Experiments in Fluids 33 (2002) 464–471 DOI 10.1007/s00348-002-0479-7

Experimental investigation of an axisymmetric, impinging turbulent jet. 1. Velocity field M. Fairweather, G.K. Hargrave

464 extensively in process engineering applications that involve cooling, heating and drying operations. It is also of interest in mass transfer applications such as mine ventilation and tunnelling operations, paint spraying and cavitation drilling, and in assessing the consequences of accidental releases of flammable and toxic materials. It is relevant to vertical-take-off-and-landing aircraft, rockets, shielded-arc welding and laser cutting and welding. The overall heat and mass transfer characteristics of impinging jets have been reviewed by Goldstein and Franchett (1988) and Jambunathan et al. (1992). The orthogonally impinging jet is of further interest Nomenclature because it presents an important test case for the develd internal diameter of jet source pipe h impingement height (i.e. pipe exit to plate separation) opment and validation of mathematical models of turbulent flow. This simple but generic flow contains both free r radial distance, origin on jet axis shear layer and near-wall regions, as well as zones of Re jet exit Reynolds number (=Vbd/m) strong, boundary-induced streamline curvature. Also, u¢ root mean square of fluctuating radial velocity pressure reflections from the surface dampen velocity U radial mean velocity fluctuations normal to the wall, causing both slower Um maximum radial mean velocity growth of the radial wall jet as compared to a free jet and uv shear stress sensitivity of the flow to streamline curvature. Recent exv¢ root mean square of fluctuating vertical velocity perimental work concerns the velocity field (Cooper et al. V mean vertical velocity relative to plate 1993; Nishino et al. 1996), with data sufficiently detailed to Vb bulk mean vertical velocity from source pipe permit the evaluation of turbulence models. Further dex vertical distance from jet source pipe velopment of second-moment (Craft et al. 1993; Dianat y vertical distance from impinged plate et al. 1996) and non-linear eddy viscosity (Craft et al. 1995) turbulence closures has also been pursued to allow the Greek symbols more accurate prediction of such flows through models d mean velocity half-width that account for the influence of pressure reflections from m kinematic viscosity the solid surface in damping velocity fluctuations normal to the wall. All this work is giving greater understanding of 1 the characteristics of impinging turbulent jets and imIntroduction The impingement of a jet on a plane surface is a flow of proving associated methods for predicting their velocity interest in many engineering applications. For orthogonal fields. The associated scalar field has also been studied, but impingement, and in the vicinity of the stagnation point, not to the same extent as the velocity field. Becker et al. it produces some of the highest Nusselt numbers seen in (1988) examined the concentration field of an impinging air jet, providing data for mean and fluctuating concensingle-phase convection, and so this flow is used trations and concentration intermittency, as well as for the two-point correlation coefficient and frequency spectra. Unfortunately, velocity information was not obtained, reReceived: 27 November 2000 / Accepted: 21 January 2002 Published online: 24 July 2002 ducing the usefulness of these data for the formulation and  Springer-Verlag 2002 validation of closures for the transport of passive scalar quantities in turbulent flows. M. Fairweather (&) Experimental velocity and concentration fields of a School of Process, Environmental and Materials Engineering, methane jet impinging on a flat surface have been reported University of Leeds, Leeds LS2 9JT, UK (Dianat et al. 1995) and predictions with a second-moment E-mail: [email protected] turbulence closure, modified to include wall reflection G.K. Hargrave effects, show reasonable agreement with these results Department of Mechanical Engineering, (Dianat et al. 1995). However, at large distances from the Loughborough University, Loughborough LE11 3TU, UK Abstract Mean and fluctuating velocities and shear stresses in an air jet impinging on a flat surface have been obtained by particle image velocimetry. A recirculation zone is revealed within the flow that carries material from the periphery of the wall jet back to its initial regions. Results within the wall jet agree with earlier data from laser Doppler anemometry, although significant differences occur with probe measurements. Data on the mixing characteristics of the flow are presented in a companion paper.

surface, in the outer regions of the radial wall jet, the predictions underestimate both mean and fluctuating concentrations. These discrepancies were attributed to differences between experimental and computational boundary conditions. In particular, the downward-directed experimental jet generated a significant negative-radialvelocity component in the air entrained, giving flow in the opposite direction to that of the wall jet. This, in turn, caused the entrained fluid to undergo a rapid reversal in direction at the upper limit of the wall jet, establishing a large recirculation zone that could re-entrain methane from the outer to the initial regions of the wall jet. Although not studied in detail, the data of Dianat et al. (1995) do indicate that negative radial velocities occurred beyond the outer regions of the wall jet. Such a recirculation zone has not been observed in recent studies (e.g. Cooper et al. 1993; Nishino et al. 1996), primarily because attention was focused on the near-field and stagnation regions of the impinging jet, where wall reflection effects are most significant. Also, most previous measurements were made by probe techniques which do not discriminate between the vertical and radial velocity components encountered in such flows. Profiles of mean radial velocity in the wall jet of an impinging axisymmetric air jet measured by Bradshaw and Love (1959) do, however, indicate that such velocities become negative outside the wall jet, and the existence of a recirculation zone is clearly visible in the predictions of this jet by Childs and Nixon (1985). Evidence that such zones may also occur in plane turbulent impinging jet flows is documented by Looney and Walsh (1984). The existence of a recirculation zone has important implications for ventilation, tunnelling and safety applications, since the re-entrainment of jet fluid from the outer to the initial regions of the wall jet could result, for example, in the build-up of unwanted flammable or toxic material, or dust. These effects may also be accentuated in many practical situations by flow confinement. The present work was therefore undertaken to resolve uncertainties raised by earlier studies about the existence of such zones in free, impinging jets, and to provide comprehensive data for the development and validation of mathematical models of turbulent flows, using non-intrusive, optical-diagnostic techniques. The results would also improve understanding of this flow. The study is split into two parts. Because of the importance of the velocity field in determining both heat and mass transfer within the flow, in this, the first part of the study, detailed information is presented on the velocity field alone. Data gathered on the scalar mixing field within the same flow are presented in a companion paper. In both studies, attention is also focused on flow within the wall jet of the impinging jet since the near-field development of the jet considered in the present work was characterised by those mechanisms elucidated by Launder and co-workers (Cooper et al. 1993; Craft et al. 1993). The study considers a low jet source pipe-to-plate separation (h/d=2). This separation was used so that the data obtained overlapped with that of Cooper et al. (1993), with a similar separation having been used by these authors because it is a case that can be simulated easily using

numerical models, and one for which heat transfer data is available (Baughn and Shimizu 1989). Extensive numerical simulations of this case are reported by Craft et al. (1993). It also provides data that is complementary to that of Becker et al. (1988) who studied the concentration field in a h/d=27 jet. Lastly, it represents a practically important case for safety applications, of concern in the present study, where rapid impingement of the jet prior to its full development is anticipated to significantly modify its dispersion characteristics.

2 Experimental work The experimental work was carried out in a 3·4·8-m room, which was sealed during the experiments to ensure stagnant conditions. The air jet employed issued from a round pipe of 13.3 mm internal diameter and 50 d in length. Air was supplied to the pipe from a compressor, with flow rates metered using a Hastings mass flow controller. The jet impinged vertically on a flat, smooth rectangular steel plate, 1.3·1.1 m in length, situated above the release pipe. Experiments that varied the distance of the jet source pipe from the edge of the plate showed that this parameter did not influence the data gathered, provided the radial measurement locations examined remained on the plate. The pipe exit was 26.6 mm from the surface (h/d=2), with no confinement around the entire rig other than the room in which the rig was housed. The pipe and plate were mounted on a hydraulic table to allow vertical positioning relative to the measurement locations. Velocity measurements were made by digital particle image velocimetry (PIV). This technique provides rapid two-dimensional mapping of velocity fields by imaging the displacement of tracer particles in a flow field with highresolution digital cameras. For this study, the PIV system was configured for cross-correlation analysis. Thus, two consecutive images of a particle image field are captured with a set time interval and the images cross-correlated to determine the particle displacements and thereby the particle velocities. The tracer particles were lm-sized olive oil droplets, generated with a TSI six-jet atomiser. These were injected into the jet pipe 3 m before the exit to ensure uniform seeding with negligible temporal variation over the length of an experiment. Tracer particles were also injected into the ambient air, with the seeder running for 20 min before the start of each experiment to build up a high concentration of particles within the room in which the experimental rig was located. The seeding level was controlled to ensure a uniform seeding density from ambient to jet fluid within the rig to remove any velocity bias associated with spatio-temporal variations in particle density. The light source was a pair of Continuum Surelite II Nd:YAG lasers. These lasers were set to generate 200-mJ pulses with a pulse width of 10 ns at a rate of 10 Hz. The two beams were configured to intersect at the point of interest and focused with a 1.5-m focal length spherical lens. The beams were formed into a laser sheet with a 100-mm focal length cylindrical lens. In the measurement region the sheet was uniform over an area 50 mm square and was approximately 1 mm thick. Imaging of the

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particles was performed with a Kodak ES1.0 Digital CCD camera. This provides images of 1000·1000 pixels, with a resolution of 8 bits. This camera was operated in a doubleexposure mode that allowed the recording of two consecutive images on the single CCD. The camera was interfaced to a PC with a Mutech MV1500 frame grabber that allowed recording of the double images at the 10-Hz repetition rate of the laser. The computer was a Pentium II 400 with 500 Mbytes of RAM, allowing recording of 400 images. The imaged field was 15·15 mm, providing an image resolution in the flow field of 15 lm. A control system sent a 10-Hz clock synchronisation pulse to the computer, triggering the image capture, and two trigger pulses to fire the lasers. The pulse separation was varied from 5 ls to 500 ls, depending on the local velocity, in order to control the particle displacement on the image. For the cross-correlation analysis, the interrogation region was maintained at 64·64 pixels, giving a measurement region in the flow field of 960·960 lm, and pulse separation varied to achieve 30–50% displacement. Instantaneous velocity profiles were captured in the region between the jet source pipe and the plate, along the stagnation line, and within the wall jet at radial displacements of 5, 10, 20 and 30 jet diameters from the stagnation point. At each measurement location, typically, 800 image pairs were recorded for each 15-mm region of the velocity profile. At 20 d, this corresponded to a total of 4,800 individual image pairs required to build the complete profile through the wall jet. From the large sample of velocity vectors recorded at each measurement location, time-averaged mean radial and vertical velocities, root mean square (rms) fluctuating velocities and the turbulence shear stress ðuvÞ were calculated. The analysis of instantaneous vector images was carried out with specially written software. In such calculations, it is important to use enough vector images to ensure statistically meaningful results (Fairweather and Hargrave 2001). The number of images was indeed found to have a critical effect on the derived time-averaged profiles, with values determined using too few clearly exhibiting high scatter, particularly in the regions where the influence of the wall and large mean radial velocities were greatest. For all the results presented below, the number of images was statistically sufficient. For example, calculation of rms fluctuating vertical velocity across the wall jet at r/d=10 required approximately 1,600 image pairs to give time-averaged results independent of the number of images used. Single-shot laser images of the complete flow were also obtained by forming the beam from a single Nd:YAG laser into a planar sheet using optics consisting of a 2-m focal length spherical lens and a short-focal-length cylindrical lens. This generated a sheet 120 mm wide and 1.5 mm thick. Flow images were then recorded using the CCD camera with 1750·550 pixels and a resolution of 16 bits. The errors in the PIV measurements are of two kinds, namely, random and systematic error, and were accounted for as described by Lawson et al. (1997). The random error arises from several sources including: electronic noise from the CCD (random component of the dark current and total shot noise), insufficient digitisation resolution,

seeding density and particle image variations across the interrogation region and velocity gradients (with nonrandom error in high mean velocity gradient regions judged not to contribute significantly to the errors). Systematic error is caused mainly by the bias generated by the fact that there is a higher probability of highvelocity particles leaving the interrogation region than low-velocity particles. Thus, the correlation is weighted towards smaller particle displacements and hence towards the slower particles in the interrogation region. In the current study, the systematic errors were small, being less than ±1% for the calculated mean velocities. The random errors produced the maximum uncertainty, mainly as a result of the presence of high-velocity gradients at some flow locations. The maximum random error in the mean velocities was estimated as ±5% in the high-shear regions of the jet, but only ±2% in the wall jet measurements. This gives a total error in the wall jet of ±3% for the mean velocities and, although difficult to estimate, implies associated errors of approximately ±4% for u¢, ±5% for v¢ and ±7% for uv.

3 Results and discussion The mean vertical-velocity profile near the exit of the jet source pipe conformed with fully developed pipe flow, being approximated by the 1/7th power law. Figures 1, 2 and 3 give radial profiles of the mean vertical and radial velocities, and normal-to-wall fluctuating velocities, close to the exit of the release pipe at x=0.2 d. The average exit velocity from the pipe, Vb, was 20 ms–1, giving an exit jet Re=18,800. The peak mean exit velocity was 25 ms–1, which, in combination with the bulk value, produces a discharge coefficient of 0.8. Mean radial velocities are near zero at x=0.2 d, although a slight influence of the pipe walls is apparent at this distance downstream. The profile of the rms of normal-to-wall fluctuating velocities indi-

Fig. 1. Radial profiles of mean vertical velocity at various distances between the pipe exit and the wall

Fig. 2. Radial profiles of mean radial velocity at various distances between the pipe exit and the wall

Fig. 3. Radial profiles of rms fluctuating velocity normal to the wall at various distances between the pipe exit and the wall

cates a centreline local turbulence intensity of 5.6%, in line with earlier results for pipe flows (Durst et al. 1995). Figures 1, 2 and 3 also give radial profiles of the mean vertical and radial velocities, and normal-to-wall fluctuating velocities, at various distances between the pipe exit and the impinged surface. For a pipe-to-plate separation of 2 d, the centreline of the jet remains within the potential core region up to the impinged surface. Data along the stagnation line of the flow, given in Figs. 1, 2 and 3, follow the trends described by Launder and co-workers (Cooper et al. 1993; Craft et al. 1993). The mean vertical velocity thus slowly decreases along the stagnation line until approximately 0.7 d from the surface, at which point it rapidly decays to zero at the surface due to the influence of the wall. Mean radial velocities remain at zero along the

stagnation line. Normal-to-wall velocity fluctuations initially grow up to 0.3 d of the surface, due to the diffusion of some turbulence from the mixing region, beyond which they decay due to dampening by the wall (Cooper et al. 1993). The results in Figs. 1, 2 and 3 also agree with earlier measurements (Cooper et al. 1993; Craft et al. 1993) away from the stagnation line. The mean vertical velocity at r/d=0.5 increases slightly up to 0.1 d from the wall and then decreases. At r/d=1.0, this velocity is effectively zero, apart from in the final profile at 0.1 d from the surface. Mean radial velocities at r/d=0.5 and 1.0 increase as the surface is approached, with large values near the surface due to the flow accelerating away from the stagnation point. The overall magnitude of the radial velocity also increases from the stagnation line to r/d=0.5 due to the expansion of the jet, although between r/d=0.5 and 1.0 it again decreases since the latter location is within the ambient air region at locations away from the surface. At distances within 0.1 d of the surface, measurements (not shown) of this velocity component continue to show an increase in peak values between r/d=0.5 and 1.0, due to the rapid acceleration of the flow away from the stagnation point, in agreement with Cooper et al. (1993) and Craft et al. (1993). Values of v¢ at r/d=0.5 also conform to the trends observed in these studies, the profile being qualitatively similar to that along the stagnation line, and with maximum values close to the wall being similar in magnitude. Although not shown, limited data obtained in the near-field region on radial fluctuating velocities and shear stresses are in line with the data of Cooper et al. (1993). Instantaneous laser sheet images of the complete flow field indicate high levels of intermittency in the outer regions of the wall jet and the presence of large-scale structures. These structures, in turn, cause entrainment air to penetrate the wall jet and reach the wall very early in its development. The laser sheet images also reveal the existence of a steady, low-velocity recirculation zone above the wall jet, with a size the same order as the impinged plate and with a time period of 8 s. This eddy carried material from downstream in the wall jet back to its initial regions, causing low levels of jet material to persist to large distances from the surface. Further experiments showed that air entrainment streamlines into the jet are approximately 45 to the vertical, allowing establishment of this recirculation eddy. The presence of the eddy was also confirmed in experiments that varied the distance of the jet source pipe from the edge of the plate. Figures 4 and 5 show profiles of mean and fluctuating velocities and turbulence shear stresses, through and beyond the wall jet at radial distances of r/d=10 and 30. For clarity, all the data in these figures have been smoothed, although raw, unsmoothed data are considered in the later figures. The development of the wall jet is clearly illustrated, as is the influence of the recirculation zone on the flow outside the wall jet. For the wall jet, these results demonstrate that its development away from the stagnation region is similar to that observed by others (Cooper et al. 1993; Dianat et al. 1995; Poreh et al. 1967), although detailed data outside this region was not gathered in earlier studies. Mean radial velocities peak at small distances

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Fig. 4. Profiles of mean and fluctuating velocities and shear stress across the wall jet at r/d=10

Data at larger distances from the surface indicate that, at r/d=10 for example, the recirculation zone extends to approximately y/d=8.5. Profiles of mean vertical velocity show the same trends observed in the mean radial velocity results, with velocities becoming negative at the same distance from the wall (approximately y/d=1.4 at r/d=10 and y/d=3.8 at r/d=30). Data at larger distances from the surface again indicate that the recirculation zone extends to approximately y/d=8.5 at r/d=10. Data for rms fluctuating horizontal and vertical velocities agree qualitatively with earlier findings (Cooper et al. 1993; Dianat et al. 1995; Poreh et al. 1967), with both data sets showing peaks within the wall jet and with maximum values of the radial component exceeding those of v¢. Beyond the limit of the wall jet, at y/d1.4 in Fig. 4 and y/d3.8 in Fig. 5, profiles of u¢ and v¢ asymptote to small, but non-zero, values due to the presence of the recirculation zone. Shear stress profiles also agree with earlier results, decaying to zero just beyond the upper limit of the wall jet and remaining effectively zero beyond that point. Although not shown, measurements at r/d=5 and 20 are consistent with these findings and confirm the trends noted above. Figures 6, 7, 8, 9 and 10 show raw, unsmoothed data from a number of traverses across the wall jet. This also permits a more detailed comparison of the present data with earlier results obtained by hot-wire anemometry (Poreh et al. 1967) and laser Doppler anemometry (Dianat et al. 1995). In these figures, the data are non-dimensionalised by the peak mean radial velocity, Um, and the velocity half-width, d. Values of Um for the present data are 3.82, 2.06, 1.04 and 0.72 ms–1 at r/d=5, 10, 20 and 30, respectively. The curves representing the results of Dianat et al. (1995) and Poreh et al. (1967) are fits which include data from a number of measurement stations at similar radial locations to those examined in the present work. The scatter in the present data is also similar in magnitude to that observed by Dianat et al. (1995) and Poreh et al. (1967).

Fig. 5. Profiles of mean and fluctuating velocities and shear stress across the wall jet at r/d=30

from the surface, with maximum values steadily decaying as the wall jet mixes with ambient fluid. Peak values also increase with distance from the wall as the wall jet grows in thickness and the influence of the wall increases. Beyond the outer limit of the wall jet, the influence of the recirculation zone manifests itself through the occurrence of negative mean radial velocities. These velocities are relatively small compared to those encountered within the wall jet itself and show peaks which move progressively away from the surface with increasing radial distance. Maximum negative values are encountered close to the stagnation Fig. 6. Profiles of normalised mean radial velocity within the wall jet point where entrainment velocities into the jet are high.

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Fig. 7. Profiles of normalised mean vertical velocity within the wall jet

Fig. 9. Profiles of normalised rms fluctuating velocity normal to the surface within the wall jet

Fig. 8. Profiles of normalised rms fluctuating radial velocity within the wall jet

Fig. 10. Profiles of normalised shear stress within the wall jet

The present results are shown for all four radial stations in Figs. 6 and 7, but exclude those at r/d=5 in Figs. 8, 9 and 10 since self-similarity of the rms fluctuating velocity and shear stress profiles is not achieved there. Also, although included in Figs. 6 and 7, there remains some doubt as to whether self-similarity is achieved by r/d=5 even for the mean profiles. This is particularly true of the mean vertical velocities, Fig. 7. By r/d=10, however, all the data of Figs. 6, 7, 8, 9 and 10 demonstrate similarity. Agreement between the present data and Dianat et al. (1995) is good for both mean radial (Fig. 6) and rms fluctuating vertical (Fig. 9) velocities. Agreement on the mean velocity profile is particularly excellent over most of

the range covered by Dianat et al. (1995), with that data again indicating that negative velocities did occur outside the wall jet. The present non-dimensionalised profiles of rms fluctuating velocity are also in reasonable qualitative agreement with Dianat et al. (1995), although the present peak values tend to fall below theirs, while occurring at approximately the same distance from the wall. The PIV measurements of both mean and rms velocities also fall below those using laser Doppler anemometry (LDA) at locations near and beyond the outer limit of the wall jet. The most likely cause of these differences is buoyancy, since the LDA results are for a methane jet aimed vertically down. Results for the spreading rate of the wall jet (Fig. 11) are also in reasonable agreement, although the

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the impinged surface. Again, these differences may be due to the intrusive nature of the probes employed by these authors, or the directional ambiguities encountered in using such probes in highly turbulent flows. Overall, good agreement is observed between the present PIV data and the LDA results of Dianat et al. (1995), particularly given the widely different conditions for which their data were obtained (i.e. methane jet firing vertically down, d=10.8 mm, h/d=12.82, Vb=152 ms–1). Significant differences are, however, found with the hot-wire results of Poreh et al. (1967). This finding is in line with that of Eriksson et al. (1998), who attributed differences in their own LDA data in a two-dimensional, plane turbulent wall jet and earlier hot-wire results to high turbulence intensity effects on the hot wires.

4 Conclusion The major conclusions of this work are Fig. 11. Growth of mean radial velocity half-width within the wall jet 1. Useful data for mean and fluctuating velocities, and

shear stresses have been obtained using the PIV technique. 2. The present PIV data agree well with earlier results on present data again fall slightly low, particularly at large impinging jet flows where laser Doppler anemometry radial distances. was used. Significant differences, however, exist beGlauert (1956) treated the wall jet problem theoretically, tween these data and earlier hot-wire anemometer dividing the flow into a free turbulent outer region and an measurements. inner region where wall effects are apparent. This analysis 3. The data clearly demonstrate a large, low-velocity reestablished that the length scale of the outer region changes circulation zone in the impinging jet flow that carries as radial distance r, whilst that of the inner region changes 1.03 material from the periphery of the wall jet back to its as dr . Using a more detailed analysis, Poreh et al. initial regions. (1967) established a smaller rate of spread of the wall jet according to dr0.90. Fitting the results of Fig. 11, assuming Data on the mixing characteristics of the same flow are a linear spreading rate over 0
Dianat M, Fairweather M, Jones WP (1996) Reynolds stress closure applied to axisymmetric, impinging turbulent jets. Theor Comput Fluid Dyn 8:435–447 Durst F, Jovanovic J, Sender J (1995) LDA Measurements in the near-wall region of a turbulent pipe flow. J Fluid Mech 295:305– 335 Eriksson JG, Karlsson RI, Persson J (1998) An experimental study of a two-dimensional plane turbulent wall jet. Exp Fluids 25:50–60 Fairweather M, Hargrave GK (2001) DPIV measurements in axisymmetric, impinging turbulent jets, Paper 1031 (CD-ROM). In: Kompenhans J (ed) Proc. 4th Int. Symposium on Particle Image Velocimetry, 2001, DLR, Gottingen, Germany Glauert MB (1956) The wall jet. J Fluid Mech 1:625–643 Goldstein RJ, Franchett ME (1988) Heat transfer from a flat surface to an oblique impinging jet. J Heat Transfer 100:84–90

Jambunathan K, Lai E, Moss MA, Button BL (1992) A review of heat transfer data for single circular jet impingement. Int J Heat Fluid Flow 13:106–115 Launder BE, Rodi W (1983) The turbulent wall jet – Measurements and modeling. Ann Rev Fluid Mech 15:429–459 Lawson NJ, Halliwell NA, Coupland JM (1997) A generalised optimisation method for double-pulsed particle image velocimetry. Opt Lasers Eng 27:656–673 Looney MK, Walsh JJ (1984) Mean-flow and turbulent characteristics of free and impinging jet flows. J Fluid Mech 147:397–429 Nishino K, Samada M, Kasuya K, Torii K (1996) Turbulence statistics in the stagnation region of an axisymmetric impinging jet flow. Int J Heat Fluid Flow 17:193–201 Poreh M, Tsuei YG, Cermak JE (1967) Investigation of a turbulent radial wall jet. J Appl Mech 34:457–463

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