Flow simulation in SOLIDWORKS for different Reynolds number

AIM: Study pipe flow simulation for various Reynold numbers.

OBJECTIVES: Perform pipe flow simulation with an inlet Reynolds number 100,1000 and 10,000 & for each case

1. Place line probes at 95%, 90% and 85% of the pipe length.
2. Compare the normalized velocity profile at each of these locations
3. Normalize the velocity profile by the inlet velocity.

THEORY:

Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.

Boundary conditions in fluid dynamics are the set of constraints to boundary value problems in computational fluid dynamics. These boundary conditions include inlet boundary conditions, outlet boundary conditions, wall boundary conditions, constant pressure boundary conditions, axisymmetric boundary conditions, symmetric boundary conditions, and periodic or cyclic boundary conditions.

Transient problems require one more thing i.e., initial conditions where initial values of flow variables are specified at nodes in the flow domain. Various types of boundary conditions are used in CFD for different conditions and purposes

Velocity profile is a graph of the speed of a fluid flow as a function of distance perpendicular to the direction of flow.

GOVERNING EQUATION:

The Reynolds number (Re) is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations.

The Reynolds number is defined as

`"Reynolds number" (Re)= (ρuD)/μ=(uD)/v`

where:

• ρ is the densityof the fluid (SI units: kg/m3)
• u is the flow speed(m/s)
• D is the diameter of the tube (m)
• μ is the dynamic viscosityof the fluid (Pa·s or N·s/m2 or kg/(m·s))
• ν is the kinematic viscosityof the fluid (m2/s).

From the above formula, velocity at a particular Reynold Number can be calculated by putting the values as ρ = 1000kg/m3, D = 0.05 m, μ = 0.0017914 Ns/m2 & ν = 1.7918 * 10-6 m2/s

1. For Reynold Number (Re) = 100 Flow Speed (u) = 0.0035828 m/s
2. For Reynold Number (Re) = 1000 Flow Speed (u) = 0.035828 m/s
3. For Reynold Number (Re) = 10000 Flow Speed (u) = 0.35828 m/s

PROCEDURE:

Modelling-

We draw a circle in front plane of 10mm diameter and pad it selecting midplane option with 100mm dimension. We shell our model with 0.10mm dimension. Thus, we get our pipe.

Select top plane and create three line from outlet side with distance of 5mm, 10mm & 15mm in three different sketches.

Flow simulation setup -

Select gear icon on top bar click on ad-ins and select SOLIDWORKS flow simulation from the list wait for sometime till the module loads. Now select Flow simulation, create lids and select two openings of the pipe to add the lids.

Click on wizard, give project name and select following options –

Analysis type = internal

Project fluid = water

Flow type = turbulent and laminar

Default wall thermal condition = adiabatic wall

Roughness = 0 micrometre

Now, right click on boundary conditions and select insert boundary condition. Select face of inlet lid of pipe, flow opening, inlet velocity and give value 0.0035828 m/s. Finally click on OK. Again, click on insert boundary condition select face of outlet lid of the pipe, pressure opening, static pressure OK. Again, select insert boundary condition, select pipe wall, wall, real wall.

Now right-click on cut plot to insert three different cut plots with distance value of -45mm, -40mm and -35mm from YZ plane. Select contour from display section, velocity as parameter, number of level 15. Adjust plot minimum and maximum by selecting plot minimum and maximum.

To insert plots right-click on XY plot->insert and create three different plots selecting each line we create in modelling and select velocity as the parameter. Similarly, create one more plot by selecting all the lines as selection.

What if Analysis –

Right-click on project title and select new parametric study.

Select add simulation parameter->boundary condition->inlet velocity. Add three variation for three inlet velocity for three Reynolds number.

Select Output parameter and select all three cut plots and 4 XY plots.

Open scenario tab copy paste the 1^st scenario two times. Edit the values in 2^nd and 3^rd scenario for inlet velocity to 0.035828 m/s & 0.35828 m/s respectively.

Click on Run.

RESULTS:

Cut plots for 85% pipe length

For Re=100

For Re=1000

For Re=10,000

Cut plots for 90% pipe length

For Re=100

For Re=1000

For Re=10,000

Cut plots for 95% pipe length

For Re=100

For Re=1000

For Re=10,000

Outlet velocity plot for 85% pipe length

Outlet velocity plot for 90% pipe length

Outlet velocity plot for 95% pipe length

Outlet velocity plot compared for 85%, 90% & 95% pipe length

CONCLUSION:

Sr.No.	Reynolds Number	% of total length of pipe	Outlet Velocity (m/s)
			Center	Wall
1	100	95%	0.007	0.001
		90%	0.007	0.001
		85%	0.007	0.001
2	1,000	95%	0.065	0.011
		90%	0.064	0.011
		85%	0.064	0.011
3	10,000	95%	0.460	0.137
		90%	0.457	0.135
		85%	0.454	0.135

From the above table we can observe that,

For Re=100 outlet velocity remains constant along the length of pipe and it is 7 times more in the center than at the wall.

For Re=1,000 outlet velocity remains constant at wall along the length of pipe but changes slightly at the center.

For Re=10,000 outlet velocity changes slightly along the length of pipe at both the locations i.e. at the center and at the wall.

Since, the pipe is horizontal, potential energy is unaltered, hence the increase in kinetic energy is at the cost of pressure energy. Therefore, as the fluid flows through a constricted passage its velocity increases whereas pressure drops. This causes the outlet velocity at the centre of pipe to increase.

The output velocity is reduced at the wall due to effects like viscosity and boundary layer formation.

For each Reynolds number, the outlet velocity at different sections i.e. 95%, 90% & 85% of total length of pipe is almost the same.

LINKS: GDrive