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 $L_{\text{Vh}}=0.09z$.     

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.     

Coriolis and rotating buoyancy effect on detailed heat transfer distributions in a two-pass square channel roughened by 45° ribs at high rotation numbers

Heat transfer measurements from a rotating two-pass square channel with two opposite leading and trailing walls roughened by 45° parallel ribs arranged in the staggered manner are performed to examine the effects of Reynolds (Re), rotation (Ro) and buoyancy (Bu) numbers on local and area-averaged Nusselt numbers (Nu and $\overline{\mathit{Nu}}$). Full-field Nu distributions over the two rib-roughened leading and trailing walls are measured at the conditions of 4000 ? Re ? 16,000, 0 ? Ro ? 0.8 and 0.0015 ? Bu ? 0.93 (0.05 ? Δρ/ρ ? 0.1) using the infrared thermography which allows for the detailed examination of the Coriolis and rotating buoyancy effects on Nu distributions over the rotating ribbed surface. Selected heat transfer data in term of Nu ratio between rotating and stationary levels illustrates the influences of rotation on local and area-averaged heat transfer performances. Area-averaged $\overline{\mathit{Nu}}$ for the turn region and the inlet and outlet ribbed legs of the rotating two-pass channel are parametrically analyzed to devise a set of empirical heat transfer correlations that permits the evaluation of the interdependent and individual effects of Re, Ro and Bu on $\overline{\mathit{Nu}}$.