Turbulent jet flow modeling using stochastic particles method
Rockney Wong · The University of Queensland · 2005
The topic of the thesis is turbulent jet flow modeling using stochastic particles method. There were two main objectives, firstly, to deepen the understanding of turbulent flow by using stochastic particle modeling. And second, is learn to reproduce or predict turbulence characteristic. Turbulence flow is important for many engineering applications. One of the fundamental characteristic of turbulent flow is that it greatly enhances the rates of the transport and mixing process, which is of great importance in many applications hence it motivate engineers to study turbulent flow. Several related turbulence theories were investigated in to better background of turbulent flow, they includes the energy cascade, Kolmogorov hypotheses and Kolmogorov scale and Reynolds stress. The turbulence-kinetic-energy model and k −e model were discussed in the report. The jet flow was modelled as homogenous decaying turbulence. The principle behaviour of turbulence flow is its randomness. The fluctuating velocity of turbulence is hard to model precisely and would be much easier to use a statistical approach to model it. The modeling method chosen to simulate the jet flow is called the stochastic particle modeling. The main aspect of the particle method is to consider a large number of particles, and each of which evolves according to the given stochastic model equation. And the model equation is called the first order Ito stochastic differential equation. Stochastic differential equation is applied to many different applications and across many disciplines other than turbulent flow. These areas include turbulence in weather, investment finance, economics, finite element analysis etc., and each of these topics were briefly discussed in the report. The velocity of the particles in the system was modelled by the first order Ito stochastic differential equation. A stochastic quantity x(t) obeys an Ito SDE written as dx(t) = a[x(t),t]dt + b[x(t),t]dW(t) Where a and b represent the drift and diffusion coefficient, and W(t) represents the Wiener process. The Ornstein-Uhlenbeck process, or simply OU process, is the simplest statistically stationary diffusion process, and the corresponding stochastic differential equation is shown below, dU(t) = -U(t) dt/T + (2σ2/T)v2dW(t) Where the timescale T was obtained in the simplified Langevin model. Several sample paths of the OU process and its autocorrelation function were plotted using Matlab. The result shows that the autocorrelation function roughly matched with the approximated function. The jet flow was simulated using Matlab. A total of 6 m-files were used to simulate the jet flow, and the purposes of each file were explained in detail in the report. The results were represented by the final position of the particles and the velocity profile at the end of the boundary. Below show the plot of the final position of the particles. The results show that the jet flow diffuses as it moves along in the x direction. The velocity profile at the end of the jet flow shows that the velocity is highest in the centre of the flow, while the edge of the flow has the lowest velocity. Therefore the velocity profile is similar to a bell-shaped curve. A comparison were made with two different entering velocities, the A computational fluid dynamic (CFD) model was built with ACE. The purposes of the model were to visualise the behaviour of the jet flow as well as compare the results with the Matlab simulation. Several resulting plots were shown in the report, they include the turbulence kinetic energy, dissipation rate and the velocity in the x-direction. However, the result from the CFD model did not match with the Matlab simulation. It was later on discovered that the method to calculate the kinetic energy and the dissipation rate was incorrect. The jet flow simulated by Matlab, however, still followed the behaviour of the jet flow. The flow diverges as it moves away from the inlet, and the velocity profile at the boundary had a simular shape compare to the CFD result.