In the present study, computational details of two parallel plane jets with nozzle separation ratio = 4.25 and Re = 11,000 are presented. A study of the turbulence has also been done. The computational domain size, grid resolution, and different discretization schemes on the predictions are discussed. The existence of a recirculation flow region, a merging region and a combined region in the two parallel plane jets configuration has been predicted qualitatively by model. Power law scheme is used for discretizing the convective terms. Calculations were made using a Power law scheme. A code is used to solve a laminar, two dimensional viscous fluid flow and heat transfer. At the last it is shown that this code is ready to use for modification for mean flow solution of the turbulent two parallel plane jets. The numerical results are compared with the experimental results. Computational details of various mean flow and turbulent parameters are presented and described with separation ratio of 4.25 and Re = 11,000. The results are compared with Nasr and Lai and are found to be in good agreement with it. The two parallel plane jets develop like a single free jet in the combined region. The outer shear layer spreads faster than the inner shear layer in the near field.
A jet is defined as a free or bounded one depending upon the distance of the confining boundaries. When the boundaries (parallel to inlet axis) are sufficiently away from the origin of the jet, it is termed as free jet. A bounded jet will occur when the flow interacts with a parallel wall. It can be classified into three types based on the orientation: (a) Impinging jet aimed toward the boundary; (b) Wall jet where fuid is discharged at the boundary; and (c) Offset jet from a vertical wall of a stagnent pool issuing parallel to a horizontal solid wall. Two parallel plane jets have numerous technological applications such as the gas turbine combustion chamber, the air conditioner unit for automobile, the air curtain unit for refrigerator system, entrainment and mixing processes in boiler, injection systems and so on. In environmental fluid mechanics, an optimum spacing between exhaust stacks (chimneys) is required to dilute disposal plums to a specified level within a given from the chimney. The details of the flow was studied by several authors. The first detail experimental study of the mean flow was reported by Tanaka [
In the present study, the mean velocity and static pressure field is presented for turbulent two parallel plane jets from the numerical study. The performance of the standard k ? ε turbulence model is evaluated for all three zones (converging zone, merging zone and combined zone) Computational details of two parallel plane jets with nozzle separation ratio= 4.25 and Re = 11,000 are presented. Power law scheme is used for discretizing the convective terms. The results are compared with experimental results of Nasr and Lai and are found to be in good agreement with it.
κ − ε Turbulence model is the most common model used in computational fluid dynamics (CFD) to simulate mean flow characteristics for turbulent flow conditions. It is a two equation model which gives a general description of turbulence by means of two transport equations to present the turbulent properties of the flow. This model solves for two variables: κ―the turbulent kinetic energy and ɛ―the rate of dissipation of kinetic energy. The wall functions are used in this model, so the flow in the buffer region is not simulated. This model is very popular in industrial application due to its good convergence rate and relatively low memory requirements.
The flow pattern of the two parallel plane jets is shown in
sub atmospheric pressure region between the jets near the nozzles. The jets draw each other and their trajectories deviate from straight lines because of mutual entrainment of the surrounding fluid.
Continuity equation
∂ U ¯ ∂ x + ∂ V ¯ ∂ y = 0 (1)
X-Momentum equation
∂ ( U ¯ ) 2 ∂ x + ∂ ( U V ¯ ) ∂ y = − 1 ρ ∂ P ¯ ∂ x + ∂ ∂ x [ ( ν + ν t ) ∂ U ¯ ∂ x − 2 3 κ ] + ∂ ∂ y [ ( ν + ν t ) ∂ U ¯ ∂ y ] (2)
Y-Momentum equation
∂ ( U V ¯ ) ∂ x + ∂ ( V ¯ ) 2 ∂ y = − 1 ρ ∂ P ¯ ∂ y + ∂ ∂ x [ ( ν + ν t ) ∂ V ¯ ∂ x ] + ∂ ∂ y [ ( ν + ν t ) ∂ V ¯ ∂ y − 2 3 κ ] (3)
Assumptions made are:
1) Steady turbulence.
2) 2-D flow, flow variations in z-direction is neglected
3) Incompressible flow, i.e. dilation term is neglected.
4) Body forces are neglected.
5) Properties ( µ , ν , ρ ) are assumed to be constant.
6) RANS equations are used for predicting the turbulent flow.
7) Boussinesq assumption is used to link Reynolds stress to velocity gradient.
8) κ − ε Model is used for determining the turbulent viscosity.
Dimensionless variables are as follows
Non-dimensional velocity in X-direction U n ¯ = U ¯ U 0
Non-dimensional velocity in Y-direction V n ¯ = V ¯ V 0
Non-dimensional coordinates X = x ¯ h and Y = y ¯ h
Non-dimensional pressure P n = p − p o ρ U 0 2
Non-dimensional turbulent kinetic energy κ n = κ U 0 2 κ n = κ U 0 2
Non-dimensional kinetic turbulent viscosity ν t , n = ν t ν
Continuity equation
∂ U n ¯ ∂ X + ∂ V n ¯ ∂ Y = 0 (4)
X-Momentum equation
∂ ( U n ¯ ) 2 ∂ X + ∂ ( U n V n ¯ ) ∂ Y = − ∂ ( 2 3 κ + P ¯ ) ∂ X . + 1 R e ∂ [ ( 1 + ν t , n ) ∂ U n ¯ ∂ X ] ∂ X + . 1 R e ∂ [ ( 1 + ν t , n ) ∂ U n ¯ ∂ Y ] ∂ Y (5)
Y-Momentum equation
∂ ( U n V n ¯ ) ∂ X + ∂ ( V n ¯ ) 2 ∂ Y = − ∂ ( 2 3 κ + P ¯ ) ∂ Y . + 1 R e ∂ [ ( 1 + ν t , n ) ∂ V n ¯ ∂ X ] ∂ X + . 1 R e ∂ [ ( 1 + ν t , n ) ∂ V n ¯ ∂ Y ] ∂ Y (6)
Non dimensional boundary conditions are provided as input for solution. A uniform inlet velocity profile was set at the opening. The top and outlet boundaries were set at a constant pressure. The symmetry boundary condition was prescribed at the symmetry plane between the two jets and only half of the flow was simulated. For turbulent kinetic energy equation, boundary condition at noz-
zleexit is κ n = κ U 0 2 = 1.5 I 2 where I a turbulent intensity is, and is equal to 0.02.
Code is run for two parallel plane jets with separation ratio of s / w = 4.25 . The domain length in the x direction was varied from 15 to 30 nozzle widths whereas it was set at 10w or 15w in they direction. The grid size of 151 × 101 is considered for all cases. The standard κ − ε turbulence model with a power law discretization scheme is used. Here the working fluid is air and Reynolds number is 11,000. The results obtained from the code are compared with the experimental solution by Nasr and Lai.
The distribution of the non-dimensional mean stream-wise velocity along the x axis [ U c U 0 ] is shown in
maximum value. Downstream from the combined point, in the combined region, the two individual jets combine to resemble a single free jet flow. Mean stream-wise velocity along the plane of symmetry for s / w = 4.25 , is compared
with the experimental results of Nasr and Lai. That shows the little difference in the deviation from the experimental results.
The distribution of lateral turbulence intensities are shown in
It is defined as the lateral distance from x axis to the point where U is equal to Umax.
Half velocity points are the lateral distances from the x axis to the points where the mean stream-wise velocity (U) is half of its local maximum mean stream wise velocity (Umax) in the outer and innershear layers, respectively.
shows that in the converging region, y − 1 2 and y + 1 2 have been reasonably well predicted by κ − ε model as observed in Nasr results. However in the merging and combined region, y + 1 2 in the outer shear layer has been unpredicted. Furthermore, it is expected that as the inner shear layers of the two jets merge to form a single jet down stream of the merging point, ymax rapidly approaches y − 1 2 .
The contour of static pressure computed by the κ − ε model is shown in
Contour of turbulence kinetic energy κ computed by the κ − ε model is shown in
The standard κ − ε turbulence model for two parallel plane jets of a small nozzle separation ratio of4.25 with a nozzle exit Reynolds number of 11,000 have been made. The recirculation flow, converging, merging and combined regions have been identified. The existence of negative and positive gauge static pressure zones on both sides of the merging point is also identified.
Mohapatra, R.C. (2017) Prediction on Turbulent Flow of Two Parallel Plane Jets Using κ − ε Model. Open Access Library Journal, 4: e3291. https://doi.org/10.4236/oalib.1103291