A mathematical model for Closed Homogeneous Constant Pressure Reactor (CHCPR) and one-dimensional Premixed Reactive Flow (PRFM) is developed for the thesis. Detailed gas phase reaction kinetics is coupled with thermodynamics and flow properties to develop the reactor models. Global reaction mechanisms are used for simulating combustion in complex flows. However, study of accurate combustion physics efficiently requires detailed chemical kinetics in simplified flow system as it gives more accurate results for studying ignition, explosion, reaction progression and other transient properties of flame. Detailed reaction mechanism with three Arrhenius rate parameters and third-body efficiencies are considered. Thermodynamic properties are calculated using the 7 coefficient NASA polynomials. CHCPR calculates the transient reaction properties like temperature, species concentration, volumetric heat release, etc., during the progression of reaction at constant pressure. PRFM solves both the reaction properties and flow properties like pressure and velocity along the length of the combustor. Addition of source terms in PRFM is considered to facilitate exchange of heat and mass from surrounding. Governing equations for the reactor models are derived in the form of a system of nonlinear Ordinary Differential Equations (ODEs), which are solved using ode15s for CHCPR and Backward Differentiation Newton-Raphson Method with Finite Difference Jacobian for PRFM. To incorporate complex flow characteristics like laminar and turbulent mixing and transport properties in the combustion test cases, ANSYS Fluent is used. Preliminary design of the gas combustor includes, design of geometry for temperature control at exit for rated power. Calculation of the fuel mass flow rate for rated power in CHCPR and diluent mass flow rate for temperature control is done in PRFM. Physics behind the simple premixed flow, bluff body and cavity flame holding are studied in ANSYS Fluent.
Closed homogenous constant pressure reactor is like a system of reactants confined in a piston-cylinder arrangement that react at each and every location within the gas volume at the same rate. Thus, there are no temperature or composition gradients within the mixture, and a single temperature and set of species concentrations suffice to describe the evolution of the system. For exothermic combustion reactions, both the temperature and volume will increase with time, pressure held constant.
In CHCPR, the system’s mass is constant with no inflow and outflow of species from the system. The thermodynamic properties are uniform and homogenous only varying with time. The system is transient zero-dimensional with rate of conversion of reactants to products is controlled by chemical reaction rates only. The conservation equations; mass conservation, species conservation, energy conservation and equation of state, are used to derive the equations for closed homogenous constant pressure reactor with assumptions:
- Some reaction rate depends on pressure as well as temperature but only temperature dependence is considered in solver.
- No phase change during reaction.
- No surface reactions
- No heat transfers between the surface and surrounding
General combustion devices are long and slender, as in a gas-turbine combustion chamber, a cement kiln or a gasifier, in which air fuel mixture enter at one end and products leave at the other. Such devices can be idealized as plug-flow thermochemical reactors. In this reactor operating in steady state, properties such as velocity, temperature, pressure, and mass fractions of species vary principally along the length of the reactor Therefore, for such reactors, equations of mass, momentum, and energy can be simplified to their one-dimensional forms.
In the context of reactive flow, mixture mass conservation, species mass conservation, momentum conservation and energy conservation was taken into account along with ideal gas equation. Heat flow in and out of the reactor is modelled adding heat flux source term in energy equation. Injection of any species or combination of species through any portion of lateral surface of the reactor is incorporated as an additional source term in RHS of conservation of mixture mass, species mass, momentum and energy. The assumptions made for the reactor model are:
- Steady state.
- Fuel and air is premixed. The input mixture of fuel and air is fully mixed.
- Uniform properties in the direction of flow i.e. one dimensional flow. That means the variation of velocity, temperature, pressure etc. in the direction perpendicular to the flow is assumed negligible.
- Species transport due to thermal and mass diffusivities are neglected due to domination of advective transport in the only one properties varying dimension.
- Ideal frictionless flow with ideal gas behavior.
- The rate of conversion of reactants to products is controlled by chemical reaction rates only. Mixing process does not affect the conversion.
- No surface reactions.