From the above motivation and literature review, we observe a number of gaps and open questions.
First, the optimal combination of equation of state behavior and turbulent models has not yet been established at high pressure conditions. The lack of systematic assignment of real gas model param-eters in high density combustion flows is noted. A framework to provide critical properties needs to be developed for each chemical species for further investigation of reacting flows. Moreover, with the large chemical kinetic models developed today, turbulent flow simulations are extremely costly.
Large carbon fuel surrogate such as n-dodecane needs skeletal chemical reaction mechanism to reduce the species number. With respect to capturing the ignition behavior of spray A, a combination of liquid break-up, chemical kinetic model and turbulent model needs to be carefully identified.
This work seeks to capture physical and chemical processes of high density flow using numerical simulations at a reasonable computation cost. Specifically, this thesis seeks to:
• Evaluate real gas and ideal gas differences in some standard flows so as to justify the need for real gas equation models, which are often more complex and avoided.
• Develop an estimation framework and evaluate real gas equation of state parameters based on intermolecular potential parameters that are available in current chemistry models.
• Apply and develop of the framework in combustion problems with multi-species. These include a LOX/kerosene fueled rocket and diesel spray.
• Extend the ASE method and develop a cost-effective species propensity method for reducing n-dodecane chemistry, demonstrating that the model results in reasonably accurate predictions for ignition delay times.
• Calibrate a CFD model for the prediction of liquid and vapor penetration length of Spray H/A by KHRT model. Further, demonstrated the use of the developed chemistry model in WM-LES simulation of ignition delay time and flame lift-off length of Spray A.
In the first part of this work, the real gas behavior of representative jet sprays is examined using Large Eddy Simulation technique. Mesh quality is carefully designed to capture the turbulent flow features. Simulations results with real gas equation of state show closer agreement with experimental data, leading to the development of a framework to provide real gas parameters for high-density combustion flow, where thousands of intermediate species have unknown properties. A LOX/kerosene rocket combustion problem is then used to demonstrate the framework of deriving real gas parameters from chemical kinetic files.
The second part of the thesis focuses on the ignition investigation of n-dodecane spray combustion.
Several most recent detail mechanisms are validated against experimental data at elevated pressure.
Reduced chemical kinetic models are derived based on methodologies developed by the group.
Lastly, CFD of auto-ignition behavior is examined for Spray A. Spray simulation is carried out based on Lagrangian-Eulerian method. A non-reacting case is calibrated with experimental data (liquid and vapor penetration length) provided by the Engine Combustion Network. Reacting simulations are then carried out using the reduced chemical kinetic model developed in the second part of the work. Real gas effects are counted for intermediate species based on the framework from the first part of the work. If these objectives are all achieved, spray combustion simulation will be advanced in terms of physically relevant models and computational cost.
Chapter 2
Modeling procedure and analysis
In this chapter transport equations for multicomponent and chemically reacting flows are first presented. This is followed by a description of real gas equations of state, thermodynamic properties and transport properties. The transport properties depend on intermolecular properties that can also be used to determine real gas equation of state parameters. Plausible correlations between intermolecular potentials and real gas equation of state parameters are then discussed. Subsequently, models needed to account for turbulence, spray processes and chemical reactions are briefly presented. This section concludes with a description of the procedure used to address the project objectives outlined in the previous chapter.
2.1 Governing equations of flow dynamics
The theoretical framework of fluid mechanics is based on the continuum assumption. The governing equations of fluid dynamics consist of the conservation of mass, momentum, energy, and species concentration. The index notation form of the conservation equations for chemically reacting flows is:
∂ ρ
∂ t +∂ (ρ ui)
∂ xi = 0, (i = 1, 2, 3) (2.1)
∂ (ρ ui) where ρ is the density, t is the time, uiis the components of the velocity vector, σi j is the viscous stress tensor, E is the specific total energy, p is the pressure, qiis the heat flux vector, τi j is the deviatoric stress tensor, Yk, ˙ωkand Dkare the mass fraction, chemical source term and mass diffusion coefficient of species k. The species conservation equation (Eq. 2.4) is solved for k = 1, ..., N − 1, where N is the total number of species. To minimize the numerical error, the Nth species is selected as the one with largest mass fraction. For an Newtonian fluid, the Stokes’ hypothesis can be used for the viscous stress tensor, σi j, found in Eq. 2.2: where the deviatoric stress tensor is expressed as,
τi j= µ ∂ ui
The mass specific total energy is defined by the sum of the specific internal energy and the kinetic energy,
E = e +1
2uiui, (2.7)
where e as the specific internal energy, related to the specific enthalpy as:
e= h − p
ρ, (2.8)
where specific enthalpy h is the sum of the specific enthalpies of all species,
h=
N k=1
∑
Ykhk. (2.9)
The detailed formulation of the thermodynamic properties will be discussed in Section 2.2.
The heat flux vector in Eq. 2.3 is defined as,
qj= −λ∂ T
where j and k, l are indexes of spatial coordinate and species. Here, λ is the heat conductivity, T is the temperature, jk, j is the multi-component species diffusion flux, hkis the partial enthalpy of species k, R is the universal gas constant, Xl is the mole fraction of species l, uk and MWk are the dimensionless diffusion velocity and molecular weight of the kth species, and DT,kandDkl are the dimensionless thermal diffusion coefficient of species k and binary mass diffusion coefficient between species k and l.
The last term in the equation referred as the Dufour effect, represents the heat flux induced by gradient of mass concentration. As noted in other works [45, 170, 171], Dufour effects appear to be insignificant at elevated pressures due to enhanced chemical reaction rates that override changes in diffusion and is therefore neglected in the current study.
The multi-component species diffusion flux term, jk, j, in Eq. 2.10 is given by,
jk, j = −
where Dk,m is the mass diffusion coefficient for species k, µt is the turbulent viscosity, Sct = µt/(ρDt) is the turbulent Schmidt number set to be 0.7 as noted in a DNS work by Brethouwer
[172], Dt is the turbulent diffusion coefficient, the Soret term contributes to the mass diffusion associated with temperature gradient, it is suggested to be negligible for supercritical pressure LOX/H2flames [45].
These transport equation can therefore be used to simulate the flow field when these terms are all defined.