Velocity statistics along the stagnation line of an axi- symmetric stagnating turbulent flow

 Velocity statistics along the stagnation line of an axi-symmetric wall stagnating turbulent flow are studied experimentally. A low turbulence, uniform air flow from a nozzle type air supply with an exit diameter of 50 mm stagnates at a wall located 50 mm downstream. A flow velocity is set to 3 m/s, 10 mm downstream from the exit of the air supply. Instantaneous values of streamwise and radial velocities are measured by laser-Doppler velocimetry. The turbulence level in the air flow is changed by use of turbulence generator. When the turbulence generator is not installed in the air supply, the mean velocity profile in the streamwise direction fits well with that of a laminar viscous flow with the rms value of velocity fluctuations low near the wall. With the turbulence generator installed, a significant turbulence structure appears near the wall. When the wall is approached, the rms value of velocity fluctuations in the streamwise direction decreases monotonically while the profile of the rms value in the radial direction reaches a maximum near the wall. The increase in the rms value of velocity fluctuations in the radial direction near the wall is attributed to the bi-modal histogram of the fluctuating velocity in the radial direction. Near the wall, the instantaneous stagnation streamline fluctuates and the probability of the mean location of the stagnation point reaches a maximum not at the stagnation line but on a circle around the stagnation line, resulting in the bi-modal histogram. Turbulence statistics, the rms value of velocity fluctuation and the turbulent kinetic energy, can be normalized successfully by similarity parameters based on the strain rate and the reference turbulent kinetic energy introduced by Champion and Libby. Received: 7 April 1995/Accepted: 27 September 1996     

Oscillating annular liquid membranes

Summary The response of annular liquid membranes to sinusoidal mass flow rate fluctuations at the nozzle exit is analyzed as a function of the amplitude and frequency of the axial velocity fluctuations at the nozzle exit and thermodynamic compression of the gas enclosed by the membrane. It is shown that both the pressure of the gases enclosed by the annular membrane and the axial distance at which the annular membrane merges on the symmetry axis are periodic functions of time which have the same period as that of the mass flow rate fluctuations at the nozzle exit. They are also nearly sinusoidal functions of time for small amplitudes of the mass flow rate fluctuations at the nozzle exit, and exhibit delay and lag times with respect to the sinusoidal axial velocity fluctuations at the nozzle exit. Both the delay and the lag times are functions of the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit and the polytropic exponent. The amplitudes of both the pressure of the gases enclosed by the annular liquid membrane and the convergence length increase and decrease, resp., as the amplitude and frequency of the mass flow rate fluctuations at the nozzle exit, resp., are increased. They also increase as the polytropic exponent is increased.

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Oszilierende rotationsschalenförmige Flüssigkeitsmembranen

Übersicht Untersucht wird das Verhalten rotationsschalenförmiger Flüssigkeitsmembranen in Abhängigkeit von der Amplitude und Frequenz der axialen Geschwindigkeitsschwankungen an der Düsenmündung und der thermodynamischen Verdichtung des eingeschlossenen Gases, wenn sich der Massestrom an der Düsenmündung sinusförmig ändert. Es wird gezeigt, daß der Druck des eingeschlossenen Gases und der axiale Mündungsabstand des Scheitels der geschlossenen Membran periodische Zeitfunktionen mit der Frequenz der Masseflußschwankung am Düsenaustritt sind. Für kleine Amplituden des Massestroms ist ihr Zeitverhalten ebenfalls fast-sinusförmig, wobei sie bezüglich der sinusförmigen axialen Geschwindigkeitsschwankungen an der Düsenmündung eine Ansprechzeit und Phasenverschiebung aufweisen. Ansprechzeit und Phasenverschiebung sind Funktionen von Amplitude und Frequenz der Massestromschwankung sowie des polytropen Exponenten. Die Amplitude von Gasdruck und Abstand des Membranscheitels von der Düse wächst bzw. fällt mit wachsender Amplitude und Frequenz des Massestroms. Beide nehmen außerdem mit dem polytropen Exponenten zu.

     

Velocity and Passive Scalar Characteristics in a Round Jet with Grids at the Nozzle Exit

Velocity and passive scalar (temperature) measurements have been made in the near field of a round jet with and without obstructing grids placed at the jet exit. The Reynolds number Re _D (based on the exit centreline velocity and nozzle diameter) is 4.9 × 10⁴ and the flow is incompressible, while the temperature rise does not affect the velocity behaviour. The streamwise development and radial spreading of the passive scalar are attenuated, relative to the unobstructed jet. Close to the jet outlet, the spatial similarity of the moments (up to the third-order) of velocity fluctuations is improved, when the jet is perturbed. An explanation, based on the reduced effect of the large coherent structures in the developing region, is provided.     

Swirl number and nozzle confinement effects in a flat-vane axial swirler

This paper presents the results of a parametric experimental study of free swirling flow at the exit of a flat-vane axial swirler. A total of 16 data sets were acquired by combining four swirler vane angles (22°, 29°, 50.5°, and 58.3°) and four exit nozzles of different diameters (30, 40, 52, and 76 mm). Sophisticated pressure probes consisting of precise microphones and a two-component LDV system were used to investigate the effect of these geometrical parameters on swirling flow regimes characterized by the swirl number. Particular attention was paid to the precessing vortex core (PVC) phenomenon observed at the exit of the swirler nozzle. It has been shown that by varying the vane angle and the diameter of the exit nozzle, it is possible to independently control the swirl number value and the occurrence of a PVC. A distinct correlation has been found between the PVC-induced pressure pulsations detected by acoustic probes and the tangential velocity fluctuations measured by LDV. The use of microphones provides a quick way to measure the frequency response of swirl flow in a wide range of geometries and flow configurations. The PVC effect does not occur at low subcritical values of the integral swirl number (S < 0.5) and in the case of strong swirl flow (S_g = 0.9 and 1.2) in the absence of constriction by the nozzle (D_e/D₀ = 1). The disappearance of the PVC effect for strong swirl flow without constriction is due to the extreme displacement of the flow to the nozzle walls. The absence of a PVC in the flow was inferred not only from measurements of the frequency response of the flow over a wide range of Re numbers, but also from the absence of specific markers in velocity RMS distributions. Measurement results are used to derive an empirical correlation of the integral swirl number and the Strouhal number with a modified geometric swirl number. This allows a generalization of the frequency characteristics of swirling flows with a PVC for flat-vane axial swirlers, which are widely used in engineering.     

Characteristics of strongly-forced turbulent jets and non-premixed jet flames

Previous researchers have demonstrated that strong pulsations of the fuel flow rate can significantly reduce the flame length and luminosity of laminar/transitional non-premixed jet flames. The physical mechanisms responsible for these changes are investigated experimentally in acoustically-forced jet flows where the peak velocity fluctuations are up to eight times the mean flow velocity. Both reacting and non-reacting flows were studied and Reynolds numbers, based on the mean flow properties, ranged from 800 to 10,000 (corresponding to peak Reynolds numbers of 1,450–23,000), and forcing frequencies ranged from 290 to 1,140 Hz. Both the first and second organ-pipe resonance modes of the fuel delivery tube were excited to obtain these frequencies. An analysis of the acoustic forcing characteristics within the resonance tube is provided in order to understand the source of the high amplitude forcing. Flow visualization of jets with first resonant forcing confirms the presence of large-scale coherent vortices and strong reverse flow near the exit of the fuel tube. With second-resonant forcing, however, vortices are not emitted from the tube as they are drawn back into the fuel tube before they can fully form. Increased fine-scale turbulence is associated with both resonant cases, but particularly at second resonance. The power spectra of the velocity fluctuations for a resonantly pulsed jet show the presence of an inertial subrange indicating that the flow becomes fully turbulent even for mean-Reynolds-number jets that are nominally laminar. It is shown that these pulsed jet flows exhibit strong similarities to synthetic jets and that the Strouhal number, based on the maximum velocity at the fuel tube exit, is the dominant parameter for scaling these flows. The Strouhal number determines the downstream location where the coherent vortices breakdown, and is found to provide better collapse of flame length data (both current and previous) than other parameters that have been used in the literature.     

Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

Density and compressibility effects in turbulent subsonic jets part 1: mean velocity field

The behavior of compressible jets originated from initially turbulent pipe flows issuing in still air has been investigated at three different subsonic Mach numbers, 0.3, 0.6 and 0.9. Helium, nitrogen and krypton gases were used to generate the jet flows and investigate the additional effects of density on the flow structure. Particle image velocimetry, high-frequency response pressure transducers and thermocouples were used to obtain velocity, Mach number and total temperature measurements inside the flow field. The jets were formed at the exit of an adiabatic compressible frictional turbulent pipe flow, which was developing toward its corresponding sonic conditions inside the pipe, and continued to expand within the first four diameters distance after it exited the pipe. Theoretical considerations based on flow self-similarity were used to obtain the decay of Mach number along the centerline of the jets for the first time. It was found that this decay depends on two contributions, one from the velocity field which is inversely proportional to the distance from the exit and one from the thermal field which is proportional to this distance. As a result, a small non-linearity in the variation of the inverse Mach number with downstream distance was found. The decay of the Mach number at the centerline of the axisymmetric jets increases by increasing the initial Mach number at the exit of the flow for all jets. The decay of mean velocity at the centerline of the jets is also higher at higher exit Mach numbers. However, the velocity non-dimensionalized by the exit velocity seems to decrease faster at low exit Mach numbers, suggesting a reduced mixing with increasing exit flow Mach numbers. Helium jets were found to have the largest spreading rate among the three different gas jets used in the present investigation, while krypton jets had the lowest spreading rate. The spreading rate of each gas decreases with increasing its kinetic energy relatively to its internal energy.     

Measurements in the vicinity of a stagnation point

This paper presents measurements of a plane jet impinging onto a normal flat plate placed up to five jet widths from the jet outlet. The small spacing ensured that the stagnation streamline remained in the potential core of the jet. The plate shear stress distribution compared well to that from an analytical solution for the laminar development of the plate boundary layer whose external velocity was determined from the measured pressure. By comparing the shear stress measured under the present low level of free stream turbulence (0.35%) at the jet exit with that of Tu and Wood [Exp. Thermal Fluid Sci. 13 (1996) 364–373] made at about 4%, it is concluded that the turbulence level at the nozzle exit has only a second-order influence on the surface shear stress around the stagnation point. Some spanwise non-uniformity was observed in the plate shear stress, but this was confined largely to the transition region. The mean velocity, Reynolds stresses, and fluctuating pressure were measured along the stagnation streamline using a fast-response pressure probe. A significant increase in the streamwise normal stress and the mean square of the pressure fluctuations occurred before they were eventually attenuated by the plate. This increase occurred in the region where the streamwise velocity was decreasing close to the plate causing extra energy production through the normal stresses. Spectra of the velocity and pressure fluctuations showed that the increase in level was mainly due to the low frequency motion, whereas the subsequent decrease occurred at higher frequencies.     

A pseudo‐viscoelastic approach for transient polymeric flow exiting a channel

The influence of elasticity of a fluid exiting a channel is examined on transient coating downstream. A hybrid spectral/boundary element approach is proposed to solve the problem. The flow inside the channel is assumed to be fully developed. A viscoelastic instability of one‐dimensional plane Couette flow is first determined for a large class of Oldroyd fluids with added viscosity, which typically represent polymer solutions composed of a Newtonian solvent and a polymeric solute. The Johnson–Segalman equation is used as the constitutive model. The velocity profile inside the channel is taken as the exit profile for the emerging free‐surface flow. The flow is assumed to be Newtonian as it emerges from the channel. An estimate of the magnitude of the rate‐of‐strain tensor components in the free‐surface region reveals that they are generally smaller than the shear rate inside the channel. The evolution of the flow front is simulated using the boundary element method. For the channel flow, the problem is reduced to a nonlinear dynamical system using the Galerkin projection method. Stability analysis indicates that the channel velocity may be linear or non‐linear depending on the range of the Weissenberg number. The evolution of the coating flow at the exit is examined for steady as well as transient (monotonic and oscillatory) channel flow. It is found that adverse flow can exist as a result of fluid elasticity, which can hinder the process of blade coating. Copyright © 2003 John Wiley & Sons, Ltd.     

An experimental study of nonrheometric flows of viscoelastic fluids: II. Flow in a liquid jet exiting from a vertical tube

A laser anemometer has been used to study the region of accelerating shear flow near the exit of a vertical tube. It is in this region that the transition between steady laminar shear flow in the upstream tube and elongational flow in the downstream liquid jet takes place.Downstream velocity profiles were measured for solutions of 0.9% polyacrylamide in 85% glycerol/water and 0.9% polyacrylamide in water. Reynolds numbers (based on wall conditions in the fully developed upstream flow) ranged from 45 to 310 and Froude numbers from 0.294 to 4.11. Tubes, having sharpedged and rounded exit corners, with diameters of 1.25 cm and 1.90 cm were usedUpstream velocity profiles were measured for a solution of 0.9% polyacrylamide in water. Reynolds numbers ranged from 16 to 670. Only tubes having sharp-edged exit corners were used.It was found that the transition region did not extend upstream into the tube but was confined to the downstream jet. The transition took place over a distance of about 3–5 tube diameters depending upon the value of the Froude number. The axial distance downstream from the tube exit plane at which the velocity profile first became flat increased with increasing Froude number. The magnitude of the jet velocity at this point decreased with increasing Froude number.The condition of the tube exit corner was found to influence the flow in the transition region. Downstream velocity profiles obtained using tubes having rounded exit corners initially develop more slowly than, but soon catch up with and eventually overtake, the corresponding profiles obtained using tubes with sharp-edged exit corners.Downstream velocity profiles obtained for the 0.9% polyacrylamide in 85% glycerol/water solution were found to develop smoothly. The transition from steady shear flow in the tube to elongational flow in the jet took place through the combined processes of acceleration of the outer layers of the jet due to radial transfer of momentum with adjacent inner layers, the process spreading steadily inwards with increasing axial distance from the tube exit plane, and acceleration of the whole due to gravity. However, the velocity profiles obtained for the 0.9% polyacrylamide in water solution did not always develop so smoothly. At a Reynolds number of 310 and Froude number of 2.06 the radial momentum transfer process was restricted to a narrow outer region of the jet until a downstream axial distance of about 2 tube diameters was reached. Thereafter, the transition to a flat profile took place smoothly.     

Measurement of the shear viscosity using a newly developed GRLDA-viscometer

A two-point laser-Doppler anemometer is used to determine velocity gradients. Measuring additionally the pressure drop in channel flow allows one to use this instrument as a viscometer. This is demonstrated by measuring two polymer solutions as well as water. Besides the velocity gradient, the system also furnishes the velocity as well as velocity fluctuations. For surfactant solutions the sudden increase in these fluctuations go hand-in-hand with the sudden shear thickening reported. This behavior thus seems to be caused by a change in type of flow field (structural turbulence) rather than a change in the rheology of the surfactant solutions.This paper is dedicated to Professor Hanswalter Giesekus on the occasion of his retirement as Editor of Rheologica Acta.     

Downwards co-current annular flow

This paper summarizes a study of the characteristics of downwards annular two-phase flow. The measurements reported are of film thickness, wave velocity and frequency, local pressure fluctuations, pressure gradient and liquid entrainment. The most important new feature of the work is the use of continuous data recording with either on-line or off-line statistical analysis. Experiments were carried out with air-water flows in tubes of 3.18 and 3.82 cm bore. It is shown that the interfacial characteristics of the flow may require at least 5 m for full development at some flow rates and most measurements were carried out with an entrance region of this length. It is also shown that the pressure fluctuations, characteristic of this two-phase flow regime, are primarily due to pressure surges caused by disturbance waves in the system passing through the exit device. A new regime map is proposed, based on experimental evidence, in which several distinctive types of interfacial behaviour are noted.     

The effect of buoyancy on flow fluctuations for horizontal plane jets in low speed applications

Low speed jets have important applications in chemical process, power and aerospace industries. Velocity fluctuations in low speed laminar jets have been investigated experimentally and theoretically, in the present work. The effects of buoyancy on the mean and fluctuating components of velocity have been highlighted. It is observed that even for forced convection dominated flow, convective instabilities and the resulting local velocity fluctuations are significantly influenced by buoyancy. Both the dominant frequency and the amplitude of velocity fluctuations depend on the jet exit temperature and spatial location within the jet. For isothermal jets, the dominant frequency of oscillation increases almost linearly with Reynolds number, while for buoyant jets nonlinearity exists at lower Reynolds numbers. Numerical simulations of the present study are found to be reasonably successful in predicting the oscillatory behavior of both isothermal and non-isothermal laminar free jets accurately.     

Experimental and numerical investigation on steady blowing flow control within a compact inlet duct

A combined experimental and numerical investigation of flow control actuation in a short, rectangular, diffusing S-shape inlet duct using a two-dimensional tangential control jet was conducted. Experimental and numerical techniques were used in conjunction as complementary techniques, which are utilized to better understand the complex flow field. The compact inlet had a length-to-hydraulic diameter ratio of 1.5 and was investigated at a free-stream Mach number of 0.44. In contrast to the baseline flow, where the flow field was fully separated, the two-dimensional control jet was able to eliminate flow separation at the mid-span portion of the duct and changed considerably the three-dimensional flow field, and ultimately, the inlet performance. A comparison between the baseline (no actuation) and forced flow fields showed that secondary flow structures dominated both flow fields, which is inevitably associated with total pressure loss. Contrary to the baseline case, the secondary flow structures in the forced case were established from the core flow stagnating on the lower surface of the duct close to the aerodynamic interface plane. High fidelity spectral analysis of the experimental results at the inlet’s exit plane showed that the baseline flow field was dominated by pressure fluctuations corresponding to a Strouhal number based on hydraulic diameter of 0.26. Not only did the two-dimensional tangential control jet improve the time-averaged pressure recovery at the inlet exit plane (13.3% at the lower half of the aerodynamic interface plane), it essentially eliminated the energy content of the distinct unsteady fluctuations which characterized the baseline flow field. This result has several implications for the design of a realistic engine inlet; furthermore, it depicts that a single non-intrusive static pressure measurement at the surface of the duct can detect flow separation.     

Flow friction on co-rotating parallel-disk assemblies with forced through-flow

The power requirement for a rotating parallel-disk assembly with through-flow is experimentally studied. The flow velocity at the test core exit is measured using a traverse hot-wire probe, from which the exit kinetic energy is determined. A traverse pitot tube is utilized to monitor the velocity distribution in the inlet duct from which the flow rate is evaluated. The total pressure characteristics, fluid power transmission, rotor efficiency and moment coefficient (i.e. power number) are determined from the measurements of static pressures, rotational speed and torque. It is disclosed that the onset of stall propagation, a unique characteristics of shear pump, can be detected from a total pressure plot.     

Vortex-In-Cell and Probability Density Function Approach for a Passive Scalar Field in a Mixing Layer

A Reynolds-averaged simulation based on the vortex-in-cell (VIC) and the transport equation for the probability density function (PDF) of a scalar has been developed to predict the passive scalar field in a two-dimensional spatially growing mixing layer. The VIC computes the instantaneous velocity and vorticity fields. Then the mean-flow properties, i.e. the mean velocity, the root-mean-square (rms) longitudinal and lateral velocity fluctuations, the Reynolds shear stress, and the rms vorticity fluctuations are computed and used as input to the PDF equation. The PDF transport equation is solved using the Monte Carlo technique. The convection term uses the mean velocities from the VIC. The turbulent diffusion term is modeled using the gradient transport model, in which the eddy diffusivity, computed via the Boussinesq's postulate, uses the Reynolds shear stress and gradients of mean velocities from the VIC. The molecular mixing term is closed by the modified Curl model.

The computational results were compared with two-dimensional experimental results for passive scalar. The predicted turbulent flow characteristics, i.e. mean velocity and rms longitudinal fluctuations in the self-preserving region, show good agreement with the experimental measurements. The profiles of the mean scalar and the rms scalar fluctuations are also in reasonable agreement with the experimental measurements. Comparison between the mean scalar and the mean velocity profiles shows that the scalar mixing region extends further into the free stream than does the momentum mixing region, indicating enhanced transport of scalar over momentum. The rms scalar profiles exhibit an asymmetry relative to the concentration centerline, and indicate that the fluid on the high-speed side mixes at a faster rate than the fluid on the low-speed side. The asymmetry is due to the asymmetry in the mixing frequency cross-stream profiles. Also, the PDFs have peaks biased toward the high-speed side.     

Resistance of a circular pipe with pulsatory variation of the flow rate

The results of an experimental investigation of the hydraulic resistance of a circular pipe for turbulent flow with periodic flow rate fluctuations are presented. The presence of resonance phenomena in the pipe is revealed. It is established that, for hydrodynamic nonstationarity, the pipe resistance is a nonmonotonous function of the frequency of the imposed flow rate fluctuations and differs from the pipe resistance in the stationary flow regime. Under the conditions considered, to find the pipe resistance it is necessary to take into account the variation of the flow kinetic energy with respect to the phase of the imposed flow rate fluctuations due to the deformation of the velocity profile.     

Buoyancy-induced airflow in a side-heated structure consisting of a cubic box and vertical ducts

Buoyancy-induced airflow in a box with one wall heated, an unheated inlet duct connected to its floor, and an exit duct with one side heated connected to its ceiling is experimentally investigated. A flow rate prediction method based on buoyancy and flow resistance balance is proposed and experimentally validated. The flow pattern and thermal stratification in the box; the flow resistance characteristics for low Reynolds numbers; the relationship among buoyancy, flow resistance, and pressure defect; the chimney effect caused by the exit duct; and the heat transfer characteristics of the heated walls are clarified. The flow rate, thermal stratification, and flow enhancement due to the chimney effect are considerably dependent on the size of the gap of the exit duct.     

Analysis of the nozzle exit flow parameter effect on the turbulence characteristics and the noise level in jets issuing from nozzles of different types

The flow, turbulence, and noise parameters of cold and hot jets flowing out of nozzles of different types at subsonic and supersonic velocities are calculated using the high-resolution RANS/ILES method. The effect of the Mach number and the temperature at the nozzle exit on the flow features, the turbulent fluctuations of the velocity, the static pressure, and the temperature, together with the overall noise level is analyzed for all the jets considered. The accuracy of the calculations is confirmed by means of comparing with the available experimental data concerning certain parameters.     

Effect of particle size on a two-phase turbulent jet

The effect of particle size on two-phase turbulent jet flow structure is studied in the present experimental investigation. Polystyrene solid particles of 210, 460, and 780 μm were used. The particles' mass loading ratios ranged from 0 to 3.6. The flow Reynolds number was 2 ‘ 10⁴, which was based on the pipe nozzle diameter and the fluid-phase centerline velocity at the nozzle exit. A two-color laser-Doppler anemometer (LDA), combined with the amplitude discrimination method and the velocity filter method, was employed for measurement. The measurement range of the jet flow was from the initial pipe exit to 90D downstream. Results are presented for the mean velocities of particle and fluid phases, the flow's turbulent intensities and the flow's Reynolds stresses. The energy spectra and the correlation functions of the two-phase jet flow were also obtained by using another one-component He-Ne LDA system.