An analytical model for azimuthal thermoacoustic modes in an annular chamber fed by an annular plenum

This study describes an analytical method for computing azimuthal modes due to flame/acoustics coupling in annular combustors. It is based on a quasi-one-dimensional zero-Mach-number formulation where N burners are connected to an upstream annular plenum and a downstream chamber. Flames are assumed to be compact and are modeled using identical flame transfer function for all burners, characterized by an amplitude and a phase shift. Manipulation of the corresponding acoustic equations leads to a simple methodology called ANR (annular network reduction). It makes it possible to retain only the useful information related to the azimuthal modes of the annular cavities. It yields a simple dispersion relation that can be solved numerically and makes it possible to construct coupling factors between the different cavities of the combustor. A fully analytical resolution can be performed in specific situations where coupling factors are small (weak coupling). A bifurcation appears at high coupling factors, leading to a frequency lock-in of the two annular cavities (strong coupling). This tool is applied to an academic case where four burners connect an annular plenum to a chamber. For this configuration, analytical results are compared with a full three-dimensional Helmholtz solver to validate the analytical model in both weak and strong coupling regimes. Results show that this simple analytical tool can predict modes in annular combustors and investigate strategies for controlling them.     

Effect of vent aspect ratio on unsteady laminar buoyant flow through rectangular vents in large enclosures

The effects of vent aspect ratio on oscillatory flow regime through a horizontal opening were studied numerically. The physical model consisted of a vertical rectangular enclosure divided into two chambers by a horizontal partition. The partitions contained a slot that connected the two chambers. The upper chamber contains cold air and the lower chamber contains hot air. A density differential due to the different temperatures drives the interaction between the two chambers. The opposing forces at the interface between the two chambers create a gravitationally unstable system, and an oscillating exchange of fluid develops. Results were obtained for cases with L/D = 1, 0.5, and 2.0, where L represents the thickness of the partition and D represents the slot width of the opening in the partition. Results indicate that the flow exchange increases with partition thickness L/D = 0.5 and decreases for L/D = 2. The frequency of the oscillatory flow pattern is also examined for the different cases. Sudden bursts of upflow with a corresponding downflow have been documented and compared with experimental observations in the literature. The time traces of velocity and temperature fields for this flow regime reveal interesting mechanisms, which have been explained.     

Unsteady fluid mechanics and heat transfer study in a double-tube air–combustor heat exchanger with porous medium

Fluid mechanics and heat transfer are studied in a double-tube heat exchanger that uses the combustion gases from natural gas in a porous medium located in a cylindrical tube to warm up air that flows through a cylindrical annular space. The mathematical model is constructed based on the equations of continuity, linear momentum, energy and chemical species. Unsteady fluid mechanics and heat transfer by forced gas convection in the porous media, with combustion in the inner tube, coupled to the forced convection of air in the annular cylindrical space are predicted by use of finite volumes method. Numerical simulations are made for four values of the annular air flow Reynolds number in the range 100 ? Re ? 2000, keeping constant the excess air ψ = 4.88, the porosity ε = 0.4, and the air–fuel mixture inlet speed Uo = 0.43 m/s. The results obtained allow the characterization of the velocity and temperature distributions in the inner tube and in the annular space, and at the same time to describe the displacement of the moving combustion zone and the annular porous media heat exchanger thermal efficiency. It is concluded that the temperature increase is directly related to the outer Reynolds number.     

Numerical calculation of local entropy generation in a methane–air burner

This study considers numerical simulation of the combustion of methane with air including 21% oxygen and 79% nitrogen in a burner and the numerical solution of the local entropy generation rate due to the high temperature and velocity gradients in the combustion chamber for various fuel flow rates (from 5 to 10 lpm). Swirling air flow is also used to burn the methane more efficiently. The effects of equivalence ratio (ϕ) and swirl number (S) on the combustion and entropy generation rate are investigated for different (consecutive) equivalence ratios (from 0.5 to 1.0) and swirl numbers (from 0 to 0.3). The numerical calculation of combustion is performed individually for these cases with the help of the Fluent CFD code. The volumetric entropy generation rate distributions and the other thermodynamic parameters are calculated numerically by using the results of the combustion calculations. The maximum values of the rates of reaction-1 and -2 decrease with the increase of ϕ. In the case of ϕ < 1, complete combustion occurs, and the combustion in the case of ϕ = 1 is very close to the complete combustion state. In the case of no swirl, the entropy generation rate decreases exponentially with the increase of ϕ in the cases of high Q_f, whereas they have quadratic profiles having their minimum values in cases of low Q_f. In terms of the entropy generation rates, the optimum equivalence ratios for Q_f = 5, 6, 7, >7 lpm in the case of S = 0 and Q_f = 10 lpm in the case of S = 0.3 are obtained as ϕ = 0.66, 0.8, 0.86, 1.0 and 0.92, respectively.     

Convective diffusion from strip-like micro-probes into colloidal suspensions

Full equations of convective diffusion are solved numerically for a strip-like (2D) electrodiffusion friction probe in a stream of microdisperse liquid, assuming a non-linear near-to-wall velocity profile ranging from simple shear flow (p = 1) to ideal slip (p = 0). The range of generalized Peclet number H from H = 0.01 (almost pure spatial diffusion) to H = 100 (diffusion layer with negligible longitudinal diffusion) covers all cases of possible experimental relevance. The main result is expressed as a relative deviation of actual total diffusion flux N from its diffusion-layer approximation N_DLA, Ψ = N/N_DLA ? 1.     

Swirl effects on harmonically excited,premixed flame kinematics

This paper describes the response of a swirling premixed flame with constant burning velocity to non-axisymmetric harmonic excitation. This work extends prior studies of axisymmetric forcing, which have shown that wrinkles are excited on the flame that propagate downstream along the mean flame surface at a speed given by U_o cos ψ, where U_o is the mean flow velocity and ψ is the flame angle. The swirl component in the flow field introduces an azimuthal transport mechanism for disturbances on the flame. As such, the flame response at any given position is a superposition of flame wrinkles excited at earlier times, upstream axial locations, and different azimuthal positions. These swirl transport effects do not arise in problems where axisymmetric flames are subjected to axisymmetric excitation, but enter quite prominently in the presence of non-axisymmetries, such as when the flame is subjected to transverse excitation. The solution characteristics are strongly dependent upon the ratio of angular rotation rate to excitation frequency, denoted by σ = Ω/ω, which describes the fraction of azimuthal rotation a disturbance makes in one acoustic period. When σ ? 1 and σ ? 1, the axial wavelength of flame wrinkles scales with the convective wavelength, λ_c, but becomes much longer for σ ～ O(1). The spatial variation in phase of flame wrinkling is also strongly dependent upon σ. Regardless of swirl number, flame wrinkles propagate in helical spirals along the solution characteristics at a phase speed equal to the local tangential velocity. The axial phase characteristics of flame wrinkling at a fixed azimuthal location, as would be measured by laser sheet imaging, are much more complex. For σ < 1, the wrinkles exhibit the familiar negative roll-off character for the phase with axial downstream distance, indicative of an axially convecting disturbance. The slope of this phase roll-off decreases with increasing σ, however, and becomes zero at σ = 1 for a compact flame. For σ > 1, the wrinkles actually have a positive roll-off character for the phase with axial downstream distance, indicating a flame wrinkle with a negative trace velocity, but whose actual propagation velocity is positive. Finally, these results show that while the flame response to transverse acoustic excitation is quite strong locally, its spatially integrated effect is much smaller for acoustically compact flames. This suggests that the dominant mechanism through which the flame responds globally to transverse excitation is the induced vortical and longitudinal acoustic fluctuations.     

Three-dimensional thermocapillary–buoyancy flow of silicone oil in a differentially heated annular pool

In order to understand the characteristics of thermocapillary–buoyancy flow, we conducted a series of unsteady three-dimensional numerical simulations of thermocapillary–buoyancy flow of 0.65cSt silicone oil (Prandtl number Pr = 6.7) in an annular pool with different depth (d = 1–11 mm) heated from the outer wall (radius r_o = 40 mm) and cooled at the inner cylinder (r_i = 20 mm) with an adiabatic solid bottom and adiabatic free surface. Simulation conditions correspond to those in the experiments of Schwabe [D. Schwabe, Buoyant–thermocapillary and pure thermocapillary convective instabilities in Czochralski systems, J. Crystal Growth 237–239 (2002) 1849–1853]. Simulation results with large Marangoni number predict three types three-dimensional flow patterns. In the shallow thin pool (d = 1 mm), the hydrothermal wave characterized by curved spokes is dominant. In the deep pools (d ⩾ 5 mm) the three-dimensional stationary flow appears and this flow pattern corresponds to the Rayleigh-Benard instability, which consists of pairs of counter-rotating longitudinal rolls. When 2 mm ⩽ d ⩽ 4 mm, the hydrothermal wave and three-dimensional oscillatory flow coexist in the pool and travel along the same azimuthal direction with the same angular velocity. The critical conditions for the onset of three-dimensional flows were determined and compared with the experimental results. The characteristics of three-dimensional flows were discussed.     

Combustion characteristics of cotton stalk in FBC

The present work reports studies on the mixing and combustion characteristics of cotton stalk with 10–100 mm in length in FBC. Experiments on a cold model show that cotton stalk cannot fluidize, and adding bed material can improve the fluidization condition. Cotton stalk can mix well with 0.6–1 mm alumina at fluidization number N = 3–7. However, when the fluidization number is higher more than 7, the mixing bed will exist a little segregation comparing with N = 3–7. Thermogravimetric experiments show that cotton stalk can be ignited easily at a lower temperature, and its devolatilization and combustion are quick. Fluidized-bed combustion of cotton stalk was tested in a 0.2 MW_th test facility. According to the temperature distribution along the bed height, when the primary and secondary air is adapted cotton stalk can be burned stably in the fluidized bed. During pure cotton stalk combustion tests, silica sand and alumina are used as bed material to compare their agglomeration characteristics. SEM/EDX analysis on agglomerate samples after combustion about 38 h suggests that the high alkali metals content causes the formation of the coating around silica sand particles. The coating consists of compounds with low-melting temperature results in agglomeration of silica sand particles. By contrast, alumina is difficult to react with alkali metals from biomass ash, and the agglomeration of alumina was not found at 910 °C. It is found that alumina is more favorable than silica sand particle for use in a fluidized bed in cotton stalk combustion.     

Operating limit of heat transport in two-phase thermosyphon with connecting pipe (heated surface temperature fluctuation and flow pattern)

An experiment on heat transport phenomena has been carried out in a two-phase thermosyphon with an adiabatic connecting pipe using water as the working fluid at atmospheric pressure. The thermosyphon has an upper liquid chamber and a lower vapor chamber, which are connected with an adiabatic pipe. A horizontal upward-facing heated surface is installed in the bottom of the lower vapor chamber.The size of the connecting pipe is an inner diameter D_p = 2, 3, 4, 5, 6 and 8 mm and a length L = 250, 500 and 1000 mm. As the heat is supplied into the thermosyphon, the temperature of heated surface starts fluctuating at a heat flux at which unstable vapor–liquid counter current flow is generated in the connecting pipe. Bubbles at the upper end of the connecting pipe were photographed when the temperature fluctuation started. It was found that the heat flux at the onset of the temperature fluctuation increases with an increase in D_p and then can be predicted well by Eq. (1), which was derived based on the flooding velocity presented by Wallis [G.B. Wallis, One dimensional two-phase flow, McGraw Hill, New York, 1969], with C_w = 0.7 for D_p = 5, 6 and 8 mm. Furthermore, we clarified that the cause of this fluctuation comes from the inlet effect of the connecting pipe and we demonstrated this finding using a bell mouth, which was installed at either the bottom end or both ends of the connecting pipe.     

Numerical study of the influence of a longitudinal sound field on natural convection in a cavity

Numerical experiments have been performed in order to investigate the convection in an enclosure of aspect ratios 5:1:1.3 subject to a horizontal temperature gradient and a longitudinal sound field. The governing equations are solved by a spectral element method. Different flow structures appear when increasing (or decreasing) the Grashof number. Without acoustic field (acoustic Froude number Fr = 0), a hysteresis occurs connected to a first steady bifurcation with breaking of symmetry, but for Fr ≠ 0, no hysteresis is observed as this symmetry is no more effective. The further transition to oscillatory flow is found to be stabilized by the acoustic field. Depending on Fr, this transition can occur with or without the breaking of the left–right symmetry.     

Acoustic decoupling of longitudinal modes in generic combustion systems

Conditions are examined under which acoustic modes of a chamber filled with hot combustion products can be considered to be decoupled from the plenum acoustics supplying the fresh reactants through a feeding manifold. It is shown that this is controlled by a coupling index Ξ = (ρ_bc_b)/(ρ_uc_u)S₁/S₂ ? (T_u/T_b)^1/2(S₁/S₂), where T_u and T_b are the fresh and burned gases temperatures and S₂/S₁ is the expansion ratio between the chamber and injection unit cross sections. It is demonstrated that the acoustic response of a coupled system can be analyzed by considering the plenum and the chamber acoustics separately for small values of the coupling parameter Ξ. Longitudinal self-sustained combustion oscillations may then lock on (i) the plenum resonant frequencies, thus becoming independent of downstream modifications of the combustion chamber acoustics, or on (ii) the combustion chamber modes, thus becoming essentially indifferent to the plenum acoustics. The case of a plenum featuring a Helmholtz resonance is investigated in further detail when the chamber exhaust impedance is varied. Exact relations under which the plenum and the chamber modes are decoupled are derived when the chamber is open to atmospheric conditions or when it is equipped with a sonic nozzle. Predictions are compared to measurements for a generic system equipped with a swirl injector, a compact chamber and terminated by an open atmospheric pressure exhaust. It is shown that in this case, self-sustained longitudinal combustion-instabilities develop preferentially near the plenum mode frequencies and are weakly sensitive to modifications in the chamber geometry.     

Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients

The characteristics of transient double-diffusive convection in a vertical cylinder are numerically simulated using a finite element method. Initially the fluid in the cavity is at uniform temperature and solute concentration, then constant temperature and solute concentration, which are lower than their initial values, are imposed along the sidewall and bottom wall, respectively. The time evolution of the double-diffusive convection is investigated for specific parameters, which are the Prandtl number, Pr = 7, the Lewis number, Le = 5, the thermal Grashof number, Gr_T = 10⁷, and the aspect ratio, A = 2, of the enclosure. The objective of the work is to identify the effect of the buoyancy ratio (the ratio of solutal Grashof to thermal Grashof numbers: N = Gr_S/Gr_T) on the evolution of the flow field, temperature and solute field in the cavity. It is found that initially the fluid near the bottom wall is squeezed by the cold flow from the sidewall, a crest of the solute field forms and then pushed to the symmetry line. In the case of N > 0, a domain with higher temperature and weak flow (dead region) forms on the bottom wall near the symmetry line, and the area of dead region increases when N varies from 0.5 to 1.5. More crests of the solute field are formed and the flow near the bottom wall fluctuates continuously for N < 0. The frequency of the fluctuation increases when N varies from −0.5 to −1.5. Corresponding to the variety of the thermal and solutal boundary layers, the average rates of heat transfer (Nu) at the sidewall remain almost unchanged while the average rates of mass transfer (Sh) at the bottom wall change much in the cases of N = 1, 0, −1.     

Optimal design of geometric parameters of double-layered microchannel heat sinks

This work uses an optimization procedure consisting of a simplified conjugate-gradient method and a three-dimensional fluid flow and heat transfer model to investigate the optimal geometric parameters of a double-layered microchannel heat sink (DL-MCHS). The overall thermal resistance R_T is the objective function to be minimized, and the number of channels N, channel width ratio β, lower channel aspect ratio α_l, and upper channel aspect ratio α_u are the search variables. For a given bottom area (10 × 10 mm) and heat flux (100 W/cm²), the optimal (minimum) thermal resistance of the double-layered microchannel heat sink is about R_T = 0.12 °C/m²W. The corresponding optimal geometric parameters are N = 73, β = 0.50, α_l = 3.52, and, α_u = 7.21 under a total pumping power of 0.1 W. These parameters reduce the overall thermal resistance by 52.8% compared to that yielded by an initial guess (N = 112, β = 0.37, α_l = 10.32, and α_u = 10.93). Furthermore, the optimal thermal resistance decreases rapidly with the pumping power and then tends to approach an constant value. As the pumping power increases, the optimal values of N, α_l, and α_u increase, whereas the optimal β value decreases. However, increasing the pumping power further is not always cost-effective for practical heat sink designs.     

Heat transfer characteristics of three interacting methane/air flame jets impinging on a flat surface

An experimental study has been conducted for three interacting methane/air flame jets (arranged in a triangular configuration) impinging normally on a flat surface. Surface heat flux distributions have been determined for various dimensionless inter-jet spacings (S/d = 3, 4, 6 and 7.58) and separation distances between the exit plane of the burners and the target plate (H/d = 2, 2.6, 5 and 7). All experiments were conducted for stoichiometric mixture at a Reynolds number of 800. The surface heat flux distributions were intimately related to flame shapes. For small inter-jet spacings and small separation distances, flames were deflected outward from the centroid of the triangular arrangement due to strong interaction between the jets. The heating was quite non-uniform at very large inter-jet spacings. Zones of low heat flux were obtained when the tip of inner reaction zones were intercepted by the plate (H/d = 2). There were sharp peaks in the heat flux distribution when the tips of the inner reaction zones just touched the impingement surface (H/d = 2.6). Heat flux distribution was non-uniform at small separation distances (H/d = 2 and 2.6). For the system of flame jets under consideration, the optimum configuration, considering the magnitude of the average heat flux and the uniformity in the heat flux distribution, was corresponding to H/d = 5 and S/d = 3.     

Multi-parameters optimization for microchannel heat sink using inverse problem method

This work describes an inverse problem method to optimize the geometric design for microchannel heat sinks using a novel multi-parameter optimization approach, which integrates the simplified conjugate-gradient scheme and a fully developing three-dimensional heat transfer and flow model. Overall thermal resistance is the objective function to be minimized with number of channels, N, channel aspect ratio, α, and the ratio of channel width to pitch, β, as search variables. With a constant bottom area (10 mm × 10 mm), constant heat flux applied to the heat sink bottom surface (100 W cm^?2), and constant pumping power (0.05 W), the optimal design values are N = 71, α = 8.24, and β = 0.6, with a minimum overall thermal resistance of 0.144 K W^?1. Increasing pumping power reduces overall thermal resistance of the optimal design; however, the design’s effectiveness declines significantly under high pumping power. The N and α values in the optimal design increase and β decreases as pumping power increases.     

Cultivation of Spirulina platensis by continuous process using ammonium chloride as nitrogen source

This work is focused on the influence of dilution rate (0.08⩽D⩽0.32 d⁻¹) on the kinetics of continuous cultivation of Spirulina platensis at two different concentrations of ammonium chloride (N₀=1.0 and 10 mM) as nitrogen source. Cell productivity increased in both series of runs up to D≅0.12–0.16 d⁻¹, and then decreased. While at N₀=1.0 mM biomass washing was certainly the cause of progressive cell concentration decrease, a combination of this phenomenon with the toxic effect of excess ammonia was responsible, at N₀=10 mM and D⩾0.20 d⁻¹, for quick stop of cell growth just beyond the achievement of maximum cell productivity (92.4 mg l⁻¹ d⁻¹). Similar profile was observed for protein productivity, that achieved a maximum value of 67.0 mg l⁻¹ d⁻¹, because of the very high protein content (72.5%) of biomass produced under these conditions. The yield of nitrogen-to-biomass was much higher at the lower N₀, because of the low protein content, and reached a maximum value of 9.7 g g⁻¹ at D=0.08–0.12 d⁻¹. The yield of nitrogen-to-protein showed less marked difference, being most of the nitrogen present in the cell as proteins or free amino-acids.     

Effect of fin thickness on the air-side performance of wavy fin-and-tube heat exchangers under dehumidifying conditions

This study investigated the effect of fin thickness on the air-side performance of wavy fin-and-tube heat exchangers under dehumidifying conditions. A total of 10 samples were tested with associated fin thickness (δ_f) of 0.115 mm and 0.25 mm, respectively. For a heat exchanger with two rows (N = 2) and fin pitch F_p of 1.41 mm, the effect of fin thickness on the heat transfer coefficient is more pronounced. The heat transfer coefficients for δ_f = 0.25 mm is about 5–50% higher than those for δ_f = 0.115 mm whereas the pressure drop for δ_f = 0.25 mm is about 5–20% higher. The unexpected difference in heat transfer coefficient subject to fin thickness is attributable to better interactions between the directed main flow and the swirled flow caused by the condensate droplet for δ_f = 0.25 mm. The maximum difference in heat transfer coefficients for N = 2 and F_p = 2.54 mm subject to the influence of fin thickness is reduced to about 20%, and there is no difference in heat transfer coefficient when the frontal velocity is above 3 m/s. For N ⩾ 4 and F_p = 2.54 mm, the influence of fin thickness on the heat transfer coefficients diminishes considerably. This is because of the presence of tube row, and the unsteady/vortex shedding feature at the down stream of wavy channel. Based on the present test results, a correlation is proposed to describe the air-side performance for wavy fin configurations, the mean deviations of the proposed heat transfer and friction correlations are 7.9% and 7.7%, respectively.     

Effects of dilution with carbon dioxide on the laminar burning velocity and flame stability of H2–CO mixtures at atmospheric condition

The objective of this investigation was to study the effect of dilution with CO₂ on the laminar burning velocity and flame stability of syngas fuel (50% H₂–50% CO by volume). Constant pressure spherically expanding flames generated in a 40 l chamber were used for determining unstretched burning velocity. Experimental and numerical studies were carried out at 0.1 MPa, 302 ± 3 K and ? = 0.6–3.0 using fuel-diluent and mixture-diluent approaches. For H₂–CO–CO₂–O₂–N₂ mixtures, the peak burning velocity shifts from ? = 2.0 for 0% CO₂ in fuel to ? = 1.6 for 30% CO₂ in fuel. For H₂–CO–O₂–CO₂ mixtures, the peak burning velocity occurred at ? = 1.0 unaffected by proportion of CO₂ in the mixture. If the mole fraction of combustibles in H₂–CO–O₂–CO₂ mixtures is less than 32%, then such mixtures are supporting unstable flames with respect to preferential diffusion. The analysis of measured unstretched laminar burning velocities of H₂–CO–O₂–CO₂ and H₂–CO–O₂–N₂ mixtures suggested that CO₂ has a stronger inhibiting effect on the laminar burning velocity than nitrogen. The enhanced dilution effect of CO₂ could be due to the active participation of CO₂ in the chemical reactions through the following intermediate reaction CO + OH ? CO₂ + H.     

Effects of spray angle on three-dimensional isothermal solid–gas flow in a confined deposition chamber

The effects of spray angle (β) on the three-dimensional isothermal solid–gas flow and deposition process in a confined deposition chamber are numerically investigated in the present study. The investigated cases include substrate spray angles equal to 90-, 75-and 45-deg. In the three spray-angle cases, β = 75-deg case has the highest deposition efficiency, lowest distribution non-uniformity and comparative average impact velocity. Accordingly, β = 75-deg is concluded as the optimal spray angle for the deposition chamber under the isothermal flow conditions. However, the relatively large amount of particles impact on the chamber wall, which is possible to block up the flow pass of the chamber, requires special cautions in practical applications.     

Generalized correlations for predicting heat transfer and pressure drop in plate heat exchanger channels of arbitrary geometry

Characteristics of the flow in chevron plate heat exchangers are investigated through visualization tests of channels with β = 28° and β = 61°. Mathematical model is then developed with the aim of deriving correlations for prediction of f and Nu for flow in channels of arbitrary geometry (β and b/l). Thermal and hydraulic characteristics are evaluated using analytical solutions for the entrance and fully developed regions of a sinusoidal duct adapted to the basic single cell. The derived correlations are finally adjusted so as to agree with experimental results from tests on channels with β = 28° and β = 65°. f and Nu calculated by the presented correlations are shown to be consistent with experimental data from the literature at Re = 2–10,000, β = (15–67)° and b/l = 0.26–0.4.