∞≈=2.0 and a Reynolds number ofRe _∞;=2.5×10⁷ and the flow confinements are δ_∞/h=0.15 (case A) and δ_∞/h=0.25 (case B), respectively. The computational results for both cases show good agreement with the experimental results. Based on these agreements, the flow quantities, which are very difficult to obtain experimentally, are analyzed by numerical simulation. Moreover, the effect of flow confinement on the pseudo-shock wave characteristics is also presented.     

Phase-field lattice-Boltzmann investigation of dendritic evolution under different flow modes

ABSTRACT

Numerical modelling offers an effective method to investigate the effect of convection on dendritic growth; however, the current numerical approach to modelling convection behaviour is simplified, e.g. only simulating a shear flow by setting a constant inlet velocity and a zero-velocity-gradient outlet boundary condition. In this work, based on a phase-field lattice-Boltzmann approach, the effect of various flow modes on dendritic growth is investigated by introducing an external force term to induce flow. Numerical tests (2-D and 3-D) validate that the results according to the force-induced flow agree well with those by the velocity-imposed flow. Intricate convection effects under complex boundary conditions are discussed in detail. Furthermore, this force-induced flow mode allows additional freedom by eliminating the restriction on the initial position of the nuclei, which provides new ways to the microstructure modelling under complex convection.     

Scaling of global momentum transport in Taylor-Couette and pipe flow

We interpret measurements of the Reynolds number dependence of the torque in Taylor-Couette flow by Lewis and Swinney [Phys. Rev. E 59, 5457 (1999)] and of the pressure drop in pipe flow by Smits and Zagarola [Phys. Fluids 10, 1045 (1998)] within the scaling theory of Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)], developed in the context of thermal convection. The main idea is to split the energy dissipation into contributions from a boundary layer and the turbulent bulk. This ansatz can account for the observed scaling in both cases if it is assumed that the internal wind velocity introduced through the rotational or pressure forcing is related to the external (imposed) velocity U, by with and for the Taylor-Couette (U inner cylinder velocity) and pipe flow (U mean flow velocity) case, respectively. In contrast to the Rayleigh-Bénard case the scaling exponents cannot (yet) be derived from the dynamical equations. Received 9 September 2000     

Numerical study on combustion of H2—O2 in a supersonic reactive expansion in a nozzle

A study on expansion flow inside a nozzle considering full mechanism chemistry of hydrogen and oxygen was carried out. In this study, a full implicit scheme for turbulent reactive flow was obtained by combining the second order TVD scheme of Yee and Harten (1987, Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates. American Institute of Aeronautics and Astronautics Journal, 25(2), 266–274) with the efficient implicit lower-upper scheme of Shuen and Yoon (1989, Numerical study of chemically reacting flows using a lower-upper symmetric successive overrelaxation scheme. American Institute of Aeronautics and Astronautics Journal, 27(12), 1752–1756). The species equations, Navier–Stokes equations and turbulence model were implemented in the numerical scheme and solved in conjunction with full detailed finite rate chemistry. The numerical scheme is verified by comparison with experimental results of a converging–diverging nozzle. Effects of inlet pressure, temperature and fuel-oxidant mass ratio on nozzle flow field were studied. Variation of chemical species under different conditions was investigated by considering a chemical mechanism. Results show that increasing inlet pressure increases the rate of reactions due to increasing the concentration of reactants. For lower inlet pressure the radical H increases slightly in the diverging part of the nozzle, while for higher pressures it decreases along the nozzle. Inlet fuel–oxidant mass ratio affects the variation of all species with a greater effect for a near stoichiometric ratio. It was also shown that a higher inlet temperature provides a more enhanced reaction zone in the diverging part of the nozzle.     

边界层流动中湍斑的直接数值模拟

用Navier-Stokes方程直接数值模拟平板边界层流动中湍斑的形成和演化过程.发展了模拟湍斑的高精度、高分辨率的高效计算方法,包括推出四阶时间分裂法以提高精度;提出三维耦合差分方法,用于关于压力的泊松方程和关于速度的亥姆霍兹方程的空间离散,建立其四阶三维耦合中心差分格式;并采用四阶紧致迎风差分格式,避免了一般四阶中心差分格式不适用于边界邻域的困难和提高了分辨率;精心地处理各种边界条件,以保持精度和稳定.该方法适用于包含边界邻域的整个区域内的湍斑模拟.通过模拟平板边界层流动中湍斑的复杂演化过程,显示了湍斑的基本特征.     

Towards a classification of models for the numerical simulation of premixed combustion based on a generalized regime diagram

The inner structure, and the physical behaviour of turbulent premixed flames are usually described, and classified by means of the regime diagram introduced by Borghi and Peters. Thereby properties related to both the flame and the (turbulent) flow are considered. In this work a diagram valid for all physical regimes, comprising suitable requirements for laminar simulations, direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds averaging based numerical simulation (RANS) is proposed. In particular the diagram describes essential situations within the validity limits of the “Borghi, Peters diagram” which physical phenomena are resolved by the simulation, and which have to be modelled. This information is used for systematic classification of various models by suggesting specific models that are appropriate depending on the regime and numerical resolution, and may provide guidance for numerical simulation methods and model development in turbulent premixed combustion. This might help users as a guideline in choosing appropriate models for a given device, and numerical effort available. The regime diagram suggested by Pitsch and Duchamp de Lageneste, which includes DNS and LES by explicitely accounting for the numerical related variable filterwidth, emerges here as one of the special two-dimensional cases possible. In contrast to the generalized regime diagram, their diagram does not include laminar simulations, and RANS based considerations, while transition between wrinkled and corrugated flamelets is not clearly established.     

<Emphasis Type="Italic">β</Emphasis>-distribution for Reynolds stress and turbulent heat flux in relaxation turbulent boundary layer of compression ramp

A challenge in the study of turbulent boundary layers (TBLs) is to understand the non-equilibrium relaxation process after sep-aration and reattachment due to shock-wave/boundary-layer interaction. The classical boundary layer theory cannot deal with the strong adverse pressure gradient, and hence, the computational modeling of this process remains inaccurate. Here, we report the direct numerical simulation results of the relaxation TBL behind a compression ramp, which reveal the presence of intense large-scale eddies, with significantly enhanced Reynolds stress and turbulent heat flux. A crucial finding is that the wall-normal profiles of the excess Reynolds stress and turbulent heat flux obey a β-distribution, which is a product of two power laws with respect to the wall-normal distances from the wall and from the boundary layer edge. In addition, the streamwise decays of the excess Reynolds stress and turbulent heat flux also exhibit power laws with respect to the streamwise distance from the corner of the compression ramp. These results suggest that the relaxation TBL obeys the dilation symmetry, which is a specific form of self-organization in this complex non-equilibrium flow. The β-distribution yields important hints for the development of a turbulence model.     

The investigation of coherent structures in the wall region of a supersonic turbulent boundary layer based on DNS database

Through temporal mode direct numerical simulation, flow field database of a fully developed turbulent boundary layer on a flat plate with Mach number 4.5 and Reynolds number Reθ =1094 has been obtained. Commonly used detection meth- ods in experiments are applied to detecting coherent structures in the flow field, and it is found that coherent structures do exist in the wall region of a supersonic turbulent boundary layer. The detected results show that a low-speed streak is de- tected by using the Mu-level method, the rising parts of this streak are detected by using the second quadrant method, and the crossing regions from a low-speed streak to the high-speed one are detected by using the VITA method respectively. Notwithstanding that different regions are detected by different methods, they are all accompanied by quasi-stream-wise vortex structures.     

Pressure recovery studies on a supersonic COIL with central ejector configuration

A chemical oxygen-iodine laser (COIL) is an electronic transition, low pressure, high throughput system. The field use of this laser demands the development of suitable pressure recovery systems. Ejector based pressure recovery systems form a potent alternative for open cycle COIL operation. The two possible configurations of motive gas injection in ejectors are peripheral and central. The present paper focuses on the investigation of a central injection low pressure ejector operated with a small scale supersonic COIL (SCOIL). The ejector handles a motive flow of nearly 120 g s⁻¹ and an entrained laser flow of nearly 3 g s⁻¹. The predicted geometry using integral methods has been validated numerically by employing Fluent 6.1 software in a 2-d axisymmetric viscous turbulent flow formulation. The numerical predictions have been experimentally validated, which indicate a pressure recovery of 63 Torr at design conditions. The results also show that the recovered pressure improves to 75 Torr for an off-design condition of higher motive flow rate.     

Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

The turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u_∞ / v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.     

Dynamics of immiscible radial viscous fingering: A numerical study

In this paper we undertake a numerical investigation of the dynamics of the interface in the problem of immiscible radial viscous fingering in a Hele-Shaw cell when the areal flow rate is maintained constant. Comparison is made with experimental results to check if there is a need to introduce velocity-dependent boundary conditions and to incorporate the effect of thickness of the film left behind by the moving interface. Some new scaling results are suggested by the numerical data. These data, along with those available from laboratory experiments, provide support for a mean field theory for radial immiscible viscous fingering published recently [Phys. Rev. Lett. 65, 2680 (1990)].     

DNS of compressible turbulent boundary layer around a sharp cone

Direct numerical simulation of the turbulent boundary layer over a sharp cone with 20° cone angle (or 10° half-cone angle) is performed by using the mixed seventh-order up-wind biased finite difference scheme and sixth-order central difference scheme. The free stream Mach number is 0.7 and free stream unit Reynolds number is 250000/inch. The characteristics of transition and turbulence of the sharp cone boundary layer are compared with those of the flat plate boundary layer. Statistics of fully developed turbulent flow agree well with the experimental and theoretical data for the turbulent flat-plate boundary layer flow. The near wall streak-like structure is shown and the average space between streaks (normalized by the local wall unit) keeps approximately invariable at different streamwise locations. The turbulent energy equation in the cylindrical coordinate is given and turbulent energy budget is studied. The computed results show that the effect of circumferential curvature on turbulence characteristics is not obvious.