Computational and experimental characterization of a liquid jet plunging into a quiescent pool at shallow inclination

A circular water jet (Re = 1.6 × 10⁵; We = 8.8 × 10³) plunging at shallow angles (θ ≈ 12.5°) into a quiescent pool is investigated computationally and experimentally. A surprising finding from the work is that cavities, of the order of jet diameter, are formed periodically in the impact location, even though the impinging flow is smooth and completely devoid of such a periodicity. Computational prediction of these frequencies was compared with experimental findings, yielding excellent agreement. The region in the vicinity of the impact is characterized by strong churning due to splashing and formation of air cavities. Measured velocity profiles indicate a concentration of momentum beneath the free surface slightly beyond the impact location (X/D_j ≈ 14), with a subsequent shift towards the free surface further downstream of this point (X/D_j ≈ 30). This shift is due primarily to the action of buoyancy on the cavity/bubble population. Comparisons of the mean velocity profile between simulations and experiments are performed, yielding good agreement, with the exception of the relatively small churning flow region. Further downstream (X/D_j ≳ 40), the flow develops mostly due to diffusion and the location of peak velocity coincides with the free surface. In this region, the free surface acts as an adiabatic boundary and restricts momentum diffusion, causing the peak velocity to occur at the free surface.     

Vaporization of a liquid hexanes jet in cross flow

The vaporization characteristics of a liquid hexanes jet in a lab-scale test section with a plain orifice-type injector were experimentally investigated. The experimental measurements were carried out on the basis of the infrared laser extinction method using two He–Ne lasers (one at 632.8 nm and the other at 3.39 μm). The momentum flux ratio (q_F/A) was varied from 20 to 60 over 20 steps, and the supplying air temperature (T_A) was changed from 20 to 260 °C over 120 steps. The objectives of the current study were to assess the vaporization characteristics of a liquid hexanes jet and to derive a correlation between flow conditions and hexanes vapor concentration in a jet-in-crossflow configuration. From the results of the experimental measurement, it was concluded that hexanes vapor concentration increased with the increase of the momentum flux ratio and the supplying air temperature. An experimental correlation between flow conditions and hexanes vapor concentration (Z_F) was proposed as a function of the normalized horizontal distance (x/d_o), the supplying air temperature (T_A), the momentum flux ratio (q_F/A), the fuel jet Reynolds number (Re_F), and the fuel jet Weber number (We_F).     

The effect of sidewalls on rectangular jets

An experimental study is presented regarding the influence of sidewalls on the turbulent free jet flow issuing from a smoothly contracting rectangular nozzle of aspect ratio 15. “Sidewalls” are two parallel plates, flush with each of the slots’ short sides, practically establishing bounding walls extending the nozzle sidewalls in the downstream direction. Measurements of the streamwise and lateral velocity mean and turbulent characteristics have been accomplished, with an x-sensor hot wire anemometer, up to an axial distance of 35 nozzle widths, for jets with identical inlet conditions with and without sidewalls. Centreline measurements for both configurations have been collected for three Reynolds numbers, Re_D = 10,000, 20,000 and 30,000. For Re_D = 20,000 measurements in the transverse direction were collected at 13 different downstream locations in the range, x = 0–35 nozzle widths, and in the spanwise direction at three different downstream locations, x = 2, 6 and 25 nozzle widths.Results indicate that, the two jet configurations (with and without sidewalls) produce statistically different flow fields. Sidewalls do not lead to the production of a 2D flow field as undulations in the spanwise mean velocity distribution indicate. They do increase the two-dimensionality of the jet increasing the longevity of 2D spanwise rollers structures formed in the initial stages of entrainment, which are responsible for the convection of longitudinal momentum towards the outer field, establishing larger streamwise mean velocities at the jet edges. In the near field, up to 25 nozzle widths, lower outward lateral velocities in the presence of the sidewalls are held responsible for the decrease of turbulent terms including rms of velocity fluctuations and Reynolds stresses. Skewness factors increase monotonically across the shear layers from negative values to positive forming sharp peaks at the outer edges of the jet, illustrative of the presence of well defined 2D roller structures in the jet with sidewalls.     

Droplet size and velocity characteristics of water-air impinging jet atomizer

A water-air impinging jets atomizer is investigated in this study, which consists of flow visualization using high speed photography and mean droplet size and velocity distribution measurements of the spray using Phase Doppler Anemometry (PDA). Topological structures and break up details of the generated spray in the far and near fields are presented with and without air jet and for an impinging angle of 90°. Spray angle increases with the water jet velocity, air flow rate and impinging angle. PDA results indicate that droplet size is smallest in the spray center, with minimum value of Sauter mean diameter (SMD) of 50 µm at the air flow rate of Q_m = 13.50 g/min. SMD of droplets increases towards the spray outer region gradually to about 120 µm. The mean droplet velocity component W along the air-jet axis is highest in the spray center and decreases gradually with increasing distance from the spray center. SMD normalized by the air nozzle diameter is found firstly to decrease with gas-to-liquid mass ratio (GLR) and air-to-liquid momentum ratio (ALMR) and then remain almost constant. Its increasing with aerodynamic Weber number indicates an exponential variation. The study sheds light on the performance of water-air impinging jets atomizers providing useful information for future CFD simulation works.     

Experimental study of parallel and inclined turbulent wall jets

An experimental study of the flow field in a two-dimensional wall jet has been conducted. All measurements were carried out using hot-wire anemometry. The experimental facility has a rectangular slot nozzle of high aspect ratio l/b = 100 (where l and b are the length and height slot, respectively). Mean velocities and Reynolds stresses were determined with three nozzle Reynolds numbers (Re = 1 × 10⁴, 2 × 10⁴ and 3 × 10⁴) and four different inclination angles between the wall and the flow velocity at the nozzle (β = 0°, 10°, 20° and 30°). Results indicate that all wall jets are self-preserving in the developed region. Normal to the wall two regions can be identified: one similar to a plane free jet and the other similar to a boundary layer. Downstream the interaction between these two regions creates a mixed or third region. The logarithmic region increases with the distance from the nozzle and with the Reynolds number. For the inclined wall jet, the spreading rate expressed in terms of jet half-width or maximum velocity decay with respect to the streamwise distance, asymptotes to a linear law. The streamwise locations where the jet becomes self-similar are farther from the exit than in parallel wall jet. The slope of both half-width and maximum velocity decay in the developed region are affected by both wall jet inclination angle and nozzle exit Reynolds number.     

The flow field around a micropillar confined in a microchannel

The flow field over a low aspect ratio (AR) circular pillar (L/D = 1.5) in a microchannel was studied experimentally. Microparticle image velocimetry (μPIV) was employed to quantify flow parameters such as flow field, spanwise vorticity, and turbulent kinetic energy (TKE) in the microchannel. Flow regimes of cylinder-diameter-based Reynolds number at 100 ⩽ Re_D ⩽ 700 (i.e., steady, transition from quasi-steady to unsteady, and unsteady flow) were elucidated at the microscale. In addition, active flow control (AFC), via a steady control jet (issued from the pillar itself in the downstream direction), was implemented to induce favorable disturbances to the flow in order to alter the flow field, promote turbulence, and increase mixing. Together with passive flow control (i.e., a circular pillar), turbulent kinetic energy was significantly increased in a controllable manner throughout the flow field.     

Flow evolution of a turbulent submerged two-dimensional rectangular free jet of air. Average Particle Image Velocimetry (PIV) visualizations and measurements

The paper presents average flow visualizations and measurements, obtained with the Particle Image Velocimetry (PIV) technique, of a submerged rectangular free jet of air in the range of Reynolds numbers from Re = 35,300 to Re = 2200, where the Reynolds number is defined according to the hydraulic diameter of a rectangular slot of height H. According to the literature, just after the exit of the jet there is a zone of flow, called zone of flow establishment, containing the region of mixing fluid, at the border with the stagnant fluid, and the potential core, where velocity on the centerline maintains a value almost equal to the exit one. After this zone is present the zone of established flow or fully developed region. The goal of the paper is to show, with average PIV visualizations and measurements, that, before the zone of flow establishment is present a region of flow, never mentioned by the literature and called undisturbed region of flow, with a length, L_U, which decreases with the increase of the Reynolds number. The main characteristics of the undisturbed region is the fact that the velocity profile maintains almost equal to the exit one, and can also be identified by a constant height of the average PIV visualizations, with length, L_CH, or by a constant turbulence on the centerline, with length L_CT. The average PIV velocity and turbulence measurements are compared to those performed with the Hot Film Anemometry (HFA) technique. The average PIV visualizations show that the region of constant height has a length L_CH which increases from L_CH = H at Re = 35,300 to L_CH = 4–5H at Re = 2200. The PIV measurements on the centerline of the jet show that turbulence remains constant at the level of the exit for a length, L_CT, which increases from L_CT = H at Re = 35,300 to L_CT = 4–5H at Re = 2200. The PIV measurements show that velocity remains constant at the exit level for a length, L_U, which increases from L_U = H at Re = 35,300 to L_U = 6H at Re = 2200 and is called undisturbed region of flow. In turbulent flow the length L_U is almost equal to the lengths of the regions of constant height, L_CH, and constant turbulence, L_CT. In laminar flow, Re = 2200, the length of the undisturbed region of flow, L_U, is greater than the lengths of the regions of constant height and turbulence, L_CT = L_CH = 4–5H. The average PIV and HFA velocity measurements confirm that the length of potential core, L_P, increases from L_P = 4–5H at Re = 35,300 to L_P = 7–8H at Re = 2200, and are compared to the previous experimental and theoretical results of the literature in the zone of mixing fluid and in the fully developed region with a good agreement.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

Dynamic mode decomposition of turbulent cavity flows for self-sustained oscillations

Self-sustained oscillations in a cavity arise due to the unsteady separation of boundary layers at the leading edge. The dynamic mode decomposition method was employed to analyze the self-sustained oscillations. Two cavity flow data sets, with or without self-sustained oscillations and possessing thin or thick incoming boundary layers (Re_D = 12,000 and 3000), were analyzed. The ratios between the cavity depth and the momentum thickness (D/θ) were 40 and 4.5, respectively, and the cavity aspect ratio was L/D = 2. The dynamic modes extracted from the thick boundary layer indicated that the upcoming boundary layer structures and the shear layer structures along the cavity lip line coexisted with coincident frequency space but with different wavenumber space, whereas structures with a thin boundary layer showed complete coherence among the modes to produce self-sustained oscillations. This result suggests that the hydrodynamic resonances that gave rise to the self-sustained oscillations occurred if the upcoming boundary layer structures and the shear layer structures coincided, not only in frequencies, but also in wavenumbers. The influences of the cavity dimensions and incoming momentum thickness on the self-sustained oscillations were examined.     

Hydrodynamic forces on a rotating sphere

The wake dynamics of a rotating sphere with prescribed rotation axis angles are quantitatively analysed by carrying out numerical simulations at Reynolds numbers of Re = 100, 250 and 300, non-dimensional rotational rates Ω¹ = 0–1 and rotation axis angles α = 0, π/6, π/3 and π/2 measured from the free stream axis. These parameters are the same as those in an earlier study (Poon et al., 2010, Int. J. Heat Fluid Flow) where the instantaneous flow structures were discussed qualitatively. This study extends the findings of the earlier study by employing phase diagrams (C_Lx, C_Ly) and (C_D, C_L) to provide a quantitative analysis of the time-dependent behaviour of the flow structures. At Re = 300 and Ω¹ = 0.05, the phase diagrams (C_Lx, C_Ly) show ‘saw tooth’ patterns for both α = 0 and π/6. The ‘saw tooth’ pattern indicates that the flow structures comprise a higher frequency oscillation component at a Reynolds number of 300 which is not observed until Re ≈ 800 for a stationary sphere. This ‘saw tooth’ pattern disappears as Ω¹ increases. The employment of the phase diagrams also reveals that different flow structures induce different oscillation amplitudes on both lateral force coefficients. With the exception of the vortices formed from a shear layer instability, all other flow regimes show larger fluctuations in C_L than C_D.     

Flow structures and heat transfer on dimples in a staggered arrangement

Vortex structures and heat transfer enhancement mechanism of turbulent flow over a staggered array of dimples in a narrow channel have been investigated using Large Eddy Simulation (LES), Laser Doppler Velocimetry (LDV) and pressure measurements for Reynolds numbers Re_H = 6521 and Re_H = 13,042.The flow and temperature fields are calculated by LES using dynamic mixed model applied both for the velocity and temperature. Simulations have been validated with experimental data obtained for smooth and dimpled channels and empiric correlations. The flow structures determined by LES inside the dimple are chaotic and consist of small eddies with a broad range of scales where coherent structures are hardly to detect. Proper Orthogonal Decomposition (POD) method is applied on resolved LES fields of pressure and velocity to identify spatial–temporal structures hidden in the random fluctuations. For both Reynolds numbers it was found that the dimple package with a depth h to diameter D ratio of h/D = 0.26 provides the maximum thermo-hydraulic performance. The heat transfer rate could be enhanced up to 201% compared to a smooth channel.     

The effect of incidence angle on the mean wake of surface-mounted finite-height square prisms

The mean wake of a surface-mounted finite-height square prism was studied experimentally in a low-speed wind tunnel to explore the combined effects of incidence angle (α) and aspect ratio (AR). Measurements of the mean wake velocity field were made with a seven-hole pressure probe for finite square prisms of AR = 9, 7, 5 and 3, at a Reynolds number of Re = 3.7 × 10⁴, for incidence angles from α = 0° to 45°. The relative thickness of the boundary layer on the ground plane, compared to the prism width, was δ/D = 1.5. As the incidence angle increases from α = 0° to 15°, the mean recirculation zone shortens and the mean wake shifts in the direction opposite to that of the mean lift force. The downwash is also deflected to this side of the wake and the mean streamwise vortex structures in the upper part of the wake become strongly asymmetric. The shortest mean recirculation zone, and the greatest asymmetry in the mean wake, is found at the critical incidence angle of α_critical ≈ 15°. As the incidence angle increases from α = 15° to 45°, the mean recirculation zone lengthens and the mean streamwise vortex structures regain their symmetry. These vortices also elongate in the wall-normal direction and become contiguous with the horseshoe vortex trailing arms. The mean wake of the prism of AR = 3 has some differences, such as an absence of induced streamwise vorticity near the ground plane, which support its classification as lying below the critical aspect ratio for the present flow conditions.     

Vortical structure evolutions and spreading characteristics of a plane jet flow under anti-symmetric long-wave excitation

The vortical evolutions and spreading characteristics of a low-speed plane jet under anti-symmetric long-wave excitations are investigated experimentally. The perturbation is introduced with two oscillating strips located at the nozzle exit. The experiments were operated at Reynolds number of 8.2 × 10³ based on the nozzle exit height. Mixing and spreading properties are influenced obviously by long-wave excitation after the end of potential core. The increments of half-width, momentum thickness, and volume flow rate depend on the excitation frequency. The results of flow visualization also reveal the dependence of excitation frequency. The power spectra of fluctuating velocities shows that the evolution of coherent structure is significantly influenced by the long-wave excitation in the downstream, but it is similar to the natural jet in the near field. The long-wave excitation at certain frequencies can promote large-scaled anti-symmetric vortical structures in the far field.     

Experimental investigation of the effects of blowing conditions and Mach number on the unsteady behavior of coolant ejection through a trailing edge cutback

The present paper shows the results of an experimental investigation into the unsteadiness of coolant ejection at the trailing edge of a highly loaded nozzle vane cascade. The trailing edge cooling scheme features a pressure side cutback with film cooling slots, stiffened by evenly spaced ribs in an inline configuration. Cooling air is also ejected through two rows of cylindrical holes placed upstream of the cutback. Tests were performed with a low inlet turbulence intensity level (Tu₁ = 1.6%), changing the cascade operating conditions from low speed (M_2is = 0.2) up to high subsonic regime (M_2is = 0.6), and with coolant to main stream mass flow ratio varied within the 0.5–2.0% range. Particle Image Velocimetry (PIV) and flow visualizations were used to investigate the unsteady mixing process taking place between coolant and main flow downstream of the cutback, up to the trailing edge. For all the tested conditions, the results show the presence of large coherent structures, which presence is still evident up to the trailing edge. Their shape and direction of rotation change with injection conditions, as a function of coolant to mainstream velocity ratio, strongly influencing the thermal protection capability of the injected coolant flow. The Mach number increase is only responsible for a positioning of such vortical structures closer to the wall, while the Strouhal number almost remains unchanged.     

Influence of aspect ratio on the flow above the free end of a surface-mounted finite cylinder

The flow above the free end of a surface-mounted finite-height cylinder was studied in a low-speed wind tunnel using particle image velocimetry (PIV). Velocity measurements were made in vertical and horizontal measurement planes above the free end of finite cylinders of aspect ratios AR = 9, 7, 5 and 3, at a Reynolds number of Re = 4.2 × 10⁴. The relative thickness of the boundary layer on the ground plane was δ/D = 1.7. Flow separating from the leading edge formed a prominent recirculation zone on the free-end surface. The legs of the mean arch vortex contained within the recirculation zone terminate on the free-end surface on either side of the centreline. Separated flow from the leading edge attaches onto the upper surface of the cylinder along a prominent attachment line. Local separation downstream of the leading edge is also induced by the reverse flow and arch vortex circulation within the recirculation zone. As the cylinder aspect ratio is lowered from AR = 9 to AR = 3, the thickness of the recirculation zone increases, the arch vortex centre moves downstream and higher above the free-end surface, the attachment position moves downstream, and the termination points of the arch vortex move upstream. A lowering of the aspect ratio therefore results in accentuated curvature of the arch vortex line. Changes in aspect ratio also influence the vorticity generation in the near-wake region and the shape of the attachment line.     

Laminar flow of power-law fluids past a rotating cylinder

In this work, the continuity and momentum equations have been solved numerically to investigate the flow of power-law fluids over a rotating cylinder. In particular, consideration has been given to the prediction of drag and lift coefficients as functions of the pertinent governing dimensionless parameters, namely, power-law index (1 ≥ n ≥ 0.2), dimensionless rotational velocity (0 ≤ α ≤ 6) and the Reynolds number (0.1 ≤ Re ≤ 40). Over the range of Reynolds number, the flow is known to be steady. Detailed streamline and vorticity contours adjacent to the rotating cylinder and surface pressure profiles provide further insights into the nature of flow. Finally, the paper is concluded by comparing the present numerical results with the scant experimental data on velocity profiles in the vicinity of a rotating cylinder available in the literature. The correspondence is seen to be excellent for Newtonian and inelastic fluids.     

Turbulent channel flow of dilute polymeric solutions: Drag reduction scaling and an eddy viscosity model

Direct numerical simulation of viscoelastic turbulent channel flows up to the maximum drag reduction (MDR) limit has been performed. The simulation results in turn have been used to develop relationships between the flow and fluid rheological parameters, i.e. maximum chain extensibility, Reynolds number, Re_τ, and Weissenberg number, We_τ and percent drag reduction (%DR) as well as the slope increment of the mean velocity profile. Moreover, based on the trends observed in the mean velocity profile and the overall momentum balance three different regimes of drag reduction (DR), namely, low drag reduction (LDR; 0 ≤ %DR ≤ 20), high drag reduction (HDR; 20 ≤ %DR ≤ 52) and MDR (52 ≤ %DR ≤ 74) have been identified and mathematical expressions for the eddy viscosity in these regimes are presented. It is found that both in LDR and HDR regimes the eddy viscosity varies with the distance from the channel wall. However, in the MDR regime the ratio of the eddy viscosity to the Newtonian one tends to a very small value around 0.1 within the channel. Based on these expressions a procedure that relies on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed for evaluating the mean velocity profile.     

LES of turbulent jet in cross-flow: Part 1 – A numerical validation study

The paper presents results of a LES based numerical simulation of the turbulent jet-in-cross-flow (JICF) flowfield, with Reynolds number based on cross-flow velocity and jet diameter Re = 2400 and jet-to-cross-flow velocity ratio of R = 3.3. The JICF flow case has been investigated in great detail, involving conduction of two independent precursor simulations, prior to the main JICF simulation, as the considered case has turbulent inflow conditions on both jet and cross-stream side. The LES results are directly compared to pointwise Laser Doppler Anemometry (LDA) measurements, showing a very good agreement on the level of various statistical quantities in all flow regions but the immediate jet-to-cross-flow exhaustion zone. Several LES computations involving grids of up to 15 million grid points have been conducted, showing no improvement in the agreement between numerical results and measurements, possibly indicating a LDA measurement problem in this particular region.     

Study on the radial jet velocity distribution of two closely spaced opposed jets

The experimental and theoretical researches on the radial jet of two opposed jets have been carried out in this paper. The radial velocities of opposed jets with various exit velocities, nozzle diameters and nozzle separations were measured experimentally by a hot-wire anemometer (HWA). The results show that, the normalized radial velocities are self-similar across various radial sections at r ? 1.5D and the radial velocity profiles can be described by a Gaussian distribution function. The half-width increases linearly with increasing radial distance at r ? 1.5D, and spreading rates of radial jet are about 0.121. The normalized radial velocity at impingement plane increases firstly, and then decreases with the increasing normalized radial distance. The normalized radial velocity is independent on nozzle diameter, nozzle separation and exit velocity. The maximum radial velocity at impingement plane is proportional to the exit velocity, and it is inversely proportional to the 0.551th power of the normalized nozzle separation. The position of the maximum radial velocity increases with the nozzle separation at L/D < 1, and keeps invariant at L/D ? 1.     

Investigation of a continuous adjoint-based optimization procedure for aeroacoustic control of plane jets

A control optimization technique using the continuous adjoint of the compressible Navier–Stokes equations is implemented for aeroacoustic optimization of plane jet flows. The purpose of the adjoint equations is to provide sensitivity information, which is afterwards used in a gradient-based minimization of a prescribed cost functional, designed to describe the far-field sound pressure level (SPL). The objective of the present paper is to demonstrate the ability to reduce the sound in the near far-field of plane jets. Furthermore, as the continuous adjoint approach can become inaccurate, due to inconsistencies between the continuous and the discretized system, the accuracy of the continuous adjoint approach is investigated. The considered cases exhibit a nozzle exit Reynolds number of Re_jet = ρu_jetD/μ = 2000 and a Mach number of M_jet = 0.9, performed using two-dimensional direct numerical simulation and three-dimensional large-eddy simulation, respectively. A comparison of the obtained gradient via adjoint and finite differences is presented and it is shown, that in order to obtain reliable gradient directions, the length of the optimization time needs to be restricted. Furthermore, a receding horizon optimization for the two-dimensional plane jet simulation is used to obtain a sound reduction over much longer time intervals. The influence of different formulations of the viscosity in the adjoint equations is finally investigated.