Skip to main content
SpringerLink
Log in

Dynamics of vapor bubbles growth at boiling resulting from enthalpy excess of the surrounding superheated liquid and sound pulses generated by bubbles

  • Original
  • Published:
Heat and Mass Transfer Aims and scope Submit manuscript

Abstract

The results of experiments investigating the exponential dependence of the vapor bubble radius on time at saturated boiling are generalized. Three different methods to obtain this dependence are suggested: (1) by the application of the transient heat conduction equation, (2) by using the correlations of energy conservation, and (3) by solving a similar electrodynamic problem. Based on the known experimental data, the accuracy of the dependence up to one percent and a few percent accuracy of its description based on the sound pressure generated by a vapor bubble have been determined. A significant divergence of the power dependence of the vapor bubble radius on time (with an exponent of 1/2) with the experimental results and its inadequacy for the description of the sound pulse generated by the bubble have been demonstrated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Abbreviations

a′:

Temperature diffusivity of the fluid (m2/s)

b :

Numerical coefficient

c′:

Specific heat of the fluid [J/(kg K)]

C :

Capacitance (F)

\(C_{*}\) :

Heat capacity of the superheated fluid layer (J/K)

f(t):

Time function

g :

Electrical conductivity (Cm)

\(g_{*}\) :

Thermal conductivity (W/K)

J S :

Jacob similarity parameter

k :

Exponent of power dependence

K :

Proportionality factor of power dependence

l * :

Parameter of thermal conductivity, m

L :

Specific heat of vaporization (J/kg)

m′:

Mass of the superheated fluid layer (kg)

n :

Exponent of power dependence

p :

Sound pressure (Pa)

P m :

Maximum sound pressure (Pa)

q :

Heat flow density (W/m2)

q 0 :

The initial density of heat flow (W/m2)

q e :

Electric charge (C)

q e0 :

Initial electric charge (C)

r :

Distance between the vapor bubble center and the point of sound pressure determination (m)

R :

Radius of the vapor bubble (m)

R * :

Parameter of exponential dependence (m)

R e :

Electrical resistance (Ω)

S :

Interphase surface of the bubble (m2)

T :

Time (s)

T :

Average temperature of the superheated fluid layer (K)

T S :

Saturation temperature (K)

U :

Voltage (V)

V :

Volume of the bubble (m3)

V′ :

Volume of superheated liquid layer (m3)

X :

Relative radius of the bubble

Y :

Relative growth rate of the bubble

Z :

Relative acceleration during the growth of the bubble

α :

Heat transfer coefficient [W/(m K)]

±δ :

Discrepancy between the theory and the experiment (%)

ε :

Constant (1/m)

θ :

Average superheat of the superheated fluid layer (K)

θ 0 :

Initial superheat of the superheated fluid layer (K)

λ′ :

Thermal conductivity of the fluid [W/(m K)]

ρ′:

Fluid density (kg/m3)

ρ′′:

Vapor density (kg/m3)

τ :

Time constant of circuit (s)

\(\tau_{*}\) :

Time constant of the exponential growth of the vapor bubble (s)

References

  1. Tong L (1969) Teplootdacha pri kipenii i dvukhfaznoe techenie (Heat transfer in boiling and two-phase flow). Mir, Moscow (Russ. Transl.)

    Google Scholar 

  2. Nesis EI (1973) Kipenie zhidkostei (Boiling of Liquids). Nauka, Moscow

    Google Scholar 

  3. Van Stralen SYD, Cole R (1979) Boiling Phenomena. Hemisphere, Washington, DC, p 447

    Google Scholar 

  4. Tolubinskiy VI (1980) Teploobmen pri kipenii (Heat transfer in boiling). Naukova dumka, Kiev

    Google Scholar 

  5. Prisnyakov VF (1988) Kipenie (Boiling). Naukova dumka, Kiev

    Google Scholar 

  6. Nakoryakov VE, Pokusaev BG, Shreyer IR (1990) Volnovaya dinamika gazo- i parozhidkostnykh sred (Wave dynamics of gas- and vapor-liquid media). Energoatomizdat, Moscow

    Google Scholar 

  7. Dorofeev BM and Volkova VI (2005) Akustika kipeniya (Acoustics of boiling). Izd, SGU (Stavropol State Univ), Stavropol

  8. Dorofeev BM (1994) Zvukovyye yavleniya pri kipenii. Dis. dokt. fiz.-mat. nauk. Stav. gos. ped. in-t, Stavropol’

  9. Dorofeev BM, Poddubnaya NA (1996) Teplofiz Vys Temp 34(6):914

    Google Scholar 

  10. Dorofeev BM, Poddubnaya NA (1999) Teplofiz Vys Temp 37(5):841

    Google Scholar 

  11. Dorofeev BM and Poddubnaya NA (1997) Vestnik Stavropol’skogo gosudarstvennogo universiteta (11):112 (In Russian)

  12. Lykov AV (1978) Teplomassoobmen: Spravochnik (Heat-mass exchange: hand-book). Energiya, Moskva

    Google Scholar 

  13. Dorofeev BM, Volkova VI (2008) High Temperature. Teplofiz Vys Temp 46(6):861

    Google Scholar 

  14. Dorofeev BM (1985) High Temperature. Teplofiz Vys Temp 23(3):479

    Google Scholar 

  15. Dorofeev BM, Volkova VI (2011) Akust Zh 57(6):793

    Google Scholar 

  16. Robinson GE, Schmidt FW, Block HR, and Green G (1974) An experimental determination of isolated bubble acoustic in a nucleate boiling system. In: Proceedings of the 5th international heat transfer conference, vol 4, B 2.9

  17. Dorofeev BM and Poddubnaya NA (2002) Boiling acoustics and heat transfer. Heat Transf Res 33(3–4):176–180

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Federal State Autonomous Educational Institution for Higher Professional Education, North-Caucasian Federal University, Stavropol, Russia

    B. M. Dorofeev & V. I. Volkova

Authors
  1. B. M. Dorofeev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Volkova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. I. Volkova.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dorofeev, B.M., Volkova, V.I. Dynamics of vapor bubbles growth at boiling resulting from enthalpy excess of the surrounding superheated liquid and sound pulses generated by bubbles. Heat Mass Transfer 52, 39–45 (2016). https://doi.org/10.1007/s00231-015-1698-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00231-015-1698-9

Keywords

Search

Navigation