Entropy production in radiation-affected boundary layers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76157/1/AIAA-1988-2640-236.pd

Visible and infra-red sensitivity of Rayleigh limit and Penndorf extension to complex refractive index of soot

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29719/1/0000053.pd

Rayleigh limit--Penndorf extension

The Rayleigh limit of the Lorenz-Mie theory is extended by the Penndorf correction. For the efficiency factors, this extension leads to Qa,s,eP = Qa,s,eR(1+[Pi]a,s,e) where superscripts P and R denote Penndorf and Rayleigh; subscripts s, a, and e, respectively, scattering absorption, and extinction; and [Pi] the Penndorf correction to the Rayleigh limit. This correction is shown to extend the Rayleigh limit from [alpha] [similar, equals] 0.3 to 0.8, [alpha] being the particle size parameter. Error contours are generated for the Rayleigh and Penndorf limits for [alpha] = 0.3, 0.5, and 0.7 in the 1.5 [les] n [les] 2.5 and 0.5 [les] k [les] 1.5 domain which covers the range of soot properties. The practical significance of the Penndorf correction is demonstrated in terms of optical diagnostics and radiative heat transfer. Also, the Planck and Rosseland mean absorption coefficients based on the Penndorf expansion are shown to yield relative to those based on the Rayleigh limit where subscripts P and R denote the Planck and Rosseland mean absorption coefficients, superscripts P and R denote Penndorf and Rayleigh, [Pi] the Penndorf correction depending on Ms and Ns which are the explicit functions of refractive and absorptive indices of particles, and on the dimensionless number [pi]DT/C2 (D being the particle diameter, T the temperature, and C2 the second radiation constant). For larger particles and/or higher temperatures the Penndorf based Planck mean coefficient is shown to deviate considerably from the Rayleigh based Planck mean coefficient. This deviation is exhibited to a somewhat lesser extent by the Penndorf based Rosseland mean coefficient.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27752/1/0000145.pd

Buoyancy-driven turbulent diffusion flames

A fundamental dimensionless number for pool fires, , in proposed. Here [sigma][beta] and Ra[beta] denote a flame Schmidt number and a flame Rayleigh number. The sublayer thickness of a turbulent pool fire, [eta][beta], is shown in terms of [Pi][beta] to be , where l is an integral scale. The fuel consumption in a turbulent pool fire expressed in terms of [eta][beta] ([Pi][beta]) and correlated by the experimental data leads to . where [varrho] is the density, D the mass diffusivity, Ra the usual Rayleigh number, and B the transfer number. The model agrees well with a previous model based on the stagnant film hypothesis.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29192/1/0000246.pd

Entropy production in flames

Thermodynamic foundations of the thermal entropy production are rested on the concept of lost heat, (Q/T) [delta]T. The thermomechanical entropy production is shown to be in terms of the lost heat and the lost work as where the second term in brackets denotes the lost (dissipated) work into heat.The dimensionless number [Pi]s describing the local entropy production s[triple prime] in a quenched flame is found to be [Pi]s~(Ped0)-2, where [Pi]s = s[triple prime]l2/k, l = [alpha]/Su0 (a characteristic length), k thermal conductivity, [alpha] thermal diffusivity, Su0 the adiabatic laminar flame speed at the unburned gas temperature, Ped0 = Su0D/[alpha] the flame Peclet number, and D the quench distance.The tangency condition [part]Ped0/[part][theta]p = 0, where [theta]b = Tb/Tb0, Tb and Tb0 denoting, respectively, the burned gas (nonadiabatic) and adiabatic flame temperatures, is related to an extremum in entropy production. The distribution of entropy production between the flame and burner is shown in terms of the burned gas temperature and the distance from the burner.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27153/1/0000147.pd

Entropic efficiency of energy systems

Thermodynamic foundations of the thermal entropy production are rested on the concept of lost heat, (Q/T)[delta]T. The thermomechanical entropy production is shown to be in terms of the lost heat and the lost work as where the second term in brackets denotes the lost (dissipated) work into heat.The dimensions number [Pi]s describing the local entropy production s[tripe prime] in a quenched flame is related to [pi]s ~ (PeDO)-2 where [Pi]s = s[triple prime]l2/k,l = [alpha]/Su0 a characteristic length, k thermal conductivity, [alpha] thermal diffusivity, Su0 the adiabatic laminar flame speed at the unburned gas temperature, PeD0 = Su0D/[alpha] the flame Peclet number, D the quench distance. The tangency condition [varpi]PeD0/[varpi][theta]b = 0, where [theta]b = Tb/Tb0, Tb and Tb0 denoting respectively the burned gas (nonadiabatic) and adiabatic flame temperatures, is related to an extremum in entropy production. The distribution of entropy production between the flame and burner is shown in terms of the burned gas temperature and the distance from burner.A fundamental relation between the Nusselt number describing heat transfer in any (laminar, transition, turbulent) forced or buoyancy driven flow and the entropy production is shown to be Nu ~ [pi]s1/2In view of this relation, the heat transfer from a pulse combustor becomes a measure for the entropic (thermal) efficiency of pulse combustion systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30349/1/0000751.pd

Entropy production in boundary layers

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77333/1/AIAA-197-774.pd

Radiation affected laminar flame propagation.

The Rayleigh limit of the Lorenz-Mie theory is extended by the Penndorf expansion from $\\alpha$ $\\cong$ 0.3 to $\\alpha$ $\\cong$ 0.8, $\\alpha$ being the particle size parameter. Error contours are generated for the Rayleigh and Penndorf limits for $\\alpha$ = 0.3, 0.5 and 0.7 in the ranges 1.5 $\\leq$ n $\\leq$ 2.5 and 0.5 $\\leq$ k $\\leq$ 1.5 which cover the range of soot properties. The practical significance of the Penndorf extension is demonstrated in terms of optical diagnostics and radiative heat transfer. Also, the Planck and Rossel and mean absorption coefficients based on the Penndorf extension relative to those based on the Rayleigh limit are shown to depend on M's and N's which are explicit functions of the complex refractive index of particles, and on the fundamental dimensionless number $\\pi$DT/C$\\sb2$ discovered in this study characterizing particulate matter--thermal radiation interaction (D being the particle diameter, T the temperature, and C$\\sb2$ the second radiation constant). For larger particles and /or higher temperatures the Penndorf-based Planck mean coefficient is shown to deviate considerably from that of the Rayleigh-based coefficient. This deviation is exhibited to a somewhat lesser extent by the Penndorf-based Rossel and mean coefficient. The range of Penndorf-based coefficients are determined by accurate numerical computations utilizing the Lorenz-Mie theory. The computations are carried out by VASET, a computer code developed in this study. Edwards' wide b and model for discrete gas radiation is adopted, and a computer code, EMSVTY, has been developed in this study. The code improves the pure rotational b and of water vapor, tabulates line width and optical depth parameters for 23 b and s of 6 typical combustion species including H$\\sb2$O, CO$\\sb2$, CO, NO, SO$\\sb2$, and CH$\\sb4$ from 200 K to 2500 K. It also demonstrates the relative significance of various gaseous species. The effect of radiative losses on a freely propagating one-dimensional laminar premixed flame is investigated in terms of the flame speed, temperature profile, and the species concentrations. Detailed chemical kinetics (CHEMKIN) and transport (TRANFIT, TPINIT, etc.) algorithms are used in conjunction with PREMIX, a flame propagation code recently developed by Kee and coworkers at S and ia National Laboratories. The losses are shown to reduce the flame speed.Ph.D.Mechanical engineeringAerospace engineeringUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162246/1/8920613.pd

Effect of Fins on the Transition to Oscillating Laminar Natural Convection in an Enclosure

Flow characteristics and evolution of heat transfer are investigated numerically within a differentially heated square cavity in the presence of thin fins which are either insulated or highly conductive and at the base wall temperature. The transition from steady-state to oscillatory and chaotic convection is observed at certain Rayleigh numbers with varying lengths of fins positioned at different locations