Transport equations for reaction rate in laminar and turbulent premixed flames characterized by non-unity Lewis number

Transport equations for (i) the rate $W$ of product creation and (ii) its Favre-averaged value $\stackrel{?}{W}$ are derived from the first principles by assuming that $W$ depends solely on the temperature and mass fraction of a deficient reactant in a premixed turbulent flame characterized by the Lewis number $Le$ different from unity. The right hand side of the transport equation for $\stackrel{?}{W}$ involves seven unclosed terms, with some of them having opposite signs and approximately equal large magnitudes when compared to the left-hand-side terms. Accordingly, separately closing each term does not seem to be a promising approach, but a joint closure relation for the sum $\overline{T_{\text{Σ}}}$ of the seven terms is sought. For this purpose, theoretical and numerical investigations of variously stretched laminar premixed flames characterized by $Le<1$ are performed and the linear relation between $T_{\text{Σ}}$ integrated along the normal to a laminar flame and a product of (i) the consumption velocity $u_c$ and (ii) the stretch rate ${\dot{s}}_w$ evaluated in the flame reaction zone is obtained. Based on this finding and simple physical reasoning, a joint closure relation of $\overline{T_{\text{Σ}}}\propto \overline{\rho W\dot{s}}$ is hypothesized, where $\rho$ is the density and $\dot{s}$ is the stretch rate. The joint closure relation is tested against 3D DNS data obtained from three statistically 1D, planar, adiabatic, premixed turbulent flames in the case of a single-step chemistry and $Le=0.34$, 0.6, or 0.8. In all three cases, the agreement between $\overline{T_{\text{Σ}}}$ and $\overline{\rho W\dot{s}}$ extracted from the DNS is good with exception of large ($\overline{c}>0.4$) values of the mean combustion progress variable $\overline{c}$ in the case of $Le=0.34$. The developed linear relation between $\overline{T_{\text{Σ}}}$ and $\overline{\rho W\dot{s}}$ helps to understand why the leading edge of a premixed turbulent flame brush can control its speed.     

High-pressure burning velocities measurements for centrally-ignited premixed methane/air flames interacting with intense near-isotropic turbulence at constant Reynolds numbers

This paper measures high-pressure turbulent burning velocities (S_T) of lean methane spherical flames at constant turbulent Reynolds numbers (Re_T ≡ u′L_I/ν), where u′ and L_I are the r.m.s. turbulent fluctuation velocity and the integral length scale of turbulence and ν is the kinematic viscosity of reactants. This is achieved by adopting a recently-built double-chamber, fan-stirred cruciform burner with perforated plates that can be used to generate intense near-isotropic turbulence with negligible mean velocities while controlling the product of u′L_I in proportion to the decreasing ν at elevated pressure (p) up to 1.2 MPa. Results show that when Re_T is fixed ranging from 6700 to 14,200, values of S_T decrease similarly as laminar burning velocities (S_L) with increasing p in minus exponential manners, revealing a global response of burning velocities to pressure. In general, the higher Re_T, the higher S_T/S_L at any fixed p. It is found that the curves of S_T/S_L as a function of u′/S_L all exhibit very strong bending under constant Re_T conditions. These results not only reveal that the important effect of Re_T on high-pressure S_T/S_L enhancement, but also suggest that recent findings related with the promotion effect of increasing pressure on S_T primarily due to the enhancement of flame instabilities via the thinner flame without any discussion on the influence of Re_T elevation at elevated pressure should be reconsidered. Moreover, we found that the modified values of S_T at mean progress variable $\overline{c}$ ≈ 0.5 show good agreements between Bunsen-type and spherical flames, suggesting that S_T determined at flame surfaces with $\overline{c}$ = 0.5 may be a better representative of itself regardless of the flame geometries. Finally, various general correlations of $S_{\text{T,}\overline{c}=0.5}$ are compared and discussed. It is found that the present scattering data under different p and Re_T conditions can be merged onto a single curve of ($S_{\text{T,}\overline{c}=0.5}$ ? S_L)/u′ = 0.14Da^0.47, where Da is the turbulent Damköhler number.     

Connecting dispersion models and wall temperature prediction for laminar and turbulent flows in channels

In a former paper, Drouin et al. [6] proposed a model for dispersion phenomena in heated channels that works for both laminar and turbulent regimes. This model, derived according to the double averaging procedure, leads to satisfactory predictions of mean temperature. In order to derive dispersion coefficients, the so called “closure problem” was solved, which gave us access to the temperature deviation at sub filter scale. We now propose to capitalize on this useful information in order to connect dispersion modeling to wall temperature prediction. As a first step, we use the temperature deviation modeling in order to connect wall to mean temperatures within the asymptotic limit of well established pipe flows. Since temperature in wall vicinity is mostly controlled by boundary conditions, it might evolve according to different time and length scales than averaged temperature. Hence, this asymptotic limit provides poor prediction of wall temperature when flow conditions encounter fast transients and stiff heat flux gradients. To overcome this limitation we derive a transport equation for temperature deviation $(T_w-〈{\overline{T}}_f{〉}_f)$. The resulting two-temperature model is then compared with fine scale simulations used as reference results. Wall temperature predictions are found to be in good agreement for various Prandtl and Reynolds numbers, from laminar to fully turbulent regimes and improvement with respect to classical models is noticeable.     

Alloy design of V-based hydrogen permeable membrane under given temperature and pressure condition

For alloy design of hydrogen permeable membrane, it is important to control pressure–composition–isotherm (PCT curve) in an appropriate manner in order to obtain high hydrogen permeability with strong resistance to hydrogen embrittlement. Based on this concept, V-based alloy membranes are designed under some given pressure conditions at a temperature in view of the partial molar enthalpy change, $\Delta {\overline{H}}_{0.2}$, and entropy change, $\Delta {\overline{S}}_{0.2}$, of hydrogen for hydrogen dissolution. It is demonstrated that the PCT curve can be controlled very precisely in view of $\Delta {\overline{H}}_{0.2}$ and $\Delta {\overline{S}}_{0.2}$. Also, the required membrane area to obtain 300 Nm³ h^?1 of hydrogen flow is estimated. It is found that, in view of the membrane area, it is favorable to apply at least 400 kPa of hydrogen pressure at feed side.     

Effect of choroidal blood flow on transscleral retinal drug delivery using a porous medium model

Transscleral drug delivery is one of the methods of depositing drug in the posterior segment (comprising retina, choroid, sclera and macula) of the human eye, to treat diseases such as age related macular degeneration (AMD). In this study, the effect of choroidal blood flow on transscleral drug delivery to the retina is investigated using a porous medium model of the sclera and the choroid. A two-dimensional geometrical model of the human eye is constructed from available measurements and determination of physicochemical properties of the sclera and the choroid, such as their effective diffusivity D and porous medium permeability K. Position and time dependent concentrations of the drug in the sclera and the choroid are predicted and the relative magnitudes of the periocular, vitreous and circulation losses are compared for various blood flow velocities $U_b$. The simulations also predict the transient mean plasma concentration $\overline{C}$ of the drug anecortave desacetate in the choroid and the effect of choroidal blood flow on the peak mean plasma concentration ${\overline{C}}_{\max }$. Comparison of predicted $\overline{C}$ with available experimental results is good.