Terms Of Mass Flux Research Articles

The modeling of aerodynamic strain rate and flame curvature effects in premixed turbulent combustion

Flame structures have been computed for exploding, imploding, and stationary laminar spherical flames of propane-air using the six-step reduced mechanism of Kennel et al. These computations yield laminar burning velocities and volumetric heat release rates, together with Markstein lengths and numbers, for both aerodynamic strain and flame curvature. The effects of flame stretch rate on both the present heat release rate profiles and burning velocities and those previously computed for methane-air flames are generalized in terms of strain rate and Markstein lengths. Flame quench is discussed in terms of mass fluxes and Markstein lengths. The positive strain rate necessary to quench a flame is quantified in terms of the rate of increase of unburned gas in the flame as a proportion of the mass flux into it. It would appear that when this ratio exceeds 0.8, the flame quenches. This approach utilizes Markstein lengths based on (1) the rate of entrainment of unburned gas and (2) the rate of formation of burned gas. The negative strain required to quench a flame is quantified in terms of laminar burning velocity extrapolated to zero at the negative side. All these findings are discussed and used to evaluate the two key turbulent combustion source term parameters, Pb and Io, that are used in the assumed probability density function (PDF) and coherent flamelet models, respectively, of turbulent combustion to quantify the effects of strain rate.

CO-LOCATED EQUAL-ORDER CONTROL-VOLUME FINITE-ELEMENT METHOD FOR MULTIDIMENSIONAL, INCOMPRESSIBLE. FLUID FLOW -PART I: FORMULATION

A co-located equal-order control-volume-based finite-element method (CVFEW) for two- and three-dimensional, incompressible, viscous fluid flow is presented. The method works directly with the primitive variables. Triangular elements and polygonal control volumes, and tetrahedral elements and polyhedral control volumes are used to discretize the calculation domains in two- and three-dimensional problems, respectively. Two available flow-oriented upwind schemes (FLO and FLOS) and a novel mass-weighted skew upwind scheme (MAW) are investigated. In each dement, the velocity components in the mass flux terms are interpolated by special functions that prevent the generation of spurious pressure oscillations. The discretized equations are solved using an iterative sequential variable adjustment algorithm. Verification of the proposed CVFEM is presented in a companion article.

CO-LOCATED EQUAL-ORDER CONTROL-VOLUME FINITE-ELEMENT METHOD FOR MULTIDIMENSIONAL, INCOMPRESSIBLE, FLUID FLOW—PART II: VERIFICATION

A co-located equal-order control-volume-based finite-element method (CVFEW) for two- and three-dimensional, incompressible, viscous fluid flow is presented. The method works directly with the primitive variables. Triangular elements and polygonal control volumes, and tetrahedral elements and polyhedral control volumes are used to discretize the calculation domains in two- and three-dimensional problems, respectively. Two available flow-oriented upwind schemes (FLO and FLOS) and a novel mass-weighted skew upwind scheme (MAW) are investigated. In each dement, the velocity components in the mass flux terms are interpolated by special functions that prevent the generation of spurious pressure oscillations. The discretized equations are solved using an iterative sequential variable adjustment algorithm. Verification of the proposed CVFEM is presented in a companion article.

On the stream function for variable‐density groundwater flow

When the stream function is used to describe variable‐density ground water flow, it should be defined in terms of mass flux. The historic use of the stream function describes volume flux and implicitly invokes the Boussinesq assumption. A comparison of the flow equations for mass‐based and volume‐based stream functions indicates that this assumption can lead to significant errors in the calculated flow field, especially when flow parallels large density gradients.

Applications of Mass Balance Approach with Censored Data

Previous work has demonstrated the desirability of estimating mean ambient water concentrations from data that may be censored, i.e., some values reported as “less than detect”. However, in order to balance mass in a water body, inputs, outputs, and storage need to be defined in terms of mass fluxes. If there is any significant correlation between flow rates or any other variables (i.e., suspended solid concentrations) used to estimate these fluxes, undesirable bias may be introduced into the mass balance when censored data are used. The problem can be particularly severe in two cases: 1) tributary load estimation for event-responsive streams, and 2) “total water” estimates of ambient concentrations of contaminants obtained by summing dissolved and suspended fractions. Example data are presented that illustrate these two cases and potential estimation procedures are evaluated and applied to the data.

Prediction of pressure drop during horizontal annular flow boiling of pure and mixed refrigerants

An experimental study on pressure drop during horizontal flow boiling of pure and mixed refrigerants of R22, R114, R12, and R152a is reported. More than 600 pressure drop data are taken for annular flow under uniform heat flux at reduced pressures of 0.08–0.16 (200–800 kPa). The range of heat flux and mass flow rate is 10–45 kW m −2 and 16–46 g s −1 (corresponding to 230–720 kg m −2 s −1 in terms of mass flux). The results are compared against well-known correlations; Bo Pierre's correlation failed to correlate half of the present data while Martinelli and Nelson's correlation overpredicted it by 20%. Pressure drops with both pure and mixed refrigerants, however, are well correlated by Martinelli's parameter, X tt . Furthermore, no composition dependence of pressure drop is found with mixtures. A simple correlation adopting the thermodynamic corresponding states principles is developed with a chart to facilitate the estimation of pressure drop during flow boiling. The prediction agrees with the measured data with a mean deviation of 8.4%.

Prediction of turbulent, axisymmetric, dense jets discharged to quiescent ambients

The analysis of dense jets is of interest with regard to environmental applications, especially in the design and evaluation of submerged, offshore outfalls from desalination plants. In this paper, the governing conservation equations of mass, momentum, energy and salinity, derived in a curvilinear coordinate system, are solved by an explicit finite-difference method. The influence of temperature and salinity on density of the jet and ambient fluid are incorporated using an equation of state. Turbulent shear stress, heat flux and mass flux terms appearing in the governing equations are evaluated using simple algebraic expressions for the eddy diffusivities that account for effects on mixing of buoyancy and intermittent turbulence near the edge of the jet. The formulation is parabolic in character, allowing the solution to be marched in the streamwise direction starting with initial distributions of velocity, temperature, salinity and discharge orientation. Cases investigated are the dense jet discharging vertically, horizontally and at various angles to the horizontal into quiescent, uniform or stratified ambient. Predictions are compared with available experimental data for a wide range of Froude numbers.

Analysis of turbulent dense jets discharged to quiescent uniform or stratified ambients

The analysis of dense jets is of interest with regard to environmental applications, especially in the design and evaluation of submerged, offshore outfalls from desalination plants. In this paper, the governing conservation equations of mass, momentum, energy and salinity, derived in a curvilinear coordinate system, are solved by an explicit finite-difference method. The influence of temperature and salinity on density of the jet and ambient fluid are incorporated using an equation of state. Turbulent shear stress, heat flux, and mass flux terms appearing in the governing equations are evaluated using simple algebraic expressions for the eddy diffusivities that account for effects on mixing of buoyancy and intermittent turbulence near the edge of the jet. The formulation is parabolic in character, allowing the solution to be marched in the stream-wise direction starting with initial distributions of velocity, temperature, salinity, and discharge orientation. Cases investigated are the dense jet discharging vertically, horizontally, and at various angles to the horizontal into quiescent, uniform or stratified ambient. Predictions are compared with available experimental data for a wide range of Froude numbers.

The Relation Between Mass Loss and Luminosity For Be Stars

AbstractThe mass loss rates of a large sample of Be stars derived from the UV and the IR are compared. The IR rates were derived using a simple equatorial disc model, and are typically a factor 100 larger than those derived from the UV. In terms of mass fluxes, the mass flux in the polar regions (derived from the UV observations) is about a factor 103 smaller than the mass flux in the equatorial regions. The dependence of MIR and Muv on stellar luminosity is studied. It is shown that MIR depends weaker on L than Muv. This suggests that two different mechanisms are responsible for the mass flux in polar and equatorial regions.

An iterative algorithm between stream function and density for transonic cascade flow

A set of Wu's equations governing the fluid flow along a given Si stream surface is solved by the use of artificial compressibility and a new iterative algorithm between the two variables stream function ^ and density p. The set of equations consists of a stream function equation and a new first-order partial differential equation for density derived from the continuity equation, momentum equation and Bernoulli's equation. The stream function equation proposed by Wu more than 30 years ago is written in general curvilinear coordinate system to allow for arbitrary boundary shapes. A strongly implicit approximate factorization algorithm (SI) of the multidimensional partial differential equations is used in numerical solutions of this set of equations. By the method proposed in this paper, the problem of nonuniqueness of density in the conventional stream function method is avoided. A number of transonic cascades are calculated and given herein to demonstrate the capability of the present method. N order to discretize the mixed-type full potential equation or stream function equation in a transonic flowfield, the artificial compressibility method1 could be considered. This method consists of modifying the density in such a way as to introduce the numerical dissipation necessary in the supersonic region. With a slight modification of the density inlhe supersonic region, the transonic flow problem becomes amenable to treatment by standard discretization techniques (central differencing) and some standard iterative procedures (SOR, ADI, explicit methods, and implicit algorithms212). The approximate factorization schemes, for example AF1, AF2, AF3, and SI, can be used to solve the conservative or nonconservative transonic full-potential equation3'5'79'12 and transonic stream function equation.2'6'10'11 For transonic flows, this scheme has proved to be fast and reliable and, therefore, is the only scheme considered in this study. For transonic cascade flow, the irrotational assumption is not valid when the entropy is nonuniform downstream of a strong shock. Without the assumption of uniform entropy or irrotational flow, the stream function equation is more suitable. However, the main difficulty with the solution of stream function in transonic flow lies in that the density is not uniquely determined in terms of mass flux. The purpose of this study is to develop efficient algorithm to overcome this difficulty. In the present paper, a set of Wu's equations1316 governing the fluid flow along Sl surface is solved by the combination of the artificial compressibility and a new iterative algorithm between the two variables \l/ and p. The set of equations consists of a stream function equation and a new first-order partial differential equation for density derived from continuity equation, momentum equation, and Bernoulli's equation. The SI algorithm is used in the numerical solutions of this set of equations. The problem of nonuniqueness of density in traditional stream function method is avoided in this study.

An efficient finite element technique for modeling transport in fractured porous media: 1. Single species transport

A mathematical model is presented for numerical simulation of solute transport in naturally fractured porous media. The model is based on the dual‐porosity conceptual approach and is capable of simulating interactions between porous rock matrix and fractures. Unlike earlier dual‐porosity transport models, which rely on parallel fracture assumptions, the present model is a unified model that is also able to represent blocky fractured systems (i.e., systems with suborthogonal fractures) by using a spherical idealization of matrix blocks. Two governing, partial differential equations are written for solute transport in the fractures and diffusion in the porous matrix blocks. These equations are coupled by mass flux terms (leakages). An efficient numerical scheme is presented for approximating the governing transport equations. The scheme effectively combines a two‐dimensional, upstream‐weighted, finite‐element approximation for transport in the fractures with a one‐dimensional Galerkin approximation for diffusion within the individual matrix blocks. Coupling of the two approximations is performed implicitly. The systems of algebraic equations resulting from both finite‐element approximations are solved by using sequential solution algorithms designed especially for this type of problem. Stability and accuracy of the numerical scheme are checked by applying the model to a number of test problems and comparing results with available analytical solutions. In all cases the numerical scheme is found to be highly stable and capable of producing reliable results with the use of relatively coarse spatial and temporal discretizations. Finally, the utility of the model is demonstrated by applying it to a hypothetical, yet realistic, problem.

Mass Influx Obtained from Low-Light-Level Television Observations of Faint Meteors

Since the advent of low-light-level television (LLLTV) systems, it has been recognized that such devices offer the ability to observe meteors as faint as 10th magnitude which allows the extension of optical meteor data to masses as small as 10-4 gram. The Space Sciences Laboratory at Marshall Space Flight Center has been actively engaged in such observations using image orthicons and intensified SEC vidicons.The results of these observations are presented along with an interpretation in terms of mass-flux. This interpretation includes the development of a relationship between peak luminosity of a meteor and mass, velocity, and zenith angle that was derived from single body meteor theory and compares favorably with results obtained from the Artificial Meteor Program. Also included in the mass-flux interpretation is an analysis of the observation response of a LLLTV system to fixed and moving point sources.