PIV measurements of a plane wall jet in a confined space at transitional slot Reynolds numbers
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- van Hooff, T., Blocken, B., Defraeye, T. et al. Exp Fluids (2012) 53: 499. doi:10.1007/s00348-012-1305-5
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Wall jets are important for a wide variety of engineering applications, including ventilation of confined spaces and cooling and drying processes. Although a lot of experimental studies have been devoted to wall jets, many of these have focused on laminar or turbulent wall jets. There is a lack of experimental data on transitional wall jets, especially transitional wall jets released into a confined space or enclosure. This paper presents flow visualizations and high-resolution Particle Image Velocimetry measurements of isothermal transitional plane wall jets injected through a rectangular slot in a confined space. As opposed to many previous studies, not only the wall jet region but also the recirculation region in the remainder of the enclosure is analyzed. The data and analysis in this paper provide new insights into the behavior of transitional plane wall jets in a confined space and will be useful for the validation of numerical simulations of this type of jets.
The dynamics of air jets have been studied extensively in the past decades. Air jets are important for a wide range of engineering applications and are—among others—used for ventilation of buildings, ships and airplanes and for drying and cooling processes. Knowledge of the flow development and mixing characteristics of the jet is, therefore, of primary importance. Previous studies have dealt extensively with the development of turbulent round, plane and wall jets, both experimentally and numerically. However, to the knowledge of the authors, experiments on transitional jets are relatively scarce, especially for transitional plane wall jets issued into a confined space. Providing and analyzing such data are the main objectives of this paper. First, an overview of past studies on wall jets and transitional jets is provided. The findings from these studies will be used to support the analysis of the experiments in this paper.
A wall jet is a jet that is confined on one side by a wall. It can be subdivided in an inner region and an outer region. The inner region, or inner layer, runs from the wall to the point of maximum velocity UM and is similar to a wall boundary layer, whereas the outer region, or outer layer, consists of the remainder of the wall jet and can be seen as a free shear layer. A formal description of the wall jet is given by Launder and Rodi (1981): “A wall jet may be defined as a shear flow directed along a wall where, by virtue of the initially supplied momentum, at any station, the streamwise velocity over some region within the shear flow exceeds that in the external stream.” Wall jets can be subdivided in two-dimensional (plane) and three-dimensional wall jets. Plane wall jets are bounded by walls on the lateral sides of the jet, which prevent its lateral expansion, whereas three-dimensional wall jets can also grow in the lateral direction and are, therefore, more complex.
The first reported experimental study of a wall jet was conducted by Förthmann (1934). Later, turbulent wall jets were experimentally investigated by Bakke (1957), Sigalla (1958), Bradshaw and Gee (1960) and Schwarz and Cosart (1961). An extensive overview of experimental work until 1980 is given by Launder and Rodi (1981). Wygnanski et al. (1992), Hsiao and Sheu (1994, 1996), Gogineni and Shih (1997), Amitay and Cohen (1997), Eriksson et al. (1998) are just a few examples of studies in which the wall jet was experimentally analyzed during the last decades of the twentieth century.
Experimental and numerical analyses of turbulent wall jets in a confined space were reported by Moureh and Flick (2003, 2005). The focus of these studies was on the wall jet characteristics and its decay and detachment from the wall. The authors concluded that the separation of the wall jet from the top surface was caused by an adverse pressure gradient as a result of the confinement of the flow. The location of jet detachment experienced an intermittent behavior, since it oscillated around an average position (Moureh and Flick 2003). In this area, the velocity measurements were characterized by weak fluctuations in the order of 1 Hz. As a result of the intermittent behavior of the location of jet detachment, there was a dynamic interaction between the wall jet flow and the corner recirculation. Consequently, the zones occupied by these two flows expanded and narrowed at the rate of these fluctuations.
Although a lot of experimental studies have been performed for laminar and turbulent wall jets, only a few have focused on transitional wall jets. One of the first experimental studies on transitional plane wall jets was conducted by Bajura and Catalano (1975). They found that the transition from laminar to turbulent flow generally occurred in the following five stages: (1) formation of discrete vortices in outer region, (2) pairing of two or more vortices in the outer region, coupled with the possible pairing of vortex-like motions in the inner region wall boundary layer, (3) lifting-off of the wall jet flow into the ambient fluid, (4) dispersion of the lifted-off flow field by three-dimensional turbulent motions and (5) re-laminarization of the upstream flow, until another vortex pairing occurs. Lichter et al. (1992) experimentally analyzed the separation and vortex development of a wall jet in a stratified tank. They observed the organization of an asymmetric dipole after separation from the wall. Hsiao and Sheu (1994) studied the behavior of double row vortical structures in the near-field region of a plane wall jet. Flow visualizations and hot-wire measurements were performed to analyze vortex formation in the inner and outer region and vortex lift-off from the wall. Gogineni and Shih (1997) performed flow visualizations, Particle Image Velocimetry (PIV) and surface pressure measurements to study the vortex pairing and jet detachment associated with the transition of plane wall jets. From their measurements, they concluded that the boundary layer detaches from the wall as a result of a local adverse pressure gradient induced by the passage of a vortex structure in the outer region of the wall jet.
The studies discussed above were all conducted either for turbulent plane wall jets with or without confinement or for transitional plane wall jets without confinement, that is, which are not strongly influenced by a secondary flow. This is in contrast to the study in the present paper, in which a recirculation flow driven by a transitional wall jet dominates the flow in the remainder of the test section. To the knowledge of the authors, only a few studies have been conducted for transitional plane wall jets that are influenced by a secondary flow resulting from a restricted size of the test section (confined flow). Nielsen et al. (2000) and Topp et al. (2000) performed hot-sphere measurements of room air flow resulting from a plane wall jet at low Reynolds numbers. Wang and Chen (2009, 2010) performed point measurements of air flow in a simplified model of an airline cabin using hot-sphere and ultrasonic anemometers. The main objective of these measurements was to establish benchmark data to validate numerical flow simulations.
In addition to these wall jet studies, experiments were also performed for transitional flow in free plane jets (Sato 1960; Sato and Sakao 1964; Beavers and Wilson 1970; Mumford 1982; Lemieux and Oosthuizen 1985; Namer and Ötügen 1988). Namer and Ötügen (1988) stated that there is strong evidence that large vortical structures control the initial jet growth. Immediately downstream of the inlet, unstable laminar shear layers break down and form vortices that carry irrotational ambient fluid into the jet and thereby induce mixing by wrapping the ambient fluid about themselves. They also indicated the dependence of jet mixing, spread rate and centerline decay on the jet Reynolds number, but found that the Strouhal number, based on the vortex formation frequency in the outer region, was independent of Re for Re-values ranging from 1,000 to 7,000. Suresh et al. (2008) studied the transitional characteristics of plane jets for Re in the range from 250 to 6,250. They showed that jet spread decreases with Re due to the dominance of finer scales in higher Re jets and large-scale structures in the outer shear layer region for low Re jets (Re < 2,000). Furthermore, they concluded that the Strouhal number is Re-dependent for Re < 2,000. Additionally, transitional round jets were studied by Angioletti et al. (2003), O’Neill et al. (2004), Kwon and Seo (2005) and Todde et al. (2009).
Not only studies on transitional jets are relevant sources of information. Also studies of vortex dynamics in confined spaces can contribute to the understanding of vortex formation, advection and decay in an enclosure. For example, van Heijst et al. (1990) experimentally studied the spin-up process in a rectangular container. Konijnenberg et al. (1994) also studied the spin-up process in a rectangular tank, both experimentally and numerically. Wells et al. (2007) performed experiments and numerical simulations to investigate the production of small-scale vorticity near no-slip sidewalls of a container and to study the formation and decay of wall-generated quasi-two-dimensional vortical structures.
The present paper reports flow visualizations and PIV measurements of a transitional plane wall jet issued into a confined space. The study is motivated by the fact that most plane wall jet studies in the past have been conducted for plane wall jets in relatively large enclosures and/or with slot Reynolds numbers (i.e., Re based on inlet height) corresponding with a turbulent regime. As opposed to many previous studies, this study will not only focus on the wall jet region but also on the recirculation region in the remainder of the enclosure. One of the practical situations in which this type of flow is important is the ventilation of enclosures. The use of a wall jet to create a recirculation region that dilutes the air in a confined space is one of the two major ventilation principles that are used to maintain a healthy, energy-efficient and comfortable indoor climate in buildings, ships, planes, etc. (e.g., Nielsen 1974; Etheridge and Sandberg 1996; Awbi 2003; Chen 2009). In order to minimize the risk of discomfort of the occupants, velocities inside an enclosure should be kept relatively low. As a result, the jet flow might become transitional at these low velocities (low Re-values). First, the experimental setup is described in Sect. 2. The flow visualizations are addressed in Sect. 3. A description of the PIV measurement setup is given in Sect. 4, after which the results of the PIV measurements are analyzed in Sect. 5. Discussion (Sect. 6) and conclusions (Sect. 7) conclude this paper.
2 Experimental setup
A water-filled experimental model has been built to perform flow visualizations and PIV measurements (Fig. 1a). It consists of (1) a water column to drive the flow by hydrostatic pressure; (2) a flow conditioning section; (3) a cubic test section having edges of L = 0.3 m constructed from glass plates with a thickness of 8 mm; and (4) an overflow. The conditioning section in front of the inlet consists of one honeycomb, three screens and a contraction to obtain a uniform water flow at the inlet and to minimize the turbulence level. More information on the experimental setup can be found in van Hooff et al. (2012).
3 Flow visualizations
4 PIV measurement setup
PIV measurement parameters. The samples are double image pairs which result in instantaneous PIV vector fields
Measuring frequency [Hz]
Number of samples [−]
Sampling time [s]
Frame rate [μs]
The two-dimensionality of the flow was tested by performing measurements in two additional vertical planes at z = 0.417 and z = 0.330, which showed no significant differences in the time-averaged flow pattern between the three vertical planes. The time-averaged velocity fields were obtained by averaging the 360 instantaneous velocity vector fields.
Two sets of PIV measurements were performed in the vertical center plane (z = 0.5) of the water cube. The first set focuses on the entire cross-section of the cube, that is, a region of interest (ROI) of L × L (Fig. 4; ROI1). The second set focuses on a smaller region of interest of 0.6 L × 0.4L (W × H) in the proximity of the inlet, enabling a higher measurement resolution (Fig. 4; ROI2). The higher resolution provides more detailed information in this area with expected large velocity gradients. This information about the inlet conditions is important as boundary conditions for future numerical simulations.
5 PIV measurement results
In this section, we will present and discuss the results of the PIV measurements. The results for the case with Re ≈ 300 are excluded because the observed flow pattern was very unstable, that is, the large recirculation region was not present in each instantaneous velocity vector field due to the very low momentum of the wall jet; therefore, averaging resulted in ambiguous results.
5.1 Analysis of time-averaged results
5.1.1 Time-averaged velocity vector fields
5.1.2 Time-averaged velocity and turbulence profiles near the inlet
5.1.3 Time-averaged velocity profiles in the entire flow domain
Profiles of U/UM at x = 0.5 are shown in Fig. 10b. As already shown in Fig. 6e, the profiles at x = 0.5 show Re-dependency in the wall jet region. The value of yC is lower for lower Re-values. From y = 0.6 to y = 0.1, U/UM decreases almost linearly from 0.15 to −0.2; again, no clear Re-dependency is present in this area. The height of the center of the recirculation zone, U/UM = 0, lies approximately at y = 0.4 for all Re-values.
Figure 10c shows U/UM at x = 0.8. Clear differences can be seen in the profiles for different Re. The negative values for U/UM in the inner region indicate detachment of the wall jet boundary layer, resulting in a small recirculation cell downstream of the detachment point. The size of this recirculation cell, and thus the area with negative values of U/UM, increases with decreasing Re. The vertical location of the maximum velocity depends strongly on Re, for example, for Re ≈ 1,000, yC = 0.754, whereas for Re ≈ 2,500, yC = 0.843. Below the wall jet region, y < 0.6, Re-dependency is still present, although the differences are far less pronounced.
5.1.4 Time-averaged vorticity profiles
5.2 Analysis of instantaneous flow field
5.2.1 Instantaneous velocity vector fields
5.2.2 Application of Q criterion
5.2.3 Analysis of Strouhal number
Since a clear periodicity of the flow was observed, the relation between Re number and Strouhal number, defined as St = (fh)/UM, with f the vortex formation frequency, h the inlet height and UM the maximum x-velocity at x = 0.1, is analyzed in this section. This relation has been the subject of several studies in the past. Namer and Ötügen (1988), among others, analyzed the relationship between Re and St for free plane jets and Re ranging from 1,000 to 7,000. They stated that in their experiments, St was independent of the Re (St ≈ 0.273), even for Re = 1,000, which is expected to result in transitional flow. However, Suresh et al. (2008) did find a dependency of St on Re for free plane jets, at least for Re < 2,000. For higher Re, they found that St reached an asymptotic value of around 0.36. It should be noted that all studies described above were performed for free plane jets in an unconfined space.
The vortex formation frequency in this study was determined based on the average distance between two adjacent vortical structures and the local maximum jet velocity UM. Other studies reported vortex formation frequencies based on Fast Fourier Transformations (FFT); however, for the vast majority of the measurements in this study; the measuring frequency was too low (sampling frequency < Nyquist frequency) to be able to determine St using a frequency spectrum. Only for Re ≈ 1,000 and Re ≈ 1,200, the measuring frequency was high enough to apply FFT and to determine the vortex formation frequency. Comparison of FFT with the used method showed a good agreement between results from both methods (±5%).
In this paper, the experimental results of a study on a transitional plane wall jet in a confined space have been presented and discussed. The experimental work consists of flow visualizations and PIV measurements to analyze the flow pattern. PIV measurements were performed for Reynolds numbers from 300 to 2,500, since the flow visualizations have shown that transitional flow is present for at least this range of Re-values.
In accordance with previous studies on transitional jets, the present study has shown that jet properties, such as time-averaged velocity, turbulence intensity and Strouhal number, show a Re-dependency. Unfortunately, a detailed comparison with previously published experimental data was not possible, since, to the knowledge of the authors, papers in which transitional plane wall jets in a confined space are analyzed using high-resolution measurements have not been published so far. However, a comparison with theoretical profiles was performed and showed that in general the measured wall jet profiles were situated between the theoretical profiles for a laminar and a turbulent wall jet. Furthermore, the comparison illustrated the effect of the flow confinement.
In Sect. 1, a short description was given of the five stages that generally occur during the transition from laminar to turbulent flow in jets, as identified by Bajura and Catalano (1975) based on flow visualizations and hot-film anemometry. In the present study, the presence of the following four stages can be identified: (1) formation of discrete vortices in the outer region (Figs. 13, 14), (2) formation of vortex-like motions in the inner region wall boundary layer (Fig. 14b), (3) separation of the wall jet from the top surface due to an adverse pressure gradient and (4) interaction of the separated wall jet with the global recirculation cell. Neither the vortex pairing in the inner and outer region nor the re-laminarization could be distinguished from the PIV measurements. The different observations are likely caused by the differences in experimental setup: the measurements in this study are performed in a confined space with an influence of the recirculation zone on the flow physics of the wall jet, whereas the measurements by Bajura and Catalano (1975) were conducted in an unconfined space, without influence of an opposing wall on the transition process. Furthermore, the measurement resolution and frequency in our study might have been too low to capture the pairing of vortices in the test section.
In addition, there are some other limitations concerning the experimental work described in this paper. First, the reflections of the glass bottom of the test section made it impossible to analyze the flow in this area of the cube. As a result, some information on the flow pattern is lacking, although one must note that the bottom of the cube is not the primary area of interest in this study, in contrast to the wall jet region. Second, the determination of the Strouhal number has not been conducted using FFT, although the suitability of the used method has been assessed using FFT. Future work should consist of measurements with a higher temporal resolution (time-resolved measurements) to enable the use of more accurate methods to determine the Strouhal number. Finally, there appears to be a small discrepancy between the velocity profiles obtained from the higher resolution measurements in the vicinity of the inlet and the profiles obtained from the measurements in the entire cross-section of the cube. The second set of profiles (Fig. 6) indicates the presence of a top-hat profile, which is not that clearly visible in the profiles obtained from the second set of measurements (Fig. 10). Furthermore, the values of U/UM below the entrance of the wall jet show small differences between ROI1 and ROI2. A possible explanation for these small deviations is the lower measuring resolution for the measurements in the entire cross-section of the cube (ROI1), in combination with relatively smaller seeding due to the larger field of view.
This study is a first step in a more extensive research project on transitional wall jets in a confined space. Future work will include measurements for different inlet opening heights h, inlet geometries and additional values of the slot Reynolds number Re = U0h/ν. Alongside the PIV measurements, point measurements will be conducted using Laser Doppler Anemometry (LDA). These point measurements in an air filled setup (2 × 2 × 2 m3) will provide time-resolved data of the air flow pattern, which will provide valuable complementary information to the data set presented in this paper. In addition, LDA is more suited than PIV to carry out a local study concerning wall jet detachment, especially its intermittency (Moureh and Flick 2003) and the local turbulence anisotropy (Moureh and Flick 2005).
This paper presents a detailed and systematic experimental analysis of a transitional plane wall jet in a confined space. To ensure that the measurements are conducted for a transitional flow regime, flow visualizations have been performed using fluorescent dye. Based on the flow visualizations, PIV measurements have been conducted for seven Reynolds numbers, ranging from 800 to 2,500. For each value of Re, two sets of measurements have been obtained: one of the flow pattern in the entire cross-section of the cube (region of interest = L × L) and one with a smaller region of interest near the inlet (0.6L × 0.4L) to increase the measurement resolution in this area with large velocity gradients. Both the time-averaged and the instantaneous vector fields have been analyzed.
The flow visualizations and the PIV measurements have indicated that the onset of jet instability occurs further downstream as Re increases.
The general flow pattern is the same for all tested Re-values (800 < Re < 2,500). The wall jet drives the large recirculation cell in the center of the cube. Smaller recirculation cells are present in the downstream top corner and just below the jet entrance in the enclosure.
The size of these small recirculation cells decreases with increasing Re.
The velocity profiles show a clear Re-dependency that increases with increasing distance from the inlet.
Jet detachment and the location of maximum jet velocity (yC) both depend on Re; the jet detachment occurs further downstream and yC increases with increasing Re.
The wall jet is not yet fully developed at small distances from the inlet, while at larger distances from the inlet, the confinement of the jet and the associated adverse pressure gradient lead to flow separation and a reversed flow.
The outer region of the measured wall jet resembles the theoretical values for a laminar wall jet for all tested Re-values. The inner region for Re ≈ 1,000 also shows a fair to good agreement with the laminar wall jet. For Re ≈ 1,750 and Re ≈ 2,500, however, the velocity profiles in the inner region are shifting toward the theoretical values of a turbulent wall jet.
Below the wall jet region, the dimensionless vorticity profiles are Re-independent, whereas in the wall jet region, the values of ωz do not overlap, but also do not show a trend with Re.
The large velocity gradients in the inner and outer region of the wall jet due to the boundary layer and the shear layer result in increased values of positive and negative z-vorticity, respectively. The weak negative vorticity in the center of the test section is associated with the large clockwise-rotating recirculation cell, and the uniform ωz-value indicates a solid-body rotation in this cell.
Kelvin–Helmholtz-type instability waves are present at the bottom part of the wall jet, which grow and lead to the formation of discrete vortical structures in the outer region.
The Q criterion shows that the positive vorticity in the inner region, and before jet detachment, is the result of shear in the boundary layer (hyperbolic region). However, in the outer region, a vortex train is present with alternating regions of Q < 0 and Q > 0, indicating the presence of rotation-dominated regions (elliptic flow) and strain-dominated regions (hyperbolic flow), respectively.
The instantaneous velocity profiles indicate a lower velocity in the outer region of the wall jet at the locations of the vortical structures. This feature is due to the presence of clockwise-rotating coherent structures, the bottom of which causes the locally lower values of the instantaneous velocity.
The number of formed vortices per unit length increases with Re, and this increase is larger than the increase in inlet velocity; therefore, the Strouhal number St increases with an increase in Re.
Twan van Hooff is currently a PhD student funded by both Eindhoven University of Technology in the Netherlands and Fonds Wetenschappelijk Onderzoek (FWO)—Flanders, Belgium (FWO project number: G.0435.08). The FWO Flanders supports and stimulates fundamental research in Flanders. Its contribution is gratefully acknowledged. Thijs Defraeye is a postdoctoral fellow of the FWO—Flanders and acknowledges its support. The measurements reported in this paper were supported by the Laboratory of the Unit Building Physics and Services (BPS) at Eindhoven University of Technology and the Laboratory of Building Physics at the Katholieke Universiteit Leuven. Special thanks go to Jan Diepens, head of LBPS, and Wout van Bommel, Harrie Smulders, Geert-Jan Maas and Peter Cappon, members of the LBPS, for their valuable contributions.
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