Solution of 2-D Incompressible Navier Stokes Equations with Artificial Compressibility Method Using Ftcs Scheme

Read the following examples and using the table on p. 45 as well as other material in the text determine which system is MOST likely being described:

The objective of this exercise is to measure the pressure distribution across the surface on an aerofoil in a wind tunnel. The aerofoil is tested under several different Mach numbers from subsonic to supercritical. The purpose of measuring the pressure distributions is to assess the validity of the Prandtl-Glauert law and to discuss the changing chracteristics of the flow as the Mach number increases from subsonic to transonic.

27. The following equation describes a 2nd order system: . The system may be described as:

\KwIn{nodal value of solution $\mathbf{u} = \left(p, \mathbf{v} \right)$, volume geometric factors $\partial (rst)/ \partial (xyz)$, 1D derivative operator $D_{ij} = \partial \hat{l}_j /\partial x_i$, model parameters $\rho, c$}

Questions 1, a and b answers: As we know (also shown in Figure 1 of this paper), the mixing vanes in the fuel assembly are not symmetric and the flow pattern might not be periodic or cyclic, so it is impossible or extremely difficult to extract information out of any “free boundary” 1x2 section from experimental data taken under the 5x5 bundle test geometry and use this information to benchmark CFD modeling of a 1x2 channel without any convincing justification of how the boundary (or missing boundary) effect is handled. The challenge is how to apply the data obtained within a 5x5 assembly without a 1x2 confined flow boundary to

equation to loop 1 of Fig. 2 and current balance equation to node 1, the state space equations (1) and (2)

u and v are found by solving the equation shown in (3.6). Ix and Iy are the hori-

In this experiment, the velocity profile for a flat plate at zero pressure gradient of a boundary layer at two different stream wise points were acquired. The investigation was also based on and how changes in Reynolds number affect the velocity distribution within boundary layers. Parameters such as the Momentum Thickness, Displacement Thickness, Shape Factor, shear stress and coefficient of friction was also calculated to gain a better understand of boundary layers. The experimental values calculated were compared to the theoretical Blasius for laminar flow and Power Law Solutions for turbulent flow to see how they varied. It was found out the higher the Reynolds number the greater the boundary layer thickness. As the

The model is set to the angle of 4.1 degrees and the 30 readings from the multitube manometer, which are connected to points on the aerofoil surface, are measured and recorded. Along with these readings the two tubes connected to the tunnel reference pressure tappings are recorded. These steps are repeated but with an angle of attack of 6.1 degrees. It was found from the experiment that the stall angle was around 8.8 degrees. This was found by increasing the angle of attack until the

The central differencing method is used to find an expression for d2u/dx2 in the form ui-1 +ui+1

4. The flow velocity increases as the flow gets closer to the barrier wall and reduces as it moves away from the wall. This is because as the flow rate is constant (Conservation of mass) while the area of the flow cross section decreases when it gets closer to the barrier wall, the flow velocity increases. This is best understood by referring to the continuity equation,

-The Reynolds number of this experiment was then calculated using equation (4) where c is the length of the aerofoil chord and is the dynamic viscosity of air.

the condition z1≠z2 is true if the two pressure taps are not horizontal (at different height).

Based on the above analysis we suggest that the solution provided by Coopers and Myers are

The lid-driven cavity flow is most probably one of the most studied fluid problems in the