DNS of heat transfer in turbulent and transitional channel flow obstructed by rectangular prisms

Direct numerical simulation (DNS) of heat transfer in a channel flow obstructed by rectangular prisms has been performed for Re_τ = 80–20, where Re_τ is based on the friction velocity, the channel half width and the kinematic viscosity. The molecular Prandtl number is set to be 0.71. The flow remains unsteady down to Re_τ = 40 owing to the disturbance induced by the prism. For Re_τ = 30 and 20, the flow results in a steady laminar flow. In the vicinity of the prism, the three-dimensional complex vortices are generated and heat transfer is enhanced. The Reynolds number effect on the time-averaged vortex structure and the local Nusselt number are investigated. The mechanism of the heat transfer enhancement is discussed. In addition, the mean flow parameters such as the friction factor and the Nusselt number are examined in comparison with existing DNS and experimental data.     

Turbulent flow around a wall-mounted cube: A direct numerical simulation

An immersed-boundary method was employed to perform a direct numerical simulation (DNS) of flow around a wall-mounted cube in a fully developed turbulent channel for a Reynolds number Re = 5610, based on the bulk velocity and the channel height. Instantaneous results of the DNS of a plain channel flow were used as a fully developed inflow condition for the main channel. The results confirm the unsteadiness of the considered flow caused by the unstable interaction of a horseshoe vortex formed in front of the cube and on both its sides with an arch-type vortex behind the cube. The time-averaged data of the turbulence mean-square intensities, Reynolds shear stresses, kinetic energy and dissipation rate are presented. The negative turbulence production is predicted in the region in front of the cube where the main horseshoe vortex originates.     

Some features of a turbulent wing–body junction vortical flow

Laser-Doppler velocimeter measurements of a wing/body junction flow field made within a plane to the side of the wing/wall junction and perpendicular both to a 3:2 elliptical nose—NACA 0020 tail wing, and a flat wall are presented. Reynolds number of the approach boundary layer was, Re_θ = 5940, and free-stream air velocity was, U_ref = 27.5 m/s. A large vortical structure residing in the outer region redirects the low-turbulence free-stream flow to the vicinity of the wing/wall junction, resulting in thin boundary layers with velocity magnitudes higher than free-stream flow. Lateral pressure gradients result in a three-dimensional separation on the uplifting side of the vortex. Additionally, a high vorticity vortical structure with opposite sense to the outer-layer vortex forms beneath the outer-layer vortex. Normal and shear stresses increase to attain values an order of magnitude larger compared to values measured in a three-dimensional boundary layer just outside the junction vortex. Bimodal histograms of the w fluctuating velocity occur under the outer-layer vortex near the wall due to the time-dependent nature of the horseshoe vortex. In such a flow the shear-stress angle (SSA) highly lags the flow-gradient angle (FGA), and the turbulence diffusion is highly altered due to presence of vortical structures.     

Open channel turbulent flow over hemispherical ribs

This paper reports an experimental investigation of open channel turbulent flow over hemispherical ribs. A row of ribs consists of hemispheres closely placed to one another in the spanwise direction and cover the entire span of the channel. The pitch-to-height ratio is varied to achieve the so-called d-type, intermediate and k-type roughness. The Reynolds numbers based on water depth, h, and momentum thickness, θ, of the approach flow are respectively, Re_h = 28,100 and Re_θ = 1800. A particle image velocimetry is used to obtain detailed velocity measurements in and above the cavity. Streamlines, mean velocity and time-averaged turbulent statistics are used to study the effects of pitch-to-height ratio on the flow characteristics and also to document similarities and differences between the present work and prior studies over two-dimensional transverse rods. It was observed that interaction between the outer flow and the shear layers generated by ribs is strongest for k-type and least for d-type ribs. The results also show that hemispherical ribs are less effective in augmenting flow resistance compared to two-dimensional transverse ribs. The levels of the Reynolds stresses and budget terms increase with increasing pitch-to-height ratio inside the roughness sublayer.     

Boundary layer receptivity measurements on compliant surfaces

This paper describes receptivity measurements in a pre-transitional boundary layer flowing over either a rigid or a compliant surface. Fluctuating velocities and frequency spectra were determined on one rigid and nine compliant surfaces. The results showed that the near wall receptivity grows linearly with Re_θ. An empirical correlation of the gain frequency spectrum for a rigid wall was also established. For the compliant surfaces, the near wall gain is increased markedly near the leading edge of the plate due to the amplification of high and mid-frequencies. These frequencies are dissipated though as the flow progresses over the compliant surface such that the receptivity is lower on all the compliant surfaces than on the rigid surface at the trailing edge. An empirical correlation for the ratio of the gains on compliant and rigid surfaces in terms of the compliant surface coefficient ζ²/Eρ_CSL² and Re_θ was established. This correlation indicates that compliant surfaces can suppress receptivity by up to 25% for a Re_θ = 400.     

On the influence of near-wall forces in particle-laden channel flows

Computation of a turbulent dilute gas–solid channel flow has been undertaken to study the influence of using wall-corrected drag coefficients and of the lift force on the dispersed phase characteristics. The incompressible Navier–Stokes equations governing the carrier flow were solved by using a direct numerical simulation approach and coupled with a Lagrangian particle tracking. Calculations were performed at Reynolds number based on the wall-shear velocity and channel half-width, Re_τ ≈ 184, and for three different sets of solid particles. For each particle set, two cases were examined, in the first one the particle motion was governed by both drag and lift wall-corrected forces, whereas in the other one, the standard drag force (not corrected) was solely acting. The lift force model used represents the most accurate available expression since it accounts for weak and strong shear as well as for wall effects. For this study, we considered elastic collisions for particles contacting the walls and that no external forces were acting. Present results indicate that the use of the lift force and of the drag corrections does not lead to significant changes in the statistical properties of the solid phase, at the exception of some statistics for the high inertia particles.     

Evolution of jets effusing from inclined holes into crossflow

The turbulent flow structure and vortex dynamics of a jet-in-a-crossflow (JICF) problem, which is related to gas turbine blade film cooling, is investigated using the particle-image velocimetry (PIV) technique. A cooling jet emanating from a pipe interacts with a turbulent flat plate boundary layer at a Reynolds number Re_∞ = 400,000. The streamwise inclination of the coolant jet is 30° and two velocity ratios (VR = 0.28, VR = 0.48) and two mass flux ratios (MR = 0.28, MR = 0.48) are considered. Jets of air and CO₂ are injected separately into a boundary layer to examine the effects of the density ratio between coolant and mainstream on the mixing behavior and consequently, the cooling efficiency. The results show a higher mass flux ratio to enlarge the size of the recirculation region leading to a more pronounced entrainment of hot outer fluid into the wake of the jet. Furthermore, the lateral spreading of the coolant is strongly increased at a higher density ratio. The results of the experimental measurements are used to validate numerical findings. This comparison shows an excellent agreement for mean velocity and higher moment velocity distributions.     

Experimental study on the magnetic convection in a vertical cylinder

The flow of paramagnetic fluid inside a cylinder placed in a bore of a superconducting magnet was studied experimentally. Single-phase closed thermosyphon configuration was employed. The lower side wall of the cylindrical enclosure was heated while the upper side wall was cooled with the thin adiabatic interface in between. The experiment was carried out with an aqueous solution of glycerol. The magnetic susceptibility of the working fluid was increased by adding Gd(NO₃)₃ × 6H₂O and was measured by a magnetic susceptibility balance. The encapsulated liquid crystal slurry (KWN-2025, Japan Capsular Product Inc.) dispersed in the working fluid was illuminated in the middle height horizontal cross-section of the enclosure to visualize the temperature field. The color images of flow mode were taken by a digital camera. The average heat transfer rates were also measured. Depending on the Rayleigh number, different spoke patterns were observed. The number of angular structures (spokes) increased with increase not only in the Rayleigh number but also in the strength of magnetic field. The heated fluid was repelled by the magnetic field, while the cooled fluid was attracted. The magnetic field enhanced the heat transfer rate.     

DNS of passive scalar transport in turbulent channel flow at high Schmidt numbers

We perform DNS of passive scalar transport in low Reynolds number turbulent channel flow at Schmidt numbers up to Sc = 49. The high resolutions required to resolve the scalar concentration fields at such Schmidt numbers are achieved by a hierarchical algorithm in which only the scalar fields are solved on the grid dictated by the Batchelor scale. The velocity fields are solved on coarser grids and prolonged by a conservative interpolation to the fine-grid.

The trends observed so far at lower Schmidt numbers Sc  10 are confirmed, i.e. the mean scalar gradient steepens at the wall with increasing Schmidt number, the peaks of turbulent quantities increase and move towards the wall. The instantaneous scalar fields show a dramatic change. Observable structures get longer and thinner which is connected with the occurrence of steeper gradients, but the wall concentrations penetrate less deeply into the plateau in the core of the channel.

Our data shows that the thickness of the conductive sublayer, as defined by the intersection point of the linear with the logarithmic asymptote scales with Sc^−0.29. With this information it is possible to derive an expression for the dimensionless transfer coefficient K⁺ which is only dependent on Sc and Re_τ. This expression is in full accordance to previous results which demonstrates that the thickness of the conductive sublayer is the dominating quantity for the mean scalar profile.     

Shroud heat transfer measurements inside a heated multiple rotating cavity with axial throughflow

Experimental measurements of heat transfer are made from the inner peripheral surface of a rotating test rig designed to be similar to a gas turbine high pressure compressor internal air system. The test rig comprises a number of annular discs sealed at their periphery by a shroud. An axial throughflow of cooling air enters the test rig and flows through the annular section between the disc bores and a central shaft. Tests were carried out for the following range of rotational speeds and axial throughflow rates: 540 < N_R < 10,800 rev/min and (corresponding to the range of rotational and axial Reynolds numbers 4 × 10⁵ < Re < 7.7 × 10⁶ and 3.3 × 10⁴ < Re_z < 2.2 × 10⁵).

The shroud Nusselt numbers are found to depend on the shroud Grashof number. They are relatively insensitive to changes in axial Reynolds number and two geometrically similar cavities give similar values of Nusselt number. The heat transfer from the shroud is governed by the mechanism of free convection. It is recommended that a modified form of a correlation for Rayleigh–Bénard convection in a gravitational force field be used, with appropriate modification, to predict shroud heat transfer.     

Flow measurements inside a heated multiple rotating cavity with axial throughflow

This paper discusses experimental results from a multiple cavity test rig representative of a high pressure compressor internal air system. Measurements of the axial, tangential and radial velocity components are presented. These were made using a two component, laser doppler anemometry (LDA) system for a range of non-dimensional parameters representative of engine conditions (Re up to 4 × 10⁶ and Re_z up to 1.8 × 10⁵). Tests were carried out for two different sizes of annular gap between the (non-rotating) drive shaft and the disc bores.

The axial and radial velocities inside the cavities are virtually zero. The size of the annular gap between disc bore and shaft has a significant effect on the radial distribution of tangential velocity. For the narrow annular gap (d_h/b = 0.092), there is an increase of non-dimensional tangential velocity V/Ωr with radial location from V/Ωr < 1 at the lower radii to solid body rotation V/Ωr = 1 further into the cavity. For the wider annular gap (d_h/b = 0.164), there is a decrease from V/Ωr > 1 at the lower radii to solid body rotation further into the cavity. An analysis of the frequency spectrum obtained from the tangential velocity measurements is consistent with a flow structure in the r– plane consisting of pairs of contra rotating vortices.     

Coherent fine scale eddies in turbulence transition of spatially-developing mixing layer

To investigate the relationship between characteristics of the coherent fine scale eddy and a laminar–turbulent transition, a direct numerical simulation (DNS) of a spatially-developing turbulent mixing layer with Re_ω,0 = 700 was conducted. On the onset of the transition, strong coherent fine scale eddies appears in the mixing layer. The most expected value of maximum azimuthal velocity of the eddy is 2.0 times Kolmogorov velocity (u_k), and decreases to 1.2u_k, which is an asymptotic value in the fully-developed state, through the transition. The energy dissipation rate around the eddy is twice as high compared with that in the fully-developed state. However, the most expected diameter and eigenvalues ratio of strain rate acting on the coherent fine scale eddy are maintained to be 8 times Kolmogorov length (η) and :β:γ = −5:1:4 in the transition process. In addition to Kelvin–Helmholtz rollers, rib structures do not disappear in the transition process and are composed of lots of coherent fine scale eddies in the fully-developed state instead of a single eddy observed in early stage of the transition or in laminar flow.     

Experimental visualization of temperature fields and study of heat transfer enhancement in oscillatory flow in a grooved channel

An experimental study was conducted of incompressible, moderate Reynolds number flow of air over heated rectangular blocks in a two-dimensional, horizontal channel. Holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in self- sustained oscillatory flow. Experiments were conducted in the laminar, transitional and turbulent flow regimes for Reynolds numbers in the range from Re = 520 to Re = 6600. Interferometric measurements were obtained in the thermally and fluiddynamically periodically fully developed flow region on the ninth heated block. Flow oscillations were first observed between Re = 1054 and Re = 1318. The period of oscillations, wavelength and propagation speed of the Tollmien–Schlichting waves in the main channel were measured at two characteristic flow velocities, Re = 1580 and Re = 2370. For these Reynolds numbers it was observed that two to three waves span one geometric periodicity length. At Re = 1580 the dominant oscillation frequency was found to be around 26 Hz and at Re = 2370 the frequency distribution formed a band around 125 Hz. Results regarding heat transfer and pressure drop are presented as a function of the Reynolds number, in terms of the block-average Nusselt number and the local Nusselt number as well as the friction factor. Measurements of the local Nusselt number together with visual observations indicate that the lateral mixing caused by flow instabilities is most pronounced along the upstream vertical wall of the heated block in the groove region, and it is accompanied by high heat transfer coefficients. At Reynolds numbers beyond the onset of oscillations the heat transfer in the grooved channel exceeds the performance of the reference geometry, the asymmetrically heated parallel plate channel. Received on 26 April 2000     

Thermal characteristics of a high heat flux micro-evaporator

Our purpose is to design a high heat flux micro-evaporator that can remove more than 100 W/cm². For this purpose a thin liquid film is evaporized. The liquid film is stabilized in micro-channels by capillary forces. The micro-channels are fabricated by chemical etching on silicon to reduce thermal resistance. For the experiments, the channel plate is heated by an ITO thin film heater deposited on the opposite side of the channel plate. Influence of heat flux, coolant flow rate, and inlet temperature on the temperature of the heater element are investigated. Water is used as working fluid. A maximal heat flux of 125 W/cm² could be achieved for water inlet temperature of 90 °C and flow rate of 1.0 mL/min. The temperature of the heater element is kept constant at about 120 °C with fluctuations within 8 °C. The measured pressure drop is less than 1000 Pa.     

Turbulent natural convection flow in a vertical channel with anti-symmetric heating

This paper presents the fluid flow characteristics of natural convection flow in an anti-symmetrically heated parallel-plate vertical channel using the Particle Image Velocimetry (PIV) system. The channel walls were subjected to uniform temperature conditions, with one wall heated above ambient and the opposing wall maintained below ambient temperature. Velocity measurements were conducted at three different sections on the horizontal plane to validate two-dimensionality of the flow and at three different heights in the vertical plane to establish vertical mean velocity profiles. The results indicate that the flow recirculation in the channel exhibits a similar character to that of a closed cavity and the induced flow rate is much lower than the one for a channel with both walls heated. A correlation for the dimensionless flow rate is developed.     

Turbulent free convection in a vertical converging channel

This paper presents the results of experimental and numerical investigations of the problem of turbulent natural convection in a converging-plate vertical channel. The channel has two isothermally heated inclined walls and two adiabatic vertical side walls. The parameters involved in this study are the channel geometry represented by the channel width at exit, the inclination of the heated walls and the temperature difference between the heated walls and the ambient. The investigation covered modified Rayleigh numbers up to 10⁸ in the computational study and up to 9.3 × 10⁶ in the experimental work. The experimental measurements focused on the velocity field and were carried out using a PIV system and included measurements of the mean velocity profiles as well as the root-mean-square velocity and shear stress profiles. The experiments were conducted for an inclination angle of 30°, a gap width of 10 mm and two temperature differences (∆T=25.4°C and 49.8°C). The velocity profiles in the lower part of the channel indicated the presence of two distinct layers. The first layer is adjacent to the heated plate and driven by buoyancy forces while the second layer extends from the point of maximum velocity to the channel center plane and driven mainly by shear forces. The velocity profile at the upper portion of the channel has shown the merging of the two boundary layers growing over the two heated walls. The measured values of the Reynolds shear stress and root mean square of the horizontal and vertical velocity fluctuation components have reached their maximum near the wall while having smaller values in the core region. The computational results have shown that the average Nusselt number increases approximately linearly with the increase of the modified Rayleigh number when plotted on log–log scale. The variation of the local Nusselt number indicated infinite values at the channel inlet (leading edge effect) and high values at the channel exit (trailing edge effect). For a fixed value of the top channel opening, the increase of the inclination angle tended to reduce flow velocity at the inlet section while changing the flow structure near the heated plates in such a way to create boundary-layer type flow. The maximum value of the average Nusselt number occurs when θ = 0 and decreases with the increase of the inclination angle. On the other hand, the increase of the channel width at exit for the same inclination angle caused a monotonic increase in the flow velocity at the channel inlet.     

The low Reynolds number turbulent flow and mixing in a confined impinging jet reactor

Turbulent mixing takes an important role in chemical engineering, especially when the chemical reaction is fast compared to the mixing time. In this context a detailed knowledge of the flow field, the distribution of turbulent kinetic energy (TKE) and its dissipation rate is important, as these quantities are used for many mixing models. For this reason we conduct a direct numerical simulation (DNS) of a confined impinging jet reactor (CIJR) at Re = 500 and Sc = 1. The data is compared with particle image velocimetry (PIV) measurements and the basic flow features match between simulation and experiment. The DNS data is analysed and it is shown that the flow is dominated by a stable vortex in the main mixing duct. High intensities of turbulent kinetic energy and dissipation are found in the impingement zone which decrease rapidly towards the exit of the CIJR. In the whole CIJR the turbulence is not in equilibrium. The strong mixing in the impingement zone leads to a rapid development of a monomodal PDF. Due to the special properties of the flow field, a bimodal PDF is generated in cross-sections downstream the impingement zone, that slowly relaxes under relaminarising conditions. The time required for meso-mixing is dominating the overall mixing performance.     

Heat transfer correlation for boiling flows in small rectangular horizontal channels with low aspect ratios

In the present experimental study, a correlation is proposed to represent the heat transfer coefficients of the boiling flows through horizontal rectangular channels with low aspect ratios. The gap between the upper and the lower plates of each channel ranges from 0.4 to 2 mm while the channel width being fixed to 20 mm. Refrigerant 113 was used as the test fluid. The mass flux ranges from 50 to 200 kg/m² s and the channel walls were uniformly heated up to 15 kW/m². The quality range covers from 0.15 to 0.75 and the flow pattern appeared to be annular. The modified Lockhart–Martinelli correlation for the frictional pressure drop was confirmed to be within an accuracy of ±20%. The heat transfer coefficients increase with the mass flux and the local quality; however the effect of the heat flux appears to be minor. At the low mass flux condition, which is more likely to be with the smaller gap size, the heat transfer rate is primarily controlled by the liquid film thickness. A modified form of the enhancement factor F for the heat transfer coefficient in the range of Re_LF200 well correlates the experimental data within the deviation of ±20%. The Kandlikar's flow boiling correlation covers the higher mass flux range (Re_LF>200) with 10.7% mean deviation.     

Comparative evaluation of three heat transfer enhancement strategies in a grooved channel

 Results of a comparative evaluation of three heat transfer enhancement strategies for forced convection cooling of a parallel plate channel populated with heated blocks, representing electronic components mounted on printed circuit boards, are reported. Heat transfer in the reference geometry, the asymmetrically heated parallel plate channel, is compared with that for the basic grooved channel, and the same geometry enhanced by cylinders and vanes placed above the downstream edge of each heated block. In addition to conventional heat transfer and pressure drop measurements, holographic interferometry combined with high-speed cinematography was used to visualize the unsteady temperature fields in the self-sustained oscillatory flow. The locations of increased heat transfer within one channel periodicity depend on the enhancement technique applied, and were identified by analyzing the unsteady temperature distributions visualized by holographic interferometry. This approach allowed gaining insight into the mechanisms responsible for heat transfer enhancement. Experiments were conducted at moderate flow velocities in the laminar, transitional and turbulent flow regimes. Reynolds numbers were varied in the range Re = 200–6500, corresponding to flow velocities from 0.076 to 2.36 m/s. Flow oscillations were first observed between Re = 1050 and 1320 for the basic grooved channel, and around Re = 350 and 450 for the grooved channels equipped with cylinders and vanes, respectively. At Reynolds numbers above the onset of oscillations and in the transitional flow regime, heat transfer rates in the investigated grooved channels exceeded the performance of the reference geometry, the asymmetrically heated parallel plate channel. Heat transfer in the grooved channels enhanced with cylinders and vanes showed an increase by a factor of 1.2–1.8 and 1.5–3.5, respectively, when compared to data obtained for the basic grooved channel; however, the accompanying pressure drop penalties also increased significantly. Received on 5 April 2001     

Fluid flow and heat transfer in a two-dimensional wavy channel

A numerical study is presented for the laminar fully developed flow and heat transfer in a two-dimensional wavy channel. The effects of the geometry, Reynolds and Prandtl number on the flow field and heat transfer are investigated. The channel is characterized by a wavy wall, heated at uniform heat flux, and an opposite wall, being plane and adiabatic. The extent of the wall waviness and the distance between the channel walls are found to significantly affect the streamlines contours as well as the heat transfer coefficients. Comparisons with the straight channel, in the same flow rate and heat transfer conditions, have been performed. Pressure drop of the wavy channel is found to be always larger than the value characteristic of a straight channel, while heat transfer performance decreases or increases depending on the values of the parameters (geometry, Reynolds and Prandtl numbers).