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

Submission: The report from part 4 including all relevant graphs and numerical analysis along with interpretations.

We calculated the number of iterations $\tau$ needed to achieve $|f^{\tau}(x) - f^{\tau}({x^\prime})| > 10^{-1}$ when given two initial conditions $x_0$ and $x^{\prime} =x_0 + \epsilon$ separated apart $\epsilon = 10^{-d}$. Here, the exponent $d$ represents the number of digits of precision $d = \lfloor \log |x_0 - x^{\prime}| \rfloor$. Fig.~\ref{fig:precisiondelta} depicts a log-log plot of data obtained from several average random initial conditions and its initial distance $\epsilon$ for different digits precision $d=\{10, 20, \ldots, 290\}$.

First, The procedures of were take an energy car and roll it down a track with a without a sail and record the data from photogate A to B and the time to took to get there make sure the photogate are 555 cm away from each other. Do the same one energy car wit just wheels and one with one 3 times each.

end rex_A = 0.0003869* exp(-0.00007921*rex_Q); % Q exponent rex_D_H = rex_D * 0.8; rex_Q_H = rex_Q * 0.98; rex_D_L = rex_D * 1.2; rex_Q_L = rex_Q * 1.03; % Calculate k and convert time steps to time in seconds for plotting results k = T/N; % Duration of each t-step timescale = transpose(0:k:T); % Zone length and number of division data zone_length = zeros(20,1); zone_sections = zeros(20,1); zone_length(1) = 5.395; zone_length(2) = 5.461; zone_length(3) = 5.461; zone_length(4) = 5.461; zone_length(5)

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.

© The Authors JCSCR. (2012). A Comparative Study on the Performance. LACSC – Lebanese Association for Computational Sciences Registered under No. 957, 2011, Beirut, Lebanon, 1-12.

seem to change in the same way. Then, go back to get the initial velocities the same, and

1) Once the simulation opens, click on ‘Show Both’ for Velocity and Acceleration at the top of the page. Now click and drag the red ball around the screen. Make 3 observations about the blue and green arrows (also called vectors) as you drag the ball around.

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

Q6b. Write down the simplified Cartesian Navier-Stokes momentum equations that you think are the closest representation to the equations you actually solved in Fluent. State why these aren’t actually the equations you solved. (10 marks)

Providing a proper equation of state for each phase has a crucial role in the numerical simulation of compressible liquid-vapor two-phase flows. Furthermore, these equations of state are required to be thermodynamically consistent, computationally cost effective and as accurate as possible, however, determining the constant parameters in these equations for any fluid type should not be cumbersome. In this paper, an equation of state is obtained for the liquid phase by Taylor expansion of internal energy about a reference point. By employing thermodynamic relations, other thermodynamic properties such as enthalpy, entropy and Gibbs function are obtained. Subsequently, this equation of state for the liquid phase is associated with a stiffened gas equation of state for the vapor phase which is proven to have a acceptable accuracy for the gases.

Also under the “Motion Model” you are using 22 Zonal and Tesseral potential fields and the “Analytic” density model. Although this is not incorrect you would receive a better estimate if you used the Jacchia Roberts density model and increased your Zonals to a larger number. I have updated the Zonals and Tesserals, in the attached MP, to use 40

The table below shows a comparison between two experiments and each statistics data set. Michelson Data Units are km/s -

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