Real Fluid Effects Research Articles

Scattering of Water Waves by Vertical Cylinders

The scattering of small amplitude water waves by an array of vertical cylinders is studied theoretically and experimentally. In the theoretical study, a method of matched asymptotic expansions is first developed to find the reflection and the transmission coefficients without considering real fluid effects. Energy loss due to the flow separation near the cylinders is modeled by adopting a linearized form of the quadratic resistance law. It is shown that this is equivalent to introduce a complex blockage coefficient. The energy loss coefficients for square cylinders and circular cylinders are determined by comparing theoretical results with experimental data.

A Study of Stall in a Low Hub–Tip Ratio Fan

An investigation has been carried out in order to define the process of rotating stall inception in a low-speed, low hub–tip ratio fan. Based on elementary cascade analysis, the fan would be expected to stall from the root. However, considerable experimental evidence indicates that tip stall is more frequently incurred. Although the analysis has been undertaken for a specific fan, it is considered to be representative of a broad range of machines. The analysis has involved two primary considerations, first the effect of streamtube contraction, which has been studied theoretically, and second, real flow effects (those not contained in the theoretical model), which have been studied experimentally. The study of streamtube contraction indicates that the root rematches to a more stable operating point, thus alleviating some of the problems in that region. The experimental investigation was undertaken on an isolated rotor, with successive build modifications to increase the likelihood of rotating stall inception at the root. It was apparent that real fluid effects tended to steepen the root pressure rise characteristic, thus enhancing the stability in that region. The performance of the fan at the tip tended to be poor, providing a pressure characteristic with a lower negative gradient than anticipated, indicating less stability than simple flow models would suggest. Hot-wire flow mapping at the rotor exit supported the overall conclusion that the rotor showed a strong reluctance to stall at the root apparently due to “centrifuging” of the boundary layer toward the tip.

Multi-module floating ocean structures

In this paper, we describe an analysis of the wave-induced motions and structural response of a very large floating structure made up of a number of modules, each of which is treated as a rigid body having six degrees of motion freedom. The modules are connected to one another by mechanical joints having elastic and damping characteristics. The platform may be held in its mean position by various means including catenary and taut cable mooring systems. Each module consists of a floating body of quite general geometry and the range of shapes may include ship- or barge-like bodies and wave-transparent bodies similar to semi-submersible platforms. The wave-induced forces and the motion responses are computed within the context of linear ship and platform motion theory. Provision is made for utilizing any procedure appropriate for the individual body geometry in computing the fluid forces on each module. Such procedures include two-dimensional strip and three-dimensional panel methods, both of which are based on ideal-fluid potential theory, and the Morison formula which includes some real fluid effects. Viscous forces are included by means of the method of equivalent linearization, with the necessary iteration built into the computer code. The results of the computation include the absolute and relative motion responses of the individual modules, the forces and reactions in the connecting structure, and the mooring and restraint loads. In addition, the relative motions between adjacent unconnected modules may be determined in order to simulate the assembly of the structure at sea.

Fixed conductance heat pipe performance with a liquid slug

Fixed conductance heat pipes (FCHPs) filled with working fluid at low or moderate temperatures develop a volume of excess liquid when operated at high temperatures. The excess liquid forms as either a puddle or a slug at the coldest end of the condenser and creates a temperature differential between the evaporator and the condensor end cap. Simple algebraic expressions are presented for predicting the thermal performance of an FCHP operating with a liquid slug formed by the combined influence of liquid density temperature dependence and meniscus depression. Both differential and two-node models are developed to account for condensation modeled either as a constant flux process or based on an isothermal vapor with a constant internal film coefficient. Numerical examples are included to illustrate the behavior of two axially grooved pipes operating over a range of heat loads with both real and ideal fluids. Prediction of evaporator temperature and liquid slug length is observed to have a weak dependence on the choice of model and mode of condensation and a strong dependence on real fluid effects.

Slow drift of a floating cylinder in narrow-banded beam seas

For a long cylinder floating on the sea surface, incident sea waves with a narrow frequency band excite body oscillations of short and long periods. Depending on the stiffness of the mooring system, the body displacement of the long-period motion can be comparable with, or even greater than that of the short-period oscillations. By combining the asymptotic methods of multiple scales and inner and outer expansions, we describe an essentially analytical theory for slow sway of both small and large amplitudes. Besides showing results for various quasi-steady and transient incident waves for a rectangular cylinder, we examine the effect of the gap between the keel of the body and the sea bottom. It is found in particular that a small gap can enhance moderate resonance by blocking the flow due to long waves and increase the apparent mass of the cylinder. Real-fluid effects are not included.

Real-fluid effects in flow cavitation

The possible role of reaj fluid effects in two aspects of flow cavitation namely inception and separation is discussed. This is primarily qualitative in the case of inception whereas some quantitative results are presented in the case of separation. Existing evidence clearly indicates that in particular viscous effects can play a significant role in determining the conditions for cavitation inception and in determining the location of cavitation separation from smooth bodies.

Vortex Dynamics and Bifurcation of Buoyant Jets in Crossflow

A model is developed which predicts the integral behavior of buoyant or nonbuoyant jets in crossflow with the superimposed effect of the counterrotating internal vortex structure which exists in a plane normal to the jet trajectory. Despite some real fluid effects, such as finite vortex core size and turbulent growth, classical irrotational vortex pair theory is an adequate first-order model for the motions induced in the surrounding fluid. If these outside motions are constrained—either by a fluid boundary or by the effects of density stratification—then a repulsive force mechanism is created. This force leads to bifurcation of the bent-over jet into two separate elements with undiluted fluid in between. The theory shows excellent agreement with available experimental data for homogenous crossflow of finite depth. An application to hypothetical cases of stratified crossflow predicts different environmental conditions under which jet bifurcation can occur.

Multiport diffuser as line source of momentum in shallow water

Multiport diffusers are linear structures consisting of many closely spaced nozzles which inject a series of high‐velocity jets into an ambient fluid. The discharge of heated water into the shallow coastal zone is considered herein as a typical practice for cooling water disposal from steam electric power generation. The flow and temperature fields, induced in the otherwise stagnant and homogeneous fluid layer, are analyzed by representing the diffuser as a line source of fluid momentum in a two‐dimensional coordinate system, thus neglecting the initial momentum transfer zone in which the three‐dimensional jets merge to produce a vertically fully mixed flow. A scaling argument which considers the effect of pressure deviations, turbulent bottom friction, and lateral turbulent diffusion shows that the flow field can be divided into the near field, of order of the diffuser length, and into the far field, at longer distances. The near field is characterized by a predominantly inviscid behavior and gives rise to a contracting slipstream motion, qualitatively similar to the slipstream produced by an airscrew. The shape of the slip streamline is found by mapping the complex potential of the flow into the log hodograph plane. The boundary conditions at the diffuser line are assumed to be a uniform normal velocity and a uniform longitudinal acceleration. The interior velocity and pressure distribution are determined through a finite difference solution using the known geometry of the slipstream. Results indicate a strong separation angle (60°) of the slipstream at the diffuser and a rapid approach to the asymptotic contraction value (½). An integral model is developed for the depth‐averaged temperature and velocity in the far field of the ‘diffuser plume’ (i.e., a localized current with elevated temperatures with weaker velocities and a uniform temperature outside). The model includes the effect of turbulent friction at the plume bottom, described by a quadratic friction law, and of lateral turbulent entrainment, described by the entrainment hypothesis of Morton et al. (1956). The far‐field model is combined with the inviscid near‐field solution, thus superimposing the real fluid effects onto the properties of the contracting slipstream. Two distinctive features characterize the diffuser plume. First, it experiences an exponential loss of fluid momentum through turbulent bottom friction which leads to an ultimate plume stagnation at a characteristic distance ƒ0LD/(16H), where ƒ0 is a quadratic friction coefficient, LD the diffuser length, and H the water depth, and also puts a limit on the total lateral entrainment flow. Second, the initial plume characteristics, and thus its rate of entrainment, are controlled by the accelerating high‐velocity slipstream in the vicinity of the line source. Experiments in a shallow laboratory basin corroborate the theoretical results, both as regards the qualitative features of the contracting slipstream and the quantitative observations of induced velocities and flow rates.

Analysis of Curved Target-Type Thrust Reversers

Abstract : The reverse-thrust performance of two-dimensional and axisymmetric curved deflectors, symmetrically situated with respect to the impinging jet, is analyzed through the use of Levi-Civita's method, Belotserkovsky's integral method, and the finite element method. The predicted results are shown to be in reasonable agreement with the available experimental data. The real-fluid effects such as Coanda effect, entrainment, and the pressure ratio are discussed in the light of the present inviscid flow analyses.

The Ion Current Density on the Surface of a Spherical Probe in a Flowing High Pressure Plasma

The positive ion current density on the surface of a spherical probe immersed in a flowing flame plasma has been measured under thin sheath conditions. The hydrodynamic Reynolds number ranged from 96 to 720. No pronounced real fluid effects have been observed in the current density although the probe is observed by Schlieren photography to exhibit boundary layer separation and wake formation. In spite of the real fluid behavior of the plasma fluid, the thin sheath theory describes the current density distribution on the probe surface very effectively. This is attributed to the formation and entrainment of a shielding layer of fluid, voided of charge during its passage through the sheath.

Measurements and computations of flow in pipe bends

Measurements are given of the total pressure and yaw relative to the pipe axis of flow in various pipe bends attached to the end of a long straight pipe, for a pipe Reynolds number of 2·36 × 105. The behaviour of the induced secondary flows is presented in detail. In a 180° bend it is found that, from the start of the bend, the secondary flows increase to a maximum and then decrease to a steady value. This effect is explained by relating the local total pressure gradient to the production of streamwise vorticity. The same flow mechanism is used to predict qualitatively the flow pattern in an S-bend in which it is found that the secondary flows cause a complete interchange of the slow moving wall fluid and the faster central core. Results of a computer program for calculating the secondary flow from a knowledge of the upstream velocity profile are included. Although real fluid effects, other than those causing the upstream velocity profile, are omitted from the computations, the measured flow pattern is reasonably well predicted in a long bend up to a bend angle of about 75°.

Added Mass of Equilateral-Triangular Cylinders

The added mass of a moving cylindrical body due to the acceleration of the surrounding fluid may be evaluated theoretically by determining the kinetic energy of the fluid surrounding the body, and experimentally by measuring the applied force and resulting acceleration of the body. A theoretical and experimental determination of the added mass for a triangular cylinder is presented. The theoretical analysis is based on the kinetic energy method and neglects any real fluid effects. The theoretical added mass coefficient is computed as 1.53 whereas the experiment gives a value of 1.57. A comparison is made with the corresponding values for cylinders of different cross sections. A short discussion on whether or not viscosity and wall effects were of such magnitude to invalidate the experimental values is also presented.

A Practical Method of Predicting Transonic-Compressor Performance

A real fluid-stream filament axial-flow-compressor performance method is deduced from theory and statistics. The nonisentropic complete radial equilibrium-momentum equation is combined with the continuity, energy, and flow-process equations to yield a group of equations which is readily adaptable to solution on a digital computer. The real fluid effects, such as subsonic viscous losses and shocks at cascade entry, are deduced from statistics in terms of a blade-loading parameter. A program suitable for rapid calculations on a digital computer is presented in schematic form. A comparison between the deduced and the measured performances of an arbitrary stage is made. The correlation obtained indicates that the performance method is reliable.

An Analysis of Axial Compressor Cascade Aerodynamics: Part I—Potential Flow Analysis With Complete Solutions for Symmetrically Cambered Airfoil Families

A method is presented whereby complete potential flow solutions for any cascade geometry may be obtained with comparatively great rapidity on desk calculators. This solution is carried out for the case of symmetrically cambered airfoils such as the 65-series compressor and circular are airfoils and the results presented in a compact graphical form completely account for the potential flow effects of camber, profile, thickness, stagger, solidity, and angle of attack. Real fluid effects will be assessed and correlated in Part II using the present results as a supporting theory.

Effect of the Volute on Performance of a Centrifugal-Pump Impeller

Abstract An experimental study of volute influence on radial flow-impeller performance was conducted by operating a single impeller with three different sets of volute vanes. In each case, over-all performance was measured and an internal-flow study within the volute was made. The results show that at their respective design flow rates the influence of the volutes is least and the deviation of performance from the free-impeller operation is small. At off-design flow rates there are major changes in the impeller performance resulting from the presence of the volutes. Large real fluid effects, coupled with a nonuniform velocity pattern at the impeller exit, result in a flow through the volute that does not resemble a potential flow. Even so, the fluid losses through the volute are comparatively small.

An Experimental and Theoretical Investigation of Two-Dimensional Centrifugal-Pump Impellers

Abstract An experimental and theoretical investigation on a series of two-dimensional centrifugal-pump impellers has been made in an effort to determine the usefulness of potential theory for the description of the flow. Computed values of the developed head and pressure distribution on the vane surfaces are compared with measurements on two, four, and six-vaned logarithmic spiral impellers. The agreement between the observed and predicted quantities is reasonably good for operating points where the influence of the inlet turn on the internal flow is least. The discrepancies which occur at other flow rates are attributed to real fluid effects which are observed in the impeller passages.