Log-law Region Research Articles

A comparative study on abnormal heat transfer of supercritical CO2 heated in vertical tubes

The heat transfer characteristics of supercritical CO2 heated in vertical smooth tube are experimentally and numerically investigated. The results show that the M-shaped velocity corresponds to heat transfer enhancement (HTE) at G = 100 kg/m2s, q = 20 kW/m2, and the heat transfer coefficient (HTC) is 15% higher than that of normal heat transfer (NHT). While, the M-shaped velocity causes significant heat transfer deterioration (HTD) before the Tpc at G = 278 kg/m2s, q = 35 kW/m2, and the HTC of HTD is 28%–42% of that in NHT. According to the numerical analysis on the M-shaped flow structure, it reveals that the zero-velocity gradient point of abNHT (HTE and HTD) always falls into the buffer layer (5 < y+ < 30). While, the zero-velocity gradient point of the heat transfer recovery (HTR) is in the log-law region (30 < y+ < 60). The u/u0 of the zero-velocity gradient point of HTE are larger than 1.35. The cross-section turbulent kinetic energy structure shows that smaller TKE in the near-wall region is the dominant factor for HTD and larger TKE in the core region is the dominant factor for HTE.

Direct numerical simulation of sand particles transporting in the atmospheric Ekman boundary layer

Abstract This study presents a direct numerical simulation that investigates the transport mechanisms of sand particles in the neutrally stable atmospheric Ekman boundary layer (AEBL). The simulation models the AEBL in a half-channel flow, taking into account the Earth's rotation and adding a Coriolis term to the Navier–Stokes equations. The Lagrangian point-particle method with one-way coupling is used to track the sand particles. The main objective is to examine the impact of gravity and particle Stokes number on the sand particle dynamics. The results indicate that gravity has a significant effect on large-size sand particles, as seen in the mean and root-mean-square sand velocity profiles. The slip velocity profiles of sand particles relative to the surrounding air show that larger particles experience higher drag forces in the viscous sublayer, which hinders their forward movement. This effect is also amplified by gravity. Furthermore, the mean profiles of the streamwise and spanwise slip velocities exhibit distinct demarcations of the viscous sublayer, buffer layer and log-law region. The spatial and temporal Voronoï analysis reveals that gravity increases the clustering level of sand particles in the entire turbulent Ekman layer and reduces the time for the change of the Voronoï volume, particularly for large-size particles.

Reduced-order representation of superstructures in a turbulent boundary layer

The present work is devoted to a low-dimensional characterization of superstructures (SS) in a turbulent boundary layer (TBL). The main purpose is to provide new insight on the spatial correlation between SS and large-scale motion (LSM) with the help of reduced-order analysis via proper orthogonal decomposition (POD). A dataset of three-dimensional streamwise fluctuating velocity fields of a TBL with Reτ=1817, obtained by direct numerical simulation, is decomposed by POD into cross-sectional POD eigenmodes and streamwise-varying mode coefficients. The spatial pattern of the POD eigenmodes of leading-order POD modes, their characteristic length scales, as well as their geometric similarity are analyzed in detail. A conditional-average method is further proposed to yield a reduced-order representation of typical local geometric patterns of the SS, which are mainly contributed to by one particular observation mode. It is found that large-scale motion-like structures constitute the core region of SS. These conditional-averaged structures are treated as elementary cells, which jointly form the skeleton of SS, i.e., uSK which is low dimensionally reconstructed by the first six POD modes. It is found that uSK presents quasi-Gaussian behavior, suggesting a quasi-equilibrium state of elementary SS cells. Finally, ⟨uSK2⟩(y) presents a log-law scaling with the decaying slope of A1SK=1.49, but the log-law region is apparently higher than that of the original velocity field, i.e., ⟨u2⟩(y).

Neutrally- and stably-stratified boundary layers adjustments to a step change in surface roughness

In this work, we study the development of the internal boundary layer (IBL) induced by a surface roughness discontinuity, where the downstream surface has a roughness length greater than that upstream. The work is carried out in the EnFlo meteorological wind tunnel, at the University of Surrey, in both thermally neutral and stable cases with varying degrees of stability. For the neutrally-stratified boundary layer, the IBL development in the log-law region shows good agreement with the diffusion model proposed by Panofsky and Dutton (Atmospheric turbulence, Wiley, New York, 1984) provided that a modified origin condition is introduced and its growth rate is dictated by a constant diffusion term. However, the model over-predicts the growth of the IBL in the outer layer, where the IBL depth grows slowly with fetch following a power function with exponent n being 0.61 (whereas the original model prescribes napprox 0.8). For the stably-stratified boundary layers, n is found to further reduce as the bulk Richardson number, textrm{Ri}_textrm{b}, increases. The analysis of the top region of the IBL shows that the slow growth rate is due to a combination of the decay of the diffusion term and a significantly negative mean wall-normal velocity, which transports fluid elements towards the wall. Considering these two effects, a modified diffusion model is proposed which well captures the growth of the IBL for both neutrally and stably-stratified boundary layers.Graphical abstract

An Empirical Wall Law for the Mean Velocity in an Adverse Pressure Gradient for RANS Turbulence Modelling

An empirical wall law for the mean velocity in an adverse pressure gradient is presented, with the ultimate goal of aiming at the improvement of RANS turbulence models and wall functions. For this purpose a large database of turbulent boundary-layer flows in adverse pressure gradients from wind tunnel experiments is considered, and the mean velocity in the inner layer is analysed. The log law in the mean velocity is found to be a robust feature. The extent of the log-law region is reduced in ratio to the boundary layer thickness with increasing strength of the pressure gradient. An extended wall law emerges above the log law, extending up to the outer edge of the inner layer. An empirical correlation to describe the reduction of the log-law region is proposed, depending on the pressure-gradient parameter and on the Reynolds number in inner viscous scaling, whose functional form is motivated by similarity and scaling arguments. Finally, there is a discussion of the conjecture of the existence of a wall law for the mean velocity, which is governed mainly by local parameters and whose leading order effects are the pressure gradient and the Reynolds number, but whose details can be perturbed by higher-order local and history effects.

Rainbow-Color Imaging Of Microbubbles Strongly Clustering In A Turbulent Boundary Layer

Rainbow-color volumetric illumination for visualizing 3D microbubble distributions was examined in order to find microbubble clustering in a spatially developing turbulent boundary layer. The color coding was defined according to the wall unit from 0 to 200, straddling viscous-sub layer, buffer layer and log-law region. This allowed understanding where the microbubbles were accumulated or diffused within the boundary layer. The results showed microbubble clouding in the low-speed streak regions along the viscous sublayer, clustering into cores of streamwise vortices ejected into the buffer layer, and intermittent exhaust of the clusters toward the log-law region. Furthermore, correlation of these behaviors with local Reynolds shear stress event (ejection, sweep) was found with quadrant analysis of the liquid velocity vector data obtained by PIV.

A Residual Thermodynamic Analysis of Turbulence – Part 1: Theory

A new theoretical groundwork for the analysis of wall-bounded turbulent flows is offered, the application of which is presented in a parallel paper. First, it is proposed that the turbulence phenomenon is connected to the onset of an irreversible process – specifically the action of a slip flow – by which a new fundamental model can be derived. Fluid cells with specific dimensions – of length connected with the local slip length and thickness connected with the distance between two parallel slipping flows – can be hypothetically constructed, in which a specific kinetic energy dissipation can be considered to occur. Second, via a maximum entropy production process a self-organized grouping of cells occurs – which results in the distinct zones viscous sublayer, buffer layer, and the log-law region to be built up. It appears that the underlying web structure may take the form of either representing a perfect web structure without any visible swirls, or a partially defect web structure where unbalanced forces may result in the generation of apparent swirls – which in turn might grow into larger turbulent eddies. Third, on the transition from laminar to turbulent flows, a nominal connection between the onset of a turbulent wall boundary layer (in a pipe flow), the Reynolds number as well as the wall surface roughness can be derived.

Turbulent flow in curved channels

Fully developed turbulent flow in channels with mild to strong longitudinal curvature is studied by direct numerical simulations. The Reynolds based on the bulk mean velocity and channel half-width $\delta$ is fixed at $20\,000$ , resulting in a friction Reynolds number of approximately 1000. Four cases are considered with curvature varying from $\gamma = 2\delta /r_c = 0.033$ to 0.333, where $r_c$ is the curvature radius at the channel centre. Substantial differences between the mean wall shear stress on the convex and concave walls are already observed for $\gamma = 0.033$ . A log-law region is absent and a region with nearly constant mean angular momentum develops in the channel centre for strong curvatures. Spanwise and wall-normal velocity fluctuations are strongly amplified by curvature in the outer region of the concave channel side. Only near the walls, where curvature effects are relatively weak, do the mean velocity and velocity fluctuation profiles approximately collapse when scaled by wall units based on the local friction velocity. Budgets of the streamwise and wall-normal Reynolds-stress equations are presented and turbulence structures are investigated through visualizations and spectra. In the case with strongest curvature, the flow relaminarizes locally near the convex wall. On the concave channel side, large elongated streamwise vortices reminiscent of Taylor–Görtler vortices develop for all curvatures considered. The maximum in the premultiplied two-dimensional wall-normal energy spectrum and co-spectrum shifts towards larger scales with increasing curvature. The large scales substantially contribute to the wall-normal velocity fluctuations and momentum transport on the concave channel side.

Pressure Gradient Effects on the Performance of Riblets Installed on Aircraft Surfaces

A method for estimating the drag reduction performance of riblets installed on the surfaces of an aircraft was extended to take the effect of the pressure gradient over the aircraft into account. This method simply and roughly estimates the effectiveness of riblets applied to arbitrary surfaces of any aircraft by fusing wind tunnel test data and computational fluid dynamics analysis. The drag reduction rate is calculated from the relationships between friction drag reduction , wall-normalized riblet spacing , and Clauser pressure gradient parameter . To obtain this relationship, a wind tunnel test with straight riblets in an adverse pressure gradient was carried out. The resulting shift in the value in the intercept of the log-law region of the mean velocity profile for riblet cases indicates that the drag reduction effect decreases as the Clauser parameter increases. Based on these results, an approximate surface for the relationship between , , and was proposed, and the drag reduction performance of riblets installed on the surfaces of a conceptual aircraft was estimated. The total drag reduction rates estimated by the extended method considering pressure gradient effects and the original method case were both about 2%, which indicates that the effects of the pressure gradient on the aircraft on overall riblet performance are small.

Effect of micro rib on aerothermal dynamic in channel flow

In the present development of gas turbine, there is a main contradiction between the limited amount of cold air, the pressure head in the gas supply system and the large flow loss caused by the cooling unit inside the turbine blade. It leads to demands for the cooling techniques to provide efficient heat transfer with lower pressure loss. Surface micro turbulator is considered as a potential cooling technique. In this study, numerical simulation and experimental research were undertaken to evaluate the turbulent flow heat transfer and pressure loss in channel with a typical 2-D micro rib on one wall with different rib heights. Investigated rib heights range from 0.0013~0.053 of the channel hydraulic diameter ratio(h/D). The Reynolds number is kept at 20,000 to control the inlet boundary layer thickness, which makes the height of all cases located between the viscous layer and the log-law region in the boundary layer with a dimensionless height h+=2~80. Reynolds-Averaged Navier–Stokes(RANS) and Large Eddy Simulation(LES) results were validated by experiment. The results show that the pressure loss and heat transfer show different trends with the h+, which is mainly due to the enhancement of near-wall turbulence caused by the small rib height and the form drag caused by the large rib height. Furthermore, the analysis of near-wall turbulence characteristics given by LES indicates the enhancement of the normal turbulence fluctuation by the small rib within the turbulent boundary layer transition zone dominates the heat transfer enhancement downstream of the rib. the heat transfer is enhanced and the pressure loss is small when the rib height changes in the boundary layer, Which leads to a better overall thermal performance(OTP). The conclusion affirms that micro rib is a potential cooling technique to attain high heat transfer performance with low pressure loss. which is of great significance to enhance the overall efficiency of gas turbine.

Density ratio effects on the topology of coherent turbulent structures in two-way coupled particle-laden channel flows

This investigation considers the effect of density ratio on the modification of coherent turbulent structures in particle-laden channel flows at a shear Reynolds number of Reτ = 180. Direct numerical simulation and Lagrangian particle tracking are used to accurately predict the motion of particles dispersed within the flow at three Stokes numbers, St+ = 0.1, 50, and 92. Particle–fluid coupling is achieved through a local element-based force feedback field in the Navier–Stokes equations, which are solved using a seventh-order accurate spectral element method. After an initial transitory period wherein the effects of particle–fluid interaction are emphasized, the low density ratio particles are found to enhance the turbulence field, increasing the frequency of Q-criterion satisfying regions, while the inertial particles suppress the turbulence, reducing the number of quasistreamwise vortices. Results indicate that the topology of the quasistreamwise vortices is altered by the presence of the particles in the viscous sublayer, the buffer layer, and the log-law region such that the distribution of the third invariant of the deviatoric tensor, R, is widened by the presence of tracer-like particles and made thinner by the inertial particles. This effect reduces the amount of unstable focus/compressing regions and stable focus/stretching regions, which account for the streamwise vortical structures observed in these types of flow. Investigating the instantaneous coupling force field surrounding turbulent structures and low speed streaks shows that particles exert their greatest influence on the fluid in the regions noted, and mechanisms by which the particulate phase interacts with turbulent vortices are analyzed.

Law of the wall for a temporally evolving vertical natural convection boundary layer

Abstract

Heat-transfer analysis of a transitional boundary layer over a concave surface with Görtler vortices by means of direct numerical simulations

This work studies the development of a thermal boundary layer during the laminar-to-turbulent transition process over a concave surface. Direct numerical simulations are performed where the temperature variable is treated as a passive scalar. The laminar flow is perturbed with wall-roughness elements that are able to produce centrifugal instabilities in the form of Görtler vortices with a maximum growth rate. It is found that Görtler vortices are able to greatly modify the surface heat-transfer by generating a spanwise periodic distribution of temperature. Similar to the Görtler momentum boundary layer, elongated mushroom-like structures of low-temperature are generated in the upwash region, whereas in the downwash region, the thermal boundary layer is compressed. Consequently, temperature gradients are increased and decreased in the downwash and upwash regions, respectively, thereby generating an overall enhancement of the heat-transfer rate of ∼400% for the investigated Prandtl numbers (Pr = 0.72, Pr = 1, and Pr = 7.07). This enhancement surpasses the turbulent heat-transfer values during the transitional region, characterized by the development of secondary instabilities. However, downstream, the heat-transfer rate decays to the typical turbulent values. Streamwise evolution of several thermal quantities such as temperature wall-normal distribution, thermal boundary layer thickness, and Stanton number is reported in different regions encountered in the transition process, namely, linear, nonlinear, transition, and fully turbulent regions. These quantities are reported locally at upwash and downwash regions, where they present minima and maxima, as well as globally as spanwise-averaged quantities. Furthermore, it is found that the Reynolds analogy between streamwise-momentum and heat-transfer holds true throughout the whole transition process for the Pr = 1 case. Moreover, the turbulent thermal boundary layer over a concave surface is analyzed in detail for the first time. The viscous sub-layer and the log-law region are described for each investigated Pr. Besides, the root-mean-squared temperature fluctuations are computed, finding that its wall-normal distribution exhibits a higher peak when Pr is increased.

The Effects of Froude Number on a Turbulent Boundary Layer with a Free-Surface

We present direct numerical simulations of a temporally developing turbulent boundary layer along a moving flat plate piercing through the free surface. The influence of the Froude number on the results is examined. We confirm the findings in the literature, that the vorticity and secondary flows generated at the free surface for low Froude numbers ($Fr\sim 0$) is primarily due to anisotropy of the normal Reynolds stresses. At intermediate Froude numbers however, the vorticity generated at the free surface is related to the curvature of the interface, and is directly injected in the outer and logarithmic portions of the turbulent boundary layer. This has an impact on its overall structure with increased levels of turbulent kinetic energy production. The deformable interface results in changes to the velocity distribution in the near-surface region and loss of self-similarity within the log-law region of the boundary layer.

Interaction of coherent flow structures in adverse pressure gradient turbulent boundary layers

With the aim to characterize the near-wall flow structures and their interaction with large-scale motions in the log-law region, time-resolved planar and volumetric flow field measurements were performed in the near-wall and log-law region of an adverse pressure gradient turbulent boundary layer following a zero pressure gradient turbulent boundary layer at a friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}=5000$. Due to the high spatial and temporal resolution of the measurements, it was possible to resolve and identify uniform-momentum zones in the region $z/\unicode[STIX]{x1D6FF}&lt;0.15$ or $z^{+}&lt;350$ and to relate them with well known coherent flow motions near the wall. The space–time results confirm that the turbulent superstructures have a strong impact even on the very near-wall flow motion and also their alternating appearance in time and intensity could be quantified over long time sequences. Using the time record of the velocity field, rare localized separation events appearing in the viscous sublayer were also analysed. By means of volumetric particle tracking velocimetry their three-dimensional topology and dynamics could be resolved. Based on the results, a conceptual model was deduced that explains their rare occurrence, topology and dynamics by means of a complex interaction process between low-momentum turbulent superstructures, near-wall low-speed streaks and tilted longitudinal and spanwise vortices located in the near-wall region.

The connection between the spectrum of turbulent scales and the skin-friction statistics in channel flow at

Data from a direct numerical simulation for channel flow at a friction Reynolds number of 1000 are analysed to derive statistical properties that offer insight into the mechanisms by which large-scale structures in the log-law region affect the small-scale turbulence field close to the wall and the statistical skin-friction properties. The data comprise full-volume velocity fields at 150 time levels separated by 50 wall-scaled viscous time units. The scales are separated into wavelength bands by means of the ‘empirical mode decomposition’, of which the two lowest modes are considered to represent the small scales and three upper modes to represent the large scales. Joint and conditional probability density functions are then derived for various scale-specific statistics, with particular emphasis placed on the streamwise and shear stresses conditional on the large-scale fluctuations of the skin friction, generally referred to as ‘footprinting’. Statistics for the small-scale stresses, conditional on the footprints, allow the amplification and attenuation of the small-scale skin friction, generally referred to as ‘modulation’, to be quantified in dependence on the footprints. The analysis leads to the conclusion that modulation does not reflect a direct interaction between small scales and large scales, but arises from variations in shear-induced production that arise from corresponding changes in the conditional velocity profile. This causal relationship also explains the wall-normal change in sign in the correlation between large scales and small scales at a wall-scaled wall distance of approximately 100. The effects of different scales on the skin friction are investigated by means of two identities that describe the relationship between the shear-stress components and the skin friction, one identity based on integral momentum and the other on energy production/dissipation. The two identities yield significant differences in the balance of scale-specific contributions, and the origins of these differences are discussed.

The modulation of particles on coherent structure of turbulent boundary layer in dilute liquid-solid two-phase flow with PIV

Liquid-solidtwo-phase wall turbulent flow is an important flow pattern in engineering field. Studying the modulation of particles on fluid plays a significant role in revealing the mechanism of momentum, heat and mass transfer, improving production efficiency and decreasing energy consumption. The statistical characteristics and coherent structure in the flat plate turbulent boundary layer in clean water condition and near-neutrally liquid-solid two-phase flow with 200 um polystyrene particles (dp+=2.29,dp+=duτv) measured by means of PIV technique were compared and analyzed. The variation rule of turbulent statistic characteristics such as mean velocity profile, turbulence intensity and Reynolds shear stress of fluid with polystyrene particles and clean water under the same free flow velocity was investigated. Based on the locally-average velocity structure function and condition sampling technique, the coherent structure was detected, and the two-dimensional spatial topologies such as the fluctuation velocity, Reynolds shear stress and spanwise vorticity in ejection and sweep events at different wall heights under two working conditions were extracted with phase-average method. It was found that in the buffer layer the flow velocity with particles was greater than that of clean water, while there was little difference between them in the logarithmic law region. Compared with the clean water, the streamwise turbulent intensity was decreased in particle-laden flow, whereas the normal turbulent intensity, the comprehensive turbulence intensity and the Reynolds shear stress were all increased, with the expense of a slightly increase of the friction drag in the fluid with particles by 3.57%. In the bursting of coherent structure, the addition of polystyrene particles suppressed the fluid streamwise fluctuation in a turbulent boundary layer, gave a rise to the normal fluctuation and Reynolds shear stress, while inhibited the streamwise development of the spanwise vortex and promoted its normal development. The addition of particles facilitated the fluctuation of the fluid microcluster, and as well as the transverse momentum transfer in the log law region of turbulent boundary layer. The particles could increase the probability of the coherent structure ejection events and had less influence on the sweep events. The number and intensity of the ejection event was the key to improve the flow normal turbulence intensity and even to improve the energy exchange near the wall. The presence of appropriate scale particles in wall turbulence could play an important role in strengthening the transfer of momentum, heat and mass, and promoting mixing and reaction in the engineering, only by slightly increasing the fraction resistance.

Roughness effects of diatomaceous slime fouling on turbulent boundary layer hydrodynamics

Biofilm fouling significantly impacts ship performance. Here, the impact of biofilm on boundary layer structure at a ship-relevant, low Reynolds number was investigated. Boundary layer measurements were performed over slime-fouled plates using high resolution particle image velocimetry (PIV). The velocity profile over the biofilm showed a downward shift in the log-law region (ΔU+), resulting in an effective roughness height (ks) of 8.8 mm, significantly larger than the physical thickness of the biofilm (1.7 ± 0.5 mm) and generating more than three times as much frictional drag as the smooth-wall. The skin-friction coefficient, Cf, of the biofilm was 9.0 × 10−3 compared with 2.9 × 10−3 for the smooth wall. The biofilm also enhances turbulent kinetic energy (tke) and Reynolds shear stress, which are more heterogeneous in the streamwise direction than smooth-wall flows. This suggests that biofilms increase drag due to high levels of momentum transport, likely resulting from protruding streamers and surface compliance.

The effect of cube-roughened walls on the response of rough-to-smooth (RTS) turbulent channel flows

Direct numerical simulations of cube-roughened rough-to-smooth channel flows are performed with the objective of studying the response of turbulence statistics in the developing flow over smooth walls. Non-equilibrium effects persist and the global recovery is slow and incomplete by the streamwise exit of the computational domains, which is at about 10 channel half heights. The estimated recovery distance in the outer regions of the flow is on the order of 50 channel half heights, but different statistics have disparate relxataion rates. The turbulence structure swiftly relaxes to a ‘near’ equilibrium very close to the wall. Within this wall layer, due to a strong mean shear, turbulence statistics and instantaneous motions resemble their fully-smooth equivalents. However, the reversion is not complete because it is interrupted by large structures that persist from the upstream roughness. As the flow encounters the step change in roughness, it expands producing strong mean-advection effects, which prevent the canonical log-law region from being established. The expansion of the mean flow also results in an adverse pressure gradient across the channel. It recovers gradually, only becoming favourable near the exit of the computational domains.

Geometrical structure analysis of a zero-pressure-gradient turbulent boundary layer

The present work focuses on the geometrical features of a zero-pressure-gradient turbulent boundary layer based on vectorline segment analysis. In a turbulent vector field, tracing from any non-singular point, along either the vector or the inverse direction, one will reach a local extremum of the vector magnitude. The vectorline between the two local extrema is defined as the vectorline segment corresponding to the given spatial point. Specifically the vectorline segment can be the streamline segment for the velocity vector case, or the vorticity line segment for the vorticity vector case. Such a quantitatively defined and space-filling vectorline segment structure reflects the natural vectorial topology. Because of inhomogeneity in the wall-normal direction, vectorline segments corresponding to the grid points at specified wall-normal distances are sampled for statistics. For streamline segments, the probability density function (p.d.f.) of the normalized segment length in different flow regions matches a model solution, and for vorticity line segments such a p.d.f. in the log-law region and beyond matches the same model solution, which indicates some universality of different flow regions and different vector field structures. Typically the joint p.d.f. of the characteristic parameters of streamline segments presents clear asymmetry, which is closely related to the skewness of the velocity derivative. Moreover, the orientation statistics of vectorline segments, characterized by the coordinate difference between the segment starting point and ending point, have been provided to quantify the flow anisotropy.