Numerical investigations of turbulent multiple jet impingement on a heated square block in a confined channel

Thermal Science and Engineering Progress 14 (2019) 100415

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Thermal Science and Engineering Progress journal homepage: www.elsevier.com/locate/tsep

Numerical investigations of turbulent multiple jet impingement on a heated square block in a confined channel N. Satish, K. Venkatasubbaiah

T

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Department of Mechanical & Aerospace Engineering, Indian Institute of Technology Hyderabad, Hyderabad 502285, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Turbulent jet impingement Square block Jet to block spacing Center distance between jets

The analysis of fluid flow and heat transfer characteristics of turbulent single and multiple jets impinging on a square block in a confined channel has been studied numerically. The study of jet impingement on a square block is important as it is directly relevant to the cooling process of food products by jet impingement and present results would be useful in understanding this process. Two-dimensional unsteady state incompressible turbulent forced convection flow is considered for the present analysis. Turbulence is modelled by Reynolds Averaged Navier-Stokes (RANS) equation with a standard k − ∊ model and enhanced wall treatment at the wall. The governing equations are solved using a finite volume-based commercial solver. The second-order upwind scheme is used for non-linear terms and the SIMPLE algorithm is used for the pressure-velocity decoupling problem. Effects of a single jet, double jet, 3 jets, and 4 jets, the center distance between jets, block size and height between the block and bottom jets on flow and heat transfer characteristics are reported. The better enhancement of heat transfer is observed from all surfaces of the block with multiple jet impingement compared with a single jet due to multiple recirculation zones than a single jet. The enhancement of heat transfer on the right surface of the block for 4 jets impingement is 113.3% compared to single jet impingement. The overall heat transfer rate is increased by 72.74% with an increase in center distance between jets from 2 to 6. Present results are validated with experimental results available in the literature.

1. Introduction Due to higher heat transfer rate, the studies of jet impingement gain a lot of interest in engineering applications like food industries for baking and cooling of different cookies, cooling of gas turbine blades and combustor walls, drying of textile products, cooling of electronic compact systems and quenching of steel plates. High heat transfer rate at the desired location can be easily obtained by jet impingement with higher velocities. Because of this feature, impinging jets are being used in the food industry to heat and cool the various food products like cereals, bread, and cookies. Multiple jets are employed to get a uniform and rapid heat transfer rate in food products (square blocks). The prediction of flow dynamics of jet impingement after striking the surface is complicated due to a sudden change in the flow direction. The flow and heat transfer characteristics of jet impingement on a solid block depend on various parameters such as the geometry of the block, flow rate, distance between jet and impingement surface and number of jets. Many people experimentally and numerically have studied the jet impingement on flat and curved surfaces. However, the studies of jet impingements on the block are very limited in the literature. The

⁎

Corresponding author. Phone no: +91 4023016074. E-mail address: [email protected] (K. Venkatasubbaiah).

https://doi.org/10.1016/j.tsep.2019.100415

2451-9049/ © 2019 Elsevier Ltd. All rights reserved.

present study focuses on flow and heat transfer characteristics of single and multiple jet impingements on the square block in a confined channel. First, we discuss the summary of experimental and numerical work related to single and multiple jet impingements on a flat surface. An experimental study [1] was carried out to know the flow characteristics of jet impingement on a plate. They have proposed a correlation of Nusselt number at the stagnation point for different jet to plate spacings. Large-eddy simulation [2] technique was used to know the dynamics of plane jet impingement and the counter-rotating cells were observed near the impingement region. Chattopadhyay [3] studied numerically the heat transfer characteristics of annular jet impingement. He concluded that the heat transfer rate was more in circular jet impingement compared to annular jet impingement for a given flow conditions. An experimental study has been carried out to know the flow characteristics of air jet impingement on a moving surface by Senter and Selliec [4]. They observed a significant change in the flow field with plate velocity. Sagot et al. [5] studied the experimental and numerical study of jet impingement on a flat surface for constant wall temperature. It is reported that the average Nusselt number is high for

Thermal Science and Engineering Progress 14 (2019) 100415

N. Satish and K. Venkatasubbaiah

Nomenclature

c C1 C2 b1 B1 b2 B2 bs Bs L w Tc Th Re u¯, v¯ Nul

ρ ν νt Prt kf k ∊ x, y ψ

Center distance between jets mm Dimensionless center distance between top jets Dimensionless center distance between bottom jets Distance between top jets and block cm Dimensionless distance between top jets and block Distance between bottom jets and block cm Dimensionless distance between bottom jets and block Block size cm Dimensionless block size Length of the domain m Width of the jet mm Jet temperature K Temperature of the block K Reynolds number Velocity components in x and y directionm/s Local Nusselt number

Density kg/m3 Kinematic viscosity m2/s Eddy viscosity m2/s Turbulent Prandtl number Thermal conductivity of fluid W/m-K Turbulent kinetic energy m2/s2 Turbulent dissipation m2/s3 x and y coordinates Flow variable

Subscripts

avg 1 2 3 4 j

constant heat flux compared to a constant wall temperature case. Effect of pulsed jet impingement on heat transfer characteristics [6] was studied for large temperature difference and different Reynolds numbers. Experimental study has been carried out for oil jet impingement on a plate [7]. The flow rate has a significant effect than the nozzle to plate spacing on the heat transfer rate and it was observed that the heat transfer coefficient increases with increasing plate surface temperature. Turbulent plane jet impingement on a moving surface has been studied numerically [8]. It is noticed that the stagnation point disappeared for the high surface to jet velocity ratios. The performance of standard k − ∊, realizable k − ∊ and k − ω turbulence models are compared [9] to know the flow dynamics of twin jet impingement. They concluded that both k − ∊ and realizable k − ∊ models given the accepted range of results compared to experimental results. Dagtekin and Oztop [10] had studied the double laminar jet impingement on the wall. In the impingement region, vortices are formed and increased the heat transfer rate with the increase in Reynolds number. Recently, Satish and Venkatasubbaiah [11] studied the numerical investigation of turbulent double jet impingement on moving plate. It was noticed the enhancement of heat transfer rate for moving plate with increase in plate velocity and for lower spacing between plate and jets. We discuss the summary of experimental and numerical work of jet impingements on curved surfaces. An experimental study of single jet impingement on cylinder had been studied by McDaniel and Webb [12]. They conducted the experiments for both sharp-edged orifice and contoured edge orifice jet impingements. The average Nusselt number dependency on Reynolds number is more for sharp edge orifice than a contoured orifice. The experimental study of jet impingement on a circular cylinder was studied by Gori and Bossi [13]. They have developed the correlation for average Nusselt number and it predicts the values less than 12% of accuracy. Cornaro et al. [14] studied round jet impingement on a semicircular cylindrical surface. The relative curvature ratio effects on heat transfer rate are reported that heat transfer rate increases with an increase in relative curvature ratio. Experimental study of turbulent jet impingement on the convex surface was performed by Chan et al. [15]. It was reported that the stagnation point Nusselt number strongly depends on jet Reynolds number. Distance between jet to impinging surface and jet Reynolds number have a very significant effect on Nusselt number distribution along the convex surface when it compared to a flat surface. Lee et al. [16] studied the heat transfer characteristics of turbulent jet impingement on the inclined concave surface. As the angle increases at a particular nozzle to surface distance the stagnation point Nusselt number decreases. An experimental study of round jets impingement on the concave surface has been conducted by Fenot et al. [17]. It was observed that the

Average Jet 1 Jet 2 Jet 3 Jet 4 Jet

average Nusselt number decreases with an increase in relative curvature due to confinement and concavity. Kayansayan and Kucuka [18] carried out an experimental and numerical study of jet impingement cooling of the concave channel. It was reported that Nusselt number is more for concave surface compared to a flat surface. Experimental and numerical work of turbulent air jet impingement on rectangular shape cookie had been studied by Nitin and Karwe [19]. It was reported that the maximum heat transfer rate is found near the stagnation point, the surface heat transfer coefficient depends on jet velocity and jet to cookie spacing and independent of thermal properties of cookie. The jet impingement on cylinder was studied experimentally and numerically by Sharma and Imran [20]. It was reported that because of confinement large flow structures minimize the heat transfer rate. Pramchandran et.al [21] have done experimental and numerical investigations of turbulent circular jet impingement on the cylinder. They reported that nozzle to cylinder distance and the ratio of nozzle diameter to cylinder shown a significant effect on Nusselt number at the stagnation point. Effect of shape confinement of turbulent slot jet impingement on the cylinder has been studied experimentally and numerically by Premachandran and Sharad Pachpute [22]. In their study, it was reported that quadrilateral and hexagonal confinement shapes enhance the heat transfer rate from the cylinder. Conjugate heat transfer analysis is performed numerically by Karwe et al. [23] to know the turbulent jet impingement characteristics over the cylinder. It was observed that Nusselt number variation over the surface is not uniform and correlation of average Nusselt number has been developed. It is also concluded that the heat transfer rate is dependent on model geometry and jet flow field. Rama kumar and Prasad [24] studied row of multiple jet impingement on the concave surface. Counter rotating vortices were observed, and the pressure and Nusselt number distributions having the second peak. Mothe and sharif [25] used RNG k − ∊ turbulence model to study the flow and heat transfer characteristics of jet impingement on the concave surface. It was reported that Nusselt number depends on the curvature of the impinging surface, Reynolds number has a significant effect on Nusselt number distribution and correlation of average Nusselt number is reported. The numerical study of turbulent jet impingement on the semicircular surface was studied by Yuetzu Yang et al. [26]. The distance between the jet and the impingement surface has less impact on the Nusselt number. Yasin varol et al. [27] studied the jet impingement on two cylinders numerically for different diameter ratios. They reported that Nusselt number increases with an increase in Reynolds number, and recirculation between cylinders has no effect on heat transfer rate from the first cylinder. Numerical study of jet impingement on a heated 2

Thermal Science and Engineering Progress 14 (2019) 100415

N. Satish and K. Venkatasubbaiah

pedestal placed on a flat plate has been reported in [28]. They have used V2F turbulence model and their results have been validated with experimental results reported in [29]. An experimental study of turbulent jet impingement on a square cylinder [30] shows a secondary peak in Nusselt number distribution and the Nusselt number distribution along the length of the cylinder has similar variation as like jet impingement on a flat plate. From the above literature survey, it is noticed that studies of single and multiple jet impingements on the square block in a confined channel are very limited. The study of multiple jet impingement on a square block is very important as it is directly relevant to the cooling process of food products by jet impingements. Studies in the past have not emphasized the flow and heat transfer characteristics of turbulent multiple jet impingements on a square block in a confined channel. The effects of various parameters such as the number of jets, jet velocity, jet block size, the center distance between jets and jets to block spacing on flow and heat transfer characteristics are limited in the literature. Hence these points have been the motivation for the present study.

2. Mathematical formulation Fig. 2. Grid independence test for single jet impingement.

Turbulent multiple jet impingement on the solid square block in a confined channel is shown in Fig. 1. The minimum center distance between jets is 0.016 m and the side of the square block is 0.048 m and the width of all jets is 8 mm. Uniform velocity, based on jet Reynolds number, through jets, is considered with 2% turbulence intensity and jet flow temperature (Tc ) is less than solid square block temperature (Th ). The confinement walls are considered as adiabatic walls. The flow phenomenon is modelled as a two-dimensional unsteady state incompressible turbulent airflow impinging on a square block. The governing equations for turbulent forced convection flows are described mathematically by the Reynolds averaged Navier-Stokes equations (RANS), including the time-averaged energy equation for the mean temperature field. Turbulence is modelled using a standard k − ∊ model with enhanced wall treatment. RANS equations for velocity and temperature fields and k − ∊ model are as follows:

∂u¯ ∂v¯ + =0 ∂x ∂y ∂u¯

∂u¯

1 ∂p¯

∂2u¯

+ u¯ ∂x + v¯ ∂y = − ρ ∂x + ν ⎡ 2 + ⎣ ∂x

+

∂ ∂u¯ ⎡ν ⎤ ∂y ⎣ t ∂y ⎦

+

∂ ∂v¯ ν ∂y ⎡ ⎣ t ∂x ⎤ ⎦

∂2u¯ ⎤ ∂y 2 ⎦

∂

+ 2 ∂x ⎡νt ⎣

∂2v¯

+ u¯ ∂x + v¯ ∂y = − ρ ∂y + ν ⎡ 2 + ⎣ ∂x

∂v¯

+

∂ ∂x

∂v¯ ∂x ⎤ ⎦

ν ⎡ ⎣ t

∂2v¯ ⎤ ∂y 2 ⎦

+

∂ ∂x

∂u¯ ⎤ ∂y ⎦

⎡νt ⎣

∂v¯ ⎤ ∂y ⎦

∂

+ 2 ∂y ⎡νt ⎣

(3)

∂ ⎡⎛ ∂T ∂T ∂T ∂ ⎡⎛ ν ∂T ⎤ ν ∂T ⎤ + + u¯ + v¯ = α+ t ⎞ α+ t ⎞ ⎢ ⎥ ⎥ ∂ ∂ ∂t ∂x ∂y ∂x ⎢ Pr x y Pr t t ⎠ ∂y ⎦ ⎠ ⎣⎝ ⎦ ⎣⎝

(4)

( ) − ∊ + ν ⎡2 ( ) + 2 ( ) + ( ⎣

(5)

⎜

∂k ∂t

∂∊ ∂t

∂k

∂k

t

∂u¯ 2 ∂x

+ u¯ ∂x + v¯ ∂y =

∂∊

∂∊

∂ ∂x

{(

∂u¯ 2 ∂x

)

⎡ ν+ ⎣

⎟

∂ ∂x

+2

(

⎡ ν+ ⎣ ∂v¯ 2 ∂y

∂k ⎤ ∂x ⎦

νt σk

∂v¯ 2 ∂y

+ u¯ ∂x + v¯ ∂y =

+ C1 ∊ ⎡νt 2 ⎣

(1)

∂u¯ ∂t

∂v¯

1 ∂p¯

∂v¯ ∂t

νt σ∊

∂u¯ ∂y

)

( ) +(

+

+

∂∊ ⎤ ∂x ⎦

∂u¯ ∂y

+

⎜

∂ ⎡ ∂y ⎣

(ν + ) νt σk

⎟

∂k ⎤ ∂y ⎦

∂v¯ 2 ⎤ ∂x

)⎦

+

∂ ⎡ ∂y ⎣

∂v¯ 2 ∂x

(ν + )

) } ⎤⎦

νt σ∊

∂∊ ⎤ ∂y ⎦

− C2 ∊

∊2 k

(6)

Where ρ is the density of the fluid; ν is the kinematic viscosity; α is the thermal diffusivity; νt is the turbulent eddy viscosity; Prt is the turbulent Prandtl number; For k − ∊ turbulence model, constants used are Cμ = 0.09 ; C1 ∊ = 1.44 ; C2 ∊ = 1.92 ; Prt = 0.9; σk = 1.0 ; σ∊ = 1.3.

∂u¯ ∂x ⎤ ⎦

(2)

Fig. 1. Schematic diagram of multiple jet impingement on a square block. 3

Thermal Science and Engineering Progress 14 (2019) 100415

N. Satish and K. Venkatasubbaiah

The average Nusselt number (Nuavg ) is evaluated by integration of the local Nusselt number along the impinging surface. 3. Numerical methods ICEM CFD meshing tool is used for generating the mesh and finite volume based ANSYS Fluent solver is used for solving the governing equations. Second-order upwind scheme is used for non-linear terms and central difference scheme for diffusion terms. The SIMPLE algorithm is used for the pressure-velocity decoupling problem in which the predictor velocities will be calculated with guess values of pressure and the pressure correction equation is solved to get the corrected velocity values. A standard k − ∊ turbulence model with enhanced wall treatment is employed to capture the gradients accurately near the wall. Jet inlet conditions are uniform velocity based on jet Reynolds number and uniform jet temperature of 300 K with a turbulence intensity is 2% . Noslip boundary conditions are imposed at the walls for the velocity field. The constant surface temperature of 400 K is applied on the impinging square block and the adiabatic boundary condition at the confinement wall for the temperature field. Outflow condition is applied at the flow exits. A structured mesh is generated with a fine mesh near the impinging zone to capture the gradients accurately. The finite volume based ANSYS Fluent software is used to solve the governing equations. The convergence criteria for all flow variables in residuals are considered at the order of 1 × 10−6 . The Courant number is kept less than unity for all simulations and the time step is 0.0001 s. The minimum value of y+ on top and bottom faces of the block for all single and multiple jets is less than 3. It is less than 0.3 for the left and right faces. More details about the solver can be found in [31]. The numerical accuracy of the present results has been validated with the experimental results available in the literature. 4. Grid independence and validation The grid independence test has been conducted with different grid sizes: coarse mesh 139200 cells, medium mesh 161980 cells and fine mesh 180180 cells for single slot jet impinging on a square block at a Reynolds number of 11000. The local Nusselt number variation along the top surface of the square block is shown in Fig. 2 for different grids. The average Nusselt number values are 62.75, 63.19 and 63.19 for coarse, medium and fine meshes. From Fig. 2 and the average Nusselt number values show the grid-independent with medium mesh. Hence all simulations are reported with medium mesh. The accuracy of the present results is validated with experimental results reported in [4,29]. Senter and Solliec [4] have studied experimentally jet impinging on a stationary and moving surface. The centerline jet velocity nondimensionalized with jet inlet velocity is shown in Fig. 3(a), in which present results are compared with experimental results reported in [4] for single jet impinging on the stationary surface at a Reynolds number of 10600. From Fig. 3(a), one can notice that present results are matching well with the experimental results reported in [4] however there is a deviation of present results with experimental results because of numerical methods and turbulence model. In the present study, the maximum deviation is 11.5% compared to experimental results. In literature [9] the maximum deviation was 25% observed between experimental and numerical results. Experimental study of turbulent jet impingement on a heated pedestal mounted on a flat plate is reported in [29] for Reynolds number of 23000. This experimental results of local Nusselt number variation on pedestal are given in [28]. For the same experimental flow conditions, the present results of local Nusselt number variation on a pedestal has been compared with experimental results of [29] which are reported in [28] and shown in Fig. 3(b). From Fig. 3(b), the local Nusselt number variation on a pedestal is matching well with the experimental results. However, there is a little deviation between present results and experimental results at the impingement region due to an assumption of

Fig. 3. Validation: (a) Single jet impingement on a stationary plate and (b) jet impingement on a heated pedestal placed on a flat plate.

The definitions of other parameters given here are used for present analysis. C1 = c1/ w is dimensionless center distance between top jets. C2 = c2/ w is dimensionless center distance between bottom jets. w is v¯ w width of jet. Re1 = 1ν is Reynolds number of jet 1. v¯1 is velocity of jet 1. v¯2 w ν

Re2 =

is Reynolds number of jet 2. v¯2 is jet 2 velocity. Re3 = v¯4 w ν

v¯3 w ν

is

Reynolds number of jet 3. v¯3 is jet 3 velocity. Re4 = is Reynolds number of jet 4. v¯4 is jet 4 velocity. ψ is a flow variable indicating u¯, v¯ and T in present problem. 2.1. Nusselt number The rate of heat transfer from the impinging hot surface carried by fluid is evaluated in terms of dimensionless number, the Nusselt number (Nu ). The equation to evaluate the convective heat transfer coefficient is given below:

h=

−kf

∂T ∂n

(Th − Tc )

(7)

∂T ∂n

is the temperature gradient in the normal direction to the impinging surface. The local Nusselt number (Nul ) is calculated with the above equation in dimensionless form as given below: ∂T

Nul =

−w ∂n (Th − Tc )

(8)

where Th is the impinging surface temperature; Tc is the inlet jet temperature; kf is thermal conductivity of the fluid; w is the jet width; 4

Thermal Science and Engineering Progress 14 (2019) 100415

N. Satish and K. Venkatasubbaiah

Re1= 11000 0.6

(a) 0.6

Zoomed view 0.08

0.08

0.5

0.07

0.5 0.06

0.06

0.4

0.05

0.4 y

0.04

y

y

y

(b)

Re1= 11000 Re3= 11000

0.3

0.04 0.03

0.3

0.02

0.02 0.01

0.2 0

0.2 0.36

0.38

0.4

x

0.42

0.1

0

0

0.44

0

0.2

0.4

0.6

x

0

0.8

0

0.2

0.4

x

0.42

0.44

0.4

0.6

x

Re1= 11000 Re2= 11000 Re3= 11000 Re4= 11000

(c)

0.6

(d)

0.6 0.08

0.08

0.5

0.5 0.06

0.06

0.4

y

0.4 0.04

y

y

y

0.38

0.1

Re1= 11000 Re2= 11000 Re3= 11000

0.3

0.04

0.3 0.02

0.02

0.2

0.2 0

0.36

0.38

0.4

x

0.42

0

0.44

0.1

0

0.36

0.36

0.38

0.4

x

0.42

0.44

0.1

0

0.2

0.4

x

0.6

0

0.8

0

0.2

0.4

x

0.6

Fig. 4. Stream function contours of single and multiple jet impingements on a square block.

5.1. Effect of single and multiple jets

2-dimensional approach and chosen numerical methodology for solving turbulent flow equations in the present study. The pedestal length ( r ) in D radial direction is 0.5 but the data is enlarged by multiplication factor 2 r ( D = 1) in Fig. 3(b) for better visibility. The average Nusselt number on pedestal is 165.7 in present study and it is 168.2 in the experimental study. In the present study, the maximum deviation is 1.5% compared to experimental results. Hence the present results are matching well with experimental results available in the literature. In addition to this the present solver was tested by authors for turbulent double jet impingement on the stationary and moving surface and results are reported in [11].

To know the effect of the single jet, double jet and multiple jet impingement on the square block, results of steady-state stream function contours are given in Fig. 4. The size of the square block is 0.048 m and the jet Reynolds number is the same for all jets with Re = 11000. The distance between the confinement wall and square block is twice of the jet width. Fig. 4(a) shows the stream function contours of single jet impingement on the top surface of the square block. The jet is located on the left side of the centerline of the square block at a distance of 0.008 m. After impinging the jet leaves in both directions over the top surface. Two large recircular zones are found on the left and right sides of the block and two recircular zones are found on either side of the jet and near to confinement wall which can be seen in the zoomed view of Fig. 4(a). The size of the recircular zones that are present near to the top confinement wall is the order of 4 to 5 times of jet width. It is noticed that some amount of fluid from jet flows below the bottom surface of the block via the left face of the block. Stream function contours of double jet impingement are shown in Fig. 4(b). One jet is impinging on the top surface and another jet is impinging on the bottom surface. The flow is symmetric on both the right and left side of the block. Two vortices, which are rotating in the opposite direction, are found on the left side and right side of the block. The size of the vortices is small compared to the vortex that is found on the left side of the block for single jet impingement. Stream function contours of 3 jets impingement on the square block

5. Results and discussion Flow and heat transfer characteristics of single and multiple jet impingement on the solid square block in a confined channel studied numerically and results are reported. The solid square block is considered as a heated block at 400 K and jet inlet temperature is 300 K. Reynolds number is defined based on jet width and jet inlet velocity. All jet widths are the same and equal to 8 mm. The effect of single jet, double jet and multiple jets, jet Reynolds number, the center distance between jets, block size and jet to block spacing on flow and heat transfer characteristics are discussed and reported here. Air is considered as the working fluid and the Prandtl number is taken as 0.744.

5

Thermal Science and Engineering Progress 14 (2019) 100415

N. Satish and K. Venkatasubbaiah

Fig. 5. Local Nusselt number distribution on all the faces of block for single and multiple jet impingements.

top surface. Stream function contours of 4 jets impingement on the square block are shown in Fig. 4(d). Two jets are placed on the top surface of the block and two jets are placed below the bottom surface of the block. Two vortices are found between the jets on the top and bottom surfaces of the block. The size of the vortex on the left side of the block is little larger than the vortex on the left side of the block for double jet impingement flow. The corresponding local Nusselt number variation along the faces of the block for single, double and multiple jet impingements is shown in Fig. 5. The local Nusselt number variation along the top surface is shown in Fig. 5(a). The local minimum Nusselt number value is at the left corner of the top surface and slowly increases to a maximum value at jet impingement region then slowly decreases towards the right corner of the top surface for single jet impingement. A sudden drop in Nusselt number is noticed at the corner due to the difference in temperature gradients which leads to a difference in the heat transfer coefficient. The turbulence intensity variation near the block is almost similar to local Nusselt number variation. Though the plots are not shown, the values of turbulent intensity at different locations are presented here. The minimum values are 8.5% and 6.1% above the top surface are noticed at the left and right corner respectively for single jet impingement case. The turbulent intensity values near left and right corners of bottom surface are 0.2% and 0.9% for single jet impingement case. A similar kind of variation is observed for double jet impingement. The bottom jet having very little influence on Nusselt number variation on the top surface of the block. It can be seen from Fig. 5(a). The Nusselt

Table 1 Overall average Nusselt number values of jet impingement on a heated square block for different parameters. Re1

Re2

Re3

Re4

C1

C2

B1

B2

Bs

Nuavg

11000 11000 11000 11000 11000 11000 11000 11000 11000 11000 11000 11000 11000

– – 11000 11000 11000 11000 11000 15000 15000 15000 15000 15000 15000

– 11000 11000 11000 15000 15000 15000 19000 19000 19000 1500 1500 1500

– – – 11000 15000 15000 15000 23000 23000 23000 11000 11000 11000

– – 2 2 2 4 6 2 2 2 2 2 2

– – – 2 2 4 6 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 2 2

2 2 2 2 2 2 2 2 2 2 2 3 4

6 6 6 6 6 6 6 4 5 6 6 6 6

21.0 39.49 38.03 38.5 42.45 38.42 73.33 64.32 54.72 50.53 47.03 45.18 43.95

are shown in Fig. 4(c). Two jets are placed on the top surface of the block and one jet is placed below the bottom surface of the block. The center distance between jet1 and jet2 that are placed above the top surface of the block is 0.016 m. Two vortices are found in between jet1 and jet2. Two extra recircular zones are found at x = 0.15 m and x = 0.65 m respectively, whereas such recircular zones are not found for double jet impingement. The shape and size of the vortices on left and right side of the block are altered with the addition of jet2 on the

6

Thermal Science and Engineering Progress 14 (2019) 100415

N. Satish and K. Venkatasubbaiah

C1 = 2

(a)

Re1= 11000 Re2= 11000 Re3= 15000 Re4= 15000

0.6

C1 = 4

(b)

0.6 0.08

0.08

0.5

0.5 0.07 0.06

0.06

0.4

0.4

0.3

y

0.04

y

y

y

0.05

0.03

0.02

0.02

0.2

0.2

0.01 0

0.36

0.38

0.4

0

0.42

x

0.1

0

0.04

0.3

0.2

0

0.44

0.4

0.6

x

0

0.8

(c)

C1 = 6

0

0.4

x

0.2

0.42

0.44

0.4

0.6

x

(d)

0.6 0.08

0.08

0.5

0.5

0.4

300.282

310 y

y

y

0.4 0.04

0.3

0.04

310 310

310 310

0.3

0.02

0.02

0.2

300.282

0.2 0

324.124

300.282 0.06

0.06

y

0.38

C1 = 6

0.6

0.36

0.38

0.4

x

0.42

325 0

0.44

0.1

0

0.36

0.1

0.36

325

0.38

0.4

x

0.42

0.44

0.1

0

0.2

0.4

x

0.6

0

0.8

0

0.2

0.4

x

0.6

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distance is maintained for top jets and bottom jets. The Nusselt number is maximum near stagnation points due to high momentum and minimum between jets. The recircular zones between jets have attained high temperature due to their rotation hence less dissipation of heat at their locations compared to heat dissipation at near stagnation points. The average Nusselt number values on the bottom surface of the block are 4.5, 65, 64.6 and 57.55 for single jet, double jet, 3 jets, and 4 jets impingements respectively. Double jet, 3 jets, and 4 jets impingements enhanced the heat transfer rate from the bottom surface. The local Nusselt number variation along the left and right surfaces are shown in Fig. 5(c) and (d). U shape variation is observed on both the surfaces for all jet impingements. For single jet impingement, there is better heat transfer is noticed at the top corner on both the surfaces due to jet and vortex interaction. It can be observed from Fig. 5(c) and (d). For double jet impingement, the Nusselt number enhancement is observed at the bottom corner of both the faces. For 3 jets impingement, the Nusselt number is improved at the top corner on both the surfaces. For 4 jet impingement, the Nusselt number variation between corners is uniform and similar for both the surfaces due to given the same flow conditions at all jets. The average Nusselt number values on the left surface of the block are 6, 15.5, 17 and 18.5 for single jet, double jet, 3 jets, and 4 jets impingements respectively. The average Nusselt number values on the right surface of the block are 8.65, 12.9, 15.5 and 18.5 for single jet, double jet, 3 jets, and 4 jets impingements respectively. The average Nusselt number values over the entire surface of the block are given in Table 1. The average Nusselt number values over the

number variation on the top surface is similar for 3 and 4 jets impingements. The minimum value of the Nusselt number is noticed at the point of interaction of vortices between jet1 and jet2 for 3 jets and 4 jets impingement due to less temperature gradient. The location of the minimum Nusselt number value is slightly shifted towards the right side for 4 jets due to the separation point of two vortices between jet1 and jet2 is slightly shifted towards the right side. The average Nusselt number values on the top surface are 64.86, 64.57, 56.9, and 57.55 for single, double, 3 and 4 jets impingements respectively. Single jet gives better heat transfer on top surface of the block. The local Nusselt number variation on the bottom surface of the block is shown in Fig. 5(b). A single jet is mounted above the top surface of a square block. The Nusselt number variation is almost uniform on the bottom surface for single jet impingement. The minimum value of Nusselt number is found on the bottom surface compared to the top surface for single jet impingement. The Nusselt number variation along the bottom surface for double jet impingement is similar to Nusselt number variation along the top surface for a single jet impingement case. The Nusselt number variation along the bottom surface for 3 jets is similar to double jet impingement due to only one jet is available on the bottom surface for both the cases and jet2 employment in 3 jets impingement has no much influence on Nusselt number variation on the bottom surface compared to double jet impingement. The Nusselt number variation along the bottom surface for 4 jets impingement is as same as the Nusselt number variation on the top surface for 4 jets impingement due to same Reynolds number for all jets and same center 7

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N. Satish and K. Venkatasubbaiah

Fig. 7. Local Nusselt number distribution on all surfaces of the block for different center distances between jets.

between top jets and bottom jets increased from 2 to 4 (both C1 and C2 ), the space available between jets increases. Hence the size of the vortices between top jets (similarly for bottom jets) increases as shown in Fig. 6(b). The size of vortices that are present on the left and right side of the block is decreased due to the top and bottom jets interactions close to the block. The size of the vortices that are present on either side of top jets (similarly for bottom jets) increases with an increase in center distance between jets. As further center distance incremental (C1 = 6 and C2 = 6) causes more space between top jets (similarly for bottom jets). Hence the size of vortices between top jets (and bottom jets) increases as shown in Fig. 6(c). For C1 = 6 and C2 = 6 the jets directly impinge on corners of a square block, after hitting the corners the jets (top and bottom jets) slightly deflect and interact near to the block in the space available on the left and right side of the block. Due to this phenomenon, the vortices that are present on the left and right side of the block gets compressed to a small size. Fig. 6(d) shows the temperature contours for C1 = 6 and C2 = 6. From Fig. 6(d), the temperature of the fluid in the recircular zones rises more quickly than at other locations due to their rotation. The temperature values are low near the corners of the block because the jets are located onto the corners of the block. The corresponding local Nusselt number variation along the block surfaces is shown in Fig. 7. From Fig. 7(a), the local Nusselt number variation along the top surface of the block for different center distances. For low center distance (C1 = 2 and C2 =2), the maximum Nusselt number is observed a small distance away from the stagnation

block are 21.0, 39.49, 38.03 and 38.5 for the single jet, double jet, 3 jets, and 4 jets respectively. The enhancement of heat transfer is 88%, 81% and 83% for double, three and four jets compared with single jet impingement. Double jet impingement is better in terms of overall heat transfer rate from the block compared with three and four jets. However, the enhancement of the heat transfer rate from the right surface is 49%, 79% and 113.8% for double, three and four jets compared with single jet impingement. Hence 4 jet impingement is preferred for better heat transfer rate from all surfaces of the block. 5.2. Effect of center distance between the jets To know the effect of center distance between jets on flow and heat transfer characteristics, the stream function and temperature contours are shown in Fig. 6 for Re1 = 11000 , Re2 = 11000 , Re3 = 15000 and Re4 = 15000 with 0.048 m square block size. The distance between top jets (or bottom jets) and the block is twice of the jet width. Fig. 6(a) shows the stream function contours of 4 jets impinging on square block for C1 = 2 (center distance between top jets) and C2 = 2 (center distance between bottom jets). Recircular zones observed on either side of jets. The symmetric flow is observed about the y-axis on the left and right side of the block. Two vortices are found between jet1 and jet2 (similarly between jet3 and jet4). Large vortices are found on the left and right sides of the block. These recircular zones formed due to upper and bottom jet flow interactions. The jet flow leaves in tangential direction after impinging top and bottom surfaces. As the center distance 8

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block. It can be seen from Fig. 7(c) and (d). As the center distance increases there is better cooling observed on corners of left and right surfaces. The average Nusselt number values for different center distance between jets are given in Table 1. The average Nusselt numbers over the block are 42.45, 38.425, 73.33 for C2 = 2 , C2 = 4 and C2 = 6 respectively. The enhancement of heat transfer for C1 = 6 and C2 = 6 is 72.74% compared with smaller center distance between jets (C1 = 2 and C2 = 2 ).

point and the minimum value of Nusselt number is found in the middle of the top surface. As the center distance increases from 2 to 4 and 6, the maximum Nusselt number is found near to the corners of the top surface due to the impingement of jets is close to corners and from that location, the Nusselt number decreases towards mid of the top surface. There is a local maximum of Nusselt number is observed at x = 0.4 m on the top surface. The average Nusselt number values on the top surface are 57.5, 44, 41.65 respectively for C1 = 2 , C1 = 4 and C1 = 6 respectively. A similar kind of local Nusselt number variation is observed on the bottom surface as shown in Fig. 7(b) but the maximum value of Nusselt number is observed on the bottom surface compared to the top surface due to high velocities of bottom jets (Re3 = 15000 Re4 = 15000 ). Higher velocities of jet3 and jet4 cause maximum Nusselt number for each and every location on the bottom surface compared to the top surface for the larger center distance between jets compared to lower center distance. There is a local maximum Nusselt number observed on the bottom and top surfaces for Center distance 4 and 6. The average Nusselt numbers on the bottom surface are 70.5, 53.5, 188 for C2 = 2 , C2 = 4 and C2 = 6 respectively. The local Nusselt number variation on the left and right surfaces of the block is shown in Fig. 7(c) and (d). At corners, the maximum Nusselt number is found and the Nusselt number between corners is almost uniform for both the left and right surfaces of the block for C1 = 2 and C2 = 2 . As the center distance increases the local maximum Nusselt number is observed between corners due to the high rotational velocity of vortices that are present on the left and right surface of the

5.3. Effect of block size Fig. 8 shows the effect of block size on flow and heat transfer characteristics for fixed distance between jets and block (B1 = 2 , B2 = 2 ), fixed flow conditions (Re1 = 11000 , Re2 = 15000 , Re3 = 19000 , Re4 = 23000 ) and fixed center distance between jets (C1 = 2 and C2 = 2 ). Fig. 8(a) shows the stream function contours of 4 jet impingement on a small block (Bs = 4 ). Very large recircular zones are formed on either side of top jets. As block size increases the meeting point of jet1 and jet3 moves away from the left surface. It can be seen from Fig. 8(b). It is noticed that the size of the vortices on the left and right side of the block increases with an increase in block size. It can be observed from Fig. 8(b) and (c). The size of the vortices on either side of top jets (and bottom jets) decreases with an increase in block size. For large block size (Bs = 6), the top jets and bottom jets meeting points are not observed on either side of the block. Fig. 8(d) shows the temperature contours of multiple jet impingement on a large block size (Bs = 6). The 9

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Fig. 9. Local Nusselt number distribution on all surfaces of the block for different block sizes.

transfer rate decreases with an increase in block size.

temperature near left and right surfaces of the block are higher than top and bottom surfaces due to presence of the larger recircular zones on either side of the block. The corresponding local Nusselt number variation along the block surfaces for different block sizes is shown in Fig. 9. Fig. 9(a) shows the local Nusselt number variation along the top surface of the block for different block sizes. The minimum and maximum local Nusselt numbers are observed for small block size Bs = 4 . At x = 0.41 m there is a local minimum value of Nusselt number is observed due to the splitting of jet2 at the impingement region. There is a Nusselt number drop observed at the corners for all block sizes. The local Nusselt number is more on the right side of the top surface due to higher jet2 velocity. The local minimum Nusselt number is shifted towards the left side as block size increases. Better cooling is observed at the corners for smaller block sizes due to the jets direct interaction with corners. A similar kind of Nusselt number variation is observed on the bottom surface. It can be seen from Fig. 9(b). Fig. 9(c) and (d) show the Nusselt number variation along the left and right surfaces respectively. For small block size, there is proper cooling is observed at the bottom corner on the left surface of the block due to the high velocity of jet3. As block size increases the Nusselt number at corners decreases and local maximum Nusselt number between corners of the left surface decreases with an increase in block size. A similar kind of variation is observed on the right surface. The Average Nusselt number values for all block sizes are given in Table 1. The average Nusselt number values over the block are 64.32, 54.72 and 50.53 for Bs = 4 , Bs = 5 and Bs = 6 respectively. The heat

5.4. Effect of height between bottom jets and block Fig. 10 shows the stream function contours of 4 jets impingement on block for different height between bottom jets and block for Re1 = 11000 , Re2 = 15000 , Re3 = 15000 , Re4 = 11000 , C1 = 2, C2 = 2 and B1 = 2 . Fig. 10(a) shows stream function contours for B2 = 2 . Vortices found between top jets (and bottom jets). Vortices found on either side of the jets and on both sides of the block. As height increases from B2 = 2 to B2 = 3, the size of the vortices between bottom jets increased due to an increased height between bottom jets and block. It can be seen from Fig. 10(b). As B2 increases the size of the vortices on either side of bottom jets increased and the size and shape of the vortices on the left (and right surface) surface of the block gets altered as shown in Fig. 10(c). The corresponding local Nusselt number variation is shown in Fig. 11. As B2 increases the Nusselt number at jet2 stagnation point increases and Nusselt number decreases near to jet1 location on the top surface of the block as shown in Fig. 11(a). For B2 = 2 the drop in Nusselt number from jet2 location to right corner of the top surface is gradual. Whereas for B2 = 3 and B2 = 4 the drop of Nusselt number is drastic from the jet2 location to the right corner. Fig. 11(b) shows the Nusselt number variation on the bottom surface. As height between bottom jets and block (B2 ) increases the local Nusselt number decreases over the bottom surface except at jet3 stagnation point for B2 = 3. The 10

Thermal Science and Engineering Progress 14 (2019) 100415

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transfer is increased by 72.74% with increase in center distance between jets from C1 = 2 (C2 = 2 ) to C1 = 6 (C2 = 6) due to interaction of jets at corners of left and right surfaces. Hence the larger center distance between the jets is preferred for better enhancement of heat transfer from the block. As block size increases the heat transfer rate decreases from the left and right surfaces of the block due to less interaction of jets with corners of the block. The enhancement of overall heat transfer is 7% with a decrease in height between the block and bottom jets from B2 = 4 to 2 due to high jet impact force and less deflection of jets. The present study is limited to normal jet impingements on the block. Present results would be useful to understand and improve the jet impingement cooling process of food products (square block) in the food industry. Future studies can be extended to 3-dimensional flow and inclined jet impingements on the block.

local maximum is observed on the left side of the bottom surface due to the high velocity of jet3. The Nusselt number variation along the left and right surfaces are shown in Fig. 11(c) and (d). As height increases the Nusselt number between corners on both the surfaces is improved. It is observed that Nusselt number variation from bottom to top on the left surface is similar to Nusselt number variation from top to bottom on the right surface. The average Nusselt number values are given in Table 1. The heat transfer rate decreases with an increase in height between bottom jets and block. 6. Conclusions Flow and heat transfer characteristics of single, double and multiple turbulent jet impingement on a heated square block in a confined channel have been numerically studied and reported here. Stream function, temperature contours and local Nusselt number variation along the block surfaces are reported for different parameters such as single jet, double jet, 3 jets, 4 jets, the center distance between jets, jets to block spacing, block size and Reynolds number. A single jet enhances the heat transfer rate from top surface of the block compared to multiple jets. The overall enhancement of heat transfer is 88%, 81% and 83% for double, three and four jets compared with single jet impingement. The enhancement of heat transfer rate from the right surface is 49%, 79% and 113.8% for double, three and four jets compared with single jet impingement. Hence 4 jet impingement is preferred for better heat transfer rate from all surfaces of the block. The overall heat

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement aaaaaa 11

Thermal Science and Engineering Progress 14 (2019) 100415

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Fig. 11. Local Nusselt number distribution of multiple jet impingement on all surfaces of the block for different heights between block and bottom jets.

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