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 |
| _version_ | 1826204195834822656 |
|---|---|
| author | Virk, Preetinder S |
| author2 | Massachusetts Institute of Technology. Department of Chemical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Chemical Engineering Virk, Preetinder S |
| author_sort | Virk, Preetinder S |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T12:50:24Z |
| format | Article |
| id | mit-1721.1/131781 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T12:50:24Z |
| publishDate | 2021 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1317812023-11-08T21:41:38Z Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120 Virk, Preetinder S Massachusetts Institute of Technology. Department of Chemical Engineering 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. 2021-09-20T17:30:14Z 2021-09-20T17:30:14Z 2018-04-16 2020-09-24T20:38:45Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131781 en https://doi.org/10.1007/s10494-018-9915-5 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media B.V., part of Springer Nature application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | Virk, Preetinder S Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120 |
| title | Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120 |
| title_full | Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120 |
| title_fullStr | Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120 |
| title_full_unstemmed | Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120 |
| title_short | Glimpses of Flow Development and Degradation During Type B Drag Reduction by Aqueous Solutions of Polyacrylamide B1120 |
| title_sort | glimpses of flow development and degradation during type b drag reduction by aqueous solutions of polyacrylamide b1120 |
| url | https://hdl.handle.net/1721.1/131781 |
| work_keys_str_mv | AT virkpreetinders glimpsesofflowdevelopmentanddegradationduringtypebdragreductionbyaqueoussolutionsofpolyacrylamideb1120 |