Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120
Abstract Flow development and degradation during Type B turbulent drag reduction by 0.10 to 10 wppm solutions of a partially-hydrolysed polyacrylamide B1120 of MW...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer Netherlands
2021
|
| Online Access: | https://hdl.handle.net/1721.1/131781 |
| Summary: | Abstract
Flow development and degradation during Type B turbulent drag reduction by 0.10 to 10 wppm solutions of a partially-hydrolysed polyacrylamide B1120 of MW
=
$=$
18x106 was studied in a smooth pipe of ID
=
$=$
4.60 mm and L/D
=
$=$
210 at Reynolds numbers from 10000 to 80000 and wall shear stresses Tw from 8 to 600 Pa. B1120 solutions exhibited facets of a Type B ladder, including segments roughly parallel to, but displaced upward from, the P-K line; those that attained asymptotic maximum drag reduction at low Re√ f but departed downwards into the polymeric regime at a higher retro-onset Re√ f; and segments at MDR for all Re√ f. Axial flow enhancement profiles of S
′
$^{\prime }$
vs L/D reflected a superposition of flow development and polymer degradation effects, the former increasing and the latter diminishing S
′
$^{\prime }$
with increasing distance downstream. Solutions that induced normalized flow enhancements S
′
$^{\prime }$
/S
m
′
<
$^{\prime }_{\mathrm {m}} <$
0.4 developed akin to solvent, with Le,p/D
=
$=$
Le,n/D
<
$<$
42.3, while those at maximum drag reduction showed entrance lengths Le,m/D
∼
$\sim $
117, roughly 3 times the solvent Le,n/D. Degradation kinetics were inferred by first detecting a falloff point (Re√f∧, S
′
∧
$^{{\prime }\wedge }$
), of maximum observed flow enhancement, for each polymer solution. A plot of S
′
∧
$^{{\prime }\wedge }$
vs C revealed S
′
∧
$^{{\prime }\wedge }$
linear in C at low C, with lower bound [S
′
$^{\prime }$
]
=
$=$
5.0 wppm− 1, and S
′
∧
$^{{\prime }\wedge }$
independent of C at high C, with upper bound S
m
′
=
$^{\prime }_{\mathrm {m}} =$
15.9. The ratio S
′
$^{\prime }$
/S
′
∧
$^{{\prime }\wedge }$
in any pipe section was interpreted to be the undegraded fraction of original polymer therein. Semi-log plots of (S
′
$^{\prime }$
/S
′
∧
$^{{\prime }\wedge }$
) at a section vs transit time from pipe entrance thereto revealed first order kinetics, from which apparent degradation rate constants kdeg s− 1 and entrance severities −ln(S
′
$^{\prime }$
/S
′
∧
$^{{\prime }\wedge }$
)0 were extracted. At constant C, kdeg increased linearly with increasing wall shear stress Tw, and at constant Tw, kdeg was independent of C, providing a B1120 degradation modulus (kdeg/Tw)
=
$=$
(0.012
±
$\pm $
0.001) (Pa s)− 1 for 8
<
$<$
Tw Pa
<
$<$
600, 0.30
<
$<$
C wppm
<
$<$
10. Entrance severities were negligible below a threshold Twe
∼
$\sim $
30 Pa and increased linearly with increasing Tw for Tw
>
$>$
Twe. The foregoing methods were applied to Type A drag reduction by 0.10 to 10 wppm solutions of a polyethyleneoxide PEO P309, MW
=
$=$
11x106, in a smooth pipe of ID
=
$=$
7.77 mm and L/D
=
$=$
220 at Re from 4000 to 115000. P309 solutions that induced S
′
$^{\prime }$
/S
m
′
<
$^{\prime }_{\mathrm {m}} <$
0.4 developed akin to solvent, with Le,p/D
=
$=$
Le,n/D
<
$<$
23, while those at MDR had entrance lengths Le,m/D
∼
$\sim $
93, roughly 4 times the solvent Le,n/D. P309 solutions described a Type A fan distorted by polymer degradation. A typical trajectory departed the P-K line at an onset point Re√ f* followed by ascending and descending polymeric regime segments separated by a falloff point Re√f∧, of maximum flow enhancement; for all P309 solutions, onset Re√ f* = 550
±
$\pm $
100 and falloff Re√f∧ = 2550
±
$\pm $
250, the interval between them delineating Type A drag reduction unaffected by degradation. A plot of falloff S
′
∧
$^{{\prime }\wedge }$
vs C for PEO P309 solutions bore a striking resemblance to the analogous S
′
∧
$^{{\prime }\wedge }$
vs C plot for solutions of PAMH B1120, indicating that the initial Type A drag reduction by P309 after onset at Re√ f* had evolved to Type B drag reduction by falloff at Re√f∧. Presuming that Type B behaviour persisted past falloff permitted inference of P309 degradation kinetics; kdeg was found to increase linearly with increasing Tw at constant C and was independent of C at constant Tw, providing a P309 degradation modulus (kdeg/Tw)
=
$=$
(0.011
±
$\pm $
0.002) (Pa s)− 1 for 4
<
$<$
Tw Pa
<
$<$
400, 0.10
<
$<$
C wppm < 5.0. Comparisons between the present degradation kinetics and previous literature showed (kdeg/Tw) data from laboratory pipes of D
∼
$\sim $
0.01 m to lie on a simple extension of (kdeg/Tw) data from pipelines of D
∼
$\sim $
0.1 m and 1.0 m, along a power-law relation (kdeg/Tw)
=
$=$
10− 5.4.D− 1.6. Intrinsic slips derived from PAMH B1120 and PEO P309-at-falloff experiments were compared with previous examples from Type B drag reduction by polymers with vinylic and glycosidic backbones, showing: (i) For a given polymer, [S
′
$^{\prime }$
] was independent of Re√ f and pipe ID, implying insensitivity to both micro- and macro-scales of turbulence; and (ii) [S
′
$^{\prime }$
] increased linearly with increasing polymer chain contour length Lc, the proportionality constant
β
=
$\beta =$
0.053
±
$\pm $
0.036 enabling estimation of flow enhancement S
′
=
$^{\prime } =$
C.Lc.β for all Type B drag reduction by polymers. |
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