O. A. Ezekoye

Kinetic and Fuel Property Effects on Forward Smoldering Combustion

In this paper, we present the results from a one-dimensional transient model of forward smoldering. Fuel oxidation and pyrolysis reactions as well as a char oxidation reaction are included in the model. The solid energy, solid species, gas energy, oxygen species (bulk gas and surface), and overall mass conservation equations were discretized in space using finite-difference techniques and were solved using VODE, an ordinary differential equation integrator designed for stiff equations. Local thermal and chemical nonequilibrium are allowed in this model and transfer coefficients are derived from a Nusselt number correlation. A base case is chosen to represent experimental conditions reported in the literature. The effects of inlet gas velocity, kinetic frequency factors, inlet oxygen concentration, and fuel properties such as specific heat, density, conductivity, and pore diameter were studied using this model.

Effects of thermal boundary conditions on flame shape and quenching in ducts

Near quenching laminar flames in parallel plate and cylindrical ducts are investigated computationally using one-step chemistry and a two-dimensional finite volume formulation. The effects of varying the heat transfer boundary conditions on the flame shape and propagation speed are examined. Two flame shapes are shown to arise, depending on the channel width and wall heat losses. A quenching criterion is developed for cases of restricted conductive or convective heat loss through the duct walls, and results are compared to the existing theory. As expected, the quenching Peclet number is found to be proportional to the square root of the overall heat loss coefficient. The importance of internal wall radiation and through-wall heat losses to the flame shape and quenching process is also examined and discussed. Radiation inside the channel is shown to inhibit quenching.

Inverse Boundary Design Combining Radiation and Convection Heat Transfer

We investigate inverse boundary design for radiation, convection and conduction combined-mode heat transfer. The problem consists of finding the heat flux distribution on a heater that satisfies both the temperature and the heat flux prescribed on a design surface of an enclosure formed by two finite parallel plates. A gray participating medium flows in laminar regime between the walls, which are gray, diffuse emitters arid absorbers. All the thermal properties are uniform. This problem is described by an ill-conditioned system of non-linear equations. The solution is obtained by regularizing the system of equations by means of truncated singular value decomposition (TSVD)

Comparison of three regularized solution techniques in a three-dimensional inverse radiation problem

Inverse methods provide a good alternative to traditional trial-and-error methods for design of thermal systems. The inverse boundary condition estimation problem in radiating enclosures involves the solution of an ill-posed system that requires regularization to obtain a reasonable physical solution. This study compares three regularized solution techniques that can be used in the inverse boundary condition estimation problems in a three-dimensional radiating enclosure. The regularized solution techniques covered in this study are the conjugate gradient method, bi-conjugate gradient method and truncated singular value decomposition.

Inverse Design Model for Radiative Heat Transfer

Inverse solution techniques are applied to the design of heat transfer systems where radiation is important. Various solutions using inverse methods are demonstrated, and it is argued that inverse design techniques provide an alternative to conventional iterative design methods that is more accurate and faster, and can provide a greatly improved first estimate of a thermal design. This estimate can then he used as a trial design in more complete thermal analysis programs for predicting system behavior, eliminating many faulty first design trials

Increased surface temperature effects on wall heat transfer during unsteady flame quenching

The coupling of thermal and chemical processes is significant during laminar flame quenching. A direct thermal response of a quenching flame is the heat transfer to the wall. The unsteady heat transfer during premixed laminar flame quenching was measured in a constant volume chamber over a range of wall temperatures from 298 K to 423 K and a range of equivalence ratios from 0.8 For all of the measurements, the maximum heat flux could be correlated to the heat release rate in the steady flame prior to quenching. The fraction of the heat release rate attributed to heat transfer was independent of the equivalence ratio but dependent on the wall temperature. The experimental results were independent of buoyancy and catalytic effects and of whether the wall was locally heated or the entire bomb was globally heated. Calculations of the heat transfer were made for both one dimensional and two dimensional flame quenching using finite difference methods with chemistry specified as a single reaction step. Comparisons of the numerical results with the experimental data emphasized the sensitivity of the heat flux to the specifications of the reaction mechanism parameters. In particular, it was found that the single step mechanism and simplified chemical transport models could not predict the dependence of the wall heat transfer on the wall temperature. It was concluded that during quenching low activation energy recombination reactions may contribute significantly to the deviation between the single step thermal reaction mechanism and the observed experimental results.

Combustion and heat transfer in model two-dimensional porous burners

A two-dimensional model of two simple porous burner geometries is developed to analyze the influence of multidimensionality on flames within pore scale structures. The first geometry simulates a honeycomb burner, in which a ceramic is penetrated by many small, straight, nonconnecting passages. The second geometry consists of many small parallel plates aligned with the flow direction. The Monte Carlo method is employed to calculate the viewfactors for radiation heat exchange in the second geometry. This model compares well with experiments on burning rates, operating ranges, and radiation output. Heat losses from the burner are found to reduce the burning rate. The flame is shown to be highly two-dimensional, and limitations of one-dimensional models are discussed. The effects of the material properties on the peak burning rate in these model porous media are examined. Variations in the flame on length scales smaller than the pore size are also present and are discussed and quantified.

Evaluation of the 1-point quadrature approximation in QMOM for combined aerosol growth laws

This work examines the applicability of various assumptions in implementation of the quadrature method of moments (QMOM) for solving problems in aerosol science involving simultaneous nucleation, surface growth and coagulation. The problem of aerosol growth and coagulation in a box and the problem of vapor condensation in a nozzle are reworked using quadrature method of moments. QMOM uses Gaussian quadrature to evaluate integrals appearing in the moment equations and therefore does not require any assumptions on the form of the size distribution function, the growth laws and coagulation kernels. Results are compared with calculations which assume a lognormal size distribution. The conditions for which one, two and higher quadrature points can be used in the quadrature formula and the issues regarding the accuracy are considered for combined aerosol nucleation, growth and coagulation processes. Results show that for these problems, the simplest 1-point quadrature scheme gives accuracy comparable with the lognormal calculations while using two and higher point quadrature gives highly accurate results. Some difficulties associated with the QMOM are discussed and some insights are provided.

The Application of an Inverse Formulation in the Design of Boundary Conditions for Transient Radiating Enclosures

This study considers the design of thermal systems that are built to radiatively heat objects from a specified initial condition to a specified steady state following a prescribed temperature history. The enclosure housing the object, the object itself and the heaters all have thermal capacity. The necessary power input distributions for the heaters during the heating process are sought to satisfy the design specifications. The problem is thus a transient inverse boundary condition estimation problem, where the geometry and the properties of the surfaces are specified and the boundary condition on the heater wall is to be found by making use of the information provided at the design surface for each time step. The boundary condition estimation problem requires the solution of a set of Fredholm equations of the first kind. Such a problem is known to be ill-posed. The introduction of the transient nature makes the inverse problem nonlinear and even more interesting, challenging, and realistic. A solution algorithm is proposed and used to produce a solution for sample problem. In order to model radiative heat transmission, the Monte Carlo method is used, which enables us to handle specularly reflecting surfaces and blockage effects. The inverse problem is solved by the conjugate gradient method, which provides smooth and accurate results after the first few steps.

Unsteady heat transfer during side wall quenching of a laminar flame

The unsteady heat transfer during laminar flame quenching on a side wall was determined in a constant volume chamber. The interaction of the flame with the wall was essentially two dimensional. Experiments were conducted for three fuels; propane, methane and ethylene, over a range of equivalence ratios at nearly atmospheric pressure. The unsteady variations of the surface temperature were measured with a resistance type thin film thermometer and with a thin film coaxial T type thermocouple. The unsteady wall heat fluxes were successfully correlated using the rate of heat release in the flame prior to quenching, qc, and a characteristic time for the passage of the flame, tc. The maximum heat flux during side wall quenching, qmax, is the same as that occurring during stagnation quenching. This result is true for the present apparatus for three fuels over a broad range of test conditions. The experimental data satisfy the relation qmax/qc=0.3–0.4.