Experiments in Fluids 33 (2002) 539–544 DOI 10.1007/s00348-002-0480-1

Experimental investigation of an axisymmetric, impinging turbulent jet. 2. Scalar field M. Fairweather, G.K. Hargrave

539 mass transfer applications where the presence of a surface causes reduced mixing, compared to that of a free jet, due to the slower growth of the radial wall jet that forms on the surface. As a consequence, it is a generic flow that is encountered frequently in cooling, heating and drying operations, in studies of ventilation during mining and tunnelling activities, paint spraying and cavitation drilling, and in assessments of the consequences of accidental releases of flammable and toxic materials. Although the subject of renewed interest lately, both experimentally (Cooper et al. 1993) and for the development of mathematical models of momentum, heat and mass transfer in turbulent flows (Craft et al. 1993; Dianat et al. 1996), work to date has largely concentrated on the velocity fields in such flows, despite the relevance of the Nomenclature mixing field to many of the applications noted above. Data d internal diameter of jet source pipe for the concentration field in the flow formed by the f instantaneous mixture fraction normal impingement of an air jet on a flat surface have f mean mixture fraction been reported (Becker et al. 1988), although velocity data f m maximum mean mixture fraction is not available for this case. Dianat et al. (1995) obtained f ¢ root mean square of fluctuating mixture fraction h impingement height (i.e. pipe exit to plate separation) velocity and concentration data in an impinging methane jet, although these data are limited in the extent to which r radial distance, origin on jet axis they improve understanding of the mixing field. In parRe jet exit Reynolds number (= Vbd/m) ticular, the work of Dianat et al. (1995), in line with some Vb bulk mean vertical velocity from source pipe earlier studies (Bradshaw and Love 1959; Childs and Nixon y vertical distance from impinged plate 1985), indicate the presence of a large recirculation zone that can re-entrain jet fluid from the outer to the initial Greek symbols regions of the wall jet, the presence of which has important d mean concentration half-width implications for ventilation, tunnelling and safety applim kinematic viscosity cations. The present work, reported in two parts, was under1 taken to improve understanding of what is a practically Introduction important flow configuration and to resolve uncertainties The impingement of a jet on a flat surface is a flow of concerning the existence of recirculation zones in free, interest in many engineering applications. It gives rise, for impinging jet flows. In the first part of the study (Fairorthogonal impingement in the vicinity of the stagnation point, to some of the highest Nusselt numbers encountered weather and Hargrave 2002), two-dimensional measurements of mean and fluctuating velocities and turbulence in single-phase convection and is equally important in shear stresses in the free- and wall jet regions of an impinging turbulent air jet were obtained using digital particle image velocimetry. The data were in good agreement Received: 27 November 2000 / Accepted: 21 January 2002 Published online: 2 August 2002 with earlier measurements in such flows obtained by laser  Springer-Verlag 2002 Doppler anemometry (Dianat et al. 1995). They also clearly demonstrate, for the flow configuration under investigaM. Fairweather (&) tion, the existence of a large, low-velocity recirculation School of Process, Environmental and Materials Engineering, zone, of a size the same order as the impinged plate and University of Leeds, Leeds LS2 9JT, UK with a time period of 8 s, that carries material from the E-mail: [email protected] periphery of the wall jet back to its initial regions, causing G.K. Hargrave low levels of jet fluid to persist to large distances from the Department of Mechanical Engineering, Loughborough University, Loughborough LE11 3TU, UK impinged surface. Abstract In this, the second part of a two-part study of an impinging air jet, measurements of mean and rms concentrations and concentration probability density functions obtained using a Mie scattering technique are reported. Results in the wall jet are in good agreement with earlier data obtained using laser Raman spectroscopy, although differences in the spreading rate of the wall jet do occur, most likely due to buoyancy. The data demonstrate the influence of the recirculation zone, identified in the first part of the study, on the mixing field in causing low levels of jet fluid to persist to large distances from the surface. This finding has important consequences for many mass transfer applications of impinging jets.

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In the present paper, a one-dimensional Mie scattering technique, employing an Nd:YAG laser and calibrated CCD camera, is used to obtain measurements of mean and root mean square (rms) concentrations and concentration probability density functions (pdfs) within the impinging air jet to characterise its scalar mixing field. Taken in conjunction with results reported in the companion paper (Fairweather and Hargrave 2002), the present work provides detailed and comprehensive measurements on a generic, but practically important, flow configuration that are of value in improving understanding and to the formulation and validation of mathematical models of turbulent flows.

2 Experimental work The air jet used in the experiments was identical to that considered in the first part of the study (Fairweather and Hargrave 2002). It issued from a circular cross-sectioned pipe, 50 d in length and with an internal diameter of 13.3 mm. Air was supplied to the pipe from a compressor, with flow rates metered using Hastings mass flow controllers to give an average exit velocity from the pipe of 20 ms–1 and Re=18,800. The jet impinged vertically onto a flat, smooth steel plate, 1.3·1.1 m in length, situated above the release pipe. The pipe exit was located 26.6 mm from the surface (h/d=2), with no confinement around the entire rig. The pipe and plate were mounted on a hydraulic table to allow vertical positioning relative to the measurement locations. The flow within the pipe was seeded using a jet atomiser operating with olive oil and generating particles of 0.5–2.0 lm. To ensure a uniform seeding rate, the particles were injected into a mixing chamber located several meters upstream of the release. Concentration measurements were obtained using a one-dimensional Mie scattering technique that employed a Nd:YAG laser that produced 8-ns pulses with 200 mJ of energy per pulse at a rate of 10 Hz. Data were gathered by rapidly recording single profiles through the radial wall jet region of the flow for which the laser was formed into a collimated beam, 500 lm in diameter. For these measurements, the laser was fired vertically down through a small, 1-mm hole in the plate that was sealed using a sapphire window. Experiments performed without the hole, in which the laser fired vertically upwards towards the surface, demonstrated that the hole had a negligible effect on the results, apart from very close to the surface. Such data have been removed from the results given in the following section. Data was gathered using a non-intensified, back-thinned CCD camera that was calibrated to define the quantum efficiency of the CCD using a continuous light source and a calibrated neutral-density filter set. This allowed quantification of the local scattered-light intensity that could then be related to local particle number density as a ratio with the known exit source conditions to give local volume fractions. The camera was aligned orthogonally to the laser beam with 1,750 pixels along its length. This arrangement allowed rapid binning of the image data and the recording of instantaneous profiles at a rate of 10 Hz. Instantaneous

data were captured through the wall jet of the flow at radial displacements of 5, 10, 20, 30 and 40 jet diameters from the stagnation point. Typically, 1,024 points were obtained along each profile through the wall jet, which, in turn, provided sufficient information to permit the derivation of concentration pdfs, as well as time-averaged mean and rms fluctuating mixture fraction data. Single-shot laser images of the complete flow were also obtained by forming the Nd:YAG laser light into a planar sheet using a 1,500-mm focal length spherical lens and a 150-mm focal length cylindrical lens. This generated a sheet 120 mm high and 1.5 mm thick that was positioned horizontally through the flow. Micrometer-sized olive oil droplets were used as tracer particles in the flow, generated by a six-jet atomiser. Flow images were then recorded using the CCD camera with 1,750·550 pixels and a resolution of 16 bits. Approximately 500 individual images were averaged to produce the contours given below. These data were again obtained by ratioing local particle number densities to those recorded at the jet source and took account of background light intensity and variations in laser intensity across the sheet. Results obtained by this technique are, however, only used for illustrative purposes below since the data are less accurate than those obtained by the single-line Mie scattering technique due to the poorer signal-to-noise ratio and errors caused by variations in light and Mie scattering intensities across the laser sheet. The largest inaccuracy in the one-dimensional Mie scattering data is due to difficulties associated with maintaining constant seeding concentrations in the jet exit flow caused by seeding level fluctuations due to the turbulent velocity field. In addition, but to a lesser extent, electronic and digitisation noise and fluctuations in laser intensity also contributed error. These errors were assessed, in line with velocity field errors (Fairweather and Hargrave 2002), to be within ±3% for mean concentrations and ±5% for f ¢.

3 Results and discussion Instantaneous laser sheet images demonstrate a high level of intermittency in the outer regions of the wall jet and the presence of large-scale structures which caused atmospheric air to penetrate the wall jet and reach the surface of the plate early on in its development. Results from the first part of the study (Fairweather and Hargrave 2002) also demonstrated that a large, low-velocity recirculation zone, of a size the same order as the impinged plate and with a time period of 8 s, was established within the flow. This carried material from the periphery of the wall jet back to its initial regions. Figure 1 shows contours of mean concentration, in volume percent, within the wall jet of the flow obtained using the laser sheet technique described above. As noted earlier, although less accurate than the single-line data presented below, these results do provide a qualitative impression of the mixing flow structure over large regions of the flow and demonstrate that low mean concentrations of jet fluid do persist to large distances from the plate. Measurements of mean and fluctuating mixture fractions along the stagnation line of the jet confirmed no

Fig. 1. Mean concentration contours within the wall jet

change in jet exit values since this portion of the flow remained within the potential core of the jet. Away from this region, at larger radial distances, mixing becomes established, and Figs. 2 and 3 show, respectively, mean and rms fluctuating mixture fraction data through the wall jet at five radial locations (r/d=5, 10, 20, 30 and 40). In agreement with earlier findings (Dianat et al. 1995), mean mixture fraction data, equivalent to the mass fraction of jet

Fig. 2. Profiles of mean mixture fraction across the wall jet at r/d=5, 10, 20, 30 and 40

Fig. 3. Profiles of rms fluctuating mixture fraction across the wall jet at r/d=5, 10, 20, 30 and 40

fluid, show maximum values close to the surface, which steadily decay both with distance from the surface and with radial distance as the wall jet mixes with ambient fluid. The rms fluctuating mixture fraction data show peak values at the approximate half-width of the mean profiles, as would be anticipated, which again gradually decay with increasing radial distance. All these profiles also show significant, almost constant values of f ¢ into the surface. Although not studied in detail by Dianat et al. (1995), the original data of these authors also indicate similar constant values of rms fluctuating mixture fraction in close proximity to the surface. The existence of finite and constant f ¢ values close to the plate is in line with instantaneous laser sheet images of the flow (Fairweather and Hargrave 2002) that demonstrate a high level of intermittency in the outer regions of the wall jet and the presence of large-scale structures that caused atmospheric air to penetrate the wall jet and reach the surface of the plate from very early on in the wall jet’s development. It is also consistent with measurements of the velocity field within the wall jet of impacting jets which demonstrate that normal-to-wall fluctuating velocities decay in close proximity to the surface (Cooper et al. 1993; Fairweather and Hargrave 2002; Poreh et al. 1967), whilst radial (Cooper et al. 1993; Fairweather and Hargrave 2002; Poreh et al. 1967) and circumferential (Poreh et al. 1967) fluctuating velocities have almost constant values in those regions where f ¢ values are constant. Both mean and rms fluctuating mixture fraction profiles at all radial stations also demonstrate that small, but non-zero, concentrations exist outside the wall jet due to the presence of the recirculation zone. Mean and rms data therefore asymptote to small, constant values in these regions. The existence of non-zero concentrations at large distances from the surface is illustrated more clearly by the concentration probability information given in Figs. 4, 5, 6, 7 and 8 at various distances through the wall jet and for five radial locations. Instantaneous concentrations at all radial locations indicate an approximately Gaussian form at vertical distances close to the surface. With increasing distance from the surface, however, intermittency increases and the pdfs take on a quasi-bi-modal distribution (illustrated by the y/d=0.6, y/d=1.0 and y/d=2.0 profiles in Figs. 4, 5 and 6, respectively). Ultimately, the distribution becomes centred around a single, small concentration value at distances beyond the vertical extent of the wall jet. These results are qualitatively similar to those found in free jets (Birch et al. 1979), although in the present case, for the vertical distances shown in the figures, the concentration pdfs do not turn into delta functions at f=0 at large vertical distances since the background levels of recirculating jet fluid cause the pdfs to be centred around some small, but non-zero, concentration. These results are of significance since, at large distances from the surface, the tail of the pdf at large f could, in the case of jets of flammable material for example, extend into the flammable range. This, in turn, would mean that ignition may occur at greater distances from the surface than might otherwise be anticipated if concentration fluctuations were assumed to tend to zero beyond the outer edge of the wall jet.

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Fig. 4. Probability density functions of mixture fraction at various distances across the wall jet at r/d=5

Fig. 5. Probability density functions of mixture fraction at various distances across the wall jet at r/d=10

Comparison of the present mixture fraction data with earlier results (Dianat et al. 1995), obtained using laser Raman spectroscopy (Birch et al. 1978), is shown in Figs. 9, 10 and 11. These figures give, respectively, profiles of normalised mean and rms fluctuating mixture fraction and the spreading rate of the wall jet in terms of the mean mixture fraction half-width. The results of Figs. 9 and 10 have been non-dimensionalised by the peak mixture fraction, f m, and the appropriate concentration half-width, d. The lines used to represent the results of Dianat et al. (1995) are fits which include data from three measurement stations at r/d=11.6, 23.1 and 46.3. The present results are shown for all five radial measurement locations. In line with results from part 1 (Fairweather and Hargrave 2002) for the velocity field, data for mean

Fig. 6. Probability density functions of mixture fraction at various distances across the wall jet at r/d=20

Fig. 7. Probability density functions of mixture fraction at various distances across the wall jet at r/d=30

mixture fraction (Fig. 9) show similarity in the measured profiles at all radial locations, whereas rms fluctuating mixture fractions (Fig. 10) have not achieved self-similarity by the r/d=5 measurement station. Agreement between the present data and that of Dianat et al. (1995) is in general good, with the scatter observed in the present results being similar to that found in the Dianat et al. (1995) data. In particular, agreement for the normalised mean mixture fraction profiles is excellent over the range considered by Dianat et al. (1995), with both sets of data indicating non-zero concentrations at the outer edge of the wall jet. The present non-dimensionalised profiles of rms fluctuating mixture fraction are good in qualitative agreement with the earlier results, with, as noted above,

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Fig. 10. Profiles of normalised rms fluctuating mixture fraction within the wall jet

Fig. 8. Probability density functions of mixture fraction at various distances across the wall jet at r/d=40

Fig. 11. Growth of mean mixture fraction half-width within the wall jet

which the data of Dianat et al. (1995) were obtained (i.e. methane jet firing vertically down, d=10.8 mm, h/d =12.82, Vb=152 ms–1). Finally, Fig. 11 compares results for the spreading rate the original data of Dianat et al. (1995) also indicating of the concentration wall jet, with a linear fit to the constant values close to the surface. The present results present data giving a gradient of 0.94 and a virtual origin do, however, tend to overestimate peak values obtained of zero. As for the velocity field (Fairweather and by Dianat et al. (1995) by up to 15%. This may be due to Hargrave 2002), the spreading rate established in the the fact that measurements reported in this work were present work is in reasonable agreement with the data of Dianat et al. (1995), although the present data again tends obtained using techniques that rely on instantaneous data rather than the time-averaged information used as to underestimate earlier findings, particularly at large radial distances. With respect to the velocity data, the the basis of the earlier laser Raman results, i.e. in the most likely cause of these discrepancies is buoyancy work described by Dianat et al. (1995), rms data were determined after accumulation of the Raman intensities effects since the results of Dianat et al. (1995) were obtained for a methane jet firing vertically down. Fits to over a finite time interval, thereby time-averaging the the present velocity (Fairweather and Hargrave 2002) and individual data prior to the calculation of rms values. concentration spreading rate data give a mean concenThis, in turn, would cause data smoothing and a lowtration to mean velocity half-width ratio of 1.25 that ering of the rms values derived. Overall, however, compares reasonably (within 8%) with the value of 1.36 agreement between the two data sets is satisfactory, observed by Dianat et al. (1995). particularly given the widely different conditions for Fig. 9. Profiles of normalised mean mixture fraction within the wall jet

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of the normal wall-impinging jet. Chem Eng Commun 67:291– 4 313 Conclusion Birch AD, Brown DR, Dodson MG, Thomas JR (1978) The turbulent An experimental study of a turbulent air jet that impinges concentration field of a methane jet. J Fluid Mech 88:431–449 orthogonally onto a flat surface has been concluded by Birch AD, Brown DR, Dodson MG, Thomas JR (1979) Studies of flammability in turbulent flows using laser Raman spectroscopy. describing measurements of mean and rms concentraProc Combust Inst 17:307–314 tions, and concentration pdfs, within the wall jet of the Bradshaw P, Love EM (1959) The normal impingement of a circular flow. The major conclusions of this work are air jet on a flat surface. Reports and Memoranda No. 3205. Aerodynamics Division, National Physical Laboratory, London, 1. Useful data for mean and fluctuating mixture fraction, UK and mixture fraction pdfs, have been obtained using the Childs RE, Nixon D (1985) Simulation of impinging turbulent jets. In: Mie scattering technique. AIAA 23rd Aerospace Sciences Meeting, Reno, Nev., 1985, pp 1–10 Cooper D, Jackson DC, Launder BE, Liao GX (1993) Impinging jet 2. The present data are in good agreement with earlier studies for turbulence model assessment – I. Flow-field experimixing results obtained in impinging jet flows using ments. Int J Heat Mass Transfer 36:2675–2684 laser Raman spectroscopy. Some differences do, how- Craft TJ, Graham LJW, Launder BE (1993) Impinging jet studies for ever, occur between data on the spreading rate of the turbulence model assessment – II. An examination of the performance of four turbulence models. Int J Heat Mass Transfer wall jet, most likely due to buoyancy. 36:2685–2697 3. Mixture fraction field data clearly demonstrate that the M, Fairweather M, Jones WP (1995) Predictions of the conexistence of a large, low-velocity recirculation zone in Dianat centration field of an impacting turbulent jet. In: Tenth Sympothe impinging jet flow, identified in the first part of the sium on Turbulent Shear Flows 2, Pennsylvania State University, study, causes low levels of jet fluid to persist to large University Park, 1995, pp 12/19–12/24 distances from the impacted surface. This finding has Dianat M, Fairweather M, Jones WP (1996) Reynolds stress closure applied to axisymmetric, impinging turbulent jets. Theor Comput important consequences for many mass transfer apFluid Dyn 8:435–447 plications of impinging jets. Fairweather M, Hargrave GK (2002) Experimental investigation of an

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