Transient natural convection flows in closed containers technical report no. 2
Measurements and calculations of natural flow convection and thermal stratification in closed containers
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Measurements and calculations of natural flow convection and thermal stratification in closed containers
The unsteady convective flow effects in a transonic compressor rotor with a circumferential-groove casing treatment are investigated in this paper. Experimental results show that the circumferential-groove casing treatment increases the compressor stall margin by almost 50% for the current transonic compressor rotor. Steady flow simulation of the current casing treatment, however, yields only a 15% gain in stall margin. The flow field at near-stall operation is highly unsteady due to several self-induced flow phenomena. These include shock oscillation, vortex shedding at the trailing edge, and interaction between the passage shock and the tip clearance vortex. The primary focus of the current investigation is to assess the effects of flow unsteadiness and unsteady flow convection on the circumferential-groove casing treatment. Unsteady Reynolds-averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) techniques were applied in addition to steady Reynolds-averaged Navier-Stokes (RANS) to simulate the flow field at near-stall operation and to determine changes in stall margin. The current investigation reveals that unsteady flow effects are as important as steady flow effects on the performance of the circumferential grooves casing treatment in extending the stall margin of the current transonic compressor rotor. The primary unsteady flow mechanism is unsteady flow injection from the grooves into the main flow near the casing. Flows moving into and out of the grooves are caused due to local pressure difference near the grooves. As the pressure field becomes transient due to self-induced flow oscillation, flow injection from the grooves also becomes unsteady. The unsteady flow simulation shows that this unsteady flow injection from the grooves is substantial and contributes significantly to extending the compressor stall margin. Unsteady flows into and out of the grooves have as large a role as steady flows in the circumferential grooves. While the circumferential-groove casing treatment seems to be a steady flow device, unsteady flow effects should be included to accurately assess its performance as the flow is transient at near-stall operation.
A theoretical analysis is presented to study the extinction characteristics of a diffusion flame near the leading edge of a thin fuel plate in slow, forced convective flows in a microgravity environment. The mathematical model includes two-dimensional Navier-Stokes momentum, energy and species equations with one-step overall chemical reaction using second-order finite rate Arrhenius kinetics. Radiant heat loss on the fuel plate is applied in the model as it is the dominant mechanism for flame extinguishment in the small convective flow regime. A parametric study based on the variation of convective flow velocity, which varies the Damkchler number (Da), and the surface radiant heat loss parameter (S) simultaneously, is given. An extinction limit is found in the regime of slow convective flow when the rate of radiant heat loss from fuel surface outweighs the rate of heat generation due to combustion. The transition from existent envelope flame to extinguishment consists of gradual flame contraction in the opposed flow direction together with flame temperature reduction as the convective flow velocity decreases continuously until the extinction limit is reached. A case of flame structure subjected to surface radiant heat loss is also presented and discussed.
The influences of slow convective flow on droplet combustion, particularly in the low Reynolds number regime, have received very little attention in the past. Most studies in the literature are semi-empirical in nature and they were motivated by spray combustion applications in the moderate to high Reynolds number regime. None of the limited number of fundamental theoretical studies applicable to low Reynolds numbers have been verified by rigorous experimental data. Moreover, many unsteady phenomena associated with fluid-dynamic unsteadiness, such as impulsive starting or stopping of a burning droplet, or flow acceleration/deceleration effects, have not been investigated despite their importance in practical applications. In this study we investigate the effects of slow convection on droplet burning dynamics both experimentally and theoretically. The experimental portion of the study involves both ground-based experiments in the drop towers and future flight experiments on board the International Space Station. Heptane and methanol are used as test fuels, and this choice complements the quiescent-environment studies of the Droplet Combustion Experiment (DCE). An analytical model that employs the method of matched asymptotic expansions and uses the ratio of the convective velocity far from the droplet to the Stefan velocity at its surface as the small parameter for expansion has also been developed as a part of this investigation. Results from the ground-based experiments and comparison with the analytical model are presented in this report.
Calculations of convective flows around objects in the outer layers of the sun that have characteristics similar to those of sunspots are presented. It is assumed that these objects are allowed to radiatively exchange heat with their surroundings, but convective motions and exchange are absent. The flow structure around the object, and the question of the overall balance or redistribution of the emerging heat flux as suggested by earlier empirical models are discussed. In all the cases studied, there was a significant increase in the kinetic energy flux and thus the lateral transport of the energy flux surrounding the object. This mainly occurred below the object to allow the heat to appear at the surface, with some time delay. The percentage reduction in the specific intensity agrees well with the observed deficits for pores or small sunspot-type regions. The diverted heat flow was not totally blocked by the object. Because the sunspot-like object is magnetic and the convective flow closely surrounds it, some conversion between internal, kinetic, and magnetic energy is likely.
Radiative heat loss from burning droplets in a slow convective flow under microgravity conditions is measured using a broad-band (0.6 to 40 microns) radiometer. In addition, backlit images of the droplet as well as color images of the flame were obtained using CCD cameras to estimate the burning rates and the flame dimensions, respectively. Tests were carried out in air at atmospheric pressure using n-heptane and methanol fuels with imposed forced flow velocities varied from 0 to 10 centimeters per second and initial droplet diameters varied from 1 to 3 millimeters. Slow convective flows were generated using three different experimental configurations in three different facilities in preparation for the proposed International Space Station droplet experiments. In the 2.2 Second Drop-Tower Facility a droplet supported on the leading edge of a quartz fiber is placed within a flow tunnel supplied by compressed air. In the Zero-Gravity Facility (five-second drop tower) a tethered droplet is translated in a quiescent ambient atmosphere to establish a uniform flow field around the droplet. In the KC 135 aircraft an electric fan was used to draw a uniform flow past a tethered droplet. Experimental results show that the burn rate increases and the overall flame size decreases with increases in forced-flow velocities over the range of flow velocities and droplet sizes tested. The total radiative heat loss rate, Q(sub r), decreases as the imposed flow velocity increases with the spherically symmetric combustion having the highest values. These observations are in contrast to the trends observed for gas-jet flames in microgravity, but consistent with the observations during flame spread over solid fuels where the burning rate is coupled to the forced flow as here.
The free-convection flow and heat transfer (generated by a body force) about a flat plate parallel to the direction of the body force are formally analyzed and the type of flow is found to be dependent on the Grashof number alone. For large Grashof numbers (which are of interest in aeronautics), the flow is of the boundary-layer type and the problem is reduced in a formal manner, which is analogous to Prandtl's forced-flow boundary-layer theory, to the simultaneous solution of two ordinary differential equations subject to the proper boundary conditions. Velocity and temperature distributions for Prandtl numbers of 0.01, 0.72, 0.733, 1, 1, 10, 100, and 1000 are computed, and it is shown that velocities and Nusselt numbers of the order of magnitude of those encountered in forced-convection flows may be obtained in free-convection flows. The theoretical and experimental velocity and temperature distributions are in good agreement. A flow and a heat-transfer parameter, from which the important physical quantities such as shear stress and heat-transfer rate can be computed, are derived as functions of Prandtl number alone.
Pressure drop oscillations in forced convection flow of Freon-11 near onset of boiling, noting flow rate for instability and limit cycles
Determination of boundary layer diffusion in forced convection flow
Penetrative convective flows induced in a spherical shell by combined effects of internal heating and mantle compressibility are investigated using mathematical and numerical formulations for compressible spherical shell convection. Isothermal stress-free boundary conditions applied at the top and the bottom of the shell are solved using a time-dependent finite difference code in a temperature, vorticity, stream function formulation for Rayleigh numbers ranging from the critical Rc up to 2000 Rc. Results indicate that compressibility, together with internal heating, could be a mechanism capable of generating spontaneously layered convection and local melting in the mantle and that non-Boussinesq effects must be considered in interpretations of geophysical phenomena.
This study is concerned with the analytical solutions of natural convection flows in closed-end cylindrical vessels to obtain exact solutions of temperature and velocity distribution in the laminar flow region under steady state condition. The temperature and velocity distributions, in general power series of displacements, are substituted into the three basic equations of continuity, momentum and energy. The relationships between coefficients of all powers are obtained through initial and boundary conditions and recurrence formulae. For constant wall temperature conditions the general solution of temperature and velocity may be expressed as a function of displacement, geometry ratio and Rayleigh number. Prandtl number does not enter as an independent parameter.
This paper describes research done to apply the Fractional Step Method to finite-element simulations of natural convective flows in pure liquids, permeable media, and in a directionally solidified metal alloy casting. The Fractional Step Method has been applied commonly to high Reynold's number flow simulations, but is less common for low Reynold's number flows, such as natural convection in liquids and in permeable media. The Fractional Step Method offers increased speed and reduced memory requirements by allowing non-coupled solution of the pressure and the velocity components. The Fractional Step Method has particular benefits for predicting flows in a directionally solidified alloy, since other methods presently employed are not very efficient. Previously, the most suitable method for predicting flows in a directionally solidified binary alloy was the penalty method. The penalty method requires direct matrix solvers, due to the penalty term. The Fractional Step Method allows iterative solution of the finite element stiffness matrices, thereby allowing more efficient solution of the matrices. The Fractional Step Method also lends itself to parallel processing, since the velocity component stiffness matrices can be built and solved independently of each other. The finite-element simulations of a directionally solidified casting are used to predict macrosegregation in directionally solidified castings. In particular, the finite-element simulations predict the existence of 'channels' within the processing mushy zone and subsequently 'freckles' within the fully processed solid, which are known to result from macrosegregation, or what is often referred to as thermo-solutal convection. These freckles cause material property non-uniformities in directionally solidified castings; therefore many of these castings are scrapped. The phenomenon of natural convection in an alloy under-going directional solidification, or thermo-solutal convection, will be explained. The development of the momentum and continuity equations for natural convection in a fluid, a permeable medium, and in a binary alloy undergoing directional solidification will be presented. Finally, results for natural convection in a pure liquid, natural convection in a medium with a constant permeability, and for directional solidification will be presented.
Differences in temperature and velocity of ascending and descending convective flows in unstable layer of clouds
A study conducting bouyancy driven convective flow experiments on the NASA KC-135 aircraft is presented. The response of a contained fluid (with an imposed temperature gradient) to changing g-levels during parabolic flight was obtained. Models for both transient and steady state flows were developed utilizing PC-based CFD software. Comparisons between the theoretical models and the physical observations are quite good.
The aerodynamic lift exerted on a long circular cylinder immersed in a convective flow pattern in an ideal fluid is calculated to establish the equilibrium position of the cylinder. The calculations establish the surprising result that the cylinder is pushed out the upwellings and the downdrafts of the convective cell, into a location midway between them. The implications for the intense magnetic flux tubes in the convection beneath the surface of the sun are considered.
The objective of the present flight experiment definition study is to investigate the effects of slow forced convective flows on the dynamics of isolated single droplet combustion and is designed to complement the quiescent, microgravity droplet combustion experiments (DCE-1 and DCE-2) of Williams and Dryer. The fuels selected for this study are the same as those of DCE, namely, a sooting alkane fuel (heptane) and a non-sooting alcohol (methanol), and imposed flow rates are chosen between 0 and 20 cm/s with varying ambient oxygen concentrations and pressures. Within this velocity range, both accelerating and decelerating flow effects will also be investigated. Two different approaches to generate the forced flow are currently under development in ground-based facilities; the first is a flow tunnel concept where the forced flow is imposed against a stationary droplet, and in the second a tethered droplet is translated at a specified velocity in a quiescent ambient medium. Depending upon the engineering feasibility a selection will be made between these two approaches so that the experiment can be accommodated in the Multiple Droplet Combustion Apparatus (MDCA) currently being designed for the International Space Station. Recently, we have finished designing and fabricating the experimental rigs using both the above mentioned concepts. The flow tunnel concept is implemented in a 2.2 second drop tower rig. Preliminary experiments have been carried out using heptane and methanol in air at atmospheric pressure. The translating droplet apparatus is scheduled to be tested in the 5 second drop facility in the near future. This report presents some of the experimental results obtained for heptane.
Transition from turbulent to laminar regime as consequence of high heating rates for internal convective flow, noting roles of Nusselt numbers and friction factors
A high-resolution numerical study on parallel systems is reported on three-dimensional, time-dependent, thermal convective flows. A parallel implentation on the finite volume method with a multigrid scheme is discussed, and a parallel visualization systemm is developed on distributed systems for visualizing the flow.