Multi-Technique Analysis of Soot Reactivity from Conventional and Paraffinic Diesel Fuels

A 2.0 L, 4-cylinder, turbocharged, common rail diesel engine was used for generating soot samples. Three fuels were tested: a “first fill” diesel fuel, a gas-to-liquid fuel (GTL) and a hydrotreated fuel derived from vegetable oils (HVO). A stationary low-load operating mode (1667 rpm and 78 Nm) was selected for testing, and some modifications in the injection process (strategy, timing and pressure) were evaluated experimentally to assess their influence in the soot reactivity. The collected soot samples were characterized using a thermogravimetric analyzer (TGA), a differential scanning calorimeter (DSC), a diffuse reflectance infrared Fourier transform spectrometer (DRIFTS) and a surface area analyzer. All techniques anticipated that HVO and GTL soot samples are more reactive (i.e. show higher potential to be oxidized at lower temperatures leading to more efficient regeneration processes in a Diesel Particle Filter – DPF) compared to diesel soot. Additionally, the four characterization techniques showed the same tendencies when analyzing the effect of the engine operating parameters. In view of the results, the paraffinic fuels – HVO and GTL – here tested confirm their promising perspective for future use in automotive diesel engines, while some guides are proposed to enhance the soot reactivity via calibration of engine operating parameters.     

A Two-Dimensional Tabulated Flamelet Combustion Model for Furnace Applications

A new tabulated chemistry approach for representing turbulent combustion in industrial furnaces is presented. This model is based on the tabulation of two dimensional diffusion flamelets to account for ternary mixtures between fuel, oxidant and burned gases which are integrated over probability density functions. To avoid excessive CPU time for the table generation, the calculation of the two dimensional flamelets is performed using the method proposed in the ADF-PCM (Approximated Diffusion Flame - Presumed Conditional Moment) approach: only the equation for the progress variable is solved, instead of the equations for all species. The progress variable reaction rate is given by a table of homogeneous reactors using the DHR model (Diluted Homogeneous Reactor) proposed by Locci et al. These approximated diffusion flames are first compared to exact diffusion flames computed using the flamelet equations and the chemistry for all species. The resulting model, called A2DF (Approximate 2 Dimensional Flamelet) is then applied to the RANS (Reynolds Averaged Navier-Stokes) simulations of Sandia Flames D and F, showing a good agreement with experimental measurements. Finally, this model is applied to the flameless and conventional combustion cases of the burner of Verissimo et al., showing a correct agreement for temperature and species predictions.     

An Anisotropic A posteriori Error Estimator for CFD

In this article, a robust anisotropic adaptive algorithm is presented, to solve compressible-flow equations using a stabilized CFD solver and automatic mesh generators. The association includes a mesh generator, a flow solver, and an a posteriori error-estimator code. The estimator was selected among several choices available (Almeida et al. (2000). Comput. Methods Appl. Mech. Engng , 182 , 379-400; Borges et al. (1998). "Computational mechanics: new trends and applications". Proceedings of the 4th World Congress on Computational Mechanics , Bs.As., Argentina) giving a powerful computational tool. The main aim is to capture solution discontinuities, in this case, shocks, using the least amount of computational resources, i.e. elements, compatible with a solution of good quality. This leads to high aspect-ratio elements (stretching). To achieve this, a directional error estimator was specifically selected. The numerical results show good behavior of the error estimator, resulting in strongly-adapted meshes in few steps, typically three or four iterations, enough to capture shocks using a moderate and well-distributed amount of elements.     

A method for implementing time-integral constitutive equations in commercial CFD packages

A method is described for obtaining viscoelastic flow solutions, based upon time-integral constitutive equations, using a general purpose CFD package. The method is general enough to be applied to any available software that has rudimentary input and output facilities and can solve a Stoke's flow problem. From this basis, flexibility of choice of constitutive equation and computational techniques is available. The method is presented in a form appropriate for solving both planar and axisymmetric flows. Delaunay triangulation is used to reconstruct a mesh for external code, and stress computation procedures are performed on this mesh. The method has only two particular requirements for the CFD package used – it must be able to output nodal values (of position and velocity) to file and it must be able to read body-forces from a file. Two methods of velocity adjustment were compared: an incremental method and a method whereby the viscoelastic stresses were incorporated directly as body-forces. Results and convergence from the two methods were found to be essentially identical, hence the direct body-force method (which is considerably easier to implement) is described in detail. The method is applied to a well-known flow problem of LDPE melt through a 4 : 1 abrupt contraction axisymmetric die. Convergence was obtained up to nearly the highest value of apparent shear rate for which published simulation results are available. Quantitative results for vortex strength, vortex opening angle and Couette correction are presented which are compared with earlier work on the problem using other methods. Agreement is generally good, giving confidence in the method. Simulations of planar flows of the same melt are performed: a decreasing corner vortex was observed. This phenomenon has been observed experimentally for flows of other substances, but is not expected for flows of LDPE melt. A parametric study of a critical strain hardening parameter is conducted to help explain the cause of the results.     

A robust near-wall elliptic-relaxation eddy-viscosity turbulence model for CFD

An eddy-viscosity model based on Durbin’s elliptic relaxation concept is proposed, which solves a transport equation for the velocity scales ratio instead of , thus making the model more robust and less sensitive to grid nonuniformities. Computations of flows and heat transfer in a plane channel, behind a step and in a round impinging jet show all satisfactory results.     

A framework for CFD analysis of helicopter rotors in hover and forward flight

A framework is described and demonstrated for CFD analysis of helicopter rotors in hover and forward flight. Starting from the Navier–Stokes equations, the paper describes the periodic rotor blade motions required to trim the rotor in forward flight (blade flapping, blade lead‐lag and blade pitching) as well as the required mesh deformation. Throughout, the rotor blades are assumed to be rigid and the rotor to be fully articulated with separate hinges for each blade. The employed method allows for rotors with different numbers of blades and with various rotor hub layouts to be analysed. This method is then combined with a novel grid deformation strategy which preserves the quality of multi‐block structured, body‐fitted grids around the blades. The coupling of the CFD method with a rotor trimming approach is also described and implemented. The complete framework is validated for hovering and forward flying rotors and comparisons are made against available experimental data. Finally, suggestions for further development are put forward. For all cases, results were in good agreement with experiments and rapid convergence has been obtained. Comparisons between the present grid deformation method and transfinite interpolation were made highlighting the advantages of the current approach. Copyright © 2006 John Wiley & Sons, Ltd.     

A new hybrid turbulence modelling strategy for industrial CFD

This paper presents a new strategy for turbulence model employment with emphasis on the model's applicability for industrial computational fluid dynamics (CFD). In the hybrid modelling strategy proposed here, the Reynolds stress and mean rate of strain tensors are coupled via Boussinesq's formula as in the standard k–εmodel. However, the turbulent kinetic energy is calculated as the sum of the normal Reynolds‐stress components, representing the solutions of the appropriate transport equations. The equations governing the Reynolds‐stress tensor and dissipation rate have been solved in the framework of a ‘background’ second‐moment closure model. Furthermore, the structure parameter C‐µ has been re‐calculated from a newly proposed functional dependency rather than kept constant. This new definition of C‐µ has been assessed by using direct numerical simulation (DNS) results of several generic flow configurations featuring different phenomena such as separation, reattachment and rotation. Comparisons show a large departure of C‐µ from the commonly used value of 0.09. The model proposed is computationally validated in a number of well‐proven fluid flow benchmarks, e.g. backward‐facing step, 180° turn‐around duct, rotating pipe, impinging jet and three‐dimensional (3D) Ahmed body. The obtained results confirm that the present hybrid model delivers a robust solution procedure while preserving most of the physical advantages of the Reynolds‐stress model over simple k–εmodels. A low Reynolds number version of the hybrid model is also proposed and discussed. Copyright © 2003 John Wiley & Sons, Ltd.     

A multiblock/multilevel mesh refinement procedure for CFD computations

A multiblock/multilevel algorithm with local refinement for general two‐ and three‐dimensional fluid flow is presented. The patched‐based local refinement procedure is presented in detail and algorithmic implementations are also presented. The multiblock implementation is essentially block‐unstructured, i.e. each block having its own local curvilinear co‐ordinate system. Refined grid patches can be put anywhere in the computational domain and can extend across block boundaries. To simplify the implementation, while still maintaining sufficient generality, the refinement is restricted to a refinement of the grid successively halving the grid size within a selected patch. The multiblock approach is implemented within the framework of the well‐known SIMPLE solution strategy. Computational experiments showing the effect of using the multilevel solution procedure are presented for a sample elliptic problem and a few benchmark problems of computational fluid dynamics (CFD). Copyright © 2001 John Wiley & Sons, Ltd.     

CFD in research for the petrochemical industry

Existing computer programs for turbulent flow simulations have been tested on their capacity to solve practical problems in engineering research for the petrochemical industry. This paper presents results of six validation studies which are all related to experimental work carried out in the Shell Group laboratories. On the basis of these studies needs for further improvement and validation of both numerical schemes and turbulence models have been formulated.The present as well as future relevance of Computational Fluid Dynamics (CFD) in engineering research is discussed in a wider context than covered by the validation studies. This analysis formed the basis for the identification of a number of CFD areas which have great potential in engineering application but need substantial further research and development to make them suitable for this purpose.     

A Modica-Mortola Approximation for Branched Transport and Applications

The M ^α energy which is usually minimized in branched transport problems among singular one-dimensional rectifiable vector measures is approximated by means of a sequence of elliptic energies defined on more regular vector fields. The procedure recalls the one of Modica-Mortola related to the approximation of the perimeter. In our context, the double-well potential is replaced by a concave term. The paper contains a proof of Γ−convergence and numerical simulations of optimal networks based on that previous result.     

A Stability Criterion for Two-Fluid Interfaces and Applications

We derive a new stability criterion for two-fluid interfaces that ensures the existence of “stable” local solutions that do not break down too fast due to Kelvin–Helmholtz instabilities. It can be seen both as a two-fluid generalization of the Rayleigh–Taylor criterion and as a nonlinear version of the Kelvin stability condition. We show that gravity can control the inertial effects of the shear up to frequencies that are high enough for the surface tension to play a relevant role. This explains why surface tension is a necessary condition for well-posedness while the (low frequency) main dynamics of interfacial waves are unaffected by it. In order to derive a practical version of this criterion, we work with a nondimensionalized version of the equations and allow for the possibility of various asymptotic regimes, such as the shallow water limit. This limit being singular, we have to derive a new symbolic analysis of the Dirichlet–Neumann operator that includes an infinitely smoothing “tail” accounting for the contribution of the bottom. We then validate our criterion by comparison with experimental data in two important settings: air–water interfaces and internal waves. The good agreement we observe allows us to discuss the scenario of wave breaking and the behavior of water-brine interfaces, and to propose a formula for the maximal amplitude of interfacial waves. We also show how to rigorously justify two-fluid asymptotic models used for applications and how to relate some of their properties to Kelvin–Helmholtz instabilities.     

Existence and Uniqueness for a Coupled Parabolic-Elliptic Model with Applications to Magnetic Relaxation

We prove the existence, uniqueness and regularity of weak solutions of a coupled parabolic-elliptic model in 2D, and the existence of weak solutions in 3D; we consider the standard equations of magnetohydrodynamics with the advective terms removed from the velocity equation. Despite the apparent simplicity of the model, the proof in 2D requires results that are at the limit of what is available, including elliptic regularity in L ¹ and a strengthened form of the Ladyzhenskaya inequality $$\| f \|_{L^{4}} \leqq c \| f \|_{L^{2,\infty}}^{1/2} \|\nabla f\|_{L^{2}}^{1/2},$$ which we derive using the theory of interpolation. The model potentially has applications to the method of magnetic relaxation introduced by Moffatt (J Fluid Mech 159:359–378, 1985) to construct stationary Euler flows with non-trivial topology.     

A Collaboration-based Approach to CFD Model Validation and Uncertainty Quantification (VUQ) Using Data from a Laminar Helium Plume

An effective approach to the model VUQ process by means of direct collaboration between computationalist and experimental data analyst is proposed. An analysis of data from a laminar helium plume experiment provides a demonstration of the proposed collaboration process. Consistency analysis serves a central role in the collaboration. It takes the data and uncertainties from both analyst and computationalist and provides an objective and quantifiable measure of agreement between the two. Despite the simplicity of the laminar helium system and the computational model, certain phenomena brought to light in the collaboration process make it difficult to find quantitative agreement in the data. These phenomena include the unsteady behavior of air flow in an open room, and the presence of helium permeation to the region near the plume. Important sources of error in the simulation include uncertainty in the room temperature (295.15 to 305.15 K), uncertainty in the helium inlet velocity (0.1215 \(\frac {m}{s}\) to 0.1415 \(\frac {m}{s}\)), and uncertainty in local helium permeation (0 % to 3 % by mass.) The collaboration process allows for a better understanding of the phenomena affecting the plume and the relative sensitivies of the system to these phenomena.     

A gas jet superposition model for CFD modeling of group-hole nozzle sprays

In the present study, a jet superposition modeling approach is explored to model group-hole nozzle sprays, in which multiple spray jets interact with each other. An equation to estimate the merged jet velocity from each of the individual jets was derived based on momentum conservation for equivalent gas jets. Diverging and converging group-hole nozzles were also considered. The model was implemented as a sub-grid-scale submodel in a Lagrangian Drop–Eulerian Gas CFD model for spray predictions. Spray tip penetration predicted using the present superposition model was validated against experimental results for parallel, diverging and converging group-hole nozzles as a function of the angle between the two holes at various injection and ambient pressures. The results show that spray tip penetration decreases as the group hole diverging or converging angle increases. However, the spray penetration of the converging group-hole nozzle arrangement is more sensitive to the angle between the two holes compared to diverging nozzle because the radial momentum component is converted to axial momentum during the jet–jet impingement process in the converging group-hole nozzle case. The modeling results also indicate that for converging group-hole nozzles the merged sprays become ellipsoidal in cross-section far downstream of the nozzle exit with larger converging angles, indicating increased air entrainment.     

Assessment of FSD and SDR Closures for Turbulent Flames of Alternative Fuels

Detailed-chemistry DNS studies are becoming more common due to the advent of more powerful modern computer architectures, and as a result more realistic flames can be simulated. Such flames involve many alternative fuels such as syngas and blast furnace gas, which are usually composed of many species and of varying proportions. In this study, we evaluate whether some of the commonly used models for the scalar dissipation rate and flame surface density can be used to model such flames in the LES context. A priori assessments are conducted using DNS data of multi-component fuel turbulent premixed flames. These flames offer unique challenges because of their complex structure having many distinct consumption layers for the different fuel components unlike in a single-component fuel. Some of the models tested showed good agreement with the DNS data and thus they can be used for the multi-component fuel combustion.