Question about Mac-Cormack method in Anderson?

granzer · October 23, 2019, 22:49

Hello,
As given in Chapter 7 of "Computational Fluid Dynamics, the basics with application" by -J.D.Anderson, the non-dimensional CD nozzle length is calculated as x/L, where L is the total length of the nozzle. But when presenting the results, the non-dimensional length varies from 0 to 3. Shouldn't it vary from 0 to 1?

granzer · October 24, 2019, 00:29

Can anyone confirm if this is a mistake or if there is a mathematical logic behind this?

FMDenaro · October 24, 2019, 08:29

Quote:

Originally Posted by granzer

Can anyone confirm if this is a mistake or if there is a mathematical logic behind this?

Anderson does not give a reason for that, the tables report x/L going up to 3 so you have to assume that L is not the total lenght.

fluid23 · October 30, 2019, 16:21

I think if you look at A/A* you will see that the throat (A/A*=1) occurs at x/L = 1.5. This means that x/L=1 is not the exit. If you look at the initial conditions (Fig 7.8) he plots 'non-dimensional distance' that goes 0 to 3, inlet-outlet with throat at 1.5. I think you would get the same result if you non-dimensionalize with x/L=1 at the exit. He even notes after defining the initial shape of the nozzle (Eq. 7.73) that x=1.5 is the throat so that convergence is x < 1.5 and divergence is x > 1.5.

Its an odd mathematical choice to be sure and seems to be totally arbitrary on his part.

October 23, 2019, 22:49	Question about Mac-Cormack method in Anderson?	#1
granzer Senior Member Mandeep Shetty Join Date: Apr 2016 Posts: 185 Rep Power: 10	Hello, As given in Chapter 7 of "Computational Fluid Dynamics, the basics with application" by -J.D.Anderson, the non-dimensional CD nozzle length is calculated as x/L, where L is the total length of the nozzle. But when presenting the results, the non-dimensional length varies from 0 to 3. Shouldn't it vary from 0 to 1?

October 30, 2019, 16:21		#4
fluid23 Senior Member Matt Join Date: Aug 2014 Posts: 947 Rep Power: 17	I think if you look at A/A* you will see that the throat (A/A=1) occurs at x/L = 1.5. This means that x/L=1 is not the exit. If you look at the initial conditions (Fig 7.8) he plots 'non-dimensional distance' that goes 0 to 3, inlet-outlet with throat at 1.5. I think you would get the same result if you non-dimensionalize with x/L=1 at the exit. He even notes after defining the initial shape of the nozzle (Eq. 7.73) that x=1.5 is the throat so that convergence is x < 1.5 and divergence is x > 1.5. Its an odd mathematical choice to be sure and seems to be totally arbitrary on his part. granzer likes this. Last edited by fluid23; October 31, 2019 at 08:23.*

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October 24, 2019, 00:29		#2
granzer Senior Member Mandeep Shetty Join Date: Apr 2016 Posts: 185 Rep Power: 10	Can anyone confirm if this is a mistake or if there is a mathematical logic behind this?