---
# System prepended metadata

title: Numerical investigation of free jet flow

---

# Numerical investigation of free jet flow

## Simulation setup

### Domain
![](https://i.imgur.com/MdduxTM.jpg)
inlet diameter = 0.03 m
outlet diameter = 0.09 m
upstream length = 1 m
Downstream length = 1 m
step height(h)= 0.03m
Expansion Ratio = 3

### Inlet condition:

Velocity ($U_o$)= 5.2 m/s
Air kinematic viscosity = 1.56*10^-5 m^2/sec
Reynolds no = 10000

### Boundary conditions:
Inlet : Uniform Velocity
outlet: Uniform pressure outlet
wall : noSlip

### Turbulence Model

k epsilon Model is used.
Intensity of turbulence $(I) = 0.16 Re^{-1/8}$
$$K = 1.5 (IU)^2$$
$$\epsilon=\frac{C_{u}^{3/4}k^{3/2}}{0.07D}$$
### Residuals
![](https://i.imgur.com/bcklggf.jpg)

### Grid Independence:
Grid Independece has been done by using 4 types of meshes.
Mesh 1: 37200 cells
Mesh 2: 81200 cells
Mesh 3: 121200 cells
Mesh 4: 209200 cells

Grid independence has been done by comparing velocity profiles for these four cases.Mesh 3 and Mesh 4 gives almost same results.
![](https://i.imgur.com/l5N6kmj.jpg)

## Results

### Flow field Comparison
Comparision of Normalized streamwise velocity profiles
![Comparision of Normalized streamwise velocittyprofiles](https://i.imgur.com/kyPJHhD.jpg)


Normalized Streamwise velocity profiles at different y
> [name=asaurabh] looks ok, but what are the different y?

Here $y/h = 0$ represents the center line.
$y/h = 1$ represents the line that is 30 mm above from the center line.
 $y/h = -1$ represents the line that is 30 mm below from the center line.

![](https://i.imgur.com/V9cwIXO.jpg)
![](https://i.imgur.com/Cj20Hgi.jpg)
![](https://i.imgur.com/GuWOnDj.jpg)

## validation case updated results:
Various plots are plotted at different lines(at $\frac{y}{h}=1$ and $\frac{y}{h}=-1$ ) in x directions versus velocity in x and y directions(represented as U,V respectively)by normalizing with mean velocity.

![](https://i.imgur.com/qvgnOmU.jpg)
![](https://i.imgur.com/EQb5yBZ.jpg)
![](https://i.imgur.com/aU2CW1k.jpg)
![](https://i.imgur.com/seGogpN.jpg)
![](https://i.imgur.com/wizoSk8.jpg)


## Forced Velocity conditions:
### Case1:
### Inlet condition:

> Velocity (U~o~)= 6.34 m/s
> Air kinematic viscosity = 1.56*10^-5 m^2/sec
> Frequency(f) = 260 Hz
forcing period (T)=1/f=0.003846 sec
> Amplitude = 1.16
## Boundary conditions:
Inlet : Sine function Velocity
outlet: Uniform pressure outlet
wall : noSlip

### Model

k epsilon Model is used.

pimpleFoam solver is used.


### Results and Discussion:
The simulations are performed for given inlet conditions by using k-epsilon model.Dawson has done the experiment in open atmosphere. So to neglect the effects of wall the channel height is increased. Vorticity is normalized by mean velocity $\omega ^{*} = \omega D/U_o$. Circulation is normalized as normalized ciruclation $\Gamma^{*}=\Gamma/U_oD.$ The forcing period(T) is inverse of frequency(f). Time is normalized as $t/T$ where $t$ is ranging from $0$ to $T$.

#### Normalized Vorticity contours over a forcing period

![](https://i.imgur.com/06L7TYv.jpg =500x200) t/T=0
![](https://i.imgur.com/AhqF27Y.jpg =500x200) t/T=0.125
![](https://i.imgur.com/rTJwpVH.jpg =500x200) t/T=0.25
![](https://i.imgur.com/GOlLt0J.jpg =500x200) t/T=0.375
![](https://i.imgur.com/uKAy7cs.jpg =500x200) t/T=0.5
![](https://i.imgur.com/wRpQDuB.jpg =500x200) t/T=0.625
![](https://i.imgur.com/fqSuEbY.jpg =500x200) t/T=0.75
![](https://i.imgur.com/IfRFKJs.jpg =500x200) t/T=0.875


#### Dawson's contour


![](https://i.imgur.com/Ft2Grvv.jpg)

##### Normalized Total circulation over a forcing period
Total circulation is circulation of flow field for one cycle.Normalized Total circulation is total circulation normalized by $\Gamma^{*}=\Gamma/U_oD.$
![](https://i.imgur.com/mlQXcD5.jpg)

### case2:

### Inlet condition:

> Velocity (U~o~)= 9.78 m/s
> Re = 6237
> Air kinematic viscosity = 1.56*10^-5 m^2/sec
> Frequency(f) = 150 Hz
forcing period (T)=1/f=0.006666667 sec
> Amplitude = 1.08
### case3:
### Inlet condition:

> Velocity (U~o~)= 6.51s
> Re = 4150
> Air kinematic viscosity = 1.56*10^-5 m^2/sec
> Frequency(f) = 150 Hz
forcing period (T)=1/f=0.006666667 sec
> Amplitude = 1.08


## Boundary conditions:
> Inlet : Sine function velocity
> outlet: Uniform pressure outlet
> wall : Slip

### Model

k epsilon Model is used with turbulence intensity value taken as 10%.
k value is calculated as 1.43 and epsilon value is calculated as 220 for case2.
k value is calculated as 0.64 and epsilon value is calculated as 65 for case3.
## Results and Discussion:
In this case, simulations are performed for the above mentioned  inlet conditions by using different turbulence intensity values(i.e 0.5,1,2,5,10).When Turbulence intensity got increased the results are getting better for these conditions.The total circulation of flow field is compared with the results of experiments with same inlet conditions. Circulation is normalized as normalized ciruclation $\Gamma^{*}=\Gamma/U_oD.$

##### case2




![](https://i.imgur.com/qoH0eY0.jpg)

##### case3
![](https://i.imgur.com/72pgt7K.jpg)
