A flammability map is also produced from the pdf fraction of the separated mixture and compared with its experimental counterpart. Correlations between spark timing velocities and mixture fraction values and ignition success or failure are then further discussed and analyzed.
General introduction
The central task of CFD is to provide an accurate description of technical processes using mathematical models to understand the dynamic behavior of the system, taking into account the regularity and thus possibly reliable predictions of the future development of the system. Thus, CFD and experiments are used together in studying the behavior of a physical process involving flow and reactions.
CFD tools for turbulent flows
In most practical engineering applications, in the turbulent flow environment, the interest lies in predicting the mean flow variables, where the RANS modeling fits the purpose perfectly. In DNS calculations, the Navier-Stokes equations are solved with specified initial conditions for the full range of scales in the turbulent flow field.
Background and Motivations
The length and width of the central wake recirculation zone is a function of the steep body dimensions and flow parameters, which also control the transfer of mass and energy between the recirculation zone and the outer flow. Most of the reported numerical works have focused on the aerodynamics and mixing of the cold flow of pale body burners, while the simulation of the reaction flow is rarely performed.
Objectives of this study
Outline of the thesis
These forces and moments are generally a function of body geometry, body orientation, and flow conditions. The flow around the airfoil follows the contour of the body, as shown in fig.
Bluff-body burners and annular jets
Aerodynamics of annular jets
Their results showed that the dimensions of the resulting recirculation zone behind the cliff body wake differ in both height and width, reflecting the difference in the flow divergence produced. This is due to the difficulty associated with modeling the main phenomenon of bluff-body flows, i.e.
Bluff-body flames
However, the quality of the prediction was insufficient in the case of bluff body flames, for example see [35]. In the case of the bluff body with strong turbulence, where the flow is characterized by strong instabilities, modeling flare adds to the degree of complexity.
Spark ignition and modelling
The timing and duration of each phase is dictated by the characteristics of the ignition circuit (including the spark plug). Because of this, most cathodic erosion occurs during the arc phase.
Reactive flow modelling
Mixture fraction
Now it may be possible, following Eq. 2.9), to define a mixture fraction based on elemental mass fraction. From the elemental mass fraction of the mixture, several conserved scalars can be derived for the definition of the mixture fraction.
Reaction progress variable
According to Bilger [12], the fast-chemistry assumption implies that the instantaneous concentrations of species and the temperature are only functions of the conserved scalar and this can drastically simplify the solution of reacting flow problems in the limit of fast chemistry. The main differences between expression (2.16) and the different definitions of the progress variable c listed above are that the reactivity R always assumes unity when one of the reactants is completely consumed.
Modes of combustion and modelling
Non-Premixed Combustion
The reaction rate is assumed equal to the slower of the chemical reactions and the rate regulated by turbulent mixing. Particle state is described by position, velocity, and reactive scalars, and particle properties are described by stochastic Lagrangian models. The main advantage of the PDF-based method is that the chemical source term appears in closed form and thus no modeling is needed.
Premixed combustion
The flame is thus assumed to be very thin, and the flame surface density Σ is introduced. The flame surface density measures the available flame area δA per volume unit δV. The average reaction rate for a species i is then modeled as: . where Ωi is the average local burning speed per unit flame area integrated along the direction normal to the flame surface.
Partially premixed combustion
Rogg et al. [137] first proposed the formulation for extending the laminar flame model for non-premixed combustion by considering the partially premixed phenomenon. Favier et al. [55] proposed a model based on a two-scalar approach for modeling the turbulent partially premixed combustion.
Chemistry reduction and tabulation
Basic steps of tabulated chemistry scheme
The basic idea of the tabular technique is that the variables of the chemical mechanism are not independent. Carefully study and analyze flame structures to reduce the number of independent variables and determine the degrees of freedom of a chemical system.
Filtering in LES
The scales larger than the filter width are called resolved scales whose contributions are calculated numerically and the scales smaller than the filter size are called sub-grid scales (SGS), whose effects are modelled. So the size of the filter becomes the grid size and the sub-filter fluxes are then called sub-grid fluxes.
Filtered Navier-Stokes equation
For Newtonian fluids, these stresses are proportional to the rates of deformation, i.e. following tensor notations, it is represented as. 3.7) the first term of dynamic viscosity µ is to relate stresses to linear deformation. The unclosed SGS stress term in equations (3.6) and (3.10) needs modeling effort, which should be constructed from the calculated filtered quantities.
Subgrid-scale stress modelling in LES
Smagorinsky model
The model assumes that the eddy viscosity is proportional to the characteristic length scale of the subgrid and to the characteristic turbulent velocity taken as the local strain rate. The characteristic length scale of the subnet is equal to the largest unresolved scale, which is equal to the size of the filter i.e.
Filtered structure function model
The appropriate value of Cs should be guessed a priori, which is quite difficult with Smagorinsky formulation. Despite these drawbacks, the Smagorinsky model is a widely accepted model and produced satisfactory results with various configurations. 3.15), the exponentn= 3 overFe2 indicates that the structure function has been applied to the resolved velocity field three times using a Laplace filter.
WALE model
Description of flow solver
- Computational grid
- Basic assumptions
- Numerics
- Time integration
- Boundary conditions
- Pre and post processing
HereQ represents any conserved quantity (for example mass, momentum, or enthalpy) averaged over the control volume, FQ represents the net fluxes across the faces of the control volume, and PQ denotes the production rate of Q within the volume V. The first term in Eq. 3.21) represents the time variation of Q within the control volume V and the second term quantifies the net surface fluxes (in the Navier-Stokes equation, this includes convective and diffusive fluxes). The Lewis number is assumed to be unity; ie the heat diffusivity is assumed equal to the mass diffusivity.
SGS combustion modeling - PCM-FPI
- Flamelet Prolongation of ILDM
- Presumed conditional moment
- Tabulation and coupling
- Schematic of experimental flow field
An enlarged view of the enclosure and the conical body of the bluff can be seen on the right side of Fig. At the end of the flow, the core jets reconnect again beyond the rear stagnation point, and then the region beyond this exhibits the characters of a normal round jet (ie the axial velocity is positive or zero).
Details of the computations
Cold flow test cases
Injection of fuel was found not to significantly change the velocity profile near the inlet of the combustor, due to the fact that the overall ratio of fuel to air flow rate is as small as 0.055 (thus the overall mixture condition is stoichiometric). . Although the cold flow measurements without fuel injection are considered equal to the flow field even with fuel injection due to the above fact, this characterization may be questionable due to the difference in Reynolds.
Cold flow results
- Mean axial and radial velocity fields
- Turbulent kinetic energy
- Turbulence resolution parameter
- RMS of axial and radial velocities
- Mixing field
- Flammability factor
In particular, the height of the CRZ fluctuates between the axial positions of z = 20 mm and z = 25 mm. However, a significant effect is noted in the region of the recirculation zone, between z = 15.5 mm and 25 mm (Fig. 4.6).
Summary of cold flow results
In the experiment, the spark energy deposit always generates a small core of hot gases, and it is the subsequent time development of this initial flame pit that determines the ignition success or failure of the overall burner [4]. The spark energy deposited is simulated by a source term in the energy equation, a common procedure followed in many earlier works.
Choice of ignition spots for LES analysis
The spark source also follows a Gaussian distribution in time to better match the energy deposition schedule obtained in the experiment, which can be inferred from the ignition current profile [3]. The list of ignition points analyzed in this chapter and in the next chapter is given in the table.
Choice of ignition timing
Since the burner is radially symmetrical, the radially eccentric ignition points discussed here are chosen to be on the left side of the burner axis in the two-dimensional view shown in the figure. The average axial velocity, radial velocity, and mixture fraction of these ignition sites are tabulated.
Failed ignition
Part of the mixture is far from the flammability limits, but since this region is quite close to the isostoichiometric surface (Figure 4.7), the deposited energy can diffuse towards the combustible region in the immediate vicinity of this ignition point and a burning core is first created, as already found in [135 ]. Later, the core is still growing, but is carried further down to finally blow up completely.
Successful ignition
At the same time, the radial velocity shows a negative trend (Fig. 5.4b), transporting a significant amount of deposited energy to the CRZ, with a favorable mixture fraction during grain displacement, giving rise to successful local ignition. The time required for the ignition core to establish a fully developed flame is approximately 45 ms for this ignition point, which is the same duration as that reported in the experimental results (see Figure 14 in [4] ).
Successful ignition
Thus, only when the spark is imposed when the axial velocity dissipates does the wick have a chance to produce an established flame before blowing. Since the mixture here is almost stoichiometric, the burning rate is high enough to help the wick propagate against the flow.
Failed ignition
The local streamline emanating from the spark location indicates that the wick motion is perpendicular to the burner axis, causing the wick to grow in a nearly stoichiometric region. In the following moments, the strong turbulence inside the CRZ stirs and spreads the reaction zone and thus leads to complete illumination of the flame.
Successful ignition
A rather large portion of the kernel is first convected to the bluff body (t= 1.8 ms), with a first increasing and then decreasing negative axial velocity. At about 10 to 15 ms, the flame starts to appear at the edges of the CRZ, burning along the isosurface of stoichiometric mixture fraction.
Successful ignition
The instantaneous shape of the CRZ can be observed from the isoline of zero axial velocity, and the CRZ contains strong shear layers arising due to the interaction of eddy bubbles. Once the flame is established, the CRZ contains hot combustion products and the size of the CRZ becomes large, as seen in Fig.
Other locations
In place A, since the flammability factor is not zero, the spark can locally initiate combustion, which is then further promoted by convection. In the subsequent moments, the flame starts to spread inside the CRZ and increases the temperature inside the CRZ and therefore viscosity and thus wipes out the turbulence inside the CRZ.
Summary of hot flow results
The need to include voltage is followed in detail by the development of the correction factor proposed to account for voltage-induced effects in the PCM-FPI technique. Then, simulation results are presented to demonstrate the impact of the new correction factor and compared with the results of the conventional PCM-FPI method.
Background
As the main ingredient to capture this phenomenon is flame expansion, which is completely missing from the chemistry table. The failure due to strong aerodynamic load is thus not reproducible in the simulation, which is a limitation of the classic PCM-FPI method.
Literature on flame turbulence interaction
- Asymptotic theory of stretched flame
- Turbulent burning rate
- Distribution of tangential strain and curvature
- Effect of Lewis number
Note that all of these terms have the dimension 1/s, which is the dimension of the strain. The PDF p(c, Z, K) is the joint probability density function of c,Z and K. 6.2.3 Distribution of tangential strain and curvature.
Development of new closure for strain correction on rate of kernel development 118
Strain rate effects on flame establishment time
In some cases, there is a non-negligible difference in the flame nucleation rate between simulations with and without the effects of flow loading. This difference mainly stems from the initial part of the core development period, which is much slower when deformation effects are taken into account, so the burning rate reduction attributed to flow deformation is dominant for the young flame core.
Fine LES calculation and mesh dependency study
The results of coarse mesh and fine mesh on average axial and radial velocity can be seen in fig. Dashed line: LES with coarse mesh (1.76M grid). the shear layer of the annular gap in both calculations is very similar.
Summary
Cold flow simulation
The mixture trapped within the CRZ is well mixed and thus the mixture fraction is nearly homogeneous due to the strong stirring velocity field present within the CRZ. The measurements reported from the experiment found no change in the mean velocity field within a few mm downstream of the bluff body with fuel injection, which is actually verified even in simulation.
Ignition test cases
It has also been shown that strain rate effects must be included in the modeling of the filtered burn rate; an ingredient missing in the conventional PCM-FPI technique. The results are validated against experimental observation to address the improvements produced by accounting for strain rate in LES-filtered burn rate.
Recommendations for future work
A detailed analysis of the flame development at these locations is proposed in the next section. Equations ( 21 ) and ( 22 ) are integrated with a single diagonal implicit Runge Kutta (SDIRK) scheme [ 43 ], after decomposition of .
Flow over a streamlined body
Flow around a bluff-body
Schematic view of a supersonic ramjet engine employing bluff-body flame-holder . 13
Area of knowledge important for process simulation
Sketch for non-premixed combustion system
Mono-dimensional flame structure of a diffusion flame [167]
Effect of turbulence on the structure of the reaction zone
Picture showing premixed flame from a Bunsen burner. The small white circle
Mono-dimensional flame structure of a premixed flame [160, 167]
The Borghi diagram for turbulent premixed combustion regimes [125]
Sketch of a freely propagating triple flame [167]
Schematic showing a finite volume cell. The fluxes (S) crossing the boundary are
Equilibrium value of Y c for the range of mixture fraction (Z ). The abscissa is
Asymptotic limits of sub-grid scale variance of progress of reaction
Flow chart showing the PCM-FPI tabulation technique and the coupling between
Experimental setup
Experimental setup
Coordinate transformation from Cartesian to polar. The X axis is normal to the
Imposed axial and radial velocity at the inlet boundary