Rate of aerodynamic atomization of droplets

Dickerson, R. A.; Schuman, M. D.

doi:10.2514/3.28129

Cited by 22 publications

(5 citation statements)

References 2 publications

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“…Assuming that the droplet is subject to drag force only, a much simplified droplet momentum equation results. The standard drag coefficient is calculated based on the empirical correlation reported by Dickerson and Schuman (19). The effect of intense mass transfer and flame on the drag coefficient is accounted for through the empirical correlation developed by Eisenklam et al (20).…”

Section: Composition Of Ambient Airmentioning

confidence: 99%

An Experimentally Verified NOx Emission Model for Gas Turbine Combustors

Hung

1975

Volume 1B: General

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An analytical model has been developed to simulate the thermal NOx emission processes in various gas turbine combustors for a variety of fuels. The NOx emissions predicted by the model are in excellent agreement with available laboratory and field data. Its capability to simulate the water injection process accurately has been demonstrated previously. Comprehensive understanding of the NOx emission processes in gas turbine combustors has been gained through the current analytical studies. NOx emissions as influenced by ambient humidity, changes in combustor geometry, type of fuel used and changes in operating parameters can now be evaluated quantitatively through a priori prediction and have been verified by available laboratory and field data. The analytical model has also been demonstrated to be a powerful guidance tool in directing the experimental testing program in an effort to reduce NOx emissions from gas turbine combustors.

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Section: Composition Of Ambient Airmentioning

confidence: 99%

An Experimentally Verified NOx Emission Model for Gas Turbine Combustors

Hung

1975

Volume 1B: General

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“…There are a number of similar correlations. For example, the following expressions of Dickerson and Shuman [40] are applicable for a wide range of droplet Reynolds numbers and give the same accuracy as approximation ( 17)…”

Section: Two-phase Releasesmentioning

confidence: 99%

Some aspects of the mathematical modelling of fireballs

Novozhilov

2003

Proceedings of the Institution of Mechanical Engineers, Part E:

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The development of large-scale reballs is a typical result of explosions associated with accidental fuel releases in the oil and process industries. The two major mechanisms that lead to reball formation are vapour cloud explosions and boiling liquid expanding vapour explosions (BLEVEs). An ability to model reballs is extremely important from the point of view of safety and risk analysis. The present paper provides a state-of-the-art review of the computational techniques available for the mathematical modelling of reballs. The emphasis is placed on computational uid dynamics (CFD) modelling, based on Reynolds-averaged Navier-Stokes (RANS) equations for reactive ow. The results of calculations and estimations of reball hazards are compared with available experimental data. New results are presented for problems that are usually given less attention in reball studies. These concern estimations of air entrainment rates into reballs and potential strategies for reball suppression. Keywords: reball, vapour cloud explosion, computational uid dynamics modelling, suppression NOTATION B m Spalding's mass transfer number C aerosol concentration in the layer surrounding the reball (kg/m 3 ) C D drag coef cient C p speci c heat (J/kg K) C R eddy breakup constant C C aerosol concentration inside the reball (kg/m 3 ) d p droplet diameter (m) D reball diameter (m) Fr Froude number g acceleration due to gravity (m/s 2 ) h height of the reball above the ground (m), speci c enthalpy (J/kg) DH c heat of combustion (J/kg) I radiation intensity (W/m 2 ) I s radiation dose (J/m 2 ) k turbulence kinetic energy (m 2 /s 2 ), thermal conductivity (W/m K) l distance along the radiation ray (m) L latent heat of phase change (J/kg) L * characteristic length scale (m) m p mass of droplet (kg) M mass of fuel (kg) Nu Nusselt number p pressure (Pa) q heat ux (W/m 2 ) Q R heat source due to radiation (W/m 3 ) R radius of the reball (m) Re p particle Reynolds number s soot conversion factor for fuel S pf source term for variable f due to particles S f source term for variable f Sh Sherwood number t time (s) t b burnout time (s) t * characteristic time-scale (s) T temperature (K) U(u, v, w) velocity vector (m/s) X (x, y, z) Cartesian coordinate (m) Y mass fraction a absorption coef cient (m 71 ) G f exchange coef cient for variable f d ij Kronecker's symbol e turbulence kinetic energy dissipation rate (m 2 /s 3 ) m dynamic viscosity (kg/m s) n kinematic viscosity (m 2 /s) The MS was

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“…As determined by the dissipation scale in the k-s model, the length of each eddy is L = c]! 2 k 312 with its lifetime given by 1/2 (9) (10) The droplet interacts with an eddy for a time taken to be the smaller of either t e or the transit time t t required for the droplet to transverse the eddy. Following Brown and Hutchinson, 13 the transit time is determined from a linearized form of the droplet equation of motion and is given as…”

Section: Droplet Modelmentioning

confidence: 99%

“…10 Once a new droplet velocity is found, the new droplet position is determined from integrating dr (8) As developed by Gosman and loannides 11 and discussed by Faeth, 12 the turbulence effects on droplet motion are simulated stochastically by superimposing on the gas field turbulent eddies, each having a length, lifetime, and u and v velocity fluctuations. As determined by the dissipation scale in the k-s model, the length of each eddy is L = c]!…”

Section: Droplet Modelmentioning

confidence: 99%

Alternative fuel spray behavior

Asheim

Peters

1989

Journal of Propulsion and Power

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The effects of alternative fuels on the combustion characteristics of a liquid fuel spray are examined. Fuel properties are varied and the effects of these variations on the structure (drop histories, temperatures, and species concentrations) of the spray flame are calculated. Also, a comparison is made of the differences in two spray flames fueled by a standard NATO fuel and a proposed alternative fuel. The calculations are performed using a reacting, two-phase, two-dimensional flow code that utilizes a Lagrangian calculation of droplet trajectories and an Eulerian approach for the gas-phase flowfield. Interactions between the drops and the gas phase are accomplished through the particle-source-in-cell technique with exchange of mass, momentum, and energy between the two phases. A global reaction scheme is used with the reaction rate determined by the minimum of either an Arrhenius rate or mixing rate. Fuel property changes that affect droplet size and volatility are shown to have significant effects on droplet trajectory patterns. However, for the flowfield examined in this paper (where the fuel spray core is very rich and the mixing of air with the fuel occurs at a relatively slow rate), these trajectory changes only moderately modify the fuel vaporization pattern within the spray. NomenclatureAI = empirical constant a = air mass fraction B M = mass transfer number B T = thermal transfer number C D = drag coefficient C p = specific heat C 1 ,C 2 ,C / , = turbulence model constants D_ = droplet diameter D = Rosin-Rammler mean droplet diameter D T = tunnel diameter F D = drag force / = fuel mass fraction H f = fuel's heat of combustion h = enthalpy / = stoichiometric air/fuel ratio k = kinetic energy of turbulence k g = gas thermal conductivity L = latent heat of vaporization L e = eddy length MW = molecular weight m = mass m d = droplet mass flow ratê evap = droplet evaporation rate N = Rosin-Rammler exponent N d = number of droplets in a parcel P = pressure Pr = Prandtl number p = product mass fraction = fuel reaction rate per unit volume = kinetic-limited reaction rate = mixing-limited reaction rate Re = Reynolds number r = radial coordinate S = source term SMD = Sauter mean diameter T = temperature T b = boiling temperature a ft r £ Subscripts d eff Superscripts = time = eddy lifetime = transit time = total velocity = axial velocity component = radial velocity component = position vector = axial coordinate = number of carbon atoms = number of hydrogen atoms = diffusion coefficient = dissipation rate of turbulence = gas viscosity = fuel viscosity = density = standard deviation = fuel surface tension = turbulence model constants = droplet relaxation time = general flow variable = droplet = effective = fuel = gas phase = inlet = outlet = droplet surface = general variable or equivalence ratio = number of carbon atoms = number of hydrogen atoms = general variable = time-averaged value

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Rate of aerodynamic atomization of droplets

Cited by 22 publications

References 2 publications

An Experimentally Verified NOx Emission Model for Gas Turbine Combustors

An Experimentally Verified NOx Emission Model for Gas Turbine Combustors

Some aspects of the mathematical modelling of fireballs

Alternative fuel spray behavior

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