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IN THIS ISSUE

### TECHNICAL PAPERS

J. Fluids Eng. 2007;129(6):669-673. doi:10.1115/1.2734183.

The effects of foil geometry on partial and transitional cavity oscillations were examined by experiments. The transitional cavity oscillation can be observed in the upstream pressure fluctuation for all foils and the amplitude of oscillation becomes larger when the maximum cavity length becomes larger than about 75% of the chord length. The Stroulal number based on the chord length correlated with the value of a parameter $σ∕2α$ and increased from 0.07 to 0.17 with the increase of $σ∕2α$ from 2.0 to 6.0 for all foils. For thicker foils, the partial cavity oscillation could not be detected in the upstream pressure fluctuation. However, semi-periodical cavity shedding corresponding to the partial cavity oscillation could be visually observed for all foils and the Strouhal number based on the mean cavity length was about 0.15–0.35 for all foils. Thus, the effect of foil geometry appears only in the strength of partial cavity oscillation.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):674-681. doi:10.1115/1.2734212.

The effects of the Reynolds number and angle of attack on the boundary layer and the aerodynamic performance of a finite swept-back wing are studied experimentally. The cross-sectional profile of the wing is NACA 0012 (aspect ratio=10), and the sweep-back angle is 15 deg. The Reynolds number is set in the range of 30,000–130,000. The boundary layer field is visualized with surface oil-flow techniques. Six characteristic flow regimes—laminar separation, separation bubble, leading-edge bubble, bubble burst, turbulent separation, and bluff-body wake—are categorized and studied by considering the Reynolds numbers and angles of attack. The characteristic behaviors of boundary layer significantly affect the lift, drag, and moment coefficients. The bubble length shortens significantly in the separation bubble and leading-edge bubble regimes as the angle of attack rises. The aerodynamic performances demonstrate that the swept-back wing model has no hysteresis.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):682-694. doi:10.1115/1.2734236.

Injectors are to be installed in a transonic wind tunnel with the ultimate objective of expanding the Reynolds number envelope. The aim of this research effort is to numerically simulate the steady mixing process involving the supersonic jets and the tunnel subsonic main stream. A three-dimensional, Reynolds-averaged Navier–Stokes numerical code was developed following the main lines of the finite-difference diagonal algorithm, and turbulence effects are accounted for through the use of the Spalart and Allmaras one-equation scheme. This paper focuses on the “design point” of the tunnel, which establishes (among other specifications) that the static pressures of both streams at the entrance of the injection chamber are equal. Three points are worth noting. The first is related to the numerical strategy that was introduced in order to mimic the real physical process in the entire circuit of the tunnel. The second corresponds to the solution per se of the three-dimensional mixing between several supersonic streams and the subsonic main flow. The third is the calculation of the “engineering” parameters, that is, the injection loss factor, gain, and efficiency. Many interesting physical aspects are discussed, and among them, the formation of three-dimensional shocks’ and expansions’ “domes”

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):695-701. doi:10.1115/1.2734195.

Background: Analytical study is presented on the transient problem of buoyancy-induced motion due to the presence of a hot aerosol sphere in unbounded quiescent fluid. Method of Approach: Because the initial flow field is identically zero, the initial stage of the process is governed by viscous and buoyancy forces alone where the convective inertial terms in the momentum and energy balances are negligible, i.e., the initial development of the field is a linear process. The previous statement is examined by analyzing the scales of the various terms in the Navier-Stokes and energy equations. This scale analysis gives qualitative limitations on the validity of the linear approximation. A formal integral solution is obtained for arbitrary Prandtl number and for transient temperature field. Results: We consider, in detail, the idealized case of vanishing Prandtl number for which the thermal field is developed much faster than momentum. In this case, analytical treatment is feasible and explicit expressions for the field variables and the drag acting on the particle are derived. Detailed quantitative analysis of the spatial and temporal validity of the solution is also presented. Conclusions: The linear solution is valid throughout space for $t<10$ diffusion times. For $t>10$, an island in space appears in which inertial effects become dominant. The transient process is characterized by two different time scales: for short times, the development of the field is linear, while for small distances from the sphere and finite times, it is proportional to the square root of time. The resultant drag force acting on the sphere is proportional to the square root of time throughout the process.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):702-712. doi:10.1115/1.2734202.

This paper examines the turbulent flow of heavy particles in horizontal channels and pipes. Calculations for the fluid are performed within an Eulerian frame of reference, while the particulate phase is considered as several continuous polydisperse media, each constituting a separate phase. The interparticle collisions include two mechanisms: collisions with sliding friction and collisions without sliding friction. The collisions of particles are accounted for, by collisions due to the difference in the average and fluctuating velocities of the several particulate fractions. This work introduces an original model for the closure for the mass and momentum equations based on the collisions as well as an original description of the particle motion in a horizontal channel, by introducing the decomposition of the particle-phase motion into two types of particle phases: falling and rebounding particles. The decomposition allows the correct calculation of the influence of the wall on the motion of particles.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):713-719. doi:10.1115/1.2734223.

This paper presents numerical results of the interfacial dynamics of axisymmetric liquid-liquid flows when the denser liquid is injected with a parabolic inlet velocity profile into a coflowing lighter fluid. The flow dynamics are studied as a function of the individual phase Reynolds numbers, viscosity ratio, velocity ratio, Bond number, and capillary number. Unsteady, axisymmetric flows of two immiscible fluids have been studied using commercial software, $FLUENT®$ with the combination of volume of fluid (VOF) and continuous surface force (CSF) methods. The flows have been categorized as “flow-accelerated regime (FAR) and “flow-decelerated regime” (FDR) based on acceleration/deceleration of the injected fluid. The injected jet diameter decreases when the average inlet velocity ratio is less than unity. The outer fluid velocity has a significant effect on the shape and evolution of the jet as it progresses downstream. As the outer liquid flow rate is increased, the intact jet length is stretched to longer lengths while the jet radius is reduced due to interfacial stresses. The jet radius appears to increase with increasing viscosity ratio and ratio of Bond and capillary numbers. The results of numerical simulations using $FLUENT$ agree well with experimental measurements and the far-field self-similar solution.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):720-730. doi:10.1115/1.2734224.

The motivation of this work is to develop a numerical tool to explore a new propeller design with dual-cavitating characteristics, i.e., one that is capable of operating efficiently at low speeds in subcavitating (fully wetted) mode and at high speeds in the supercavitating mode. To compute the hydrodynamic performance, a three-dimensional (3D) potential-based boundary element method (BEM) is presented. The BEM is able to predict complex cavitation patterns and blade forces on fully submerged and partially submerged propellers in subcavitating, partially cavitating, fully cavitating, and ventilated conditions. To study the hydroelastic characteristic of potential designs, the 3D BEM is coupled with a 3D finite element method (FEM) to compute the blade stresses, deflections, and dynamic characteristics. An overview of the formulation for both the BEM and FEM is presented. The numerical predictions are compared to experimental measurements for the well-known Newton Rader (NR) three-bladed propeller series with varying pitch and blade area ratios. Comparison of the performance of the Newton Rader blade section to conventional blade sections is presented.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):731-736. doi:10.1115/1.2734238.

Recent testing of high-speed cavitating turbopump inducers has revealed the existence of more complex instabilities than the previously recognized cavitating surge and rotating cavitation. This paper explores one such instability that is uncovered by considering the effect of a downstream asymmetry, such as a volute on a rotating disturbance similar to (but not identical to) that which occurs in rotating cavitation. The analysis uncovers a new instability that may be of particular concern because it occurs at cavitation numbers well above those at which conventional surge and rotating cavitation occur. This means that it will not necessarily be avoided by the conventional strategy of maintaining a cavitation number well above the performance degradation level. The analysis considers a general surge component at an arbitrary frequency $ω$ present in a pump rotating at frequency $Ω$ and shows that the existence of a discharge asymmetry gives rise not only to beat components at frequencies, $Ω−ω$ and $Ω+ω$ (as well as higher harmonics), but also to rotating as well as surge components at all these frequencies. In addition, these interactions between the frequencies and the surge and rotating modes lead to “coupling impedances” that effect the dynamics of each of the basic frequencies. We evaluate these coupling impedances and show not only that they can be negative (and thus promote instability) but also are most negative for surge frequencies just a little below $Ω$. This implies potential for an instability involving the coupling of a surge mode with a frequency around $0.9Ω$ and a low-frequency rotating mode about $0.1Ω$. We also examine how such an instability would be manifest in unsteady pressure measurements at the inlet to and discharge from a cavitating pump and establish a “footprint” for the recognition of such an instability.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):737-746. doi:10.1115/1.2734186.

The flow field in a cylindrical container driven by a flat-bladed impeller was investigated using particle image velocimetry (PIV). A range of Reynolds numbers (0.005–7200), based on the container radius $rw$, were investigated using four Newtonian fluids: water $(Re=7200,6800)$, 85/15 glycerin/water mixture $(Re=108)$, pure glycerin $(Re=8)$, and corn syrup $(Re=0.02,0.005)$. Two impellers with a radius of $0.43rw$ and $0.95rw$ were used to drive the flow. The $0.43rw$ impeller was shown to generate a vortex near the tip of the blades. The peak magnitude of the vortices and the size of the vortices in the radial direction decreased with increasing Reynolds number. Additionally, the vortex generated at the high Reynolds number was unsteady with a trailing shear layer that periodically shed vorticity into the flow field. The structure of the flow in the region between the blade and the cylinder wall showed a Reynolds number dependence, though the two lowest Reynolds number (0.02 and 8) flows investigated had quantitatively similar flow structures. These cases were found to have a closed region of reverse flow between the blade tip and the cylinder wall. No recirculating flow was indicated for the $Re=108$ and 7200 cases. These data indicate that there may be a critical condition below which there is little dependence in the flow structure on the Reynolds number.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):747-763. doi:10.1115/1.2734188.

This paper experimentally investigates the individual and combined effects of periodic unsteady wake flows and freestream turbulence intensity (FSTI) on flow separation along the suction surface of a low-pressure turbine blade. The experiments were carried out at a Reynolds number of 110,000 based on the suction surface length and the cascade exit velocity. The experimental matrix includes freestream turbulence intensities of 1.9%, 3.0%, 8.0%, and 13.0%, and three different unsteady wake frequencies with the steady inlet flow as the reference configuration. Detailed boundary layer measurements are performed along the suction surface of a highly loaded turbine blade with a separation zone. Particular attention is paid to the aerodynamic behavior of the separation zone at different FSTIs at steady and periodic unsteady flow conditions. The objective of the research is (i) to quantify the effect of FSTIs on the dynamics of the separation bubble at steady inlet flow conditions and (ii) to investigate the combined effects of $Tuin$ and the unsteady wake flow on the behavior of the separation bubble.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2007;129(6):764-772. doi:10.1115/1.2734206.

An experimental investigation of an aerodynamic shroud applied to an axial ventilation fan system is reported. The aerodynamic shroud consists of a pressurized plenum and Coanda attachment surface, which also serves as the shroud for the fan. This combination delivers a curved surface wall jet of high momentum air into the tip region of the fan and subsequently into the downstream diffuser region. Simultaneous improvements of performance and efficiency were found for a specific fan geometry with an aerodynamic shroud system when compared with a standard production fan (no shroud) system. Overall, the addition of the aerodynamic shroud was able to increase the system flowrate by 34% while simultaneously improving the efficiency by 13%. A higher efficiency condition $(+17%)$ was also found that resulted in a somewhat lower improvement in flow rate $(+23%)$. These results clearly show that the best blade design for the aerodynamic shroud system is different than the best blade design for a system that does not include the aerodynamic shroud. Particle image velocimetry measurements made at the exit plane of the system’s diffuser provide insight into the mechanistic basis for the performance measurements.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):773-779. doi:10.1115/1.2734249.

Unsteady static pressure signals due to flow instability in two types of centrifugal compressors were analyzed by employing the phase portrait reconstruction method. The sampled data corresponded to several streamwise locations along the shroud wall over a wide range of operation from design to near surge. Singular value decomposition analysis yielded successfully the discernable features of flow instability, i.e., stall and surge, which were observed with a decrease of mass flow rate. The effects of the signal-to-noise ratio was found to be the most troublesome in predicting the onset of flow instability upon pursuing the attractor behavior of the portraits. Under the latter difficult circumstance, the correlation integrals were also conveniently calculated to help to check the onset. It was clearly indicated that the behavior near rotating stall was not always recognized by the phase portrait in three-dimensional space, while the corresponding correlation integral obviously decreased close to stall. Monitoring of unsteady signals based on the phase portraits and the correlation integrals, therefore, led to a good judgement of a nonlinear fluid dynamic system response and to prevent compressors from a disastrous damage due to flow instability.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):780-790. doi:10.1115/1.2734225.

A random flow generation (RFG) algorithm for a previously established large eddy simulation (LES) code is successfully incorporated into a finite element fluid flow solver to generate the required inflow/initial turbulence boundary conditions for the three-dimensional (3D) LES computations of viscous incompressible turbulent flow over a nominally two-dimensional (2D) circular cylinder at Reynolds number of 140,000. The effect of generated turbulent inflow boundary conditions on the near wake flow and the shear layer and on the prediction of integral flow parameters is studied based on long time average results. Because the near-wall region cannot be resolved for high Reynolds number flows, no-slip velocity boundary function is used, but wall effects are taken into consideration with a near-wall modeling methodology that comprises the no-slip function with a modified form of van Driest damping approach to reduce the subgrid length scale in the vicinity of the cylinder wall. Simulations are performed for a 2D and a 3D configuration, and the simulation results are compared to each other and to the experimental data for different turbulent inflow boundary conditions with varying degree of inflow turbulence to assess the functionality of the RFG algorithm for the present LES code and, hence, its influence on the vortex shedding mechanism and the resulting flow field predictions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):791-798. doi:10.1115/1.2734237.

A new simulation technique called the system modal approximation method (SMA) for fluid transients in complex pipeline systems has been proposed. The superiority of this technique compared to other existing methods has been verified. Thus far, however, detailed considerations have been limited to pipelines having elementary boundary conditions. In the present paper, for the generalization of the SMA method, calculation methods are newly proposed for the case in which the boundary conditions are given by the time-variant nonlinear relationship between pressure and flow rate, such as the conditions in a safety valve, and its usefulness is verified by comparison to experimental measurements.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 2006;129(6):799-805. doi:10.1115/1.2734250.

This paper presents an experimental study to characterize fluid leakage through a rough metal contact. The focus is on an original experimental setup and procedure designed to measure the fluid micro (or nano) leak rate with great precision over several orders of magnitude. Liquid leak-rate measurements were carried out under two distinct operating conditions, i.e., in the case of a pressure gradient applied between contact edges and in the case of a pure diffusive effect resulting from a species concentration gradient. Experimental leak-rate results are discussed in terms of effective contact permeability—or transmissivity—and in terms of effective contact diffusivity versus contact tightening.

Commentary by Dr. Valentin Fuster

### TECHNICAL BRIEF

J. Fluids Eng. 2007;129(6):806-810. doi:10.1115/1.2734251.

The theory of micropolar fluids based on a Cosserat continuum model is utilized for analysis of two benchmarks, namely, plane-Couette and pressure-driven channel flows. In the obtained theoretical velocity distributions, some new terms have appeared in addition to linear and parabolic distributions of classical fluid mechanics based on the Navier-Stokes equations. Utilizing the principles of irreversible thermodynamics, a new dissipative boundary condition is developed for angular velocity at flat plates by taking the couple-stress vector into account. The obtained results for the velocity profiles have been compared to results of recent and classical experiments. This paper demonstrates that continuum mechanical theories of higher orders, for instance Cosserat model, are able to describe a complex phenomenon, such as hydrodynamic turbulence, more precisely.

Commentary by Dr. Valentin Fuster

### ANNOUNCEMENT

J. Fluids Eng. 2007;129(6):811. doi:10.1115/1.2750331.
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ASTM's Subcommittee G02.10 on Erosion would like to hear from you if you have any interest in cavitation erosion testing. Do you (or your organization):

Commentary by Dr. Valentin Fuster