The transpired turbulent boundary layer in an adverse pressure gradient

An experimental program was carried out to study the effect of transpiration on a turbulent boundary layer in an adverse pressure gradient. A wind tunnel with a porous test wall was designed so that the blowing velocity and the strength of the pressure gradient could be varied in the course of the experiments. The effect of transpiration on the location of the separation point was observed. Measurements of mean velocity profiles and heat transfer rates were compared with predictions of a boundary layer calculation method based on an effective viscosity model. Predictions of skin friction were satisfactory, but there was noticeable error in the predicted velocity profile shapes near separation. It was also found that a form of the law of the wake provides a good representation of velocity profiles with blowing and could be used as the basis tor an integral method of prediction.     

Heat transfer through the turbulent incompressible boundary layer in the presence of moderate pressure gradient

From the assumption that the “universal law of the wall” is applicable to the turbulent boundary layer for moderately accelerating and decelerating flows along a wall it is shown that the thickness and the eddy diffusivity variation through the thickness can be derived at any Reynolds number.

With the additional assumption that the eddy diffusivities for momentum and heat are equal solutions were carried out to the energy equation to obtain Stanton number variations with Reynolds number for both uniform wall temperature and uniform wall heat flux. Two Reynolds number values were considered at which the heating commenced, Prandtl numbers of 0.01, 0.7 and 10 were used and these cases were examined for a number of arbitrarily chosen uniform pressure gradient parameters corresponding to one dimensional diverging or converging ducts.     

Hydrodynamics and heat transfer in bubbly flow in the turbulent boundary layer

In the work presented is a new approach to modelling the bubbly flow in the boundary layer. The approach is based on summation of dissipation energy coming from the shearing turbulent flow in the absence of bubbles and the dissipation contribution from the presence of bubbles. As a result we obtain the dissipation of equivalent single phase turbulent flow. The model has been solved using the method of asymptotic correction to provide an explicit differential equation describing the velocity profile. That can be solved with the assumption of constant void fraction distribution to yield the analytical velocity profile. Alternatively, author has developed his own model of lateral void migration, which is distinct from other models by virtue of presence of another rotational velocity. Velocity distributions calculated using the new model have been compared against the experimental data of turbulent bubble flows with small void fraction. A good consistency between calculations performed using a new model and available experimental data has been obtained. Additionally, a solution of the temperature field is also given. In the case of a constant void fraction distribution analytical distribution of the Nusselt number is given or the set of differential equations needs to be solved.     

Heat transfer in the boundary layer with asymptotic favorable pressure gradient

Numerical modeling of Prandtl equations was undertaken in order to investigate into the effect of mainstream acceleration on characteristics of dynamic and thermal boundary layers. Unlike in dynamic boundary layer, nondimensional characteristics of thermal boundary layer proved to be rather conservative to the action of the favorable pressure gradient. It was found that, unlike the skin-friction coefficient and the momentum-thickness Reynolds number, the Stanton number and the energy-thickness Reynolds number both exhibit no saturation with increasing the Kays acceleration parameter. Also, an analysis of the violation of Reynolds analogy by the stream acceleration is given.     

Heat transfer for Marangoni‐driven boundary layer flow

Marangoni convection induced by variation of the surface tension with temperature along a surface influences crystal growth melts and other processes with liquid–vapor interfaces, such as boiling in both microgravity and normal gravity in some cases. This paper presents the Nusselt number for Marangoni flow over a flat surface calculated using a similarity solution for both the momentum equations and the energy equation assuming developing boundary layer flow along a surface. Solutions are presented for the surface velocity, the total flow rate, and the Nusselt number for various temperature profiles, Marangoni numbers, and Prandtl numbers. For large bubbles, the predicted boundary layer thickness would be less than the bubble diameter, so the curvature effects could be neglected and this analysis could be used as a first estimate of the effect of Marangoni flow around a vapor bubble. © 2002 Scripta Technica, Heat Trans Asian Res, 31(2): 105–116, 2002; DOI 10.1002/htj.10019     

Free-stream turbulence effects on the heat transfer through the turbulent boundary layer behind a fence

Experimental results on the reattachment length and heat transfer behind a fence under a variable free-stream turbulence of air are presented. The study covered Re_L0 from 2×10⁵ to 2×10⁶, turbulence from 0.1 to 7 %, and fence heights from 0.002 to 0.0135 m. Shorter reattachment lengths and augmented heat transfer at the reattachment were observed under higher turbulences.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet

Studies are made on the viscoelastic fluid flow and heat transfer characteristics over a stretching sheet with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for the cases of prescribed surface temperature (PST) and prescribed surface heat flux (PHF). The momentum equation is decoupled from the energy equation for the present incompressible boundary layer flow problem with constant physical parameters. Exact solution for the velocity field and the skin-friction are obtained. Also, the solutions for the temperature and heat transfer characteristics are obtained in terms of Kummer’s function. The work due to deformation in energy equation, which is essential while formulating the viscoelastic boundary layer flow problems, is considered. This paper examines the effect of viscoelastic parameter, Eckert number, Prandtl number and non-uniform heat source/sink parameter on temperature distribution, wall temperature gradient for PST-case and wall temperature for PHF-case.     

Study of transition from laminar to turbulent boundary layer on a tilted flat plate using heat transfer measurements

The boundary layer transition over a flat tilted plate has been studied by means of heat transfer measurements.Aheat flux sensor has been developed,in order to measure the efficiency of convective heat transfer for varioustypes of surfaces or flows.Its operation at constant temperature allows direct and fast measurements of heat flux.The present paper reports the development of the sensor and presents its application to the study of transition in aboundary layer depending on the angle of incidence of the external flow.An exponential relationship betweencritical Reynolds number and pressure gradient parameter has been found.     

CFD analysis of convective heat transfer at the surfaces of a cube immersed in a turbulent boundary layer

Steady Reynolds-Averaged Navier–Stokes (RANS) CFD is used to evaluate the forced convective heat transfer at the surfaces of a cube immersed in a turbulent boundary layer, for applications in atmospheric boundary layer (ABL) wind flow around surface-mounted obstacles such as buildings. Two specific configurations are analysed. First, a cube placed in turbulent channel flow at a Reynolds number of 4.6 × 10³ is considered to validate the numerical predictions by comparison with wind-tunnel measurements. The results obtained with low-Reynolds number modelling (LRNM) show a satisfactory agreement with the experimental data for the windward surface. Secondly, a cube exposed to high-Reynolds number ABL flow is considered. The heat transfer in the boundary layer is analysed in detail. The dimensionless parameter y¹, which takes into account turbulence, is found to be more appropriate for evaluating heat transfer than the commonly used y⁺ value. Standard wall functions, which are frequently used for high-Reynolds number flows, overestimate the convective heat transfer coefficient (CHTC) significantly (±50%) compared to LRNM. The distribution of the CHTC–U₁₀ correlation over the windward surface is reported for Reynolds numbers of 3.5 × 10⁴ to 3.5 × 10⁶ based on the cube height and U₁₀, where U₁₀ is the wind speed in the undisturbed flow at a height of 10 m.     

Heat and mass transfer with condensation in laminar and turbulent boundary layers along a flat plate

An experimental and numerical study of heat and mass transfer in an incompressible boundary layer with condensation over a flat plate is presented. The air-steam flow at atmospheric pressure is saturated; its velocity is smaller than 6 m s⁻¹; the Reynolds number calculated with the abscissa along the plate ranges from 10⁴ to 10⁵ for the laminar boundary layer and from 3 × 10⁵ to 10⁶ for the turbulent one. The temperature différence between the main flow and the cold wall does not exceed 20°C. A finite-difference method is used to calculate the velocity, temperature and concentration fields; the numerical results are in good agreement with experiments for laminar and turbulent boundary layer.     

Influence of free-stream turbulence intensity on heat transfer in the two-dimensional turbulent boundary layer of an accelerated compressible flow

For the accelerated compressible flow in a two-dimensional convergent-divergent nozzle the influence of free-stream turbulence on heat transfer in the turbulent boundary layer has been investigated empirically. The turbulence intensity varied from nearly zero to about 20%, the nozzle entrance Reynolds number reached up to about 10⁷. The experimental set-up and the turbulence measurement technique are carefully described. For three different loading cases the measured data of free-stream turbulence intensity and fluctuation are given along the nozzle axial length as well as the local Stanton number in comparison to those of accelerated flow without free stream turbulence. For low Reynolds numbers (Re_x < 10⁶) no clear change of heat transfer has been observed, while for Re_x < 10⁶ a weak and nearly linear dependency of Stanton number on free-stream turbulence intensity can be pointed out.     

Heat transfer in a turbulent particle-laden channel flow

The objective of this paper is twofold: (i) to present and analyze particle temperature statistics in turbulent non-isothermal fully-developed turbulent gas–solid channel flow for a large range of particle inertia in order to better understand particle heat transfer mechanisms; (ii) to examine the performance of a recent Probability Density Function (PDF) model provided by Zaichik et al. (2011) [1]. In order to achieve such objectives, a Direct Numerical Simulation (DNS) coupled with a Lagrangian Particle Tracking (LPT) was used to collect fluid and particle temperature statistics after particles reach a statistically stationary regime. A non-monotonic behavior of particle temperature statistics is observed as inertia increases. The competition between different mechanisms (filtering inertia effect, preferential concentration, production of fluctuating quantities induced by the presence of the mean velocity and/or mean temperature gradients) are responsible for such a behavior. This competition is investigated from the exact transport equations of particle temperature statistical moments, fluid statistics conditionally-averaged at particle location, and instantaneous particle distribution in the flow field. Using these data, the accuracy of a PDF model is also assessed in the second part. From this assessment, it is seen that, despite the assumptions made, the model leads to a satisfactory prediction of most of the particle temperature statistics for not too high particle inertia.     

Experimental study of the blowing impact on a hot turbulent boundary layer

We present an experimental study of non-isothermal blowing through a porous flat plate using hot and cold wires anemometry. The calibration procedure is presented, taking into account the influence of the temperature. King’s law coefficients are determined and a cosinus method is employed to calibrate the angle of the cross wires. A first set of measurements permits to investigate the influence of the temperature on the hot wire and the Seebeck effect on the cold wire. The experimental results are presented. We observe that blowing has a strong influence on the velocity and temperature profiles as well as on the velocity–velocity and velocity–temperature correlations and on the flow statistics. The velocity and temperature spectra are also given, showing that their slopes are modified by the blowing.     

Heat transfer by shock-wave/boundary layer interaction on a flat surface with a mounted cylinder

The detailed convective heat transfer is observed on a flat surface where the cylinder is mounted in a supersonic flow field. During the test, the thermal image of a wall temperature distribution is taken by an infra-red camera under the constant heat flux condition on the flat surface. From the measured wall temperature information, heat transfer coefficients are calculated. The shadow graph and the oil flow tests are conducted to examine the shock-wave structure and the surface shear flow around the protruding body, respectively. The entire flow also is simulated numerically. The upstream flow Mach number, total pressure and Reynolds number are about 3, 600 kPa and 2.3 × 10⁶, respectively. The swept-back effect of a cylinder to the approaching flow is considered in the range from 0° to 30°. From the results, the large increase of heat transfer is observed in a shock-wave/turbulent boundary layer interaction region and the peak heating appeared especially on a flow reattachment region. When the cylinder is swept backward to the main flow, the heat flux promotion decreases as much as its effective area. These results will provide the valuable information for the thermal analysis in a complicated shock-induced separation region.     

Experimental study of the turbulent heat flux balance components in the cross-section of a retarded turbulent boundary layer

The paper presents experimental data on distribution of the turbulent heat flux transport equation terms in the cross-section of an equilibrium retarded turbulent boundary layer. Comparison of individual terms of the equation with the known approximations is made.     

Heat transfer from a cylinder in axial turbulent flows

Local convective heat transfer coefficients were measured on a two-diameter long cylinder in axial flows of air at conditions unexplored so far, by using thermochromic liquid crystals (TLC) coated on an electrically heated strip-foil consisting bonded to the external surfaces. The Reynolds numbers (Re) based on the cylinder diameter were between 8.9 × 10⁴ and 6.17 × 10⁵, and the flow in front of the cylinder was modified in some cases by the use of a turbulence generating grid, or by circular disc inserts of two sizes placed upstream of the cylinder. These created a major change in the local convective heat transfer coefficient distribution on the cylinder. Increase of the turbulence intensity from Tu < 0.1% to Tu = 6.7% at the same Re increased the average calculated Nusselt number Nu over the cylinder by 25%, and decreased the Nu non-uniformity over the surface. One of the flow modification inserts also reduced significantly the Nu non-uniformity. The position of flow reattachment was measured using tufts. Our heat transfer data agree well with the small amount if data published of others, when extrapolated to their conditions. Correlations between the Nu and Re in the form Nu = CRe^e were established and presented for the average Nu on the front, middle and rear cylinder surfaces, and the variation of the local exponent e was shown along the cylinder. Introducing a new technique, a TLC-coated heated flat plate mounted in the flow above the cylinder in the meridional plane was demonstrated to help visualize the flow field above the cylinder. A track of maximum convective coefficients on this plate was found similar in position to the stream line dividing the forward and backward flows in a case measured for the separated flow in a past study.