Natural convection flows in porous trapezoidal enclosures with various inclination angles

Simulations were carried out using penalty finite element analysis with bi-quadratic elements to investigate the influence of uniform and non-uniform heating of bottom wall within a trapezoidal enclosure of various inclination angles $(\phi )$. Parametric study has been carried out for a wide range of Rayleigh number $(\mathit{Ra})({10}^3?\mathit{Ra}?{10}^6)$, Prandtl number $(\mathit{Pr})(0.026?\mathit{Pr}?988.24)$ and Darcy number $(\mathit{Da})({10}^{-3}?\mathit{Da}?{10}^{-5})$. Numerical results are presented in terms of stream functions, isotherm contours and Nusselt numbers. The heat transfer is primarily due to conduction at lower values of Darcy number $(\mathit{Da})$ and convection dominant heat transfer is observed at higher Da values. The intensity of circulation increases with increase in Darcy number. Increase in the intensity of circulations and larger temperature gradient are also observed with increase in $\phi$ from 0° to 45° especially at larger Pr and Ra. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating at all Rayleigh and Darcy numbers, but average Nusselt number is lower for non-uniform heating. Local heat transfer rates are found to be relatively greater for $\phi =0°$. It is observed that the local heat transfer rate at the central portion of bottom wall is larger for non-uniform heating case. Average Nusselt number plots show higher heat transfer rates at the bottom wall for $\phi =0°$ as compared to $\phi =45°$ and $\phi =30°$. It is observed that the average heat transfer rate at the bottom wall is found to be invariant with respect to $\phi$ at higher Ra for non-uniform heating. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and the power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regimes.     

Hydrogen production from woody biomass by steam gasification using a CO2 sorbent

In ${\mathrm{H}}_2$ production from woody biomass by steam gasification using CaO as a ${\mathrm{CO}}_2$ sorbent, the effect of reaction parameters such as the molar ratio of CaO to carbon in the woody biomass $([\mathrm{Ca}]/[\mathrm{C}])$, reaction pressure, and reaction temperature was investigated on ${\mathrm{H}}_2$ yield and conversion to gas. In the absence of CaO, the product gas contained ${\mathrm{CO}}_2$. On the other hand, in the presence of CaO ($[\mathrm{Ca}]/[\mathrm{C}]=1,2$, and 4), no ${\mathrm{CO}}_2$ was detected in the product gas. At a $[\mathrm{Ca}]/[\mathrm{C}]$ of 2, the maximum yield of ${\mathrm{H}}_2$ was obtained. The ${\mathrm{H}}_2$ yield and conversion to gas were largely dependent on the reaction pressure, and exhibited the maximum value at $0.6\mathrm{MPa}$. It is noteworthy that ${\mathrm{H}}_2$ was obtained from woody biomass at a much lower pressure compared to other carbonaceous materials such as coal $(>12\mathrm{MPa})$ and heavy oil $(>4.2\mathrm{MPa})$ in steam gasification using a ${\mathrm{CO}}_2$ sorbent. ${\mathrm{H}}_2$ yield increased with increasing reaction temperature. Woody biomass is the one of the most appropriate carbonaceous materials in ${\mathrm{H}}_2$ production by steam gasification using CaO as a ${\mathrm{CO}}_2$ sorbent, taking the reaction pressure into account.     

Numerical investigation of a high pressure hydrogen jet of 82 MPa with adaptive mesh refinement: Concentration and velocity distributions

To investigate the safety properties of high-pressure hydrogen discharge or leakage, an under-expanded hydrogen jet flow with a storage pressure of 82 MPa from a small jet orifice with a diameter of 0.2 mm is studied by three-dimensional (3D) numerical calculations. The full 3D compressible Navier-Stokes equations are utilized in a domain with a size of about 3 × 3 × 6 m which is discretized by employing an adaptive mesh refinement (AMR) technology to reduce the number of grid cells. By AMR, the local mesh resolutions can narrowly cover the Taylor microscale $l_T$ and direct numerical simulations (DNS) are performed. Both the instantaneous and mean hydrogen concentration distributions in the present jet are discussed. The instantaneous concentrations of hydrogen $C_{{\text{H}}_2}$ on the axis presents significant turbulent pulsating oscillations. The centerline value of the intensity of concentration fluctuation ${\stackrel{?}{\sigma }}_{{\text{H}}_2}$ asymptotically comes to 0.23, which is in a good agreement with the existing experimental results. It substantiates the conclusion that the asymptotic centerline value of ${\stackrel{?}{\sigma }}_{{\text{H}}_2}$ is independent of jet density ratio. The probability distributions function (PDF) of instantaneous axial $C_{{\text{H}}_2}$ agree approximately with the Gaussian distribution while skewing a little to the higher range. The time averaged hydrogen concentration ${\overline{C}}_{{\text{H}}_2}$ along the radial directions can also be described as a Gaussian distribution. The axial ${\overline{C}}_{{\text{H}}_2}$ of 82 MPa hydrogen jet tends to obey the distribution discipline approximated with ${\overline{C}}_{{\text{H}}_2}=4200/(z/\theta )$ where z is the axial distance from the nozzle and $\theta$ is the effective ejection diameter, which is consistent with the experimental results. In addition, the hydrogen tip penetration $Z_{\text{tip}}$ is found to be in a linear relationship with the square root of jet flow time $\sqrt{t}$. Meanwhile, the jet's velocity half-width $L_{\text{Vh}}$ approximately gains an linear relation with z which can be expressed as $L_{\text{Vh}}=0.09z$.     

Composite relation for laminar free convection in inclined channels with uniform heat flux boundaries

A composite correlation of the average Nusselt number and the channel Rayleigh number for buoyant air flow through inclined channels with uniform heat flux boundaries is presented. The form of the correlation is based on dimensional analysis and is a superposition of the developing and fully developed flow limits. In the limit of fully developed flow, an analytical solution for the Nusselt number is derived. The developing flow limit follows the format of the correlation for a single plate. The composite relationship based on the top wall temperature is $\overline{\text{Nu}}={\left[\frac{6.25(1+r)}{{\text{Ra}}^{″}\sin ?}+\frac{1.64}{({\text{Ra}}^{″}\sin ?{)}^{2/5}}\right]}^{-1/2}$, where r is ratio of the heat flux at the top and bottom wall. At inclination angles of $30°\le ?\le 90°$, this correlation predicts the available data base for $10\le {\text{Ra}}^{″}\le {10}^5$ and agrees with the analytical solution for $1\le {\text{Ra}}^{″}\le {10}^2$.     

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.     

Role of lattice strain and texture in hydrogen embrittlement of 18Ni (300) maraging steel

Hydrogen embrittlement causes engineering components to fail unexpectedly. Maraging 300 steel was hydrogen charged and subjected to slow strain rate tensile test until fracture. Electron backscatter diffraction analysis of fractured specimen revealed that cracks initially propagated intergranulary along prior-austenite grain boundaries. When cracks faced martensitic $\left\{111\right\}\alpha$ planes parallel to normal direction (ND) they were deflected and continued to propagate transgranulary through $\left\{001\right\}\alpha //\text{ND}$ planes. Finally, cracks were arrested by $\left\{111\right\}\alpha //\text{ND}$ planes. Crystallographic planes on which cracks propagate/are arrested, correlate well with planes that exhibit highest/lowest magnitude of lattice strain determined during tensile loading using in situ synchrotron X-ray diffraction.