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IN THIS ISSUE

### TECHNICAL PAPERS

J. Fluids Eng. 2006;129(3):253-262. doi:10.1115/1.2427075.

Velocity and pressure measurements are presented for a blade passage with and without leading edge contouring in a low speed linear cascade. The contouring is achieved through fillets placed at the junction of the leading edge and the endwall. Two fillet shapes, one with a linear streamwise cross-section (fillet 1) and the other with a parabolic cross-section (fillet 2), are examined. Measurements are taken at a constant Reynolds number of 233,000 based on the blade chord and the inlet velocity. Data presented at different axial planes include the pressure loss coefficient, axial vorticity, velocity vectors, and yaw and pitch angles. In the early stages of the development of the secondary flows, the fillets are seen to reduce the size and strength of the suction-side leg of the horseshoe vortex with associated reductions in the pressure loss coefficients and pitch angles. Further downstream, the total pressure loss coefficients and vorticity show that the fillets lift the passage vortex higher above the endwall and move it closer to the suction side in the passage. Near the trailing edge of the passage, the size and strength of the passage vortex is smaller with the fillets, and the corresponding reductions in pressure loss coefficients extend beyond the mid-span of the blade. While both fillets reduce pressure loss coefficients and vorticity, fillet 1 (linear fillet profile) appears to exhibit greater reductions in pressure loss coefficients and pitch angles.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):263-272. doi:10.1115/1.2427077.

A large eddy simulation (LES) was applied to predict the unsteady flow in a low-speed axial-flow fan assembly subjected to a highly “turbulent” inflow that is generated by a turbulence grid placed upstream of the impeller. The dynamic Smagorinsky model (DSM) was used as the subgrid scale (SGS) model. A streamwise-upwind finite element method (FEM) with second-order accuracy in both time and space was applied as the discretization method together with a multi-frame of reference dynamic overset grid in order to take into account the effects of the blade-wake interactions. Based on a simple algebraic acoustical model for axial flow fans, the radiated sound power was also predicted by using the computed fluctuations in the blade force. The predicted turbulence intensity and its length scale downstream of the turbulence grid quantitatively agree with the experimental data measured by a hot-wire anemometry. The response of the blade to the inflow turbulence is also well predicted by the present LES in terms of the surface pressure fluctuations near the leading edge of the blade and the resulting sound power level. However, as soon as the effects of the turbulent boundary layer on the blades become important, the prediction tends to become inaccurate.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):273-278. doi:10.1115/1.2427076.

For experimental investigations of the thermodynamic effect on a cavitating inducer, it is nesessary to observe the cavitation. However, visualizations of the cavitation are not so easy in cryogenic flow. For this reason, we estimated the cavity region in liquid nitrogen based on measurements of the pressure fluctuation near the blade tip. In the present study, we focused on the length of the tip cavitation as a cavitation indicator. Comparison of the tip cavity length in liquid nitrogen $(80K)$ with that in cold water $(296K)$ allowed us to estimate the strength of the thermodynamic effect. The degree of thermodynamic effect was found to increase with an increase of the cavity length. The temperature depression was estimated from the difference of the cavitation number of corresponding cavity condition (i.e., cavity length) between in liquid nitrogen and in cold water. The estimated temperature depression caused by vaporization increased rapidly when the cavity length extended over the throat. In addition, the estimated temperature inside the bubble nearly reached the temperature of the triple point when the pump performance deteriorated.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):279-292. doi:10.1115/1.2427079.

This paper presents comparisons between two-dimensional (2D) CFD simulations and experimental investigations of the cavitating flow around a symmetrical 2D hydrofoil. This configuration was proposed as a test case in the “Workshop on physical models and CFD tools for computation of cavitating flows” at the 5th International Symposium on cavitation, which was held in Osaka in November 2003. The calculations were carried out in the ENSTA laboratory (Palaiseau, France), and the experimental visualizations and measurements were performed in the IRENav cavitation tunnel (Brest, France). The calculations are based on a single-fluid approach of the cavitating flow: the liquid/vapor mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. Results presented in the paper focus on cavitation inception, the shape and the general behavior of the sheet cavity, lift and drag forces without and with cavitation, wall pressure signals around the foil, and the frequency of the oscillations in the case of unsteady sheet cavitation. The ability of the numerical model to predict successively the noncavitating flow field, nearly steady sheet cavitation, unsteady cloud cavitation, and finally nearly supercavitating flow is discussed. It is shown that the unsteady features of the flow are correctly predicted by the model, while some subtle arrangements of the two-phase flow during the condensation process are not reproduced. A comparison between the peer numerical results obtained by several authors in the same flow configuration is also performed. Not only the cavitation model and the turbulence model, but also the numerical treatment of the equations, are found to have a strong influence on the results.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):293-301. doi:10.1115/1.2427078.

The main purpose of this study is to investigate liquid entrainment mechanisms of annular flow by computational fluid dynamics (CFD) techniques. In the modeling, a transient renormalization group (RNG) $k-ε$ model in conjunction with an enhanced wall treatment method was employed. In order to reconstruct the two-phase interface, the volume of fluid (VOF) geometric reconstruction scheme was adopted. Simulation results indicated that disturbance waves were generated first on the two-phase interface and that their evolution eventually resulted in the liquid entrainment phenomena. The most significant accomplishment of this work is that details of the entrainment mechanism are well described by the numerical simulation work. In addition, two new entrainment phenomena were presented. One entrainment phenomenon demonstrated that the evolution of individual waves caused the onset of liquid entrainment; the other one showed that the “coalescence” of two adjacent waves (during the course of their evolution) played an important role in the progression of liquid entrainment. Further analysis indicated that the two entrainment phenomena are inherently the same entrainment mechanism. The newly developed entrainment mechanism is based on conservation laws.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):302-310. doi:10.1115/1.2427080.

An analysis is made of the linear stability of wide-gap hydromagnetic (MHD) dissipative Couette flow of an incompressible electrically conducting fluid between two rotating concentric circular cylinders in the presence of a uniform axial magnetic field. A constant heat flux is applied at the outer cylinder and the inner cylinder is kept at a constant temperature. Both types of boundary conditions viz; perfectly electrically conducting and electrically nonconducting walls are examined. The three cases of $μ<0$ (counter-rotating), $μ>0$ (co-rotating), and $μ=0$ (stationary outer cylinder) are considered. Assuming very small magnetic Prandtl number $Pm$, the wide-gap perturbation equations are derived and solved by a direct numerical procedure. It is found that for given values of the radius ratio $η$ and the heat flux parameter $N$, the critical Taylor number $Tc$ at the onset of instability increases with increase in Hartmann number $Q$ for both conducting and nonconducting walls thus establishing the stabilizing influence of the magnetic field. Further it is found that insulating walls are more destabilizing than the conducting walls. It is observed that for given values of $η$ and $Q$, the critical Taylor number $Tc$ decreases with increase in $N$. The analysis further reveals that for $μ=0$ and perfectly conducting walls, the critical wave number $ac$ is not a monotonic function of $Q$ but first increases, reaches a maximum and then decreases with further increase in $Q$. It is also observed that while $ac$ is a monotonic decreasing function of $μ$ for $N=0$, in the presence of heat flux $(N=1)$, $ac$ has a maximum at a negative value of $μ$ (counter-rotating cylinders).

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):311-318. doi:10.1115/1.2427084.

Jet-crossflow experiments were performed in a water channel to determine the Reynolds number effects on the plume trajectory and entrainment coefficient. The purpose was to establish a lower limit down to which small scale laboratory experiments are accurate models of large scale atmospheric scenarios. Two models of a turbulent vertical surface jet (diameters $3.175mm$ and $12.7mm$) were designed and tested over a range of jet exit Reynolds numbers up to $104$. The results show that from Reynolds number 200–4000 there is about a 40% increase in the entrainment coefficient, whereas from Reynolds number 4000–10,000, the increase in entrainment coefficient is only 2%. The conclusion is that Reynolds numbers significantly affect plume trajectories when the model Reynolds numbers are below 4000. Changing the initial turbulence in the exit flow from 12% to 2% without changing its mean velocity profile caused a less than one source diameter increase in the final plume rise.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):319-324. doi:10.1115/1.2427083.

We demonstrate that flagellated bacteria can be utilized in surface arrays (carpets) to achieve mixing in a low-Reynolds number fluidic environment. The mixing performance of the system is quantified by measuring the diffusion of small tracer particles. We show that the mixing performance responds to modifications to the chemical and thermal environment of the system, which affects the metabolic activity of the bacteria. Although the mixing performance can be increased by the addition of glucose (food) to the surrounding buffer or by raising the buffer temperature, the initial augmentation is also accompanied by a faster decay in mixing performance, due to falling pH and oxygen starvation, both induced by the higher metabolic activity of the bacterial system.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):325-332. doi:10.1115/1.2427087.

A molecular dynamics simulation of flow over two side-by-side cylinders with atomically rough surfaces is presented. The model is two-dimensional with $3×105$ liquid argon atoms. The surface roughness is constructed by external protrusion of atoms on the surface of the cylinders with specified amplitude and width. Two cylinders, with diameters of $d=79.44$ (molecular units), are placed at a distance of $D$ in a vertical line. The solids atoms are allowed to vibrate around their equilibrium coordinates to mimic the real solid structure. The influence of various parameters, such as roughness amplitude, topology, periodicity, and the gap between cylinders on the hydrodynamics of flow, especially drag and lift forces, is studied. It was noted that even very little surface roughness, with amplitude on the order of a few nanometers, can influence the drag forces. Both roughness texture and the number of roughening elements affects the drag and lift coefficients. The gap between the cylinders showed to be an effective parameter, especially on the lift force for flow over the nanoscale cylinders.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):333-337. doi:10.1115/1.2427088.

A mathematical model describing the hydrodynamics of the flow within a disengaged wet transmission clutch is presented. The primary improvement of this model over the existing ones is the inclusion of the surface tension effect, which is expressed in the pressure equation as an additional term. The drag torque predicted by the model correlates well with the test data for nongrooved clutch packs. The significance of the surface tension in this type of flows is discussed as well.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):338-349. doi:10.1115/1.2427082.

The use of in-line static mixers has been widely advocated for an important variety of applications, such as continuous mixing, heat and mass transfer processes, and chemical reactions. This paper extends previous studies by the authors on industrial static mixers and illustrates how static mixing processes of single-phase viscous liquids can be numerically simulated. Mixing of Newtonian, shear-thinning, and shear-thickening fluids through static mixer, as well as thermal enhancement by static mixer is studied. Using different measuring tools, the global performance and costs of SMX (Sulzer mixer X) and helical static mixers are studied. It is shown that the SMX mixer manifests a higher performance; however, the required energy to maintain the flow across a SMX mixer is significantly higher.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):350-358. doi:10.1115/1.2427081.

The response of backflow at the inlet of an inducer to the flow rate fluctuation is studied by using three-dimensional numerical calculations based on the $k-ϵ$ turbulence model for the discussion of its effect on cavitation instabilities. It is first shown that the size of the backflow region can be correlated with the angular momentum in the upstream and the phase of the backflow significantly delays behind the quasi-steady response even at a very low frequency. It is then shown that the conservation relation of angular momentum is satisfied with minor effects of the shear stress on the boundary. The supply of the angular momentum by the negative flow is shown to be quasi-steady due to the fact that the pressure difference across the blade causing the backflow is quasi-steady at those frequencies examined. A response function of the angular momentum in the upstream to flow rate fluctuation is derived from the balance of the angular momentum and the results of the numerical calculations. This clearly shows that the backflow responds to the flow rate fluctuation as a first-order lag element. The effects of the backflow cavitation on cavitation instabilities are discussed assuming that the delay of cavity development is much smaller than the delay of the backflow. It was found that the backflow cavitation would destabilize low frequency disturbances due to the effects of the positive mass flow gain factor but stabilize high frequency disturbances due to the effect of the cavitation compliance.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):359-367. doi:10.1115/1.2427085.

This paper presents results of the simulation of two vehicles overtaking each other at highways conditions $(30m∕s)$. The simulation was fully unsteady and tracks the maneuver for several body lengths from downstream to upstream. Different mesh strategies have been investigated and assessed. Structured methods with sliding planes have been found the most feasible. The results shown include the effects of relative speed and lateral separation. The passing maneuver is described in detail, and a number of physical phenomena are identified. In particular, the rapid fluid compression and acceleration at the nose passing situation yields a pulse in the drag of the overtaken vehicle. The high pressure bow wave followed swiftly by the low-pressure wake affects the side force and lateral stability at positions slightly different than the nose passing.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(3):368-375. doi:10.1115/1.2427086.

It is important to clarify the characteristics of flow-induced vibrations in hard disk drives in order to achieve an ultrahigh magnetic recording density. In particular, it is necessary to reduce the flow-induced disk vibrations referred to as disk flutter. This paper describes the correlation between the disk vibration amplitude and the pressure fluctuation between a pair of high-speed corotating disks. It also reveals the effects of the arm thickness and arm shape on the disk vibrations and the static pressure between the disks. The disk vibrations were measured using a laser Doppler vibrometer (LDV). The static pressure downstream of the arm between a pair of narrow disks was measured by a method in which a side-hole needle was used as a measurement probe. In addition, the direction of air flow along the trailing edge of the arm was measured using a hot-wire anemometer. The experimental results revealed that the arm inserted between the disks suppresses the disk vibrations. However, the shape and thickness of the arm did not quantitatively affect the disk vibrations. The root-mean-square (RMS) static pressure fluctuation downstream of the arm decreased remarkably, whereas the mean static pressure increased when the arm was inserted between the disks. Furthermore, the circumferential variations in both the RMS and mean static pressures reduced when the arm was inserted. Therefore, it is suggested that the disk vibrations are excited by an increase in the static pressure fluctuation, mean dynamic pressure, and circumferential variation in the static pressure between the disks. Consequently, the disk vibrations can be suppressed by inserting the arm or a spoiler.

Topics: Pressure , Vibration , Disks
Commentary by Dr. Valentin Fuster