Comparison of Vortex Structures and Turbulent Heat Transport for a Single Jet and Multiple Jets in Crossflow

Air-cooled heat exchangers (ACHEs) are equipped with large fans and placed on top of high pipe racks in liquefied natural gas (LNG) plants, and they discharge a large amount of hot air into the atmosphere. The performance of ACHEs can be significantly reduced if the hot exhaust air recirculates back into the ACHEs under crosswind conditions, leading to hot air recirculation (HAR) [1]. The flow pattern of the hot air discharged from a single ACHE fan under crosswind conditions is similar to that of a jet in cross flow (JICF). However, several hundred ACHEs are usually placed in an array and the flow pattern can significantly vary compared to that of a single ACHE owing to the interactions between the ACHEs. A better understanding of the physics and differences between a single jet and multiple jets will therefore help predict the HAR phenomena and facilitate mitigating the impact on LNG production.

Numerous experimental and numerical investigations have been performed to reveal the qualitative time-averaged and quantitative instantaneous behaviors regarding the complicated vortical structures, entrainment and mixing, and instabilities in the JICF. Mahesh [2] provided an annual review of several previous studies. Fric and Roshko [3] applied the smoke-wire technique to visualize the vortical structures for different jet-to-crossflow velocity ratios and concluded that the vortical structures of the wake vortex in JICF are formed from the vorticity near the boundary layer of the crossflow wall. Wu et al. [4] applied proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) analysis techniques to extract the flow structures and frequencies. The horseshoe vortex was found to be related to the low-frequency modes, and the shear-layer vortexes were apparently related to the high-frequency modes. The POD and DMD analysis methods were described by Wu et al. Iyer and Mahesh [5] studied the nature of shear-layer instability of JICF using a direct numerical simulation and DMD, and confirmed that the dominant frequencies and spatial shear-layer modes from direct numerical simulation and DMD are significantly altered by the jet-exit velocity profile.

For the multiple jets, Zang and New [6] conducted experiments and studied the dynamics of parallel twin jets with jet-to-jet separation distances of 1.5D to 3D (jet diameters) for various jets to crossflow velocity ratios. The pair of inner vortexes associated with the two counter-rotating vortex pair (CVPs) were induced to move toward each other along the symmetric plane, and the two CVPs apparently merged into a single CVP when the separation distance was suffciently small. Ali and Alvi [7] also performed the experiment to reveal the flow dynamics of jet arrays in supersonic crossflow. The experiment also demonstrated that the CVPs merge and a nearly two-dimensional flow field is produced when the spacing between the jets is reduced. However, the studies of multiple jets with more than two jets and with a significantly close jet-to-jet spacing in the spanwise direction in a subsonic crossflow are limited. Therefore, this study investigated multiple jets with a narrow spacing of 1.6D between adjacent air-discharging fans of ACHEs in a real LNG plant, where D is the diameter of the fan.

In this study, the prediction accuracy of the large eddy simulation (LES) in the unsteady flow field of an internal single JICF was first verified by comparison with experimental data and past simulation results. Subsequently, a single jet and multiple jets were studied and compared using the verified numerical approach to reveal differences in vortical structure, flow, temperature field, and shedding frequency. Furthermore, the interaction mechanism between the adjacent jets was revealed.

Computational fluid dynamics (CFD) simulations numerically solve the continuity equation, Navier–Stokes equations of fluid flow, and energy equation.

where $C$ is the model parameter, and $Δ$ is the filter cutoff width. In standard Smagorinsky model, $C$ is a constant value; conversely, in DSM, $C$ varies in space and time and is evaluated as a function of the local flow field. As a result, the DSM, which was the model used in this study, can more accurately calculate the turbulent eddy viscosity [8,9].

The main simulation methods used in this study are shown in Table 1. The hybrid scheme, which blends a large portion of the central differencing scheme with a small portion of the upwind scheme, was used in this study to achieve both numerical stability and a high accuracy.

A verification study was performed using the numerical simulation methods described in Table 1 to confirm the accuracy of the LES predictions for a single jet. The simulation conditions used were the same as those used in the experiments conducted by Sherif and Pletcher [10]. The main physical parameters of the jet and cross flow are listed in Table 2.

The simulation model used in the single-jet study is shown in Fig. 1. The size of the domain was 16D in the streamwise direction, 8D in the spanwise direction, and 12D in the wall-normal direction. The no-slip boundary condition was applied to the jet nozzle and bottom walls, and the free-slip wall condition was applied to the side walls and top wall. The meshes used for the simulations are shown in Fig. 2. The number of cells in the mesh was approximately $11.21×106$⁠. A relatively fine mesh in the proximity of the wall was generated, and it was confirmed that the $y+$ value for the near-wall mesh cells was less than 2.5. However, the mesh downstream of the jet was relatively coarse to reduce the computational time. A mesh sensitivity study was performed using coarse mesh 1 (⁠$1.71×106$ cells), coarse mesh 2 (⁠$4.24×106$ cells), the aforementioned medium mesh (⁠$11.21×106$ cells), and a fine mesh (⁠$25.69×106$ cells). The mesh refinement ratio between the two successive meshes was approximately 1.3. The RMS fluctuation predictions of the temperature profile, shown in Fig. 3, indicate that the difference between the results of coarse mesh 1 and coarse mesh 2 was significantly large. However, the difference between the predictions of coarse mesh 2 and the medium mesh became smaller after refining the mesh, and the results of the medium mesh were very close to those of the fine mesh after further refinement. Also, the predictions of the medium mesh matched well with the experimental results, as discussed later in this section. Hence, the medium mesh was adequate for the LES.

A time-step interval of $Δt=5×10−4s$ was used in the simulation. For the adequacy of the temporal resolution, two criteria were considered when deciding the time-step interval. The first criterion was that the time-step interval must be sufficiently small to retain the maximal Courant–Friedrichs–Lewy numbers below 1, which criterion was met in the verification study. The second criterion was that the time-step interval be smaller than the period corresponding to the characteristic frequency in JICF. Based on the findings of Fric and Roshko [3], the maximum characteristic wake Strouhal number of the wake vortex shedding behind the jet near the bottom wall is smaller than 0.2 for several different Reynolds numbers $Rec$ based on the crossflow velocity, and the JICF velocity ratio ranging from 2 to 10. Under the current study conditions, the velocity fluctuation frequency was approximately 1.7 Hz, corresponding to a time scale of approximately $Δt=0.588s$⁠. Thus, the time-step interval used in the simulation was sufficiently small to be adequate for LES.

where $u$ is the local velocity, $Uc$ is the crossflow velocity distant from the bottom plate, $δ$ is the boundary-layer thickness, which was 0.5D in the study, and $z$ is the distance from the bottom plate.

where $u$ is the local velocity, $Umax$ is the velocity at the center of the jet inlet, $r$ is the distance from the center of the jet nozzle, $R$ is the internal radius of the jet nozzle, and $Re$ is based on the mean jet inlet velocity. The exponent $n$ (6.4) was evaluated based on Eq. (6).

The quantities used for nondimensionalization include the jet diameter $D$ for the length and the mean crossflow velocity $Uc$ for the velocity, and velocity fluctuation variables. The temperature $T$ and temperature fluctuation $T′$ were normalized as $T+=(T−Tc)/(Tj−Tc)$ and $T′/ΔT$⁠, where $Tc$ is the crossflow fluid temperature, $Tj$ is the jet fluid temperature, and $ΔT=(Tj−Tc)$⁠. The time $t$ used in this study was normalized as $tUc/D$⁠. The vorticity $ω$ was normalized as $ωD/Uc$⁠.

The CFD predictions were compared with the experimental data of Sherif and Pletcher [10], as well as the simulation results of Ziefle and Kleiser [12], who performed their study using the same simulation conditions and a skew-symmetric central spatial discretization scheme with fourth-order accuracy. This comparison was conducted to verify the accuracy of the LES predictions in the present study. Figures 4 and 5 present a comparison of the mean velocity magnitude, RMS fluctuations of the velocity magnitude, mean temperature, and RMS fluctuations of the temperature along the vertical lines at two different X locations on the central plane. The measurements were confirmed to agree reasonably with past simulation results. Note that the hybrid scheme, which blends a large portion of the central differencing scheme and a small portion of the upwind scheme, can predict the peak values for the mean and RMS fluctuations of the velocity and temperature with a high accuracy. The inclusion of a small portion of the upwind scheme does not result in a significant numerical diffusion and indicates a comparable prediction accuracy with other spatial discretization methods. Therefore, the numerical approaches used in this study can predict the unsteady flow and temperature fields of JICF with a high accuracy.

The simulation model and meshes used in the five-jet study are shown in Figs. 6 and 7. The size of the domain was 18D in the streamwise direction, 8D in the spanwise direction, and 16D in the vertical direction. Note that the length in the wall-normal direction was extended to reduce the blockage ratio. The periodic boundary condition was applied to the two side walls to indicate an infinite number of multiple jets. The mesh size was maintained to be nearly the same as that of a single jet, and the number of cells in the mesh was approximately $19.44×106$⁠. The jet-to-jet spacing was set to 1.6D, which was the same as the typical distance between adjacent air-discharging fans of ACHEs in an LNG plant.

The vortical structures of single and multiple jets are compared in Figs. 8 and 9 using the isosurfaces of the second invariant of the velocity gradient tensor (Q-criterion) for the instantaneous flow and mean flow fields, respectively, as well as streamlines of the mean flow field. In the single jet, five typical coherent vortical structures are clearly observed: (1) horseshoe vortex, (2) shear-layer vortex, (3) wake vortex, (4) counter-rotating vortex pair (CVP), and (5) hanging vortex, as described by Fric and Roshko [3], Zhao et al. [13], and Yuan et al. [14]. The most significant large-scale vortex structures observed in the single jet are the CVP, as shown in Figs. 8(a) and 8(c). The hanging vortex proceeds around the jet on the lateral side and finally forms the CVP, as shown in Fig. 8(a). The horseshoe vortex forms at the jet upstream and extends to the rear of the jet with two legs, as shown in Fig. 8(a). The wake vortex is also clearly observed in the instantaneous field, as shown in Fig. 9.

For the multiple jets, the most significant vortex structure CVP observed in the single jet is no longer discernible, as visualized in the streamlines computed from the mean flow shown in Fig. 8(c). Instead of the enlarged body of the single jet in the streamwise direction, the jet body of the multiple jets is significantly constrained in the spanwise direction, as shown in Fig. 9. Owing to the constraint and interaction between adjacent jets, the streamwise velocity $u$ in the multiple-jet body is remarkably increased compared with that of the single jet, as shown in Fig. 9. A closer examination of the velocity vector field near the rear of the jet nozzle (Fig. 10) revealed the difference in the origin of the CVP. Compared with the single jet, the vortexes in the wake of the nozzles of the multiple jets are no longer located significantly close to the jet nozzle, as marked by the circular arrows. Instead, the elongated wakes appear beside the accelerated flow in the space between the adjacent jets, at approximately one jet diameter distant from the nozzle in the crossflow direction. The streamlines computed from the mean velocity indicate that the CVP is slightly formed for a notably short distance in the multiple jets, but cannot further evolve owing to the significant constraint in the spanwise direction and the strong stretch in the streamwise direction caused by the high streamwise velocity in the body of the multiple jets. Conversely, the horseshoe vortex is formed in front of the multiple jets, but the two legs are no longer present in the wake of the jets, as shown in Fig. 8(a). This is because the horseshoe vortex cannot travel downstream owing to the constraint of the significantly close jet-to-jet spacing. Furthermore, the wake vortex, such as that in the single jet, does not appear downstream of the multiple jets, and no coherent vortex structures are clearly identified (Fig. 9), except for numerous small-scale vortexes. Note that Figs. 8(a) and 8(b) reveal a noticeable difference in the hanging vortex between the single and multiple jets. In multiple jets, the hanging vortex appears to be split into two disconnected parts: the lower part remains near the jet exit, whereas the upper part appears on the lateral side of the compressed jet body. The splitting phenomenon is demonstrated in Fig. 11 using the gray isosurface of the Q-criterion for the mean flow, the isosurface of the Q-criterion for the instantaneous flow field colored by the normalized vorticity $ωx+$⁠, and the instantaneous normalized vorticity $ωx+$ contour on the ZY plane. For the single jet, the jet body primarily evolves into a trumpet shape, as indicated by the black arrow in Fig. 11(a), owing to the presence of the CVP. The vortex with a large vorticity $|ωx+|$ continues on the lateral side of the shear-layer vortex ring along the black arrow direction and appears as two segments of hanging vortexes located on the lateral side of jet body, as shown in the gray isosurface of the Q-criterion applied to the mean flow in Fig. 11(a). For multiple jets, similar to the single jet, the shear-layer vortex rings expand vertically along the black arrow over a distance of 1.5D after exiting the nozzle, and the two segments of the hanging vortex also appear in the lower part of the jet body, as shown in the gray isosurface of Fig. 11(b). However, the shear-layer vortex ring narrows along the yellow arrow owing to the constraint in the spanwise direction. Consequently, the vortex on the lateral side of the shear-layer vortex rings merges into the jet body inside the shear-layer vortex ring, as shown in the instantaneous normalized vorticity $ωx+$ contour of the ZY plane, preventing the formation of the hanging vortex on the lateral side of the gray isosurface in the narrowed region. Subsequently, the shear-layer vortex rings continue to evolve along the orange arrow at an equal spanwise distance, once again forming two segments of hanging vortexes on the lateral side of the multiple-jet body in the upper part of the gray isosurface, as shown in Fig. 11(b). Therefore, the hanging vortex is split in the narrowed region, forming the lower and upper parts separately. The upper part of this hanging vortex resembles a new type of vortex with a shape similar to that of elongated cat ears, thus is called an “elongated cat-ear-shaped vortex” in this study.

The shedding frequencies of the major vortex structures for the single and multiple jets are compared in this section. In this study, approximately 12 TB of data was stored for performing the POD analysis, which was first validated using the 2D cylinder flow. The inputs for the POD analysis in the present study are instantaneous snapshots of the vorticity and velocity fields on 2D planes at various locations, obtained from the LES results. Specifically, the POD analysis was performed using 2048 snapshots of the vorticity $ωy$ and streamwise velocity $u$ on different 2D planes. These snapshots were taken at a sampling interval of $Δtsampling=5×10−3s$⁠, or every ten time-steps, over a total time span of $tsampling=10.24s$ in the simulation. Details regarding the theory of POD analysis can be found in the literature [4,15,16]. The dominant shedding modes and their frequencies were determined to reveal the differences in the shedding frequencies of the major vortex structures for the single and multiple jets. Figure 12 presents the shedding frequencies of the shear-layer vortex, whereas Fig. 13 shows the shedding frequency of the vortexes at the rear of the jet. For ease of observation, the POD mode contours are plotted with the mean velocity vectors shown in Figs. 12 and 13. As one of the major vortex structures in JICF, the shear-layer vortex exhibits a relatively high frequency and kinetic energy. The shedding frequency of the shear-layer vortex for the single jet is approximately 36 Hz, which conversely decreases to 32 Hz for the multiple jets, as shown in Fig. 12. This reduction in the shedding frequency for the multiple jets is likely attributable to the interaction between the adjacent jets, which constrains the shedding of the shear-layer vortex, as depicted in Fig. 9.

The shedding frequency of the vortexes at the rear of the jet is also examined for comparison, as shown in Fig. 13. For the single jet, the wake vortex and the origin of the CVP are characterized by a dominant shedding frequency of 5.4 Hz in POD mode 2. However, in the multiple jets, the elongated vortexes that appear beside the accelerated flow between the adjacent jets do not exhibit dominant frequencies. As discussed in Sec. 4.1, the interaction between the adjacent jets, particularly the flow acceleration between them, significantly affects the formation of the CVP and wake vortex. The impact of this interaction will be further discussed in Sec. 4.3.

The interaction mechanism between the multiple jets is discussed in this section. As detailed in Sec. 4.2, the shear-layer vortex sheds with a higher frequency of 32 Hz in the multiple jets. The evolution of the jet interaction between the adjacent jets was first visualized using the velocity vectors on the XY planes, displayed with POD mode contours of the shear-layer vortex shedding at three different moments in Fig. 14. The visualization shows that the flow path between the adjacent jets can enlarge and shrink in the spanwise direction with the same frequency (32 Hz) as that of the shear-layer vortex shedding. The enlarging and shrinking of the flow path can cause variations in the streamwise velocity (⁠$u$⁠) downstream. The spanwise velocity $v$ at points P1 and P2, as well as the streamwise velocity $u$ at point P3, were sampled from the 2048 saved simulation results. A portion of the data is plotted in Figs. 15(a) and 15(b), with the locations of the sampling points shown in Fig. 15(c). A fast Fourier transform (FFT) analysis of the sampled velocities, obtained with a sampling time interval of $Δtsampling=5×10−3s$ or every ten time-steps, over a total time span of $tsampling=10.24s$⁠, was conducted to identify the dominant frequencies. The plot of the spanwise velocity $v$ reveals that the flow between the adjacent jets behaves as a pulsating jet with a fluctuating spanwise velocity $v$⁠. The velocity difference $Δv=vp1−vp2$ was computed and plotted along with the streamwise velocity $u$ at the downstream point P3, as shown in Fig. 15(b), to identify the enlargement and shrinking of the flow path between the adjacent jets. If $Δv>0$⁠, the flow path shrinks; a larger value indicates a rapid contraction in the flow path between adjacent jets. Figure 15(b) shows that the streamwise velocity $u$ at the downstream point P3 generally increases when $Δv$ increases, although a small time lag exists owing to the difference in the location of the sampling points. Conversely, when $Δv<0$⁠, the flow path enlarges and the streamwise velocity $u$ at P3 decreases when $Δv$ decreases. Although the fluctuation of the streamwise velocity $u$ appears to be less regular, the FFT analysis of the sampled streamwise velocity $u$ clearly shows a peak frequency of 32 Hz, indicating that a pulsating jet forms between the adjacent jets. A statistical analysis used to quantify the relationship between $Δv=vp1−vp2$ and the streamwise velocity $u$ is shown in Fig. 16, demonstrating that the streamwise velocity $u$ increases when $Δv$ increases. According to Chang et al. [17,18], large-scale vortex structures are more likely to break into small vortexes in a pulsating jet compared with classical jets. Consequently, the newly generated pulsating jets between adjacent jets produce many small wakes downstream. This is the one of the reasons why the small vortexes are formed at the rear of the jet, as demonstrated in Fig. 9. Furthermore, the power spectral density (PSD) of the spanwise velocity $v$ and the dominant frequencies at the different points in the streamwise direction between the adjacent jets, obtained by using the FFT analysis shown in Fig. 17, reveals that the shedding frequency of 32 Hz persists up to a distance of less than 1D from the jet-to-jet space in the streamwise direction.

The streamwise velocity fluctuation $urms$ and wall-normal velocity fluctuation $wrms$ for the single and multiple jets are compared in Figs. 18(a) and 18(b). The figures clearly show that the streamwise and wall-normal velocity fluctuations on the lateral sides of the multiple jets are significantly larger than those of the single jet owing to the interaction between the shear-layer vortex rings in the spanwise direction of the adjacent jets. The high turbulence intensity at the space between the adjacent jets (Y/D = 0.8) is further confirmed by the $urms$ and $wrms$ contours on the ZX plane, as shown in Figs. 18(c) and 18(d). Thus, turbulence heat transport significantly increases in multiple jets owing to the generation of numerous pulsating jets in the space between the adjacent jets.

To examine differences in the flow and temperature fields, the time-averaged profiles of the streamwise velocity $〈u〉$⁠, the spanwise velocity $〈v〉$⁠, the wall-normal velocity $〈w〉$⁠, and the temperature $〈T+〉$ in the streamwise directions at X = 2D and 3D were compared, as shown in Fig. 19. The location of the plotted data is shown in Fig. 20. For the single jet, the profiles for both the time-averaged velocity $〈u〉$ and $〈w〉$ maintained similar shapes at different X locations in the streamwise direction, respectively, whereas the time-averaged spanwise velocity $〈v〉$ significantly increases in the downstream owing to the development of CVP. Conversely, for the multiple jets, the magnitudes of the time-averaged velocities $〈u〉$⁠, $〈v〉$⁠, and $〈w〉$ notably decrease within a distance of 1D in the streamwise direction because large-scale coherent vortex structures, such as CVP, do not develop owing to the spanwise constraints. Owing to less entrainment of low-temperature crossflow and the lack of large-scale vortex structures in the multiple jets, the temperature in the multiple jets is significantly higher and more uniform compared to the single jet, as shown in Figs. 19(g) and 19(h).

Furthermore, the absolute values of the heat flux $|〈u′T′〉|$⁠, $|〈v′T′〉|$⁠, and $|〈w′T′〉|$ were compared in the streamwise direction for the single and multiple jets, as shown in Fig. 21. At X = 1D, notable heat fluxes are observed at the borders of the single jet near $Y=±1D$ and at those of multiple jets near $Y=±0.8D$ in the spanwise direction, caused by the interaction between the jet and the crossflow. For the single jet, the heat fluxes $|〈v′T′〉|$ and $|〈w′T′〉|$ induced by the CVP are generally larger than $|〈u′T′〉|$ at X = 2D. For the multiple jets, the heat flux $|〈u′T′〉|$ at X = 2D is dominant in the range of $Y=−0.4D∼+0.4D$ at the rear of the jet. Figure 9 shows that the shear-layer vortex ring in the multiple jets continues over a longer distance in the streamwise direction because the CVP does not form in the multiple jets and does not easily destroy the shear-layer vortex ring. Consequently, the heat flux $|〈w′T′〉|$ at the border of two jets in the range of $Y=±0.8D$ is notably enhanced in the multiple jets, as shown in Fig. 21(d).

The streamlines for the mean flow field and the mean temperature field for the single and multiple jets are compared in Fig. 22. Streamlines originating from the jet nozzle and the locations near the bottom wall in front of the jet are indicated in red and black, respectively. As indicated in Sec. 4.1, the CVP observed in the single jet is no longer formed in the multiple jets. The black streamlines originating from the locations near the bottom wall in front of the jets show a significant separation of flow at the rear of the multiple jets closer to the jet nozzles. Additionally, a secondary recirculation flow is formed downstream of the jet. This separation of flow and secondary recirculation flow contribute to a notable increase in temperature mixing, as illustrated in Fig. 22(b), which can result in significant HAR in the LNG plant. A further investigation regarding the formation of a separation flow and secondary recirculation flow in multiple jets is presented in Fig. 23. The same visualization of vortical structures for the mean flow field of multiple jets is shown in gray in Fig. 23(a) from the front view, the same as that shown in Fig. 8(b). The lower parts of the hanging vortex between the adjacent jets are marked with black curves and appear as two lung-shaped vortical structures with a triangular space between them, indicated by the red dotted line in the front view, as shown in Fig. 23(a). The crossflow passes through this triangular space to the downstream region of the multiple jets. This gap distance $L$ near the bottom wall is significantly larger and rapidly decreases in the Z direction. Therefore, a larger amount of crossflow tends to pass near the crossflow bottom wall, generating a jet flow with a high streamwise velocity, as depicted in Fig. 23(b). This leads to a separation of flow at the rear of multiple jets and the development of a secondary recirculation flow, as illustrated by the streamlines in Fig. 22(a) and the velocity vectors in Fig. 23(b). Subsequently, a recirculation flow also develops as a secondary flow in the downstream region of the multiple jets.

An LES was conducted for a single jet and five spanwise jets with a jet-to-jet spacing of 1.6 for the jet nozzle diameter. The jet-to-crossflow velocity ratio $VR$ was 3.3, and the Reynolds number $Rec$ based on the crossflow velocity and jet nozzle diameter was 2100. The results of the verification study indicate that the present LES can reproduce the typical vortex structures of the jet in a crossflow and accurately predict the mean velocity, mean temperature, RMS velocity fluctuation, and RMS temperature fluctuation.

The significant differences in the vortical structures, flow, temperature fields, and vortex-shedding frequency were determined by comparing the single and multiple jets. For the multiple jets, the CVP is formed only in a significantly short distance and does not evolve in the streamwise direction. The hanging vortex is found to be split into two disconnected parts, and an elongated cat-ear-shaped vortex is generated on the lateral side of the multiple-jet body. No coherent large-scale vortical structures, such as the wake vortex and horseshoe vortex legs, are observed at the rear of the multiple jets, with the exception of a lot of small-scale vortexes. Instead of the formation of CVP in the single jet, a notable separation flow and secondary recirculation flow are generated in the downstream of the multiple jets; thus, the temperature mixing is significantly enhanced, which significantly increases the risk of HAR in an LNG plant. The POD analysis reveals that the dominant shedding frequency of the shear-layer vortex in the multiple jets decreased to 32 Hz compared with 36 Hz in the single jet, which is most likely owing to the constraint of adjacent jets. Moreover, the interaction mechanism between adjacent jets was revealed in this study. Analyzing the sampling data in the flow path between the adjacent jets demonstrated that the flow in the jet-to-jet space behaves as a pulsating jet flow with a frequency of 32 Hz, which can continue at less than 1D in the streamwise direction. The width of the flow path in the spanwise direction alternately decreases and increases, inducing the fluctuation in the streamwise velocity. Therefore, numerous small wakes are generated in the wake of the jets.

Furthermore, the difference in the turbulent heat transport between the single and multiple jets is also revealed, indicating that the turbulent heat fluxes $|〈v′T′〉|$ and $|〈w′T′〉|$ induced by the CVP are generally larger than $|〈u′T′〉|$ for the single jet. Conversely, for the multiple jets, the heat fluxes $|〈u′T′〉|$ at the rear of the jet and $|〈w′T′〉|$ in the jet-to-jet borders of multiple jets increase owing to the pulsating jet flows generated between the adjacent shear-layer vortexes.

CFD simulations were conducted using the modified Multiphysics CFD software frontflow/red (ffr), which was developed as part of the FSIS project granted by the Japanese government. Its source program is open and available from the website.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

$C$ =

SGS model parameter

$cp$ =

specific heat of fluid at constant pressure

$D$ =

jet nozzle diameter

$L$ =

distance

$r$ =

jet nozzle radius

$S¯ij$ =

strain-rate tensor of fluid

$T+$ =

normalized temperature $(T−Tc)/(Tj−Tc)$

$Tc$ =

crossflow fluid temperature

$Tj$ =

jet fluid temperature

$u$ =

streamwise velocity

$urms$ =

streamwise velocity fluctuation

$Uc$ =

mean crossflow velocity

$Uj$ =

mean jet velocity

$Umax$ =

maximum velocity in the jet center

$|u′T′|$ =

absolute heat flux in the streamwise direction

$v$ =

spanwise velocity

$vrms$ =

spanwise velocity fluctuation

$VR$ =

jet-to-crossflow velocity ratio

$|v′T′|$ =

absolute heat flux in the spanwise direction

$wrms$ =

wall-normal velocity fluctuation

$|w′T′|$ =

absolute heat flux in the wall-normal direction

$X,Y,Z$ =

streamwise, spanwise, and wall-normal directions in Cartesian coordinates with origin at jet slot center (⁠$X=0,Y=0,Z=0$⁠)

$y+$ =

dimensionless wall distance

$〈〉$ =

long-time average

$δ$ =

boundary-layer thickness of crossflow

$Δ$ =

grid-filter width

$δij$ =

Kronecker delta

$Δt$ =

time-step interval

$λ$ =

thermal conductivity of fluid

$μ$ =

fluid viscosity

$μSGS$ =

SGS turbulent viscosity

$ρ$ =

fluid density

$τij$ =

subgrid scale (SGS) stress

$τkk$ =

SGS stress

$ωx$ =

vorticity component in the x direction

$ωy$ =

vorticity component in the y direction