Flow Over Forward Facing Step Biology Essay

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The flow over forward facing step helps to analyse the foremost fluid flow behaviour which can typically occur. The aspects typically are separation of fluid flow from laminar to turbulent nature. Here we analyse the solution with and without abstract which produce flow separation, reattachment patterns and recirculation of stream flow. Some numerical methods on the analysis of CFD problem concerning on Turbulent Forward Facing Model is studied & considerable investigations is carried out. A similar Forward Facing Step geometry is constructed & turbulence is checked using 2 algorithms such as k- Epsilon: 2 equation turbulence Model and Spallart & Allmaras one equation. Both the turbulent models are implemented using 5% and 10% tolerance values.

First we generate the geometry in Ansys workbench and appropriately meshed for calculate grid independence solution which doesn't changed if we refined mesh. The analysis is extended to 3-dimensional mesh as well. The 3-D geometry is meshed by sweep and inflation, solved in Fluent by using the fluid properties like density, viscosity, inlet velocity and Raynolds number, using k-epsilon turbulent model and Spallart & Allmaras.

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From the data conferred using the investigated literature, a paralleled speculation is drawn & related, & from this, the results are compared using the current solution.

Introduction:

Computational Fluid Dynamics is the study of fluid behaviour which is influenced by its changing parameters. Forward facing step help us to realize about the various flow parameters of the fluid such as velocity, pressure, turbulence. The basic objective of doing a CFD analysis is to identify the geometry of the passage or body concerned through which the fluid has to pass through. Then, the geometry is appropriately meshed, so that its particle behaviour can be studied. From this, the general flow can be identified which further attributes the fluid nature. Studying about flow parameters play a vital role in various engineering applications such as air conditioning, piping designs, heat exchangers etc

Even though, there are lot of researches and numerical experimental had been carried by various researchers earlier regarding CFD and forward facing step, to explain the concept of grid independence, boundary layer and convergence. Few of them are, Michael John Sherry, David Lo Jacono, and John Sheridan experimentally proved flow separation by using particle image velocimetry and pressure tapping with wild rane of Reynolds number for Forward facing step for turbulence boundary layer. The experiments perform by using two facilities one is recirculation water channel for particle image velocimetry study and another by using low speed boundary layer wind tunnel for pressure measurement. The recirculation region range using the PIV results were resolute by calculating the streamlines above the surface. Finally they investigated using the particle image velocimetry technique and concluded that the offset between results at the same Reynolds number is due to a combined effect of the upstream flow conditions, predominantly the boundary layer thickness and body geometry effects. And they found pressure distribution also similar to which found previously on similar geometry. Most importantly analysis that found was the reduction in minimum pressure due to turbulent mixing within the boundary layer for flows with a δ/h (step height) ratio greater than one.

Gackstatter and Tropea (1984) experiment concluded on the flow over an obstacle mounted in a channel, flow is a characteristics of the Reynolds number, blockage ratio and length-to height ratio. The experiments were conducted in a fully developed path for a Reynolds number range 150< Re 4500 (depends on the obstacle height h). Three blockage ratios were employed 4; 2 and 1.33 regarding the effect of Reynolds number. They concluded about the three characteristic regions. The laminar region - characterised by a steady increase of xR/h with Reynolds number; the transitional region - identified by an abrupt reduction in xR/h in some cases, a partial recovery; and a turbulent region - in which xR/ h does not change characteristic, but these results not enough to clarify the problem.

DESCRIPTION OF PROBLEM

The mean of this report is to perform various simulations about the forward facing step and understand the flow characteristics. We used ANSYS workbench for the creation of Geometry, meshing and grid generation etc., and used ANSYS FLUENT for defining the boundary conditions, input flow parameters, description of material properties, monitoring the observations and plotting the results, and comparing with available experiment and numerical data.

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The schematic of the given geometry is as follows. (Fig. 1). The flow of the fluid should satisfy the Reynolds number which is dependent on the channel length (H), viscosity (μ) and the density of the fluid (ƿ). According to the problem, a fluid flows with uniform velocity Ui inside the channel having the step Height H with the Reynolds number.

(Figure.1 Schematic diagram of the flow)

Geometry:

According to given data first geometry created in workbench. By using given dimensions 2D geometry formed in X-Yplane. Then extrude in z direction the geometry to convert 2D into 3D

2D figure of channel without obstacle.

having 1mm thickness because workbench can only accept three dimensional geometries so that we require to give thickness for geometry. Same geometry further refine for solving problem with obstacle.

Fig 2.1 shows 3d geometry.

3D figure without obstacle.

Grid Generation.

Grid generation plays a vital role in the computational fluid dynamics. For getting finer solution and improvement in quality you must go for the superior grid formation and solution become efficient when using well constructed mesh. So that it's important to choose grid generation method for the particular problem in.

Mostly three techniques are commonly used in CFD i.e structured Grid method, unstructured grid method and Hybrid grid method. For this problem we are using unstructured grid method. Unstructured grid methods utilize a random collection of elements to fill the domain. Because the arrangement of elements has no distinct pattern, the mesh is called unstructured. These types of grids normally use triangles in 2D and tetrahedral in 3D. For a superior CAD model a good mesher automatically place triangles on the surface and for volume its tetrahedral.

The advantage of unstructured grid methods is that they are much automated and, therefore, require little user time or effort. The user need not worry about laying out block structure or connections. Additionally, unstructured grid methods are well.

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. Sweep method is used for linking the side faces. 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 are 10 from the edges or boundaries, because this is the area where the analysis is done.

Fig :are dila

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 5 mm in x-direction and 10 mm in y-direction from the global co-ordinates.

Fig 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 channel. To get more accurate solution, the mesh generated near the step is very fine because this is the area where the turbulence is created in the area surrounding the step. That is why the mesh near the step is very fine. Mesh is such that it is finest near the step and becomes coarser as the radius of the sphere of influence ends.

Boundary conditions:

It is very crucial to define the boundary conditions of the forward facing step channel in order to perform the study. The geometry given has an inlet which is the velocity-inlet (8H) and at the opposite end fluid outflow is defined as pressure-outlet (7H) and the step Height (H) for case (1) and same problem with obstacle having 0.2H x 0.2H in case (2) with Reynolds number equal to 5000. Boundaries of the geometry consider as a Wall. The front surface and back surface perpendicular to z axis is call symmetry.

Assumptions Made:

If the velocity & density of the fluid, together with the step height is assumed, then the other quantity i.e. viscosity can be calculated. Alternatively, one of the fluids can be used which is readily available in the Fluent database. The process is isothermal so the temperature remains constant throughout the flow. We assumed Air as the fluid that is flowing inside the channel

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We consider the value of H=0.1m

I.e. Step Height = 0.1m

Hence, Velocity Inlet Height = 0.8m

Pressure Outlet Height = 0.7m

The specification of the fluid chosen is governed by the Reynolds's number. Therefore, by the Reynolds's number,

R = ƿ x Ui x H / μ = 5000

Fluid flowing through the channel: Air

Where, ƿ is the density of the fluid i.e. air =1.225 kg/m³

μ is the viscosity, which is 1.7894e-5 Ns/m2

Since the step height is 0.1m & the Reynolds's number is 5000.

Velocity of the fluid (Ui) =(R x μ) / (ƿ x H)

Velocity of the fluid, Ui = 7.3 m/s

Therefore, the velocity is calculated to be Ui= 7.3m/s

Hydraulic Diameter

For inlet

Dh= 4A/Pw = 1.975mm

For outlet

Dh= 4A/Pw = 1.971mm

Pw= weighted perimeter

A= Cross sectional area.

Consider Turbulent Intensity (k) = 10%

In Fluent, the following is performed:

The grid is checked.

Its materials property is defined, as to which fluid is chosen to pass through the subjected geometry

The Viscous under Control, which is the turbulent model, is selected as either to be Spallart-Allmaras or k-epsilon.

Next, the boundary conditions are defined. In this, the concerned fluid is selected as the fluid medium.

For this geometry, the hydraulic diameter at the inlet is found to be, 1.975mm While for the outlet, it is 1.971mm

Under, Solve à Initialize menu, the solution is initialized from inlet. Side prevailing conditions

The solution is then tried for iterations to until 250

In the mean-time, a monitor for residual is checked for continuity, energy, k & epsilon.

A surface monitor is opened up for checking the convergence of static pressure at the inlet side.

Next SolveàIterate.

We get proper scaled residuals with iterations worked up to second-ordered accuracy.

Investigation Required:

To analyze and discuss about the convergence and Grid Independence criteria.

To perform analysis using the realisable k-ε two equations and Spallart & Allmaras One Equation.

To analyze and compare the results with and without obstacle.

All the above simulations and results needs to be compared with the experimental analysis that had been performed on the forward facing step earlier.

GRID INDEPENDENCE

Grid Independence can be defined as the number of smaller unit spaces used, to improve the accuracy of the results. Higher the geometry is meshed, to a degree of being 'fine', higher is the possibility of grid independence. For determining Reattached Length Creation of the grids is one of the important factors in computational fluid dynamics. The common CFD technique is to start out with a coarse meshed geometry, and then slowly proceed with finer meshes, unless the results are lesser than the pre-defined acceptable error. According to Jiyuan Tu, Gaun Heng Yoeh, Chaoqun Liu [Ref 2], one of the best method to get accurate reattachment length is, to generate the mesh with finer grids than the previous one to observe reattachment length and stop once you don't find any significant change with the reattachment length than the previous mesh, then only grids are to be supposed grid independent.

For solving a problem for forward facing step we created with sequentially refined grids. From the table, it is proved that when we make the grids finer and finer we used to get closer result of the reattachment length.

For analysis of velocity profile and pressure profile for different grid sizes we have to draw a line at distance of 5 mm from the step line A.

Velocity and Pressure profile

Velocity profile before the step without obstacle

Fig.AB. shows velocity profiles before the forward facing step for different grids. Light blue curve is the coarser grid with 13234 grid points(faces); red curve is for the more refined grid of 19852 mesh faces and green curve is for 33722 mesh points(faces).From the fig AB we are able to view that the velocity is zero initially, but a significant increase is seen in velocity in the turbulent region.

After the mesh faces 19852 the variation in the solution has stopped. So, more refinement of the grid after 19852 is not required, because at this mesh faces the solutions becomes grid independent and the solution doesn't vary further.

Pressure profile before the step without obstacle

As pressure and velocity are inversely proportional, so the pressure is maximum at close to wall, whereas the velocity is minimum close to the walls. In the fig .ab we are able to observe that, the profiles are varying from each other.

Solution is to be found stable for the blue curve with mesh faces 19852 and the red with 29644 and thus grid independence is achieved. In this case further refinement of grid 19852 is not

required. By selecting this grid of 19852, we can save computational time required.

Velocity profile after the step without obstacle

Fig.AB. 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 in the case of without obstacle.

To conclude, Red curve is for 19852 grid points (faces) is selected. Because further refinement doesn't make any difference to curve i.e. solution becomes grid independence.

Pressure profile after the step without obstacle

. In the fig .ab we are able to observe that, the profiles are varying from each other. Solution is to be found stable for the green curve with mesh faces 33722 and the red with 19852 and thus grid independence is achieved. In this case further refinement of grid 19852 is not

required. By selecting this grid of 19852, we can save computational time required.

Convergence Criterion:

Convergence defines as limiting behavior, particularly of an infinite sequence toward some limit. Mostly CFD problems in general are non-linear, and the solution techniques use an iterative process to successively improve a solution, until 'convergence' is reached. As this definition indicates, the exact solution to the iterative problem is unknown, but want to be sufficiently close to the solution for a particular required level of accuracy. Convergence therefore does need to be associated with a requirement for a particular level of accuracy. This requirement depends upon the purpose to which the solution will be applied.

Convergence is also define by the level of residuals, the amount by which discredited equations are not satisfied, and not by the error in the solution.In short convergence is a numerical method property which gives solution such that there is no much variation in the results. And the iteration continues till zero. Convergence of values occurs when, continuity, equation, k-epsilon, gives the same output for a particular iteration. The iterations are carried on, till the values obtained no longer show any change from the previous value.

[Ref: 4]. In this problem we have plotted the convergence graph for Realizable K-ε two Equations (see figure 4.3.2) and Spallart-Allmaras one Equation

Velocities in x, y directions, Turbulent Kinetic Energy (k), continuity equations are taken into consideration for convergence plot. From the figure, the convergence plot lies in the range from 1e+00 to 1e-16 which is quiet acceptable with the experimental results.

Above figure shoes the iterative solutions of first order and second order convergence. For the first order equation solution gets converge at 1250 iterations. For more accurate result, further iterations are done by having second order equation and it is plainly seen that the residual has been reached the same level. Similarly the entire convergence graph that has been plotted resembles the same profile. From this I conclude that after iteration of the first and second order discretization the graph gets converged.

Comparison of k--ε two equations and Spallart Allmaras Eqn:

Partial differential equations play a key role in turbulence modelling, because the mixing length L and eddy-viscosity were based on that. But later on they are defined in terms of algebraic equations or in terms of a combination of algebraic and differential equations and this lead to terminology involving the number of differential equations. This can be observe in terms of zero, one and two differential equations. Here, we concentrate on the Realizable K-ε for two equations and Spallart-Allmaras for one Equation.

K-ε Equation defines Eddy viscosity with two transport equation for turbulent energy (k) and its rate of dissipation (ε).[Ref.5] Spallart-Allmaras Equation defines to define Eddy Viscosity with a single transport equation and hence it is popular for wall boundary-layer and free-shear flows and is used in both boundary-layer and Navier-Stokes methods.

Hence it is very essential is to discuss about how the reattachment length is affected by the above different equation models. In this project, we compare them by creating the structured grids (no. of grids = 13234), two different readings are taken for Spallart-Allmaras Equation and K-ε two equations separately and they are plotted below for comparison. (See figure 4.4.1)

Significance and Comparison of Y+ Value:

Y+ often used to describe how coarse or fine a mesh is for a particular flow pattern. y+ is a non-dimensional distance. It is important in turbulence modelling to determine the proper size of the cells near domain walls. The turbulence model wall laws have restrictions on the y+ value at the wall. For instance, the standard K-epsilon model requires a wall y+ value between approximately 40 and 400. A faster flow near the wall will produce higher values of y+, so the grid size near the wall must be reduced.

Main intend of this project is to analyze the value of Y+. In this problem, by keeping the length of the channel Y = 195mm, the value of Y+ is plotted against the wall. From

The definition of y+ for the K-e model is defined as follows:

Y+ = U*y/ μ

Where, μ is the velocity at the nearest wall, is the distance to the nearest wall and is the viscosity of the fluid. Is often referred to simply as y plus and is commonly used in boundary layer theory and in defining the law of the wall.

the figure ---, it seems that value of Y+ varies between 40 and 90 which is quiet not acceptable while compared with the experimental results for turbulent flow. The value of Y+ must lie between 40 and 400. But here we assumed that Reynolds number 5000 and according to calculation velocity of fluid is 7.3 m/s. For getting Y+ value in between standard range 40-400 the Reynolds number must be more than 5000 so we get increased velocity.