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Turbulence Effects on Convective Heat Transfer

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Handbook of Thermal Science and Engineering

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Abstract

The subject of this chapter is the influence of flow field turbulence on heat transfer augmentation to both the turbulent and laminar boundary layers. Initially, the response of turbulence to the presence of a wall is reviewed as background to one of the key constraints in the interaction of turbulence to both turbulent and laminar boundary layers. Next, research on the influence of external turbulence to the flat plat turbulent boundary layer is discussed in terms of both the physics of the interaction of external turbulence with a developing turbulent boundary layer and the correlation of the resulting enhancement. A simple physics based eddy diffusivity model for the external turbulence is presented and predictive results using this model are presented and discussed. The influence of turbulence on laminar boundary layer heat transfer augmentation to stagnation region and other laminar regions is also reviewed. Initially, the influence of both the strain field and leading edge surface on the intensification of small scale turbulence and the blocking of relatively large scale turbulence is discussed. A physically based correlating method for stagnation region heat transfer augmentation is presented along with historical and alternate models. Heat transfer augmentation mechanisms in laminar regions with no intensification are also discussed and the simple physics based eddy diffusivity model for the turbulent boundary layer is extended to laminar flow prediction.

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Abbreviations

C:

turbine airfoil chord length (m2)

Cf/2:

skin friction coefficient = τ/(ρU∞2/2)

CP:

specific heat at constant pressure (J/kg/K)

Cμ:

constant for k – ε model, Cμ = 0.09

D:

pin, cylinder or leading edge diameter (m)

E2(k1):

one dimensional energy spectrum function of v′, E2(k1) = U E2(f)/2/π (m3/s2)

f:

frequency (1/s)

fMIX:

blending function for mixing length and outer layer model

fμ:

damping function for k – ε model

h:

heat transfer coefficient (W/m2/K)

HB:

the Hancock-Bradshaw correlating parameter, HB = \( {\left(\frac{{\mathrm{u}}^{\prime }}{\mathrm{U}}\right)}_{\mathrm{e}}\times 100/\left(\ \frac{{\mathrm{L}}_{\mathrm{e}}^{\mathrm{u}}}{\updelta_{.995}}+2.0\right) \)

k:

thermal conductivity (W/m/K)

k:

turbulent kinetic energy (m2/s2)

K:

turbulent flow acceleration parameter, ν/U∞2 dU∞/dx

k1:

wavenumber, k1 = 2πf/U (m−1)

L:

macro-scale of turbulence (m)

Lu:

energy scale, Lu = 1.5 |u’|3/ε (m)

\( {\mathrm{L}}_{\mathrm{u}}^{\mathrm{e}} \) :

dissipation scale, Lu = 1.5 |u’|3/ε (m)

l :

mixing length (m)

Nu:

diameter Nusselt number, Nu = hD/k

Pr:

Prandtl number, Pr = ν/α

ReD:

diameter Reynolds number

Reθ:

momentum thickness Reynolds number

ReΔ2:

enthalpy thickness Reynolds number

St:

Stanton number, h/ρ CP U∞

St′:

Stanton prime, h/ρ CP u′

t:

time (s)

T+:

inner variable nondimensional temperature (K)

TL + :

correlating parameter for turbulent boundary layer heat transfer

TLR:

turbulence parameter for turbulent heat transfer, TLR = Tu (ReΔ2/1000)1/4(Δ2/Lu)1/3

TRL:

turbulence parameter for stagnation heat transfer, TRL = Tu ReD5/12 (D/Lu)1/3

Tu:

turbulence level, Tu = u′/U∞

U:

streamwise velocity (m/s)

U+:

velocity nondimensionalized on inner variables, U+ = U(Y)/uτ

U:

streamwise velocity (m/s)

uτ:

shear velocity, uτ = U.•(Cf/2)1/2 (m/s)

u′:

rms streamwise fluctuation velocity (m/s)

v′:

rms endwall normal fluctuation velocity (m/s)

V:

normal velocity (m/s)

W:

spanwise velocity (m/s)

w′:

rms spanwise fluctuation velocity (m/s)

x:

axial distance (m)

y:

endwall normal distance (m)

Y + :

dimensionless normal distance from wall in inner variables, Y+ = y uτ /ν

α:

thermal diffusivity, m2/s

δ , δ0.995:

boundary layer thickness, m

δ2 , θ:

momentum thickness, m

Δ2:

enthalpy thickness, m

ε:

turbulent dissipation rate, m2/s3

εM:

eddy diffusivity, m2/s

κ:

mixing length model constant

λ:

Taylor microscale, m

λX:

streamwise integral scale of turbulence, m

η, eta:

Kolmogorov length scale, η = (ν3/ε)1/4, m

μ:

absolute viscosity, Pa s

ν:

kinematic viscosity, m2/s

ρ:

fluid density, mass per unit of volume, kg/m3

τ:

shear stress, kg/m-s2

ω:

specific dissipation, k – ω model, s−1

∞, e:

free-stream conditions, unaffected by wall

0:

low free-stream turbulence value

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Authors and Affiliations

  1. Mechanical Engineering Deptartment, University of North Dakota, Grand Forks, ND, USA

    Forrest E. Ames

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  1. Forrest E. Ames
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Corresponding author

Correspondence to Forrest E. Ames .

Section Editor information

  1. Armour College of Engineering, Department of Mechanical, Materials and Aerospace Engineering, Illinois Institute of Technology, Chicago, Illinois, USA

    Sumanta Acharya

  2. Gas Technology Institute, Des Plaines, Illinois, USA

    Yaroslav Chudnovsky

  3. Universidade Federal do Rio de Janeiro - UFRJ, Rio de Janeiro, Rio de Janeiro, Brazil

    Renato Machado Cotta

  4. Department of Mechanical Engineering, Louisiana State University, Baton Rouge, Louisiana, USA

    Ram Devireddy

  5. Mechanical and Aerospace Engineering, University of California Los Angeles, Los Angeles, California, USA

    Vijay K. Dhir

  6. Cekmeköy Campus, Özyegin University, Çekmeköy - Istanbul, Turkey

    M. Pinar Mengüç

  7. Department of Mechanical and Industrial Engineering, Faculty of Applied Science + Engineering, University of Toronto, Centre for Advanced Coating Technologies, Toronto, Ontario, Canada

    Javad Mostaghimi

  8. Department of Mechanical Engineering, University of California, Riverside, California, USA

    Kambiz Vafai

  9. Herff College of Engineering,Department of Mechanical Engineering, The University of Memphis, Memphis, Tennessee, USA

    Sumanta Acharya

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Ames, F.E. (2018). Turbulence Effects on Convective Heat Transfer. In: Handbook of Thermal Science and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-26695-4_17

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