Friction Factor Comparison Between Mixing Length Theory and Empirical Correlation

Equivalent sand grain roughness is required for estimating friction factor for engineering applications from empirical relation via Haalands equation. The real surfaces are different from the sand grain profile. The correlations for friction factor were derived from use of discrete roughness elements with regular shapes such as cones, bars etc. The purpose of the paper is to derive analytical expression of friction factor for a 2 dimensional semi-cylindrical roughness (not exactly a 3 dimensional sand grain but for the circular profile of cross- section) using Navier Stoke equation and mixing length theory. This is compared with the modified series mathematical representation of Haalands equation for friction factor in terms of equivalent sand grain roughness. The comparison is valid for high Reynolds number where the velocity profile is almost flat beyond boundary layer and approximately linear all throughout the boundary layer. The high Reynolds number approximation for Haalands equation is derived and the series form of the friction factor compares approximately with the series form derived from first principles, where in the exponents of the series expansion are close.

Effect of Nozzle Outlet Type On the Flow Field Velocity and Impact Pressure of High Pressure Water Jet Peening

Water jet peening can effectively improve the fatigue strength of metal materials, and the outlet shape of nozzle greatly affects the effect of water jet peening. In this paper, the effects of nozzle outlet shape on water jet velocity and impact pressure is studied by numerical simulation, and the jet velocity and dynamic pressure for different standoff distances are also discussed. The results show that the water jets of square, circular and triangular nozzles are highly concentrated, and the water jet of elliptical nozzles is the most divergent. The axial velocity attenuation of the square nozzle along the axis is slower than that of the other three nozzles. The water axial velocity of the elliptical nozzle attenuates fastest and the length of the core segment of the water jet is the smallest. Within a certain axial distance, the dynamic pressure area in the central area of the elliptical water jet is obviously larger than that of the other three nozzles, and the effective treatment range is large, which is more suitable for the welding surface strengthening operation.

Measurements of Turbulent Transport in a Square Channel with One Ribbed Wall

The velocity field of the fully developed turbulent flow in a one-sided ribbed square channel (rib-height-to-channel-height ratio of k/h = 0.0667, rib-pitch-to-rib-height ratio of p/k = 9) were measured at Reynolds numbers (based on the channel height h and the mean bulk velocity uB) of Reh = 50 000 and 100 000 by means of Laser-Doppler-Anemometry (LDA). Triple velocity correlations differed slightly between both Reynolds numbers when normalized by the bulk velocity and the channel height, similarly to the first- and second-order statistical moments of the velocity. Their near-wall behavior reflected the crucial role of turbulent transport near the rib crest and within the separated shear layer. Sweep events occurred with the elongated flow structures of the flapping shear layer and gained in importance towards the channel bottom wall, while strong ejection events near the rib leading and trailing edges coincided with flow structures bursting away from the wall. Despite the predominant occurrence of sweep events close to the ribbed wall within the inter-rib spacing, ejection events contributed with higher intensity to the Reynolds shear stress. Ejection and sweep events and their underlying transport phenomena contributing to the Reynolds shear stress were almost Reynolds number-insensitive in the resolved flow range. The invariance to the Reynolds number can be of benefit for the use of scale-resolving simulation methods in the design process of rib structures for heat exchange applications.

Flow Characteristics of Gerotor Motors with Pin and Nonpin Designs

The geometric design of a gerotor motor has a significant impact on its function, performance, quality, reliability and cost. When designing a gerotor motor all these features must be considered. A gerotor motor can be classified into two types based on the geometric design; gerolor (pin design) and gerotor (nonpin design). In this article geometric parameters of the two design types are discussed briefly and the operation of the gerotor motor is described as well. A numerical analysis is carried out by using computational fluid dynamics (CFD) tool (PumpLinx) to analyze the fluid flow and predict the performance of both types of gerotor designs. Various characteristics of the two designs of the gerotor motor are investigated and compared which include the gerotor design, fluid flow rate, velocity, pressure and output torque. Comparison of the results found out that using pin design gerotor motor, the flow rate, flow velocity, pressure and torque will vary greatly. Nonpin design can significantly reduce variations in all the flow characteristics thereby enhancing the stability and reduction in the leakage risk.

Numerical Study of Unsteady Cavitating Flow in an Inducer with Omega Vortex Identification

To accurately capture the behaviors of cavitation and reveal the unsteady cavitating flow mechanism, a condensate pump inducer is numerically analyzed in a separate numerical experiment with LES at critical cavitation number sind,c under the design point. Based on the new Omega vortex identification method, the correction between the flow structures and cavities is clearly illustrated. Besides, the pressure fluctuations around the inducer are analyzed. Special emphasis is put on the analysis of the interactions between the cavities, turbulent fluctuations, and vortical flow structures. The Omega vortex identification method could give an overall picture of the whole cavitating flow structures to present a clear correlation between the vortices and cavities. The results show that the shear cavitation dominant the cavitation characteristics under the design point. The pure rigid rotation region mainly concentrates at the edge of the cavities while the other sheet-like cavities near the casing walls are characterized by strong turbulence fluctuations. Besides, based on the analysis of the correlation between the cavities and flow structures, the rotating cavitation under the design point may mainly attribute to the interaction between the tip leakage vortex cavitation and the next blade.

Second Moment Closure Modeling and DNS of Stratified Shear Layers

Buoyant shear layers encountered in many engineering and environmental applications have been studied by researchers for decades. Often, these flows have high Reynolds and Richardson numbers, which leads to significant/intractable space-time resolution requirements for DNS or LES. On the other hand, many of the important physical mechanisms, such as stress anisotropy, wake stabilization, and regime transition, inherently render eddy viscosity-based RANS modeling inappropriate. Accordingly, we pursue second-moment closure (SMC), i.e., full Reynolds stress/flux/variance modeling, for moderate Reynolds number non-stratified, and stratified shear layers for which DNS is possible. A range of sub-model complexity is pursued for the diffusion of stresses, density fluxes and variance, pressure strain and scrambling, and dissipation. These sub-models are evaluated in terms of how well they are represented by DNS in comparison to the exact Reynolds averaged terms, and how well they impact the accuracy of full RANS closure. For the non-stratified case, SMC model predicts the shear layer growth rate and Reynolds shear stress profiles accurately. Stress anisotropy and budgets are captured only qualitatively. Comparing DNS of exact and modeled terms, inconsistencies in model performance and assumptions are observed, including inaccurate prediction of individual statistics, non-negligible pressure diffusion, and dissipation anisotropy. For the stratified case, shear layer and gradient Richardson number growth rates, and stress, flux and variance decay rates, are captured with less accuracy than corresponding flow parameters in the non-stratified case. These studies lead to several recommendations for model improvement.

Liquid Droplet Impact Over Hydrophobic Mesh Surfaces and Assessment of Weber Number Dependent Characteristics

Impacting droplets and droplet ejection from hydrophobic mesh surfaces have interest in biomedicine, heat transfer engineering, and self-cleaning of surfaces. The rate and the size of newborn droplets can vary depending on, the droplet fluid properties, Weber number, mesh geometry, and surface wetting states. In the present study, impacting water droplets onto hydrophobic mesh surface is investigated and impact properties including, spreading, rebounding, and droplet fluid penetration and ejection rates are examined. Droplet behavior is assessed using high recording facilities and predicted in line with the experiments. The findings reveal that the critical Weber number for droplet fluid penetrating/ejecting from mesh screen mainly depends on the droplet fluid capillary length, and hydrophobic mesh size. The contact time of impacting droplet over mesh surface reduces with increasing droplet Weber number, which opposes the case observed for impacting droplets over flat hydrophobic surfaces. The restitution coefficient attains lower values for impacting droplets over mesh surfaces than that of flat surfaces. The rate and diameter of the ejected droplet from the mesh increases as droplet Weber increases. At the onset of impact, streamline curvature is formed inside droplet fluid, which creates a stagnation zone with radially varying pressure at the droplet fluid mesh interface. This reduces the ejected droplet diameter from mesh cells as mesh cells are located away from the impacting vertical axis.

Estimation of Turbulent Length Scales at a Turbocharger Inlet using Stereoscopic Particle Image Velocimetry

Stereoscopic Particle Image Velocimetry measurements are carried out at the inlet of a turbocharger compressor at four different shaft speeds from 80,000 rpm to 140,000 rpm and over the entire range of flow rates from choke to mild surge. This paper describes the procedure used in processing the PIV data leading to the estimates of turbulent length scales - integral, Taylor, and Kolmogorov, to enhance the fundamental understanding and characterization of the compressor inlet flow field. The analysis reveals that at most operating conditions the three different length scales have markedly different magnitudes, as expected, while they have somewhat similar qualitative distributions with respect to the duct radius. For example, at 80,000 rpm and at a flow rate of 15.7 g/s (mild surge), the longitudinal integral length scale is of the order of 15 mm, the Taylor scale is around 0.5 mm, and the Kolmogorov scale is about 10 microns. With the onset of flow reversal, the turbulent kinetic energy and turbulent intensity at the compressor inlet are observed to increase rapidly, while the magnitudes of the Kolmogorov scale and to a certain extent, the Taylor scale are found to decrease suggesting that the increased turbulence gives rise to even smaller flow structures. The variation of length scales with compressor shaft speed has also been studied.

Features of the Flow of a Model Liquid Into a Medium with a Variable Degree of Rarefaction

Experimental results of observing ethanol micro-jets expiring into a highly rarefied medium (vacuum) through a nozzle are presented. The study of the process was carried out both at the horizontal and vertical liquid stream from the source compared to the direction of gravity The residual background gas pressure in the vacuum chamber was maintained at a level much lower than the saturated vapor pressure of the working fluid at a given outlet temperature. The possibility of modeling complex processes of micro-fluids expiring into a medium with a given rarefied atmosphere on a compact vacuum gas-dynamic stand is shown. It is established that the long-term flow from a thin capillary or a small-diameter hole into a vacuum or a highly rarefied gas medium differs significantly from the well-studied flow modes into a dense gas medium, as well as from the pulsed flow modes into a vacuum. The paper describes the main features of the flow and the conditions for the occurrence of instability. It is shown that the long-term flow of a liquid micro-jet in a vacuum has a high degree of surface instability, with a large number of sudden changes in the direction, structure, and observed density. An explanation of the reasons for the destruction of the micro-jet is proposed. The formation of surface gas caverns causing explosive destruction of the micro-jet with the release of vapor-liquid droplets is established.

The Effect of Surface Geometry of Solid Wall On the Collapse of a Cavitation Bubble

The objective of this paper is to reveal the influence of different surface geometric conditions on the dynamic behavior characteristics of a laser-induced bubble collapse. A high-speed camera system was used to record the oscillation process of the laser-induced bubble on plane solid walls with different roughness and a wall containing reentrant cavities full of water or gas. The focus is on the quantitative analysis of the morphological characteristics of the cavitation bubble near the solid wall under different surface forms during the first two oscillation period. The results show that the dimensionless ratio γ, defined as the distance from the center of the bubble to the wall divided by the maximum radius of the bubble, has a great influence on the change of the cavitation shape in the direction of the vertical wall. Different surface geometries without gas in our cases have no significant effect on the collapse time of cavitation bubbles. While for the surface containing gas, the direction of movement of the bubble accompanying the micro-jet will greatly change during the collapse of the cavitation bubble, and the collapse time seems to be independent of the dimensionless ratio γ. These achievements shed the light for the engineering to avoid the damage of the micro-jet caused by design suitable surface geometry.