Boundary Layer Dissipation Research Articles

Dissipation in Skewed Boundary Layers

Abstract The entropy generation within a turbulent, collateral boundary layer is well understood and is characterised by a dissipation coefficient, Cd. However, it is common for the transverse pressure gradients in turbomachines to create highly skewed boundary layers, where the velocity varies in direction as well as magnitude. A combined experimental and high-fidelity computational approach is used to quantify the effect of skew on the dissipation coefficient for the first time. At a nominal condition of 14 degrees of skew and Reθ of 1000, the increase in dissipation coefficient is 20% as determined from direct numerical simulation, and 28% from experimental measurements, relative to the collateral boundary layer. Experimental data over a range of skew angles and Reθ values show that Cd increases approximately linearly with skew so that, at a skew of 25°, loss is 70% greater than in the collateral boundary layer. The implications for loss estimation are examined by evaluating boundary layer loss, in the Harrison turbine cascade, with and without the influence of skew on Cd. By accounting for the skew in the boundary layer, a new proposed model has been used to calculate the loss coefficient in the Harrison cascade to within 4% of the experimentally measured value.

Data-Driven Radial Compressor Design Space Mapping

Abstract Estimates of turbomachinery performance trends inform system-level compromises during preliminary design. Existing empirical correlations for efficiency use limited experimental data, while analytical loss models require calibration to yield predictive results. From a set of 3708 radial compressor computations, this paper maps efficiency as a function of mean-line aerodynamics, and determines the governing loss mechanisms. An open-source turbomachinery design code creates annulus and blade geometry, then runs a Reynolds-averaged Navier–Stokes simulation for compressors sampled from the mean-line design space. Polynomial surface fits yield a continuous eight-dimensional representation of the design space for analysis, predicting efficiency with a root-mean-square error of 1.2% points. The results show a balance between surface dissipation in boundary layers and mixing loss due to casing separations sets optimum values for inlet Mach number, hub-to-tip ratio, de Haller number, and backsweep angle. Surface dissipation drives the effect of flow coefficient, with high surface areas at low values, and high velocities at high values. Compact compressor designs are achieved by increasing inlet Mach number, reducing hub-to-tip ratio, and minimizing the radial loading coefficient—all of which reduce efficiency approaching design space boundaries. An interactive web-based tool makes the results available to practising engineers, demonstrating large ensembles of automated designs and simulations as a higher-fidelity replacement for legacy empirical correlations in preliminary design.

Quantum graph wave external triggering: Energy transfer and damping.

The propagation of wave trains resulting from a local external trigger inside a network described by a metric graph is analyzed using quantum graph theory. The external trigger is a finite-time perturbation imposed at one vertex of the graph, leading to a consecutive wave train into the network, supposedly at rest before the applied external perturbation. A complete analytical solution for the induced wave train is found having a specific spectrum as well as mode's amplitudes. Furthermore the precise condition by which the external trigger can transfer a maximal energy to any specific natural mode of the quantum graph is derived. Finally, the wave damping associated with boundary-layer dissipation is computed within a multiple time-scale asymptotic analysis. Exponential damping rates are explicitly found related to their corresponding mode's eigenvalue. Each mode energy is then obtained, as well as their exponential damping rate. The relevance of these results to the physics of waves within networks are discussed.

Enhancing spatial inference of air pollution using machine learning techniques with low-cost monitors in data-limited scenarios.

Ensuring environmental justice necessitates equitable access to air quality data, particularly for vulnerable communities. However, traditional air quality data from reference monitors can be costly and challenging to interpret without in-depth knowledge of local meteorology. Low-cost monitors present an opportunity to enhance data availability in developing countries and enable the establishment of local monitoring networks. While machine learning models have shown promise in atmospheric dispersion modelling, many existing approaches rely on complementary data sources that are inaccessible in low-income areas, such as smartphone tracking and real-time traffic monitoring. This study addresses these limitations by introducing deep learning-based models for particulate matter dispersion at the neighbourhood scale. The models utilize data from low-cost monitors and widely available free datasets, delivering root mean square errors (RMSE) below 2.9 μg m-3 for PM1, PM2.5, and PM10. The sensitivity analysis shows that the most important inputs to the models were the nearby monitors' PM concentrations, boundary layer dissipation and height, and precipitation variables. The models presented different sensitivities to each road type, and an RMSE below the regional differences, evidencing the learning of the spatial dependencies. This breakthrough paves the way for applications in various vulnerable localities, significantly improving air pollution data accessibility and contributing to environmental justice. Moreover, this work sets the stage for future research endeavours in refining the models and expanding data accessibility using alternative sources.

Investigation of non-ideal effects in compressible boundary layers of dense vapors through direct numerical simulations

In this work, we present an investigation about the sources of dissipation in adiabatic boundary layers of non-ideal compressible fluid flows. Direct numerical simulations (DNS) of transitional, zero-pressure gradient boundary layer flows are performed for two fluids characterized by different complexity of the fluid molecules, namely, “air” and siloxane MM. Different sets of thermodynamic free-stream boundary conditions are selected to evaluate the influence of the fluid state on both the frictional loss and the dissipation mechanisms. The thermophysical properties of siloxane MM are calculated with a state-of-the-art equation of state. Results show that the dissipation due to both time-mean strain field, irreversible heat transfer, and turbulent dissipation differs significantly depending on both the molecular complexity of the fluid and its thermodynamic state. The dissipation coefficient calculated from the DNS results is then compared against the one obtained using a reduced-order model (ROM), which solves the two-dimensional boundary layer flow equations for an arbitrary fluid [M. Pini and C. De Servi, “Entropy generation in laminar boundary layers of non-ideal fluid flows,” in 2nd International Seminar on Non-Ideal Compressible Fluid Dynamics for Propulsion and Power (Springer, 2020), pp. 104–117]. Results from both the DNS and the ROM show that low values of the overall dissipation are observed in the case of fluids made of simple molecules, e.g., air, and if the fluid is at a thermodynamic state in the proximity of that of the vapor–liquid critical point.

Analysis of the spreading radius in droplet impact: The two-dimensional case

We study droplet impact problems in a 3D cylindrical or equivalent 2D Cartesian geometry. Such structures do have an approximate experimental realization, and they are often simulated as a testbed for computational methods. We focus on droplet impact on a smooth homogeneous surface as well as head-on collision of two droplets. We perform an energy-budget analysis and introduce a correlation, which predicts the maximum spreading radius as a function of Reynolds number and Weber number. We show how the dissipation term in this analysis can be decomposed into boundary-layer dissipation in the droplet lamella (where applicable) and head loss. We use existing results in the literature (simulations and experiments) as well as our own simulation results to validate the correlation. Dissipation by head loss is a key term in the analysis: only by modeling it accurately, one can obtain good agreement between the simulations and the theory.

A Framework for Estimating Effects of Combustor Turbulence on Turbine Profile Loss Generation

Abstract This paper describes a framework to quantify the effect of freestream turbulence, generated by mixing processes in a combustor, on turbulent boundary layer loss generation in the high-pressure turbine downstream of the combustor. The regime of freestream turbulence common to gas turbine aero engines is identified and it is shown that the dissipation loss coefficient in this regime can be determined using existing measurements of the effect of freestream turbulence on skin friction. The paper shows that combustor-generated freestream turbulence can increase the profile loss coefficient of a typical high-pressure turbine blade by as much as 28%. A relation has been derived between a non-dimensional turbulence parameter, which characterizes the freestream turbulence, and the increase in turbine boundary layer dissipation, which quantifies the decrease in turbine efficiency. The relation provides guidelines for combustor turbulence modifications that lead to turbine performance benefits. The framework has been applied in example trade studies which show that increasing the size of dilution ports and increasing the length of the combustor can decrease high-pressure turbine profile loss generation to potentially increase stage efficiency up to 0.5%.

Topological structures for microchannel heat sink applications – a review

The microchannel heat sink (MCHS) has the advantages of small heat transfer resistance, high heat transfer efficiency and small size, which exhibits good heat transfer performance in the field of active heat dissipation of electronic devices integrated with high heat flux density. In this paper, the application of MCHS in thermal management is reviewed in recent years, and the research progress of microchannel topology on enhancing heat transfer performance is summarized. Firstly, the research progress on the cross-sectional shape of the microchannel shows that the heat transfer area and fluid flow dead zone of the microchannel is the keys to affecting the heat transfer performance; Secondly, the microchannel distribution and the bionic microchannel structure have a great role in enhancing heat transfer performance, especially in microchannel temperature uniformity; Thirdly, the disturbing effect caused by interrupted structures in microchannels such as ribs and concave cavities has become a hot topic of research because it can weaken the thermal boundary layer and increase heat dissipation. Finally, the commonly used MCHS materials and cooling media are summarized and introduced. Based on the above reviews of MCHS research and applications, the future trends of MCHS topologies are presented.

The Impact of Land Surface Properties on Haboobs and Dust Lofting

Abstract Haboobs are dust storms formed by strong surface winds in convective storm outflow boundaries, or cold pools, which can loft large quantities of mineral dust as they propagate. Both cold pools and the dust they loft are impacted by land surface properties resulting in complex surface interactions on haboobs. As a result of these additional complexities brought about by surface interactions, it is unclear which surface parameters and physical processes are important for predicting haboob intensity and dust concentrations. Here we applied the Morris one-at-a-time (MOAT) global sensitivity statistical method to an ensemble of 120 idealized simulations of daytime and nighttime haboobs to investigate the land surface properties that affect both dust mobilization and cold pool dynamics. MOAT identifies and ranks the importance of different input factors, which for the prediction of haboob strength and dust concentrations are 1) initial cold pool temperature, 2) surface type (vegetation), 3) soil type (clay content), and 4) soil moisture. The underlying physical mechanisms driving these feedbacks were then analyzed using a traditional one-at-a-time factor analysis. Time of day is significant for determining boundary layer height and dissipation via surface fluxes, leading to shallower, more intense cold pools/haboobs at night. Most of the land parameters modify the cold pool through impacts on surface fluxes, while surface type is dominated by roughness length effects. By ranking the importance of these surface factors, we have identified which variables are most sensitive and must be constrained via observations and data assimilation in numerical dust prediction models.

Transfer of Orbital Angular Momentum to Freely Levitated High-Density Objects in Airborne Acoustic Vortices

Vortex-field acoustic levitation is an application of acoustic vortices that allows the manipulation of a wide range of materials in various media. However, to date, its levitation capability in air is limited to relatively low-density objects. Here, by optimizing an array-tube setup, we levitate iridium ($22.56\phantom{\rule{0.2em}{0ex}}\mathrm{g}/{\mathrm{cm}}^{3}$) in a first-order acoustic vortex in air. This technique makes it possible to observe the orbital angular momentum transfer carried by acoustic vortices to freely levitated high-density objects, of which the highest rotation speed reaches up to 6500 revolutions per second and increases with a decrease in the object size and an increase in the source amplitude. It is revealed that the thermal-viscous boundary layer dissipation is the dominant effect and leads directly to the rapid rotation of high-density objects. This work can expand the application scope of acoustic vortices, especially in the fields of containerless processing of various materials and rapid rotation of objects, and help to understand the mechanisms of orbital angular momentum transfer to matter.

Bayesian estimations of dissipation, sound speed, and microphone positions in impedance tubes.

Sound speed, microphone positions, and tube wall dissipation are critical parameters for absorption and impedance measurements using the transfer-function method in an impedance tube. This work applies a Bayesian method, based on a reflection coefficient model of an air layer and a boundary layer dissipation model, to estimate the values of these parameters for tube measurements. This estimation is based on experimental measurements obtained in the empty impedance tube with a rigid termination. Analysis results demonstrate that this method is able to accurately estimate the dissipation coefficient, the sound speed, and the microphone positions for highly accurate tube measurements.

Dissipation and Bathymetric Sensitivities in an Unstructured Mesh Global Tidal Model

AbstractThe mechanisms and geographic distribution of global tidal dissipation in barotropic tidal models are examined using a high resolution unstructured mesh finite element model. Mesh resolution varies between 2 and 25 km and is especially focused on inner shelves and steep bathymetric gradients. Tidal response sensitivities to bathymetric changes are examined to put into context response sensitivities to frictional processes. We confirm that the Ronne Ice Shelf dramatically affects Atlantic tides but also find that bathymetry in the Hudson Bay system is a critical control. We follow a sequential frictional parameter optimization process and use TPXO9 data‐assimilated tidal elevations as a reference solution. From simulated velocities and depths, dissipation within the global model is estimated and allows us to pinpoint dissipation at high resolution. Boundary layer dissipation is extremely focused with 1.4% of the ocean accounting for 90% of the total. Internal tide friction is much more distributed with 16.7% of the ocean accounting for 90% of the total. Often highly regional dissipation can impact basin‐scale and even ocean wide tides. Optimized boundary layer friction parameters correlate very well with the physical characteristics of the locality with high friction factors associated with energetic tidal regions, deep ocean island chains, and ice covered areas. Global complex M2 tide errors are 1.94 cm in deep waters. Total global boundary layer and internal tide dissipation are estimated, respectively, at 1.83 and 1.49 TW. This continues the trend in the literature toward attributing more dissipation to internal tides.

Heavy footprints of upper-ocean eddies on weakened Arctic sea ice in\u2009marginal ice zones

Arctic sea ice extent continues to decline at an unprecedented rate that is commonly underestimated by climate projection models. This disagreement may imply biases in the representation of processes that bring heat to the sea ice in these models. Here we reveal interactions between ocean-ice heat fluxes, sea ice cover, and upper-ocean eddies that constitute a positive feedback missing in climate models. Using an eddy-resolving global ocean model, we demonstrate that ocean-ice heat fluxes are predominantly induced by localized and intermittent ocean eddies, filaments, and internal waves that episodically advect warm subsurface waters into the mixed layer where they are in direct contact with sea ice. The energetics of near-surface eddies interacting with sea ice are modulated by frictional dissipation in ice-ocean boundary layers, being dominant under consolidated winter ice but substantially reduced under low-concentrated weak sea ice in marginal ice zones. Our results indicate that Arctic sea ice loss will reduce upper-ocean dissipation, which will produce more energetic eddies and amplified ocean-ice heat exchange. We thus emphasize the need for sea ice-aware parameterizations of eddy-induced ice-ocean heat fluxes in climate models.

Damping rate measurements and predictions for gravity waves in an air–oil–water system

Dissipation of standing gravity waves of frequencies within 1–2 Hz is investigated experimentally. The waves are generated in a rectangular tank filled with water, the surface of which is covered with an oil layer of mean thickness, d. Damping rates are measured as a function of d, and compared with results from established theoretical models—in particular, with those from a recently developed three-fluid dissipation model that considers waves in a system of semi-infinitely deep fluids that lie above and below an interfacial fluid layer of finite thickness. Based on a comparison of experimental data with predictions, the oil–water interfacial elasticity, E2, is empirically determined to be a linear function of d. The theoretical predictions include contributions from the three-fluid dissipation model, which accounts for energy losses due to shear layers at the interfaces, friction in the fluid bulk, and compression–expansion oscillations of the elastic interfaces; and from a boundary-layer dissipation model, which accounts for energy losses due to boundary layers at the tank's solid surfaces. The linear function, E2(d), is used to compute the three-fluid model damping rate. An effective viscosity of the oil–water system is used to compute the boundary-layer model damping rate. The theoretical predictions are, on average, within 5% of measurements for all the wave frequencies considered. The promise shown by the three-fluid model is highlighted, as are the assumptions involved in the analysis and comparisons.

Nonlinear evolution equation for modeling waves at the boundary of a stratified flow of viscous liquids in an inclined channel

The dynamics of perturbations of the interface of a two-layer Poiseuille flow in a flat closed inclined channel is studied. The velocity profiles of wave motion are analytically found neglecting dissipation, dispersion and pumping of perturbations. On the basis of the found solution, a nonlinear evolution integro-differential equation for plane moderately long perturbations of the interface of the liquids is derived. The coefficients of the equation are represented by integrals over the layer thicknesses from functions depending on the stationary flow and perturbation profiles. The equation takes into account viscous dissipation: one of the integrals in this equation corresponds to dissipation in lion-stationary boundary layers, and the other corresponds to the transfer of energy from the flow to the wave. For the case of small flow velocities, the coefficients of the equation are analytically calculated. The equation has also been generalized to the quasi-two-dimensional case when the gradients along the transversal coordinate are small.

Numerical investigation of distributed roughness effects on separated flow transition over a highly loaded compressor blade

Large eddy simulations were conducted to investigate the effects of distributed roughness on separated flow transitions over a highly loaded compressor blade at a Reynolds number (Re) of 1.5 × 105. The distributed roughness elements were located downstream of the velocity peak on the suction surface, and four numerical cases with increasing peak amplitude of the roughness elements (k+ = 0, 23, 50, and 112) were considered. The results showed that low- and high-speed streamwise streaks appeared alternately along the spanwise direction over the distributed roughness elements. The streaks remained steady earlier; however, as the streamwise counter-rotating vortices were induced by a significant spanwise velocity component, the low-momentum fluid in the near-wall region was transported away from the blade surface and interacted with the outer separated shear layers, which caused unsteady merging of streaks and promoted the destabilization of separated shear layers. Compared with the baseline case (k+ = 0), the strong shear effect between the low- and high-speed streamwise streaks near the roughened blade surface accelerated the distortion of spanwise vortices, and three-dimensional hairpin vortex structures broke down into small-scale turbulent eddies at a shorter streamwise distance. With increase in the roughness magnitude, the level of the production term of turbulent kinetic energy was reduced due to weakened vortex dynamics, and the viscous dissipation in turbulent boundary layers also became weaker. Therefore, the profile losses of the three roughness cases, k+ = 23, 50, and 112, were decreased by 7.2%, 10.1%, and 15.5%, respectively.

Shelf Seas Baroclinic Energy Loss: Pycnocline Mixing and Bottom Boundary Layer Dissipation

AbstractObservations of turbulent kinetic energy dissipation rate () from a range of historical shelf seas data sets are viewed from the perspective of their forcing and dissipation mechanisms: barotropic to baroclinic tidal energy conversion, and pycnocline and bottom boundary layer (BBL) dissipation. The observations are placed in their geographical context using a high resolution numerical model (NEMO AMM60) in order to compute relevant maps of the forcing (conversion). We analyze, in total, 18 shear microstructure surveys undertaken over a 17 year period from 1996 to 2013 on the North West European shelf, consisting of 3,717 vertical profiles of shear microstructure: 2,013 from free falling profilers and 1,704 from underwater gliders. A robust positive relationship is found between model‐derived barotropic to baroclinic conversion, and observed pycnocline integrated . A fitted power law relationship of approximately one‐third is found, giving a simple new parameterization. We discuss reasons for this apparent power law and where the “missing” dissipation may be occurring. We conclude that internal wave related dissipation in the bottom boundary layer provides a robust explanation and is consistent with a commonly used fine‐scale pycnocline dissipation parameterization.

Influences of a Quasi-stationary Front on Particulate Matter in the Low-latitude Plateau Region in China

ABSTRACT By utilizing observation and reanalysis data and statistical methods to comprehensively assess the main characteristics of particulate matter (PM) on the low-latitude plateau (LoLaP) of southwestern China, this study analyzed the influence of the Kunming quasi-stationary front (KMQSF) on the PM concentration during winter in this region. We found that the location and intensity of the KMQSF significantly affected the distribution pattern of the PM and induced high concentrations in some areas during a typical pollution event in 2016. Furthermore, we investigated all of the KMQSF synoptic weather that occurred from 2014 till 2019 and categorized it into nine types, which produced different pollution patterns. When the KMQSF moved westward from the center of the LoLaP, the easterly wind transported PM to the western part of the region, which led to an increase in the mean daily PM10 and PM2.5 concentrations in Kunming, a capital city in that area; simultaneously, however, the PM10 and PM2.5 levels remained high in Guiyang, a capital city in the eastern part of the LoLaP. When the KMQSF gradually retreated from the western to the eastern part of the LoLaP, the PM in Kunming dropped as the westerly wind increased in strength, whereas the PM in Guiyang continued to rise as the planetary boundary layer (PBL) height (PBLH) and boundary layer dissipation (BLD) rate decreased. When the KMQSF disappeared, temperature inversion, a shallow PBL and weak BLD across the entire region caused pollutants to accumulate, resulting in the highest mean daily PM10 and PM2.5 concentrations for both cities.

Meteorological Change and Impacts on Air Pollution: Results From North China

AbstractThere have been speculations that the severe air pollution experienced in North China was the act of meteorological change in general and a decreasing northerly wind in particular. We conduct a retrospective analysis on 1979–2016 reanalysis data from ERA‐Interim of European Centre for Medium‐Range Weather Forecasts over a region in North China to detect meteorological changes over the 38 years. No significant reduction in the northerly wind within the mixing layer is detected. Statistically significant increases are detected in the surface temperature, boundary layer height and dissipation, and significant decreases in relative humidity in the region between the first and second 19‐year periods from 1979 to 2016. We build regression models of PM2.5 on the meteorological variables using data in 2014, 2015, and 2016 to quantify effects of the meteorological changes between the two 19‐year periods on PM2.5 under the emission scenarios of 2014–2016. It is found that despite the warming, dew point temperature had been largely kept under control as the region had gotten dryer. This made the effects of temperature warming largely favorable to PM2.5 reduction as it enhances boundary layer height and dissipation. It is found that the meteorological changes would lead to 1.29% to 2.76% reduction in annual PM2.5 averages with January, March, and December having more than 4% reduction in the 3 years. Thus, the meteorological change in North China had helped alleviate PM2.5 to certain extent and should not be held responsible for the regional air pollution problem.

Dissipation of Turbulent Kinetic Energy in the Oscillating Bottom Boundary Layer of a Large Shallow Lake

AbstractMixing rates and biogeochemical fluxes are commonly estimated from the rate of dissipation of turbulent kinetic energy ε as measured with a single instrument and processing method. However, differences in measurements of ε between instruments/methods often vary by one order of magnitude. In an effort to identify error in computing ε, we have applied four common methods to data from the bottom boundary layer of Lake Erie. We applied the second-order structure function method (SFM) to velocity measurements from an acoustic Doppler current profiler, using both canonical and anisotropy-adjusted Kolmogorov constants, and compared the results with those computed from the law of the wall, Batchelor fitting to temperature gradient microstructure, and inertial subrange fitting to acoustic Doppler velocimeter data. The ε from anisotropy-adjusted constants in SFM increased by a factor of 6 or more at 0.2 m above the bed and showed a better agreement with microstructure and inertial method estimations. The maximum difference between SFM ε, computed using adjusted and canonical constants, and microstructure values was 25% and 50%, respectively. This difference was 30% and 55%, respectively, for those from inertial subrange fitting at times of high-intensity turbulence (Reynolds number at 1 m above the bed of more than 2 × 104). Comparison of the SFM ε to those from law of the wall was often poor, with errors as large as one order of magnitude. From the considerable improvement in ε estimates near the bed, anisotropy-adjusted Kolmogorov constants should be applied to compute dissipation in geophysical boundary layers.