Calculation of a Turbulent Boundary Layer Downstream of a Step Change in Surface Temperature

1979 ◽  
Vol 101 (1) ◽  
pp. 144-150 ◽  
Author(s):  
L. W. B. Browne ◽  
R. A. Antonia
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Surface Temperature ◽  
Reynolds Shear Stress ◽  
Turbulent Viscosity ◽  
Step Change ◽  
Mean Temperature ◽  
Thermal Layer ◽  
Good Agreement

Mean temperature and heat flux distributions in a thermal layer that develops within a momentum boundary layer subjected to a step change in surface temperature are calculated using two different methods. The method of Bradshaw and Unsworth, which uses the method of Bradshaw, Ferriss and Atwell to determine the mean velocity and Reynolds shear stress distributions and then assumes a constant turbulent Prandtl number for the heat flux calculation, yields heat flux distributions that are significantly different than the available experimental results at small distances from the step. Good agreement between calculations and experimental values is achieved when the distance x from the step is about 20 δ0, where δ0 is the boundary layer thickness at the step. To obtain good agreement with measurements of heat flux and mean temperature near the step, estimated distributions of turbulent viscosity and effective Prandtl number have been derived using an iterative updating procedure and the calculation method of Patankar and Spalding. These distributions are compared with those available in the literature. Calculated heat flux distributions show that the internal thermal layer is only likely to reach self-preserving conditions when x exceeds 40 δ0.

The Response of a Turbulent Boundary Layer to a Double Step-Change in a Wall Heat Flux

1983 ◽  
Vol 105 (4) ◽  
pp. 841-845 ◽  
Author(s):  
J. Andreopoulos
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Turbulent Boundary Layer ◽  
Growth Rates ◽  
Temperature Fluctuations ◽  
Step Change ◽  
Wall Heat Flux ◽  
Third Order ◽  
Double Step ◽  
Thermal Layer

Extensive measurements were made of the response of a turbulent boundary layer to a double step change of wall heat flux. The measurements include mean temperature and velocity as well as temperature-velocity correlations up to third order occurring in the ϑ2 and vϑ transport equations together with the skewness and flatness of temperature fluctuations. Two thermal layers start to develop within the primary boundary layer due to the change in heat flux at boundary. These layers are characterized with different growth rates which depend on the wall heat flux. Most of the changes in the downstream stations take place inside the second thermal layer.

Hydrodynamic and Thermal Boundary Layers Over a Flat Plate With Slip Flow and Constant Surface Heat Flux

2008 ◽  
Author(s):  
Abdul Aziz
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Surface Temperature ◽  
Slip Flow ◽  
Accommodation Coefficient ◽  
Constant Heat Flux ◽  
Slip Parameter ◽  
Energy Equations ◽  
Local Reynolds Number

In this paper the boundary layer flow over a flat plat with slip flow and constant heat flux surface condition is studied. Because the plate surface temperature varies along the x direction, the momentum and energy equations are coupled due to the presence of the temperature gradient along the plate surface. This coupling, which is due to the presence of the thermal jump term in Maxwell slip condition, renders the momentum and energy equations non similar. As a preliminary study, this paper ignores this coupling due to thermal jump condition so that the self-similar nature of the equations is preserved. Even this simplified problem for the case of a constant heat flux boundary condition has remained unexplored in the literature and was therefore chosen for study in this paper. For the hydrodynamic boundary layer, velocity and shear stress distributions are presented for a range of values of the parameter characterizing the slip flow. This slip parameter is a function of the local Reynolds number, the local Knudsen number, and the tangential momentum accommodation coefficient representing the fraction of the molecules reflected diffusively at the surface. As the slip parameter increases, the slip velocity increases and the wall shear stress decreases. These results confirm the conclusions reached in other recent studies. The energy equation is solved to determine the temperature distribution in the thermal boundary layer for a range of values for both the slip parameter as well as the fluid Prandtl number. The increase in Prandtl number and/or the slip parameter reduces the dimensionless surface temperature. The actual surface temperature at any location of x is a function of the local Knudsen number, the local Reynolds number, the momentum accommodation coefficient, Prandtl number, other flow properties, and the applied heat flux.

Response of a turbulent boundary layer to a step change in surface heat flux

1977 ◽  
Vol 80 (1) ◽  
pp. 153-177 ◽  
Author(s):  
R. A. Antonia ◽  
H. Q. Danh ◽  
A. Prabhu
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Turbulent Boundary Layer ◽  
Surface Heat Flux ◽  
Temperature Fluctuations ◽  
Step Change ◽  
Surface Heat ◽  
The Mean ◽  
Thermal Layer ◽  
Intermittency Factor

Measurements of both the velocity and the temperature field have been made in the thermal layer that grows inside a turbulent boundary layer which is subjected to a small step change in surface heat flux. Upstream of the step, the wall heat flux is zero and the velocity boundary layer is nearly self-preserving. The thermal-layer measurements are discussed in the context of a self-preserving analysis for the temperature disturbance which grows underneath a thick external turbulent boundary layer. A logarithmic mean temperature profile is established downstream of the step but the budget for the mean-square temperature fluctuations shows that, in the inner region of the thermal layer, the production and dissipation of temperature fluctuations are not quite equal at the furthest downstream measurement station. The measurements for both the mean and the fluctuating temperature field indicate that the relaxation distance for the thermal layer is quite large, of the order of 1000θ0, where θ0is the momentum thickness of the boundary layer at the step. Statistics of the thermal-layer interface and conditionally sampled measurements with respect to this interface are presented. Measurements of the temperature intermittency factor indicate that the interface is normally distributed with respect to its mean position. Near the step, the passive heat contaminant acts as an effective marker of the organized turbulence structure that has been observed in the wall region of a boundary layer. Accordingly, conditional averages of Reynolds stresses and heat fluxes measured in the heated part of the flow are considerably larger than the conventional averages when the temperature intermittency factor is small.

Instantaneous Heat Flux Simulation of a Motored Reciprocating Engine: Unsteady Thermal Boundary Layer With Variable Turbulent Thermal Conductivity

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Abdalla Agrira ◽  
David R. Buttsworth ◽  
Mior A. Said
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Boundary Layer ◽  
Heat Flux ◽  
Prandtl Number ◽  
Thermal Boundary Layer ◽  
Combustion Engine ◽  
Turbulent Viscosity ◽  
Spark Ignition Engine ◽  
Turbulent Prandtl Number

Due to the inherently unsteady environment of reciprocating engines, unsteady thermal boundary layer modeling may improve the reliability of simulations of internal combustion engine heat transfer. Simulation of the unsteady thermal boundary layer was achieved in the present work based on an effective variable thermal conductivity from different turbulent Prandtl number and turbulent viscosity models. Experiments were also performed on a motored, single-cylinder spark-ignition engine. The unsteady energy equation approach furnishes a significant improvement in the simulation of the heat flux data relative to results from a representative instantaneous heat transfer correlation. The heat flux simulated using the unsteady model with one particular turbulent Prandtl number model agreed with measured heat flux in the wide open and fully closed throttle cases, with an error in peak values of about 6% and 35%, respectively.

Calculation of a Turbulent Boundary Layer Downstream of a Small Step Change in Surface Roughness

1975 ◽  
Vol 26 (3) ◽  
pp. 202-210 ◽  
Author(s):  
R A Antonia ◽  
D H Wood
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Shear Stress ◽  
Turbulent Boundary Layer ◽  
Reynolds Shear Stress ◽  
Step Change ◽  
Rough Wall ◽  
Small Step ◽  
Mean Velocity ◽  
Good Agreement

SummaryMeasurements of mean velocity and Reynolds shear stress have been made in a turbulent boundary layer downstream of a small step change in surface roughness. Upstream of the step the surface is smooth, while downstream it consists of a d-type rough wall made up by a series of two-dimensional elements of square cross section placed transversely across the flow and spaced one element width apart in the direction of the flow. The calculated mean velocity and Reynolds shear stress profiles obtained using the method of Bradshaw, Ferriss and Atwell are in good agreement with the measurements throughout the relaxation region of the layer. Well downstream the calculation method adequately reproduces the self-preserving features of a d-type rough wall.

Unsteady Stagnation Point Heat Transfer

1965 ◽  
Vol 87 (2) ◽  
pp. 221-230 ◽  
Author(s):  
B. T. Chao ◽  
D. R. Jeng
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Surface Temperature ◽  
Thermal Boundary Layer ◽  
Essential Feature ◽  
Step Change ◽  
Stream Velocity ◽  
Two Dimensional ◽  
Time Solution

An analysis is presented for the unsteady laminar, forced-convection heat transfer at a two-dimensional and axisymmetrical front stagnation due to an arbitrarily prescribed wall temperature or heat flux variation. The flow is incompressible and steady. The procedure begins with a consideration of the thermal boundary-layer response caused by either a step change in surface temperature or heat flux. Two appropriate asymptotic solutions, valid for small and large times, respectively, are found and satisfactorily joined for Prandtl numbers ranging from 0.01 to 100. The key to the small time solution is the transformation of the energy equation in the Laplace transform plane to an ordinary differential equation with a large parameter. An essential feature of the large time solution is the use of Meksyn’s transformation variable and the method of steepest descent in the evaluation of integrals. It is found that, for both two-dimensional and axisymmetrical stagnation, the time required for the thermal boundary layer to attain steady condition, for either a step change in surface temperature or heat flux, varies inversely with the free stream velocity and directly with 1/4 power of the Prandtl number of the fluid.

Viscomagnetic Heat Flux Experiments as a Test of Gas Kinetic Theory in the Burnett Regime

1978 ◽  
Vol 33 (7) ◽  
pp. 749-760 ◽  
Author(s):  
G. E. J. Eggermont ◽  
P. W. Hermans ◽  
L. J. F. Hermans ◽  
H. F. P. Knaap ◽  
J. J. M. Beenakker
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Heat Flux ◽  
External Magnetic Field ◽  
Room Temperature ◽  
Flow Direction ◽  
Rectangular Channel ◽  
Gas Kinetic Theory ◽  
The Magnetic Field ◽  
Good Agreement

In a rarefied polyatomic gas streaming through a rectangular channel, an external magnetic field produces a heat flux perpendicular to the flow direction. Experiments on this “viscom agnetic heat flux” have been performed for CO, N2, CH4 and HD at room temperature, with different orientations of the magnetic field. Such measurements enable one to separate the boundary layer contribution from the purely bulk contribution by means of the theory recently developed by Vestner. Very good agreement is found between the experimentally determined bulk contribution and the theoretical Burnett value for CO, N2 and CH4 , yet the behavior of HD is found to be anomalous.

Experimental and numerical simulation studies on heat transfer to calorimeters engulfed in diesel pool fires

2017 ◽  
Vol 35 (2) ◽  
pp. 156-176 ◽  
Author(s):  
Sudheer Siddapureddy ◽  
SV Prabhu
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Surface Temperature ◽  
Heat Fluxes ◽  
Numerical Code ◽  
Pool Fires ◽  
Steel Pipes ◽  
Adiabatic Surface ◽  
In Fire ◽  
Good Agreement

Characterization of heat transfer to calorimeters engulfed in pool fires is extremely important. To estimate the heat flux to the calorimeters, experiments are performed with horizontal stainless steel 304L pipes engulfed in diesel pool fires. The concept of adiabatic surface temperature is applied to predict the incident heat flux to horizontally oriented calorimeters engulfed in diesel pool fires. Plate thermometers are used to measure the adiabatic surface temperature for diesel pool fires. The estimated subsurface temperatures inside the steel pipes using the adiabatic surface temperature concept and the measured temperatures are in good agreement. Adiabatic surface temperature is also computed from fire simulations. The incident heat fluxes to the steel pipes engulfed in fire predicted from the simulations are found to be in good agreement with the experiments. The fire numerical code is validated against the 1 m pool fire experimental results of centerline temperature distribution and irradiances away from fire. A correlation is provided for the estimation of adiabatic surface temperature for large diesel pool fires. These results would provide an effective way for thermal test simulations.

Sign in / Sign up

Export Citation Format

Share Document