Ahsan A. (ed.) Evaporation, Condensation and Heat transfer

Подождите немного. Документ загружается.

Heat Transfer and Hydraulic Resistance in Rough Tubes Including with Twisted Tape Inserts

499

10000 100000

0,02

0,04

0,06

0,08

0,1

t=0.5mm (¹ 5, table 2)

t=0.75 mm (¹ 6, table 2)

t=1 mm (¹ 7, table 2)

t=1.25 mm (¹ 8, table 2)

Fig. 16. Dependence of hydraulic resistance factor of rough tubes with rectangular thread

roughness profile on Re: line – for smooth tube (by calculation)

10000 100000

0,02

0,04

0,06

0,08

0,1

t=0.5 mm (¹ 9, table 2)

t=0.75 mm (¹ 10, table 2)

t=1 mm (¹ 11, table 2)

t=1.25 mm (¹ 12, table 2)

Fig. 17. Dependence of hydraulic resistance factor of rough tubes with rounded thread

roughness profile on Re: line – for smooth tube (by calculation)

Evaporation, Condensation and Heat Transfer

500

10000 100000

0,04

0,05

0,06

0,07

0,08

0,09

0,1

t=0.5 mm (¹ 2, table 2) - triangular

t=0.75 mm (¹ 3, table 2) - triangular

t=1 mm (¹ 7, table 2) - rectangular

t=1.25 mm (¹ 12, table 2)- rounded

Fig. 18. Dependence of hydraulic resistance factor of rough tubes with various thread

roughness profile and with similar heights of ledges on Re

Generalization of experimental data of a hydraulic resistance of tubes with a triangular

roughness profile is executed as follows (Tarasevich et al., 2007):

at Re=6000…80000

()

⎡

⎤

⎢

⎥

⎣

⎦

-0.8

ξ = 0.15 + 0.69× Δ+0.06×logΔ× exp -Re / 125.9 × Δ

; (2)

at Re=80000…250000

()

-0.03

ξ = (0.041 - 0.47 Δ)×Re

. (3)

Experimental data on a hydraulic resistance of tubes with a rectangular roughness profile at

Re <80000 have been generalized by dependence of an exponential aspect:

()

⎡

⎤

⎛⎞

⎢

⎥

⎜⎟

⎝⎠

⎣

⎦

-0.5

ξ =0.02+1.3×Δ+ (0.24 + 0.1× logΔ)× exp -Re / 1000 × Δ

. (4)

Heat Transfer and Hydraulic Resistance in Rough Tubes Including with Twisted Tape Inserts

501

Generalisation of dependence of a hydraulic resistance of tubes with a roughness of the

rectangular profile at Re> 80000 and with a rounded roughness profile has not been spent

yet in connection with ambiguous character of dependences in this cases.

2.2.2 Hydraulic resistance of tubes with the full thread roughness and with twisted

tape inserts at air flow

The presents authors also have gained the big data array on a hydraulic resistance of

tubes with various full thread profiles of a roughness and with twisted tape inserts

(S/d=2.5…7).

In fig. 19-22 the dependences of hydraulic resistance factor ξ of tubes with a triangular

roughness profile on number

Re are shown at various extent of twisting S/d. It is obvious

that with increase in extent of a twisting (decrease S/d) the hydraulic resistance is

augmented. The common character of dependence of factor

on Re in rough channels with

a twisting is analogous to dependence for a case without twisting, however at Re>20000 the

self-similar regime is observed, and the factor ξ is not augmented almost, i.e. the twisting a

little suppresses a turbulization oscillated by roughness ledges.

In fig. 23 the comparison of a hydraulic resistance of tubes with the twisted tape insert

(S/d

= 2.5) and various height of a triangular roughness profile is shown. It is obvious that

the increase of rate Δ promotes growth of a hydraulic resistance and in the twisting

conditions.

In fig. 24 the comparison of a hydraulic resistance of rough tubes with various profiles of a

roughness but with similar roughness height at an equal twisting is presented. Leading-outs

can be made same as well as at comparison of rough tubes without a twisting (fig. 18).

In fig. 25-28 and fig.29-32 the dependences of hydraulic resistance factor

of tubes with a

rectangular and rounded roughness profiles on Reynolds number

Re at various extent of

twisting S/d are presented accordingly. The common character of these dependences is

analogous to dependences for tubes with a triangular roughness profile (fig. 19-22) and

differs quantitatively.

Generalization of experimental data of a hydraulic resistance of tubes with a triangular

roughness profile and with twisted tape inserts is executed as follows (Tarasevich et al.,

2007):

at Re =3000…30000

()

⎡

⎤

⎣

⎦

-(0.0023×exp Δ / 0.0143 +0.39)

ξ = S / d × 0.16 × exp -Re / 3700 + 0.065 + 2.3Δ

; (5)

and at Re =30000…80000

()

⎛⎞

⎜⎟

⎝⎠

0.4

S/d

ξ =0.5× =0.5×

Δ /d

(6)

For tubes with the rectangular and rounded ledges of roughness such generalization is not

executed yet in connection with a difficult ambiguous aspect of these dependences at

various magnitudes S/d

and Δ.

Evaporation, Condensation and Heat Transfer

502

2000 10000 100000 400000

0,030,03

0,040,04

0,050,05

0,060,06

0,070,07

0,080,08

0,090,09

0,10,1

0,110,11

0,120,12

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 19. Dependence of hydraulic resistance factor of rough tubes with triangular roughness

profile (Table 2, № 1) on Re at various S/d

2000 10000 100000 400000

0,04

0,05

0,06

0,07

0,08

0,09

0,1

0,11

0,12

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 20. Dependence of hydraulic resistance factor of rough tubes with triangular roughness

profile (Table 2, № 2) on Re at various S/d

Heat Transfer and Hydraulic Resistance in Rough Tubes Including with Twisted Tape Inserts

503

10000 100000

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 21. Dependence of hydraulic resistance factor of rough tubes with triangular roughness

profile (Table 2, № 3) on Re at various S/d

2000 10000 100000 400000

0,06

0,1

0,15

0,2

0,25

0,3

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 22. Dependence of hydraulic resistance factor of rough tubes with triangular roughness

profile (Table 2, № 4) on Re at various S/d

Evaporation, Condensation and Heat Transfer

504

10000 100000

0,04

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,2

t=0.25 mm (¹ 1, table 2)

t=0.5 mm (¹ 2, table 2)

t=0.75 mm (¹ 3, table 2)

t=1 mm (¹ 4, table 2)

Fig. 23. Dependence of hydraulic resistance factor of tubes with various triangular

roughness profile and with twisted tape insert (S/d=2.5) on Re

10000 100000

0,06

0,08

0,1

0,12

0,14

0,16

0,18

0,2

t=0.5 mm (¹ 2, table 2)

t=0.75 mm (¹ 3, table 2)

t=1 mm (¹ 7, table 2)

t=1.25 mm (¹ 12, table 2)

Fig. 24. Dependence of hydraulic resistance factor of rough tubes with various thread

roughness profile with similar heights of ledges and with twisted tape insert (S/d=2.5) on Re

Heat Transfer and Hydraulic Resistance in Rough Tubes Including with Twisted Tape Inserts

505

2000 10000 100000 400000

0,03

0,04

0,06

0,08

0,1

0,120,12

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 25. Dependence of hydraulic resistance factor of rough tubes with rectangular

roughness profile (Table 2, № 5) on Re at various S/d

2000 10000 100000 400000

0,04

0,06

0,08

0,1

0,12

0,14

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 26. Dependence of hydraulic resistance factor of rough tubes with rectangular

roughness profile (Table 2, № 6) on Re at various S/d

Evaporation, Condensation and Heat Transfer

506

2000 10000 100000 400000

0,06

0,1

0,15

0,2

0,25

0,3

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 27. Dependence of hydraulic resistance factor of rough tubes with rectangular

roughness profile (Table 2, № 7) on Re at various S/d

2000 10000 100000 400000

0,06

0,1

0,15

0,2

0,25

0,3

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 28. Dependence of hydraulic resistance factor of rough tubes with rectangular

roughness profile (Table 2, № 8) on Re at various S/d

Heat Transfer and Hydraulic Resistance in Rough Tubes Including with Twisted Tape Inserts

507

2000 10000 100000 400000

0,03

0,04

0,05

0,06

0,07

0,08

0,09

0,1

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 29. Dependence of hydraulic resistance factor of rough tubes with rounded roughness

profile (Table 2, № 9) on Re at various S/d

2000 10000 100000 400000

0,04

0,05

0,06

0,07

0,08

0,09

0,1

0,11

0,12

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 30. Dependence of hydraulic resistance factor of rough tubes with rounded roughness

profile (Table 2, № 10) on Re at various S/d

Evaporation, Condensation and Heat Transfer

508

2000 10000 100000 400000

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

0.14

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 31. Dependence of hydraulic resistance factor of rough tubes with rounded roughness

profile (Table 2, № 11) on Re at various S/d

2000 10000 100000 400000

0,05

0,06

0,07

0,08

0,09

0,1

0,11

0,12

0,13

0,14

0,15

0,16

s/d=2.5

s/d=3.5

s/d=4

s/d=5

s/d=7

without tape

Fig. 32. Dependence of hydraulic resistance factor of rough tubes with rounded roughness

profile (Table 2, № 12) on Re at various S/d