Local heat transfer around a wall-mounted cube at 45° to flow in a turbulent boundary layer

The flow and local heat transfer around a wall-mounted cube oriented 45° to the flow is investigated experimentally in the range of Reynolds number 4.2 × 10³–3.3 × 10⁴ based on the cube height. The distribution of local heat transfer on the cube and its base wall are examined, and it is clarified that the heat transfer distribution under the angled condition differs markedly to that for cube oriented perpendicular to the flow, particularly on the top face of the cube. The surface pressure distribution is also investigated, revealing a well-formed pair of leading-edge vortices extending from the front corner of the top face downstream along both front edges for Re>(1−2)×10⁴. Regions of high heat transfer and low pressure are formed along the flow reattachment and separation lines caused by these vortices. In particular, near the front corner of the top face, pressure suction and heat transfer enhancement are pronounced. The average heat transfer on the top face is enhanced at Re>(1−2)×10⁴ over that of a cube aligned perpendicular to the flow.     

DNS of heat transfer in transitional, accelerated boundary layer flow over a flat plate affected by free-stream fluctuations

Direct numerical simulations (DNS) of flow over and heat transfer from a flat plate affected by free-stream fluctuations were performed. A contoured upper wall was employed to generate a favourable streamwise pressure gradient along a large portion of the flat plate. The free-stream fluctuations originated from a separate LES of isotropic turbulence in a box. In the laminar portions of the accelerating boundary layer flow the formation of streaks was observed to induce an increase in heat transfer by the exchange of hot fluid near the surface of the plate and cold fluid from the free-stream. In the regions where the streamwise pressure gradient was only mildly favourable, intermittent turbulent spots were detected which relaminarised downstream as the streamwise pressure gradient became stronger. The relaminarisation of the turbulent spots was reflected by a slight decrease in the friction coefficient, which converged to its laminar value in the region where the streamwise pressure gradient was strongest.     

Accurate heat transfer measurements using thermochromic liquid crystal. Part 1: Calibration and characteristics of crystals

Encapsulated thermochromic liquid crystal (TLC) can accurately measure surface temperature in a variety of heat transfer and fluid flow experiments. Narrow-band TLC, where the colour changes over a temperature range of 1 °C, can be used to determine surface temperature within an uncertainty of 0.1 °C. Wide-band TLC, typically active over 5–20 °C, allow the possibility of mapping surface temperature distributions. In part 1 of this two-part paper, an extensive set of calibrations for narrow-band and wide-band TLC is reported. This generic study provides insight into the importance and influence of the various factors governing the colour–temperature relationship. These governing effects include the variation in optical path, the spectrum of the illumination source, the lighting and viewing angles, the differences between cooling or heating cycles (hysteresis), the variation with the number of heating or cooling cycles (aging) and how this varies with TLC film thickness. Two narrow-band crystals are also specifically calibrated for application to experiments on a transparent disc rotating at high speed (5000 rpm). Part 2 of this paper describes how these accurately-calibrated crystals were used to measure the transient surface temperature on, and heat transfer to, a rotating disc.     

Accurate heat transfer measurements using thermochromic liquid crystal. Part 2: Application to a rotating disc

Encapsulated thermochromic liquid crystal (TLC) can accurately measure surface temperature in a variety of heat transfer and fluid-flow experiments. In Part 1 of this two-part paper, two narrow-band liquid crystals were specifically calibrated for application to experiments on a disc rotating at high speed (5000 rpm). Part 2 describes how these crystals were used to measure the surface temperature on the disc in a transient experiment that models the flow of internal cooling air in a gas turbine. The TLC was viewed through the transparent polycarbonate disc using a digital video camera and strobe light synchronised to the disc frequency. The convective heat transfer coefficient, h, was subsequently calculated from the one-dimensional solution of Fourier’s conduction equation for a semi-infinite wall. The analysis accounted for the exponential rise in the air temperature driving the heat transfer, and for experimental uncertainties in the measured values of h. The paper focuses on the method used, and sample experimental results are provided to demonstrate the accuracy and potency of the technique.     

Visco-elastic boundary layer flow past a stretching plate with suction and heat transfer

In this paper the study of visco-elastic (Walters' liquid B model) flow past a stretching plate with suction is considered. Exact solutions of the boundary layer equations of motion and energy are obtained. The expressions for the coefficient of skin friction and of boundary layer thickness are obtained.     

Heat transfer enhancement in a turbulent natural convection boundary layer along a vertical flat plate

An experimental study on heat transfer enhancement for a turbulent natural convection boundary layer in air along a vertical flat plate has been performed by inserting a long flat plate in the spanwise direction (simple heat transfer promoter) and short flat plates aligned in the spanwise direction (split heat transfer promoter) with clearances into the near-wall region of the boundary layer. For a simple heat transfer promoter, the heat transfer coefficients increase by a peak value of approximately 37% in the downstream region of the promoter compared with those in the usual turbulent natural convection boundary layer. It is found from flow visualization and simultaneous measurements of the flow and thermal fields with hot- and cold-wires that such increase of heat transfer coefficients is mainly caused by the deflection of flows toward the outer region of the boundary layer and the invasion of low-temperature fluids from the outer region to the near-wall region with large-scale vortex motions riding out the promoter. However, heat transfer coefficients for a split heat transfer promoter exhibit an increase in peak value of approximately 60% in the downstream region of the promoter. Flow visualization and PIV measurements show that such remarkable heat transfer enhancement is attributed to longitudinal vortices generated by flows passing through the clearances of the promoter in addition to large-scale vortex motions riding out the promoter. Consequently, it is concluded that heat transfer enhancement of the turbulent natural convection boundary layer can be substantially achieved in a wide area of the turbulent natural convection boundary layer by employing multiple column split heat transfer promoters. It may be expected that the heat transfer enhancement in excess of approximately 40% can be accomplished by inserting such promoters.     

Stability of a disperse-mixture flow in a boundary layer

The hydrodynamic stability of a dilute disperse mixture flow in a quasi-equilibrium region of a boundary layer with a significantly nonuniform particle concentration profile is investigated. The mixture is described by a two-fluid model with an incompressible viscous carrier phase. In addition to the Stokes drag, the Saffman lifting force is taken into account in the interphase momentum exchange. On the basis of a numerical solution of the boundary-value problem for a modified Orr-Sommerfeld equation, neutral stability curves are analyzed and the dependence of the critical Reynolds number on the governing parameters is studied. It is shown that taking into account the particle concentration nonuniformity in the main flow and the Saffman lifting force significantly changes the stability limits of the two-phase laminar boundary layer flow. The effect of these factors on the boundary layer stability is considered for the first time.     

Turbulent flow past a transverse cavity with inclined side walls. 2. Heat transfer

Convective heat transfer in a transverse cavity with a small aspect ratio, angle of wall inclination ϕ = 30–90°, and heated bottom, frontal, and rear walls of the cavity is studied experimentally. Temperature distributions are measured in longitudinal and transverse sections on three walls; temperature fields are measured over the entire heated surface. Local and mean heat-transfer coefficients are calculated. The highest intensification of heat transfer is found to occur on the rear wall for low values of ϕ Reconstruction of the one-cell structure to the two-cell structure of the primary vortex in the cavity leads to a drastic decrease in heat transfer over the cavity span from the end faces toward the center in the case with ϕ = 60 and 70°. A certain increase in the mean heat-transfer coefficient averaged over the entire heated surface is noted for ϕ = 60°. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 23–29, July–August, 2007.     

Numerical experiments on the stability of leading edge boundary layer flow: A two-dimensional linear study

A numerical study is performed in order to gain insight to the stability of the infinite swept attachment line boundary layer. The basic flow is taken to be of the Hiemenz class with an added cross-flow giving rise to a constant thickness boundary layer along the attachment line. The full Navier-Stokes equations are solved using an initial value problem approach after two-dimensional perturbations of varying amplitude are introduced into the basic flow. A second-order-accurate finite difference scheme is used in the normal-to-the-wall direction, while a pseudospectral approach is employed in the other directions; temporally, an implicit Crank-Nicolson scheme is used. Extensive use of the efficient fast Fourier transform (FFT) algorithm has been made, resulting in substantial savings in computing cost. Results for the two-dimensional linear regime of perturbations are in very good agreement with past numerical and theoretical investigations, without the need for specific assumptions used by the latter, thus establishing the generality of our method.     

Turbulent boundary layer flow with a step change from smooth to rough surface

A direct numerical simulation (DNS) dataset of a turbulent boundary layer (TBL) with a step change from a smooth to a rough surface is analyzed to examine the characteristics of a spatially developing flow. The roughness elements are periodically arranged two-dimensional (2-D) spanwise rods, with the first rod placed 80θ_in downstream from the inlet, where θ_in denotes the inlet momentum thickness. Based on an accurate estimation of relevant parameters, clear evidence for mean flow universality is provided when scaled properly, even for the present roughness configuration, which is believed to have one of the strongest impacts on the flow. Compared to previous studies, it is shown that overshooting behavior is present in the first- and second-order statistics and is locally created either within the cavity or at the leading edge of the roughness depending on the type of statistics and the wall-normal measurement location. Inspection of spatial two-point correlations of the streamwise velocity fluctuations shows a continuous increase of spanwise length scales of structures over the rough wall after the step change at a greater growth rate than that over smooth wall TBL flow. This is expected because spanwise energy spectrum shows presence of much energetic wider structures over the rough wall. Full images of the DNS data are presented to describe not only predominance of hairpin vortices but also a possible spanwise scale growth mechanism via merging over the rough wall.     

DNS,LES and RANS of turbulent heat transfer in boundary layer with suddenly changing wall thermal conditions

The objectives of this study are to investigate a thermal field in a turbulent boundary layer with suddenly changing wall thermal conditions by means of direct numerical simulation (DNS), and to evaluate predictions of a turbulence model in such a thermal field, in which DNS of spatially developing boundary layers with heat transfer can be conducted using the generation of turbulent inflow data as a method. In this study, two types of wall thermal condition are investigated using DNS and predicted by large eddy simulation (LES) and Reynolds-averaged Navier–Stokes equation simulation (RANS). In the first case, the velocity boundary layer only develops in the entrance of simulation, and the flat plate is heated from the halfway point, i.e., the adiabatic wall condition is adopted in the entrance, and the entrance region of thermal field in turbulence is simulated. Then, the thermal boundary layer develops along a constant temperature wall followed by adiabatic wall. In the second case, velocity and thermal boundary layers simultaneously develop, and the wall thermal condition is changed from a constant temperature to an adiabatic wall in the downstream region. DNS results clearly show the statistics and structure of turbulent heat transfer in a constant temperature wall followed by an adiabatic wall. In the first case, the entrance region of thermal field in turbulence can be also observed. Thus, both the development and the entrance regions in thermal fields can be explored, and the effects upstream of the thermal field on the adiabatic region are investigated. On the other hand, evaluations of predictions by LES and RANS are conducted using DNS results. The predictions of both LES and RANS almost agree with the DNS results in both cases, but the predicted temperature variances near the wall by RANS give different results as compared with DNS. This is because the dissipation rate of temperature variance is difficult to predict by the present RANS, which is found by the evaluation using DNS results.     

Tomographic PIV investigation of coherent structures in a turbulent boundary layer flow

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in the logarithmic region of the turbulent boundary layer in a water tunnel.The Reynolds number based on momentum thickness is Reθ = 2 460.The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low speed fluid,which is flanked on either side by highspeed ones.Statistical support for the existence of hairpins is given by conditional averaged eddy within an increasing spanwise width as the distance from the wall increases,and the main vortex characteristic in different wall-normal regions can be reflected by comparing the proportion of ejection and its contribution to Reynolds stress with that of sweep event.The pre-multiplied power spectra and two-point correlations indicate the presence of large-scale motions in the boundary layer,which are consistent with what have been termed very large scale motions(VLSMs).The three dimen-sional spatial correlations of three components of velocity further indicate that the elongated low-speed and highspeed regions will be accompanied by a counter-rotating roll modes,as the statistical imprint of hairpin packet structures,all of which together make up the characteristic of coherent structures in the logarithmic region of the turbulent boundary layer(TBL).     

The boundary layers of an unsteady incompressible stagnation-point flow with mass transfer

In the current work, the boundary layers of an unsteady incompressible stagnation-point flow with mass transfer were further investigated. Similarity transformation technique was used and the similarity equation group was solved using numerical methods. Interesting observation is that there are multiple solutions seen for negative unsteadiness parameters, β. The influences of mass transfer, unsteadiness parameter, and Prandtl numbers on velocity and temperature profiles, wall drag, and wall heat fluxes were investigated and analyzed. The asymptotic behaviors for the similarity equations in limiting situations were theoretically analyzed. It is found that solutions exist for all mass transfer parameters for β≥−1. For a certain mass transfer parameter, there are two solutions when β_c<β<0; there is one solution for (β=β_c)∪(β≥0); there is no solution for β<β_c, where β_c is a critical unsteadiness parameter dependent on mass transfer parameter.     

A visual study on complex flow structures and flow breakdown in a boundary layer transition

A visualization study is conducted on the excited laminar-turbulent transition within a flat plate boundary layer flow in a water tunnel. The hydrogen bubble technique is employed to investigate the complex characteristics of the flow structure and its breakdown in the later stages of the transition. A new flow structure is observed, which involves two secondary hairpin vortices outboard of both legs of a primary hairpin vortex. This complex structure is argued to be a precursor of a turbulent spot in this K-type transition. Also reported in the paper is the evolution of the flow structure and its subsequent breakdown, manifested by the emergence of dark spots, low-speed fluid bumps, and near-wall hairpin vortex groups. The results indicate that the near-wall flow breakdown is the result of instability of a local three-dimensional high-shear layer between the low-speed fluid bump and the outer higher-speed region.     

Disturbed boundary layer flow with local time-dependent surface heating

Local flows in a laminar boundary layer flowing over surface heating elements are investigated. Mathematical models of disturbed flows are constructed on the basis of an asymptotic analysis and the similarity parameters are determined. The time-dependent local heating regimes ensuring control of separation and flow stability in the boundary layer are studied. The results of a numerical and analytic analysis are obtained.     

Heat transfer and skin-friction in a turbulent boundary layer under a non-equilibrium longitudinal adverse pressure gradient

The experimental data on the effect of weak and moderate non-equilibrium adverse pressure gradients (APG) on the parameters of dynamic and thermal boundary layers are presented. The Reynolds number based on the momentum thickness at the beginning of the APG region was Re^** = 5500. The APG region was a slot channel with upper wall expansion angles from 0 to 14°. The profiles of the mean and fluctuation velocity components were measured using a single-component hot-wire anemometer. The friction coefficients were determined using two methods, namely, the indirect Clauser method and the direct method of weighting the lower wall region on a single-component strain-gage balance. The heat transfer coefficients were determined by a transient method using an IR camera. It is noticed that in the pressure gradient range realized the universal logarithmic region in the boundary layer profile is conserved. The values of the relative (divided by the parameters in zero gradient flow at the same value of Re^**) friction and heat transfer coefficients, together with the Reynolds analogy factor, are determined as functions of the longitudinal pressure gradient. The values of the relative friction coefficient reduced to c_f/c_f0 = 0.7 and those of the heat transfer to St/St₀ = 0.9. A maximum value of the Reynolds analogy factor (St/St₀)/(c_f/c_f0) = 1.16 was reached for the pressure gradient parameter β = 2.9.     

Analytical solutions for thermal forcing vortices in boundary layer and its applications

Using the Boussinesq approximation, the vortex in the boundary layer is assumed to be axisymmetrical and thermal-wind balanced system forced by diabatic heating and friction, and is solved as an initial-value problem of linearized vortex equation set in cylindrical coordinates. The impacts of thermal forcing on the flow field structure of vortex are analyzed. It is found that thermal forcing has significant impacts on the flow field structure, and the material representative forms of these impacts are closely related to the radial distribution of heating. The discussion for the analytical solutions for the vortex in the boundary layer can explain some main structures of the vortex over the Tibetan Plateau.     

Numerical simulation of quasi-streamwise hairpin-like vortex generation in turbulent boundary layer

A mechanism for generation of near wall quasi-streamwise hairpin-like vortex （QHV） and secondary quasi-streamwise vortices （SQV） is presented. The conceptual model of resonant triad in the theory of hydrodynamic instability and direct numerical simulation of a turbulent boundary layer were applied to reveal the formation of QHV and SQV. The generation procedures and the characteristics of the vortex structures are obtained, which share some similarities with previous numerical simulations. The research using resonant triad conceptual model and numerical simulation provides a possibility for investigating and controling the vortex structures, which play a dominant role in the evolution of coherent structures in the near-wall region.     

Investigating flow topologies in boundary layer transition using direct numerical simulation

A numerical method developed for simulating three-dimensional incompressible boundary layer flow is presented. K-type transition up to the two-spike stage is simulated, and flow topologies at various stages of transition are determined. Comparison with flow topologies from other simulations of turbulent and transitioning flows is made. Financial support provided by Air Operations Division, Aeronautical and Maritime Research Laboratory, Defence Science and Technology Organisation, Australia.     

Control of cross flow in the three-dimensional boundary layer using space-periodic body force action

The possibility of attenuation of the cross flow in the three-dimensional incompressible laminar boundary layer on a sideslipping wing under the action of body force sources simulating the time-average forces generated by a surface electric discharge is estimated. The effect of the distance between the sources and the sideslip angle of the wing on the cross flow velocity is investigated for the source intensity observed experimentally.