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RESEARCH PAPERS

J. Basic Eng. 1970;92(3):405-410. doi:10.1115/1.3425012.

An analysis is made of the rate of the mass flow through a vacuum seal separating two rarefied gas environments. The determination of the mass throughflow characteristics involves the formulation and solution of a coupled system of six integral equations. The formulation is performed using the methods of kinetic theory. Numerical solutions are carried out for a wide range of values of the seal geometrical parameter. Mass flow results evaluated from these solutions are presented graphically. In addition, representative distributions of the mass fluxes at the participating surfaces are given.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):411-418. doi:10.1115/1.3425015.

Data are presented for the flow of deionized water solutions of linear, unbranched polymers—Separan AP-30, Polyox WSR-35 and Polyox WSR-301, and mixtures of the latter two in a 0.0235 in. tube. The Reynolds numbers vary from about 1200 to about 12,000. Measurements were made at 4 deg C and near room temperature. Occurrence of transition is confirmed by oscillograph traces and pressure ratio calculations in addition to the usual “break” on a friction factor-Reynolds number graph. From the calibration data, it appears that for small tubes there is a critical parameter, such as molecular weight or polymer length, below which transition occurs as for water, but above which the transition Reynolds number depends on polymer concentration. The low and high polymers were mixed to vary molecular weight distribution of samples. It was found that the higher molecular weight polymer dominates the transition process, but in the turbulent regime the effects are roughly additive.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):419-428. doi:10.1115/1.3425017.

A centrifugal compressor stage with an unusually high inlet hub/tip ratio of 0.87 was designed for a pressure ratio of 2.0 at a corrected mass flow of 2.45 lb per sec. The geometry was selected so that the centrifugal stage could replace several of the last stages of a multistage axial compressor. The stage was tested with two diffuser schemes. One diffuser consisted of a series of drilled conical pipes, whereas the other employed multirow vaned cascades. Sea level aerodynamic tests of the compressor stage with each diffuser showed a peak total-to-total efficiency at design speed of 83.8 percent for the pipe diffuser and 82.9 percent for the vaned cascade diffuser. Additional tests were conducted with a vaneless diffuser to determine effects of impeller discharge tip clearance and inlet prewhirl on impeller performance.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):430-435. doi:10.1115/1.3425021.

The flow of a homogeneous incompressible fluid past a right circular cylinder in a rotating frame is considered; the axis of the cylinder is taken parallel to the axis of rotation while the cylinder is bounded above and below by two infinite parallel flat plates. A series of experiments are presented which qualitatively describe the flow for an aspect ratio of 1.0 and Rossby and Ekman number ranges of (10)−2 < Ro < 1.0 and (10)−4 < E < (10)−3 , respectively. The flow regimes differ significantly from those occurring in nonrotating systems.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):437-447. doi:10.1115/1.3425025.

Previously reported experiments on incompressible flow through a step expansion in a pipe, as influenced by suction at the smaller diameter of the step, have been extended to examine effects of inlet flow on suction requirements and performance of the device as a (short) diffuser. Here the performance for a fully developed turbulent pipe flow is considered and compared to previous results for an inlet flow with thin boundary layer. Whenever overall diffuser length is restricted to values less than some upper limit for a given expansion ratio, then for either inlet flow condition, the present device is shown to produce higher pressure recoveries (adjusted for suction power) than conical diffusers.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):450-458. doi:10.1115/1.3425028.

Sources of noise in axial-flow machines are studied theoretically with the aid of a simplified two-dimensional model. The analysis leads to estimates of the discrete-frequency sound output from interacting blade rows, and provides a basis for subsequent study of broad-band sources.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):459-463. doi:10.1115/1.3425031.

Experiments were carried out to study the effect of dilute aqueous polymer solutions on flow-generated cavitation inception. The cavitation inception on 1/4 and 1/2 -in-dia models with a hemispherical nose in a blowdown water tunnel was definitely inhibited at Reynolds numbers from 7 × 104 to 3.1 × 105 . Reduction of the incipient cavitation number to 30 percent of its value for tap water was observed, depending on the kind of polymer used, its concentration, and the Reynolds number. Flow velocity field visualization was achieved by optical techniques, which measured the flow velocities and was used to correct values computed from venturi pressure drop. For guar gum (300 ppm) tests, the computed velocities were approximately 8 percent low.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):467-480. doi:10.1115/1.3425036.

Using the author’s earlier flow model for the tip clearance flow, an expression is derived for the decrease in stage efficiency due to tip clearance. The analysis which includes all the dominant flow and blade parameters that affect the flow in the clearance region is compatible with fundamental physical principles, though not precise mathematically. The predictions agree closely with several compressor, fan, pump, and turbine data available. An alternate model which takes into account the presence of the vortex core is proposed. The theoretical treatment of the flow, more complete than hitherto available, predicts blade-to-blade variation in outlet angles accurately and stagnation pressure losses qualitatively. The predictions are compared with various experimental data available in the literature.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):483-492. doi:10.1115/1.3425040.

Mixing-throat cavitation in a liquid jet pump results from high jet velocities, low suction (NPSH) pressure, or low discharge pressure. Incipient cavitation at the jet boundary has no effect on jet pump efficiency, but under severe conditions it spreads to the walls. A limiting flow condition results which is independent of discharge pressure. Efficiency deteriorates rapidly and the pump head-flow characteristics can no longer be predicted by conventional theory. Eight correlation parameters (1937–1968) and their interrelations are examined. A Cavitation Index σL is recommended for correlation of cavitation-limited flow results. Limiting flow data from 14 references on water, oils, and mercury, plus additional data on three water jet pumps are compared, showing that 11 sets of data on water, oils, and mercury can be represented by the single-number index σL , with a range of 0.8 to 1.67. Conventional jet pumps are described by σL = 1.0 to 1.4 and σL = 1.35 is recommended for conservative use. The limiting flow function Y (NPSH) is shown to be a useful tool in comparing cavitation response to design changes. System design to avoid cavitation is facilitated by a simple limiting flow equation, ML (R, σL , NPSH, Vn ), and the equation is compared with recently published data. Cavitation can be avoided by reducing Vn , and R, or by raising suction port pressure. Flow passage contours, including nozzle-to-throat spacing, influence σL and the limiting flow ratio can also be improved by reducing σL (0.9 or less) through careful design. Systems handling high gas-solubility liquids can be improved by reducing gas content; fluid properties otherwise have little effect on this jet pump phenomenon.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):495-502. doi:10.1115/1.3425045.

The purpose of this study was to obtain extensive experimental data on the effect of skin-friction drag by suspending solid particles in air. The investigation was divided into two parts: The first study consisted of obtaining extensive experimental data on the pressure gradients (which are proportional to skin friction) encountered in circular pipes when a mixture of air with solid particles suspended in it flows through the pipe. The second part deals with the skin friction as measured on a flat plate placed flush with the floor of a wind tunnel having a dusty sub-layer. These studies involved a large range of Reynolds numbers, particle sizes, and weight-flow ratios. A theory is also presented to try and explain some of the complex flow phenomena encountered in a two-phase flow system.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):503-508. doi:10.1115/1.3425046.

An initial value method is introduced in this paper for the solution of a class of nonlinear two-point boundary value problems. The method can be applied to the class of equations where certain physical parameters appear either in the differential equation or in the boundary conditions or both. Application of this method to two problems in Fluid Mechanics, namely, Blasius’ boundary layer equation with suction (or blowing) and/or slip and the unsteady flow of a gas through a porous medium, are presented as illustrations of this method. The trial-and-error process usually required for the solution of such equations is eliminated.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):510-513. doi:10.1115/1.3425048.

A finite difference solution is presented for the laminar, compressible wake behind a flat plate at zero angle of attack. The solution of the boundary layer equations is carried out in the von Mises coordinate plane. A coordinate transformation which maps the infinite region into a finite one is also introduced. The accuracy and range of validity of the asymptotic and preasymptotic theories of Goldstein and Tollmien for the incompressible wake are discussed. The effect of the Mach number and initial conditions on the evolution of the wake is investigated. The analysis is applicable outside a trailing edge region of O(LRc −3/4 ) and for a constant density-viscosity product and Prandtl number unity.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):515-521. doi:10.1115/1.3425051.

Observed average breakup lengths are presented for free orifice jets of superheated water and liquid nitrogen, and subcooled water. Dimensionless, semiempirical expressions are developed for both flashing, and aerodynamic and/or capillary, breakup, and verified with data. The distribution function for breakup length is predicted for the superheated case with the help of Boltzmann statistics.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):523-535. doi:10.1115/1.3425054.

This paper presents a finite-difference method for solving laminar and turbulent-boundary-layer equations for incompressible and compressible flows about two-dimensional and axisymmetric bodies and contains a thorough evaluation of its accuracy and computation-time characteristics. The Reynolds shear-stress term is eliminated by an eddy-viscosity concept, and the time mean of the product of fluctuating velocity and temperature appearing in the energy equation is eliminated by an eddy-conductivity concept. The turbulent boundary layer is regarded as a composite layer consisting of inner and outer regions, for which separate expressions for eddy viscosity are used. The eddy-conductivity term is lumped into a “turbulent” Prandtl number that is currently assumed to be constant. The method has been programed on the IBM 360/65, and its accuracy has been investigated for a large number of flows by comparing the computed solutions with the solutions obtained by analytical methods, as well as with solutions obtained by other numerical methods. On the basis of these comparisons, it can be said that the present method is quite accurate and satisfactory for most laminar and turbulent flows. The computation time is also quite small. In general, a typical flow, either laminar or turbulent, consists of about twenty x-stations. The computation time per station is about one second for an incompressible laminar flow and about two to three seconds for an incompressible turbulent flow on the IBM 360/65. Solution of energy equation in either laminar or turbulent flows increases the computation time about one second per station.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):536-543. doi:10.1115/1.3425055.

A finite array of arbitrarily spaced parallel rods is considered. It is assumed that momentum deficit may be superposed locally. The momentum deficit is computed behind each cylinder—considering it as a single cylinder—using one of the accepted theories. Then the momentum deficits at each point due to all the cylinders are superposed. From this an overall velocity distribution is calculated. Experiments with various rod diameters and spacings were conducted. The results were within 3 percent of the theoretically predicted local velocity, and under 10 percent of the predicted local velocity defect (at locations of significant velocity deficits).

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):545-550. doi:10.1115/1.3425060.

The boundary-layer equations for both laminar and turbulent incompressible flows over slender bodies of revolution in axial flow are solved by an implicit finite-difference method. The Reynolds shear-stress term is eliminated by means of an eddy-viscosity concept. Velocity profiles and values of local skin-friction coefficient are obtained for various slender circular cylinders in both laminar and turbulent flows. The deviation of the cylinder skin friction from that of a flat plate is studied. The calculated velocity profiles for turbulent flow are compared with those of both Richmond’s and Yasuhara’s experimental data and with Rao’s proposed formulation of the law of the wall in thick, axisymmetric turbulent boundary layers. In both cases excellent agreement is obtained.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):555-561. doi:10.1115/1.3425065.

The natural frequency of a spherical gas-filled bubble oscillating in a viscous compressible liquid is derived. Surface tension is also included in this solution, but gravity, gas diffusion and thermal conduction are neglected. The solutions of Minneart Richardson, Neppiras and Noltingk, Hirose and Okuyama, and Houghton are shown to be special cases of this solution. The effects of liquid compressibility, surface tension, and viscosity on the natural frequency of a bubble in water is determined as a function of the static radius. The effect of ratio of specific heats of gas in a bubble is also examined.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):563-573. doi:10.1115/1.3425070.

A study of the cavitation erosion behind blunt bodies with varying hydrodynamic factors of flow, such as, the test time, length of cavity, velocity, and pressure; the geometrical parameters of the system, namely, the size and shape of the cavitating body, its aspect-ratio, and its surface roughness; and the mechanical properties of the materials, namely, the density, yield strength, tensile strength, engineering strain energy, hardness, ultimate resilience, percent elongation, percent reduction in area and elastic modulus are reported. The study of the volume eroded along with the hydrodynamic factors of the flow and the geometrical parameters of the system in general indicated that a critical zone of cavitation conditions exists in which the erosion caused is very severe. This critical zone is described by a range of values of V/l (α Strouhal frequency, f for detachment of cavities). Among the correlations studied for the inverse of rate of volume eroded as a function of individual and twin mechanical properties, the product of ultimate resilience and Brinell hardness showed the best correlation.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):580-586. doi:10.1115/1.3425076.

The mass flow rate of methane and 19 natural gas mixtures through critical flow nozzles has been calculated. The calculation assumes the flow to be one-dimensional and isentropic. The pressure range is 0 to 1000 psi and the temperature range is from 450 to 700 deg Rankine. From a study of the results, a simple empirical method for making this mass flow rate calculation is proposed. This method would apply to natural gas mixtures whose composition is known and whose components have no more than four carbon atoms.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):590-595. doi:10.1115/1.3425080.

The primary external causes of ischemic ulcers or bedsores are (a) pressure, (b) abrasion with associated shear deformations, (c) moisture, and (d) lack of cleanness. These disturbances perturb the microcirculation and inhibit the mass transport necessary to support local metabolism. These external factors can be managed through engineering analysis and design. A technique has been developed to measure the pressure distributions between the body and various support systems without perturbing the pressure distribution using a thin, pliable, pneumatic-cell, pressure-sensor. Data are presented for several existing support devices, and design requirements have been determined for an external support system for the chronically ill and debilitated which will periodically relieve and redistribute external pressures and prevent the formation (and aid in treatment) of ischemic ulcers. The design is based primarily on the physiologically allowable time-at-pressure data and the anatomy.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):597-603. doi:10.1115/1.3425083.

An analytic investigation of the cavitation hypothesis of brain injury is performed by designing a mathematical model of the skull and brain subjected to an impact load. The skull is characterized as a thin, homogeneous, isotropic, elastic spherical shell, and the brain is assumed to be an ideal acoustic fluid. Using extensional shell theory, the skull-brain system is described by three coupled, simultaneous, linear partial differential equations with variable coefficients. The equations are solved by finite difference techniques. Results demonstrate that two prime focal points of reduced pressure occur within the fluid shortly after the onset of impact. These are located at the impact pole and at the counter pole or “contrecoup” site.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):604-609. doi:10.1115/1.3425084.

Because of the small size of the human red blood cell, it is difficult to measure the elasticity of the cell membrane. Previous techniques of measuring membrane elasticity involve high stress and strain and therefore do not adequately characterize the membrane’s elasticity near its equilibrium (biconcave) shape. In order to determine elasticity at low stress and strain, an experiment was designed to involve minimal membrane stress. In the experiment, the red cells are expelled from glass micropipettes on the order of 3 microns in internal diameter. The cell is in a folded deformed shape within the confines of the tip but once it leaves the pipette the cell returns to its biconcave shape. With the use of dimensional analysis, the characteristic relaxation times of the red cells and of geometrically similar, fluid-filled model cells are compared and a modulus of elasticity of approximately 106 dynes/cm2 is calculated.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):610-618. doi:10.1115/1.3425085.

In this study, a set of two parameters was used to describe the state of dynamic equilibrium for hardening and softening behavior in a variety of metallic materials, subjected to cyclic and static loading conditions, temperatures, and strain rates in the range of practical interest. The parameters consisted of a time-temperature parameter and a cyclic stress-strain parameter. Stable or near-stable values of cyclic stress and strain and of creep rate were extracted from numerous sources in the literature. Values for each parameter were calculated from that data and their functional relationship was studied. Results suggest a single relationship between the two parameters for pure FCC metals for both creep and fatigue.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):619-626. doi:10.1115/1.3425086.

A discussion is presented on the behavior of materials during erosion. A rigorous analysis must make an assumption as to the mechanism of material removal, i.e., either ductile or brittle. One expects then, when comparing experimental results, that considerable differences in erosion characteristics will be apparent between these two classes of materials. In this paper it is shown that these differences do exist; however, for certain brittle materials, a considerable similarity to ductile materials exists. This similarity is in the dependence of erosion on abrasive particle velocity and diameter and on the material properties of the eroded surface.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):627-632. doi:10.1115/1.3425089.

An analysis is developed to determine the relaxation of cylindrical compression springs at temperatures where creep is predominantly steady state and the effect of transient creep and anelastic strain is small. Springs which operate under these conditions must be designed for limited life. Equations are derived which predict the relaxation of springs directly from tensile creep data for various materials. Using creep data for 18-8 stainless steel and Inconel-X, families of design curves are presented which give the time-temperature initial-stress relationships for various stress-relaxation ratios. These curves are useful in selecting an initial design stress for a specific operating temperature.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):633-638. doi:10.1115/1.3425090.

Based on the elastic interaction between a solute atom and a tensile crack-tip stress field, a mechanism of stress-corrosion cracking was proposed and analyzed. This elastic interaction provides a potential for solute atoms to migrate toward the tip of a crack. The elastic interaction and the equilibrium concentration of solute atoms near a crack tip were calculated. The solute atom concentration increases rapidly toward the crack tip if the solute atom is interstitial or if it relaxes the crack-tip stress field. The high concentration of solute atoms at the tip of a crack will enhance the reaction between solute and solvent atoms. The weak fracture strength of the reaction product may cause crack growth. Two crack growth models were analyzed: One is based on the assumption of the “homogeneity” of the fracture and deformation properties of a material, and the other takes a structural size of a material into consideration. The proposed models are compared with available data on magnesium-aluminum alloy, 4340 steel, and soda-lime glass.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):639-652. doi:10.1115/1.3425091.

This is a two-part paper, which stresses the materials science approach to understanding dust erosion mechanisms. The first part is an experimental phase, studying the effects upon solid-particle erosion, of such material and environmental variables as target alloy composition and heat-treat condition; dust particle velocity, size, concentration, velocity, and kinetic energy; carrier-gas true temperature and impingement angle. All test variables and their limits were chosen to simulate the range of engineering conditions and erosive environments encountered in helicopter turbine service. Actual erosion data are compared with erosion levels predicted by existing theories on particulate erosion. The second part is a diagnostic phase, programmed to detect and study visible phenomena associated with the erosion processes, using high-magnification electron microscopy. Phenomenological evidence obtained from the erosion surfaces and erosion products are used to define probable physical models of the erosion mechanisms.

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):655-661. doi:10.1115/1.3425096.

A method of measuring stress relaxation by the use of stressing frames, wherein a constant strain is maintained on the specimen, is discussed. The elastic strain introduced into the specimen during loading, at the start of the exposure, and the elastic strain relieved during unloading, at the end of the exposure, are measured. The difference in elastic strains can be used to determine the amount of stress relaxation that has taken place. The method seems to produce reliable measurements and has the advantages that it requires no very costly equipment, and the tests require little or no attention during the exposure periods. Although each test yields only one stress-time data point, many tests can be run simultaneously.

Commentary by Dr. Valentin Fuster

DISCUSSIONS

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):435-436. doi:10.1115/1.3425023.
FREE TO VIEW

An analysis of low Rossby number and low Ekman number flow between parallel plates shows that the interior flow is irrotational and two-dimensional for all Rossby numbers and Ekman numbers in the range R0 ≪1, E≪1. The extra condition R0 ≪E1/2 is not needed for this proof.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

TECHNICAL BRIEFS

Commentary by Dr. Valentin Fuster
J. Basic Eng. 1970;92(3):663-665. doi:10.1115/1.3425098.

A simple theory is given for unsteady lift on a flat-plate airfoil due to chordwise velocity perturbations. Horlock’s theory for a frozen gust pattern convected at the free-stream velocity is included as a special case, and a distinction is drawn between streamwise and chordwise velocity perturbations.

Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster
Commentary by Dr. Valentin Fuster

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