Conjugate natural convection from an array of discrete heat sources: part 2 — a numerical parametric study

Coupled conduction and natural convection transport within a discretely heated cavity have been investigated numerically. One vertical wall of the cavity is composed of discrete, isoflux heat sources mounted in a substrate of finite thermal conductivity. The opposite vertical wall and the horizontal walls are assumed to be isothermal and adiabatic, respectively. The governing steady-state partial differential equations for the fluid and solid region are solved simultaneously using a control volume formulation, coupled with an additive correction multigrid procedure that increases the convergence rate of the solution. The fluid Prandtl number and heater/fluid thermal conductivity ratio are fixed at 25 and 2350, respectively, corresponding to a dielectric fluid (FC-77) and heaters manufactured from silicon. With increasing modified Rayleigh number (10⁴ < Ra_Lz^* < 109), the cavity flow becomes more boundary layer-like along the vertical walls, and multiple fluid cells develop in the central region. Thermal spreading in the substrate increases with decreasing modified Rayleigh number and with increasing values of the substrate/fluid thermal conductivity ratio (10⁻¹ <- R_s ≤ 10³). For large R_s, the discrete heat sources lose their thermal identity, and the streamlines and isotherms resemble those associated with a differentially heated cavity. Thermal spreading in the substrate also has a significant effect on circulation in the cavity and on maximum surface temperatures.     

Radiative and collisional effects in a cylindrically confined plasma—II. Absorption effects

A comprehensive model has been developed for radiation emission and absorption in cylindrically confined plasmas, and calculations have been performed for the asymptotic region of an argon arc plasma. Radiation absorption is shown, in general, to have a negligible effect on bound level populations. The exception is for the near wall region of the 35 A arc, for which self-absorption in the lines of the 4s-4p array has a significant effect. For the 4s-4p array, absorption also significantly reduces the radiation flux to the constrictor wall.     

Spectral distribution of radiation from the cascade arc plasma

A mathematical model has been developed for radiation emission and absorption in the cascade arc plasma, and calculations have been performed to determine the complete spectral distribution of radiation emerging from the argon arc. Although self-absorption effects are negligible for the continuum radiation, they are significant for much of the line radiation. The radiation flux emerging from the arc, as well as the efficiency for conversion from electrical to radiant energy, increase with increasing arc current and pressure and decreasing arc radius. The relative contribution of line radiation to the total arc radiation decreases with increasing current and pressure and decreasing radius.     

Absorption,extinction and phase function measurements for algal suspensions of chlorella pyrenoidosa

Optical property measurements have been made for unicellular algal suspensions of C. pyrenoidosa in the spectral range from 380 to 720 nm. The measurements include the extinction and absorption cross sections and the scattering phase function. Although the spectral dependence of the extinction cross section is weak, there is a strong wavelength dependence for absorption which is related to cell pigment content. The absorption cross section increases with increasing cell size and pigment content. The scattering albedo is approximately 0.9 over the entire spectrum, and the scattering phase function is strongly peaked in the forward direction.     

Heat transfer,development length,and friction factor correlations for the asymptotic region of a laminar arc constrictor

A rigorous equilibrium model is formulated for the laminar flow of plasma through the heating region of a constricted arc plasma generator. The resulting equations are solved for an argon gas using an implicit finite-difference scheme, and the wall shear stress and heat transfer are computed from momentum and energy balances for a wide range of flow rates and arc currents. Friction factors based on this method are in agreement with empirical values to within approximately 10 per cent, and heat transfer calculations agree with the orders of magnitude predicted by a simplified arc model. A dimensionless number peculiar to the constricted arc, the so-called Ohmic heating parameter, is used to correlate the mean Nusselt numbers in the asymptotic arc regime. When the fluid properties are based on the mean temperature, the product of friction factor and Reynolds number is found to be a constant for currents below 200 Amp and to vary with the Ohmic heating parameter for larger currents. Correlations are also presented for the thermal development length, and the agreement with experiment is good.     

Conjugate natural convection from an array of discrete heat sources: part 1 — two- and three-dimensional model validation

Two- and three-dimensional (2- and 3-D) numerical models have been developed for conjugate natural convection in a discretely heated cavity. Experimental results obtained for the same geometry, using water and FC-77 as the coolants, were in excellent agreement with the 3-D numerical predictions. In contrast, because of the inability to account for thermal spreading in the lateral direction, the 2-D model overpredicted measured average surface temperatures of the discrete heat sources. However, the 2-D model still predicted general trends and flow patterns that were experimentally obtained. The nature and extent of 3-D effects on the flow and heat transfer have been delineated.     

Secondary flow in horizontal channels heated from below

Experiments have been performed to investigate onset and development of the buoyancy driven secondary flow in a horizontal parallel plate channel with uniform bottom heating. Flow visualization in water (Pr ≈ 7) was performed by injecting a continuous sheet of dye into the bottom boundary layer just up-stream of the heated surface, and operating conditions in the ranges 125 < Re < 1,000 and4.7 x 10⁴ < Gr ^* < 8.0 x 10⁶ were considered. Top, side, and end views revealed onset of the secondary flow as thermal plumes, which rise from the heated surface and form pairs of counter-rotating vortices. Subsequent development of the flow is characterized by a breakdown in the regular plume structure and transition to buoyancy driven turbulence. Onset of the secondary flow is advanced by increasing the heat flux and/or decreasing the flow rate, and results may be correlated in terms of a critical Grashof number and a dimensionless longitudinal distance. Liquid crystal sheets applied to the heated surface reveal significant spanwise temperature variations due to the secondary flow. The unsteadiness of the flow is discussed and comparisons are made to previous experimental and numerical work.     

Measurement of the turbulent flow field in a free-surface jet of water

Measurements of the mean velocity and turbulence intensity are presented for a rectangular jet of water ejecting into a gaseous ambient. Data are reported for streamwise locations up to 30 nozzle widths from the discharge and spanwise locations covering the inner 80% of the jet width. The flow conditions at the nozzle discharge were controlled by using different nozzle designs (parallel-plate and converging) and flow manipulators (wire grid and screens). The results track the mean velocity and turbulence intensity profiles with streamwise distance, highlighting changes in both the profile shapes and magnitudes for both measured quantities. Independent of nozzle configuration, the mean velocity profile was shown to be most nonuniform and the turbulence intensity most nonhomogeneous at the nozzle discharge. With increasing streamwise distance, the mean velocity profile underwent a gradual transition to a completely uniform condition, while the turbulence field decayed and became homogeneous. The rate of viscous dissipation was shown to depend strongly on the nozzle exit condition. This work was supported by the National Science Foundation under grant numbers CTS-8912831 and CTS-9307232     

Procedures for Modeling Laminar Cascade ARC Behavior

Past efforts at modeling laminar, cascade arc behavior are reviewed. The models are delineated in terms of their inherent restrictions and are compared on the basis of ease of application, as well as ability to provide useful engineering information and important physical insights. It is concluded that, although approximate analytical models have suggested important trends, they have almost universally failed to accurately quantify arc behavior. The most successful procedures have been those which use finite-difference methods for the solution of a comprehensive set of flow equations. Greatest success is derived from the use of a multi-fluid model which accounts for arc thermochemical nonequilibrium effects.