A review of about a decade of development of the generalized Riemann problem (GRP) scheme is presented. The method is briefly outlined, followed by various numerical and physical extensions. The range of versatile applications of the GRP method is illustrated through numerous examples.

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A k-ε turbulence model is developed to calculate wall turbulent shear flows under various pressure gradient conditions. In the present model, we set the dissipation rate of turbulent energy at a wall equal to zero, though the wall limiting behavior of velocity fluctuations is reproduced exactly. Thus, the model assures computational expediency and convergence. The proposed model is constructed to properly take into account the effect of pressure gradients on shear layers. It was found by Nagano, Tagawa and Tsuji (Turbulent Shear Flows 8, (1992), 7) that in adverse pressure gradient flows the Van Driest constant decreased with increasing dimensionless pressure gradient parameter P⁺. Therefore, the present model incorporates the modified Van Driest dumping function which is a function of P⁺. The validity of the proposed model was tested by application to a turbulent channel flow and boundary layers with P⁺ < 0, P⁺ = 0 and P⁺ > 0. The model predictions indicate that agreement with the experiment and the direct simulation data is very good over a wide range of pressure variations.

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In this study, wavelet analysis is applied to velocity signals of a plane turbulent jet, in order to investigate the eddy structure in the dimensions of time and scale. First, a review of the definitions and the basic properties of wavelet analysis are introduced, and a revised form of the Mexican hat and the wavelet power spectrum are proposed. To illustrate some typical behaviors of the wavelet coefficient phase, a numerically generated signal is analyzed. Then from the velocity signals of a jet on the centerline and in the mixing layer, the structural features of the eddy are analyzed in terms of instantaneous frequency and onset time/position. The results reveal that eddies of very different scale and the breakdown of a large eddy are displayed in the wavelet coefficient phase, as well as the successive branchings of a large eddy structure. Furthermore, it is found that the scale of the eddy and intermittency in the mixing layer can be obtained by wavelet analysis. The wavelet power spectra agree fairly well with the Fourier power spectra and just correspond to the actual kinetic energy per unit time at each wave number.

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This paper describes the approximate viscous solution to the analytical approach, based on the conservation of angular momentum flux, formulated previously by Kitoh (J. Fluid Mech, Vol. 175, p. 429, (1987)) to predict the decay of the swirling motion along a curved duct. Only the inviscid approximate solution was presented by Kitoh (1987) . The present approximate solution takes into account the frictional forces on the pipe wall and, includes an additional factor to compensate for the absence of the radial velocity components in the original formulation, when the inlet streamwise swirl intensity is low. As a consequence of the frictional effects, different decay patterns for the swirl intensities along a curved duct are observed. Measurements in 180-degree bends with different levels of inlet swirl intensities by Hawthorne (Proc. R. Soc. Lond. A, Vol. 206, p. 374, (1951) ) Shimizu & Sugino (Bulletin JSME, Vol. 23, p. 1443, (1980) ) were used to compare with the present approximate solution. Good agreement can be obtained in both cases.

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A simple analysis, based on the scaling of the Navier-Stokes equations, is presented for general flow situations involving separation bubbles. Three possible functional relations between the separation bubble length L and Reynolds number Re are derived : (i) L∝Re, (ii) L∝1/Re, and (iii) L=constant. These relations are shown to correspond to the experimentally observed behavior of laminar, transitional and turbulent separation bubbles, respectively. The results of the analysis are discussed in the context of several internal and external separated flows in various geometries, and the corresponding empirical constants are evaluated from available experimental and numerical data.

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Pseudoshock in straight channel flows was numerically simulated by solving the two-dimensional time-averaged Navier-Stokes equations. The objectives of the present simulation were to investigate the influence of parameters on the structure of pseudoshocks and to validate the model of the pseudoshock mechanism proposed in the previous paper. In this simulation, Harten-Yee's second-order-accuracy TVD scheme was used for high resolution of the shock wave and numerical stability, and Baldwin-Lomax's algebraic model was used for turbulent flows. The computational results agreed well with the experimental ones and with the proposed model ofλ- and X-type pseudoshocks.

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A two-phase flow model based on local relative velocity, which was previously proposed by the authors, was extended to a model for gas-liquid-solid three-phase flows. The extension was carried out utilizing a hypothetical two-phase flow, which was conceived by removing one of the three phases. In order to examine the usefulness of the extended model, the measured area-averaged volumetric fractions of gas-liquid-solid three-phase bubbly or slug flow in vertical pipes were correlated based on the basic equations of the extended model. The accuracy of the obtained correlation was compared with those of the drift-flux correlation, the correlation based on a multiplier method and the correlation based on a gas-liquid-solid three-phase slug flow model. Consequently, it was confirmed that the extended model gives simpler and more accurate correlations for the area-averaged volumetric fractions of the gas-liquid-solid three-phase flows.

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The equation of motion for a cluster of spheres moving in fluid at low Reynolds numbers is developed under the consideration of hydrodynamic interaction among the spheres. The hydrodynamic forces of the spheres in the equation of motion are estimated using their relative velocities. The relative velocities are derived by applying the conventional reflection method for the Stokes flow field to the newly developed reflection method for the Oseen flow field. In order to discuss the effectiveness of this method, experiments on two equal-sized spheres with equal densities falling freely in quiescent glycerol are carried out. The width of the test tank with a square cross section is 100 times the sphere diameter. The positions of the spheres with time lapse are measured using a stroboscope-camera system. The numerical results show good agreement with the experimental results.

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Experimental investigation was carried out in an attempt to obtain data and phenomenological explanation of spherical Couette flow in a magnetic fluid for the situation where the outer sphere rotates while the inner sphere is stationary. Data for torque characteristics were obtained when a magnetic field was imposed on the fluid, using a bar magnet which was situated in a stationary inner sphere. The torque increases when the intensity of the magnetic field is increased, resulting in an increase of the effective viscosity. The rate of torque increase caused by the magnetic field is greater for larger gap width. The regime in which main flow is dominant (the simple linear Couette flow with negligible weak secondary flow) appeared to be extended with an increase of Reynolds number, suppressing the strong secondary flow, while with further increase of Reynolds number, the torque characteristics approach the zero magnetic field case, showing very weak effect of magnetic field.

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Flows through parallel plates containing a cylinder are numerically calculated for nematic liquid crystalline polymers using a simplified model of the Leslie-Ericksen theory. A tensor expression for the orientation of the director is used in the basic equations in order to avoid the difficulty in calculation due to the tumbling of the director. The orientation of the director is affected by the contraction and expansion flows, and tumbling occurs. An area where the molecule aligns in the direction of the flow exists behind the cylinder. It extends downstream as the parameter λ approaches the value one. The flow field does not change significantly from that of Newtonian fluids.

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The double linearization theory is extended to a three-dimensional straight cascade between parallel-plane end walls operating at supersonic axial velocity. Numerical examples are presented to show unsteady aerodynamic responses and flutter boundaries in correlation with cascade parameters. The three-dimensional effects are evaluated by comparing the three-dimensional theory predictions with the strip theory ones. To attain a large steady loading on the first mode bending flutter boundary, it is advantageous to design blades with angle of attack and camber decreasing from hub to tip. The three-dimensional effects are small for the lightly loaded cascades of the supersonic leading-edge locus.

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A numerical technique for the computation of three-dimensional turbulent flows through a turbine stage with bucket tip clearance is presented. To calculate nozzle and bucket flow regions simultaneously, steady interaction is assumed to occur at the connecting boundaries. To analyze the exact flow-region geometry of the bucket tip clearance, an H-type computational grid system, which is also used in the nozzle and bucket flow regions, is used in the tip clearance region. A finite volume method is used to obtain the spatially discretized governing equations, while the damping surface technique is employed for the time integration. In the present analysis, a two-equation model of turbulence is introduced to estimate the turbulence effect. In order to verify the validity of the present method, computations are carried out for the flow through turbine stages of different tip clearance heights. The results show clear simulation of secondary flow phenomena such as the tip leakage vortex and passage vortex motions in the bucket flow region. The effects of the clearance height on the turbine stage flow fields are also well predicted qualitatively.

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Selective withdrawal from a two-layered thermally stratified cross-flow through a single round hole with and without a hood (cap) is considered. Experimental measurements of drawdown, the critical withdrawal rate and the mean temperature profile in the vicinity of the hole are provided for both cases. Flow visualization is reported, which provides detailed information on the structure and dynamics of mixing of warm and cold water. Flow visualization studies show the formation and shedding of a horseshoe vortex at moderate withdrawal rates for a hooded case, which is independent of stratification. The presence of a hood inhibits drawdown of the interface over the hole and thus reduces the amount of drawdown at any withdrawal rate.

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This paper presents a limited parametric study of the unbalanced response of a rigid rotor supported by an eccentric squeeze film damper bearing. The rotor unbalance response is approximated by a trigonometric series whose coefficients are determined by the collocation method. The results indicate that for small static misalignments and unbalances, nonsynchronous components are negligible and the rotor response is an offset ellipse. Nonsynchronous components increase as both the unbalance and the static misalignment are increased. However, the amplitude of the rotor response is independent of the static misalignment direction. There is a tendency for the rotor to self-center in the vicinity of the resonance. This self-centering effect is more pronounced as the unbalance is increased and it is reduced as the static misalignment is increased. For large unbalances and static misalignments, both main resonant jump and secondary resonant jump are predicted at speeds above twice the system critical speed.

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The characteristics of flow pattern, heat transfer and pressure drop of evaporation of HCFC 22 inside a horizontal tube are experimentally revealed. The experiment is conducted with a double-tube evaporator, where the refrigerant flows inside the inner tube and the heating water flows countercurrently in the surrounding annulus. The inner tube is an internally grooved copper tube having a 9.52 mm o. d. and an 8.72 mm mean i. d. The ranges tested for the refrigerant are as follows : mass velocity of 110 to 220 kg/ (m²s), vapor pressure of 0.4 to 0.65 MPa and heat flux of 5 to 35 kW/m². The flow pattern observed through sight glasses changes from the wavy-annular type to the annular type and then to the mist flow type as the evaporation progresses along the tube. These transitions of flow patterns occur at much lower values of vapor qualities than those predicted from the Baker map modified by Scott for a smooth tube. The heat transfer coefficients in the wavy-annular and annular flow regions are about 2 to 4 times higher than those of smooth tubes, and are expressed as a simple function of the Lockhart-Martinelli parameters. The empirical equations for the heat transfer coefficient in the mist flow region and in the single phase heat transfer region are also presented. The accuracy of these equations along with the value of the transition quality is confirmed in a comparison between the design calculations and the experimental data.

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A theoretical study of the droplet deposition and heat transfer of a vertically heated tube cooled internally by a turbulent air-water dispersed flow has been performed. In the analysis of the droplet deposition on the wall, an equation for the dimensionless droplet deposition velocity k_d/u* is proposed, and the calculated results show good agreement with experimental data measured by many authors. In the heat transfer analysis, a model is proposed taking into account the presence of an initial liquid film on the wall that flows uniformly until the dryout point. The calculations of wall temperature distribution and heat transfer enhancement are performed and compared with experimental values measured by other authors, and a satisfactory agreement is obtained. The heat transfer enhancement is found to be caused mainly by the evaporation of the liquid film on the wall, which is quite different from the case of a single-component mist flow. It is assumed that in an actual case, the liquid film on the wall breaks down nonuniformly before the dryout point, depending on the wall heat flux and the liquid film flow rate.

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The objective of this research was to investigate the influence of the in-cylinder surfaces on the net emission of particulate matter in the exhaust of a single-cylinder diesel engine. In order to obtain this information, time resolved sampling was performed to characterize the particulate matter emitted in the engine exhaust. A rotating probe sampled the free exhaust plume once every engine cycle. The rotation of the probe was synchronized with the engine cycle in such a way that the samples could be taken at any predetermined crank angle degree window. The sampling probe was designed for isokinetic sampling in order to obtain reliable results. To accomplish this, the unsteady flow through the probe was modeled based on the measured instantaneous velocities and temperatures of the exhaust. Two methods were used to characterize the exhaust particulate matter in real time : a filter for mass concentration measurements, and an electrical aerosol analyzer (EAA) for size distribution and volume concentration measurements. The results showed about 45% higher mass concentrations as well as larger diameter particles emitted during blowdown than late in the displacement phase of the exhaust stroke. This suggests that high in-cylinder shear rates and velocities which are associated with the blowdown process cause the deposited soot to be reentrained from the surfaces of the combustion chamber, where reentrainment is favored by conditions of high surface shear.

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