Viscous Shear Stress Research Articles

Mathematical derivation of a unified equations for adjoint lattice Boltzmann method in airfoil and wing aerodynamic shape optimization

Unified equations of the adjoint lattice Boltzmann method (ALBM) are derived for five applicable objective functions in 2D/3D aerodynamic shape optimization problems. The derived equations include the adjoint equation, boundary condition, terminal condition and gradient of the cost function. In this research, firstly, these relations are extracted for each objective in details and then the general form of ALBM equations are presented for all defined practical aerodynamic objective function. Five applicable cost functions which are the most important objectives in optimization of aerodynamic geometries include desired pressure and viscous shear stress (VSS) inverse design, drag and moment at fixed lift and finally lift to drag ratio at fixed angle of attack. The new extracted relations are based on the circular and spherical function scheme, and are valid for viscous/inviscid, compressible/incompressible and 2D/3D flows in all continuous flow regimes. Proof of new extracted general relations have been performed by authors.

Induction and real-time ultrasonic monitoring of 3D cartilage-like tissue by a low shear stresses-based bioreactor

Osteoarthritis is a significant socioeconomic illness that mainly affects the articular cartilage, a tissue with a low capacity for self-healing, making it an ideal target for regenerative medicine and tissue engineering. Current interventions to treat cartilage injuries may not be completely effective. In this study, we have developed a novel bioreactor that creates viscous shear stress by flow perfusion. This bioreactor could induce ex vivo maturation of biomimetic 3D cartilage scaffolds, providing a potential solution to this problem. Infrapatellar fat pad mesenchymal stem cells (IPFP-MSCs) were used as a cellular source of the functionalized 3D scaffolds made of 1,4-butanediol thermoplastic polyurethane (bTPUe) modified with pyrene butyric acid (PBA). Our results indicate that our bioreactor induced chondrogenic differentiation, as confirmed by DNA quantification, extracellular matrix determination, and metabolic assay, without any conditioned medium. To control the biomechanical stimulation on IPFP-MSCs, a low-intensity ultrasonic transmission system has been developed and embedded in the bioreactor. Combined with a finite element model (FEM), tissue growth and differentiation can be deconvoluted in real-time from the recorded ultrasonic propagation and interaction across the graft. The FEM reconstructs this complex interaction. This is the first time a low-shear stress-based bioreactor has been reported to not only induce chondrogenic evolution but also monitor it in real time.

Active control of the free surface of a rivulet of a nematic liquid crystal with an electric field

Active control of a rivulet of a nematic liquid crystal is achieved by local modification of the effective viscosity with an applied electric field. Specifically, using the nematic 5CB, control of the free surface of the rivulet is achieved through manipulation of the effective viscosity induced by the competition of moments due to viscous shear stress alignment and electric field alignment. The experimentally observed dependencies of the rivulet height on the volume flux and the strength of the applied electric field are successfully captured by a theoretical model based on the Ericksen-Leslie equations. Published by the American Physical Society 2024

Numerical study on influence of protrusion heights on Reynolds stress and viscous stress variations in turbulent vortical structures

Analysing the influence mechanism of the riblet protrusion height on turbulent drag components is more beneficial in organising the vortical structure over the riblet surface. Therefore, the Large Eddy Simulation (LES) is used to investigate the vortex structure over the riblet surface with different protrusion heights. Then, the variations of Reynolds stress and viscous shear stress in a turbulent channel are analysed. As a result, the drag reduction rate increases from 3.4% when the riblets are completely submerged in the turbulent boundary layer to 7.9% when the protrusion height is 11.2. Further analysis shows that the protrusion height affects the streamwise vortices and the normal diffusivity of spanwise and normal vortices, thus driving the variation of Reynolds stress. Compared with the smooth surface, the vorticity strength and the number of streamwise vortices are weakened near the wall but increase in the logarithmic layer with increased protrusion height. Meanwhile, the normal diffusivity of spanwise vorticity decreases with the increase of protrusion height, and the normal diffusivity of normal vorticity is the smallest when the protrusion height is 11.2. Moreover, the protrusion height affects the velocity gradient of the riblet tip and riblet valley, thus driving the variation of viscous shear stress. With the increase of protrusion height, the velocity gradient of the riblet tip increases dramatically but decreases in the riblet valley.

Experimental and model study of swirling fluid flow in a converging channel as a simulation of blood flow in the heart and aorta

The study of swirling flows in channels corresponding to the static approximation of flow channels of the heart and major vessels with a longitudinal-radial profile zR2 = const and a concave streamlined surface at the beginning of the longitudinal coordinate has been carried out. A comparative analysis of the flow structure in channel configurations zRN = const, where N = –1; 1; 2; 3, in the absence and presence of a concave surface was carried out. The numerical modelling was compared with the results of hydrodynamic experiments on the flow characteristics and the shape of the flow lines. The numerical model was used to determine the velocity structure, viscous friction losses and shear stresses. Numerical modelling of steady-state flows for channels without a concave surface showed that in the channel zR2 = const there is a stable vortex flow structure with the lowest viscous friction losses. The presence of a concave surface of sufficient size significantly reduces viscous friction losses and shear stresses in both steady state and pulsed modes.

Numerical study on the influence of riblet yaw-angle on drag reduction rate with different immersion heights

This paper uses the Large-eddy simulation method to investigate the influence of riblet yaw angle on drag reduction rate with different immersion heights, revealing that the vortex structure is gradually transformed from riblet-tip vortex pairs to boundary vortex forms with the increase of yaw angle, and analyzing the influence mechanism of immersion height on the critical yaw angle. The result shows that the drag-reduction rate of riblets decreases as the yaw angle increases, and the critical angle of the riblet varies with the different immersion heights. When the immersion height is 0.7, 0.5, and 0.3, the critical yaw angle is close to 30, 40, and 50°, respectively. As the immersion height increases, the cross-flow velocity at the riblet tip is more accessible to reach the critical velocity at which a boundary vortex can be formed, resulting in a smaller critical yaw angle for larger immersion heights. Furthermore, with the yaw angle increases, the normal diffusivity of normal vorticity and spanwise vorticity increase and decrease, respectively, which indicates that the lateral flow fluctuations decrease beyond a critical yaw angle, while the Reynolds stress component due to energy dissipation induced by the streamwise velocity decreases. Meanwhile, with the formation of a boundary vortex, the ability of the riblet to reduce viscous shear stresses increases due to the reduction of near-wall velocity gradient, and the emergence of a high-pressure region on the windward side of the riblet and a low-pressure region on the leeward side, consequently augmenting the differential pressure drag. This work provides valuable insights for designing riblets with heightened effectiveness at larger yaw angles, thereby extending their applicability under diverse flow conditions.

Characterization of Stream, Hyperconcentrated and Debris Flows from Seismic Signals: Insights into Sediment Transport Mechanisms and Flow Dynamics

AbstractSediments in steep channels can be mobilized to form stream flows, hyperconcentrated flows and debris flows, which can cause damage to downstream communities. However, the understanding of the sediment‐transport mechanisms that control these processes remains incomplete due to the lack of effective monitoring methods. In this study, we utilize seismic data captured during these sediment‐laden flows through field experiments and in situ monitoring to offer insights into flow mechanics and sediment transport mechanisms. Results show that sediment transport in stream flows and hyperconcentrated flows is primarily supported by viscous shear and turbulent stresses, whereas grain collisional stresses play a significant role in debris‐flow dynamics. By characterizing impact rates, basal impulses and flow discharge, seismic monitoring can reveal the internal flow dynamics and bulk flow characteristics as well as the characteristics of sediment transport. Increasing solid concentrations can elicit positive nonlinearities in the frequency‐based scaling relationships between seismic power and hydrographs, indicating transitions in the seismic signal from turbulence‐bedload‐dominated to bedload‐dominated, and grain collisional‐dominated regimes. By introducing the ratio of the real shear stress to the critical shear stress, we refined the phase space for sediment stability. Combining this criterion with the absolute seismic power enables us to establish ground‐motion thresholds for distinguishing different flow types. Our results highlight opportunities to use seismic data for the quantitative inversion of these fluvial processes and debris flows as well as early warning strategies.

A review on flow instability in hydro-viscous drive

Hydro-viscous drive (HVD) plays a significant role in smoothly transferring torque and flexibly regulating the velocity of the disks. By hydro-viscous drive, we mean that the viscous shear stress of the thin oil film between a multi-layer assembly of rotating parallel disks is generated to transmit torque and power. The laminar-to-turbulent transition is an extremely complicated issue due to the combined effects of squeeze and shear on the oil film within the microscale friction pair system. Hence, a comprehensive and thorough analysis of flow instability in fluid-thermal-solid interaction of tribodynamic behavior is highly desirable. Following a brief introduction of fundamentals of HVD, this paper provides an overall review on the instability mechanisms for three types of canonical flow dynamic models, i.e., plane squeeze flow, plane shear flow, and rotating-disk flow. The effects of various aspects of wall conditions and working media, such as surface microstructure, and temperature-dependent viscosity, on flow instability are then summarized, which can serve as a reference and guidance for optimizing the design of friction pair systems. Based on the review of the former progress, this paper not only explores the in-depth mechanisms regarding the laminar-to-turbulent transition in microchannel flow, but also provides the possibility of bridging the gap between flow instability and tribodynamic behavior.

In vitro hemodynamics of fabric composite membrane for cardiac valve prosthesis replacement

This study aimed to investigate the hemodynamics of a novel fabric composite that can be used as a substitute for bovine pericardium. The structure is composed of ultrahigh molecular weight polyethylene (UHMWPE) fabric coated with thermoplastic polyurethane (TPU) membranes on both sides. In vitro experiments were carried out on two composite valve samples with different specifications and a bovine pericardial one with the same dimension and structure. Hemodynamic properties including the effective orifice area (EOA) and regurgitant fraction (RF) were obtained and compared through pulsatile-flow testing in a pulse duplicator. Using the particle image velocimetry (PIV) technique, frames of the downstream velocity field in the aortic valve chamber were captured during cardiac cycles. Then, the field of Reynolds shear stress (RSS), viscous shear stress (VSS), and turbulent kinetic energy (TKE) at peak systole were calculated. A fluid–structure interaction (FSI) model has also been used to verify the pulsatile-flow testing. Compared with the bovine pericardial valve, composite valves have nosuperiority regarding EOA and RF due to their slightly higher rigidity. However, shear stresses of composite valves were lower than those of the bovine pericardial valve indicating more stable blood flows, which means that composite leaflets have the potential to reduce the risks of thrombosis and hemolysis induced by the mechanical contact between the blood flow and leaflets of valve prostheses.

Rheology of dense suspensions of ideally conductive particles in an electric field

The rheological behaviour of dense suspensions of ideally conductive particles in the presence of both electric field and shear flow is studied using large-scale numerical simulations. Under the action of an electric field, these particles are known to undergo dipolophoresis (DIP), which is the combination of two nonlinear electrokinetic phenomena: induced-charge electrophoresis (ICEP) and dielectrophoresis (DEP). For ideally conductive particles, ICEP is predominant over DEP, resulting in transient pairing dynamics. The shear viscosity and first and second normal stress differences $N_1$ and $N_2$ of such suspensions are examined over a range of volume fractions $15\,\% \leq \phi \leq 50\,\%$ as a function of Mason number $Mn$ , which measures the relative importance of viscous shear stress over electrokinetic-driven stress. For $Mn < 1$ or low shear rates, the DIP is shown to dominate the dynamics, resulting in a relatively low-viscosity state. The positive $N_1$ and negative $N_2$ are observed at $\phi < 30\,\%$ , which is similar to Brownian suspensions, while their signs are reversed at $\phi \ge 30\,\%$ . For $Mn \ge 1$ , the shear thickening starts to arise at $\phi \ge 30\,\%$ , and an almost five-fold increase in viscosity occurs at $\phi = 50\,\%$ . Both $N_1$ and $N_2$ are negative for $Mn \gg 1$ at all volume fractions considered. We illuminate the transition in rheological behaviours from DIP to shear dominance around $Mn = 1$ in connection to suspension microstructure and dynamics. Lastly, our findings reveal the potential use of nonlinear electrokinetics as a means of active rheology control for such suspensions.

Aerodynamic Uncertainty Quantification of a Low-Pressure Turbine Cascade by an Adaptive Gaussian Process

Stochastic variations of the operation conditions and the resultant variations of the aerodynamic performance in Low-Pressure Turbine (LPT) can often be found. This paper studies the aerodynamic performance impact of the uncertain variations of flow parameters, including inlet total pressure, inlet flow angle, and turbulence intensity for an LPT cascade. Flow simulations by solving the Reynolds-averaged Navier–Stokes equations, the SST turbulence model, and γ−Re˜θt transition model equations are first carried out. Then, a Gaussian process (GP) based on an adaptive sampling technique is introduced. The accuracy of adaptive GP (ADGP) is proven to be high through a function experiment. Using ADGP, the uncertainty propagation models between the performance parameters, including total pressure-loss coefficient, outlet flow angle, Zweifel number, and the uncertain inlet flow parameters, are established. Finally, using the propagation models, uncertainty quantifications of the performance changes are conducted. The results demonstrate that the total pressure-loss coefficient and Zweifel number are sensitive to uncertainties, while the outlet flow angle is almost insensitive. Statistical analysis of the flow field by direct Monte Carlo simulation (MCS) shows that flow transition on the suction side and viscous shear stress are rather sensitive to uncertainties. Moreover, Sobol sensitivity analysis is carried out to specify the influence of each uncertainty on the performance changes in the turbine cascade.

Experimental and Model Study of a Swirling Fluid Flow in a Converging Channel As a Simulation of Blood Flow in the Heart and Aorta.

Study of swirling flows in channels corresponding to the static approximation of flow channels of the heart and major vessels with a longitudinal-radial profile zR2 = const and a concave streamlined surface at the beginning of the longitudinal coordinate has been carried out. A comparative analysis of the flow structure in channel configurations zRN = const, where N = -1, 1, 2, 3, in the absence and presence of a concave surface was carried out. The numerical modeling was compared with the results of hydrodynamic experiments on the flow characteristics and the shape of the flow lines. The numerical model was used to determine the velocity structure, viscous friction losses, and shear stresses. Numerical modeling of steady-state flows for channels without a concave surface showed that in the channel zR2 = const there is a stable vortex flow structure with the lowest viscous friction losses. The presence of a concave surface of sufficient size significantly reduces viscous friction losses and shear stresses in both the steady state and pulsed modes.

Contribution of viscous shear to friction in cold rolling of low-carbon steel

This work shows that for temperatures, pressures and shear rates that are common in cold rolling of low-carbon steel, viscous shear stress significantly contributes to the total friction force. Experiments were carried out to validate the theory on lubricant film formation and elasto-hydrodynamic lubrication, both with laboratory scale tribometers and a semi-industrial pilot mill facility. These experiments showed that at high shear rates, that are common in cold rolling, the lubricant does not behave as a Newtonian fluid anymore; moreover the viscosity at high pressure cannot accurately be described by a simple exponential law. With the correct relations implemented in a rolling model, both rolling force and forward slip are predicted with good accuracy for hydrodynamically lubricated cold rolling experiments.

Turbulence effect on total mechanical energy budget and energy loss of turbulent flows with different hydraulic regimes in open-channel transitions

ABSTRACT In this study, a modified form of the total mechanical energy budget equation is developed for 3-D turbulent flows with different hydraulic regimes in open-channel transitions, from which the effect of all turbulence parameters can be evaluated by applying some equalizations and RANS numerical simulations. The total energy equation is also used to extract an explicit relationship for energy loss based on turbulence parameters. The findings are presented in the form of the application of the relationship to calculate the energy loss based on simulation results for subcritical turbulent flow and hydraulic jump in open-channel transitions, which leads to identifying the effect of non-homogeneity and anisotropy of turbulence on flow energy balance. The results show that the work done by viscous shear stresses, the viscous diffusion of turbulence, and the turbulent diffusion have little to no effect on the total mechanical energy budget of open-channel turbulent flows; instead, the effect of the variations of turbulent kinetic energy and the work done by turbulence stresses is more significant. The benefit of using the modified energy equation is demonstrated by the potential for evaluating the details that were not previously considered.

An algorithm to couple smoothed particle hydrodynamics and finite element method for fluid–structure interaction problems

An algorithm for coupling the smoothed particle hydrodynamics (SPH) method and the finite element method (FEM) is proposed for fluid–structure interaction (FSI) problems. The SPH module solves the fluid motion, and the FEM module describes the deformation of structures. In the algorithm, a structure is considered as a solid boundary in the SPH module and dealt with using the dynamic boundary condition. Only three layers of SPH boundary particles are set to represent the structure surface, and the interaction forces between the SPH boundary and fluid particles, including the water pressure and the viscous shear stress, are quantified in a same way as the inter-fluid particle forces. Further, the computed forces on the SPH boundary particles exerted by the fluid are redistributed to the structure FEM nodes based on a well-defined projection scheme. In the FEM module, the deformation and motion of the structure under the exerted fluid forces are solved, and accordingly, the position and velocity of the SPH boundary particles are updated by interpolation from the new properties at the FEM nodes. The proposed SPH-FEM coupled model is validated in three FSI benchmarks. For the deformation of an elastic plate under hydrostatic water pressure, the relative difference between the computed and the analytical maximum vertical displacement at the plate midpoint is about 1.5%. For the deformation of an elastic gate subjected to a time-varying dam-break flow, the relative root mean squared errors in the computed vertical and horizontal displacement of the gate are, respectively, 5.5% and 2.2%. It is demonstrated that the proposed model performs well in simulating the deformation of structures under both hydrostatic water pressure and dynamic impacts of dam-break flows.

In Vitro Experimental Study on Hemodynamics of Transcatheter Aortic Valve Replacement

The patient-specific aortic silicone model was established based on CTA data. The digital particle image velocimetry (DPIV) test method in the modified ViVitro pulsatile flow system was used to investigate the aortic hemodynamic performance and flow field characteristics before and after transcatheter aortic valve replacement (TAVR). The results showed that the hemodynamic parameters were consistent with the clinical data, which verified the accuracy of the model. From the comparative study of preoperative and postoperative effective orifice area (0.33 cm2 and 1.78 cm2), mean pressure difference (58 mmHg and 9 mmHg), percentage of regurgitation (52% and 8%), peak flow velocity (4.60 m/s and 1.81 m/s) and flow field distribution (eccentric jet and uniform jet), the immediate efficacy after TAVR is good. From the perspective of viscous shear stress and Reynolds shear stress, the risk of hemolysis and thrombotic problems was low in preoperative and postoperative patient-specific models. This study provides a set of reliable DPIV testing methods for aortic flow field, and provides biomechanical basis for the immediate and long-term effectiveness of TAVR from the perspective of hemodynamics and flow field characteristics. It has important application value in clinical diagnosis, surgical treatment and long-term evaluation.

Effect of soluble surfactant on the interface dynamics of a rising droplet

In this study, we present numerical simulations examining the impact of soluble surfactant on the interface dynamics of a rising droplet. To achieve this, the droplet interface is tracked using an arbitrary Lagrangian–Eulerian approach, and the bulk and interfacial surfactant concentration evolution equations fully coupled with the incompressible Navier–Stokes equations are solved. We systematically evaluate the boundary of interfacial dynamics evolution by varying certain dimensionless parameters. Specifically, we study the effects of changes in parameters such as the Langmuir number, the Biot number, the Damkohler number, the bulk Peclet number, and the elastic number on interfacial tangential velocity, interfacial concentration and its gradient, interfacial viscous shear stress, and droplet rising velocity. Our findings confirm the validity of the stagnant-cap model for describing the interfacial fluidity of a surfactant-laden rising droplet. Increasing the Langmuir number and decreasing the Damkohler number can inhibit interface fluidity, but there is a threshold for the Damkohler number. Additionally, the overall increase in interface tension may mask the hindering effect of the locally increased concentration gradient on the interfacial fluidity. The Biot number has no impact on the steady state of the interface, but a slow adsorption rate may result in a bimodal retardation before the interface reaches a steady state. A clear threshold exists for the Peclet number to hinder the interface velocity, and a too high Peclet number leads to strong nonlinearity in the interface physical quantities. Variations in the elastic number significantly affect the evolution of the interface, causing the interface velocity to pass through several states, ranging from almost no retardation, uniform retardation, stagnant-cap retardation to complete retardation.

Transient behaviour of decelerating turbulent pipe flows

This investigation characterises the time response and the transient turbulence dynamics undergone by rapidly decelerating turbulent pipe flows. A series of direct numerical simulations of decelerating flows between two steady Reynolds numbers were conducted for this purpose. The statistical analyses reveal that rapidly decelerating turbulent flows undergo four coherent, unambiguous transitional stages: inertial (stage I), a dramatic change of sign in the viscous force associated with the decay of the viscous shear stress at the wall together with a mild turbulence decay in the viscous sublayer; friction recovery (stage II), a recovery in viscous force and progressive decay in the turbulent inertia at the near-wall region; turbulence decay (stage III), a balanced decay in both turbulent inertia and viscous force at the near-wall and overlap regions; core relaxation (stage IV), slow turbulence decay at the core region. The FIK identity derived by Fukagata, Iwamoto and Kasagi (Phys. Fluids, vol. 14, 2002, L73–L76) was used to understand further how the flow dynamics influence the time response of the skin friction coefficient ( $C_f$ ). The results show that although $C_f$ plateaus during the fourth stage, the turbulent contribution keeps decaying, undershoots and finally recovers to attain its final steady value. The time evolution of the azimuthal vorticity ( $\omega _\theta$ ) flux reveals that as the flow is decelerated, a layer of negative $\omega _\theta$ is produced at the wall during the flow excursion. As time progresses, this negative vorticity propagates in the wall-normal direction, attenuating the pre-existing vorticity and producing a decay in the turbulence levels.

Study on flow loss mechanism in a supercritical fluid radial inflow turbine nozzle

This paper uses ANSYS-CFX to simulate a 100kW supercritical CO2 radial inflow turbine. The internal vortex structure of the nozzle is identified based on Q-criterion and helicity. The internal flow loss of the nozzle is quantified based on Kock-Herwig’s theory of entropy production. Finally, the mechanism of internal loss formation in the nozzle is analyzed by combining the distribution law of entropy production. The analysis of the internal flow loss of the nozzle shows that the flow loss inside the supercritical CO2 radial inflow turbine nozzle is mainly caused by turbulent dissipation, and the turbulent pulsation induced by viscous shear stress plays a dominant role in this process.

Numerical Study of Dielectric Fluid Bubble Behavior in Microchannel Evaporator in Presence of Diverging Electric Field

Herein, the diverging dielectrophoretic (DEP) electrode is designed to extract the vapor bubbles generated in a flow-boiling evaporator. The DEP and hydrodynamic forces acting on the undeformable single vapor bubble in the diverging electrode are estimated by the uncoupled flow and electrostatic simulation. The Maxwell stress, static pressure, and viscous shear stress on the bubble surface are considered. The diverging DEP electrode successfully generates a net force that acts on the bubble in the flow direction. The DEP force is dominant against drag at a low imposed mass flux and high applied electric field, where heat transfer enhancement could be expected. A large DEP force pushing the bubble toward the electrode is found when the bubble is close to the electrode.