Jet Exit Diameter Research Articles

Experimental study on flow characteristics of jet ventilation in crossflow in confined mine spaces

The increasing depth of mine excavation presents greater challenges in mine ventilation and in managing cooling energy consumption. Therefore, there is an urgent need for comprehensive research on jet ventilation influenced by low-speed crossflows. This study investigated the impact of flow velocity ratios (R) and jet exit diameters (d) on flow-field distribution and flow characteristics through velocity measurements and smoke flow visualization experiments. The results of the study revealed two distinct types of air lakes formed by jet ventilation in crossflow (JVIC), with one being wall-attached and the other suspended. Notably, a significant secondary flow phenomenon was observed in the near-field near the upper wall. Additionally, the deflection angle (θj) of JVIC decreases as R and d/D increase, leading to the formation and movement of a semi-confined point (SP) and a confined point (CP) in the -x direction. Moreover, the wall confinement effect diminishes the jet’s diffusion and deflection ability in the -z direction, leading to increased penetration in the x direction. Before the formation of the SP, the deflection section of the jet lengthens, followed by a rapid shortening upon its formation. Finally, the study further developed empirical equations for the jet axial trajectory and diffusion width.

Propulsive characteristics of single-pulsed jets with tube and orifice openings

The effects of the nozzle exit geometry on the unsteady propulsive characteristics of single-pulsed jets are studied numerically. For both tube and orifice nozzles, the jet exit configuration is parameterized by the diameter ratio RD, which is defined as the ratio of the nozzle entrance D0 to the jet exit diameters D. It is found that the diameter ratio has significant influence on the propulsive characteristics of the single-pulsed jet during its entire ejection phase. The total impulse production is augmented considerably as the diameter ratio increases until a critical value of RD_cir≈2.0 is approached. The larger impulse production by the orifice nozzles over the tube nozzle stems from the persistent over-pressure contribution at the jet exit due largely to the fact that the flow contraction near the jet exit of the orifice nozzle results in the intensification of the radial velocity gradients and higher local pressure. By using the existing prediction of the contraction coefficient Cc to account for the flow contraction, a theoretical model has been developed with the quasi-one-dimensional flow approximation to predict the pressure thrust at the jet exit during the steady discharging stage, showing good agreement with the present numerical results. Moreover, the pressure force acting on the vertical wall of the orifice nozzle, which is proportional to the wall area, is found to be primarily responsible for the larger transient variations in the jet impulse during the onset and end of the jet ejection phase as the diameter ratio increases.

Flow measurements of jet impingement upon a semicylinder with crossflow

In this work, time-resolved particle image velocimetry (TR-PIV) measurements have been carried out to investigate the structural features of a submerged transverse round liquid turbulent jet discharged into a confined laminar crossflow. The duct Reynolds number based on crossflow velocity is fixed at Re=3000, and the impinging jet is directed to a semicylindrical concave surface located in one of the walls of a vertical square duct. The spatial development and flow dynamics are analyzed along several orthogonal planes parallel/perpendicular to the jet axis for jet Reynolds numbers based on the jet exit diameter of Rej=3000, 6000 and 9000 (jet-to-crossflow velocity ratios of r=3.27, 6.53 and 9.80), respectively. For this purpose, mean and ensemble-averaged velocity and vorticity distributions, turbulent statistics, and Reynolds shear stresses are obtained for various injection rates. Spectral analysis reveals the shedding frequencies of the wake vortices, and the pairing and breakup processes of the evolving large-scale coherent structures have been related to the measured wake Strouhal numbers. Our results indicate that due to the curvature of the target surface and the upwash of the jet impact, the size of coherent structures decreases with increase in the value of Rej. Proper orthogonal decomposition (POD) of the flow using the snapshot method is applied to extract the dominant features of the turbulent flow. It is observed that at the symmetry plane and for Rej=3000, 6000 and 9000, the energy collected by the first two dominant eddies contribute to 14.98%, 18.68%, and 17.89% of the turbulence kinetic energy, respectively. Our results show that the evolution of the time-resolved temporal coefficients of degenerate pairs of modes (1, 2) represent the flapping motion of the jet. Moreover, the amplitude of the oscillations of the flapping jet and the complexity of the flow structure increase for increasing values of Rej.

Effect of tabs on the shear layer dynamics of a jet in cross-flow

Direct numerical simulations (DNS) of a jet in cross-flow (JICF) with a triangular tab at two positions are performed at jet-to-cross-flow velocity ratios of $R = 2$ and $4$ with a jet Reynolds number of 2000 based on the jet's bulk velocity and exit diameter. The DNS and dynamic mode decomposition show the sensitivity of the tab's effect on the jet upstream shear layer (USL) structure and cross-section to $R$ , echoing the experimental discoveries of Harris et al. (J. Fluid Mech., vol. 918, 2021). Furthermore, DNS reveals that the presence of a tab placed on the upstream side of the nozzle significantly modifies the USL through production of streamwise vortices that curl around the spanwise vortex tubes originating from the primary instability of the USL. This provides an explanation for the improvement in mixing that has been associated with an upstream tab. The streamwise vortex structure shows remarkable similarities to the ‘strain-oriented vortex tubes’ observed for disturbed plane shear layers by Lasheras & Choi (J. Fluid Mech., vol. 189, 1988, pp. 53–86). For both $R$ cases, the USL instability is delayed, the jet penetration is reduced, and the jet cross-section is flattened, although the tab has a less pronounced effect on the USL structure at higher velocity ratios, where the formation of the streamwise vortices is delayed. In contrast, a tab placed 45 $^\circ$ from the upstream position produces significantly different effects compared with the upstream tab. At $R = 4$ , the jet cross-section is significantly skewed away from the tab and a tertiary vortex is formed, as observed in past studies of round JICFs at relatively high $R$ and low Reynolds numbers. The ability of the tab to produce a controllable steady-state tertiary vortex has implications for a variety of applications. The 45 $^\circ$ tab produces asymmetric effects in the wake of the jet at $R = 2$ , but the effect on the jet cross-section is much smaller, highlighting the sensitivity of jets at high $R$ to asymmetric perturbations.

Similarity scaling of the axisymmetric turbulent jet

In this work, we find that a free axisymmetric jet in air displays self-similarity in the fully developed part of the jet (≳30 jet exit diameters from the jet exit). We report accurate measurements of first, second, and third order spatially averaged statistical functions of the axial velocity component performed with a laser Doppler anemometer, including the outer (high intensity, ≳20%) regions of the jet. The measurements are compared to predictions derived from a simple jet model, which is described in a separate publication, and we discuss the implications for the further study of self-similarity in a free jet. It appears that all statistical functions included in this study can be scaled with a single geometrical scaling factor—the downstream distance from a common virtual origin, z−z0.

Jet noise predictions by time marching of single-snapshot tomographic PIV fields

This work combines the latest advancements in time marching of 3D vector fields from tomographic particle image velocimetry, with an adapted version of Lighthill’s formulation, for the prediction of far-field jet noise. Three-dimensional velocity vector fields of the jet flow are first reconstructed from a tomographic volume of 4times3times9.5 D_{j}^3, with D_{j} = 5 cm being the jet-exit diameter. (The jet-exit Mach number M_{j} ranges from 0.10 to 0.20.) The obtained vector fields are then used as input to a recently developed procedure for the time marching of the vorticity field, which relies upon the vortex-in-cell methodology. This yields time series of each three-dimensional velocity field, from which the far-field pressure is computed via Lilley’s acoustic analogy (through evaluation of the Lighthill’s stress tensor). It is shown that the estimate of the far-field noise spectrum compares well with the spectrum measured directly from a far-field microphone in the anechoic A-tunnel facility of TU Delft, in the Strouhal number range from approximately 1 to 12.Graphical

Fast triple-parameter extremum seeking exemplified for jet control

A fast triple-parameter extremum seeking method is applied for jet control based on the pioneering work of Gelbert et al. (J Process Control 22(4):700, 2012). The simultaneous adaptation of three input parameters takes less time than the single-input adaptation of each parameter combined. The key enablers are phase-shifted sinusoids for the input each of which is evaluated by an extended Kalman filter (EKF). An acceleration of the adaption is obtained by a combined EKF coupling the output to all inputs. The method is illustrated for an analytical optimization problem and experimentally demonstrated for a turbulent jet mixing control. The considered Reynolds numbers $${\hbox {Re}}_D$$ based on the jet exit diameter and velocity are 5700, 8000 and 13,300. The main jet is manipulated by a pulsed radially injected minijet which is varied by a mass flow controller and an electromagnetic valve up to high frequencies. The mixing performance is characterized by the centerline jet decay rate and monitored by a hot-wire sensor five diameters downstream at the end of the potential core. The proposed triple-parameter extremum seeking method optimizes the actuation mass flow ratio, frequency and duty cycle. The decay rate increases 11-fold from the unforced reference value of 0.05 to the optimal actuation level of 0.56. The reproducibility is demonstrated with various initial actuation parameters. Moreover, the adaptive control robustly tracks the optimal open-loop actuation for varying $${\hbox {Re}}_D$$ ; the optimal decay rate remains unchanged given the mass flow rate, frequency and duty cycle are optimized. The unforced and actuated flow are investigated with hot wires and visualizations. The three-input ES significantly outperforms a two-parameter optimization for the same configuration in multiple respects (Wu et al. in AIAA J 56(4):1463, 2018): First, the jet decay rate is $$8\%$$ faster. Second, the convergence time for three parameters is only $$25 \%$$ of the adaptation period of two parameters when $${\hbox {Re}}_D$$ is varied. Finally, the current steady-state error is $$45\%$$ less than that of the two-parameter optimization. We expect the proposed triple-parameter extremum seeking to be applicable for a large range of flow control experiments.

Interactions of large-scale structures in the near field of round jets at high Reynolds numbers

A possible interaction between vortical structures in a round jet shear layer, viz. vortex rings and streamwise vortices, is explored following Davoust et al. (J. Fluid Mech., vol. 709, 2012, pp. 408–444). These authors reported a radial organization of streamwise vorticity in a jet at high diameter-based Reynolds number ( ), contrary to the classically observed azimuthal organization. They hypothesized that the observed weaker vortex rings in such jets could be deformed by streamwise vortices and further reoriented and stretched in the streamwise direction. As this hypothesis was based on the observations of one configuration of a jet flow, our study aims at assessing it by varying the key parameter, i.e. the relative strength of the vortex rings and the streamwise vortices, through forcing, along with various jet configurations. We first analyse a low-Mach-number, transitional jet, using high-speed stereo particle image velocimetry in a cross-sectional plane at two jet exit diameters from the nozzle exit. The axisymmetric mode is acoustically excited at various amplitudes to increase the strength of the rings relative to streamwise vortices, at a Strouhal number ( ) of 0.49, the most energetic frequency in the unforced jet. Starting from a radial array in the unexcited jet, a gradual shift towards an azimuthal configuration is obtained with increasing excitation level. Quantification of the relative strengths of the streamwise vortices and vortex rings confirms that a radial array is observed whenever the streamwise vortices are more intense than the rings, and conversely for the azimuthal configuration. We then extend the analysis to other jet cases in terms of , and state of the exiting boundary layer. We observe that the correlation between the radial or azimuthal organization of streamwise vortices and the relative strengths of the vortical structures holds systematically, confirming the possibility of the proposed interaction. A detailed analysis of the forced jets also sheds light on some interesting effects of acoustic excitation on the vortical organization in round jets.

DNS analysis of the effects of combustion on turbulence in a supersonic H2/air jet flow

In this paper, the effects of combustion on turbulence features are investigated by direct numerical simulation (DNS) of supersonic round turbulent hydrogen jet flows. Two DNS cases are conducted: the one is combustion hydrogen/air jet and the other is non-combustion jet with the same components as a comparison case. In the DNS, the supersonic jet consists of 85% hydrogen and 15% nitrogen in volume with temperature of 305 K and jet velocity of 900 m/s. The ambient air velocity is 20 m/s and temperature is 1150 K. The Reynolds numbers based the jet exit diameter and hydrogen jet velocity both are 22000 and the jet Mach numbers both are 1.2. The DNS results show that occurrence of combustion significantly delays the transition of the jet flow, and results in a 38% decrease in the peak of turbulent kinetic energy, compared with the non-combustion jet flow. The decreasing of the Reynolds number due to the heat release is considered as the main reason. Compared with the non-combustion jet flow, the combustion jet flow has more complete coherent vortex rings in the early stage. In addition, the positive and minus energy fluxes of combustion jet flow are always larger than that of non-combustion jet flow.

A new type of self-excited flapping jets due to a flexible film at the nozzle exit

This paper reports a new type of flapping turbulent jets that are self-excited by flutter of a flexible film with a leading edge fixed axially and centrally at a round nozzle exit. Both flutter conditions of a film and flapping-jet characteristics are investigated by varying the film material and dimensions of length (L), span (S) and thickness (δ). Visual observation, flow visualization and hot-wire anemometry are used to examine the flapping jet versus the free counterpart without involving any film. Experiments are made at L/D = 0.5 ∼ 2.0 and the jet Reynolds number of Re = 10,000 to 50,000; where Re ≡ UoD/ν with D, Uo and ν being the jet-exit diameter, exit-averaging velocity and fluid viscosity, respectively.Results show that the film’s flutter domain reduces with increasing its overall stiffness and varies with the film’s shape, size and thickness. The jet-flapping frequency fF rises as either L decreases or Uo increases. For the rectangular FEP film of L/D = 0.5 ∼ 2.0, the jet-flapping Strouhal number StF ≡ fFD/Uo varies over the range of 0.05 ≤ StF ≤ 0.23. This StF is noticeably lower than that (≈ 0.5 ∼ 0.7) of the primary vortex passage in the non-flapping free jet, but extraordinarily one to two orders of magnitude higher than those for the self-excited oscillation of a jet from conventional fluidic nozzles.

Laser-induced plasma image velocimetry

A novel velocimetry method is proposed for point velocity measurement, which is based on tracking a laser-induced plasma in a flow. The plasma’s behaviour is first analysed spatially, temporally and spectrally in quiescent air. The dependence of this technique on the delay time between subsequent plasma images and the processing methods are described. It is found that, for optimized operation of the technique in a turbulent air jet (exit diameter 10.0 mm from a 480 mm long pipe; with an averaged velocity of 50 m/s at the jet exit resulting in Reynolds number of 34,000) with 100 µs time delay between plasma images, the systematic and random components of the velocity uncertainty are − 0.51 m/s and ± 3.6 m/s along the laser beam direction, and 1.25 m/s and ± 0.86 m/s along other directions perpendicular to the laser beam. These uncertainties are mainly caused by the asymmetric laser energy deposition during the formation of plasma, and the associated spatial resolution (in this realisation of the instrument) of 5 mm. The mean velocity measurements in the turbulent air jet flow are consistent with the reported flow behaviour in the literature for mean velocity: the turbulent intensity of axial velocity fluctuations is comparable to those in the literature but difference arises due to the limited spatial resolution. This velocimetry method is an alternative to traditional tracer-based velocimetry methods, because it does not require ‘seeding’ of particles or other substances in the flow. It also has the ability to measure local gas mixture composition, using laser-induced breakdown spectroscopy approach, simultaneously with flow velocity, but this aspect is not explored in the current study.Graphical abstractConcept of Laser-Induced Plasma Image Velocimetry (LIPIV) applied to a turbulent jet flow. The LIPIV technique measures the flow velocity vector by using the temporal displacement of the laser-induced plasma in a flowing fluid. For this reason, two sequential images of the plasma with time delay Δt are used.

Mapping of the turbulent round jet developing region using a constant temperature anemometer (CTA)

The fully developed round turbulent jet has been extensively studied, whereas the developing region is much less understood. The high shear and turbulence intensities in the most interesting parts of the developing region make them inaccessible to common measurement techniques such as Constant Temperature Anemometry (CTA) due to the high demands on the measurement techniques for accuracy of the measurements. Turbulence measurements are therefore planned using our in-house laser Doppler anemometer (LDA) system based on its capability to provide accurate measurements and with its inherent ability to properly distinguish velocity components. A rigorous measurement with the intended LDA system however demands impractical processing time, so knowing the critical points at which measurement are to be taken will save valuable time. This information is herein acquired significantly faster and more practically, however less accurately, with single-wire CTA. A high-resolution measurement was done using a computer-controlled single-wire CTA with the wire probe mounted perpendicular to the incoming flow from the jet orifice. The measurements covered several points in the radial (r-direction) along x/D=10, x/D=15, x/D=20 and x/D=30 downstream (where D is the jet exit diameter), with spatial resolutions ranging from 1 to 3 mm between the points, depending on how far the measurement was from the jet centerline. A proper alignment was also conducted prior to measurement so that the same points can be reached again for LDA measurement on the same jet afterwards. The radial profiles of mean velocity and turbulence intensity at each downstream position are presented to show the statistics of the air flow inside and outside the jet. As expected from theory, the mean profiles display a nearly Gaussian shape, spread out and tapered with the downstream direction. The highest velocities are located at the centerline.

The effect of exit Reynolds number on soot volume fraction in turbulent non-premixed jet flames

Soot volume fraction (SVF) was measured in five attached turbulent non-premixed jet flames of a C2H4H2N2 fuel mixture using the Laser-Induced Incandescence (LII) technique. The five flames comprise two sets with exit strain rates of 4100 and 7500 s−1, respectively. Within each set, the exit Reynolds number was changed both by varying the jet diameter and the fuel exit velocity of the flames. Measurements of the mean, instantaneous and integrated SVF reveal a weak inverse dependence on the exit Reynolds number. A minor dependence of the axial and radial profiles of soot intermittency on the exit Reynolds number is also observed. The total soot yield is found to scale linearly with both the jet exit diameter and the fuel flow rate for the two flame sets of different exit strain. The total soot yield is also found to be a strong function of both the exit strain and the flame volume, but to be almost independent of the exit Reynolds number. A non-negligible effect of buoyancy on SVF is also deduced from the global correlations.

Global linear stability analysis of jets in cross-flow

The stability of low-speed jets in cross-flow (JICF) is studied using tri-global linear stability analysis (GLSA). Simulations are performed at a Reynolds number of 2000, based on the jet exit diameter and the average velocity. A time stepper method is used in conjunction with the implicitly restarted Arnoldi iteration method. GLSA results are shown to capture the complex upstream shear-layer instabilities. The Strouhal numbers from GLSA match upstream shear-layer vertical velocity spectra and dynamic mode decomposition from simulation (Iyer & Mahesh, J. Fluid Mech., vol. 790, 2016, pp. 275–307) and experiment (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93–129). Additionally, the GLSA results are shown to be consistent with the transition from absolute to convective instability that the upstream shear layer of JICFs undergoes between $R=2$ to $R=4$ observed by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129), where $R=\overline{v}_{jet}/u_{\infty }$ is the jet to cross-flow velocity ratio. The upstream shear-layer instability is shown to dominate when $R=2$, whereas downstream shear-layer instabilities are shown to dominate when $R=4$.

Effect of inclination angle of a pair of air jets on heat transfer into the flat surface

An experimental investigation is performed to study the effect of the inclination angle of air jets on heat transfer from a horizontal surface. A pair of inclined circular jets issuing from the straight pipes of length to diameter ratio of 40 is considered. The inclination angles of 0°, 10°, 20°, 30° 45°, and 60° are selected while the Reynolds number is varied from 10,000 to 40,000 based on a jet exit diameter. Jets to impingement plate distance (L/D) as well as the spacing distance (S/D) are changed from 2 to 8. The results of the temperature contours as well as the Nusselt number contours are illustrated to study the characteristics of heat transfer from a flat surface cooled by a pair of oblique jets. The experimental results show that the maximum magnitude of average heat transfer coefficient is achieved in the range of inclination angle from 10° to 20°. Empirical correlations are presented to predict the value of average Nusselt number as a function of Re, Pr, and θ. Moreover, a comparison between the values of average Nusslet number of the present study and those available in the literature is carried out.

Electro-mechanical efficiency of plasma synthetic jet actuator driven by capacitive discharge

A simplified model is established to estimate the jet exit density variation of a plasma synthetic jet actuator (PSJA) driven by a capacitive arc discharge. This model, in conjunction with phase-locked planar particle imaging velocimetry (PIV) measurements, enables the calculation of jet mechanical energy for different operating conditions. Discharge energy is directly calculated based on waveforms of applied voltage and discharge current. The ratio of jet mechanical energy to discharge energy provides the absolute electro-mechanical efficiency. Results indicate that PSJA is characterized by a rather low electro-mechanical efficiency in the order of 0.1%, while the maximum observed value under tested conditions is 0.22%. Electro-mechanical efficiency improves significantly with nondimensional energy deposition, and appears largely independent of jet exit diameter.

Determining the discharge rate from a submerged oil leak jet using ROV video

With expanded deep sea drilling in the Gulf of Mexico, and possibly the Arctic, it is imperative to have a technology available to quickly and accurately measure the discharge rate from a submerged oil leak jet. This paper describes an approach to measure the discharge rate using video from a Remotely Operated Vehicle (ROV). ROV video can be used to measure the velocity of visible features (turbulent eddies, vortices, entrained particles) on the boundary of an oil leak jet, from which the discharge rate can be estimated. This approach was first developed by the Flow Rate Technical Group (FRTG) Plume Team, of which the authors Savaş and Shaffer were members, during the response to the Deepwater Horizon (DWH) oil leak. Manual tracking of visible features produced the first accurate government estimates of the oil discharge rate from the DWH. However, for this approach to be practical as a routine response tool, software is required that automatically measures the velocity of visible features. To further develop this approach, experiments were conducted to simulate a submerged oil leak jet using a dye-colored water jet in the U.C. Berkeley Tow Tank facility. Jet exit diameters were 10.2cm and 20.3cm. With flow rates up to 11gal/s, Reynolds numbers in the range of the DWH oil leak jets (up to 500,000) were achieved. The dye-colored water jets were recorded with high speed video and radial profiles of velocity were mapped with Laser Doppler Anemometry (LDA). Particle Image Velocimetry (PIV) software was applied to measure the velocity of visible features. The velocities measured with PIV software were in good agreement with the LDA measurements. Finally, the PIV software was applied to ROV video of the DWH oil leak jet. The measured velocities were 10–50% lower than manual measurements of velocity. More research is required to determine the reasons why PIV software produced much lower velocities than manual tracking for the DWH oil leak jet.

Active control of impinging jet for modification of mixing

The objective of the present study is to modify mixing and heat transfer in impinging jets using a single-frequency excitation imposed at the jet exit. The excitation frequency is selected to be Stθ = fθ/UJ,max = 0.017 where θ is the jet-exit momentum thickness and UJ,max is the jet-exit maximum velocity. In free jets, this excitation results in turbulence suppression in a downstream location. On the other hand, in impinging jets, the effect of excitation significantly depends on the distance (H) between the jet exit and the impinging wall. For large H (e.g. H / D = 10, D is the jet exit diameter), the Nusselt number near the stagnation point (Nustag) decreases due to turbulence suppression by the excitation. For small H (e.g. H / D = 2), Nustag is almost unchanged but the secondary peak much suppressed. On the other hand, Nustag increases for H / D = 6 due to turbulence enhancement by the excitation. The different behaviors of Nusselt number with respect to H / D are closely related to the changes in vortical structures by excitation.

Experimental study on the characteristics of a two-electrode plasma synthetic jet actuator

Performance of a two-electrode plasma synthetic jet actuator has been experimentally studied by discharge measurements with high-speed shadowgraphy technology. Results show that the breakdown voltage and the peak discharge current of the actuator may be decreased by decreasing the ambient pressure and increasing the discharge frequency. The discharge developed in the actuator cavity is a spark-arc discharge. In the actuator could be created a strong “precursor shock” and a high kinetic energy jet. During the development of the plasma synthetic jet, the speed of the “precursor shock” is invariable and the jet propagates with an approximately local sonic velocity (350 m/s). But with decreasing jet exit diameter and ambient pressure, the increase of the cavity volume and the discharge frequency could lead to decreasing strength of the “precursor shock”. Heating efficiency of the gas in the cavity will decrease with the increase of the cavity volume and discharge frequency, and the jet velocity is decreased as well. The jet exit diameter and the ambient pressure can have their optimal values for affecting the velocity of the jet. Under all the working conditions we have studied, the plasma actuator may create a strong “precursor shock” and a high-speed jet, and also may have the potential to be used in high-speed active flow control.

Experimental study of counter-rotating vortex pair trajectories induced by a round jet in cross-flow at low velocity ratios

Circular flush Jets In Cross-Flow were experimentally studied in a water tunnel using Volumetric Particle Tracking Velocimetry, for a range of jet to cross-flow velocity ratios, r, from 0.5 to 3, jet exit diameters d from 0.8 to 1 cm and cross-flow boundary layer thickness δ from 1 to 2.5 cm. The analysis of the 3D mean velocity fields allows for the definition, computation and study of Counter-rotating Vortex Pair trajectories. The influences of r, d and δ were investigated. A new scaling based on momentum ratio r m taking into account jet and cross-flow momentum distributions is introduced based on the analysis of jet trajectories published in the literature. Using a rigorous scaling quality factor Q to quantify how well a given scaling successfully collapses trajectories, we show that the proposed scaling also improves the collapse of CVP trajectories, leading to a final scaling law for these trajectories.