Calibration of new dust dispersion systems in 1 m3 standard dust explosion vessel for fibrous biomass testing

Biomass is considered as an alternative fuel for partial/complete replacement of coal in power generation. The data on coal, agricultural and chemical dusts explosion properties are available in the literature but reliable data on fibrous biomass is not available. This is because the standard C-tube dispersion system in the 1m3 dust explosion vessel does not allow fibrous biomass to flow. In this paper alternative dust dispersion systems (Rebound nozzle, Hemispherical dispersion cup and Spherical grid nozzle) were designed and calibrated against the standard dispersion system using non-fibrous and fibrous dusts. The criterion for the calibration was the achievement of same Pmax, Kst, mass burned (%), flame speed and spherical flame propagation. The ignition delay and inlet air valve off timing were varied using gas explosions to achieve the same turbulence levels in the vessel that produced similar results as with standard system. The calibrated conditions for the rebound nozzle were; 0.70s ignition delay and 0.75s valve off timing and for spherical grid nozzle were; 0.50s ignition delay and 0.65s valve off timing. All of the injection systems with an external store of the dust were problematic with fibrous dust and would only pass fibrous dusts milled to <63µm and were not suitable for the practical dusts with sizes up to 1mm that are in current use in power stations burning pulverised biomass. The alternative was to place the dust inside the vessel and to disperse it using a blast of compressed air and the hemispherical cup was developed for this purpose. The hemispherical dispersion cup produced reliable results at 0.60s ignition delay and 0.65s valve off timing with gas explosions. The dust explosion tests using the hemispherical dispersion cup produced the same results for Pmax and proportion of injected mass burned (%) but had lower values of Kst and flame speed and the flame propagation was shown to not be spherical

A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

The Optimum Position of Water Heat Transfer Coils Downstream of a Radial Swirler in a 20kW Heater

A 76mm outlet diameter radial swirler with 8mm vane depth was investigated in a 140mm combustor diameter condensing 20 kW ultra-low NOx boiler. The aim was to show that small turbulent flames could achieve compact ultra-low NOx water heating. Low NOx was achieved using lean well mixed low flame temperature combustion with a 0.7 equivalence ratio (Ø). Thermal NOx formation was also minimised by cooling the flame downstream of the swirler outlet. A water cooled heat transfer coil was traversed into the flame to determine how close to the swirler exit the heat transfer could occur, without a major increase in the combustion inefficiency. This was shown to be 70mm from the radial swirler throat outlet. Rapid fuel and air mixing was achieved using fuel injection through the wall of the 76mm swirler outlet throat, assisted by a 41mm diameter outlet orifice at the exit of the 76mm internal diameter wall fuel injector. This created swirling flow with higher axial velocities and a more concentrated high turbulence region downstream of the orifice outlet. A 4 mb burner pressure loss was used, which is typical of domestic forced draught combustion systems. The air inlet temperature was 400K, which is typical of reverse air flow cooled combustion chambers at domestic water heater conditions. The strong swirling flow interaction with the heat exchanger coil give an 89% thermal efficiency with the front of the coil 70mm from the swirler outlet. The emissions measurements showed that the combustion inefficiency was below 0.1%, the CO/CO2 ratio <0.001 and the NOx emissions were 5ppm at 0% oxygen with the heat exchanger at 70mm from the radial swirler outlet. This design easily met the 2018 EU legislation for eco-design of domestic water heaters

Influence of Fuel Injection Location in a Small Radial Swirler Low NOₓ Combustor for Micro Gas Turbine Applications

The influence of fuel injection location in a low NOₓ (1) micro-gas turbine [MGT] in the ∼50kWe (kW electric) size range was investigated, for NG and propane, to extend the power turn down using a pilot fuel injector. The low NOx main combustor (1) was a radial swirler with vane passage fuel injection and had ultra-low NOₓ emissions of 3ppm at 15% O2 at 1800K with natural gas, NG at a combustion intensity of 11.2 MW/m2bara (MW thermal). This was a 40mm diameter outlet eight bladed radial swirler in a 76mm diameter combustor, investigated at 740K air temperature at atmospheric pressure. However, power turn down was poor and the present work was undertaken to determine the optimum position of pilot fuel injection that would enable leaner mixtures to be burned at low powers. Central injection of pilot fuel was investigated using 8 radial outward holes. This was compared with pilot fuel injected at the 76mm wall just downstream of the 40mm swirler outlet. It was show that the central injection pilot was poor with a worse weak extinction than for radial passage fuel injection. The 76mm outlet wall injection was much more successful as a pilot fuel location and had a weak extinction of 0.18Ø compared with 0.34Ø for vane passage fuel injection. NOₓ emissions were higher for wall fuel injection, but were still relatively low at 16ppm at 15% oxygen for natural gas. This indicates that wall fuel injection could be combined with vane passage fuel injection to improve the micro-gas turbine low NOₓ performance across the power range

A generalization of the q-Saalschutz sum and the Burge transform

A generalization of the q-(Pfaff)-Saalschutz summation formula is proved. This implies a generalization of the Burge transform, resulting in an additional dimension of the ``Burge tree''. Limiting cases of our summation formula imply the (higher-level) Bailey lemma, provide a new decomposition of the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe

Impact of non-central vents on vented explosion overpressures

It is normal practice to use centrally positioned vents or single vents in most experimental work and in the application of explosion venting in industry. This work seeks to investigate the influence of non-central and multiple distributed vents on the explosion overpressure. A 10L cylindrical vessel of 460mm length and 162mm diameter (L/D=2.8) was used for vented explosion with free venting (without a vent cover). Three different vent coefficient (Kv) were investigated, Kv, 3.6, 5.4 and 10.9 for both non-central and 4 hole vents. 10% methane-air and 7.5% ethylene-air mixtures were investigated to determine the influence of the mixture reactivity. The position of the spark ignition was in the centre of the end flange opposite the vent. It was shown for the non-central vent that the flame speed upstream of the vent was lower than for a central vent and this reduced the mass flow through the vent, which reduced the overpressure and reducing the external explosion due to the lower exit velocity of the unburnt gas and hence lower external turbulence. The external flame jets downstream of the vent was influenced by the increase in characteristic length scale of the vent, which was changed by increasing the number of vents

Vent static burst pressure influences on explosion venting

The overpressure generated in a 10L cylindrical vented vessel with an L/D of 2.8 was investigated, with end ignition opposite the vent, as a function of the vent static burst pressure, Pstat, from 35 to 450mb. Three different Kv (V2/3/Av) of 3.6, 7.2 and 21.7 were investigated for 10% methane-air and 7.5% ethylene-air. It was shown that the dynamic burst pressure, Pburst, was higher than Pstat with a proportionality constant of 1.37. For 10% methaneair Pburst was the controlling peak pressure for K Pburst in the literature and in EU and US standards. For higher Kv the overpressure due to flow through the vent, Pfv, was the dominant overpressure and the static burst pressure was not additive to the external overpressure. Literature measurements of the influence of Pstat at low Kv was shown to support the present finding and it is recommended that the influence of Pstat in gas venting standards is revised

Gas explosion venting: comparison of experiments with design standards and laminar flame venting theory

European and USA design standards for gas explosion venting are quite different in their predictions, with the European standards always giving a higher predicted explosion Pred for the same vent coefficient, Kv. The format of the two predictions are different with the US standards following the approach of Swift expressing the vent area as a ratio to the surface area of the vessel, As/Av and the European standard using the vent coefficient approach. Kv= V2/3/Av. It is shown that these two approaches are directly related as As is proportional to V2/3. The reactivity parameter in the US standards is the laminar burning velocity, UL, and in the European venting standards it is the deflagration parameter, KG = dp/dtmax/V1/3. It is shown that these two reactivity parameters are linearly related. The USA standard is shown to be compatible with spherical flame venting theory and with experimental data other than that of Bartknecht. There is also good agreement with the present results for a 10L vented vessel for which the spherical laminar flame venting theory gives reasonable agreement but predicts the Pred to be higher than measured. This is because of the assumption that at the maximum value of Pred the bulk flame area is equal to As which is not valid. The US standard also has corrections for flame self acceleration, which is a vessel size effect, and for the influence of vessel size on the external explosion, which are not factors addressed in the European standards. The European standard is the equation for the results of Bartknecht for a 10 m3 vessel and the results of higher and lower volumes in Bartknecht’s results are all lower that for 10 m3. The experimental results reviewed, for methane and propane maximum reactivity vented explosions, include data for vessels larger than that on which the European standards are based and they all give significantly lower values of Pred than those of Bartknecht.

Turbulent Combustion Parameters in Gas Explosions with Two Obstacles with Variable Separation Distance

Most of the congested gas explosions studies have focused on quantifying global flame acceleration and maximum overpressure through obstacle groupings rather than detailed analysis of the flame propagation through the individual elements of the congested region. Fundamental data of the turbulent flow and combustion parameters would aid better understanding of gas explosion phenomena and mechanisms in the presence of obstacles in addition to the traditional flame speeds and overpressures that are usually reported. In this work we report near stoichiometric methane/air explosion tests in an elongated vented cylindrical vessel 162 mm internal diameter with an overall length-to-diameter, L/D of 27.7. Single and double obstacles (both hole and flat-bar types) of 20-40% blockage ratios, BR with variable obstacle scale were used. The spacing between the obstacles was systematically varied from 0.5 m to 2.75 m. Turbulence parameters were estimated from pressure differential measurements and geometrical obstacle dimensions. This enabled the calculation of the explosions induced gas velocities, rms turbulent velocity, turbulent Reynolds number and Karlovitz number. This allowed the current data to be plotted on a premixed turbulent combustion regimes diagram. The bulk of the data fell in the thickened-wrinkled flames regime. The influence of the calculated Karlovitz number on the measured overpressures was analysed and was related to obstacle separation distance and obstacle scale characteristics