Summary
While the theory concerning critical discharges of single-phase flow, in particular of gases, is well known, the direct opposite is true for two-phase mixtures. The question still remains to be answered whether critical flow occurs for two-phase flow with the same implications that it carries for single-phase flow. A theoretical analysis, which is supported by experimental data, is presented in this paper and indicates that the implications for single-phase and two-phase critical flow differ significantly. While single-phase flow is restricted by so-called sonic choking, the extra freedom available in a two-phase flow system, the slip ratio, restricts the maximum flow in the latter. Furthermore, two-phase critical flow is achieved when the slip ratio takes on a value such that the rate of momentum gain by convection per unit volume becomes identical in each fluid phase.
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Abbreviations
- A :
-
cross-sectional area of flow, ft2
- D :
-
equivalent diameter or diameter of test section, ft
- f :
-
friction factor, dimensionless
- G :
-
mass flow rate, lb m /sec-ft2
- g :
-
gravitational constant, 32.2 ft/sec2
- g c :
-
conversion factor, 32.2 lb m -ft/lb f -sec2
- k :
-
ū 2/ū 1, slipratio, dimensionless
- p :
-
static pressure, lb f /ft2
- t :
-
time, sec
- ū :
-
average velocity, ft/sec
- v :
-
specific volume, ft3/lb m
- W :
-
mass rate, lb m /sec
- x :
-
length in direction of flow, ft
- α :
-
void fraction, dimensionless
- ρ :
-
density, lb m /ft3
- τ :
-
shear force, lb f /ft2
- χ :
-
quality, dimensionless
- i :
-
refers to the i-th phase
- k :
-
refers to the k-th phase
- n :
-
refers to the number of phases
- 1:
-
refers to liquid phase
- 2:
-
refers to vapor phase
References
Isbin, H. S., J. E. Moy and J. R. DaCruz, A.I.Ch.E. Journal 3 (1957) 361.
Faletti, D. W., Two-Phase Critical Flow of Steam-Water Mixtures, Ph.D. Thesis, Univ. of Washington, 1959.
Zaloudek, F. R., The Low Pressure Critical Discharge of Steam-Water Mixtures from Pipes, HW-68934, 1961.
Muraoka, J., Steam-Water Critical Flow Test-Design Test 1040, HW-69488, 1961.
Fauske, H. K., Contribution to the Theory of Two-Phase, One-Component Critical Flow, Dissertation in partial fulfillment of ScD. degree, 1961.
Fauske, H. K., Critical Two-Phase, Steam-Water Flows, 1961 Proc. Heat Transfer and Fluid Mech. Inst., Stanford University Press.
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Work performed under the auspicies of the U.S. Atomic Energy Commission.
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Fauske, H.K. Some ideas about the mechanism causing two-phase critical flow. Appl. sci. Res. 13, 149–160 (1964). https://doi.org/10.1007/BF00382043
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DOI: https://doi.org/10.1007/BF00382043