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J. Fluids Eng. 1991;113(4):523-525. doi:10.1115/1.2926510.
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Abstract
Commentary by Dr. Valentin Fuster

RESEARCH PAPERS

J. Fluids Eng. 1991;113(4):526-537. doi:10.1115/1.2926511.

The results of recent experiments demonstrate that the phenomenon of vortex shedding resonance or lock-on is observed also when a bluff body is placed in an incident mean flow with a periodic component superimposed upon it. This form of vortex shedding and lock-on exhibits a particularly strong resonance between the flow perturbations and the vortices, and provides one of several promising means for modification and control of the basic formation and stability mechanisms in the near-wake of a bluff body. Examples are given of recent direct numerical simulations of the vortex lock-on in the periodic flow. These agree well with the results of experiments. A discussion also is given of vortex lock-on due to body oscillations both normal to and in-line with the incident mean flow, rotational oscillations of the body, and of the effect of sound on lock-on. The lock-on phenomenon is discussed in the overall context of active and passive wake control, on the basis of these and other recent and related results, with particular emphasis placed on active control of the circular cylinder wake.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):538-543. doi:10.1115/1.2926512.

Uncertainties are inherent in computational fluid dynamics (CFD). These uncertainties need to be systematically addressed and managed. Sources of these uncertainties are identified and some aspects of uncertainty analysis are discussed. Some recommendations are made for quantification of CFD uncertainties. A practical method of uncertainty analysis is based on sensitivity analysis. When CFD is used to design fluid dynamic systems, sensitivity-uncertainty analysis is essential.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):544-554. doi:10.1115/1.2926513.

A model is developed to simulate two-dimensional laminar flow over an arbitrarily shaped body, a portion of which is subjected to time varying harmonic motion. The model is tested by comparison to previous numerical simulations for flow over a square cavity, oscillatory flow through a wavy channel and boundary layer flow along a flat plate. The model is applied to predict the flow over a flat plate with a section forced in simple sinusoidal motion. The dimensionless vibration amplitude, H0 , and the Reynolds number, Re are maintained at 0.1 and 1000, respectively. The Strouhal number, St , defined as the ratio of the flow advective time scale to the plate oscillation period, is varied in the range 0.0 ≦ St ≦ 1.0. The friction and pressure coefficients over the vibrating portion of the body are analyzed using Fast Fourier Transform techniques. For low frequency vibrations (low Strouhal number) the pressure and friction coefficients match the steady state results for flow over a fixed sinusoidal bump. A small amplitude pressure wave generated by the oscillating plate propagates downstream with the flow. For high frequency vibrations (high Strouhal number) the pressure and friction coefficients over the vibrating portion of the body deviate from the steady state results and a high amplitude pressure wave propagates downstream. The pressure at one chord length upstream is also affected. As St increases the flow becomes highly nonlinear and harmonics appear in the downstream velocity and pressure fields. The nonlinearity is controlled by the convective acceleration term near the vibrating plate surface.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):555-562. doi:10.1115/1.2926514.

The complete form of the Navier-Stokes equations is solved in this paper for a steady, incompressible, fully developed laminar flow in a curved duct of elliptic cross section. This is achieved by the use of the control volume-based finite difference method via the numerically generated boundary fitted coordinate system. The curvature ratio is included in the primitive variable governing equations, which are solved based on the SIMPLE algorithm. Solutions are obtained for the minor-axis to major-axis ratios of the elliptic duct, 0.2, 0.5, and 0.8, and for Dean numbers ranging from 11.41 to 635.7. It is found that only one pair of vortices appears on the cross-section, even at a Dean number of 635.7. The friction factor and the ratios of the curved duct to straight duct are tabulated and the correlation equation is developed. Furthermore, the distribution of the axial velocity is displayed graphically to illustrate its variations with the Dean number and the minor-axis to major-axis ratio of the elliptic duct on the horizontal symmetry line and on the half-vertical symmetry line. The present method is also applied to solve for a fully developed laminar flow in a curved square flow. The results are compared with the data available in the literature and very close agreement is observed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):563-568. doi:10.1115/1.2926515.

Three different discretization schemes were used to study the flow in a 90-degree bend square duct. The numerical method consists of a general curvilinear coordinate formulation of the governing equations and a non-staggered grid for the variables. A stable method of implementing the higher-order schemes is proposed. The second-order upwinding and QUICK schemes give results which compare more favourably with the experimental data than the first-order upwinding method. In 3-D flow problems, the grid-refinement is severely limited by the amount of computer storage and the use of higher-order upwinding schemes provides a better alternative in obtaining accurate flow predictions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):569-573. doi:10.1115/1.2926516.

Zielke’s technique of using a method of characteristics to simulate transient phenomena of a liquid transmission line is accurate, easy to apply to complicated systems and therefore, frequently used. However, it requires a very large amount of computation time and computer storage to simulate frequency-dependent friction in a transient liquid flow. Searching for a way to counteract these disadvantages, the authors took note of the fact that the weighting function, which is the root of the above problems, is given by exponential functions or other functions depending on dimensionless time. In order to perform mathematically equivalent calculation without approximations, they have developed a new method which requires much less computation time and computer storage than Zielke’s method. The calculation process is shown by a block diagram to facilitate visual understanding of the method.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):574-578. doi:10.1115/1.2926517.

The boundary layer over a wavy wall and fully-developed flow in a duct with a wavy wall are considered. Numerical solutions of the Navier-Stokes equations have been obtained to provide insights into the various steady flow regimes that are possible, and to illustrate the nuances of predicting flows containing multiple separation and reattachment points.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):579-586. doi:10.1115/1.2926518.

A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations, together with a two-layer turbulence model, has been used to describe steady flow in a two-dimensional channel with a wavy wall. Comparisons of calculations with experiments demonstrate the effects of alternating pressure gradients induced by alternating surface curvatures, and multiple separations and reattachments. The numerical method and the turbulence model are shown to capture the overall features of such a flow, including the breakdown of the logarithmic law of the wall in strong pressure gradients and in separated flow.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):587-590. doi:10.1115/1.2926519.

Pipes with V shape riblets were tested at Reynolds numbers between 5×103 and 4×104 . All riblet pipes indicated some drag reduction. The model with h = 0.55 mm and h/S = 0.483 showed the maximum drag reduction of 8 percent and the widest range of Reynolds number over which the riblet reduces drag. The riblet shape desirable for drag reduction in pipe flows was almost the same as that in flat plate boundary layers, but the value of S+ which provided the maximum drag reduction was quite different; S+ = 23 for pipe flows and S+ = 12 for flat plate boundary layers.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):591-597. doi:10.1115/1.2926520.

The effect of suction on the second (Mack) mode of instability in supersonic and hypersonic two-dimensional boundary layers is investigated. The results show that suction has a stabilizing effect on these waves; it reduces the peak amplification and shifts it toward a higher frequency. In the presence of suction, the most amplified Mack mode remains two-dimensional. The effectiveness of suction in stabilizing Mack waves decreases as the Mach number increases. Variations of the growth rates of the most amplified Mack mode and the corresponding frequencies and wave numbers with mass flux are found to be almost linear. The frequencies and wave numbers corresponding to the most amplified Mack mode increase by increasing the suction level.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):598-601. doi:10.1115/1.2926521.

The effect of suction on the first mode of instability of compressible two-dimensional boundary layers is investigated. Suction is found to be more effective in stabilizing the viscous instability, and hence it is more effective at low Mach numbers. Suction decreases the amplification rates at all frequencies and narrows down the band of unstable frequencies. Moreover, for a given frequency, suction decreases the amplification rates at all streamwise locations. Variations of the growth rates of the most amplified first-mode waves with mass flux are found to be almost linear.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):602-607. doi:10.1115/1.2926522.

Easily applied methods are proposed, based on tests with air and water, for direct determination of the onset of transition in flow passages using static and dynamic wall pressure data. With increasing Reynolds number from laminar flow, the characteristic feature of transition is the change from steady to oscillating pressure readings. It is established that the power spectral density (psd) representations exhibit a distinctive change in profile at transition. Further, it is shown that the root-mean-square (rms) values of the wall pressure fluctuations rise sharply at transition. The critical Reynolds numbers recorded via the change from steady to unsteady pressure readings are almost the same as those deduced from the psd and rms pressure data or from the familiar friction factor-Reynolds number plots.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):608-615. doi:10.1115/1.2926523.

Three-dimensional developing turbulent flow in a square duct involving turbulence-driven secondary motion is numerically predicted with an anisotropic low-Reynolds-number k-ε turbulence model. Special attention has been given to both regions close to the wall and the corner, which are known to influence the characteristics of secondary flow a great deal. Hence, the no-slip boundary condition at the wall is directly used in place of the common wall function approach. The resulting set of equations simplified only by the boundary layer assumption are first compared with previous algebraic stress models, and solved with a forward marching numerical procedure for three-dimensional shear layers. Typical predicted quantities such as mean axial and secondary velocities, friction coefficients, turbulent kinetic energy, and Reynolds shear stress are compared with available experimental data. These results indicate that the present anisotropic k-ε turbulence model performs quite well for this complex flow field.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):616-619. doi:10.1115/1.2926524.

The mean velocity profile across a fully developed turbulent duct flow is obtained from an eddy viscosity relation combined with an empirical outer region wake function. Results are in good agreement with experiments and with direct numerical simulations in the same flow at two Reynolds numbers. In particular, the near-wall trend of the Reynolds shear stress and its variation with Reynolds number are similar to those of the simulations. The eddy viscosity method is more accurate than previous mixing length or implicit function methods.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):620-628. doi:10.1115/1.2926525.

This paper reports experimental investigations on mean and turbulence characteristics of three-dimensional, incompressible, isothermal turbulent wall jets generated from orifices having the shapes of various segments of a circle. In Part 1, the mean flow characteristics are presented. The turbulence characteristics are presented in Part 2. The influence of the geometry on the characteristic decay region of the wall jet is brought out and the differences with other shapes are discussed. Mean velocity profiles both in the longitudinal and lateral planes are measured and compared with some of the theoretical profiles. Wall jet expansion rates and behavior of skin-friction are discussed. The influence of the geometry of the orifice on the various wall jet properties is presented and discussed. Particularly the differences between this class of geometry and rectangular geometries are critically discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):629-634. doi:10.1115/1.2926526.

The mean flow characteristics of three-dimensional, incompressible, isothermal turbulent wall jets generated from orifices having the shapes of various segments of a circle are presented in Part 1 of this paper. In this part, the turbulence characteristics are presented. Turbulence quantities measured include normal stresses and Reynolds shear stresses in the characteristic-decay and in the radial-decay regions of the wall jets investigated. These results are compared with those available for two-dimensional and three-dimensional wall jets. The presence of counter-gradient regions and the feature of “energy reveral” are discussed.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):635-642. doi:10.1115/1.2926527.

Experimental measurements were carried out in an incompressible three-dimensional turbulent shear layer in the vicinity of an appendage mounted perpendicular to a flat plate. The thickness of the turbulent boundary layer as it approached the appendage leading edge was 76 mm or 1.07 times the maximum thickness of the appendage. As the oncoming boundary layer passed around the appendage, a strong secondary flow was formed which was dominated by a horseshoe root vortex. This secondary flow had a major effect in redistributing both the mean flow and turbulence quantities throughout the shear layer, and this effect persisted to a significant degree up to at least three chord lengths downstream of the appendage leading edge.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):643-647. doi:10.1115/1.2926528.

The maximum pressure head resulting from one-speed closure of wide open valves is investigated. The dimensionless variables formulated in this study make the subtle effect of the initial valve head loss explicit and separate from that of the pipe frictional head loss. The maximum head is related to initial pipe frictional head loss, the initial valve head loss, the inherent flow characteristic of the valve, and the closure period by plots of dimensionless variables. The trends of the variation of the maximum pressure head are discussed. An example is used to illustrate the usage of the plots, and to show the advantage of having a global perspective of the phenomenon in the selection and sizing of valves from the water hammer point of view.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):648-653. doi:10.1115/1.2926529.

Torque measurements, which can be related to viscous dissipation, were made in a simulated disk drive consisting of a single or multiple corotating disk stack enclosed in an axisymmetric shroud. The effects of rotational velocity, axial and radial spacing, and the position and thickness of simulated read/write arms between disks on torque were studied. Correlations are presented to describe the results of the unobstructed cases and the cases with the read/write arms at their innermost position, and a method is introduced to calculate the torque at intermediate arm positions.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):654-659. doi:10.1115/1.2926530.

Within the framework of the technological development of the VULCAIN rocket engine (Ariane V European project), initiated by the Centre National d’Etudes Spatiales (CNES) for the Agence Spatiale Européenne (ESA), the Société Européenne de Propulsion (SEP) is in charge of the design and building of the liquid hydrogen turbopump. In order to characterize the hydraulic performance of the pump, an air test facility reproducing the pump geometry was built by SEP and fitted in the Laboratoire de Mécanique des Fluides et d’Acoustique of the Ecole Centrale de Lyon. Benefits and disadvantages of air tests of hydraulic pumps are discussed. The pump is composed of three stages. The first one is an axial inducer stage. The second and third ones are centrifugal stages with vaned diffusers and are separated by a U bend and a vaned return channel. Results of the first measurement campaign are presented. They consist of overall pressure, wall static pressure and velocity measurements. Local quantities (velocity triangle, pressure) and mean quantities (pressure rise, losses, efficiency) are given. Recirculating and wake flow analysis are included. The goals of the study are the understanding of the flow behavior and the improvement of the prediction methods. Predicted and measured quantities (losses, efficiency, kinetic momentum) are compared. The hydrogen performances are deduced, they agree with the specified performances of the pump. This validation is one of the main results achieved.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):660-667. doi:10.1115/1.2926531.

The results of LDV measurements and investigation of the detailed flow field in a radial inflow turbine nozzle are presented. The flow velocities were measured at upstream, inside and downstream of the nozzle blades for two different mass flow rates, using a three-component LDV system. Results are presented as contour plots of mean velocities, flow angles, and turbulence intensities. The flow field inside the nozzle blade passages was found to be influenced by the upstream scroll geometry. The flow turbulence increased in the downstream flow direction. The LDV mean flow results on the blade-to-blade midspan plane which is parallel to the end walls were also compared with an inviscid, “panel method” solution.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):668-674. doi:10.1115/1.2926532.

Laser-Doppler measurements of mean and turbulent velocity characteristics are reported in the developing region of the isothermal flow of a model of an industrial oxy-fuel burner. The burner consists of a central axisymmetric jet surrounded by sixteen circular jets, simulating the injection of oxygen in pratical burners. Errors incurred in the laser-Doppler measurements are estimated and bias effects due to unequal number density of seed particles in the various jet flows are investigated. The experiments have been carried out to investigate the mixing efficiency of the burner assembly without swirl motion and to assess the accuracy of calculation procedures in industrial burners. The results show that the present flow develops faster than related coaxial free jets with the same velocity ratio between central and peripheral air streams due to the comparatively high mixing rate peculiar to the present configuration. The existence of zones characterized by large turbulence anisotropy indicates the need to take account of the normal stresses in any proposed mathematical model to simulate the present flow field.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):675-680. doi:10.1115/1.2926533.

We consider the steady flow of five commonly encountered hydrocarbons in their dense gas regime. Isentropic flows are first examined and it is shown that dense gas effects lead to a non-monotone variation of the Mach number with density. It is also demonstrated that these effects may give rise to an increase, rather than the classical decrease, in the Mach number across oblique compression shocks. Significant increases in the shock detachment angle are also reported.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):681-688. doi:10.1115/1.2926534.

A mathematical formulation is developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible, two-dimensional Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. Two approaches to determine the aerodynamic sensitivity coefficients, namely, the finite difference approach, and the quasi-analytical approach are discussed with regards to their relative accuracies and involved computational efforts. In the quasi-analytical approach, the direct and the adjoint variable methods are formulated and assessed. Also, several methods to solve the system of linear algebraic equations, that arises in the quasi-analytical approach, are investigated with regards to their accuracies, computational time and memory requirements. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flow-field solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):689-694. doi:10.1115/1.2926535.

A theoretical study of the free-surface flow of a viscoelastic fluid around a horizontal cylinder is reported in this paper. The fluid layer has initially a uniform thickness, and, at some instant of time, it starts to flow due to the presence of a gravity field. The result sought is the film thickness as a function of time and angular position. The mass- and momentum-conservation principles are employed in conjunction with the Maxwell constitutive equation. Using an integral method, a system of two nonlinear equations is obtained. The results are compared with the ones for a Newtonian fluid, and the elastic effects are shown to change dramatically the flow.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):695-698. doi:10.1115/1.2926536.

This work is concerned with the effects of flow separation and surface nuclei on the operation of a fixed geometry Cavitation Susceptibility Meter (CSM) with laminar flow. Cavitation is induced under controlled conditions at the throat of a glass venturi tube for the measurement of the active nuclei concentration in water samples as a function of the applied tension. Both cavitation and flow velocity are monitored optically by a Laser Doppler Velocimeter. The throat pressure is determined indirectly from the upstream pressure and the local flow velocity. The results show that laminar flow separation and surface nuclei effects are the most stringent operational limitations. Separation in the diffuser increases the minimum attainable throat pressure above the susceptibility of most cavitation nuclei commonly found in technical waters. Surface nuclei can generate extensive sheet or spot cavitation at relatively high tensions even on optically finished glass surfaces. These phenomena are difficult to eliminate and bring therefore into question the practical utility of CSM’s with laminar flow and fixed geometry for the measurement of the dependence of the cavitating nuclei concentration over wide ranges of the applied tension, as required for cavitation studies.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):700-706. doi:10.1115/1.2926539.

An optical interferometric technique has been used to determine the 3-D shape of cavitation erosion pits. The method which is particularly suitable to the determination of pit diameter and pit depth is used for a statistical analysis of cavitation erosion pits. We analyzed numerous samples which were eroded at various velocities with two different fluids (mercury and water) on two geometrically similar venturi test sections of different length scales. General properties of histograms of pit size are pointed out. The influence of flow velocity on pitting rates corresponding to limited ranges of pit size is discussed. The contribution of each pit diameter to the total eroded surface is analyzed. Some results are given on pit depths and pit volumes.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

TECHNICAL BRIEFS

J. Fluids Eng. 1991;113(4):707-709. doi:10.1115/1.2926540.

It is shown that the hypothesis of local isotropy is implausible in the presence of significant mean rates of strain. In fact, it appears that in uniform shear flow near equilibrium, local isotropy can never constitute a systematic approximation, even in the limit of infinite Reynolds number. An estimate of the level of mean strain rate for which local isotropy is formally a good approximation is provided.

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):709-712. doi:10.1115/1.2926541.

Gas contained in a rectangular laser cell of large length and small width is subjected to large, transient, spatially nonuniform, volumetric heating when pumped. The heating time scale is much longer than the time required for an acoustic wave to traverse the width but can be comparable to the time required for an acoustic wave to traverse the length. Approximate equations describing the motion are derived by applying partial acoustic filtering to the equations of motion: pressure waves traversing the width are removed while pressure waves traversing the length are retained. For a simplified one-dimensional example, a significant density variation is found across the width of the laser cell; moreover, this density variation is in good agreement with a numerical solution of the unapproximated gas dynamic equations although the latter requires two orders of magnitude more computational time

Commentary by Dr. Valentin Fuster
J. Fluids Eng. 1991;113(4):712-714. doi:10.1115/1.2926542.
Abstract
Commentary by Dr. Valentin Fuster

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