It is essential to determine the sensitivity and the inertia of the cylindrical Pirani gauge under different conditions when modeling it. For this purpose, it is appropriate to study the Taylor-Couette flow between two stationary concentric cylinders with finite length. In this work is considered the possibilities for instability and self-organization of the flow in the gaseous medium between the cylinders with the wall inhomogeneous temperature profile of the inner cylinder (the fiber). These processes can affect the accuracy and sensitivity of the gauge. The heat and the energy transfer in setting on different forms of temperature distributed on the inner cylinder in the form of stationary temperature are studied. The realization of such conditions is difficult technically feasible in some cases, but their set in mathematical model gives more opportunities to study the stability and the flow self-organization in the gaseous medium between the cylinders.
REFERENCES
1.
S.
Chapman
and T.
Cowling
, The Mathematical Theory of Non-Uniform Gases
(Cambridge University Press
, Cambridge
, 1952
).2.
S.
Albertoni
, C.
Cercignani
, and L.
Gotusso
, Numerical evaluation of the slip coefficient
, Phys. Fluids
6
, 993
–996
(1963
).3.
C.
Cercignani
and F.
Sernagiotto
, Cylindrical Couette flow of a rarefied gas
, Physics of Fluids
10
, 1200
–1204
(1967
).4.
M.
Cole
, New thermal pulse vacuum gauge
, Vacuum
38
(8-10
), 897
–899
(1988
).5.
G. A.
Bird
, Molecular Gas Dynamics and the Direct Simulation of Gas Flows
(Oxford University Press
, Oxford
, 1994
).6.
C.
Cercignani
, Rarefied Gas Dynamics, From Basic Concepts to Actual Calculations
(Cambridge University Press
, Cambridge
, 2000
).7.
R.
Bird
, W.
Stewart
, and E.
Lightfoot
, Transport Phenomena
, 2nd edn (John Wiley
, New York
, 2002
).8.
W.
Jitschin
und S.
Ludwig
, Pulsed hot filament vacuum gauge with Pirani sensor
, Vakuum in Forschung und Praxis
16
, 23
–29
(2004
).9.
J.
Park
, P.
Bahukudumbi
, and A.
Beskok
, Rarefaction effects on shear driven oscillatory gas flows: A DSMC study in the entire Knudsen regime
, Phys. Fluids
16
, 317
(2004
).10.
H.
Ploechinger
and F.
Salzberger
, Pulsed Pirani vacuum gauge, Vakuum in Forschung und Praxis
(2005
), author profiles for this publication at: http://www.researchgate.net/ publication/260123890.11.
F
Sharipov
and G
Bertoldo
, “Numerical modelling of Pirani sensor,” in XVIII IMEKO World Congress, Metrology for a Sustainable Development
, Rio de Janeiro, Brazil
, September, 17-22, 2006
.12.
D.
Emerson
, Gu
Xiao-Jun
, S.
Stefanov
, S.
Yuhong
, and W.
Barber
, Nonplanar oscillatory shear flow: From the continuum to the free-molecular regime
, Phys. Fluids
19
, 107105
(2007
).13.
P.
Tzeng
, W.
Chou
, C.
Liu
, and W.
Li
, Improvement of the gas-surface collision rule for adiabatic walls in DSMC modeling of rarefied gas convection in a micro enclosure
, Journal of Aeronautics, Astronautics and Aviation, Series A
43
(3
), 147
–158
(2011
).14.
F.
Sharipov
, Data on the velocity slip and temperature jump on a gas-solid interface
, J. Phys. Chem. Ref. Data
40
, 023101
(2011
).15.
P.
Gospodinov
, V.
Roussinov
, and S.
Stefanov
, Nonisothermal oscillatory cylindrical Couette gas, flow in the slip regime: A computational study
, European Journal of Mechanics B/Fluids
33
, 68
–77
(2012
).16.
D.
Kalempa
and F.
Sharipov
, Numerical modeling of thermoacoustic waves in a rarefied gas confined between coaxial cylinders
, Vacuum
109
, 326
–332
(2014
).17.
P.
Gospodinov
, V.
Rousinov
, and M.
Mironova
, “Cylindrical nonisothermal oscillatory Couette gas flow in the slip regime: Wall shear stress and energy transfer, numerical investigation
”, IntellectualArchive.com online publications, Intellectual Archive Bulletin
, Feb. 19, 2014, pp. 2
–19
.18.
A.
Mohammadzadeh
, A.
Rana
, and H.
Struchtrup
, DSMC and R13 modeling of the adiabatic surface
, International Journal of Thermal Sciences
101
, 9
–23
(2016
).19.
P.
Gospodinov
, D.
Dankov
, and V.
Roussinov
, “Thermo acoustic waves in rarefied gas between two coaxial cylinders at a sudden change of the temperature of the outer cylinder,” in AMiTaNS’16
, AIP Conference Proceedings
1773
, edited by M.D.
Todorov
(American Institute of Physics
, Melville, NY
, 2016
), paper 080001, 7
p.20.
P.
Gospodinov
, D.
Dankov
, V.
Roussinov
, and S.
Stefanov
, “Stationary cylindrical Couette flow at different temperature of cylinders: the local Knudsen number effect,” in AMiTaNS’11
, AIP Conference Proceedings
1404
, edited by M.D.
Todorov
and C.I.
Christov
(American Institute of Physics
, Melville, NY
, 2011
), pp. 451
–456
.21.
P.
Gospodinov
, D.
Dankov
, V.
Roussinov
, and M.
Mironova
, Numerical simulation of the pulsed Pirani gauges, in AMiTaNS’17
, AIP Conference Proceedings
1895
, edited by M.D.
Todorov
(American Institute of Physics
, Melville, NY
, 2017
), paper 080003.22.
H.
Oualli
, A.
Boubdallah
, S.
Hanchi
, and M.
Gad-Ei-Hak
, Taylor-Couette flow control using a radially oscillating inner cylinder
, Geophysical Research Abstracts, EGU General Assembly
2010
, Vol. 12
, EGU2010-1252.23.
H.
Oualli
, M.
Mekadem
, M.
Lebbi
, and A.
Bouabdallah
, Taylor-Couette flow control by amplitude variation of the inner cylinder cross-section oscillation
, Eur. Phys. J. Appl. Phys.
71
, 11102
(2015
).24.
A.
Lalaoua
and A.
Bouabdallah
, On the onset of Taylor vortices in finite-length cavity subject to a radial oscillation motion
, Journal of Applied Fluid Mechanics
9
(4
), 1887
–1896
(2016
).
This content is only available via PDF.
© 2022 Author(s).
2022
Author(s)
You do not currently have access to this content.
