Citation:

PANGAEA.949208

Name: Optimal growth as function of Wo (Re_o=8000,A=infty)
Published: 2022-09-29
License: https://creativecommons.org/licenses/by/4.0/
Keywords: nonlinear instability; transition to turbulence

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Published: 2022-09-29 • DOI registered: 2023-01-13

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Abstract:

The data are obtained via an in-house Matlab script (developed by Dr. Baofang Song) to compute the non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows. In this study, a Newtonian fluid driven by pulsatile and oscillatory flow rate flows in a straight pipe. In pulsatile flow, there are three governing parameters: steady Reynolds number (defined by the steady flow component), pulsation amplitude (ratio of oscillatory and steady flow component) and Womersley number (dimensionless pulsation and oscillation frequency). In oscillatory flow, due to vanishment of steady flow component, oscillatory Reynolds number (defined by the oscillation flow component) and Womersley number. The Reynolds number defined by the thickness of Stokes layer is alternatively used for the oscillatory Reynolds number. The study was carried out in a manner that one governing parameter varies while other governing parameters are fixed.

The data file 'TG_Wo_Reo8000.dat' shows the dependence of the maximum energy amplification on the Womersley number for the oscillatory Reynolds number of 8000.

This file includes twelve columns: the first column indicates the Womersley number; the second column indicates the pulsation period; the third column indicates the optimal axial wavenumber; the fourth column indicates the optimal azimuthal wavenumber; the fifth column indicates the initial time of the optimal perturbation; the sixth column indicates the final time of the optimal perturbation; the seventh column indicates the evolution time of the optimal perturbation; the eighth column indicates the initial time of the optimal perturbation normalized by the pulsation period; the nineth column indicates the final time of the optimal perturbation normalized by the pulsation period; the tenth column indicates the evolution time of the optimal perturbation normalized by the pulsation period; the eleventh column indicates the maximum energy amplification; the twelfth column indicates the Reynolds number which is defined with the characteristic length of the thickness of the Stokes layer.

Keyword(s):

nonlinear instability; transition to turbulence

Comment:

#t0:initial time; tf:end time;

VARIABLES = "Wo", "T", "k_z", "k_θ", "t0", "tf", "tf-t0", "t0/T", "tf/T", "(tf-t0)/T", "TG", "Re_delta"

ZONE T="data, all modes, opf", I=11, J=1

Parameter(s):

#	Name	Short Name	Principal Investigator
1	Womersley number	Wo	Xu, Duo
2	Pulsation period	T	Xu, Duo
3	Axial wave number	k_z	Xu, Duo
4	Azimuthal wave number	k_θ	Xu, Duo
5	Time of perturbation	t0	Xu, Duo
6	Time of perturbation energy maximum	tf	Xu, Duo
7	Time of perturbation energy maximum - Time of perturbation (tf-t0)	tau	Xu, Duo
8	Time of pertubartion by pulsation period	t0/T	Xu, Duo
9	Time of pertubartion energy maximum by pulsation period	tf/T	Xu, Duo
10	Time of perturbation energy maximum - Time of perturbation by pulsation period	(tf-t0)/T	Xu, Duo
11	Transient energy growth	TG	Xu, Duo
12	Reynolds number of the Stokes layer	Re_δ	Xu, Duo

License:

Creative Commons Attribution 4.0 International (CC-BY-4.0)

Status:

Curation Level: Enhanced curation (CurationLevelC) * Processing Level: PANGAEA data processing level 2 (ProcLevel2)

Size:

132 data points

Data

Download dataset as tab-delimited text — use the following character encoding:

1 Wo	2 T	3 k_z	4 k_θ	5 t0	6 tf	7 tau	8 t0/T	9 tf/T	10 (tf-t0)/T	11 TG	12 Re_δ
5	125.66	2.8	1	56.54866776	69.11466777	12.566	0.45	0.54999705	0.09999705	17115217.65616810	1131.37084990
6	87.27	2.4	1	30.54326191	56.72326191	26.180	0.35	0.65000070	0.30000070	462961617.79498280	942.80904158
7	64.11	3.2	1	22.43994753	48.08594753	25.646	0.35	0.75000539	0.40000539	1581760400.85994050	808.12203564
8	49.09	3.6	1	17.18058482	36.81558482	19.635	0.35	0.75000094	0.40000094	997401920.88126840	707.10678119
9	38.79	4.4	1	13.57478307	29.08878307	15.514	0.35	0.74999903	0.39999903	226046597.77295940	628.53936105
10	31.42	5.0	1	10.99557429	23.56157428	12.566	0.35	0.74998820	0.39998820	34520129.11188500	565.68542495
13	18.59	6.8	1	6.50625697	13.94225697	7.436	0.35	0.75001494	0.40001494	259842.11195603	435.14263458
15	13.96	8.4	1	4.88692191	10.47192190	5.585	0.35	0.74999616	0.39999616	25501.44539324	377.12361663
20	7.85	12.0	0	2.74889357	5.10489357	2.356	0.35	0.64997524	0.29997524	685.76714469	282.84271247
30	3.49	19.6	1	1.22173048	1.91973048	0.698	0.35	0.54996227	0.19996227	26.07568495	188.56180832
40	1.96	26.5	1	0.68722339	1.08022339	0.393	0.35	0.55015326	0.20015326	5.47733821	141.42135624