Turbulent Flow Over A Forward Facing Step Biology Essay

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The study deals with a comparative study to analyse the fluid flow behaviour which can occur in the domain. Comparison is done between the experimental data and computational fluid dynamics results. CFD method is used to solve a forward facing step problem with and without a obstacle. The domain is modelled and analysed in FLUENT to obtain further understanding of the flow parameters and to access the computational methods employed to model the relevant physics of the experiment.

A general understanding of CFD is studied and considerable research is carried out. The domain is studied in Spallart and Almaras one equation and k-epsilon: 2 equation turbulence methods. Comparison is then made with existing experiment to confirm CFD‟s results and flow in the domain.

Concept of convergence, grid independent solution with literature review is carried out. Results obtained from both are discussed to examine validation of CFD methods which must satisfy flow parameters like inlet velocity, Reynolds number, density and viscosity.

A turbulent flow flowing through several types of paths causes an increase in friction of flow and disturbance in transportation of scalar, this often occurs in fluid machinery, and in the atmosphere, etc. This occurs due to the reattachment and separation of turbulent flow. This friction in fluid machinery leads to energy loss in the fluid, also disturbance in transportation of scalar results into variation in flow parameters. Thus, to improve mechanical efficiency, this flow friction within the path should be reduced.

Recently, detailed investigation on the flow with several effects is done by studying turbulent characteristics, and the performance is predicted for turbulence a model which was evaluated using Computational fluid dynamics in order to improve the turbulence model for prediction of turbulent flows. For gaining detailed knowledge of turbulent flow with reattachment and separation, CFD study must be carried out for more complicated turbulence models such as turbulent flow over an obstacle which is to be modelled as the typical flow in a complex flow field and it causes flow reattachment of separation, in order to understand transport phenomena over there. Because, this detailed turbulent phenomena, flow properties and structures of forward facing step (FFS), flow should be studied for determining the fundamental characteristics of turbulent flow with reattachment and separation.

Actually flow is a characteristic of the obstacle age ratio, Reynolds number and length-to height ratio. The experiments which were conducted in completely developed path for a Reynolds number range 150< Re 4500 (depends on the obstacle height h). Three obstacle age ratios were employed 4; 2 and 1.33 regarding the outcome of Reynolds number. Conclusion was done for three characteristic regions. They concluded about the three characteristic regions. First is laminar region - characterised by a steady increase of xR/h with Reynolds number; second is the transitional region - recognized by an abrupt reduction in xR/h in few cases, a partial recovery; and a turbulent region - in which xR/ h does not vary characteristic, but these results are not sufficient to explain the problem.

The basic aim of this analysis is to investigate turbulent flow over a forward-facing step. CFD is a very powerful tool with wide variety of applications, with which we can determine detailed turbulence phenomena along with experimental techniques. A forward facing step is similar to a vehicle being tested in wind tunnels. However, it is difficult to construct physical model to investigate flows over complex geometries like vehicle bodies, aeroplanes, turbo-machineries etc., since it requires huge capital investment to test the object's geometry. Thus, a computational analysis of the turbulent flow over a forward-facing step (FFS) is carried out to examine and obtain detailed data of the effect of the forward-facing step using given Reynolds number for the flow. In particular, flow parameters near the step in the first case and with that of the obstacle case are selectively explored.

2. Description of the problem

We have to perform CFD simulationf on turbulent flow for a forward facing step (FFS) of the channel and also for the channel which consists of a obstacle located in the channel. Analysis of the results of both the geometry is to be done. Comparison of the results is to be made with the experimental data provided.

2.1 Geometry

Figure : 3 Dimensional domain of selected geometry

The modelling of the channel according to the dimensions is done using ANSYS-Workbench. The model is created in x-y plane in the 2d form, and extruded in z-direction by 1 mm to obtain the 3D geometry of the domain.

The domain is classified as follows.

Case I: Domain without obstacle.

Case II: Domain with obstacle.

To study and compare internal flow from the inlet of the channel to the outlet of the channel with an obstruction in the form of a step in the channel.

Figure : Case I: domain without obstacle

Figure : Case II: domain with obstacle

A laminar flow enters the inlet of the channel or duct with an velocity of 7.3 m/s which is calculated from the Reynolds number 5000 (given).In this case the step height (H) is of

10 mm which is assumed. The fluid enters in the laminar form in the inlet of the channel which is larger in diameter compared to the outlet diameter and it strikes the step situated in between the channel.

Mainly, the requirement is to model the flow through the channel using single passage to analyse periodic boundaries. Following figure show the setup fig. 4.

2.2 Boundary Conditions

Figure : Boundary conditions for FFS

Boundaries of the geometry are assigned as walls which also includes forward facing step. There is friction created at this wall due to the viscosity and momentum of the fluid which is considered as air. In this geometry there are 4 walls to be undertaken for consideration out of which one is the forward facing step. The inlet where the fluid enters along the X-axis has been taken as velocity inlet and the outlet of the channel is taken as pressure outlet. As the geometry under consideration is 3-d, the front surface and backward surface are linked together which are perpendicular to the Z-axis and they are assigned as Symmetry

In Case II, the whole geometry is same the only difference in the second geometry is it consists of a obstacle of width 0.2H x 0.2H and at a distance of 2H before the forward facing step(FFS). The obstacle boundary is also considered as wall only.

Reynolds number given is 5000 and the velocity calculated comes to be 1.975m/s.

2.3 Numerical investigations of forward facing step

Medium: Air

Velocity of air (Ui).

Re =

Re = Reynolds number = 5000 (given)

H = 10 mm (assumed)

Ui = Velocity of air

= Density = 1.225 kg/m3

µ = Viscosity = 1.7894 x e-5 N-s/m2

Calculating from the velocity from the above equation we get,

Ui = 7.3 m/s

To find hydraulic diameter of 3-d geometry at inlet.

DH =

H = height= 80 mm

t = Thickness = 1 mm

A = Area of cross-section = height(h)x thickness(t)

Pw = Wetted perimeter = 2x[height x thickness(t)]

DH = 1.975 mm

2.4 Assumptions

Air is assumed as the fluid medium. Assumptions are made on the basis that the geometry is appropriately designed and dimensioned. There is no damage or deformation in the stage of designing and even in the stage of analyzing.

Once the mesh generation of the geometry is completed in Ansys workbench it is imported to the fluent. For the best grid Spallart and Almaras one - equation is used mostly. K-É› two- equation turbulence model is used for standard wall functions and maximum analysis is done in it.

Reynolds number

5000

Inlet velocity

1.975mm

Table : Inlet conditions

Firstly the fluid medium is assumed to be air and it is incompressible in nature i.e. its density does not change along the channel. Inlet and outlet temperature is assumed to be equal. To mention the boundary condition at the inlet, the inlet velocity is calculated and it comes to be 7.3 m/s and it does not vary along the z-direction. Reynolds number given (Re) is 5000.The hydraulic diameter at the inlet in the case of 3-d geometry comes to be 1.975 mm at the inlet.

3. Grid generation

Selection of grid is plays a vital role in CFD solution. Also, depends a lot on the quality of grid solution. Meshes are distinguished by connectivity of points.

The meshes that have regular connectivity are called structured meshes that mean that each point has the same number of neighbours. On the other hand, meshes which consist of irregular connectivity where each point can have a different number of neighbours are called unstructured meshes. Usually, "structured geometries are used to solve regular or simple geometries and for complex geometries unstructured meshes are used."

In general, geometry of the channel is found to be complex just near the forward facing step and after this step the geometry does not change. Even in the geometry of channel with a obstacle, the shape of obstacle is critical and the forward facing step. Hence because of the critical areas in both geometries, unstructured meshes are selected for the purpose of meshing.

3.1 Grid generation for FFS

Grid generation in 3-dimensional case is done considering the aspect to generate coarser grid so that the software limitations in reading number of mesh faces and longer computing time can be avoided.

In this case 3D grids are generated by linking side wall faces. Firstly for linking the side wall faces, sweep method is used. As the thickness does not make considerable effect, sweep number divisions are taken 2 only. Further inflation of the method is done, in which the boundaries are selected. In the figure below the number of layers taken is 10 from the edges.

Figure : exagarated view of mesh generated

Figure : Detailed view of the highlighted area of fig5

As the critical area for analysis is near the forward facing step, a fine mesh is required near the step. Because of which sphere of influence is introduced, and its centre is eccentric at the distance of 5 mm in x-direction and 10 mm in y-direction from the global co-ordinates.

Fig.6 shows the detail view of the boundary layers and sphere of influence for the critical area for analysis, used at the leading edge of the domain. To get more accurate solution, the mesh generated near the step is very fine because this is the area where the turbulence is created. Mesh is such that it is finest near the step and becomes coarser as the radius of the sphere of Influence ends.

4. Demonstration of Convergence

Convergence means a point, when the numerical solution must approach towards the exact solution of differential equation.

Usually in practical situations an evidence at solution is converging to the exact solution is converging to the exact solution is difficult because the exact solution is unknown and the aim of the numerical approach is to gain a solution which is not possible analytically. (Sayma, 2009)

This feature of convergence is various for various types of numerical methods like commonly used grid independence, iterative procedures, pseudo time stepping.

Considering this channel case, calculations are performed using iterative procedures in which the residuals are monitored. This are difference between the solution at a particular iteration and the next iteration for steady type of problems. Solution is converged when this residuals approaches to zero. This in actually represents that the solution to the system of discretised algebraic equations has been obtained. It is not always compulsory that the solution is converged to the exact solution. (Sayma, 2009)

4.1 Discussion over domain geometry analysis:

This can be viewed in various ways, but generally it is done when the mass flow rate and Velocity is equal at the inlet and outlet and all the residuals are levelled where the slope is zero. From the following figure concept of convergence is explained.

following figure the concept of convergence can be explained.

Figure : Residuals of K-É› solution for channel

Above figure represents two iterative solutions of the 3-D channel geometry.1st calculation is done using first order till the convergence is achieved. It is visible that the solution gets converged at 1000 iterations. Then the same is iterated for the second order equation The solution is iterated for 3000 iterations. It can be seen all residuals have levelled off. This represents that convergence is complete.

5. Grid independence

For any solution, grid plays a crucial role to reveal the quality and accuracy of the result. This is an substitute and most commonly method used to explain the concept of convergence.

For a particular case, suppose the calculations are carried out using certain number of grid points, say "n" then result out for the flow variables at these grid points may be adequate. But, suppose the same case is calculated roughly using one and half or twice the number of grid points that were previously used (1.5n / 2n) then the results for the same flow variables may be somewhat different or may be found to be more accurate as the grid becomes more finer. If the solution is still varying when the grid is varied that represents it is a function of number of grid points. In this type of case, grid points must be increased until the solution which is no longer sensitive of grid points is reached, by this way the grid independence can be achieved. (Anderson, 1995)

The effect of grid density can be more significant. This can be analysed by results below. In this particular case where it is essential to estimate the internal flow of channel, we have generated unstructured 3D grids having boundary layers along the wall surface with different number of grid points. We have analysed them on the basis of number of grid points present in mesh of the geometry. Following are the parameters over which the grid independence is achieved,

1. Velocity profile.

2. Pressure profile.

3. Reynolds number and Mass flow rate.

In this problem particularly, a turbulent flow is generated just near the forward facing step in the geometry of without obstacle. The velocity retards in channel after it pases the step. Similarly in the geometry with obstacle, the turbulent flow is generated near the obstacle and the velocity also retards after it passes the forward facing step. To explain shortly, after the turbulence is created due to some disturbance and the velocity retards after some distance in the channel after passing the obstacle in its flow path.

Two vertical lines are drawn one before the step and the other after the step. At both this lines the velocity and pressure profile are checked and the discussion are as follows.

Velocity profile before step in the geometry without obstacle.

Figure : Line drawn at a distance of -5mm before the step

A line is drawn before the forward facing step for the purpose of analysis of velocity profiles and pressure profiles for different grid sizes at 5mm.

Figure : velocity profile at a distance of -5mm from the step

Fig.9 shows velocity profiles before the forward facing step for different grids. Blue curve is the coarser grid with 12456 grid points; red curve is for the more refined grid of 17348 mesh faces and green curve is for more fine 29644 grid points. From the fig.9 we are able to view that the velocity is negligible initially, but a significant increase is seen in velocity near the corner of FFS. After the grid points 17348 the variation in the solution has stopped. So, more refinement of the grid after 17348 is not required, because at this mesh faces the solutions becomes grid independent and the solution doesn't vary further.

5.2 Pressure profile before step in the geometry without obstacle.

Figure : pressure profile at a distance of -5mm from the step

As velocity and pressure are inversely proportional, since the velocity is minimum at close to wall, whereas the pressure is maximum close to the walls. In the fig.10 we are able to observe that, the profiles are varying from each other. Solution is to be found unstable for the red curve with mesh faces 17348 and the green curve with 29644 and thus grid independence is not achieved completely even for the finest mesh. It can be seen that the grid independence is quiet difficult to achieve practically. (Anderson, 1995)

5.3 Velocity profile after the step in the geometry without obstacle:

Figure : Line drawn at a distance of 5mm after the step

Figure : velocity profile at a distance of 5mm from the step

Fig.12 shows velocity profiles after the forward facing step for different grids.

Similar is the case for analysis, the only difference is that the line is drawn after the step in the domain. According to the discussion above regarding grid independence in the case of without obstacle. To conclude, Red curve is for 17348 grid points is selected. Because further refinement doesn't make any difference to curve i.e. solution is grid independent.

5.4 Pressure profile after step in the geometry without obstacle.

Figure : pressure profile at a distance of 5mm from the step

As velocity and pressure are inversely proportional, since the velocity is minimum at close to wall, whereas the pressure is maximum close to the walls. In the fig.13 we are able to observe that, the profiles are varying from each other. Solution is to be found stable for the red curve with mesh faces 17348 and the green curve with 29644 and thus grid independence is achieved.

6.1 Results and discussion.

In any exercise this is the most critical part. Here, we are going to discuss the computational results obtained by CFD and the experimental results provided for the same type of circumstances that are considered. In this the contours of pressure, velocity are discussed with that of the experimental data. Also comparison is made between the two cases with and without obstacle, on the basis turbulence bubbles, velocity and pressure profiles.

6.1 CASE I: Domain without obstacle

6.1.1 Velocity contours of the domain

Figure : contours of velocity variation

In the fig.14. it can be observed that the velocity from the inlet remains constant till FFS. As the fluid strikes the step, a closed turbulence bubble is created downstream of the step and also a longitudinal bubble is created upstream, visible in blue colour. These bubbles are contours of velocity magnitude in meter/seconds. The red bubble near the corner of FFS shows that more disturbance is created in laminar flow after striking . Here the velocity is maximum and its value is 11.2m/s, further velocity retards which visible is by yellow colour. Velocity is minimum at the walls because of the friction created by fluid on the walls.

6.1.2 Pressure Contours of the domain

Figure : contours of pressure variation

The fig.15 show exactly opposite of the data of fig14 i.e. of velocity contours. Here static pressure is maximum just at the step and its value is 37 Pascal i.e. downstream, which is visible by red area and minimum after the step represented by dark blue colour. On the other hand the velocity is minimum where the pressure is maximum, which shows the inverse relationship between velocity and pressure.

6.2 CASE II: Domain with obstacle

6.2.1 Velocity contours of the domain

Figure : contours of velocity variation

From the fig 17 it is observed that the fluid strikes the obstacle, due to which the turbulence bubble is created downstream just after the obstacle. Turbulence bubble is visible in dark blue colour before the FFS. The main difference to be noted here is that there is no other turbulence bubble upstream of FFS which is because of the introduction of obstacle and also the velocity starts retarding just after the obstacle and no significant disturbance in the flow is created at the FFS.

6.2.2 Pressure contours of the domain

Figure : contours of pressure variation

The fig.18 show exactly opposite of the data of fig.17 i.e. of velocity contours. Here static pressure is maximum just near the area of obstacle, which is visible by red area and minimum at the corner of step. On the other hand the velocity is minimum where the pressure is maximum, which show the inverse relationship between velocity and pressure. In this case significant pressure is not created at FFS, due to presence of obstacle.

6.4. Comparison of the domain in Case I and Case II on the basis of streamlines

Figure : Velocity streamlines of the domain in both cases

Case I Case II

As seen in fig3 it shows the difference in turbulence region which is created due to change in geometry.

In the case I, it's visible that two closed turbulent bubbles are created a small-one downstream and the bigger one upstream of FFS represented by blue lines. Whereas, in case II only one closed turbulent bubble is created after the obstacle. It can be observed by introduction of obstacle made in case II, helps to reduce the turbulence region which is created upstream of FFS. In Case II velocity retardation starts just after the obstacle which is visible in light blue colour.

To describe briefly, velocity starts reducing earlier in case II and and the flow of fluid is not disturbed as significantly as in case I.

Comparison between experimental and literature data :

6.3 Importance of y+ value

Y+ is a non-dimensional distance. Mostly it is used for the purpose to describe how coarse or fine a mesh should be for a particular flow pattern. It's importance comes into play when while determining the proper size of the cell near domain walls. The turbulence model wall laws have restriction on y+ values and they are model requires a wall y+ value between 40 and 400 approximately.

Defination of y+ for the k- É› model is defined as follows.

Y+ =

Figure : Y+ values plot

For the flow without obstacle, the value of wall y+ obtained is found to be 6.4. Although, it does not lie in the recommended range of 40 - 400 but like mentioned earlier, grid spacing is not the only parameter which affects this value. For the present case, the value of Reynolds number considered is 5000 which is less than what is encountered usually in turbulent flows, so as a outcome the inlet velocity is affected and also the y+ value. So, because of this it is difficult to keep the y+ value in the recommended range.

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