Measurement of Pressures and Temperatures

Measurement  of  Pressures   and  Temperatures    

Václav  Uruba   CTU  Prague,  AS  CR  

State  of  Fluids  

•  Liquids  

•  Gases  –  equa;on  of  state  

•  Any  physical  quan;ty  is  func;on  of   temperature  T  and  pressure  P

PV RT=

3

3,484 10 P kg3

T m

ρ = ⋅ ^{− ⎡}⎢⎣ ^⎤⎥⎦

7 0,75

2,561 10 kg

T m s

µ = ⋅ ^{− ⎡}⎢ ^⎤⎥

⎣ ⎦

4 0,87

1,83 10 J

T K m s

λ = ⋅ ^{− ⎡}⎢ ^⎤⎥

⎣ ⎦ ^{l =1,098T}_P^1,25 [ ]^m

Ideal  gas  -­‐  air  

State  Quan;;es  

•  Temperature  –  THERMOMETERS    

•  Pressure  –  MANOMETERS  

•  Both  STATIC  –  flowing  fluid  

TOTAL  

(stagna;on)   STATIC  

High  veloci;es  

1 2 0

1 1

2

T M

T

γ − ⁻

⎛ ⎞

= +⎜⎝ ⎟⎠

(^{γ =1,4})

Adiaba;c  Compression  

T  –  sta;c  temperature  

T₀  –  total  (stagna;on)  temperature  

Temperature  on  a  sensor  

•  We  measure  recovery  temperature  

•  For  

0

1 Tr T

r T T

= − <

−

( )

0 : _r 0

M → T = T = T

Tr

0 : _r 0

M > T ≤ T

PRESSURE  

Pressure  Units  

•  Pascal  [Pa  =  N/m²]  

•  mm  H₂O  (9.81  Pa)  

•  mm  Hg,  Torr  (133.322  Pa)  

•  bar  (10⁶  dyn/cm²  =  10⁵  Pa)  

•  atm  (1.0133  x  10⁵  Pa)  –  sea  level  

•  at  (kgf/cm²  =  0.981  x  10⁵  Pa)  –  tech.  atm.  

•  psi  (Pound-­‐force  per  square  inch  =  6895  Pa)  

Manometers  

•  Types  

– Differen;al  pressure  -­‐  PSID  

– Absolute  pressure  (rel.  to  ref.)  -­‐  PSIA   – Gauge  pressure  (rel.  to  atm.)  -­‐  PSIG   – Vacuum  pressure  (nega;ve  gauge)  

– Sealed  pressure  (rel.  to  atm.  at  sea  level)  -­‐  PSIS  

•  Principles  

– Liquid  column   – Elas;c  parts  

Liquid  Column  

•  Water    k  =  9.8  

•  Alcohol    k  =  7.6  

•  Mercury  k  =  133  

p h g = ρ

[ ] [ ]

p Pa = h mm k ⋅

k = ρ ⋅ g

Technology  

•  Elas;c  parts  

–  Bourdon  tubes   –  Diaphraghms   –  Bellows    

•  Deforma;on  indica;on  

–  Mechanical  

–  Piezoresis;ve  strain  gauge   –  Capaci;ve  

–  Electromagne;c   –  Piezoelectric   –  Op;cal  

–  Poten;ometric   –  …  

Bourdon  tubes  

Sealed  tubes  

Elas;c  elements  

Capacitance  measuring  

•  Robust  

•  Linear  

•  Precise  

•  Stable  

•  Big  

•  Low  frequency  

Piesoresis;ve  diaphragms  

•  High  sensi;vity  

•  High  frequencies  

•  Small  

•  Temperature   influence  

•  Nonlinear  

•  Fragile  

Pressure  scanners  

•  Piesoresis;ve    

•  Up  to  64  sensors  

•  Electronics    

Pressure-­‐Sensi;ve  Paints  

•  Deac;va;on  of  photoexcieted  

molecules  of  organic  luminosphores  by   oxygen  molecules  (quenching).  

•  Discovered  by  H.  Kautsky  and  H.  Hirsch   in  1935.  

•  Certain  materials  are  luminous  when   excited  by  the  correct  light  wavelength.  

•  The  luminescence  is  dependent  on  air   pressure.  

Pressure-­‐Sensi;ve  Paints  

•  Qualita;ve    

•  Only  high  pressures  α  high  veloci;es  

Surface  pressure  distribu;on  

TEMPERATURE  

Methods  

•  Thermal  expansivity  

•  Electrical  sensors  

•  Op;cal  methods  

Method  of  thermal  expansivity  

•  Liquid  in  Glass  Thermometers  

•  Filled  System  Thermometers  

•  Bimetallic  Thermometers  

Electrical  sensors  

•  Thermocouples  

•  Resistance  Temperature  Detectors  (RTDs)  

•  Thermistors  (THERMal  resISTORS)  

Thermocouples  

+  

•  Cheep  

•  Small,  small  iner;a  

•  Big  range   -­‐  

•  Small  sensi;vity  

•  Worse  precision  

•  Reference  

Resistance  Temperature  Detectors  

( )

0 1

Rt = R +αt

+  

•  Precision,  stability  

•  Simple  

•  Range  (50-­‐1000K)   -­‐  

•  Bigger  

•  Price  

pla;num:    0.0038  

wire  

2w,  3w,  4w  

Thermistors  

•  Semiconductors  (oxids  of  Mn,  Ni,  Co,  Cu,  Fe,  Ti)  

•  Steinhart-­‐Hart  equia;on  

( )

( )

1/ ln ln

T = ⎡⎣A B+ R + C R ⎤⎦

+  

•  Sensi;vity   -­‐  

•  Nonlinear  

•  Low  temp  (upto  300°C)  

Op;cal  Methods  

•  Liquid  crystals  

•  Radia;on  Thermometers  (RTs)  

•  Thermal  Imaging  (Thermography)  

•  Laser-­‐Induced  Fluorescence    

•  Rayleigh  scamering  

Temperature   of  surface!!!  

Temperature   of  fluid  

Liquid-­‐crystal  temperature-­‐sensi;ve   films  

•  Hydrophobic  deriva;ves   of  polyvinyl  alcohol  and   cholesteric  liquid  crystals    

•  Encapsuled  (fric;on)  

•  Temperature  -­‐5  to   +150°C  

•  Thickness  30-­‐50μm  

•  High  sensi;vity  

Radia;on  Thermometers   (infrared)  

•  Non-­‐contact  sensors  

•  Electromagne;c   radia;on  received  

•  Range  -­‐40  °C  to  3000  °C  

Thermal  Imaging  

•  Infrared  range  of  the  electromagne;c   spectrum  (9  000–14  000nm)  

•  Black  body  radia;on  law  (Planck)  

SURFACE  !!!  

PLIF  

•  Planar  laser-­‐induced  fluorescence  (planar-­‐LIF)  -­‐  instant   whole-­‐field  concentra;on  or  temperature  maps  in  

liquid  flows.  

See  more  in  „Op;cal  methods“  

Rayleigh  scamering  

•  The  Rayleigh  signal  is  dependent  on:  

–  Laser  intensity  

–  Scamering  cross  sec;on   –  Number  density  

•  If  species  composi;on  and  pressure  are  

known  in  the  gas  the  gas  temperature  can  be   determined  from  imaging  of  the  Rayleigh   scamering.  

See  more  in  „Op;cal  methods“