Internal Flows Driven by Wall-Normal Injection

We describe the dynamics of large-scale structures in a developed turbulent flow between a train of waves and a flat wall. A water channel facility, for which the wavelength, $\Lambda$, of the bottom wall equals the channel height and the wave amplitude is ten times smaller, is used. The channel is sufficiently wide so that structures of spanwise scale O$\{1.5\Lambda\}$ meander laterally. The paper dicusses the temporal behaviour and the meandering motion at a Reynolds number of 4500, defined with the half channel height and the bulk velocity. Digital particle image velocimetry is performed in a horizontal plane with a field of view of $2.6\Lambda\times 2.7\Lambda$. Ten ensembles of 90 consecutive image pairs are acquired at a rate of 15 Hz, a temporal resolution sufficient to assess how the largest flow scales evolve in time. The streamwise velocity $u(x,z,t)$ is filtered using the dominant eigenfunctions that are obtained by a proper orthogonal decomposition analysis. The very large temporal scales of the meandering motion of the O$\{1.5\Lambda\}$ structures could be followed over measurement times of up to 6 s, during which they are convected downstream by distance of 65 wavelengths. The observed coherent lengths in the streamwise direction are significantly larger than the streamwise domain extent of all large-eddy simulation and direct numerical simulation reported so far.

Characterisation of transverse turbulent motion in quasi-two-dimensional aerated flow: Application of four-point air-water flow measurements in hydraulic jump

For successful powder deposition and a good quality of deposited layers, the following factors are of great importance: uniform powder injection into the plasma jet, transfer of heat and velocity of plasma particles (ions and electrons) to powder particles as well as the temperature and speed of molten powder particles before the collision with the substrate. For each powder type, depending on the distribution of particle granulation (µm) and density (kg/m3), it is necessary to determine the amount of powder supply (g/min) in the plasma for defined gas flows (l/min), types of plasma gases (Ar, He, H2, N2 or their mixtures) and power supply levels (kW). For the transfer of heat and speed of plasma particles to powder particles, there must be an interaction between the ions and electrons from the plasma and the powder particles. For already known plasma jet speed and temperature values at atmospheric pressure, trajectories of individual particles can be calculated using the equations of motion taking into account viscous friction and inertia. The paper describes the relation between the speed of Al2O3 powder injection and the velocity of individual Al2O3 powder particles in the plasma depending on the distance from the anode opening, as well as the relation between powder granulation and the temperature of the surface of powder particles depending on powder injection and the level of plasma gun power supply at atmospheric pressure.

Application of stable isotopes in soil studies has improved quantitative evaluation of evaporation and other hydrological processes in soil. This study was carried out to determine the effect of tillage on evaporative loss of water from the soil. Zero tillage and conventional tillage were compared. Suction tubes were installed for soil water collection at the depths 0.15, 0.50, and 1.0 m by pumping soil water with a peristaltic pump. Soil water evaporation was estimated using stable isotopes of water. The mean isotopic composition of the soil water at 0.15 m soil depth were -1.15‰ (δ18O) and -0.75‰ (δD) and were highly enriched compared with the isotopic compositions of the site precipitation. Soil water stable isotopes (δ18O and δD) were more enriched near the surface under zero tillage while they were less negative down the profile under zero tillage. This suggests an occurrence of more evaporation and infiltration under conventional then zero tillage, respectively, because evaporative fractionation contributes to escape of lighter isotopes from liquid into the vapour phase leading to enrichment in heavy isotopes in the liquid phase. The annual evaporation estimated using the vapour diffusion equation ranges from 46-70 and 54-84 mm year-1 under zero and conventional tillage, respectively, indicating more evaporation under conventional tillage compared with zero tillage. Therefore, to reduce soil water loss, adoption of conservation tillage practices such as zero tillage is encouraged.

The increase in fuel costs and looming restrictions on carbon dioxide emissions are driving the shipowner into reducing the ship’s resistance and required installed power. It was earlier reported that, merchant vessels operating at lower speeds, the frictional drag accounts of almost 70–80% of the total drag; thus, there is a strong demand for the reduction in the fluid frictional drag, especially in the marine transportation business. The use of air as a lubricant, by injecting below the plate or the body, which is famously known as microbubble drag reduction (MBDR) in order to reduce that frictional drag is an active research topic. Latest developments in this field suggests that there is a potential reduction of 80% in frictional drag in case of flat plates and about 30% reduction in case of ships, which encourages researchers to investigate further. In this study, 3D numerical investigations into frictional drag reduction by microbubbles were carried out in Star CCM+ on a channel for different flow velocities, different void fractions and different cross sections of flow at the injection point. This study is the first of its kind in which variation of coefficient of friction both in longitudinal and transverse directions was studied along with actual localized variation of void fraction at these points. The numerical framework consists of the Reynolds-averaged Navier–Stokes (RANS) equations and the standard k−e turbulence model with standard wall function treatment, which is validated in both conditions of with and without microbubbles with the existing experimental data. The design exploration study was carried out for various flow speeds, injector flow rates, cross sections of the channel/heights of channels and of course void fractions. Coefficient of friction and void fraction values are measured at 12 longitudinal positions, and at each longitudinal position, 11 in number transverse and 10 in number depthwise positions were studied. In all, for one simulation, data at more than 1000 positions were collected. More than 60 simulations were carried out to understand the effect. From the study, it is concluded that since it is a channel flow and as the flow is restricted in confined region, effect of air injection is limited to smaller area in transverse direction as bubbles were not escaping in transverse direction.

Analytical analysis of fluid flow in cylindrical microchannels subjected to uniform wall injection at various Reynolds numbers is presented. The classical Navier-Stokes equations are used in the present study. Mathematically, using an appropriate change of variable, Navier-Stokes equations are transformed to a set of nonlinear ordinary differential equations. The governing equations are solved analytically using series solution method. The presented analytical results can be used for the prediction of velocity profiles and pressure drops in the cylindrical micro channels. The results are validated against available data in the literature and have shown good agreement.

*† In this article, a semi-analytical formulation is provided for the rotational, steady, inviscid, compressible motion of a solid rocket motor that is modeled as a slender porous chamber. The analysis overcomes some of the deficiencies encountered in previous work on the subject. The method that we employ consists of reducing the problem’s mass, momentum, energy, ideal gas, and isentropic relations into a single integral equation that can be solved numerically. Furthermore, Saint-Robert’s power law representation is used to link the pressure to the sidewall mass injection rate. At the outset, results are presented for the axisymmetric porous cylinder and compared to two closed-form analytical solutions developed under one-dimensional and two-dimensional, isentropic flow conditions. The comparison is carried out assuming either uniformly distributed mass flux or constant radial injection speed along the porous wall. Our amended formulation is shown to agree with the one-dimensional solution obtained for the case of uniform wall mass flux and with the asymptotic approximation obtained by Majdalani for the constant wall injection speed (Majdalani, J., On Steady Rotational High Speed Flows: The Compressible Taylor-Culick Profile, Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, Vol. 463, No. 2077, 2007, pp. 131-162). While all solutions agree on the critical distance to reach sonic conditions, differences among them occur near choking and these could be partly attributed to the level of approximation entailed in the integral approximation.

In this work, a compressible biglobal stability approach is used to investigate the growth characteristics of hydrodynamic and vorticoacoustic waves in porous tubes with uniform wall injection. The retention of compressibility effects enables us to construct a physics-based formulation that is capable of predicting both hydrodynamic and vorticoacoustic wave motions simultaneously with no need for mode decomposition. At first, we show that, in the absence of a mean flow, the stability framework reproduces traditional Helmholtz frequencies and modal shapes. This confirms the embedment of the wave equation within the compressible Navier–Stokes framework. We then proceed to simulate the idealized motion in solid rocket motors, often modeled as porous tubes, where a mean flow expression is available. Specifically, using the compressible Taylor–Culick profile as a base flow, our solver produces a comprehensive frequency spectrum that returns both hydrodynamic and vorticoacoustic modes in one swoop with the added benefit of pinpointing the flow-induced longitudinal, radial, and mixed frequencies at user-prescribed tangential modes. Moreover, we find that increasing the flow Mach number leads to a slight reduction in the vorticoacoustic frequencies relative to their strictly acoustic counterparts. Similar results are obtained while increasing the Reynolds number and aspect ratio, thus affirming the origin of frequency shifts often observed in motor firings. Finally, the vorticoacoustic velocity fluctuations are shown to resemble those obtained asymptotically. Particularly, their depths of penetration appear to be controlled by the penetration number, a dimensionless parameter that combines the effects of sidewall injection, oscillatory frequency, viscosity, and chamber radius.

An improved low-Reynolds number model was adopted to predict the dynamic and thermal fields in flows with transpiration. The performance of the adopted model was first contrasted with the direct numerical simulation (DNS) data of channel flow with uniform wall injection and suction. The validity of the present model applied to flows with a high level of transpiration was further examined. To explore the model's performance in complex environments, the model was applied to simulate a transpired developing channel flow. By contrasting the predictions with DNS data and measurements, the results indicated that the present model reproduced correctly the deceleration and acceleration of the flow caused by the injection and suction from the permeable part of the wall. The turbulence structure of transpired flows was also well captured and the superior performance of the adopted model was reflected by the predicted correct level of ε with the maximum being located at both the injection and the suction walls. The predicted thermal field by the present model also compared favourably with the DNS data and measurements. Copyright © 2000 John Wiley & Sons, Ltd.

Analytical analysis of fluid flow in an annular microchannel subjected to uniform wall injection at various Reynolds numbers is presented. The classical Navier–Stokes equations are used in the present study. Mathematically, using an appropriate change of variable, Navier–Stokes equations are transformed to a set of nonlinear ordinary differential equations. The governing equations are analytically solved using series solution method. Some analytical results are given for the prediction of velocity profiles and pressure distributions in annular microchannels. The agreement between the computational fluid dynamics and the analytical predictions is very good. However, the analytical results are valid in a limited range of radius ratios and needs more study.

In this work we develop an experimental approach to determine the influence of flow characteristics on the burning of solids (auto-extinguishable propellants) inside a hybrid rocket motor. An experimental device utilizing gaseous mixtures which simulates real conditions as closely as possible (high blowing mass transport at the wall) was used to characterize the main flow as a function of geometric and aerodynamic parameters. At first the isothermal case was studied to explore the mixing zone. In a second step a diffusion flame was stabilized to separate the influence of aerodynamics from that of combustion. These results underline the parameters having a preponderant influence on the burning and stabilization of a flame in such a combustion chamber.