Time-periodic laminar mixed convection in an inclined channel

The steady-periodic regime of laminar mixed convection in an inclined channel is studied analytically, with the following boundary conditions: the temperature of one channel wall is stationary, while the temperature of the other wall is a sinusoidal function of time. Analytical expressions of the velocity field, of the temperature field, of the pressure drop, of the friction factors, as well as of the Nusselt number at any plane parallel to the walls are determined. It is found that, for every value of the Prandtl number greater than 0.277, there exists a resonance frequency which maximizes the amplitude of the friction factor oscillations at the unsteady-temperature wall. Moreover, for any plane which lies between the midplane of the channel and the unsteady-temperature wall, every value of the Prandtl number yields a resonance frequency which maximizes the amplitude of the Nusselt number oscillations.     

Conditional analysis of lifted hydrogen jet diffusion flame experimental data and comparison to laminar flame solutions

Simultaneous point measurements of temperature, mixture fraction, major species, and OH concentrations in a lifted turbulent hydrogen jet flame are reprocessed to obtain the Favre average and conditional mean profiles. Large discrepancies between the Favre average and the ensemble average temperature, H₂O, and OH mole fractions are found at the lifted flame base, due to density weighting of fairly large samples of unreacted mixtures. Conditional statistics are used to reveal the reaction zone structure in mixture fraction coordinates. The cross-stream dependence of conditional reactive scalars, which is most notable at the lifted flame base and decreases to negligible levels with increasing streamwise positions, could be attributed to radial differences in both the Damköhler number and the level of partial premixing. Conditional results indicate that the lifted flame is stabilized at the outer region of the jet characterized by low strain rates and lean mixtures. Comparison of the measured conditional mean OH vs H₂O with a series of stretched laminar partially premixed flame and diffusion flame calculations reveals that strong partial premixing takes place at the lifted flame base and the strain rates vary from a=14,000 to 100 s⁻¹. The level of partial premixing and the strain rate decrease with increasing downstream locations. The range of estimated scalar dissipation rates (χ≈1–0.13 s⁻¹) at a further downstream location (x/D=33.3) is in agreement with reported values and the flame composition reaches an equilibrium condition at x/D=194.4. These results combined with previously reported data provide a benchmark data set for evaluation and refinement of turbulent combustion models for lifted hydrogen jet flame predictions.     

Explicit analytical solutions of 2-D laminar natural convection

There are many natural convection processes in various fields, and it is still a hot topic to investigate the fluid dynamics and heat transfer of natural convection. The analytical solutions are meaningful in both theoretical investigation and practical applications. Specially, they are very useful to computational fluid dynamics and heat transfer as the benchmark solutions to check the numerical solutions and to develop numerical differencing schemes, grid generation methods and so forth. Two explicit analytical solutions of 2-D steady laminar natural convection along a vertical porous plate and between two vertical plates were derived for better understanding the flow and heat transfer as well as promoting the computational fluid dynamics and computational heat transfer.     

Viscous dissipation effects on the asymptotic behaviour of laminar forced convection for Bingham plastics in circular ducts

The present study concentrates on the effects of viscous dissipation and the yield shear stress on the asymptotic behaviour of the laminar forced convection in a circular duct for a Bingham fluid. It is supposed that the physical properties are constant and the axial conduction is negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial distributions of wall heat flux which yield a thermally developed region. It is shown that if the asymptotic value of wall heat flux distribution is vanishes, the asymptotic value of the Nusselt number is zero. The case of the asymptotic wall heat flux distribution non-vanishing giving a value of the Nusselt number dependent on the Brinkman number and on the dimensionless radius of the plug flow region was also analysed. For an infinite asymptotic value of wall heat flux distributions, the asymptotic value of the Nusselt number depends on the dimensionless radius of the plug flow region and on the dimensionless parameter which depends on the asymptotic behaviour of the wall heat flux. The condition of uniform wall temperature and convection with an external isothermal fluid were also considered. The comparison with other existing solutions in the literature in the Newtonian case is analysed.     

Turbulent mixing and molecular transport in highly under-expanded hydrogen jets

Highly under-expanded hydrogen jets releasing in quiescent air atmosphere are studied using highly resolved numerical simulations accounting for complex multicomponent molecular transport phenomena. In a first step of the analysis, the main overall features of the hydrogen jet structure are described and compared to those of the classical under-expanded air jet at the same nozzle pressure ratio (NPR). Even if the global flow topology remains quite similar in both cases (i.e., hydrogen and air discharges), the modification of both mean density and mean velocity gradients leads to different relative energy levels for each velocity component. The corresponding change of fluid properties mainly leads to an enhanced mixing at the jet periphery. In comparison to the air case, the turbulence development within the internal part of the under-expanded hydrogen jet surrounding the subsonic core also yields a different structure. While a significantly higher peak of streamwise turbulent stress is observed downstream of the reflected shock, the vorticity dynamics is dampened by viscous diffusion and velocity divergence (i.e., volumetric expansion) contributions. Then, the performance of the simplified Hirschfelder and Curtiss approximation of the multicomponent molecular diffusion phenomena is evaluated with respect to the detailed multicomponent transport representation, as deduced from the EGLIB library. The detailed representation of molecular phenomena is shown to have a significant influence on the estimated local levels of hydrogen mass flux, leading to a non-negligible alteration of the global jet structure.     

Fully developed mixed convection and flow reversal in a vertical rectangular duct with uniform wall heat flux

Combined forced and free flow in a vertical rectangular duct is investigated for laminar and fully developed regime. The velocity field, the temperature field, the friction factor and the Nusselt number are evaluated analytically by employing finite Fourier transforms. The thermal boundary condition considered is an axially uniform wall heat flux and a peripherally uniform wall temperature, i.e. an H1 boundary condition. The necessary and sufficient condition for the onset of flow reversal is determined either in the case of upward flow in a cooled duct or in the case of downward flow in a heated duct. The special case of free convection, i.e. the case of a purely buoyancy-driven flow, is discussed. The occurrence of effects of pre-heating or pre-cooling in the fluid is analysed. It is pointed out that although these effects occur in rectangular ducts, they are not present either in circular ducts or in parallel-plate channels.     

Soot properties of laminar jet diffusion flames in microgravity

The soot properties of round, non-buoyant, laminar jet diffusion flames are described, based on experiments carried out in microgravity conditions during three flights of the Space Shuttle Columbia (Flights STS-83, 94 and 107). Experimental conditions included ethylene- and propane-fueled flames burning in still air at an ambient temperature of 298 K and ambient pressures of 35-100 kPa. Measurements included soot volume fraction distributions using deconvolved laser extinction imaging and soot temperature distributions using deconvolved multiline emission imaging. Mixture fractions were estimated from the temperature measurements. Flow field modeling based on the work of Spalding is presented. It is shown that most of the volume of these flames is inside the dividing streamline and thus should follow residence time state relationships. Most streamlines from the fuel supply to the surroundings exhibit nearly the same maximum soot volume fraction and maximum temperature. The present work studies whether soot properties of these flames are universal functions of mixture fraction, i.e., whether they satisfy soot state relationships. Soot state relationships were observed, i.e., soot volume fraction was found to correlate reasonably well with estimated mixture fraction for each fuel/pressure selection. These results support the existence of soot property state relationships in steady non-buoyant laminar diffusion flames, and thus in a large class of practical turbulent diffusion flames through the application of the laminar flamelet concept.     

On the existence of parallel flow for mixed convection in an inclined duct

The necessary condition for the occurrence of parallel mixed convection flow in an inclined duct is determined by employing the Boussinesq approximation. A sample case involving an inclined infinitely-wide plane channel is discussed to illustrate this condition. It is shown that, according to the necessary condition, parallel flow cannot occur in this case. Indeed, the investigated flow is the superposition of a parallel streamwise flow and a secondary flow. An exponential equation of state for the fluid is assumed and the balance equations are solved analytically to determine the dimensionless velocity distribution, as well as the conditions for the occurrence of flow reversal.     

Combined forced and free flow in a vertical circular duct subjected to non-axisymmetric wall heating conditions

The fully developed mixed convection flow in a vertical circular duct is investigated analytically, under the assumption of laminar parallel flow. A wall heat flux uniform in the axial direction and dependent on the angular coordinate is considered. As a consequence, the fluid temperature is three dimensional, since it changes in the radial, axial and angular directions. An analytical method based on Fourier series expansions of temperature and velocity fields is adopted to determine the velocity and the temperature distributions as well as the friction factor and the average Nusselt number. The general solution, expressed in terms of Bessel functions, is applied to study a case that has a special importance in technical applications: a duct whose wall is half subject to a uniform heat flux and half adiabatic. The positive and negative threshold values of the ratio between the Grashof number Gr and the Reynolds number Re for the onset of the flow reversal phenomenon are determined. A comparison between the average Nusselt number for the considered non-axisymmetric case and that for the case of a duct subject to a uniform wall heat flux is performed.     

Heat transfer due to double laminar slot jets impingement onto an isothermal wall within one side closed long duct

In this study, heat transfer due to double impinging vertical slot jets onto an isothermal wall was investigated numerically for laminar flow regime. Navier–Stokes and energy equations were discretized with a finite volume procedure on a non-staggered grid arrangement using SIMPLEM (SIMPLE-Modified) algorithm. The effect of the jet Reynolds number, the jet-isothermal bottom wall spacing, and the distance between two jets on heat transfer and flow field was examined. Air was chosen as the working fluid (Pr = 0.71). It is found that multi-cellular flow is formed in the impingement region due to interaction between two jets and entrainment effects in the duct. The mean Nusselt number increases almost linearly with increasing of Reynolds number at isothermal surface. When Reynolds number of the first jet is higher than second one the heat transfer is enhanced significantly.     

Non-axisymmetric forced and free flow in a vertical circular duct

The fully developed laminar mixed convection in a vertical circular duct is studied analytically, with reference to non-axisymmetric boundary conditions such that the fluid temperature does not change along the axial direction. The Boussinesq approximation is applied by taking the average temperature in a duct section as the reference fluid temperature. The dimensionless momentum and energy balance equations are solved by employing Fourier series expansions of the temperature and the velocity fields. The solution shows that the temperature field is not influenced by the velocity distribution and that the Fanning friction factor is not affected by buoyancy. On the other hand, the velocity field is strongly influenced by the buoyancy forces and may display flow reversal phenomena. Two special cases are studied in detail: a duct with a sinusoidal wall temperature distribution; a duct subjected to an external convection heat transfer with two environments having different reference temperatures.     

Predicting radiative characteristics of hydrogen and hydrogen/methane jet fires using FireFOAM

A possible consequence of pressurized hydrogen release is an under-expanded jet fire. Knowledge of the flame length, radiative heat flux as well as the effects of variations in ground reflectance is important for safety assessment. The present study applies an open source CFD code FireFOAM to study the radiation characteristics of hydrogen and hydrogen/methane jet fires. For combustion, the eddy dissipation concept for multi-component fuels recently developed by the authors in the large eddy simulation (LES) framework is used. The radiative heat is computed with the finite volume discrete ordinates model in conjunction with the weighted sum of grey gas model for the absorption/emission coefficient. The pseudo-diameter approach is used in which the corresponding parameters are calculated using the formulations of Birch et al. [24] with the thermodynamic properties corrected by the Able-Noble equation of state. The predicted flame length and radiant fraction are in good agreement with the measurements of Schefer et al. [2], Studer et al. [3] and Ekoto et al. [6]. In order to account for the effects of variation in ground surface reflectance, the emissivity of hydrogen flames was modified following Ekoto et al. [6]. Four cases with different ground reflectance are computed. The predictions show that the ground surface reflectance only has minor effect on the surface emissive power of the smaller hydrogen jet fire of Ekoto et al. [6]. The radiant fractions fluctuate from 0.168 to 0.176 close to the suggested value of 0.16 by Ekoto et al. [6] based on the analysis of their measurements.     

EINOx scaling in a non-premixed turbulent hydrogen jet with swirled coaxial air

The effect of swirl flow on pollutant emission (nitrous oxide) was studied in a non-premixed turbulent hydrogen jet with coaxial air. A swirl vane was equipped in a coaxial air feeding line and the angle of the swirl vane was varied from 30 to 90 degrees. Under a fixed global equivalence ratio of φ_G = 0.5, fuel jet air velocity and coaxial air velocity were varied in an attached flame region as u_F = 85.7–160.2 m/s and u_A = 7.4–14.4 m/s. In the present study, two mixing variables of coaxial air and swirl flow were considered: the flame residence time and global strain rate. The objective of the current study was to analyze the flame length behavior, and the characteristics of nitrous oxide emissions under a swirl flow conditions, and to suggest a new parameter for EINOx (the emission index of nitrous oxide) scaling. From the experimental results, EINOx decreased with the swirl vane angle and increased with the flame length (L). We found the scaling variables for the flame length and EINOx using the effective diameter (d_F,eff) in a far-field concept. Normalized flame length (L divided by d_F,eff) fitted well with the theoretical expectations. EINOx increased in proportion to the flame residence time (∼τ_R^1/2.8) and the global strain rate (∼S_G^1/2.8).     

A review on membraneless laminar flow-based fuel cells

The review article provides a methodical approach for understanding membraneless laminar flow-based fuel cells (LFFCs), also known as microfluidic fuel cells. Membraneless LFFCs benefit from the lamination of multiple streams in a microchannel. The lack of convective mixing leads to a well-defined liquid-liquid interface. Usually, anode and cathode are positioned at both sides of the interface. The liquid-liquid interface is considered as a virtual membrane and ions can travel across the channel to reach the other side and complete the ionic conduction. The advantage of membraneless LFFC is the lack of a physical membrane and the related issues of membrane conditioning can be eliminated or becomes less important. Based on the electrode architectures, membraneless LFFCs in the literature can be categorized into three main types: flow-over design with planar electrodes, flow-through design with three-dimensional porous electrodes, and membraneless LFFCs with air-breathing cathode. Since this paper focuses on reviewing the design considerations of membraneless LFFCs, a concept map is provided for understanding the cross-related problems. The impacts of flow and electrode architecture on cell performance and fuel utilization are discussed. In addition, the main challenges and key issues for further development of membraneless LFFCs are discussed.     

Heat-transfer distribution for an impinging laminar flame jet to a flat plate

Impinging flame jets are widely used in applications where high heat-transfer rates are needed, for instance in the glass industry. During the heating process of glass products, internal thermal stresses develop in the material due to temperature gradients. In order to avoid excessive thermal gradients as well as overheating of the hot spots, it is important to know and control the temperature distribution inside a heated glass product. Therefore, it is advantageous to know the relation describing the convective heat–flux distribution at the heated side of a glass product. In a previous work, we presented a heat–flux relation applicable for the hot spot of the target [M.J. Remie, G. Särner, M.F.G. Cremers, A. Omrane, K.R.A.M. Schreel, M. Aldén, L.P.H. de Goey, Extended heat-transfer relation for an impinging laminar flame jet to a flat plate, Int. J. Heat Mass Transfer, in press]. In this paper, we present an extension of this relation, which is applicable for larger radial distances from the hot spot.     

Non-Boussinesq turbulent buoyant jet resulting from hydrogen leakage in air

This paper is devoted to introduce a numerical investigation of a vertical axisymmetric non-Boussinesq buoyant jet resulting from hydrogen leakage in air as an example of injecting a low-density gas jet into high-density ambient. As the domain temperature is assumed to be constant and therefore the density of the mixture is a function of the concentration only, the binary gas mixture is assumed to be of a linear mixing type. Also, it is assumed that the rate of entrainment to be a function of the plume centerline velocity and the ratio of the mean plume and ambient densities. On the other hand, the local rate of entrainment may be considered to be consisted from two components; one is the component of entrainment due to jet momentum while the other is the component of entrainment due to buoyancy. Firstly, the integral models of the mass, momentum and concentration fluxes are obtained and transformed to a set of ordinary differential equations using some non-dimensional transformations known as similarity transformations. The given ordinary differential system is integrated numerically and the mean centerline mass fraction, jet width and mean centerline velocity are obtained. In the second step, the mean axial velocity, mean concentration and mean density of the jet are obtained. Finally in the third step of this article, several quantities of interest, including the cross-stream velocity, Reynolds stress, velocity-concentration correlation (radial flux), turbulent eddy viscosity and turbulent eddy diffusivity, are obtained. In addition, the turbulent Schmidt number is estimated and the normalized jet-feed material density and the normalized momentum flux density are correlated.     

Theoretical analysis of heat transfer in laminar pulsating flow

Pulsation effect on heat transfer in laminar incompressible flow, which led to contradictory results in previous studies, is theoretically investigated in this work starting from basic principles in an attempt to eliminate existing confusion at various levels. First, the analytical solution of the fully developed thermal and hydraulic profiles under constant wall heat flux is obtained. It eliminates the confusion resulting from a previously published erroneous solution. The physical implications of the solution are discussed. Also, a new time average heat transfer coefficient for pulsating flow is carefully defined such as to produce results that are both useful from the engineering point of view, and compliant with the energy balance. This rationally derived average is compared with intuitive averages used in the literature. New results are numerically obtained for the thermally developing region with a fully developed velocity profile. Different types of thermal boundary conditions are considered, including the effect of wall thermal inertia. The effects of Reynold and Prandtl numbers, as well as pulsation amplitude and frequency on heat transfer are investigated. The mechanism by which pulsation affects the developing region, by creating damped oscillations along the tube length of the time average Nusselt number, is explained.     

Periodic laminar flow and heat transfer in a channel with 45° staggered V-baffles

A numerical investigation has been carried out to examine periodic laminar flow and heat transfer characteristics in a three-dimensional isothermal wall channel of aspect ratio, AR = 2 with 45° staggered V-baffles. The computations are based on the finite volume method, and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers based on the hydraulic diameter of the channel ranging from 100 to 1200. To generate two pair of main streamwise vortex flows through the tested section, V-baffles with an attack angle of 45° are mounted in tandem and staggered arrangement on the lower and upper walls of the channel. Effects of different baffle heights on heat transfer and pressure drop in the channel are studied and the results of the V-baffle pointing upstream are also compared with those of the V-baffle pointing downstream. It is apparent that in each of the main vortex flows, a pair of streamwise twisted vortex (P-vortex) flows can induce impinging flows on a sidewall and a wall of the interbaffle cavity leading to drastic increase in heat transfer rate over the channel. In addition, the rise in the V-baffle height results in the increase in the Nusselt number and friction factor values. The computational results reveal that the optimum thermal enhancement factor is around 2.6 at baffle height of 0.15 times of the channel height for the V-baffle pointing upstream while is about 2.75 at baffle height of 0.2 times for the V-baffle pointing downstream.     

Numerical analysis of laminar heat transfer in a channel with diamond-shaped baffles

Laminar periodic flow and heat transfer in a two dimensional horizontal channel with isothermal walls and with staggered diamond-shaped baffles is investigated numerically. The computations are based on the finite volume method, and the SIMPLE algorithm has been implemented. The fluid flow and heat transfer characteristics are presented for Reynolds numbers based on the hydraulic diameter of the channel ranging from 100 to 600. Effects of different baffle tip angles on heat transfer and pressure loss in the channel are studied and the results of the diamond baffle are also compared with those of the flat baffle. It is observed that apart from the rise of Reynolds number, the reduction of the baffle angle leads to an increase in the Nusselt number and friction factor. The computational results reveal that optimum thermal performance is at the baffle angle of 5° for baffle height and spacing of 0.5 and 1 times of the channel height, respectively. The thermal performance of the 5°–10°diamond baffle is found to be higher than that of the flat baffle for all Reynolds numbers used.     

Numerical simulation of high-pressure hydrogen jet flames during bonfire test

Characteristics of high-pressure hydrogen jet flames resulting from ignition of hydrogen discharge during the bonfire test of composite hydrogen storage vessels are studied. Firstly, a 3-D numerical model is established based on the species transfer model and SST k − ω turbulence model to study the high-pressure hydrogen jet flow. It is revealed that under-expanded jets are formed after the high-pressure hydrogen discharging from the vessel. Secondly, the mathematical methods are adopted to study the high-pressure hydrogen jet flames. The effects of pressure, initial temperature and the nozzle diameter on the jet flames are investigated. The results show that the jet flame length increases with the increase of discharge pressure, but decreases with the increase of nozzle diameter and temperature difference between the filling hydrogen temperature and the environment temperature. Finally, the simulation models are established to study the characteristics of hydrogen jet flames in an open space. The effects of barrier walls on the distribution of jet flames are also studied. The results show that the barrier walls can greatly reduce the damage from hydrogen jet flames to testers and properties around.