Experimental study of flow characteristics of an oblique impinging jet

Abstract

An experimental study has been performed by using particle image velocimetry to investigate the effect of nozzle-to-plate separation distance (L) and jet impingement angle on the flow characteristics of an obliquely inclined submerged water jet. Measurements were taken for L = 1D, 2D, 4D and 6D (where D is the diameter of the nozzle) for the jet impingement angle (θ) of 45° and 26°, and the flow characteristics in the uphill and the downhill regions are investigated at Reynolds number of 2600 (based on the nozzle diameter D and the jet velocity $U_{{\text{o}}}$). It is observed that surface spacing has an opposite effect in the uphill and the downhill regions in terms of wall jet flow. In the uphill region, the tendency of the wall jet to grow increases with increase in L/D. However, in the downhill region, the jet velocity and its thickness are observed to reduce as the separation distance is increased. The distance between the stagnation point and the geometric centre is observed to decrease with increase in L/D because of jet–ambient fluid interaction in the uphill region. The jet width is observed to grow for θ = 45° in the downstream of the plate due to enhanced jet–ambient fluid interaction. Flow at θ = 26° shows that after impingement the entire jet deviates towards the downhill side, which indicates the existence of a critical impingement angle below which there is no flow of the jet in the uphill region. RMS velocity fluctuations and shear stress show an increased turbulence level downstream of the plate in the downhill region for smaller impinging distance implying higher jet–ambient fluid interaction and increased jet width. They, along with the negative turbulence production term, reveal the region of flow separation and reattachment. The decrease in the peak value of Nusselt number can be related to the drop in the jet momentum at the stagnation point with increase in the surface spacing.

Graphic abstract

1 Introduction

In the recent years, jet impingement cooling and mixing have gained much attention, as it provides high localized and overall heat transfer as compared to other conventional cooling devices such as fans and blowers. Jet impingement has found widespread industrial applications such as cooling of electronic components (Hollworth and Durbin 1992; Chaudhari et al. 2010), turbine blades and grinding process (Babic et al. 2005), drying of papers and wetted surface, metal annealing, fuel injection in engine, localized cooling and heating. Various researchers have focused on heat transfer and flow dynamics study of normal impinging jets based on various parameters such as nozzle–plate separation distance (L), Reynolds number (Re) and nozzle and plate geometries. Gardon and Akfirat (1965) through their experiments showed that velocity and boundary layer thickness are not sufficient parameters to explain the heat transfer distribution and the role of turbulence must be taken into account. They proposed that the formation of secondary peak in Nusselt number is because of the transition of flow from laminar to turbulence. Gulati et al. (2009) studied the effect of nozzle shape, nozzle–plate separation distance and Reynolds number of heat transfer of air jet impinging normally on the surface. From their study, they reported that the peak Nusselt number decreases when the nozzle–plate separation distance was increased from L/D = 0.5 to L/D = 12, and increases with increase in the Reynolds number. Using an infrared thermal imaging technique, Lytle and Webb (1994) studied the heat transfer characteristics of an air jet impingement at very small nozzle–plate separation distance (0.1 ≤ L/D ≤ 1). They reported a decrease in heat transfer with increasing distance between nozzle and plate and also proposed a power law dependence of stagnation point Nusselt number on the nozzle–plate separation distance. O’Donovan and Murray (2007) studied the heat transfer distribution of normally impinging air jet at varying nozzle-to-plate surface spacing (0.5 ≤ L/D ≤ 8). They reported that the occurrence of secondary peak in heat transfer distribution at nozzle–plate separation distance (L/D ≤ 2) is because of the combined effect of high wall jet velocity along with an abrupt increase in the turbulence intensity. Yadav and Agrawal (2018b) conducted particle image velocimetry (PIV)-based measurements to investigate the occurrence of secondary peak in heat transfer at lower L/D and reported that the formation of secondary vortex is responsible for secondary peak.

The problem becomes more complex when the jet impinges the target surface obliquely. Due to inclination of the surface with respect to the nozzle, the jet no longer impinges symmetrically and different flow behaviour is observed on either side of the jet axis. Due to this asymmetry, the stagnation point no longer lies along the jet centreline but shifts towards the uphill region, and consequently, the location of maximum Nusselt number which occurs at the stagnation point also gets shifted (Goldstein and Franchett 1988; Sparrow and Lovell 1980; Stevens and Webb 1991; Beitelmal et al. 2000). Further, the peak Nusselt number was observed to decrease with a decrease in the impingement angle (Goldstein and Franchett 1988; Beitelmal et al. 2000). Stevens and Webb (1991) experimentally investigated the effect of jet impingement angle on the local heat transfer in case of free liquid jet and observed that the Nusselt number profile shows asymmetric behaviour and that its peak magnitude increases slightly with a decrease in the impingement angle. This behaviour of peak magnitude is opposite to that observed with normal impinging jet. According to the authors, this behaviour is observed because of non-occurrence of entrainment phenomenon and pre-impingement jet spreading for the free liquid jet. Beitelmal et al. (2000) studied the effect of inclination on the heat transfer rate of impinging air jet in the impingement angle (θ) range of 90° to 40° and vertical distance from nozzle-to-plate (z/D) of 4–12. They concluded that the shift of maximum heat transfer point was not sensitive to the change in the Reynolds number range covered in their experiments (4000–12,000). The location of maximum heat transfer was observed to occur between z = 1 D and 3 D in the uphill region.

O’Donovan and Murray (2008) experimentally investigated the effect of jet impingement angle and nozzle-to-plate surface spacing on the heat transfer distribution of impinging air jet by varying the impingement angle from 90° to 30° and nozzle-to-plate spacing (H/D) from 2 to 8. They reported that while in the uphill region, the heat transfer rate increases with increase in the surface spacing, it decreases with increase in surface spacing in the downhill region (Fig. 1). They also observed that the shift in peak Nusselt number increases from the geometric centre as the surface spacing is reduced. The peak value of Nusselt number was observed to decrease with increase in the surface spacing. Choo et al. (2012) investigated the effect of inclination angle on impinging air jet at small spacing between nozzle and plate surface. They reported a significant difference in the heat transfer characteristics at low nozzle-to-plate surface spacing (L/D ≤ 1) as compared to higher nozzle-to-plate surface spacing (L/D > 1). For a given flow condition, the peak Nusselt number decreases with decrease in impingement angle for larger nozzle-to-plate surface spacing; the peak Nusselt number increases with decrease in impingement angle for lower nozzle-to-plate surface spacing. They also studied the effect of surface spacing in the range L/D = 0.125 to 1 and reported that the peak Nusselt number increases with decrease in the surface spacing. Foss (1979) used hot-wire anemometry (HWA) to measure the wall velocity for the jet inclined at θ = 45° to the plate and reported that the maximum wall jet velocity is located at z/D = 0.05 from the surface. Beltaos and Rajaratnam (1977) measured the wall pressure and wall shear stress in case of obliquely impinging air jet with static taps and Preston tube, respectively, and gave an empirical relation based on the jet impingement angle. Naib and Sanders (1997) used the laser Doppler anemometry (LDA) technique to measure the velocity of submerged water jet inclined at different angles (45° ≤ θ ≤ 90°) and provided a general law describing the decay of wall jet velocity. Jalil and Rajaratnam (2006) studied the effect of jet impingement angle on the wall boundary layer and shear stress for water jet impinging obliquely on the surface. They measured the thickness of deflected jet and wall jet velocity by using point gauge and Prandtl tube, respectively. They reported that the wall jet width and velocity decrease monotonically along the plate while the boundary layer thickness stays constant. Wang et al. (2017) conducted experiments at a constant nozzle-to-plate surface spacing (H/D = 3) to study the flow characteristics at different impingement angles (0° ≤ θ ≤ 90°) in a fully developed submerged jet. In their study, they focused on the flow distribution in the free jet region and also on the flow structure in the impingement region.

Fig. 1

Mean Nusselt number distribution, O’Donovan and Murray (2008), a L/D = 6, b θ = 45°

From the literature survey, it is observed that while most of the studies on inclined impinging jet have been conducted from the heat transfer point of view, the studies focusing on the flow field are limited and have been done largely using single-point measuring techniques. In this context, the first objective of the present study is to employ the particle image velocimetry technique to investigate the flow characteristics of an obliquely inclined impinging submerged water jet in the uphill and the downhill regions, for different nozzle-to-plate surface spacings. The second major objective is to study the variation of stagnation point from geometric centre with nozzle–plate separation. PIV provides whole-field view of the instantaneous flow and is therefore more informative as compared to single-point measurement techniques. The nozzle-to-plate surface spacing for the present experiment has been taken within the potential core region (L/D = 1, 2, 4 and 6) and the jet impingement angle is taken as 45° and 26°. The Reynolds number is kept constant at 2600 (based on the nozzle diameter D and jet velocity $U_{{\text{o}}}$) throughout the experiment. The uphill and downhill regions are explored separately by comparing the mean flow and velocity fluctuation at different nozzle-to-plate separation distances.

2 Experimental set-up and parameter definition

2.1 Experimental set-up

Figure 2 shows schematic of the experimental set-up used for the study of inclined jet impingement. The set-up is the same as the one employed earlier by Yadav and Agrawal (2018a). Water from a reservoir tank is pumped to the test section via a settling tank with the help of a centrifugal pump. The settling tank is equipped with a pressure gauge, ensuring a constant pressure throughout the experiment. The flow rate is measured with the help of a venturimeter. The solenoid valve controls the flow as required. The test section is connected to a reservoir and any excess fluid is pumped to this reservoir.

Fig. 2

Schematic of the experimental set-up. 1. Test section; 2. Impingement plate; 3. Nozzle; 4. Laser; 5. Laser support table; 6. CCD camera; 7. Flow meter; (8, 9). Venturimeter; 10. Solenoid valve; (11, 15, 16). Flow control valve; 12. Settling tank; 13. Pressure sensor; 14. Reservoir tank; (17, 18). Pump; 19. Supporting stand

The test section where measurements are made is a rectangular tank, made of acrylic sheet of 15 mm thickness. The inner dimensions of test section are 705 mm × 555 mm × 555 mm. In order to maintain a constant water height in the test section, a reservoir tank is attached to it, where the excess water gets collected. The water from here is pumped back to the reservoir tank. The inner and the outer diameters of the pipe are 15.5 mm and 20 mm, respectively. The length of the pipe is taken to be sufficiently large (1800 mm) to ensure fully developed flow at the pipe exit. The impinging plate has a 16-cm square cross-section and is adjusted such that the centre of the plate coincides with the centreline of the jet axis. Arrangements have been made so that the plate can rotate with respect to the nozzle axis if required.

The PIV system used in the experiment consists of twin Nd/YAG pulsed lasers (Beamtech, China). The laser beam has a wavelength of 532 nm and gives the maximum output energy of 200 mJ/pulse. The illuminating area is a 2D plane passing through the axis of the jet. A 1392 × 1024 pixel 12-bit CCD camera is used for recording the images. The laser and CCD are synchronized by using a synchronizer which is controlled by a computer from where various parameters such as time delay between two pulses and frequency can be controlled. For the present study, 270 image pairs have been captured for different surface spacings. A convergence test revealed that the variation in RMS is less than 1% between 200 and 250 image pairs. Therefore, to be on the safer side, we collected 270 pair of images.

A three-step analysis process is employed with the size of interrogation window varied from 64 pixel × 64 pixel in first pass to 16 pixel × 16 pixel in third pass. A standard overlap of 50% was employed between two consecutive interrogation windows. Four major factors have been considered for the uncertainty in the velocity measurement; these factors are uncertainty in instruments, processing error, sampling and particle lag (Lazar et al. 2010; Raffel et al. 1998; Wang et al. 2007; Yadav et al. 2016; Coleman and Steele 2009). The combined uncertainty in mean velocity is 2.2%.

2.2 Parameter definition

Figure 3 describes the various regions and the coordinate system employed in the present study. The distance between nozzle and the plate is measured along the x direction. The r-z coordinate is measured along and normal to the plate surface. The radial and the streamwise direction are along the r axis, while the normal and the cross-streamwise direction are measured along the z-axis. The distance of the plate from the nozzle (L) is measured along the x-axis.

Fig. 3

Nozzle–plate orientation and parameter description

Analysis of the jet in the free jet region is done in the x–y coordinates (Fig. 3). For this, the origin is taken at the nozzle exit. All the parameters in Sect. 3.1 are measured along the x–y coordinates. For the analysis of the wall jet, the origin is taken at the geometric centre of the jet, the point where the jet centreline impinges on the plate. All the parameters from Sect. 3.2 onwards have been plotted in the r-z coordinates.

3 Results and discussion

3.1 Jet development in the free jet region

To examine the development of the jet in the free jet region, velocity vectors along the x and y coordinates are plotted in Fig. 4 at L/D = 4 and θ = 45°. The x–y coordinates are defined through Fig. 3. In the absence of any impingement surface, an axisymmetric growth of the jet is expected in the free jet region. The jet interacts with the ambient fluid, resulting in growth of the shear layer. In that event, the jet width increases while the velocity decreases monotonically. However, when the impinging surface is kept at an oblique angle to the nozzle, the jet starts to deviate primarily in one direction, as observed from Fig. 4. Note that after x = 3D, the jet starts to deviate appreciably towards the downhill region indicating that the impingement region extends to 1 D from the surface. The isocontour of the axial velocity component ($U_{x}$) normalized with the bulk exit velocity ($U_{{\text{o}}}$) is also shown in Fig. 4. The potential core length is observed to extend up to x = 3D.

Fig. 4

Axial velocity contour in the free jet region imposed with the contour plot at θ = 45° and L/D = 4

The mean axial velocity profile ($U_{x}$) at different axial locations for θ = 45° and θ = 26° is plotted in Fig. 5. We observe that for both θ = 45° and 26°, the velocity is reasonably symmetric up to x = 3D from the nozzle. The velocity is maximum at the jet centreline and decreases to become zero outside the jet flow. As the jet propagates into the ambient fluid, the shear layer increases; consequently, the jet width also increases. In the region 3D < x < 4D, the peak of the velocity begins to shift towards the downhill region. The presence of the impingement surface therefore affects the flow till 1D upstream of the surface. The velocity profiles overlap in the potential core region. Note that at x = 3.5D, the velocity peak at θ = 26° is higher than that of θ = 45° which reflects the relatively less conversion of the kinetic energy into the pressure energy.

Fig. 5

Axial velocity variation at different distance from the nozzle at L/D = 4; a θ = 45°, b θ = 26°

The normal stress profile ($v_{x}^{\prime}$) at different axial locations from the nozzle is plotted in Fig. 6. The RMS is minimum at the centreline and increases to reach a maximum at the jet boundary, before reducing again. Observe that the RMS is higher where the jet interacts with the ambient fluid, clearly marking the shear region. The RMS has higher values for θ = 45° (Fig. 6a) as compared to θ = 26° (Fig. 6b). Observe the increased RMS at the centreline after x = 3D. The shear layer penetrates the potential region and the jet is fully developed. A close observation at θ = 45° (Fig. 6a) shows that the peak stress increases with increasing axial distance from the nozzle, indicating the growth of jet shear layer and consequently the jet width.

Fig. 6

Normal stress profile at different axial locations from the nozzle at L/D = 4; a θ = 45°, b θ = 26°

3.2 Mean flow characteristics

The mean velocity vectors imposed with the radial velocity contour ($U_{r}$) for various nozzle-to-plate separation at θ = 45° are compared in Fig. 7. Once the jet is discharged into the ambient stationary fluid, it begins to draw in fluid from the ambient due to the shear acting between the fluid layers. It leads to the development of the jet shear layer before the impingement. This, in turn, reduces the jet velocity as a consequence of the momentum conservation. When the plate is kept at a distance more than the potential core length, the impact velocity of the jet on the surface reduces (Fig. 7d) as compared to the jet impinging the plate kept near to the nozzle (Fig. 7a). The impingement region is observed to increase radially with increase in the nozzle–plate separation (L/D). After impingement, the jet gets deflected along the surface and moves towards both the uphill and the downhill regions. The jet deflection in each region has a dependence on the jet inclination angle and the nozzle–plate separation. Unlike normal jet impingement, the jet impinging obliquely on the plate shows asymmetric deflection and the jet deviates largely in the downhill region. The velocity contour plotted in Fig. 7 reflects the jet spreading and development along the wall. It is observed that the jet width decreases along the plate up to a certain distance from the geometric centre. This is attributed to the effect of incoming velocity towards the plate. After a certain distance, the jet starts to grow and the jet width increases. The variation of jet width with nozzle-to-plate separation distance is discussed in detail in the next section.

Fig. 7

Mean velocity for different nozzle-to-plate spacing at θ = 45° a L/D = 1, b L/D = 2, c L/D = 4, d L/D = 6

3.3 Flow characteristics in the uphill region

Mean velocity vectors in the uphill region at θ = 45° and 26° have been compared and are shown in Fig. 8 for L/D = 6 to investigate the effect of impingement angle on the wall jet flow. Observe that for θ = 45° (Fig. 8a), a wall jet is formed which progress along the wall surface and then starts to roll up, entraining the ambient fluid. The recirculation increases the mixing of ambient fluid with the boundary layer flow. This would enhance the heat transfer in the uphill region. A close observation for θ = 26° (Fig. 8b) shows that the jet is not deflected towards the uphill region after impinging on the plate and no wall jet flow regime is observed on this side. The jet impinging on the surface is rather deflected entirely towards the downhill region. This indicates the existence of a critical angle of impingement below which the jet does not deflect towards the uphill region. Using dye visualization technique, the critical angle of inclination was observed to be about 27°–28°. The flow in the uphill region for the case of θ = 26° is restricted due to an adverse pressure gradient. This gradient increases with decrease in the impingement angle and beyond a critical angle the flow cannot overcome the pressure barrier and no flow occurs in the uphill region. The restriction of jet flow leads to a precipitous drop in the heat transfer in the uphill region at lower impingement angles as observed in Fig. 1a.

Fig. 8

Mean velocity vector in uphill region for impingement angle a θ = 45°, b θ = 26° for L/D = 6

In order to investigate the effect of the nozzle–plate separation on the flow behaviour, velocity vectors for L/D = 1 are compared against L/D = 6 for θ = 45° case (Fig. 9). Observe that the flow is confined to a smaller vicinity around the plate at L/D = 1, while at L/D = 6 the wall jet formed moves along the plate and then starts to roll up, entraining the ambient fluid and forming a recirculation zone. With the increase in L/D, the jet shear layer grows in the free jet region and the vortices developed contribute in the deviation of jet in the uphill region after impinging on the surface.

Fig. 9

Comparison of mean flow at θ = 45° in uphill region a L/D = 1 b L/D = 6

The wall jet moves along the surface and brings in more ambient fluid near the plate surface. This increases the heat transfer as observed in Fig. 1b. The wall jet along with vortical structure enhances the heat transfer rate, as reported in the literature (Akansu et al. 2008; O’Donovan and Murray 2008).

The peak Nusselt occurs at the stagnation point. The stagnation point for oblique jet impingement does not occur at the geometric centre of the jet. Rather, it shifts away towards the uphill side as reported in various studies (Goldstein and Franchett 1988; Sparrow and Lovell 1980; Stevens and Webb 1991; Beitelmal et al. 2000). The stagnation point shifts at a distance r = s from the geometric centre towards the uphill side. The velocity vector field near the stagnation region is shown in Fig. 10 for θ = 26° and θ = 45°. Observe that at θ = 26°, the jet is not deflected towards the uphill side, irrespective of the nozzle–plate separation distance (Fig. 10a, b). As θ is increased to 45°, the jet shows deflection towards the uphill side (Fig. 10c, d). Further observe that the stagnation point is nearer to the geometric centre for L/D = 6 (Fig. 10d) as compared to L/D = 1 (Fig. 10c). The stagnation point is affected by both the impingement angle θ and nozzle–plate separation distance L/D. The non-dimensionalised distance of the stagnation point from the geometric centre (s/D) for different L/D at θ = 45° and θ = 26° is given in Table 1. Note that the distance s/D decreases as the nozzle–plate separation increases. Our result is in close agreement with the results of Goldstein and Franchett (1988) and O’Donovan and Murray (2008). With increase in L/D, the jet interacts with the ambient fluid before impingement, leading to the development of vortical structures. As a result of which, a part of the jet gets deflected in the uphill region after impingement and the stagnation point moves towards the geometric centre. The distance s/D for θ = 26° is observed to be greater than that of θ = 45° suggesting that the jet deflects primarily in the downhill region. From Fig. 1b, it is observed that the peak Nusselt number increases and shifts towards the uphill region with a decrease in L/D. The increase in the peak value of Nusselt number is attributed to a higher jet momentum at the stagnation point. The peak value, however, decreases with decrease in the impingement angle as noted from Fig. 1a. The stagnation point moves farther away in the uphill region where there is no primary jet flow; hence, the jet momentum at the stagnation point reduces, causing a precipitous drop in the Nusselt number.

Fig. 10

Velocity vector near the stagnation region a θ = 26° and L/D = 4, b θ = 26° and L/D = 6, c θ = 45° and L/D = 1, d θ = 45° and L/D = 6

Table 1 Distance between geometric centre and stagnation point (s/D) for different surface spacing (L/D) at θ = 45° and Re = 2600

3.4 Flow characteristics in the downhill region

As observed from Fig. 7, the jet impinging obliquely on the surface deviates mostly in the downhill region. A detailed analysis of this flow characteristic is required in the downhill region. Figure 11 shows the variation of maximum wall jet velocity ($U_{m}$) in the streamwise direction for different L/D at θ = 45° and 26°. The maximum velocity is normalized with the jet exit bulk velocity ($U_{{\text{o}}}$). Previous results have shown that the nozzle–plate separation distance has no effect on the location of maximum wall jet velocity. The location of maximum velocity lies between z = 0.15 D and z = 0.25 D, for L/D considered in the present experiment. As observed from Fig. 7, the jet for smaller L/D has little interaction with the ambient fluid before impinging on the surface, and the jet hits the surface with a relatively higher velocity. In that event, the wall jet for L/D = 1 has a higher velocity along the plate as compared to the other separation distance (Fig. 11a).

Fig. 11

Comparison of maximum wall jet velocity in downhill region a θ = 45° b θ = 26°

The higher wall jet velocity is responsible for a higher rate of heat transfer in the downhill region as reported by Akansu et al. (2008) and O’Donovan and Murray (2008). For L/D ≥ 2, the wall jet velocity achieves a constant value after r/D = 1.5. The jump in the velocity profile for L/D = 1 is due to the fact that when the plate is kept very near to the nozzle (L/D ≤ 1), it affects the flow and the jet exit velocity decreases. Note from Fig. 11 that as the impingement angle decreases, the maximum wall jet velocity for a given L/D increases because of favourable pressure gradient in the downhill region. In non-dimensional terms, the wall jet velocity $U_{m}$ can be related to the distance from the geometric centre in the streamwise direction (r) by power law:

$$ \frac{{U_{m} }}{{U_{{\text{o}}} }} = k\left( \frac{r}{D} \right)^{ - n} $$

Table 2 shows the value of velocity decay rate n for various L/D at different impingement angles in the region 0.2D ≤ r ≤ 3.0D. Observe that the decay rate decreases with an increase in the separation distance between the nozzle and plate. The decay rate is also observed to depend upon the impingement angle θ. The maximum wall jet velocity has been observed to increase with decrease in the impingement angle. Higher the wall jet velocity, higher will be the effect of shear, and hence, there is more jet–ambient fluid interaction which enhances the heat transfer, as depicted in Fig. 1a. At L/D = 6, the impingement angle has no effect on the velocity decay rate.

Table 2 Maximum wall jet velocity decay rate for various L/D and θ at Re = 2600

The variation of wall jet half width ($z_{0.5}$) with radial distance from the geometric centre for different L/D at θ = 45° and θ = 26° is plotted in Fig. 12. Observe that for θ = 45° (Fig. 12a) the jet width in the impingement region is greater for larger L/D. This is due to development of jet in the free region prior to impingement on the surface. After impinging, the jet moves along the plate and the jet half width decreases along the radial direction, attaining a local minima at r ≈ 1.3 D. This trend is followed as a result of contraction of the velocity distribution in the impingement region, also reported by Wang et al. (2017). Beyond r = 1.3 D, the jet grows linearly with distance and then increases with distance as $\frac{{z_{0.5} }}{D} = k\left( \frac{r}{D} \right)$. The growth rate $k$, at θ = 45° is given in Table 3 in the region 1.5 D ≤ r ≤ 3 D. Observe that L/D = 1 has the highest growth rate, followed by L/D = 2, 4, and 6. The growth rate is related to the shear acting between the wall jet and ambient fluid. A high wall jet velocity in case of smaller L/D leads to higher mixing of ambient fluid because of higher shear, increasing the jet width in the downstream of the plate. However, the growth of jet width in case of θ = 26° shows a different behaviour from that of θ = 45° (Fig. 12b). Notice that the jet flow at the lower impingement angle begins to behave much like that of planar jet. The impingement region increases up to r = 2D. The jet growth rate at θ = 26° is also given in Table 3 for r > 2D. The effect of L/D diminishes on the growth rate for θ = 26°. For L/D = 6, the jet develops in the free jet region and therefore it has a higher jet half width $(z_{0.5} )$ in the impingement zone; followed by L/D = 4 and 2. The development of the jet in the free jet region plays a crucial role in the development of the wall jet for lower impingement angle.

Fig. 12

Comparison of wall jet half width in the downhill region a θ = 45° b θ = 26°

Table 3 Growth rate of jet half width at different L/D at θ = 45° and Re = 2600

3.5 Development of the wall jet in the downhill region

Figure 13 shows the streamwise velocity profile at different downstream locations (r/D) at L/D = 1, 2, 4, and 6 for θ = 45°. The velocity U and the direction z have been normalized with maximum streamwise velocity $(U_{m} )$ and half jet width $(z_{0.5} )$ along the same characteristic line (r/D), respectively. The velocity first increases with increase in the distance normal to the surface, attains maximum value, and then decreases with further increase in the normal distance. The region from the wall to the maximum wall jet velocity location ($z_{m}$) is termed as inner shear region, while the region from the maximum velocity location to the distance where the wall jet velocity approaches to zero is termed as outer shear region. In the downstream locations, the location of maximum velocity with respect to the jet half width decreases due to non-uniform growth of half jet width and the ratio $Z_{m} /Z_{0.5}$ tends to zero far downstream, as reported by Myers et al. (1963) and Hammond (1982). Similar trends have been reported elsewhere (Glauert 1956; George et al. 2000; Fillingham and Novosselov, 2018; Hashiehbaf et al. 2015). The location in the outer shear region where the velocity approaches zero is observed to be a function of nozzle–plate separation (Fig. 13a–d) and impingement angle (not shown). As L/D is increased, the jet in the free region develops before impinging the surface, and thus the wall jet layer is larger. For L/D = 1 and 2 (Fig. 13a, b), the velocity approaches zero at $z/z_{0.5} = 1.5$, while this location moves to $z/z_{0.5} = 2.0$ for L/D = 6 (Fig. 13d). The velocity profile is also observed to become negative after a certain distance for small L/D (Fig. 13a, b). This distance represents the location where the wall jet mixes with the ambient fluid. This location of mixing point shifts away from the surface with increase in surface spacing.

Fig. 13

Normalized wall jet profile at θ = 45° for different surface spacings for a L/D = 1, b L/D = 2, c L/D = 4, d L/D = 6

In order to understand the phenomenon of interaction of wall jet with the ambient fluid, the wall normal cross-streamwise RMS velocity profiles ($V_{{{\text{rms}}}}$) at different L/D and impingement angles are plotted in Fig. 14. Observe that for θ = 45°, the peak stress value decreases as L/D is increased; the peak value being 0.6, 0.4, 0.3 and 0.15 for L/D = 1, 2, 4 and 6, respectively. This indicates a reduction in turbulence fluctuation. The location of the peak value corresponds to the location where maximum entrainment occurs. Similar trends were observed by Knowles and Myszko (1998) and Hashiehbaf et al. (2015). For L/D = 1 and 2 (Fig. 14a, b), the stress value increases with increasing distance along the plate and attains maxima at r = 1.5 D. The stress then reduces with further increase in distance. As observed from Fig. 14c, d, the RMS velocity increases in the downstream for L/D = 4 and 6. The fluctuation enhances interaction of the wall jet with ambient fluid, resulting in the growth of wall jet in the downstream of the impingement point. Yadav and Agrawal (2018b) have reported that the location of the maxima corresponds to the location of flow separation and reattachment in case of normal jet impingement. It is conjectured that the flow separation and reattachment point shifts downstream as the nozzle–plate separation increases. The effect of the nozzle–plate separation on peak stress value diminishes as the impingement angle is decreased (not shown). Decreasing the impingement angle smoothens the flow in the downhill region because of a favourable pressure gradient. This leads to less fluctuation in the normal direction, resulting in lesser RMS values. The wall jet momentum therefore plays a crucial role in the jet–ambient fluid interaction. Higher mean velocity of wall jet will be followed by higher velocity gradient or shear. The shear further helps in the growth of the wall jet along the plate. The longitudinal RMS profile (streamwise) also shows the same trend and the peak is observed to decrease as L/D increases. For L/D = 1, the streamwise RMS is 70% of the wall jet velocity, while the cross-streamwise RMS is 40%. The peak value reduces to 40% and 20%, respectively, for L/D = 6.

Fig. 14

Velocity fluctuation normal to the surface at different radial locations at θ = 45° for a L/D = 1, b L/D = 2, c L/D = 4, d L/D = 6

Similar behaviour was observed for normal jet impingement (Knowles and Myszko 1998; Yadav and Agrawal 2018b) and impingement on curved surface (Hashiehbaf et al. 2015)^.

The variation of Reynolds shear stress with surface spacing for θ = 45° is shown in Fig. 15. The shear stress is zero at the wall. Unlike free jet flow, the shear stress in case of the wall jet flow is maximum at the location of maximum streamwise velocity. At L/D = 1 (Fig. 15a), the peak stress value occurs between 2D ≤ r ≤ 3D which signifies a larger mixing region as compared to other radial locations. At L/D = 2 (Fig. 15b), the peak shifts in the region 2.5 D ≤ r ≤ 3.5 D. The mixing region is observed to shift downstream with increase in L/D. Comparing Fig. 15 with Fig. 14 shows that the location of maximum shear stress corresponds to the location of maximum wall shear stress for a given L/D. The peak stress value increases with decrease in the nozzle–plate separation distance, suggesting better mixing of ambient fluid with the wall jet at lower L/D and, therefore, higher heat transfer as reported in other studies (Akansu et al. 2008; O’Donovan and Murray 2008). The Reynolds stress profile is showing closer values at L/D = 1 and 2 (Fig. 15a, b), while there is a significant difference in the peak of Nusselt number profile as shown in Fig. 1b. The Reynolds stress profile is also a function of the Reynolds number. The experiments conducted by O’Donovan and Murray (2008) were at much higher Reynolds number (> 10,000) and therefore a significant difference is observed. The present experiment is conducted at Re = 2600. We believe that this difference of the present experiment as compared to that of the results shown in Fig. 1b is primarily because of the study conducted at different Reynolds Number.

Fig. 15

Reynolds shear stress at different radial locations at θ = 45° for a L/D = 1, b L/D = 2, c L/D = 4, d L/D = 6

Figure 16 shows the turbulence production (P) at different L/D. The turbulence production term $\left( { - \left\langle {u^{\prime}v^{\prime}} \right\rangle \frac{{{\text{d}}U}}{{{\text{d}}z}}} \right)$, represents the production of turbulent energy at the cost of the mean flow energy. In the outer shear region, the velocity gradient is negative $\left( {\frac{{{\text{d}}U}}{{{\text{d}}z}} < 0} \right)$. In this region, the velocity fluctuations $u^{\prime}$ and $v^{\prime}$ are positively correlated. Therefore, the turbulence production term is positive in the outer shear region (Fig. 16a–d). The peak of P decreases when there is an increase in L/D. In the inner shear region, the velocity gradient is positive $\left( {\frac{{{\text{d}}U}}{{{\text{d}}z}} > 0} \right)$ and the fluctuations are negatively correlated. The turbulence production term is again positive. However, in the inner shear region, the turbulence production term is observed to be negative at certain locations from the impingement point (Fig. 16). This indicates the zone of opposing shear and is linked to the transfer of energy to the mean motion. This “energy reversal” was also reported by Eskinazi and Erian (1969). The negative value of production occurs in the near wall reattachment region. This behaviour is also observed by Cimarelli et al. (2019) for flow over a blunt bluff body.

Fig. 16

Turbulence production at different radial locations at θ = 45° for a L/D = 1, b L/D = 2, c L/D = 4, d L/D = 6

4 Conclusions

In the present study, the flow characteristics of an oblique submerged water impinging jet at different nozzle-to-plate surface spacings (L/D = 1, 2, 4 and 6) and impingement angle of 26° and 45° have been investigated experimentally at Reynolds number of 2600. The main conclusions that can be drawn from the present study are:

• 1. PIV measurements reveal that for θ = 26°, the jet after impingement deviates entirely in the downhill region and no flow occurs in the uphill region. This indicates the existence of a critical angle of impingement and is being presented for the first time with supporting velocity field. This phenomenon is responsible for the precipitous drop in heat transfer at low impingement angles.

• 2. For θ = 45°, as L/D is decreased, the stagnation point (s) shifts away from the geometric centre in the uphill region. As L/D is increased, there is more interaction of the jet–ambient fluid and the viscous effect penetrates towards the jet centre, increasing the amount of jet deviating towards the uphill region. The decrease in the peak value of Nusselt number can be related to the drop in the jet momentum at the stagnation point with increase in the nozzle–plate separation distance.

• 3. The mass of jet deviating towards the uphill region after impingement increases as L/D is increased. This phenomenon is because of jet–ambient fluid interaction in the free jet region. The wall jet moves along the surface, interacts with the ambient fluid, and brings in more fresh fluid in the wall jet.

• 4. The location of maximum wall jet velocity with respect to jet half width reduces downstream of the impingement region. As the nozzle–plate separation distance is increased, the outer shear region is enriched as a result of growth of the jet in the free jet region.

• 5. In the downhill region, the wall jet velocity and jet half width decrease with increase in L/D. Higher jet velocity for smaller surface spacing causes high shear between the wall jet and ambient fluid, forming vortical structures, and bringing large amount of ambient fluid near the surface, resulting in increased velocity fluctuations. With decrease in the impingement angle, the effect of the surface spacing is reduced. A higher amount of mixing of wall jet with ambient fluid is observed in the downstream of the plate at lower surface spacing for θ = 45°.

• 6. The specific locations of the peak value of the normal shear stress and Reynolds shear stress signifies the region of flow separation and reattachment. Due to this, there is larger mixing of ambient fluid with the wall jet.

• 7. The negative turbulence production near the wall in the inner shear region at specific locations indicates reattachment of the flow and indicates the specific location for formation of vortices.

The present results give a significant insight on the physical phenomenon leading to various heat transfer characteristics in an oblique jet impingement and can serve as a benchmark for further numerical studies.