Boundary Layer Model Research Articles

Can the atmospheric boundary layer-based potential evaporation model increase the accuracy of generalized complementary functions?

ABSTRACT Complementary functions could reliably and effectively estimate actual evaporation and receive wide attention in recent years. However, estimating potential evaporation (Epo) greatly influences the accuracy of complementary functions. In this study, we compare the atmospheric boundary layer model (ABL2021) with the Priestly–Taylor model (P-T) and the maximum evaporation model (YR2019) for estimating Epo. Eighty-six flux sites are utilized to fit parameters for three generalized complementary functions, including the sigmoid function (H2018), the polynomial function (B2015), and the exponential function (G2021) with various potential evaporation models. The results suggest that ABL2021 shows the best agreement with the observations at large lake sites. The uncertainties for estimation of actual evaporation induced by different potential evaporation models are larger than different complementary functions. ABL2021 significantly reduces the differences in performance between different complementary functions. It suggests that ABL2021 improves the accuracy of the generalized complementary functions in most cases and can provide a calibration-free method for Epo estimation. G2021 performs better and shows more flexibility than the other generalized complementary functions. Therefore, G2021 combined with ABL2021 shows a potential to develop a robust method for estimating actual evaporation based on the complementary principle.

MATHEMATICAL MODELING OF THE PROCESS OF SEPARATION OF MIXTURES BY LIQUID EXTRACTION

While designing liquid-phase extraction processes, one of the main conditions is to determine the kinetic characteristics of the exchange processes necessary to determine the flows and masses of the components. Existing mass transfer models describe mass transfer processes on a semi-empirical and empirical basis with a limited range of applications, simplifying the real picture in most cases. In this regard, the development of models that more widely describe the processes of liquid-phase extraction and allow their application is considered one of the important tasks. Based on the generalization of the Chilton-Colborne hydrodynamic analogy in gradient flows and further development of the Landau-Levich boundary layer model, a mathematical model has been developed to determine the mass transfer coefficients in the extraction process in continuous and dispersed phases using minimal experimental data obtained at the stage of hydrodynamic studies

Computational fluid dynamics for naval hydrodynamics

This article describes key issues which have to be addressed to apply Computational Fluid Dynamics to Naval Hydrodynamics. The specific aspects of Naval Hydrodynamics are discussed and illustrated by recent simulations and comparisons with available experiments. Free-surface flows with or without waves and even violent phenomena such as ventilation or cavitation can be modelled with mixture-fluid surface capturing. Turbulence modelling of thick boundary layers and vortical flows requires anisotropic RANS models or hybrid RANS/LES in case of strongly separated flows. Moreover, fluid–structure interaction in the form of rigid or flexible body motion and multi-body systems is crucial to represent ship manoeuvring and propulsion. Finally, the paper underlines the central role played by anisotropic adaptive grid refinement in the accurate simulation of marine flows.

Boundary Layer Modelling of Flow Acceleration and Energy Transfer Effects in Smart Pavement Design

The integration of remote technology into the construction industry has advanced the emergence of smart, self-learning infrastructure across all levels of land transportation design and development. However, energy harvesting capabilities for smart road ventilation purposes have not yet been fully researched as the world gravitates towards energy sustainability. This study thus presents a mathematical investigation of the self-draining design potentials of road pavements, leveraging on energy absorption and conversion to accelerate conductive and convective ventilation of these pavements during wet conditions, as a means of ensuring the skid resistance and safety of such pavements are not compromised. Applying numerical methods with the aid of commercial software code MATLAB®, the classical physics of fluid-surface interaction was used to model accelerated drainage of microflood off paved surfaces through methodical modification of the thickness of the boundary layer associated with the flow regime over the flat road surface. Results indicate significant influences of energy exchange, thermal, and viscous diffusivity on flow acceleration. Alterations in parameters such as the slip factor, thermally induced Brownian motion or phoretic characteristics of the fluid particles at the boundary induce accelerated flow at the surface of the pavement. The findings contribute to the advancement of smart infrastructure by offering practical insights into the potential benefits of integrating energy-harvesting technologies into road pavement systems. By optimizing flow acceleration mechanisms, smart pavements can play a crucial role in improving road safety and sustainability in urban environments.

Liquid plugs in narrow tubes: application to airway occlusion

We study liquid plugs in the pulmonary airways based on the two-phase axisymmetric weighted residual integral boundary-layer model of Dietze et al. (J. Fluid Mech., vol. 894, 2020, A17), which was originally developed to study liquid films coating the inner surface of a cylindrical tube in interaction with a core gas flow. The augmented form of this model, which was never applied beyond a proof of concept, allows for the representation of liquid pseudo-plugs. Here, we demonstrate its predictive power vs experiments and direct numerical simulations, in terms of the dynamics of plug formation and the characteristics of developed liquid plugs, such as their shape, flow field, speed and length, as well as the associated wall stresses and their spatial derivatives. In particular, we show that the augmented model allows us to establish a direct continuation path from travelling-wave solutions (TWS) to travelling-plug solutions (TPS). We then apply the model to predict mucus plugs in the conducting zone of the tracheobronchial tree, based on the lung architecture model of Weibel. We proceed by numerical continuation of travelling-state solutions in terms of the airway generation, whereby we impose the wavelength of the linearly most-amplified convective instability (CI) mode or that of the absolute instability (AI) mode. We identify the critical airway generation for liquid-plug formation (TWS/TPS transition), maximum potential for wall-stress-induced epithelial cell damage and CI/AI transition, and investigate how these phenomena are affected by the main control parameters, i.e. airway orientation vs gravity, air flow rate, mucus properties and airway size.

Mechanisms and models of the turbulent boundary layers at transcritical conditions

Mechanisms and models of the turbulent boundary layers at transcritical conditions

The role of secondary voids in the mechanism of ductile fracture at a crack tip

The mechanics and mechanisms of ductile fracture, ahead of a blunting crack tip, have been studied extensively. Several computational studies analyzing the effect of initial void volume fraction, void shape, void spatial distribution and the mode of loading (KI,KII etc.) on crack-void interaction and its consequence on the mechanism of fracture have been reported. The influence of small size secondary voids on the failure of ligament between the large primary voids and, hence, on fracture toughness has been analyzed using the Gurson-type homogenized models of ductile fracture. In the present work, the two populations of voids ahead of a crack tip are modeled discretely. A plane strain, central line cracked boundary layer model under small-scale yielding is considered. The role of initial shape and spatial distribution of secondary voids, matrix strain hardening and mode of imposed loading in the mechanism of ductile crack growth initiation and advance is analyzed in detail. For completeness sake, numerical calculations are also performed using a homogenized representation of the secondary voids. The results so obtained are then compared with the predictions based on discrete modeling of the secondary voids. Our numerical studies revealed that plastic flow localization resulting from a small initial volume fraction of favorably distributed secondary voids may alter the path of crack growth initiation and advance, thus, influencing the ductile fracture toughness.

Estimating the sensitivity of the Priestley–Taylor coefficient to air temperature and humidity

Abstract. The Priestley–Taylor (PT) coefficient (α) is generally set as a constant value or is fitted as an empirical function of environmental variables, and it can bias the evaporation estimation or hydrological projections under global warming. By using an atmospheric boundary layer model, this study derives a theoretical and parameter-free equation for estimating α as a function of air temperature (T) and specific humidity (Q). With observations from several waterbodies and non-water-limited land sites, we demonstrate that, in addition to estimating the value of α well, the derived expressions can also capture the sensitivity of α to T and Q, that is, dα/dT and dα/dQ. α is generally negatively associated with T and Q, in which regard T plays a more fundamental role in controlling α behaviors. Based on climate model data, we further show that this negative relationship between α and T is of great importance for long-term hydrological predictions. We also provide a lookup graph for practical and broad uses to directly find the values of dα/dT and dα/dQ under specific conditions. Overall, the derived expression gives a physically clear and straightforward approach to quantify changes in α, which is essential for PT-based hydrological simulation and projections.

Hypersonic Stability and Breakdown Measurements on the AFRL/AFOSR BOLT II Flight Geometry

The Air Force Research Laboratory/Air Force Office of Scientific Research (AFRL/AFOSR) introduced the Boundary Layer Turbulence (BOLT II) flight experiment to further the understanding and modeling of a hypersonic turbulent boundary layer on a geometry that features concave surfaces with swept leading edges. In support of the flight experiment, this paper identifies and documents the transition instabilities and quantifies the breakdown to turbulence on a 25%-scale BOLT II model in hypersonic flow. Experiments were conducted in the conventional Actively Controlled Expansion wind tunnel facility and the Mach 6 Quiet Tunnel located at the Texas A&M University National Aerothermochemistry and Hypersonics Laboratory. Global surface heating was viewed using infrared thermography with on-surface measurements made using high-frequency Kulite and PCB Piezotronics surface pressure transducers. Modal growth was observed among the sensors both upstream and downstream of the model. Off-surface measurements were made in the mixed-mode region utilizing constant-temperature hot-film anemometry in the Mach 6 Quiet Tunnel. Comparisons were made to the Direct Numerical Simulation (DNS) results from the University of Minnesota. Amplified content was observed between f=53 and 75 kHz in the root-mean-square voltage fluctuations of the hot-film measurements.

Direct numerical simulation of skin friction drag reduction on supersonic turbulent boundary layers with micro-blowing

The flow control mechanism and skin friction drag reduction characteristics of micro-blowing on a Ma2.25 supersonic turbulent boundary layers are investigated through direct numerical simulations, and the effects of blowing intensity and micro-hole arrangement on turbulent structure and skin friction drag in the local control region and downstream region are considered. The results show that the skin friction drag decreases remarkably in the control region under the influence of micro-blowing, and a certain drag reduction can still be maintained in the downstream region. The drag reduction performance in the control region is jointly determined by blowing intensity and micro-hole arrangement. The drag reduction performance of the staggered arrangement is 5.7% and 11.1% higher than that of the inline arrangement at blowing intensities of 0.2% and 0.5%, respectively. However, it is found that the drag reduction in the downstream region is only determined by the blowing intensity and almost independent of the micro-hole arrangement. The effect of micro-blowing on turbulent structures is quantitatively characterized by energy spectrum analysis, and it shows that the streamwise scales of the near-wall streaks are significantly reduced under the influence of micro-blowing. In addition, the compressibility of fluids and the local reverse transfer in the strong expansion region are significantly improved under the influence of micro-blowing. These effects should be considered when performing Large Eddy Simulation modeling of supersonic turbulent boundary layers with micro-blowing.

A comparative study of fatigue crack driving force considering in-plane constraint effect

Nonlinear fracture mechanics parameters, ΔCTODp and ΔJ are implicitly used to characterize the crack driving force (CDF) in estimating Fatigue Crack Growth Rate (FCGR) in ductile material. However, in the presence of structure geometry effect, evaluation of effective CDF remains to be clarified. In this regard, a comparative study was conducted and the in-plane-constraint parameter was introduced to quantify geometry effect based on the constraint theory. Using modified boundary layer model (MBL) with multi-stage node releasing embedded, the effect of in-plane-constraint on ΔCTODp and ΔJ was investigated. Results indicate that ΔCTODp can demonstrate geometry effect on CDF, as it correlates well with plastic deformation. Compartively, the effective cyclic J-integral (ΔJop) was found to have a significant dependency only on the crack closure level, thus incapable of capturing the effect of geometry on CDF. A humpbacked curve was found between in-plane constraint level and ΔCTODp. Further investigation reveals that the gain of in-plane constraint on FCGR can be attributed to the interaction between in-plane constraint and crack closure, as well as the interplay between in-plane and out-of-plane constraint. This work not only reveals the mechanism of the in-plane constraint effect on CDF, but also provides a basis for establishing FCG model across different structure geometries.

Equilibrium atmospheric boundary layer model for numerical simulation of urban wind environment

The numerical simulation of urban wind environments faces difficulties in capturing the turbulent characteristics due to the large computational domain. Traditional Reynolds-averaged methods (RANS) can effectively capture the average wind characteristics of urban areas. However, due to the significant dissipation and attenuation of turbulent energy in the downstream direction, this method fails to provide accurate turbulent characteristics after time-averaging processing. Therefore, in order to obtain a higher-precision turbulent wind field distribution within urban areas, this paper proposed a new numerical method named an equilibrium atmospheric boundary layer model (EABL) by modifying the control equation of the shear stress transport k–ω model. During the process, the equilibrium atmospheric boundary layer was achieved successfully, and the attenuation problem of the turbulent kinetic energy and dissipation rate during the computational fluid dynamics numerical simulation was resolved. Simultaneously, a wind tunnel experiment and six turbulence models [standard k–ε, realizable k–ε, renormalization group k–ε, large eddy simulation—narrowband synthesis random flow generator (LES-NSRFG) and LES vortex method and EABL] were employed to simulate the wind field characteristics in an actual residential area. The simulation results demonstrate that, relative to traditional RANS models, the EABL model enhances the simulation accuracy of turbulence characteristics by over two times. Furthermore, compared to LES models, the EABL model can reduce computational time by threefold.

Turbulent Ice–Ocean Boundary Layers in the Well-Mixed Regime: Insights from Direct Numerical Simulations

Abstract The meltwater mixing line (MML) model provides a theoretical prediction of near-ice water mass properties that is useful to compare with observations. If oceanographic measurements reported in a temperature–salinity diagram overlap with the MML prediction, then it is usually concluded that the local dynamics are dominated by the turbulent mixing of an ambient water mass with near-ice meltwater. While the MML model is consistent with numerous observations, it is built on an assumption that is difficult to test with field measurements, especially near the ice boundary, namely, that the effective (turbulent and molecular) salt and temperature diffusivities are equal. In this paper, this assumption is tested via direct numerical simulations of a canonical model for externally forced ice–ocean boundary layers in a uniform ambient. We focus on the well-mixed regime by considering an ambient temperature close to freezing and run the simulations until a statistical steady state is reached. The results validate the assumption of equal effective diffusivities across most of the boundary layer. Importantly, the validity of the MML model implies a linear correlation between the mean salinity and temperature profiles normal to the interface that can be leveraged to construct a reduced ice–ocean boundary layer model based on a single scalar variable called thermal driving. We demonstrate that the bulk dynamics predicted by the reduced thermal driving model are in good agreement with the bulk dynamics predicted by the full temperature–salinity model. Then, we show how the results from the thermal driving model can be used to estimate the interfacial heat and salt fluxes and the melt rate. Significance Statement We investigate the turbulent dynamics and thermodynamical properties of water masses below ice shelves using new data from high-resolution simulations. This is important because there are currently too few observations of ice–ocean boundary layer dynamics to construct reliable models of ice-shelf melting as a function of ocean conditions. Our results demonstrate that the turbulent diffusivities of salt and temperature are approximately equal in the well-mixed regime. This implies a linear correlation between the mean temperature and salinity profiles, consistent with the meltwater mixing line prediction that is often used to interpret polar observations. We take advantage of this correlation to propose a reduced model of ice–ocean boundary layers that can predict ice-shelf melt rates at relatively low computational cost.

Performance and modeling of freezing crystallization in desalination: Heat transfer and impurities flow

This work applies the freezing crystallization in the desalination and establishes the theoretical models with experiments, to correlate the technical parameters with product properties. We first establish the heat flow models to simulate the 3-dimensional spatiotemporal temperature distribution and deduce the two heat flows through the ice layer, in which the latent heat from the phase transition plays a dominant role in heat transfer. Next, mass transfer and boundary layer models are proposed to evaluate the desalination efficiency and demonstrate the roles of kinetic and thermodynamic factors on the impurity migration. Later, three process optimization strategies, including cooling rate regulation, air bubble-assisted, and crystal seed-induced techniques, are imported to enhance the separation efficiency. At last, sweating is incorporated to reach the secondary purification effect, in which the desalination ratio under the optimal trajectory exceeds 83 %. The established sweating models accurately predict the product properties with time and can trace the impurities flow from the ice layer and adherent inclusion. The inclusion occupies a major discharged melt at the initial sweating stage, but more ice layer begins to melt and enter into the sweating liquid, confirming that a slight increase in product purity accompanies the huge yield loss.

Modifications to the CLASS Boundary Layer Model for Improved Interaction Between the Mixed Layer and Clouds

AbstractThe impact of clouds on the mixed layer (ML) is critical for understanding the evolution of boundary layer humidity and temperature over the course of a day. We found that accounting for moistening of the cloud layer (CL) by humidity originating in the ML dramatically alters the interaction between the ML and the CL in a one‐dimensional cloud‐topped boundary layer model: Chemistry Land‐surface Atmosphere Soil Slab (CLASS) (Vilà‐Guerau de Arellano et al., 2015, https://doi.org/10.1017/CBO9781316117422). We demonstrate that enabling CLASS to moisten the lower CL improves the prediction of humidity (and the flux of humidity) both above and below the ML top (h). To account for this moistening, we propose a length scale, L, above h, over which mixing of mass fluxes into the environment occurs. The mass fluxes are assumed to decrease linearly from h to a height L meters above h, analogous to a convective plume detraining into the environment at a height‐independent rate. Accounting for this process is accomplished by modifying the differential equations representing the growth of the jumps (sharp changes in humidity and temperature) at h. From analysis of a large number of diurnal Large Eddy simulations (covering approximately 11,000 different early morning initial conditions), we provide a regression model for parameterizing L from early morning weather variables. With the regression‐based estimate of L, the modified model (CLASS‐L) accounts for moistening the lower CL, and as a result, yields improved humidity dynamics, humidity flux profiles, and cloud growth under a broad range of conditions.

Numerical Study on Rotor–Building Coupled Flow Field and Its Influence on Rotor Aerodynamic Performance under an Atmospheric Boundary Layer

In urban settings, buildings create complex turbulent conditions, affecting helicopter flight performance during missions and increasing safety risks during takeoff and landing. A numerical study on rotor–building coupled flow field is carried out to address rotor aerodynamic performance under building interferences in natural atmospheric conditions. A high-fidelity atmospheric boundary layer (ABL) model described by an exponential law is established herein. The solution of the coupled flow field is based on the Reynolds-averaged Navier–Stokes (RANS) equations, with the rotor’s rotation achieved through the overset grid method. Based on the dominant wind features, the building flow field is distributed into four regions, where the updraft along the headwind side impacts the rotor, bringing about a 76% increase in pitching moment. On the lateral side of the building, distorted rotor wake squeezed upward into the rotor disk, leading to severe blade–vortex interaction (BVI). During low-altitude hovering over rooftops, the mixing of building shed vortices with forward flow wakes causes the formation of a circulation region on the rotor’s windward side, resulting in a thrust loss of approximately 7.8%. Meanwhile, the flow environment on the leeward side of the buildings is more stable. Therefore, it is recommended that helicopters adopt a headwind approach during rooftop operations. However, an 11.4% loss in the average hover figure of merit is observed due to consistent thrust losses caused by the recirculation region.

An Improved Non‐Local Planetary Boundary Layer Parameterization Scheme in Weather Forecasting and Research Model Based on a 1.5‐Order Turbulence Closure Model

AbstractPlanetary boundary layer (PBL) modeling is a primary contributor to uncertainties in a numerical weather prediction (NWP) model due to difficulties in modeling the turbulent transport of surface fluxes. The Weather Research and Forecasting model (WRF) has provided many PBL schemes that may feature a non‐local transport component driven by large eddies or a one‐and‐half order turbulence closure model, but few of them possess the two features at once. In the present study, a turbulent kinetic energy (TKE)‐based eddy diffusivity/viscosity method is integrated into the non‐local Asymmetric Convective Model version 2 (ACM2) PBL scheme and implemented in WRF. The original first‐order eddy‐diffusivity term in ACM2 is discarded and an extra prognostic equation for TKE, which considers the tendency of TKE by buoyancy, wind shear, vertical transport, and dissipative processes, is supplied to calculate the diffusivity/viscosity. Non‐local transport is modeled the same as ACM2 using the transilient matrix method. Idealized tests using prescribed surface heat flux and roughness length are performed. TKE‐ACM2 displays advantages over the PBL scheme developed by Bougeault and Lacarrère (hereinafter referred to as Boulac) and ACM2 in the wind speeds (WS) profile because it better matches large‐eddy simulations results in the surface momentum flux. Real case simulations show that TKE‐ACM2 generally outperforms in the diurnal vertical profiles of WS under stable conditions. TKE‐ACM2 also produces a better alignment under moderately unstable conditions in the early nighttime at the urban LiDAR station. However, the model exhibits discrepancies more apparently under a more unstable condition during the winter daytime.

Challenges and perspective on the modelling of high-Re, incompressible, non-equilibrium, rough-wall boundary layers

The present paper gives an overview of the recent modelling activities under NATO-STO AVT-349, focussed on the understanding and modelling of boundary layers for incompressible, high-Reynolds-number flows subject to non-equilibrium conditions such as strong pressure gradients, three-dimensionality, and surface roughness and heterogeneity. For this, we consider simpler cases where the above flow conditions are present separately or in a reduced number of combinations. First, we focus on the effect of roughness on the outer flow and the problems associated to its characterisation and prediction, with a particular emphasis on the conditions necessary for outer-layer similarity to hold. We then focus on how the presence of adverse and favourable pressure gradients affects the effect of roughness, and to what extent the figures used to quantify it are still useful under such conditions. We also consider the effect of surface heterogeneity, the shortcomings when modelling it and how these can be addressed. We then focus on the effect on the outer layer of pressure gradients and non-equilibrium conditions, to what extent similarity holds in those conditions, and how RANS models perform for such flows, identifying routes for their improvement to handle pressure gradients and non-equilibrium. We also discuss the use of data-driven and machine-aided methods in closure models.

CFD analysis of local influences in offshore wind measurements employing a floating LiDAR system

In the present work, the CFD modeling of neutral and stable atmospheric boundary layers regarding the horizontal homogeneity condition is discussed to assess the impact of local influences in wind measurements made by a Light Detection and Ranging (LiDAR) remote sensor installed at an offshore site. The LiDAR will be mounted on a real floating, production, storage, and offloading (FPSO) vessel, 200 km far from the coast, and the simulations serve as preliminary study for the impact of the geometry presence, in the air flow and in the measurements taken by the LiDAR. The reproduction of the homogeneity condition is discussed and the impacts of the presence of the ship structure are quantified considering the scanning scheme of the LiDAR. Turbulence is modeled with the k-ε and k-ω models for the neutral case, and k-ε with a modification following the Monin-Obukhov Similarity Theory for the stable boundary laye. By carrying out simulations with empty and blocked (i.e., with the FPSO installed) domains, we show that the effect of the platform is local and only significant at small heights. The neutral and stable cases show similar deviations (≤ 2 %) between the velocity fields in the blocked and empty domains. The neutral case shows locally a little more impact than the stable case, and the reason for that is discussed. We also found that the LiDAR scanning scheme could attenuate the impacts of the flow distortion in comparison with direct punctual measurements.

Ductile crack growth of high-graded pipeline steels in the presence of Lüders plateau

Strain-based engineering critical assessment methods allows certain amount of plastic strain during installation and in service, for pipelines crossing seismically-active areas. Most strain-based engineering critical assessment methods are established for materials with smooth stress-strain relationship, leaving the so-called Lüders plateau influence on ductile fracture response seldomly explored. This work studied the effect of the Lüders plateau on mode I ductile crack growth with the modified boundary layer (MBL) model under plane strain conditions. The “up-down-up” constitutive model was implemented and the Gurson damage model was selected to simulate crack propagation. Factors including the plateau length and softening modulus in the “up-down-up” constitutive model, strain hardening of the matrix material and the initial void volume fraction parameter were analyzed. Numerical results show that the Lüders plateau modifies the crack tip constraint and the damage evolution, and the plateau length plays the dominant role on ductile crack growth behaviour in the presence of Lüders plateau.