Premixed Combustion

In premixed combustion, fuel and oxidizer are mixed on a molecular level prior to chem-ical reaction. Although this work focuses on non-premixed congurations, forced ignition is preferably initiated in a zone of ammable mixture, where the level of premixedness between fuel and oxidizer may be high enough to ascribe the growth of the ame kernel to premixed combustion. In technical applications premixed ames are essentially turbulent and result in clean and intense combustion in comparison to diusion ames. Nonethe-less, premixed combustion is more subject to instabilities. In particular, acoustic waves induce variations in the local heat release, which may feed back. Flame ashback into the nozzle or autoignition in the premixing unit can seriously aect the integrity of premixed combustion systems.

The principles of laminar and turbulent ames propagation are shown in Figure 2.2, where wall friction and heat exchange are neglected. Turbulent structures are displayed as wrinkling the ame front. The laminar ame speed, sL, is dened as pointing towards the unburnt mixture as:

s_L = ˙m/ρ_u, (2.30)

where ˙m represents the consumption rate along the ame front and ρu the density of the fresh gas. The velocity of the burnt gas behind the ame front is obtained from mass conservation law: (ρu/ρ_b)s_L.

Figure 2.2: Principles of laminar and turbulent ames propagation speed, sLand sT respectively. (Re-produced from [62])

In premixed ames, the local reaction rates are essentially controlled by the balance between heat release, due to the exothermic reaction, and thermal diusion within the

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ame reacting zone. Subsequently, three regions are distinguished in premixed ames: a preheat zone, the inner reaction zone and an oxidation zone. Figure 2.3 shows the struc-ture of a one-dimensional, laminar, methane-air premixed ame. In the preheat zone,

Figure 2.3: Structure of one-dimensional laminar methane-air premixed ame [131].

heat is transferred from the inner reaction zone to the fresh gas by thermal diusion.

Most of the reaction heat is released within the inner reaction zone, which is about 10 times smaller than the ame thickness, δ = 0.1. The ame temperature, T0, corresponds to the temperature at the maximal fuel consumption rate, while the highest temperature is obtained at the end of the post-ame zone, where radicals are recombined. Under adi-abatic conditions, the radicals corresponds to the adiadi-abatic ame temperature. Göttgens et al. [72] introduced a denition of the ame thickness, δf, based on scaling laws as:

δ_f = D_th,u

s_L = λ_u

ρ_uc_ps_L, (2.31)

where all quantities are evaluated in the fresh gas, subscript u. Poinsot and Veynante [139] proposed a denition based on the maximal temperature gradient that presents a practical interest for numerical simulations.

δ_f = Tb − Tu

max|^∂T_∂x| (2.32)

Turbulent ame speed has been the focus of numerous experiments, and was reviewed by Bradley [20]. At low turbulence levels, the turbulent ame speed is found to increase almost linearly with the turbulence intensity, whereas this eect is reduced at higher levels.

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The impact of turbulence on premixed combustion has been investigated by Damköhler [39], who rst proposed the existence of dierent turbulent combustion regimes. Several diagrams propose a denition of the regimes of premixed combustion [131]. Figure 2.4 show the regime classication in terms of the turbulent velocity to laminar ame speed ratio u⁰/s_L and integral length scale to ame thickness ratio lt/δ_f. Two non-dimensional numbers are used to classify these regimes (Figure 2.4). The Damköhler number, Da, relates the turbulent time scale, τt, to the chemical time scale, τC, as:

Da = τt/τC = δfsL/u⁰lt. (2.33) While the Karlowitz Number, Ka, compares the chemical time scale, τC, to the Kol-mogorov time scale, τK.

Ka = τ_C/τ_K = (δ_f/η_K)². (2.34) Both numbers are related to the turbulent Reynolds number, Ret, as:

Re_t= u⁰l_t

ν = Da²Ka². (2.35)

The region of laminar ames is delineated by the line of unity turbulent Reynolds number:

Figure 2.4: Regime diagram for turbulent premixed combustion [18, 131]. (Reproduced from [160])

Re_t= 1. The well-stirred reactor regime is dened by a mixing time shorter than reaction time, τt < τ_C, Da < 1. This regime is not of technical relevance, nor is the regime of wrinkled amelets that are found in low turbulence intensity, u⁰ < s_L. The Klimov-Williams criterion, Ka = 1, separates the corrugated amelets from the thin reaction zones. In the regime of corrugated amelets, the smallest turbulent scales are bigger

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than the ame thickness, and are subsequently not able to aect the ame structure.

The regime of 1 < Ka < 100 is referred to as the regime of thin reaction zones [131]

or of thickened wrinkled ames [139]. Kolmogorov eddies are able to interact with the preheat zone. However, in this regime the inner reaction layer is not disturbed by turbulent motion. In contrast, eddies ten times smaller than the ame thickness, δf/η_K > 10, Ka >

100, are able to disrupt the inner reaction layer, resulting in broken reaction zones.

From experimental measurements of the turbulent ame speed, sT, Damköhler [39]

suggested that turbulence increases the reaction consumption rate, in the same proportion to the ame surface area. He proposed a scaling law:

s_T = s_L A

A_T. (2.36)

Figure 2.2 illustrates this formula, where A denotes the laminar ame front area propa-gating at laminar ame speed and AT represents the area of the ame surface projected orthogonally to the direction of ame propagation. The turbulent ame front area, AT, is moving at the turbulent ame speed sT. Damköhler [39] estimated the eect of turbulence on the increase of ame surface area as:

A = A_T u⁰ sL

. (2.37)

Hence, the turbulent ame speed can be derived from the laminar ame speed and the turbulent velocity accordingly:

s_T = s_Lu⁰

s_L. (2.38)

Further models have been proposed for modeling the turbulent velocity within RANS and LES simulations, as reviewed by Düsing [51]. The majority of these models can be generalized as:

s_T = s_L

 1 + C

u⁰ s_L

n

. (2.39)