Parametric study and optimization on heat transfer and flow characteristics in a rectangular channel with longitudinal vortex generators

Figures & data

Figure 1. Schematic diagram of the considered channel.

Table 1. Geometric dimension of the LVG for Case F.

Parameter	Symbol/unit	Case F
Transverse pitch	Pt/mm	4
Longitudinal pitch	Pl/mm	100
Attack angle	β/deg	44
Length	LVG/mm	14
Thickness	WVG/mm	2.2
Height	HVG/mm	1.8
Location	L4/mm	60
Major axis of ellipse	S1/mm	8
Short axis of ellipse	S2/mm	2
Row	N	4

Figure 2. Nu and f-factor comparisons for various major axis lengths of the elliptical pole.

Figure 3. Nu and f-factor comparisons for various short axis lengths of the elliptical pole.

Figure 4. Nu and f-factor comparisons for various LVG thicknesses.

Figure 5. Nu and f-factor comparisons for various LVG lengths.

Figure 6. Velocity distributions at different cross sections at u_in = 0.8 m/s.

Figure 7. Nu and f-factor comparisons for various LVG heights.

Figure 8. Nu and f-factor comparisons for various LVG attack angles.

Figure 9. Velocity distributions at different cross sections at u_in = 0.8 m/s.

Figure 10. Nu and f-factor comparisons for various transverse pitches.

Figure 11. Nu and f-factor comparisons for various longitudinal pitches.

Table 2. Levels of each factor in this study.

Code	Factors (unit)	Level 1	Level 2	Level 3	Level 4
A	LVG length, LVG/mm	10	14	16	18
B	LVG height, HVG/mm	1.5	1.8	2.1	2.4
C	LVG attack angle, β/deg	5	15	30	44
D	Transverse pitch, Pt/mm	4	5	6	7
E	Longitudinal pitch, Pl/mm	70	80	90	100

Table 3. The orthogonal array of L₁₆ (5⁴).

Number of test	A	B	C	D	E
Test 1	1	1	1	1	1
Test 2	1	2	2	2	2
Test 3	1	3	3	3	3
Test 4	1	4	4	4	4
Test 5	2	1	2	3	4
Test 6	2	2	1	4	3
Test 7	2	3	4	1	2
Test 8	2	4	3	2	1
Test 9	3	1	3	4	2
Test 10	3	2	4	3	1
Test 11	3	3	1	2	4
Test 12	3	4	2	1	3
Test 13	4	1	4	2	3
Test 14	4	2	3	1	4
Test 15	4	3	2	4	1
Test 16	4	4	1	3	2

Figure 12. Contribution ratio of each factor.

Table 4. SN ratio for each case.

Number of test	A	B	C	D	E	SN ratio (η)
Test 1	1	1	1	1	1	0.27327
Test 2	1	2	2	2	2	0.47053
Test 3	1	3	3	3	3	0.42006
Test 4	1	4	4	4	4	0.23898
Test 5	2	1	2	3	4	0.55405
Test 6	2	2	1	4	3	0.22211
Test 7	2	3	4	1	2	0.50318
Test 8	2	4	3	2	1	0.34332
Test 9	3	1	3	4	2	0.83665
Test 10	3	2	4	3	1	0.79963
Test 11	3	3	1	2	4	0.34024
Test 12	3	4	2	1	3	0.35837
Test 13	4	1	4	2	3	0.81447
Test 14	4	2	3	1	4	0.66538
Test 15	4	3	2	4	1	0.57657
Test 16	4	4	1	3	2	0.36634

Table 5. Factorial effect and contribution ratio.

	Level	A	B	C	D	E
Ratio	1	0.3507	0.6196	0.3005	0.4501	0.4982
	2	0.4057	0.5394	0.4899	0.4921	0.5442
	3	0.5837	0.4600	0.5664	0.5350	0.4538
	4	0.6057	0.3268	0.5891	0.4686	0.4497
R (Max–Min)	1.0159	0.2550	0.2929	0.2886	0.0850	0.0945
Contribution ratio (%)	100.00	25.10	28.83	28.41	8.36	9.30

Figure 13. SN ratio of each factor.

Table 6. Optimal conditions from factorial effect analysis.

	LVG/mm	HVG/mm	β/deg	Pt/mm	Pl/mm
Optimal condition 1	18	1.5	44	6	80
Optimal condition 2	16	1.5	30	7	80

Figure 14. JF factor comparison of two optimal conditions.