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Mathematical modelling of chemical reaction with propane
Abstract
The main goal of the present study is to promote a more effective use of agricultural residues as an alternative renewable fuel for cleaner energy production with reduced greenhouse gas emissions. The complex experimental study and mathematical modelling of the processes developing during the co-firing of biomass pellets with gaseous fuel were carried out. The experimental study of the effect of co-firing on the main gasification and combustion characteristics was carried out by varying the propane supply and additional heat input into the pilot device with an estimation of the effect of co-firing on the thermal decomposition of pallets. The mathematical model is developed using the environment of MATLAB (2-D modelling) and MATLAB package “pdepe” (1-D modelling) with account variations of supplying the heat energy and combustible volatiles into the bottom of the combustor. The dominant exothermal chemical reactions were used to evaluate the effect of co-firing on the main combustion characteristics and composition of products CO2 and H2O. The results prove that the additional heat from the propane flame allows control of the thermal decomposition, the formation of volatiles, and the development of combustion dynamics, thus completing the combustion of biomass and leading to cleaner heat energy production.
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This paper deals with a simplified model taking into account the interplay of compressible, laminar, axisymmetric flow and the electrodynamical effects due to Lorentz force’s action on the combustion process in a cylindrical pipe. The combustion process with Arrhenius kinetics is modelled by a single step exothermic chemical reaction of fuel and oxidant. We analyze non-stationary PDEs with 6 unknown functions: the 3 components of velocity, density, concentration of fuel and temperature. For pressure the ideal gas law is used. For the inviscid flow approximation ADI method is used. Some numerical results are presented.
The study is aimed at cleaner and more efficient heat energy production through investigation and analysis of the thermal decomposition of lignocellulosic biomass pellets with different elemental composition, the heating values and contents of hemicellulose, cellulose and lignin. The estimation is provided for the influence of biomass composition on the combustion characteristics for softwood, wheat straw and wheat straw lignin pellets. The kinetics of thermal decomposition was studied experimentally, using a pilot device for two-stage processes of thermochemical conversion including gasification and combustion of biomass pellets under varying conditions. The experimental study includes time-dependent measurements of the biomass pellet weight loss during gasification and the correlating variations of the flame temperature, heat production rates, combustion efficiency and composition of the products at different stages of thermochemical conversion. Estimation is also given for the influence of the biomass composition on the combustion characteristics and heat energy production.
Experimental study and mathematical modelling were aimed to provide electric control of biomass thermochemical conversion and analysis of the DC electric and electromagnetic effects on combustion dynamics to obtain a cleaner and a more effective heat energy production. Mathematical modelling of the formation of flame velocity and temperature profiles was performed considering the Lorentz force effect on the flame. The results of numerical simulation show that increasing the electrodynamic Lorentz force parameter Pe leads to the increase of flame vorticity enhancing thus the fuel mixing with the air and to the correlating decrease of the flame temperature and reaction rates. Experimental study and analysis of the DC field effect on development of the swirling flow dynamics shows that the electric field-induced ionic wind disturbs the formation of the swirling flow velocity field by enhancing the upstream swirling flow formation and mixing of the axial flow of combustible volatiles with an upstream air swirl. The field-enhanced mixing of the axial flow of volatiles with an air leads to improvement of combustion conditions and to an increase in combustion efficiency giving a more complete combustion of volatiles by increasing the produced heat energy at thermo-chemical conversion of biomass.
We study the numerical methods for solving the initial-boundary value problems of some nonlinear heat transfer equations in multi-layer domain. The approximation of corresponding initial boundary value problems is based on the finite volume method (FVM), on the boundary element method (BEM), and on the finite-difference scheme (FDS). These methods enable to reduce the nonlinear heat transfer problem described by nonlinear partial differential equations (PDEs) to initial value problem for system of nonlinear ordinary differential equations (ODEs) of the first order. An example of the initialboundary problem for PDEs (with power functions) ∂u(x,t)/∂t= ∂2λ (u(x, t)σ+1/ +a(u(x, t))β, x ⋯ [0, l], t > 0, (1) by σ ≥ 0, β > 0, λ > 0, a ≥ 0 and with conditions u(0, t) = u(l, t) = 0, u(x, 0) = u0(x) ≥ 0 is considered. A large number of papers in the time period of 1970-1990 are devoted to the quasilinear parabolic equations with the blow-up solutions. In papers [4], [5], [6], [10], [3], [11], [7], [8], [9], [21], [12] the theoretical investigations (selfsimilar solutions and a'priori estimations for solving Cauchy and boundaryvalue problems) and numerical experiments (see [13], [14], [18], [19], [1]) by λ = a = 1 were done. In this paper we study the behaviour of the solutions at the time and also when t → ∞, depending on the parameters σ, β, λ, a. Depending on the parameters two type of solutions are obtained: 1) for large value of the time t the solution is stationary or tends to zero, 2) in the fixed time moment the solution has "blow up" phenomena - the solution is unbounded and tends to infinity in a small interval or in all domains by a fixed time moment.
We apply a detailed chemistry, complex transport combustion model to a two-dimensional, axisymmetric laminar diffusion flame in which a cylindrical fuel stream is surrounded by a coflowing oxidizer jet. Unlike some models in which diffusion in the axial direction is neglected, we treat the fully elliptic problem. A discrete solution is obtained by combining a steady-state and a time-dependent solution method. A time-dependent approach is used to help obtain a converged numerical solution on an initial coarse grid using a flame sheet starting estimate. Grid points are then inserted adaptively and Newton’s method is used to complete the problem. We investigate both a confined coflowing and an unconfined coflowing methane-air diffusion flame and comparisons with experimental data are made.
An extended overview of the chemical composition of biomass was conducted. The general considerations and some problems related to biomass and particularly the composition of this fuel are discussed. Reference peer-reviewed data for chemical composition of 86 varieties of biomass, including traditional and complete proximate, ultimate and ash analyses (21 characteristics), were used to describe the biomass system. It was shown that the chemical composition of biomass and especially ash components are highly variable due to the extremely high variations of moisture, ash yield, and different genetic types of inorganic matter in biomass. However, when the proximate and ultimate data are recalculated respectively on dry and dry ash-free basis, the characteristics show quite narrow ranges. In decreasing order of abundance, the elements in biomass are commonly C, O, H, N, Ca, K, Si, Mg, Al, S, Fe, P, Cl, Na, Mn, and Ti. It was identified that the chemical distinctions among the specified natural and anthropogenic biomass groups and sub-groups are significant and they are related to different biomass sources and origin, namely from plant and animal products or from mixtures of plant, animal, and manufacture materials. Respective chemical data for 38 solid fossil fuels were also applied as subsidiary information for clarifying the biomass composition and for comparisons. It was found that the chemical composition of natural biomass system is simpler than that of solid fossil fuels. However, the semi-biomass system is quite complicated as a result of incorporation of various non-biomass materials during biomass processing. It was identified that the biomass composition is significantly different from that of coal and the variations among biomass composition were also found to be greater than for coal. Natural biomass is: (1) highly enriched in Mn > K > P > Cl > Ca > (Mg, Na) > O > moisture > volatile matter; (2) slightly enriched in H; and (3) depleted in ash, Al, C, Fe, N, S, Si, and Ti in comparison with coal. The correlations and associations among 20 chemical characteristics are also studied to find some basic trends and important relationships occurring in the natural biomass system. As a result of that five strong and important associations, namely: (1) C–H; (2) N–S–Cl; (3) Si–Al–Fe–Na–Ti; (4) Ca–Mg–Mn; and (5) K–P–S–Cl; were identified and discussed. The potential applications of these associations for initial and preliminary classification, prediction and indicator purposes related to biomass were also introduced or suggested. However, future detailed data on the phase–mineral composition of biomass are required to explain actually such chemical trends and associations.
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