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Thermal boundary condition effects on heat transfer in turbulent rough-wall boundary layers

Einfluß der thermischen Randbedingungen auf die Wärmeübertragung in turbulenten Grenzschichten an rauhen Wänden

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Abstract

Measurements and predictions are presented which investigate the effects of thermal boundary condition on heat transfer in the turbulent rough-wall boundary layer. Stanton number measurements are reported for the turbulent flow of air over rough plates with a variety of thermal boundary conditions on two separate rough surfaces. The cases considered are constant wall temperature, constant wall heat flux, step wall temperature, and piecewise linear wall temperature distributions. These measurements and data from other sources are compared with predictions using finite difference solutions of the discrete element roughness model and with superposition solutions. The predictions and the measurements are in good to excellent agreement.

Zusammenfassung

In dieser Arbeit werden Messungen und Berechnungen gezeigt, die den Einfluß der thermischen Randbedingungen auf die Wärmeübertragung in turbulenten Grenzschichten an rauhen Wänden untersuchen. Es werden Messungen der Stanton Zahl für turbulente Luftströmung über rauhe Platten an zwei separaten Oberflächen unter einer Reihe von thermischen Randbedingungen dargestellt. Die betrachteten Fälle sind konstante Wandtemperatur, konstanter Wärmestrom durch die Wand, abgestufte Wandtemperatur und stückweise konstante Wandtemperatur. Diese Messungen, sowie Daten anderer Untersuchungen, werden mit Berechnungen durch Finite-Differenzen Lösungen des Diskrete-Elemente-Rauhheits-Modells und Superpositionslösungen verglichen. Berechnungen und Messungen liegen in guter bis ausgezeichneter Übereinstimmung.

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Abbreviations

A :

plate surface area

a j :

parameter in Eq. (17)

b i :

finite step in wall temperature; Eq. (17)

C D :

roughness element drag coefficient

C f :

skin friction coefficient

C p :

specific heat

d 0 :

roughness element base diameter

d(y):

local roughness element diameter

g(ξ, x):

kernel function in Eq. (20)

H :

enthalpy

H 0,∞ :

freestream total enthalpy

h(ξ, x):

kernel function in Eq. (16)=ϱ C p U ∞ St (x, ξ)

k :

roughness element height

K :

roughness element thermal conductivity

l m :

mixing length

L :

roughness element spacing

m j :

slope in piecewise linear wall temperature variation; Eq. (17)

M :

number of ramps in Eq. (17)

N :

number of steps in Eq. (17)

Nu d :

roughness element Nusselt number

P :

pressure

Pr :

Prandtl number

Pr t :

turbulent Prandtl number

q c :

conductive heat loss rate

q r :

radiative heat loss rate

q w″:

wall heat flux

r :

recovery factor

Re d :

Reynolds number based on local roughness element diameter

Re x :

x-Reynolds number

St :

Stanton number

St t :

Stanton number for constant wall temperature

T :

local fluid static temperature

T 0 :

freestream stagnation temperature

T r :

freestream recovery temperature

T R :

roughness element temperature

T w :

wall (plate) temperature

u :

mean longitudinal velocity

u′v′:

Reynolds shear stress factor

U ∞ :

freestream velocity

(U A)eff :

effective overall conductance forq c calculation

v′h′:

turbulent heat flux factor

v :

mean normal velocity

W :

plate heater power

x :

axial distance from nozzle exit

y :

coordinate normal to surface

y + :

y-plus;131-6

β r(a, b):

incomplete beta function

β x :

blockage factor

β y :

blockage factor

Γ(x):

gamma function

δ :

boundary layer thickness

ε :

plate surface emissivity

μ :

viscosity

ν :

kinematic viscosity

ξ :

integration parameter

ϱ :

density

φ :

unheated length

t :

turbulent

w :

wall

∞:

freestream

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Authors and Affiliations

  1. Thermal & Fluid Dynamics Laboratory Mechanical and Nuclear Engineering Department, Mississippi State University, 39762, MS, USA

    R. P. Taylor, M. H. Hosni, J. W. Garner & H. W. Coleman

Authors
  1. R. P. Taylor
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  2. M. H. Hosni
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  3. J. W. Garner
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  4. H. W. Coleman
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Taylor, R.P., Hosni, M.H., Garner, J.W. et al. Thermal boundary condition effects on heat transfer in turbulent rough-wall boundary layers. Wärme - und Stoffübertragung 27, 131–140 (1992). https://doi.org/10.1007/BF01599926

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