Introduction
The focus of this assignment is to study flow characteristics in the transition regime in converging diverging nozzles using fluent. GAMBIT was used to create the mesh geometry. Solidworks CAD software was used to create the geometry. The Study will also describe the method used for simulating flows and the specific geometry and flow conditions. Fluent has been used to model the fluid flow in a convergent-divergent nozzle.
Literature review
For this assignment, compressible flow through a convergent-divergent nozzle was modelled in FLUENT. For continence the model was represented in 2D which enclosed the flow domain. The flow domain was adjusted based on the dimension of the nozzle (flow domain representation). Due to the nature of the flow symmetry of the geometry, only half of the full geometry was modelled.
An axisymmetric, converging-diverging nozzle with wall shape made of circular segments. The nozzle inlet/outlet and throat sections are made of two circles. The inlet and throat circles meet at a point with a common tangent forming the inlet wall of the nozzle and the exhaust wall is tangent to the throat * circle. Figure 1 shows the general shape of the nozzle. The nozzle has an outlet cross section area of 2800mm2. The 2-D geometry is obtained based on the cross sectional areas flow boundary.
Flow Type
Because the flow has high Reynolds number it is turbulent flow and K-epsilon was selected for the model. Overtime if the flow rate does not change the system will be in equilibrium (steady state) but if it does it will be a transient solution. For this simulation we have a steady state solution.
Boundary Conditions
Ethane gas was specified at the inlet of the convergent divergent nozzle. The inlet temperature was 341 K. A fixed uniform mass flow 2.59 kg/s was specified at the inlet. As mentioned previously axis symmetric boundary conditions were specified at the central axis of the nozzle. The interior surfaces of the nozzle were specified as a wall. At the outlet the temperature, velocity and pressure were specified.
Grid and Mesh Type
The cross section area of the nozzle changes non-uniform manure therefore the standard K-? model has been used as it is the most suitable model. The analysis were started by using quadrilateral grid which can be can be further refined for by grid adaption technique.
Results
The analysis was performed to study dynamic ethane gas flow behaviour in a convergent-divergent nozzle. On the inlet, the flow was subsonic (M=0.256) and as the flow accelerates at the throat it reaches to sonic (M=1) and flow further accelerate to super sonic (M=1.25) in the divergent region. In divergent supersonic region the flow expands and shock wave has been observed on the contour plot. The velocity, temperature and pressure will also be studied in the analysis
The following contour plots were obtained from the analysis taken place during the lab sessions. The contour plots demonstrate the fluid flow inside a convergent divergent nozzle. The initialisation of the flow started at the inlet pressure of 260000 Pa and velocity of 85 m/sec.
Residuals
Residuals are the errors of the discredited equations. Residuals are calculated for each equation. Residuals should reduce as the numerical process progresses. They are often used to monitor the behavior of the numerical process
The residual plots show a convergence after about 28 iterations.
Modelling Issues
Numerical Analysis
After creating the mesh geometry on GAMBIT the flow simulation was done using FLUENT. The model geometry was 2 dimensional axisymmetric. The simulation for pressure ration was performed and Figure 3 above were obtained. The theory was based on the assumption of isentropic flow. The contour plot shows the flow in 2D.
This assignment shows how the use of CFD software can be used to reinforce fundamental concepts of thermodynamics. It also shows how the software (Fluent) can be used to investigate the effect of specific terms in the governing equations.
In the theory as well as simulations, it was assumed that the flow is inviscid.
Conclusion
For simplicity this analysis was carried out on 2D, but the actual flow on 3D can be complex. All the flow features on 2D may not show the flow correctly. The result can be less accurate. Other real world convergent-divergent fluid flow factors such as shock and after shock need to be considered in order to achieve a better accuracy.
References
