a review of critical flow venturis
DESCRIPTION
Sonic NozzlesTRANSCRIPT
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A Review of Critical Flow Venturis
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Sonic Nozzles
Aamth
RTcc
av
p
0
*R0
th RTCAPm M
zRTPM
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y = -4.5881x + 1.0002
0.976
0.978
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0.002 0.0025 0.003 0.0035 0.004 0.0045 0.005
Re-1/2
Cd
0.976
0.978
0.98
0.982
0.984
0.986
0.988
0.99
0.992
0 50000 100000 150000 200000
Re
Cd
Discharge Coefficient Cd
0
*R0
th RTCAPm M
dth
PS Cmm
PSm
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Isentropic, 1-Dimensional Flow, Perfect Gas
Velocity at each cross section of a convergent-divergent critical venturi (Reynolds 1886, Rayleigh 1916)
121
2
121
*
211
211
,1,
MaMaMaf
fAA
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Isentropic, 1-Dimensional Flow, Perfect Gas, Fully Expanded (no shocks)
0TT
0PP
)75.0(aw RT
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Inviscid Core FlowSmith and Matz 1962, “A non-one-dimensional flow exists because of the centrifugal forces created by the turning of the flow in the contraction section.”
1-D:
2-D:
Hall 1962, Kliegel and Levine 1969 0.12 %
44
33
22
cored, 1
C where 2, 3, and 4 are gas species dependent components and
Λ is the expansion parameter (R or 1 + R).
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Velocity Boundary Layer: Cd scales with Re-1/2
x
x.Re72081
Blasius: boundary layer on a flat plate
Laminar: Tang 1969, Geropp 1971, similarity transformations
Turbulent: Stratford 1964, integral boundary layer technique
Mickan 2006
Transition at Re 1 x 106
nmnm aaC 2221bld, ReRe1
where Ω = r*/R is the throat curvature ratio (nominally 0.25 for an ASME / ISO venturi), a1 and a2 are coefficients, and m and n are exponents whose values depend on whether the flow is laminar or turbulent.
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0.955
0.960
0.965
0.970
0.975
0.980
0.985
0.990
0.995
1.000
0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014
Re -1/2
mex
pt /
m2 =
Cd
0.955
0.960
0.965
0.970
0.975
0.980
0.985
0.990
0.995
1.000
0.01 0.1 1 10 100 1000
m expt (g/s)
mex
pt /
m2
0.955
0.960
0.965
0.970
0.975
0.980
0.985
0.990
0.995
1.000
0.0E+00 5.0E+05 1.0E+06 1.5E+06 2.0E+06 2.5E+06
Re
mex
pt /
m2
21Re /dC
Reynolds Number Scaling
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Boundary Layer Transition
Ishibashi and Arnberg, The Effect of Inlet Geometry on the Critical Flowrate of Toroidal Throat Venturi Nozzle, CFVN Workshop, Quedlinburg, Germany, June, 2005
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Analytical Cd predictions agree well with experiments
Johnson and Wright 2008
Mickan 2006
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Gas Species Effects
• Solid lines from Nakao and Takamoto, Discharge Coefficients of Critical Flow Venturi Nozzles for CO2 and SF6, Transactions of the ASME, December, 2000, d = 0.295 to 2.36 mm.
• Points from NIST experiments, d = 0.387 mm.
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Cd can be treated as numerous uncoupled physical phenomena
Cd = CR*Cinv Cvbl CTbl C Cvib + higher order terms
Vibrational relaxation (CO2 , SF
6 )
Thermal expansion of CFV material
Thermal boundary layer
Velocity boundary layer
Real gas effectsInviscid core flow