Influence of nozzle geometry on underexpanded axisymmetric free jet characteristics

The effect of nozzle geometry on the structure of a supersonic free jet is investigated both experimentally and numerically for three simple nozzle geometries. In the experiments, the relation between the Mach disk height and diameter and the nozzle pressure ratio are investigated using the schlieren method. In contrast to results obtained in previous studies, our experimental results show that the Mach disk height changes depending on the nozzle geometry. Numerical investigations were conducted by introducing flows upstream of the nozzle and the influence of these upstream flows on free jet configuration has been discussed.     

Wave pattern characteristics of a two-phase nozzle flow by shock propagation

In this paper, the wave pattern characteristics of shock-induced two-phase nozzle flows with the quiescent or moving dusty gas ahead of the incident-shock front has been investigated by using high-resolution numerical method. As compared with the corresponding results in single-phase nozzle flows of the pure gas, obvious differences between these two kinds of flows can be obtained. Received 14 June 1996 / Accepted 19 October 1996     

On the flow field generated by a gradually varying flow through an orifice

The motion of a vortex ring generated by gradually varied flows through a thin-edged orifice has been investigated experimentally using particle image velocimetry. This flow reproduces the primary characteristics of many biological flows, such as cardiac flows through valves or jellyfish and squid propulsion. Even though vortex ring formation has been extensively studied, there is still interest in gradually varying inflows, i.e. the ones that are mostly found in previous conditions. The main purpose of this paper is to extend the time scaling already proposed in the literature to the entire cycle of vortex ring formation, pinch-off and free motion. To this end, eight inflow time laws have been tested, with different acceleration and deceleration phases. They have been selected in relation to practical applications by their resemblance to the main characteristics of cardiovascular and pulsed locomotion flows. Analysis of measured velocity and vorticity fields suggested a general criterion to establish the instant of vortex pinch-off directly from the imposed velocity program. This allows the proper scaling of the entire time evolution of the vortex ring for all tested inflows. Since it is quite easy to identify this instant experimentally, these results give a simple, practical rule for the computation of scales in vortex ring formation and development in the case of gradual inflows. The “slug model” has been used to test the proposed scaling and to obtain predictions for the vortex position, circulation and vorticity which are in agreement with experimental data.     

An integrated 2-D Navier–Stokes equation and its application to 3-D internal flows

An efficient two-dimensional (2-D) analytical and numerical procedure has been proposed to investigate three-dimensional (3-D) internal flows through a passage with a spatially variable depth, in which the viscous forces act significantly on both upper and lower walls. The integral 2-D version of the Navier–Stokes equation was obtained by integrating the full Navier–Stokes equation in a 3-D form over the depth of the passage. In order to examine the validity of the integrated momentum equations, fully-developed flows in straight noncircular ducts were investigated analytically prior to numerical investigations. It has been shown that the exact solutions for circular, elliptical and equilateral triangular ducts are obtainable from the integrated Navier–Stokes equation. Having confirmed its wide applicability to internal flows, numerical computations were conducted to investigate the oscillation mechanism of a fluidic oscillator. Comparison of the present prediction and experiment reveals the validity of the present treatment.     

Direct Numerical Simulation of Self-Similar Turbulent Boundary Layers in Adverse Pressure Gradients

Direct numerical simulations of the Navier–Stokes equations have been carried out with the objective of studying turbulent boundary layers in adverse pressure gradients. The boundary layer flows concerned are of the equilibrium type which makes the analysis simpler and the results can be compared with earlier experiments and simulations. This type of turbulent boundary layers also permits an analysis of the equation of motion to predict separation. The linear analysis based on the assumption of asymptotically high Reynolds number gives results that are not applicable to finite Reynolds number flows. A different non-linear approach is presented to obtain a useful relation between the freestream variation and other mean flow parameters. Comparison of turbulent statistics from the zero pressure gradient case and two adverse pressure gradient cases shows the development of an outer peak in the turbulent energy in agreement with experiment. The turbulent flows have also been investigated using a differential Reynolds stress model. Profiles for velocity and turbulence quantities obtained from the direct numerical simulations were used as initial data. The initial transients in the model predictions vanished rapidly. The model predictions are compared with the direct simulations and low Reynolds number effects are investigated.     

Turbulent drag reduction in dam-break flows

The role of turbulence is investigated in dam-break flows, where a finite volume of fluid is released from a compartment into a long, rectangular channel. After a sudden removal of the lock gate, a gravity current, undular bore, or solitary wave develops, depending on the ambient fluid height in the channel. The temporal evolution of the moving front has been measured and evaluated. It was observed that the dilution using a very small amount (a few weight ppm) of a long chain polymer (polyethylene-oxide) in the fluid strongly affected flow properties. Pronounced drag reduction has been found in dry bed flows (whereas the polymer increased the viscosity of the fluid). The presence of a few mm-thick ambient fluid layer in the channel effectively destroyed drag reduction, in spite of the fact that strong turbulence was obvious and the propagation velocity of the front was almost unchanged.     

Numerical solutions for impulsively started and decelerated viscous flow past a circular cylinder

A finite difference study of the unsteady two-dimensional flow past a circular cylinder has been conducted using vorticity and streamfunction as the dependent variables. The two cases considered were impulsively started and decelerated flows. The impulsively started problem was considered to validate the method and has yielded results which agree quite closely with existing results from both calculations and experiments. The decelerated flow analysis produced results which can be explained in terms of induced velocity effects from existing wake vortices for both suddenly stopped and uniformly decelerated flows.     

On pipe diameter effects in surfactant drag-reducing pipe flows

Remarkable power saving in a fluid transport system is possible if the surfactant drag reduction technology is used. Application of surfactant drag reduction to district heating and cooling systems has been investigated in the past. The establishment of the scale-up law in drag-reducing pipe flows is one of the most important problems in this application. Main purpose of this study is aimed to develop a reliable scale-up law in surfactant drag-reducing flows. As the basic data of surfactant solutions, both non-Newtonian viscosity and viscoelasticity were experimentally determined. A turbulent eddy diffusivity model based on the Maxwell model was employed to estimate the drag reduction of surfactant solutions. The predictions by the turbulence model developed in this study with proper rheological characteristics of surfactant solutions has resulted in a reliable estimation of the pipe diameter effect in surfactant drag-reducing flows over the pipe diameter range from 11 to 150mm. Received: 30 June 1997 Accepted: 29 December 1997     

Stereoscopic PIV measurements of flow in the nasal cavity with high flow therapy

Knowledge of the airflow characteristics within the nasal cavity with nasal high flow (NHF) therapy and during unassisted breathing is essential to understand the treatment’s efficacy. The distribution and velocity of the airflow in the nasal cavity with and without NHF cannula flow has been investigated using stereoscopic particle image velocimetry at steady peak expiration and inspiration. In vivo breathing flows were measured and dimensionally scaled to reproduce physiological conditions in vitro. A scaled model of the complete nasal cavity was constructed in transparent silicone and airflow simulated with an aqueous glycerine solution. NHF modifies nasal cavity flow patterns significantly, altering the proportion of inspiration and expiration through each passageway and producing jets with in vivo velocities up to 17.0 ms⁻¹ for 30 l/min cannula flow. Velocity magnitudes differed appreciably between the left and right sides of the nasal cavity. The importance of using a three-component measurement technique when investigating nasal flows has been highlighted.     

Viscous liquid film flow down an inclined corrugated surface. Calculation of the flow stability to arbitrary perturbations using an integral method

Viscous liquid film flow along an inclined corrugated (sinusoidal) surface has been studied. Calculations were performed using an integral model. The stability of nonlinear steady-state flows to arbitrary perturbations was examined using the Floquet theory. It has been shown that for each type of corrugation there is a critical Reynolds number for which unstable perturbations occur. It has been found that this value greatly depends on the physical properties of the liquid and geometric parameters of the flow. In particular, in the case of film flow down a smooth wall, the critical waveformation parameter depends only on the angle of inclination of the flow surface. The values of the corrugation parameters (amplitude and period) were obtained for which the film flow down a wavy wall is stable to arbitrary perturbations up to moderate Reynolds numbers. Such parameter values exist for all investigated angles of inclination of the flow surface.     

Direct numerical simulation of bubble dynamics in subcooled and near-saturated convective nucleate boiling

With the long-term objective of Critical Heat Flux (CHF) prediction, bubble dynamics in convective nucleate boiling flows has been studied using a Direct Numerical Simulation (DNS). A sharp-interface phase change model which was originally developed for pool boiling flows is extended to convective boiling flows. For physical scales smaller than the smallest flow scales (smaller than the grid size), a micro-scale model was used. After a grid dependency study and a parametric study for the contact angle, four cases of simulation were carried out with different wall superheat and degree of subcooling. The flow structures around the growing bubble were investigated together with the accompanying physics. The relation between the heat flux evolution and the bubble growth was studied, along with investigations of bubble diameter and bubble base diameter evolutions across the four cases. As a validation, the evolutions of bubble diameter and bubble base diameter were compared to experimental observations. The bubble departure period and the bubble shapes show good agreement between the experiment and the simulation, although the Reynolds number of the simulation cases is relatively low.     

Numerical simulation of turbulence suppression: Comparisons of the performance of four k-? turbulence models

The standard k-ε model and three low-Reynolds number k-ε models were used to simulate pipe flow with a ring device installed in the near-wall region. Both developing and fully developed turbulent pipe flows have been investigated. Turbulence suppression for fully developed pipe flows revealed by hot-wire measurements has been predicted with all three low-Reynolds number models, and turbulence enhancement has been predicted by the standard k-ε model. All three low-Reynolds number models have predicted similar distributions of velocities, turbulence kinetic energy, and dissipation rate. For developing pipe flows, the region of turbulence suppression predicted by the three low-Reynolds number models is much more extensive (up to 30 pipe diameters downstream of the device) than for full developed flow; whereas the standard k-ε model has only predicted turbulence enhancement.     

Axisymmetric flow around bodies in the developed cavitation mode

As a rule, axisymmetric cavitation flows are investigated by means of numerical computations in the absence of analytic solutions. However, substantial difficulties are still encountered here which are discussed in detail in the survey report of Birkhoff [1]. One of the integral equation methods used earlier for numerical computations of a plane cavitation flow [2] is considered below. General considerations about its application for the computations of axisymmetric flows are presented in [3]. This method turns out to be effective for the numerical computations of axisymmetric flows, as well as for an analytical investigation of the curvature of the meridian section of the cavern boundary near the point of its separation from the body. This latter question has been examined earlier in [4], where it has been shown for the case of a circular cone with a rectilinear generator that the curvature becomes infinite. The order of the infinity has not been established.     

Flow pattern transition in liquid-liquid flows with a transverse cylinder

The effect of a cylindrical bluff body on the interface characteristics of stratified two-phase, oil-water, pipe flows is experimentally investigated with high speed Particle Image Velocimetry (PIV). The motivation was to study the feasibility of flow pattern map actuation by using a transverse cylinder immersed in water in the stratified pattern, and particularly the transition from separated to dispersed flows. The cylinder has a diameter of 5 mm and is located at 6.75 mm from the bottom of the pipe in a 37 mm ID acrylic test section. Velocity profiles were obtained in the middle plane of the pipe. For reference, single phase flows were also investigated for Reynolds numbers from 1550 to 3488. It was found that the flow behind the cylinder was similar to the two dimensional cases, while the presence of the lower pipe wall diverted the vorticity layers towards the top. In two-phase flows, the Froude number (from 1.4 to 1.8) and the depth of the cylinder submergence below the interface affected the generation of waves. For high Froude numbers and low depths of submergence the counter rotating von Karman vortices generated by the cylinder interacted with the interface. In this case, the vorticity clusters from the top of the cylinder were seen to attach at the wave crests. At high depths of submergence, a jet like flow appeared between the top of the cylinder and the interface. High speed imaging revealed that the presence of the cylinder reduced to lower mixture velocities the transition from separated to dual continuous flows where drops of one phase appear into the other.     

Numerical investigation of the expansion dynamics and generation of magnetic fields in plasma jets

The processes of interaction between concentrated energy fluxes and solid targets have been investigated in a number of studies. The generation of magnetic fields in erosional plasma formations has been experimentally observed [1–4]. However, the evolution of magnetic fields in plasma jets has not yet been studied in sufficient detail. This paper is devoted to a numerical investigation of unsteady three-dimensional erosion plasma flows and the generation in those flows of magnetic fields resulting from the action of laser radiation on solid targets. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 135–140, November–December, 1986. The authors are grateful to I. V. Nemchinov and B. T. Fedyushin for useful discussion of their results.     

Numerical analysis of a symmetrically heated vertical channel with obstruction

 In this paper, a numerical investigation of laminar natural convection flows in a vertical channel with obstructions is carried out. The main purpose was to analyze the effects of the locations of symmetric obstructions. The computations were performed in a two-dimensional domain and a symmetric uniform wall temperature has been taken as thermal boundary condition. The governing equations were solved using a control volume method and the SIMPLER algorithm for the velocity–pressure coupling was employed. The profiles of the local Nusselt number were given for three different locations of the obstructions. The variation of the average Nusselt number and inlet flow rate versus the modified Rayleigh number were investigated. The results demonstrated that the average Nusselt number decreases as the distance of the obstructions from the inlet increases. Received on 17 January 2000     

Prediction of asymmetric vortical flows around slender bodies using Navier-Stokes equations

Steady and unsteady asymmetric vortical flows around slender bodies at high angles of attack are solved using the unsteady, compressible, this-layer Navier-Stokes equations. An implicit, upwind-biased, flux-difference splitting, finite-volume scheme is used for the numerical computations. For supersonic flows past point cones, the locally conical flow assumption has been used for efficient computational studies of this phenomenon. Asymmetric flows past a 5° semiapex-angle circular cone at different angles of attack, free-stream Mach numbers, and Reynolds numbers has been studied in responses to different sources of disturbances. The effects of grid fineness and computational domain size have also been investigated. Next, the responses of three-dimensional supersonic asymmetric flow around a 5° circular cone at different angles of attack and Reynolds numbers to short-duration sideslip disturbances are presented. The results show that flow asymmetry becomes stronger as the Reynolds number and angles of attack are increased. The asymmetric solutions show spatial vortex shedding which is qualitatively similar to the temporal vortex shedding of the unsteady locally conical flow. A cylindrical afterbody is also added to the same cone to study the effect of a cylindrical part on the flow asymmetry. One of the cases of flow over a cone-cylinder configuration is validated fairly well by experimental data.     

Volumetric-correlation PIV to measure particle concentration and velocity of microflows

Volumetric-correlation particle image velocimetry (VPIV) is a new technique that provides a 3-dimensional 2-component velocity field from a single image plane. This single camera technique is simpler and cheaper to implement than multi-camera systems and has the capacity to measure time-varying flows. Additionally, this technique has significant advantages over other 3D PIV velocity measurement techniques, most notably in the capacity to measure highly seeded flows. Highly seeded flows, often unavoidable in industrial and biological flows, offer considerable advantages due to higher information density and better overall signal-to-noise ratio allowing for optimal spatial and temporal resolution. Here, we further develop VPIV adding the capability to measure concentration and increasing the robustness and accuracy of the technique. Particle concentrations are calculated using volumetric auto-correlations, and subsequently the velocities are calculated using volumetric cross-correlation corrected for variations in particle concentration. Along with the ability to calculate the particle concentration profile, our enhanced VPIV produces significant improvement in the accuracy of velocity measurements. Furthermore, this technique has been demonstrated to be insensitive to out-of-plane flows. The velocity measurement accuracy of the enhanced VPIV exceeds that of standard micro-PIV measurements, especially in near-wall regions. The 3D velocity and particle-concentration measurement capability of VPIV are demonstrated using both synthetic and experimental results.     

A dual-camera cinematographic PIV measurement system at kilohertz frame rate for high-speed, unsteady flows

A digital dual-camera cinematographic particle image velocimetry (CPIV) system has been developed to provide time-resolved, high resolution flow measurements in high-Reynolds number, turbulent flows. Two high-speed CMOS cameras were optically combined to acquire double-pulsed CPIV images at kilohertz frame rates. Bias and random errors due to camera misalignment, camera vibration, and lens aberration were corrected or estimated. Systematic errors due to the camera misalignment were reduced to less than 2 pixels throughout the image plane using mechanical alignment, resulting in 3.1% positional uncertainty of velocity measurements. Frame-to-frame uncertainties caused by mechanical vibration were eliminated with the aid of digital image calibration and frame-to-frame camera registration. This dual-camera CPIV system is capable of resolving high speed, unsteady flows with high temporal and spatial resolutions. It also allows time intervals between the two exposures down to 4 μs, enabling the measurements of speed flows 5–10 times higher than possible with frame-straddling using similar cameras. A turbulent shallow cavity was then chosen as the experimental object investigated by this dual-camera CPIV technique.