Analysis of Step 4 - Revision history

Xonnainty at 13:33, 26 August 2020

2020-08-26T13:33:15Z

Xonnainty at 03:52, 26 August 2020

2020-08-26T03:52:41Z

Xonnainty: /* Comparing results at spatial resolution of 256^3 */

2020-08-25T20:08:24Z

‎Comparing results at spatial resolution of 256^3

Xonnainty at 20:07, 25 August 2020

2020-08-25T20:07:50Z

Xonnainty at 20:06, 25 August 2020

2020-08-25T20:06:44Z

Xonnainty at 20:06, 25 August 2020

2020-08-25T20:06:14Z

Xonnainty at 19:05, 25 August 2020

2020-08-25T19:05:49Z

Xonnainty at 19:04, 25 August 2020

2020-08-25T19:04:58Z

Xonnainty at 18:30, 25 August 2020

2020-08-25T18:30:39Z

Xonnainty at 18:02, 25 August 2020

2020-08-25T18:02:46Z

@@ Line 9: / Line 9: @@
 The simulations of '''YALES2''', '''DINO''' and '''Nek5000''' are presented in the following subsections for two different
 resolutions in space (<math>256^3</math> and <math>512^3</math>), in order to check the impact of the '''spatial resolution''' on the results. Additional data for other grids are also available (<math>384^3</math>
-for both '''YALES2''' and '''DINO''', and 7683 only for '''DINO'''). They are not discussed at length in the text and in separate figures in the interest of space, but the corresponding values are included in the Tables 4 and 5 summarizing all results of '''Step 4'''. Additionally, all results at all grid resolutions are available online in the benchmark repository <ref name="TGV-coria-cfd">[https://benchmark.coria-cfd.fr benchmark.coria-cfd.fr]</ref>.
+for both '''YALES2''' and '''DINO''', and <math>768^3</math> only for '''DINO'''). They are not discussed at length in the text and in separate figures in the interest of space, but the corresponding values are included in the Tables 4 and 5 summarizing all results of '''Step 4'''. Additionally, all results at all grid resolutions are available online in the benchmark repository <ref name="TGV-coria-cfd">[https://benchmark.coria-cfd.fr benchmark.coria-cfd.fr]</ref>.
 Starting with the evolution of maximum temperature versus time, a perfect visual agreement between all three
 codes is observed at all resolutions. This quantity does not appear to be difficult to predict correctly, as already observed previously for the non-reacting flow in '''Step 3''', provided that the pressure variation due to the heat release is correctly taken into account.

@@ Line 1: / Line 1: @@
 '''Step 4''' is definitely the most complex but also the most interesting case to compare '''high-fidelity codes''' for '''turbulent reacting flows''', since it contains all the features relevant for '''turbulent combustion'''. Therefore, a more detailed analysis is useful. The comparisons will involve:
-. The '''evolution of maximum temperature''' versus '''time''', as depicted in Fig. 10;
+. The '''evolution of maximum temperature''' versus '''time''';
-. '''Velocity fields''' at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerlines of the domain, as shown in Fig. 11;
+. '''Velocity fields''' at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerlines of the domain;
-. '''Profiles of temperature''', '''heat release''' and '''mass fractions''' of <math>H_2</math>, <math>O_2</math> and <math>OH</math> at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the
+. '''Profiles of temperature''', '''heat release''' and '''mass fractions''' of <math>H_2</math>, <math>O_2</math> and <math>OH</math> at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerline of the domain.
-centerline of the domain, as illustrated in Figs. 12 and 13.
 The simulations of '''YALES2''', '''DINO''' and '''Nek5000''' are presented in the following subsections for two different
@@ Line 12: / Line 11: @@
 for both '''YALES2''' and '''DINO''', and 7683 only for '''DINO'''). They are not discussed at length in the text and in separate figures in the interest of space, but the corresponding values are included in the Tables 4 and 5 summarizing all results of '''Step 4'''. Additionally, all results at all grid resolutions are available online in the benchmark repository <ref name="TGV-coria-cfd">[https://benchmark.coria-cfd.fr benchmark.coria-cfd.fr]</ref>.
 Starting with the evolution of maximum temperature versus time, a perfect visual agreement between all three
-codes is observed at all resolutions, as shown in Fig. 10 (with a resolution of <math>512^3</math>
+codes is observed at all resolutions. This quantity does not appear to be difficult to predict correctly, as already observed previously for the non-reacting flow in '''Step 3''', provided that the pressure variation due to the heat release is correctly taken into account.
-). This quantity does not appear
 to be difficult to predict correctly, as already observed previously for the non-reacting flow in '''Step 3''', provided that the pressure variation due to the heat release is correctly taken into account.
 == Comparing results at spatial resolution of <math>256^3</math> ==
@@ Line 21: / Line 18: @@
 for '''YALES2'''
 and '''DINO''' and 2523
-for '''Nek5000'''. The corresponding results for '''velocity''' (Fig. 11) and '''temperature''' (Fig. 12, left)
+for '''Nek5000'''. The corresponding results for '''velocity''' and '''temperature''' at time <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerlines of the domain show visually a perfect agreement. Nevertheless, the three codes show slight differences concerning heat release and some '''mass fractions profiles''' (in particular <math>O_2</math> and <math>OH</math>) around the center of the domain. These differences – though small
 at time <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerlines of the domain show visually a perfect agreement. Nevertheless, the
 three codes show slight differences concerning heat release and some '''mass fractions profiles''' (in particular <math>O_2</math> and <math>OH</math>)
-around the center of the domain, as it can be observed from Figs. 12 (right) and 13. These differences – though small
 – are larger than those experienced in the non-reacting case. Note that there is originally no oxygen in this region,
 explaining why the mass fraction of <math>O_2</math> is still smaller than the mass fraction of <math>OH</math> there. One reason behind these
@@ Line 59: / Line 53: @@
 Only the quantities showing visible discrepancies at a resolution of <math>256^3</math>
 (heat release, <math>Y_{O_2}</math>, <math>Y_{OH}</math>) are discussed here in the interest of brevity, since all other quantities already revealed a perfect agreement for the previous resolution.
-It can be observed in Figs. 14 and 15 that doubling the spatial resolution in each direction did not improve the
+It can be observed in the figures below that doubling the spatial resolution in each direction did not improve the
 comparisons in a clear way; marginal differences still exist between the codes, and a convergence towards a unique
 solution is not really visible. To discuss this issue in more detail, a refined analysis is necessary, as discussed in the

@@ Line 48: / Line 48: @@
 [[File:yoh_y_lm_256_withzoom.png|250px]]
-Mass fraction profiles of <math>H_2</math>, <math>O_2</math>, and <math>OH</math> at </math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2\tau_{ref} = 0.5 ms</math> for 3-D reacting case (Step 4)
+'''Mass fraction profiles''' of <math>H_2</math>, <math>O_2</math>, and <math>OH</math> at </math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2\tau_{ref} = 0.5 ms</math> for 3-D reacting case (Step 4)
 with <math>N = 256^3</math> grid points.

@@ Line 5: / Line 5: @@
 . '''Velocity fields''' at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the centerlines of the domain, as shown in Fig. 11;
-. Profiles of temperature, heat release and mass fractions of <math>H_2</math>, <math>O_2</math> and <math>OH</math> at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the
+. '''Profiles of temperature''', '''heat release''' and '''mass fractions''' of <math>H_2</math>, <math>O_2</math> and <math>OH</math> at <math>t = 2 \tau_{ref} = 0.5 ms</math> along the
 centerline of the domain, as illustrated in Figs. 12 and 13.

@@ Line 72: / Line 72: @@
 [[File:yoh_y_lm_512_withzoom.png|250px]]
-Mass fraction profiles of <math>O_2</math> (left), and <math>OH</math> (right) at <math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2 \tau_{ref} = 0.5 ms</math> for '''3-D reacting case'''
+'''Mass fraction profiles''' of <math>O_2</math> (left), and <math>OH</math> (right) at <math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2 \tau_{ref} = 0.5 ms</math> for '''3-D reacting case'''
 ('''Step 4''') with <math>N = 512^3</math> grid points.

@@ Line 33: / Line 33: @@
 a finer spatial resolution, as discussed in the next subsection.
-[[File:vx_x_lm_256.png]]
+[[File:vx_x_lm_256.png|250px]]
-[[File:vy_y_lm_256.png]]
+[[File:vy_y_lm_256.png|250px]]
 '''Velocity''' at time <math>t = 2τref = 0.5 ms</math> for '''3-D reacting case''' ('''Step 4''') with <math>N = 256^3</math> grid points.
-[[File:T_y_lm_256.png]]
+[[File:T_y_lm_256.png|250px]]
-[[File:hr_y_lm_256_withzoom.png]]
+[[File:hr_y_lm_256_withzoom.png|250px]]
 '''Temperature''' (left) and '''heat release profiles''' (right) at <math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2 \tau_{ref} = 0.5 ms</math> for '''3-D reacting case'''
 ('''Step 4''') with <math>N = 256^3</math> grid points.
-[[File:yh2_y_lm_256.png]]
+[[File:yh2_y_lm_256.png|250px]]
-[[File:yo2_y_lm_256_withzoom.png]]
+[[File:yo2_y_lm_256_withzoom.png|250px]]
-[[File:yoh_y_lm_256_withzoom.png]]
+[[File:yoh_y_lm_256_withzoom.png|250px]]
 Mass fraction profiles of <math>H_2</math>, <math>O_2</math>, and <math>OH</math> at </math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2\tau_{ref} = 0.5 ms</math> for 3-D reacting case (Step 4)
@@ Line 64: / Line 64: @@
 next subsection.
-[[File:T_y_lm_512.png]]
+[[File:T_y_lm_512.png|250px]]
-[[File:hr_y_lm_512_withzoom.png]]
+[[File:hr_y_lm_512_withzoom.png|250px]]
 '''Temperature''' (left) and '''heat release profiles''' (right) at <math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2 \tau_{ref} = 0.5 ms</math> for '''3-D reacting case''' ('''Step 4''') with <math>N = 512^3</math> grid points.
-[[File:yo2_y_lm_512_withzoom.png]]
+[[File:yo2_y_lm_512_withzoom.png|250px]]
-[[File:yoh_y_lm_512_withzoom.png]]
+[[File:yoh_y_lm_512_withzoom.png|250px]]
 Mass fraction profiles of <math>O_2</math> (left), and <math>OH</math> (right) at <math>x = 0.5 L</math>, <math>z = 0.5 L</math>, and time <math>t = 2 \tau_{ref} = 0.5 ms</math> for '''3-D reacting case'''

← Older revision		Revision as of 18:30, 25 August 2020
Line 1:		Line 1:
	'''Step 4''' is definitely the most complex but also the most interesting case to compare '''high-fidelity codes''' for '''turbulent reacting flows''', since it contains all the features relevant for '''turbulent combustion'''. Therefore, a more detailed analysis is useful. The comparisons will involve:		'''Step 4''' is definitely the most complex but also the most interesting case to compare '''high-fidelity codes''' for '''turbulent reacting flows''', since it contains all the features relevant for '''turbulent combustion'''. Therefore, a more detailed analysis is useful. The comparisons will involve:
−
−	~~[[File:.pdf]]~~
−
−	~~Profile of temperature at <math>t = 2 \tau_{ref} ms</math>, <math>x = 0.5L</math>, and <math>z = 0.5L</math> for '''3-D non-reacting multi-species flow''' ('''Step 3''')~~
−
−	~~[[File:.pdf]]~~

	1. The '''evolution of maximum temperature''' versus '''time''', as depicted in Fig. 10;		1. The '''evolution of maximum temperature''' versus '''time''', as depicted in Fig. 10;

@@ Line 1: / Line 1: @@
 '''Step 4''' is definitely the most complex but also the most interesting case to compare '''high-fidelity codes''' for '''turbulent reacting flows''', since it contains all the features relevant for '''turbulent combustion'''. Therefore, a more detailed analysis is useful. The comparisons will involve:
-[[File:]]
+[[File:.pdf]]
 Profile of temperature at <math>t = 2 \tau_{ref} ms</math>, <math>x = 0.5L</math>, and <math>z = 0.5L</math> for '''3-D non-reacting multi-species flow''' ('''Step 3''')
-[[File:]]
+[[File:.pdf]]
 . The '''evolution of maximum temperature''' versus '''time''', as depicted in Fig. 10;