The document summarizes a simulation of flow over a flat plate using COMSOL. It describes defining the 2D model geometry and parameters, applying boundary conditions of no slip at the walls and varying pressure at the inlet, and solving the Navier-Stokes equations on a fine mesh. Results include 1D plots of velocity versus position and pressure versus position, and a 2D surface velocity plot showing the hydrodynamic boundary layer. The conclusion notes difficulty extracting lift and drag forces but finding guidance in other papers.

1. COMSOL: Flow Over a Flat
Plate
Alvaro Lopez Arevalo
Submission Date: 11/21/2014
Introduction
The objective of this report is that of simulating flow over a flat plate in 2-D, using the COMSOL CFD
interface, to enable calculations of parameters of interest such as the total drag force.
When analyzing, flow past an object, generally, we are often concerned about certain factors that directly
affect the character of the flow, namely: shape of the object, orientation, speed, and fluid properties. In
this short summary regarding the simulation mentioned earlier, we are mainly concerned with finding
both pressure and velocity distributions over the plate.

2. Model definition and procedure
Every model that is to be simulated needs to start with the selection of the space in which you want to
design your model (e.g 2-D, 3_D,etc), in this case we pick 2-D, selection of the physics of the problem-
the CFD module- and then whether we want a time dependent simulation or a steady one. In this case we
opted for a steady simulation.
Next, I defined global parameters that could define both geometry and important properties of the liquid
with which we are to work, namely: viscosity, density, height of the plate, it’s width, etc. It is germane to
notice that the working fluid is a liquid different from water,and that the global parameters represent an
amazing tool when personalizing the analysis anyone else would like to perform for it allows you to edit
these parameters mentioned at all times of the process of designing.
Thereafter,the geometry is easy defined since we have defined input parameters for the length and width
of such plate, and for the working fluid; that is, all is required to do is to input the parameter and the
software automatically gives dimensions to your geometry. Then, we select the material with which our
medium will be made of. Since we don’t know yet what liquid is the one we are working with, we can
only enter the properties of interest that will define enough the medium we are working, these properties
are: viscosity, and density.
Setting the Boundary Conditions to Solve the Navier Stokes Equation:
 Inlet:
We start by defining the initial conditions at the inlet. Since our motive is that of having a Pressure driven
flow, the initial condition that need to be specified at the inlet needs to be 𝑃𝑖𝑛 > 𝑃𝑜𝑢𝑡.

3.  Outlet:
For this boundary condition, we define the outlet pressure to be 0. It should be noted that the parameters
being used can be change freely by making use of the parameters section explained above.
 Walls: No slip condition.
The no slip condition, or wall boundary condition, will be applied at the surface of the plate. Below is
shown what boundaries are that of interest:

4. Results: Plots and Graphs
After having specified all boundary conditions, we are ready to run the simulation, which in-turn,
implicates solve the Navier-Stokes equations. So first we define our mesh being in this case a fine mesh.
The latter, would look like this:
Finally, we click compute under the study node, and through working with the results node we get the
following plots with its corresponding discussion:

5.  1-D plot: Velocity vs. y at the leading edge
Here we have the plot of the velocity profile versus the y dimension for varying pressure inlets. The result
was pretty accurate, for it is known that the profile of velocity is supposed to be of quadratic fashion.
Also, we can appreciate thet when 𝑃𝑖𝑛 = 0, blue constant line, velocity seems to be 0, and there is no
flow; that is, without a pressure gradient, there is no flow over the flat plate.
 1-D plot: Pressure vs. x

6. Here we show the plot of Pressure vs the x dimension. We can see that we have a negative gradient that
drives the flow for inlet pressures greater than 0, this is, the case for a pressure driven flow.
 2-D plot: Surface Velocity
In this plot, we are able to visualize both the magnitude of the velocity of the flow, and the hydrodynamic
boundary layer. Typically, what this plot ensures is whether the simulation resembles the physics of the
problem or not. In this case, we are able to see that the maximum velocity occurs, symmetrically, at the
spacing between the plates and the upper and lower walls.
Conclusion
The difficulty at the end of the simulation, results section, was that of extracting both the lift and drag
forces on the plate. Usually, this is done by performing a surface integral along the surface of the plate
having as the integrand both the shear stress and the pressure distribution as a function of the orientation
of the object of interest. I have been able to find already some papers in which these forces have been
found; therefore, by scrutinizing the latter I should be able to come up with an estimate of such forces
acting on th3e immersed body.