Jet Centerline Velocity Research Articles

Noise prediction of a subsonic turbulent round jet using the lattice-Boltzmann method

The lattice-Boltzmann method (LBM) was used to study the far-field noise generated from a Mach, M(j)=0.4, unheated turbulent axisymmetric jet. A commercial code based on the LBM kernel was used to simulate the turbulent flow exhausting from a pipe which is 10 jet radii in length. Near-field flow results such as jet centerline velocity decay rates and turbulence intensities were in agreement with experimental results and results from comparable LES studies. The predicted far field sound pressure levels were within 2 dB from published experimental results. Weak unphysical tones were present at high frequency in the computed radiated sound pressure spectra. These tones are believed to be due to spurious sound wave reflections at boundaries between regions of varying voxel resolution. These "VR tones" did not appear to bias the underlying broadband noise spectrum, and they did not affect the overall levels significantly. The LBM appears to be a viable approach, comparable in accuracy to large eddy simulations, for the problem considered. The main advantages of this approach over Navier-Stokes based finite difference schemes may be a reduced computational cost, ease of including the nozzle in the computational domain, and ease of investigating nozzles with complex shapes.

Velocity and concentration measurements in initial region of submerged round jets in stagnant environment and in coflow

Velocity and concentration fields are measured in submerged round jets in a stagnant environment and in coflow using laser Doppler anemometry and laser-induced fluorescence. Measurements are made in the initial region within distances of 40 jet exit diameter at jet Reynolds number between 1000 and 5000 and coflow-to-jet velocity ratio from 0 to 0.43. Different behaviors of jet spreading and dilution are found in jets at three different ranges of Reynolds number in which the jets are classified as initially laminar, transitional or turbulent. In the zone of established flow, the jet centerline velocity and concentration decay with downstream distance at different rates in the three groups of jets. For jets in coflow, axial development of normalized forms of centerline mean excess velocity and mean concentration at different velocity ratios can be reasonably well collapsed onto universal trends through the use of momentum length scale. Turbulence properties inside a jet are increased by the presence of a strong coflow. Inside the zone of flow establishment, some strange features are observed on jet turbulence properties. The length of zone of flow establishment increases from the turbulent jets, to the transition jets and to the laminar jets. The zone lengths for concentration are shorter than those for velocity by one to two jet exit diameters. Both lengths are shortened further in the presence of a coflow. For jets a stagnant environment and in the strong jet flow region of jets in coflow, jet widths increase linearly with downstream distance in transitional and turbulent jets. Self-similarity of radial profiles of mean velocity or excess velocity, mean concentration, turbulence intensities and concentration fluctuation level is explored in the zone of established flow.

Investigation of piezoelectrically generated synthetic jet flow

The purpose of this paper is to investigate the compressible turbulent synthetic jet flow characteristics of a dual diaphragm piezoelectric actuator. Experimentally, a flow visualization system was established to obtain the particle streak images scattered from 10-μm red fluorescent spheres for observing the synthetic jet flowfield produced by a dual diaphragm piezo actuator. The centerline velocity of the synthetic jet was also measured by using a hot-wire anemometry system. In the analysis, the computational approach adopted the transient three-dimensional conservation equations of mass and momentum with the moving boundary specified to represent the piezo diaphragm motion. The standard k-e two-equation turbulent model was employed for turbulence closure. For the actuator operating at the frequency of 648 Hz, the particle streakline images in the cross-sectional plane visualized a turbulent jet flow pattern in the far-field area. The hot-wire anemometry data indicated that the measured centerline velocity of synthetic jets reached 3.8 m/s at y/d = 50. The predictions were compared with the visualized particle streak images and centerline velocity of the synthetic jet in order to validate the computer code. The numerical simulation revealed the time-periodic formation and advection of discrete vortex pairs. Caused by the outward movement of the piezo diaphragms, air near the orifice was entrained into the actuator cavity when the vortex pairs were sufficiently distant from the orifice.

Effect of computational grid in industrial‐scale boiler modeling

PurposeThe purpose of this paper is to study the effect of a computational grid in computational fluid dynamics‐based mathematical modeling, focusing on but not limiting the attention to industrial‐scale boilers.Design/methodology/approachA full boiler model is used to show the difficulties related to judging iteration and discretization errors in boiler modeling. Then, a single jet is studied in detail to determine the proper degree of local grid refinement required in the vicinity of jets in the full boiler model. Both a nonreactive axisymmetric jet exhausting into a quiescent atmosphere and a reactive jet exhausting into a crossfiow are studied.FindingsOver two million computational cells are required for the grid‐independent solution for a single jet. Local grid refinement is shown to be a good option for improving the results consistently without an excessive increase in the number of computational cells. Using relatively coarse grids of tetrahedral cells with a finite‐volume‐based solver may cause serious errors in results, typically by overpredicting the jet spreading rate and underpredicting the mean axial centerline velocity. Relatively coarse grids of hexahedral cells are less prone to error in a case where a jet exhausts into a quiescent atmosphere. However, their performance deteriorates when a crossfiow is introduced. As assumed, the differences in the predicted reaction rate and species concentrations are significant in the reactive case. It is confirmed that the standard k‐ε model tends to overpredict the axisymmetric jet spreading rate. The estimated inlet turbulence intensity is not among the most critical factors in modeling. Estimations of the axisymmetric jet centerline velocity from the analytical correlation may not coincide with the modeling results.Practical implicationsThe error caused by the computational grid may easily dominate the errors caused by simplifying models used in industrial‐scale boiler modeling (turbulence, combustion, radiative heat transfer, etc.).Originality/valueThe present study deals with grid independency issues in industrial‐scale boiler modeling in a systematic and profound manner.

Aerodynamics of an isolated slot-burner from a tangentially-fired boiler

The aerodynamic development of fully turbulent isothermal jets issuing from rectangular slot-burners was modelled by obtaining a solution to the Reynolds averaged Navier–Stokes equations. A finite-volume method was used with the standard k–ε, RNG k–ε and Reynolds stress turbulence models. The slot-burners were based on physical models, which were designed to be representative of typical burner geometries found in tangentially-fired coal boilers. Two cases were investigated, in which jets from three vertically stacked rectangular nozzles discharged at 90° and then 60° to the wall containing the burner. The nozzle angle had little effect on jet centreline velocity decay, with the 60° nozzle showing a marginally higher rate of decay. The jets from the 60° nozzles were found to deviate slightly from their geometric axis slightly due to internal pressure redistribution in the flow at the nozzles. The simulations were validated against the physical models and were found to reproduce the flow field of the jets accurately with the Reynolds stress model producing the best results.

Investigation on Jet Mixing Rate Based on DNS of Excitation Jets

To establish a good measure of mixing rate, DNS (direct numerical simulation) of the controlled jets are conducted. In the computation, the spatial discritization is performed by hybrid scheme in which sixth order compact scheme in streamwise direction and Fourier series in cross section are adopted. The Reynolds number is 1500. The mixing properties are estimated by two measures such as statistical entropy and mixedness parameter, which are constructed based on a scalar concentration. Compared with simple measure, i.e., means jet width, centerline velocity and turbulent kinetic energy, it is found that : (1) the statistical entropy is the good measure to describe the mixing state in different controlled jet, (2) the fluctuating statistical entropy distribution enable to express the highly mixed region, and (3) its production term correlates to the vortical structure. As well as the statistical entropy, the mixedness parameter also has useful properties for estimation of mixing efficiency. These findings suggest that these measures are expected to contribute to the optimazion of jet mixing.

Active control of high-speed and high-Reynolds-number jets using plasma actuators

Localized arc filament plasma actuators are used to control an axisymmetric Mach 1.3 ideally expanded jet of 2.54 cm exit diameter and a Reynolds number based on the nozzle exit diameter of about 1.1×106. Measurements of growth and decay of perturbations seeded in the flow by the actuators, laser-based planar flow visualizations, and particle imaging velocimetry measurements are used to evaluate the effects of control. Eight actuators distributed azimuthally inside the nozzle, approximately 1 mm upstream of the nozzle exit, are used to force various azimuthal modes over a large frequency range (StDF of 0.13 to 1.3). The jet responded to the forcing over the entire range of frequencies, but the response was optimum (in terms of the development of large coherent structures and mixing enhancement) around the jet preferred Strouhal number of 0.33 (f = 5 kHz), in good agreement with the results in the literature for low-speed and low-Reynolds-number jets. The jet (with a thin boundary layer, D/θ ∼ 250) also responded to forcing with various azimuthal modes (m = 0 to 3 and m = ±1, ±2, ±4), again in agreement with instability analysis and experimental results in the literature for low-speed and low-Reynolds-number jets. Forcing the jet with the azimuthal mode m = ±1 at the jet preferred-mode frequency provided the maximum mixing enhancement, with a significant reduction in the jet potential core length and a significant increase in the jet centreline velocity decay rate beyond the end of the potential core.

Suppression of global modes in low-density axisymmetric jets using coflow

Experiments conducted in helium axisymmetric jets with an annular coflowing air stream yield critical values of the velocity ratio U2∕U1 needed to suppress global instability inherent in these low-density flows. Global mode suppression was achieved for coflowing velocities less than approximately 20% of the jet centerline velocity, though the critical velocity ratio displayed a nonmonotonic relationship with the initial shear layer momentum thickness. The experiments are supported by spatio-temporal inviscid stability theory, where the convective-absolute transition was tracked in an operating domain including U2∕U1 and D∕θ. For initially thick shear layers, the experimental observations are in good agreement with linear theory, but deviate considerably as the separating shear layer thickness is reduced.

An over-pressure correction to the slug model for vortex ring circulation

The slug model provides a formula for the circulation of vortex rings formed by starting jets ejected from a nozzle or orifice in terms of the time history of the jet velocity. For rapidly initiated jets, however, the model under-predicts circulation by an amount that remains nearly constant as circulation increases. To remedy this shortcoming, the present study derives an equation for circulation directly from the governing equations for the flow, illustrating that the circulation can be expressed as the sum of a flux term, $\Gamma_U$, determined by the jet centreline velocity and a ‘source’ term, $\Gamma_p$, determined by over-pressure at the jet centreline during vortex ring formation. For impulsively or nearly impulsively initiated jets, $\Gamma_p$ is modelled using potential flow analysis since over-pressure is significant primarily during the rapid jet initiation in these cases. The effects of the jet initiation and boundary-layer growth on the jet centreline velocity are also considered to provide a realistic model for $\Gamma_U$. Models for nozzle and orifice configurations are developed. In the case of a nozzle-type generator, the need to model the jet centreline velocity leads to an approximate solution for starting flow near the exit of an infinitely long pipe. For the nozzle case, the model results agree with available circulation measurements to within ${\pm}$6.2% for a wide range of conditions, except for jet velocity programs that are nearly triangular. In the orifice case, the model agrees with available results to within ${-}$13%. Both cases show substantial improvement over the slug model, which is in error by ${-}$21% to ${-}$67% for the data considered.

Large Eddy Simulation of the sound field of a round turbulent jet

In this paper we will use Large Eddy Simulation (LES) to obtain the flow field of a turbulent round jet at a Reynolds number based on the jet orifice velocity of 11000. In the simulations it is assumed that the flow field is incompressible. The acoustic field of the jet is calculated with help of the Lighthill acoustic analogy. The coupling between the flow solver and the acoustic solver is discussed in detail. The Mach number used in the acoustic calculation was equal to 0.6. It is shown that the decay of the jet centerline velocity and centerline rms are in good agreement with experimental data of [12]. Furthermore, it is shown that the influence of the LES modeling on the acoustic field is very small, if the dynamic subgrid model is used.

Planar imaging of CH, OH, and velocity in turbulent non-premixed jet flames

Simultaneous planar laser-induced fluorescence of the CH and OH radicals and two-dimensional particleimage velocimetry were used to investigate the structure of turbulent non-premixed methane/nitrogen jet flames ( Re jet =18,600) in an oxygen coflow. The motivation for this study is to investigate the relationship among regions of high CH/OH concentration and kinematic quantities such as vorticity, strain rate, and dilatation. The results show that in the lower part of the flame, the direction of the two-dimensional principal compressive strain axis exhibits a preferred orientation of about 45° with respect to the flow direction, whereas near the flame tip, the strain exhibits a more random orientation. Furthermore, CH structures are more likely to align orthogonal to the principal compressive strain axis in the downstream half of the flame. Probability density functions (PDFs) show that the most probable value of vorticity on CH structures is about Δ U /δ (where Δ U is the difference between the jet centerline and coflow velocities and δ is the full width at half-maximum of velocity profile), but near zero on the OH structures. Furthermore, joint PDFs of strain and dilatation show that CH structures are more likely to be associated with positive dilatation than are OH structures. These results are consistent with previous studies that have shown that jet flame kinematics are substantially affected by heat release and further show that these effects are more closely correlated with zones of high CH concentration than with zones of high OH concentration.

Experiments on Vertical Turbulent Plane Jets in Water of Finite Depth

Detailed experiments on vertical turbulent plane jets in water of finite depth were carried out in a two-dimensional water tank. The jet velocities were measured with a laser Doppler velocimeter (LDV). The LDV measurement covers the entire flow regime: the zone of flow establishment (ZFE), the zone of established flow (ZEF), the zone of surface impingement (ZSI), and the zone of horizontal jets (ZHJ). From the experimental results, the following conclusions are reached. First, the jet flow is independent of the Reynolds number if the Reynolds number is sufficiently large to produce a turbulent jet. Second, in the initial ZFE, the jet flow is nonsimilar and is characterized by the two free shear layers along the two edges of the jet orifice. Third, the jet flow in ZEF is self-similar. Both mean and fluctuation velocities are scaled with the mean jet centerline velocity. The turbulent shear stress is predictable by Prandtl's third eddy viscosity model. The spreading of the confined vertical jets is larger than that of a free jet, so is the faster decay of jet centerline velocity. Fourth, in ZSI the jet flow is nonsimilar and high turbulent intensities were found. The vertical turbulent jet transforms into two opposite horizontal surface jets after the impingement. And finally, the maximum velocity of the horizontal surface jet in ZHJ decays according to a power law.

A New Estimation Method of Turbulent Flow Structures Effective for Impingement Heat Transfer Augmentation.

The primary purpose of this work is to construct a new method how to define the turbulent flow structures effective for heat transfer augmentation. The flow field consists of a submerged liquid jet issuing from a convergent slot nozzle and a circular cylinder for heat transfer placed perpendicular to and on the jet centerline. Two small cylinders were inserted into the jet stream to examine the effectiveness of heat transfer augmentation. Time-series data of the jet centerline velocities were analyzed by a wavelet transformation. The information entropy and expectation can successfully extract the intermittent turbulent structures effective for the impingement heat transfer augmentation from the developing jet structures.

Large eddy simulation of a plane jet

Large eddy simulations of spatially evolving planar jets have been performed using the standard Smagorinsky, the dynamic Smagorinsky, and the dynamic mixed models and model performance evaluated. Computations have been performed both at a low Reynolds number, Red=3000, in order to make comparisons with a previous DNS at the same Reynolds number, and at a higher value, Red=30 000, to compare with high Reynolds number experiments. Model predictions with respect to the evolution of jet half-width, centerline velocity decay, mean velocity profiles, and profiles of turbulence intensity are evaluated. Some key properties of the SGS models such as the eddy-viscosity constant and the subgrid dissipation are also compared. It is found that the standard Smagorsinsky model is much too dissipative and severely underpredicts the evolution of the jet half-width and centerline velocity decay. The dynamic versions of the Smagorinsky model and the mixed model allow for streamwise and transverse variation of the constant in the eddy-viscosity expression which results in much better performance and good agreement with experimental and DNS data. The mixed model has an additional scale-similarity part which, in a priori tests against filtered jet DNS data, is found to predict the subgrid shear stress profile. Although the subgrid shear stress obtained by the dynamic Smagorinsky model is substantially smaller than that obtained in the a priori tests using the jet DNS data, surprisingly, in the a posteriori computations, the dynamic Smagorinsky model performs as well as the dynamic mixed model. Analysis of the mean momentum equation gives the reason for such behavior: the resolved stress in computations with the dynamic Smagorinsky model is larger than it should be and compensates for the underprediction of the subgrid shear stress by the Smagorinsky model. The numerical discretization errors have been quantified. The error due to noncommutativity of spatial differentiation and physical space filtering on nonuniform grids is found to be small because of the relatively mild stretching used in the present LES. The modeling error is found to be generally smaller than the discretization error with the standard Smagorinsky model having the largest modeling error.

Opposed round jets issuing into a small aspect ratio channel cross flow

Round jets (diameter D) discharging into a confined cross flow (dimension 3.16 D × 21.05 D) are investigated experimentally. Two configurations are considered: (1) a single jet (momentum flux ratio, J = 155) and (2) two opposed jets with two different momentum flux ratios ( J = 60, and 155). A two-component laser-Doppler anemometer is used to make a detailed map of the normal stresses and mean velocities in the symmetry plane of the jets. In addition, smoke-wire and laser-sheet visualization are used to study the flow. The rate of bending of the single confined jet is found to be higher than the rate of bending of an unconfined jet with the same momentum flux ratio. In the far field, the jet centerline velocity is observed to decay more slowly than the unconfined jet, indicating poor turbulent diffusion of linear momentum. Annular shear layer vortices are visualized on the upstream edge of the jet in the near field. In the far field, the flow visualization suggests that the jet loses its integrity and fragments into independent regions that are convected by the cross flow. In the opposed jet configuration at the high momentum flux ratio ( J = 155), the jets impinge in the center of the duct, and a pair of vortices is observed upstream of the impingement region. The flow visualization implies that the impingement vortices form quasi periodically and have a finite life span. In the impingement region, the jets are observed to penetrate alternately beyond the symmetry plane of the duct. In the two-jet configuration with J = 60, the jets do not impinge on each other owing to the higher rate of bending. Instead, the flow visualization indicates that the shear layers of the jets penetrate to the central region and periodically pinch off regions of the potential-like cross-flow fluid where they meet. The pinch-off regions of cross-flow fluid are convected by the turbulent flow for large distances, yet remain essentially unmixed.

How sensitive are jet centerline velocities to an opposing flow? Implications for using the centerline method to quantify regurgitant jet flow

A method for quantifying peak mitral and tricuspid regurgitant jet flow rate that utilizes a measure of jet orifice velocity ( U o, m s -1), a distal centerline velocity ( U m, m s -1), and the intervening distance ( X, cm) was recently developed. This method, however, modeled the regurgitant jet as a free jet, whereas many atrial jets are counterflowing jets because of jet opposing intra-atrial flow fields (counterflows). This study evaluated the feasibility of using the free jet quantification equation in the atrium where ambient flow fields may alter jet centerline velocities and therefore reduce the accuracy of jet flow rate calculations. A 4 cm wide chamber was used to pump counterflows of 0, 4, and 22 cm s -1 against jets of 2.3, 4.8, and 6.4 m s -1 originating from a 2 mm diameter orifice. For each counterflow–jet combination, jet centerline velocities were measured using laser Doppler anemometry. For free jets (no counterflow), flow rate was calculated with 98% mean accuracy. For all jets in counterflow, the calculation was less accurate as (i) the ratio of jet orifice velocity to counterflow velocity decreased ( U o/ U c, where U c is counterflow velocity), i.e. the counterflow was relatively more intense, and (ii) centerline measurements were made further from the orifice. But although counterflow lowered jet centerline velocities beneath free jet values, it did so only significantly in the jet's distal portion, while the initial portion ( X/D < 16, where D is jet orifice diameter) of a jet in counterflow behaved essentially as a free jet. Therefore, regurgitant jets, although not classically free because of systolic atrial inflow, will decay in their initial portions as free jets and hence are candidates for quantification with the centerline technique.

Quantification of Mitral and Tricuspid Regurgitation Using Jet Centerline Velocities: An In Vitro Study of Jets in an Ambient Counterflow.

A method for quantifying mitral and tricuspid regurgitant volume that utilizes a measure of jet orifice velocity U(0) - m/sec), a distal centerline velocity (U(m) - m/sec), and the intervening distance (X - cm) was recently developed; where jet flow rate (Q(cal) - L/min) is calculated as Q(cal) = (U(m)X)(2)/(26.46U(o)). This method, however, modeled the regurgitant jet as a free jet, whereas many atrial jets are counterflowing jets because of jet opposing intra-atrial flow fields (counterflows). This study concentrated on the feasibility of using the free jet quantification equation in the atrium where ambient flow fields may alter jet centerline velocities and reduce the accuracy of jet flow rate calculations. A 4-cm wide chamber was used to pump counterflows of 0, 4, and 22 cm/sec against jets of 2.3, 4.8, and 6.4 m/sec originating from a 2-mm diameter orifice. For each counterflow-jet combination, jet centerline velocities were measured using laser Doppler anemometry. For free jets (no counterflow), flow rate was calculated with 98% mean accuracy. For all jets in counterflow, the calculation was less accurate as: (i) the ratio of jet orifice velocity to counterflow velocity decreased (U(o)/U(c), where U(c) is counterflow velocity), i.e., the counterflow was relatively more intense, and (ii) centerline measurements were made further from the orifice. But although counterflow lowered jet centerline velocities beneath free jet values, it did so only significantly in the jet's distal portion (X/D > 16, i.e., >16 orifice diameters from the origin of the jet). Thus, the initial portion (X/D < 16) of a jet in counterflow behaved essentially as a free jet. As a result, even in significant counterflow, jet flow rate was calculated with >93% accuracy and >85% for jets typical of mitral and tricuspid regurgitation, respectively. Counterflow lowers jet centerline velocities beneath equivalent free jet values. This effect, however, is most significant in the distal portion of the jet. Therefore, regurgitant jets, although not classically free because of systolic atrial inflow or jet-induced intra-atrial swirling flows, will decay in their initial portions as free jets and thus are candidates for quantification with the centerline technique. (ECHOCARDIOGRAPHY, Volume 13, July 1996)

Analysis of and Experimental Measurements made on a Moving Air-Assisted Sprayer with Two-Dimensional Air-Jets Penetrating a Uniform Crop Canopy

Air-assisted crop sprayers use air-jets to enhance the transport and deposition of agricultural pesticides in crops that are difficult to spray using conventional equipment. However, the use of air-jets can cause excessive environmental contamination or give an ineffective treatment if the flow characteristics are poorly matched to the target crop. To establish a scientific basis for improving the design and control of air-assisted sprayers, this paper presents an analysis of the momentum and turbulent kinetic energy conservation equations for a two-dimensional air-jet penetrating a uniform crop canopy from a moving sprayer. From the analysis of these equations the velocity and turbulent kinetic energy along the jet centre-line are shown to decay exponentially with penetration distance. The decay exponents are shown to be proportional to the inverse of the jet width, the square of the ratio of sprayer speed to initial air-jet velocity and the crop density. Velocity and turbulence kinetic energy measurements are presented for a two-dimensional air-jet penetrating an artificial crop canopy. The canopy was constructed from a regular array of flow blockage planes which were adjusted to give an experimental range for area density (i.e. the cross-sectional area of blockage normal to the initial air-jet flow direction per unit volume) between 0·7 m - 1and 3·0 m - 1for two different values of plane spacing of 0·23 m and 0·46 m. The experimental results verify the exponential decay form for the distributions of air flow properties along the jet centre-line. The values derived for the exponential decay coefficient for both jet centre-line velocity and turbulent kinetic energy were found to give a poor correlation with the canopy area density over the full range of experiments. Instead, this correlation exhibited an asymptotic characteristic as the exponential decay coefficients for mean centre-line velocity and turbulent kinetic energy become very large at finite area density during high planar blockage. A rationale for this additional effect of crop structure is presented in terms of the additional losses produced by local flow channelling within dense canopies. The asymptotic characteristic was successfully modelled by redefining the crop density as the weighted sum of the inverse of the two orthogonal mean flow gaps in the artificial crop canopy. This new form of crop density replaces area density in an otherwise conventional model for momentum and turbulent kinetic energy losses due to small-scale volume averaging of air-jet and crop interactions.

A model based on dimensional analysis for non-invasive quantification of valvular regurgitation under confined and impinging conditions

The most descriptive measure of valvular insufficiency is the regurgitant volume. Current techniques for measuring it, however, are invasive and semi-quantitative at best. Cape and colleagues have recently developed a non-invasive technique for the quantitation of regurgitant flows corresponding to free jets cases. This technique is, unfortunately, not applicable to cases of jets constrained and/or impinging on the atrial walls as observed in many cases of mitral regurgitation. The purpose of this paper was therefore to develop an equation based on dimensional analysis, for calculating peak regurgitant flow rates from quantities than can be measured by Doppler ultrasound/echocardiography. The result is an equation for flow rate, Q o, as a function of orifice velocity, U o, a downstream centerline velocity, U m, at a distance, x, from the orifice, the diameter of the receiving chamber, D c, and the impingement height, H: Q 0 =(π U 0/4 )[a( U 0/U m )H cD d c x e] [2/c+d+e)] where a, c, d and e can be found by multiple linear regressions on pulsed Doppler jet centerline velocity data. The assumptions made in the derivation are such that they should be physiologically applicable. The advantage of this method compared to the previous one is its theoretical justification and ability to quantify accurately peak regurgitant flow rate, and total regurgitant volume.

An experimental study of a jet with local buoyancy enhancement

We report here an experimental study of the behaviour of a fully developed axisymmetric turbulent jet whose buoyancy is enhanced by volumetric heating over the region between two streamwise stations. The buoyancy enhancement is achieved by ohmic heating of an electrically conducting liquid jet, and the measurements are made using a laser Doppler velocimeter. It is found that, with heating, the axial component of mean velocity can increase appreciably relative to the unheated jet; however the turbulent intensity (normalized by the jet centreline velocity) decreases. The shape of the normalized mean velocity distribution across the jet is not significantly affected by the heating, but that of the fluctuating velocity is. The decay of the centreline velocity is considerably slowed down, or even reversed, due to the heating; similarly the spread rate is arrested at larger values of the Richardson number. As a result of the enhanced buoyancy the mass flux in the jet at first increases more rapidly than in the unheated jet but further downstream remains nearly constant over a distance of the order of the length of the heat injection region.