Jet Velocity Profile Research Articles

Velocity profiles in a water jet of a Pelton nozzle: CFD simulations on both 2D and 3D geometries

Hydropower is an important energy sector deployed all over the World with a significant share in the global electricity production. Due to the ongoing climate changes, the lack of water in summer periods compromises the performance of hydraulic machines, whose efficiency quickly decreases when they operate at strong part-load conditions.Among the most known hydraulic turbines, Pelton is suitable to be used with high geodetic heights and relatively low flow rates. When dealing with flow rates 30% lower than the Best Efficiency Point (BEP), the efficiency drastically decreases mainly due to the non-uniform velocity profiles of the water jets coming out from the nozzles. The quality of the jet is affected by the distributor geometry, bending pipes and spear valves with the respective supports located upstream.The aim of this work is to investigate different velocity profiles of the water jet coming out from a Pelton nozzle geometry by means of Computational Fluid Dynamics (CFD) simulations performed by ANSYS® Fluent solver. Four different spear valve angles were simulated on a 2D-axisymmetric geometry, starting from a reference case of = 50° with increasing steps of 5°, maintaining a fixed positioning of the spear valve that corresponds to a partial load operation of the machine.In addition, also a 3D simulation has been carried out and the streamlines along a symmetry plane are shown. The results of the 3D simulations were compared to the 2D-axisymmetric ones taking into account the aforementioned reference case, showing how this last simplification of the computational domain leads to almost the same macroscopic results.

Positively buoyant jets: Semiturbulent to fully turbulent regimes

Using a high-speed camera, laser imaging and ultrasound velocimetry, we study positively buoyant miscible jets. Based on the appearance of the laminar length, we classify the flow into fully turbulent and semi-turbulent regimes. We quantify the regime transition boundaries and propose empirical correlations to predict the laminar length. To have a global view of the flow, we also analyze the quasi-steady jet characteristics (jet radius, spread angle, virtual origin, velocity profiles and energy dissipation) and starting jet characteristics (penetration length and tip velocity).

Jet propulsion of a squid-inspired swimmer in the presence of background flow

Inspired by recent studies of a squid-like swimmer, we propose a three-dimensional jet propulsion system composed of an empty chamber enclosed within a deformable body with an opening. By prescribing the body deformation and jet velocity profile, we numerically investigate the jet flow field and propulsion performance under the influence of background flow during a single deflation procedure. Three jet velocity profiles, i.e., constant, cosine and half cosine, are considered. We find that the maximum circulation of the vortex ring is reduced at a higher background flow velocity. This is because stronger interaction between the jet flow and background flow makes it harder to feed the leading vortex ring. Regarding thrust production, our analysis based on conservation of momentum indicates that with the constant profile the peak thrust is dominated by the time derivative of the fluid momentum inside the body, while momentum flux related thrust accounts for the quasi-steady thrust. For the cosine profile, its peak is mainly sourced from momentum flux associated with the unsteady vortex ring formation. No prominent thrust peak exists with the half cosine profile whose thrust continuously increases during the jetting. For all the three jet velocity profiles, added-mass related thrust attributed to body deformation enhances the overall thrust generation non-negligibly. Under the present tethered mode, the background flow has negligible influence on the thrust attributed to momentum flux and momentum change of the fluid inside the body. However, it indeed affects the over pressure-related thrust but its effect is relatively small. The overall thrust declines due to the significantly increased drag force at large incoming flow speed despite the rise of added-mass related thrust. Unsteady thrust involving vortex ring formation becomes more important in the overall thrust generation with an increased background flow velocity, reflected by larger ratios of the unsteady impulse to jet thrust impulse.

Attached and Attaching Three-Dimensional Jets From Circular Nozzles: Analytical Model

Abstract Here we consider velocity profiles of three dimensional attaching and attached jets emerging from circular nozzles. Like their well-studied two-dimensional counterparts, these wall jets lose momentum due to interactions with nearby surfaces. Unlike their two-dimensional counterparts, simple and quantitative expressions for the velocity profiles of three-dimensional wall jets remain elusive. Here we present a quantitative analytical model of the three-dimensional velocity profiles of attached jets inclusive of a local skin coefficient of friction. We compare these expressions to experimental velocity profiles at moderate and high nozzle Reynolds numbers to find reasonable quantitative agreement. This work has implications for a variety of industries including nuclear waste processing, where jet flows in mixing vessels suspend solids and gases trapped in radioactive waste tanks.

Non-isothermal mixing characteristics in the extreme near-field of turbulent jets in hot crossflow: Effects of jet exit turbulence and velocity profile

The non-reacting and reacting jets-in-crossflow (JICF) are important flow configurations for effective mixing and combustion in practical applications. Many studies in the literature examine the overall mixing characteristics of isothermal, unconfined, non-reacting JICF. This experimental study expands on our recently published work that examined mixing characteristics in the near-field of a non-reacting jet in a hot vitiated crossflow (1500 K) for the jet-to-crossflow density ratio between 3.2 and 7.8 issuing from a round jet with a fully developed turbulent pipe flow exit profile. In this study, effects of the changing jet exit velocity profile to top-hat as well as exit turbulence levels (28% and 40%) with parabolic profiles are examined. Temperature measurements were made using laser Rayleigh scattering. The jet trajectory, centerline concentration decay based on adiabatic mixing assumption, Favre-averaged scalar dissipation, and mixing time scales were compared with the previous study results. Center-plane mixing metrics indicated that top-hat and pipe flow jets behave similarly, with better near-field mixing at lower momentum flux ratios and higher density ratios. The elevated turbulence cases have a higher near-field mixing efficiency with rates that are nearly independent of momentum flux ratios above 9.3 at a constant density ratio. Scalar dissipation analysis showed that the elevated turbulence jets differ from the nominal turbulence top-hat and pipe exit jet cases with a lack of strong peaks and slightly higher upstream crossflow magnitudes. Reducing the density ratio resulted in a decrease in the windward and leeward dissipation region size and magnitude.

A new lepto-hadronic model applied to the first simultaneous multiwavelength data set for Cygnus X–1

ABSTRACTCygnus X–1 is the first Galactic source confirmed to host an accreting black hole. It has been detected across the entire electromagnetic spectrum from radio to GeV gamma-rays. The source’s radio through mid-infrared radiation is thought to originate from the relativistic jets. The observed high degree of linear polarization in the MeV X-rays suggests that the relativistic jets dominate in this regime as well, whereas a hot accretion flow dominates the soft X-ray band. The origin of the GeV non-thermal emission is still debated, with both leptonic and hadronic scenarios deemed to be viable. In this work, we present results from a new semi-analytical, multizone jet model applied to the broad-band spectral energy distribution of Cygnus X–1 for both leptonic and hadronic scenarios. We try to break this degeneracy by fitting the first-ever high-quality, simultaneous multiwavelength data set obtained from the CHOCBOX campaign (Cygnus X–1 Hard state Observations of a Complete Binary Orbit in X-rays). Our model parametrizes dynamical properties, such as the jet velocity profile, the magnetic field, and the energy density. Moreover, the model combines these dynamical properties with a self-consistent radiative transfer calculation including secondary cascades, both of leptonic and hadronic origin. We conclude that sensitive TeV gamma-ray telescopes like Cherenkov Telescope Array (CTA) will definitively answer the question of whether hadronic processes occur inside the relativistic jets of Cygnus X–1.

Pulsed-jet propulsion via shape deformation of an axisymmetric swimmer

By using an axisymmetric immersed-boundary model, we numerically investigate the thrust generation of a deformable body via pulsed jetting. We focus on a single discharging process resulting from the deflation of the body as inspired by the jetting mechanism of cephalopods, such as squids. We examine three jet velocity profiles, namely, impulsive, half-cosine, and cosine, in the relatively low Reynolds number regime. For the impulsive profile, we demonstrate via wake visualization that the leading vortex ring does not pinch off from the trailing jet although its circulation stops growing after a critical formation number (hereby, the formation number is defined as the ratio between the length and diameter of the jet plug) of 6–7. The exact value of the critical formation number depends on the jet velocity profile, suggesting that jet acceleration and viscous dissipation play significant roles in vortex ring evolution. In terms of thrust generation, our results indicate that besides the jet momentum flux, an important source of thrust generation is jet acceleration. The implication is that the jet velocity profile is a key factor in determining the propulsive performance.

An explicit CFD model for the DBD plasma actuators using wall-jet similarity approach

A simple model for simulating the surface plasma-induced jets is proposed. The characteristics of the wall jet are estimated based on thrust imposed by the plasma and then related to the similarity solution for the viscous wall jet problem to obtain a plasma wall jet velocity profile. Then the plasma-induced flow field outside the plasma discharge region is simulated by simply imposing a plasma wall jet velocity profile in a single streamwise location. The validity of the model for simulating the effect produced by the dielectric barrier discharge (DBD) plasma actuators is tested against some experimental and numerical simulation results.

Propulsive Efficiency of Wake Ingestion

Wake ingestion has been studied in order to develop a physics-based understanding of its effect on engine power and propulsive efficiency. A combination of analysis and testing has been employed. A control volume analysis of the one-dimensional flow through an actuator disk has been used to derive a set of equations for the power and propulsive efficiency of a propeller ingesting a wake. This analysis shows that wake ingestion reduces both the power available from the exhaust jet and the useful thrust power of the propeller. The net effect is predicted to be a reduction in the propulsive efficiency, defined as the ratio of the useful power to the power available. A simple experiment was performed to test this prediction. Wake and jet velocity profiles were measured for a series of bodies with thrusts equal to their different drags. These were used to calculate the propulsive efficiency. It is concluded that, although the propulsive efficiency is reduced by wake ingestion, the range of the aircraft is increased.

Global linear analysis of a jet in cross-flow at low velocity ratios

The stability of the jet in cross-flow is investigated using a complete set-up including the flow inside the pipe. First, direct simulations were performed to find the critical velocity ratio as a function of the Reynolds number, keeping the boundary-layer displacement thickness fixed. At all Reynolds numbers investigated, there exists a steady regime at low velocity ratios. As the velocity ratio is increased, a bifurcation to a limit cycle composed of hairpin vortices is observed. The critical bulk velocity ratio is found at approximately for the Reynolds number , above which a global mode of the system becomes unstable. An impulse response analysis was performed and characteristics of the generated wave packets were analysed, which confirmed results of our global mode analysis. In order to study the sensitivity of this flow, we performed transient growth computations and also computed the optimal periodic forcing and its response. Even well below this stability limit, at , large transient growth ( in energy amplification) is possible and the resolvent norm of the linearized Navier–Stokes operator peaks above . This is accompanied with an extreme sensitivity of the spectrum to numerical details, making the computation of a few tens of eigenvalues close to the limit of what can be achieved with double precision arithmetic. We demonstrate that including the meshing of the jet pipe in the simulations does not change qualitatively the dynamics of the flow when compared to the simple Dirichlet boundary condition representing the jet velocity profile. This is in agreement with the recent experimental results of Klotz et al. (J. Fluid Mech., vol. 863, 2019, pp. 386–406) and in contrast to previous studies of Cambonie & Aider (Phys. Fluids, vol. 26, 2014, 084101). Our simulations also show that a small amount of noise at subcritical velocity ratios may trigger the shedding of hairpin vortices.

Numerical forcing scheme to generate passive scalar mixing on the centerline of turbulent round jets in a triply periodic box

Numerical studies of passive scalars in three-dimensional (3D) periodic box turbulence have often used arbitrary scalar forcing schemes to sustain the variance. These existing methods represent certain flow configurations, but they have not been derived using specific velocity and scalar profiles. In this work, a forcing technique is devised to generate centerline scalar mixing of round jets in a triply periodic box. It is derived from the scalar transport equation using a Reynolds-like decomposition of the scalar field. The equation is closed by applying the known mean velocity and scalar profiles of axisymmetric jets. The result is a combination of a mean gradient term and a linear scalar term. Direct numerical simulations at different Reλ have been performed with these source terms for unity Schmidt numbers. Scalar flux values and scaling exponents of energy spectra from simulations are comparable to experimental values. In addition, a dimensional analysis shows that the normalized scalar statistics, such as variance, flux, and dissipation rate, should only be a function of Reynolds number; indeed, such quantities computed from our simulations approach constant values as the Reynolds number increases. The effects of velocity forcing on scalar fields are also investigated; changing velocity forcing terms may result in unstable scalar fields even under the same scalar forcing. It may indicate that an appropriate relation between the velocity and scalar forcing schemes can help producing a proper scalar mixing environment.

A Methodology for Modelling of Steady State Flow in Pelton Turbine Injectors

Pelton turbine is a high head-impulse type turbine. The high-speed jet strikes the symmetrical semi ellipsoidal buckets, thus transferring the momentum within short period of time, impulse. The conversion of potential energy of water to kinetic energy in the form of jet is done by a nozzle with internally fitted spear or needle, the assembly in known as injector. The jet quality includes but is not limited to jet velocity, velocity distribution ‘velocity profile’, core location etc. In this study, the modeling of flow in Pelton turbine injector is done by commercial Computational Fluid Dynamics (CFD) solver on a three-dimensional flow domain. The results obtained from CFD modelling are then compared against the experimental observations and previously published literatures. The jet streamline, jet velocity profile and jet core location are then studied. As observed experimentally, the mean jet diameter reduces as the nozzle opening decreases. In addition, like the experimental observations, the jet first contracts and then expands. The diameter of the contraction is then normalized with nozzle exit diameter and is plotted for both experimental observations as well as the results of the numerical simulation. The maximum error between experimental and numerical analysis of jet contraction is 20%. The jet core is located at region axially ahead of needle tip.

Impinging sweeping jet and convective heat transfer on curved surfaces

The application of an impinging sweeping jet, which oscillates periodically with a large angle, to convective heat transfer has received attention owing to its capability to provide a more spatially uniform and enhanced heat removal rate when compared to a steady jet. Herein, we study how the surface curvature affects the heat transfer performance of a sweeping jet and couple it with the representative flow characteristics. Heat transfer measurement and quantitative flow visualization are conducted experimentally for concave and convex surfaces as well as a flat surface. Whereas concave surfaces have a better heat transfer rate than a flat surface, the enhancement of the heat transfer is relatively small for a convex surface. For both concave and convex surfaces, the Nusselt number does not increase monotonically with the curvature magnitude but has a peak for a moderate curvature. The variation in heat transfer performance with the surface curvature is correlated with the phase-averaged velocity profile of the wall jet deflected after an impingement and the turbulence kinetic energy inside the jet. For both concave and convex surfaces, the wall jet becomes thinner than a flat surface in general, which contributes to improved heat transfer. However, whereas the turbulence kinetic energy is significantly larger for a concave surface of a moderate curvature than that of a flat surface, the turbulence kinetic energy for a convex surface is reduced from that of a flat surface, resulting in degradation of the heat transfer performance.

Convective heat transfer on a flat target surface impinged by pulsating jet with an additional transmission chamber

A series of experimental tests are performed for the pulsating jet impingement heat transfer by varying the Reynolds number (5000 ≤ Re ≤ 15000), operation frequency (5 Hz ≤ f ≤ 40 Hz) and dimensionless nozzle-to-surface distance (2 ≤ H/d ≤ 10) while fixing the duty cycle as DC = 0.5. The maximum uncertainty in the measurement of Nusselt number is estimated to be about ±7%. Meanwhile, numerical simulations are performed to demonstrate the instantaneous flow field of the pulsating jet impingement. Particular attention is paid to examine the influence of transmission chamber on the pulsating jet impingement heat transfer. The results show that by using an additional transmission chamber, the pulsating jet impingement heat transfer is enhanced. For example, the circumferentially-averaged Nusselt number around the stagnation point (x/d ≤ 2) is increased up 8%~16% by the adding of a transmission chamber in related to the baseline case under Re = 10000 and H/d = 6. Due to the presence of transmission chamber, the exiting jet velocity profile at the orifice outlet is varied. In related to the baseline case, the transmission chamber makes the time-averaged ejecting velocity in the central zone increase but decrease in the edge zone. As the peak velocity in the central zone of orifice outlet is effectively increased by the use of transmission chamber, the jet impinging velocity approaching to the target surface is also strengthened, resulting in a stronger jet impingement in the vicinity of the stagnation point.

Airflow pattern and performance of wall confluent jets ventilation for heating in a typical office space

To investigate an air distribution system with the potential to provide a comfortable thermal environment and efficient ventilation performance in heating mode, this study compared the numerical results of the RNG k-[Formula: see text] model, realizable k-[Formula: see text] model and SST k-ω model with experimental data obtained from a typical office with wall confluent jets ventilation (WCJV) for heating. The SST k-ω model was chosen for numerical study of WCJV. The findings showed that the WCJV performed better than mixing ventilation (MV) in the heating mode because WCJV could entrain less ambient air and maintain the jets’ momentum and energy to reach the occupied zone. The effects of supply air temperature difference (in the range of 2.00°C to 7.79°C) and supply air velocity (in the range of 2.20 m/s to 8.50 m/s) on the jet velocity profiles and ventilation performance of WCJV were also quantified. The results showed that the jet velocity profile was more sensitive to the supply air velocity than to the supply air temperature difference. Accordingly, reducing the supply air velocity might result in poorer thermal environment and air quality in the occupied zone because the warm air jets cannot spread out over the floor area. The results can be helpful in understanding WCJV used for ventilation under heating mode.

Numerical investigation of the jet velocity profile and its influence on the Pelton turbine performance

Numerical investigation of the unsteady flow patterns around the bucket can be helpful to improve the Pelton turbine efficiency. In fact, by studying the loss mechanisms in the flow, one can optimize the bucket design. For this purpose, an accurate investigation of the water jet is also necessary as an inlet condition for the bucket flow. The water jet ejected from the nozzle is actually non-uniform, due to the upstream turbulence and secondary flow in the distributor, bending pipes, needle and supports. This non-uniformity causes a deviation of the water jet from the ideal jet center, which is tangent to the jet circle, and it directly affects the flow patterns around the bucket. Whereas water splashing makes experimental observations very challenging, a numerical approach is effective and convenient to study the unsteady flow pattern in a Pelton turbine. In the present research, numerical analysis of the two-phase flow through the distributor, bending pipe and nozzle, has been performed. The jet velocity profile has been verified with experimental results, which are measured in the model test equipment, and good agreement is obtained for both velocity profile and jet deviation. In addition, the analysis of the bucket unsteady flow is performed using the aforementioned non-uniform jet velocity profile and the calculated flow pattern around the bucket is compared to the previous calculation using a uniform velocity profile at the inlet boundary. The difference between the two cases is discussed based on the quantitative and qualitative evaluation from the numerical analysis.

On absolute instability of free jets

We analyze the nature of instability (absolute or convective) of a jet velocity profile obtained in preceding experimental studies. It is surprisingly found that local instability of the velocity profile near the orifice is absolute. Physical mechanism of absolute instability is revealed. Hence, absolute instability of a jet does not require counterflow, as was considered before. However, the instability observed in experiments is convective due to rapid spreading of the jet downstream from the orifice and the change of instability nature from absolute to convective. Possible methods of the prolongation of local absolute instability and its applications are discussed.

Early-time jet formation in liquid–liquid impact problems: theory and simulations

We perform a thorough qualitative and quantitative comparison of theoretical predictions and direct numerical simulations for the two-dimensional, vertical impact of two droplets of the same fluid. In particular, we show that the theoretical predictions for the location and velocity of the jet root are excellent in the early stages of the impact, while the predicted jet velocity and thickness profiles are also in good agreement with the computations before the jet begins to bend. By neglecting the role of the surrounding gas both before and after impact, we are able to use Wagner theory to describe the early-time structure of the impact. We derive the model for general droplet velocities and radii, which encompasses a wide range of impact scenarios from the symmetric impact of identical drops to liquid drops impacting a deep pool. The leading-order solution is sufficient to predict the curve along which the root of the high-speed jet travels. After moving into a frame fixed in this curve, we are able to derive the zero-gravity shallow-water equations governing the leading-order thickness and velocity of the jet. Our numerical simulations are performed in the open-source software Gerris, which allows for the level of local grid refinement necessary for a problem with such a wide variety of length scales. The numerical simulations incorporate more of the physics of the problem, in particular the surrounding gas, the fluid viscosities, gravity and surface tension. We compare the computed and predicted solutions for a range of droplet radii and velocities, finding excellent agreement in the early stage. In light of these successful comparisons, we discuss the tangible benefits of using Wagner theory to confidently track properties such as the jet-root location, jet thickness and jet velocity in future studies of splash jet/ejecta evolution.

Effect of Shrouding Gas Temperature on Characteristics of a Supersonic Jet Flow Field with a Shrouding Laval Nozzle Structure

Coherent jet technology was been widely used in the electric arc furnace steelmaking process to protect the kinetic energy of supersonic oxygen jets and achieve a better mixing effect. For this technology, the total temperature distribution of the shrouding jet has a great impact on the velocity of the main oxygen jet. In this article, a supersonic shrouding nozzle using a preheating shrouding jet is proposed to increase the shrouding jet velocity. Both numerical simulation and experimental studies were carried out to analyze its effect on the axial velocity, total temperature and turbulence kinetic energy profiles of the main oxygen jet. Based on these results, it was found that a significant amount of kinetic energy was removed from the main oxygen jet when it passed though the shock wave using a high-temperature shrouding jet, which made the average axial velocity of the coherent jet lower than for a conventional jet in the potential core region. However, the supersonic shrouding nozzle and preheating technology employed for this nozzle design significantly improved the shrouding gas velocity, forming a low-density gas zone at the exit of the main oxygen jet and prolonging the velocity potential core length.

Formation of free round jets with long laminar regions at large Reynolds numbers

The paper describes a new, simple method for the formation of free round jets with long laminar regions by a jet-forming device of ∼1.5 jet diameters in size. Submerged jets of 0.12 m diameter at Reynolds numbers of 2000–12 560 are experimentally studied. It is shown that for the optimal regime, the laminar region length reaches 5.5 diameters for Reynolds number ∼10 000 which is not achievable for other methods of laminar jet formation. To explain the existence of the optimal regime, a steady flow calculation in the forming unit and a stability analysis of outcoming jet velocity profiles are conducted. The shortening of the laminar regions, compared with the optimal regime, is explained by the higher incoming turbulence level for lower velocities and by the increase of perturbation growth rates for larger velocities. The initial laminar regions of free jets can be used for organising air curtains for the protection of objects in medicine and technologies by creating the air field with desired properties not mixed with ambient air. Free jets with long laminar regions can also be used for detailed studies of perturbation growth and transition to turbulence in round jets.