A geometric study on shell side heat transfer and flow resistance of a six-start spirally corrugated tube

Figures & data

Figure 1. Geometries of a six-start spirally corrugated tube. (a) Geometric model of tube and (b) Geometric parameters of tube.

Figure 2. Shell side flow channel model of a six-start spirally corrugated tube.

Figure 3. Results of validity verification.

Table 1. Geometric parameters of six-start spirally corrugated tubes with different pitches.

Number	Corrugation depth e/mm	Equivalent diameter di/mm	Pitchp/mm	Lengthl/mm	p/di	e/di	p/e
1–1	4	11.40	35	600	3.07	0.35	8.75
1–2	4	11.40	37.5	600	3.29	0.35	9.38
1–3	4	11.40	40	600	3.51	0.35	10
1–4	4	11.40	42.5	600	3.73	0.35	10.63
1–5	4	11.40	45	600	3.95	0.35	11.25
1–6	4	11.40	47.5	600	4.17	0.35	11.88

Table 2. Shell side Nusselt number of six-start spirally corrugated tubes with different pitches.

Re (× 10^4) (mm)	1	2	3	4	5	6
p = 35	112.755	192.633	282.969	370.396	452.895	532.391
p = 37.5	113.562	190.298	279.869	364.398	444.563	522.387
p = 40	113.636	192.097	279.203	362.291	447.955	520.356
p = 42.5	113.970	190.490	278.173	362.109	441.881	520.335
p = 45	114.030	190.543	275.683	361.845	441.582	520.898
p = 47.5	114.240	190.773	274.475	357.755	437.090	512.210

Figure 4. Ratio of Nu_c/Nu_s between six-start spirally corrugated tubes and smooth tubes.

Figure 5. Secondary velocities of six-start spirally corrugated tubes with different pitches.

Figure 6. Shell side vorticities of six-start spirally corrugated tubes with different pitches.

Figure 7. Shell side temperature distribution of six-start spirally corrugated tubes with different pitches.

Figure 8. The shell side flow resistance coefficients of six-start spirally corrugated tubes with different pitches.

Figure 9. Ratio of the shell side flow resistance coefficient (f_c/f_s) between six-start spirally corrugated tubes and smooth tubes.

Table 3. Geometric parameters of six-start spirally corrugated tubes with different corrugation depths.

Number	Corrugation depth	Equivalent diameter	Pitch	Length	p/di	e/di	p/e
	e/mm	di/mm	p/mm	L/mm
2–1	1.5	9.61	35	600	3.64	0.16	23.33
2–2	2	10.10	35	600	3.47	0.20	17.5
2–3	2.5	10.29	35	600	3.40	0.24	14
2–4	3	10.93	35	600	3.20	0.27	11.67
2–5	3.5	11.20	35	600	3.13	0.31	10
2–6	4	11.40	35	600	3.07	0.35	8.75
2–7	4.5	11.45	35	600	3.06	0.39	7.78

Table 4. Shell side Nusselt number of six-start spirally corrugated tubes with different corrugation depths.

Re (× 10^4) (mm)	1	2	3	4	5	6
e = 1.5	110.672	193.510	285.997	371.800	454.166	535.878
e = 2	115.486	198.926	292.741	381.062	465.081	547.898
e = 2.5	114.133	194.445	284.863	369.641	449.476	530.278
e = 3	117.928	198.645	288.590	374.115	462.631	540.251
e = 3.5	115.178	192.625	284.829	373.107	452.937	533.272
e = 4	112.755	192.633	282.969	370.396	452.895	532.391
e = 4.5	109.355	186.015	275.602	361.006	438.104	516.831

Figure 10. Ratio of Nu_c/Nu_s between six-start spirally corrugated tubes and smooth tubes.

Figure 11. The shell side flow resistance coefficient of the six-start spirally corrugated tubes with different corrugation depths.

Figure 12. Ratio of the shell side flow resistance coefficient (f_c/f_s) between six-start spirally corrugated tubes and the smooth tubes (a) Model of Nusselt number (b) Model of flow resistance coefficient.

Figure 13. Residual plots of regression models (a) Model of Nusselt number and (b) Model of flow resistance coeffitient.

Figure 14. Relative errors between derived and simulaed. (a) Relative errors of Nu and (b) Relative errors of f.