John Dorian

The University of Sacred Heart

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The mixing elbow configuration is commonly used in piping systems for power plants and process industries. It is important to predict the flow field and temperature field in the mixing region to ensure that the design performs as intended with respect to mixing. Using this exercise, it is possible to visualize the mixing phenomenon in the elbow region as a function of inlet velocities and temperatures. Comparisons can be made for different inlet temperature and velocity combinations and for solutions using schemes with higher orders of accuracy. By making use of second order discretization and grid adaptions, the flow field has been more accurately predicted.

The preliminary solution in this laboratory is concerned with the effect of reducing the residuals of the simulation in order to produce a more accurate solution. Initially the values of residuals were set at 1x10-3. This gave the solutions which are represented in figures 1-6.

Figures 2 and 3 are graphics of the velocity contours and static temperature contours respectively. These graphics show the distribution of temperature and velocity in the mixing elbow, using colours to display the magnitude. Both figures show that the highest values of temperature and velocity occur at the point of mixing (at the secondary inlet). When the flow is mixed, the higher temperatures and velocities occur on the right hand side of the mixing elbow. Figures 4 and 5 are graphical representations of the velocity vectors (m/s); the scale has been increased in figure 5 thus giving a more accurate representation. These graphics show the direction and velocity of the flow, it is highest at the point of mixing and continues to be higher than the downstream flow after the fluids have mixed. Figure 6 shows the temperature distribution across the inlet, this can also be seen on the contour graphic. As this is a preliminary solution, the residuals are high. This gives a linear distribution across the inlet exit, high on the right hand side (peaking at 3.1x103) and low (2.96x102k) on the left.

Figure 1 shows a graph of the solution convergence. The solution in this first case converged after 57 iterations. By reducing the residuals further we can check whether the solution still has there is still convergence

The elbow solution computed in the ﬁrst part of this laboratory uses ﬁrst-order discretization. The resulting solution is very diﬀusive; mixing is over predicted, as can be seen in the contour plots of temperature and velocity distribution. Changing to second-order discretization for all listed equations will improve the accuracy of the solution.

Figure 8 shows the graphical representation of the static temperature contours using second-order discretization. Comparing this figure to figure 3 which used a first order scheme demonstrates the high levels of diffusivity which is accounted for in the more accurate solution. The higher order solution shows a flow which is more compact and doesn’t reach the left hand side of the system. Enabling second order discretization has produced a solution with different characteristics to the first order solution. Cells which look affected by a change in temperature and velocity in the first orders scheme are unaffected in the higher order solution.

Figure 9 is a plot of the temperature distribution across the exit using the second order discretization scheme. Unlike the linear shape of the figure 6 plot, the second order scheme produces a parabolic curve for the distribution. This is due to the increased accuracy of the solution.

The elbow solution can be improved further by refining the grid to better resolve the flow details. The grid can be adapted based on the temperature gradients in the current solution. Before adapting the grid, an acceptable range of temperature gradients over…