Effective Drag Coefficient Research Articles

Neutral beam driven impurity flow reversal in tokamaks

A theory is outlined for explaining the observed effects of neutral beam injection on impurities in tokamak plasmas. In the collisional regime, it is shown for a representative model problem that for sufficiently strong co-injection the outward impurity flux component produced by the radial electric field becomes larger than the inward flux components due to the density gradient, rotation and direct beam-impurity momentum exchange, thereby producing an outward impurity flux. In the mixed regime, a preliminary version of the theory provides a reasonable interpretation of the PLT impurity flow reversal experiments when the effective viscous drag coefficient that is observed experimentally is used in the model. This preliminary theory, when adjusted to match the PLT results, predicts significant impurity reversal in TFTR and in a plasma of the size of FED and INTOR.

Characterization of gas bubbles injected into molten metals under laminar flow conditions

Velocity and volume measurements of gas bubbles injected into liquid metals under laminar flow conditions (at the orifice) have been achieved. A novel experimental approach utilizing noises generated by bubbles was used to collect the necessary data. Argon gas was bubbled through tin, lead, and copper melts, and gas bubble formation frequencies (and hence bubble sizes) were determined. It was found that the bubble size generated for a particular orifice diameter was dependent upon the magnitudes of the orifice Froude and Weber numbers. Maximum formation frequencies increased slightly with decreasing orifice diameter, and the transition point from varying to constant frequency occurred at an orifice Weber number of approximately 0.44. Velocities of gas bubbles rising through the metals were greater than those previously reported for studies in which only one bubble was in the melt at any time. Effective drag coefficients of the rising bubbles were found to agree with data previously generated in aqueous systems.

Regenerative turbofans - A comparison with nonregenerative units

A theoretical study was made of the performance of regenerative turbofans. Particular attention was paid to the feasibility of small regenerative turbofans from the aerodynamic drag, mechanical arrangement, and weight viewpoints. It was concluded that, on a thermodynamic and aerodynamic basis, compared with conventional nonregenerative, high pressure ratio, high bypass ratio units regenerative turbofans can have specific fuel consumptions about 17% lower for flight, and up to 24% lower for sea level static, operation. It was assumed that the effective nacelle drag coefficients of regenerative turbofans would not be higher than those of nonregenerative engines provided greater installation complexity is acceptable. The predicted thrust-to-weight ratio of regenerative units is approximately 3.2:1 compared with 6:1 for high pressure-high bypass ratio machines. Typically, assuming that both engine types are suitable alternatives for a particular aircraft, this weight penalty would be counteracted by a fuel saving after about 4 hr flying without reserves. The corresponding figure for small aircraft, for which high pressure ratio turbofans appear to be impractical, is about 2 hr. In the absence of major developments in regenerator technology regenerative turbofans appear to be restricted to relatively low thrust applications.

Turbulent vortex rings

We consider the motion of the mass of fluid ejected through a sharp-edged orifice by the motion of a piston. The vorticity formed by viscous forces within the separated flow at the sharp edge rolls up to form a concentrated vortex which, after a development period, consists of a core of very fine scale turbulence surrounded by a co-moving bubble of much larger scale turbulence. This bubble entrains outer fluid, mixes with it, and deposits the majority into a wake together with some small fraction of the total vorticity of the ring. Enough fluid is retained to account for the slow growth of the whole fluid mass. A theory which takes account of both the growth process and the loss of vorticity is proposed. By comparison with experimental measurements we have determined that the entrainment coefficient for turbulent vortex rings has a value equal to 0.011 ± 0.001, while their effective drag coefficient is 0.09 ± 0.01. These results seem to be independent of Reynolds number to within experimental accuracy.

Motion of a turbulent buoyant thermal in a calm stably stratified atmosphere

A simple model for the motion of a turbulent buoyant thermal in a calm, stably stratified atmosphere is proposed. Using this model, the average motion of the thermal can be described in terms of its initial density difference, velocity and effective radius, and the three nondimensional gross parameters: mass entrainment constant, effective drag coefficient, and turbulence dissipation rate. Relations between the local turbulence field and the three gross parameters are discussed. Also, the maximum height a thermal can reach in a stable atmosphere for various initial conditions and gross parameters can be approximated by a simple power law relation.

Surface exchange characteristics of leaves subject to mutual interference

The drag on young apple trees was measured in turbulent air flow in a large wind tunnel. Leaf density was altered by thinning between runs. The leaf drag coefficient was calculated on the assumption that there was no significant aerodynamic interference between leaves at the lowest density. From this, and the effective drag coefficients at the higher densities, shelter factors (pd) were derived, defining the extent of mutual interference with momentum absorption.Evaporation rates from leaves subject to mutual aerodynamic interference were measured using an artificial tree which could be readily thinned. Water vapour transfer resistances and coefficients were obtained from these measurements, and shelter factors (pv) calculated in terms of the coefficients at the lowest leaf density. At low wind speeds (about 1 m sec−1) the shelter factors for mass and momentum exchange were similarly affected by leaf density but at higher wind speeds Pv >Pd.The transfer resistance for unsheltered leaves is described by an expression in terms of wind speed and leaf dimension, which gives results very similar to those obtained with the expression given by Monteith (1965). When leaves are subject to significant mutual interference resistances to mass transfer are about 50% higher.

Drag coefficients of water droplets decelerating in air

The relation of drag coefficient to Reynolds number for decelerating water droplets was tested by releasing into a 50 m s−1 airstream droplets up to 230 μm in diameter. After travelling for 1.83 m in the airstream, the droplets passed through a small hole into still air, and the distances they subsequently travelled could be predicted fairly well by assuming that the effective drag coefficients were about 20 per cent below the steady-velocity values.

Drag coefficients of water droplets decelerating in air

AbstractThe relation of drag coefficient to Reynolds number for decelerating water droplets was tested by releasing into a 50 m s−1 airstream droplets up to 230 μm in diameter. After travelling for 1.83 m in the airstream, the droplets passed through a small hole into still air, and the distances they subsequently travelled could be predicted fairly well by assuming that the effective drag coefficients were about 20 per cent below the steady‐velocity values.

Motion of an Isolated Buoyant Thermal

Using a simplified model, the governing equations of the motion of an isolated buoyant thermal are formulated. The general solutions which include both large and small density differences and both the initial accelerating motion and the final decelerating motion, are obtained. The asymptotic behavior for large time is given and compared with experimental results. The effect of various parameters, such as density difference, mass entrainment, and effective drag coefficient are also discussed.

Effective Drag Coefficient for Gas-Particle Flow in Shock Tubes

Effective drag coefficients for flows of suspensions of spherical glass particles in air were derived from simultaneous measurements of pressure and particle concentration in the flow behind weak shock waves. Average particle diameters were 29 and 62μm. The instantaneous concentration was determined by light scattering, and the results agree well with earlier shock-tube data based on streak records. They exhibit several unexpected features: the correlation between drag coefficient and Reynolds number is much steeper (∝ Re−1.7) than the generally used “standard” curve but approaches it at Reynolds numbers of several hundred; the correlation is independent of the particle concentration over the range of the experiments, that is, for particle-to-gas flow rate ratios between about 0.05 and 0.36; if the Reynolds number immediately behind the shock front is changed by varying the shock strength, the points move along the correlation, but if it is changed by changing the particle size, the entire correlation is shifted although to a smaller extent than would correspond to the direct effect of particle diameter on the Reynolds number. To account for the observations, a flow model is developed which allows for microscopic longitudinal and lateral perturbations of the particle motion that are the result of various causes, such as particle interactions with wakes of other particles, lateral forces caused by particle rotation, or electrostatic forces. Because of the nonlinearity of the equation of motion, the averaged particle motion is different from that of a particle without perturbations. The effective drag coefficient for the average particle motion is therefore different from the standard drag coefficient applied along the actual motion. With this model and plausible assumptions for the average lateral velocity component of the particle motion, all features of the experimental data can be qualitatively explained.

Shock tube studies of C 2 formation with the use of C 13

Particle-laden flows can be observed in many scientific and engineering problems. The present study focused on the initial state of the shock–particle interaction when the total volume fraction is constant and the particles can be regarded as static. Three-dimensional (3D) particle-resolved simulations were conducted using a stratified multiphase flow model with Euler equations. We conducted a convergence study by keeping the total particle volume fraction constant and changing the number of particles (Np). Therefore, the particle size changed accordingly. The distributions of the root mean square (RMS) velocity, internal energy, kinetic energy, and turbulent kinetic energy were investigated. A quantitative analysis of the energy distributions in the upstream domain, particle-curtain domain, and downstream domain was conducted. Herein, we proposed a modified one-dimensional (1D) volume-averaged model that can be applied to a situation where a shock wave interacts with a spherical particle-curtain. The model predicts the appropriate artificial effective drag coefficient by fitting the positions of the reflected and transmitted shocks in the particle-resolved results.