Secondary Motion Research Articles

CFD analysis of a ringless piston's secondary motion and the validity of Reynolds equation

CFD analysis of a ringless piston's secondary motion and the validity of Reynolds equation

Effect of straight riblets of the underlying surface on wall bounded flow drag

Direct numerical simulations of thin, straight riblets were conducted to investigate the physical mechanisms involved when the inertial effects within the ribs become important. The main parameter that we assess here is the ribs’ height to spacing ratio (a=h/s). In all cases, ‘k’-type behaviour was observed despite the absence of the pressure drag component. This trend also refers to the destruction of the near-wall cycles and was indicated by the shortening of Reynolds stress structures, mimicking the flows over rough walls. Closely-packed ribs with large h/s have a tendency to generate Kelvin–Helmholtz (KH) like structures at the tips, inducing large pressure fluctuations. Conversely, sparser ribs with low h/s trigger the formation of large mean secondary flows that suppress the pressure fluctuations. We further split the drag contribution of these distinct flow features by decomposing the roughness function into the dispersive and the Reynolds-stress terms. This analysis concludes that the fully-rough (logarithmic) scaling within the drag-increasing regime is transitional, and as the Reynolds number increases, deviates to a more gradual power-law scaling due to the drag increasing mechanism of streamwise aligned secondary motions.

Secondary motions and wall-attached structures in a turbulent flow over a random rough surface

Large-eddy simulations (LESs) are performed to explore the effects of roughness on the secondary motions (SMs) and wall-attached structures in a turbulent open-channel flow over a random rough surface at a friction Reynolds number of Reτ≈1000. Turbulent flow over two groups of rough walls – a homogeneous random arrangement and a clustered arrangement – is considered, and the results are compared with the turbulence over a smooth wall. The results show that the two roughness arrangements exhibit minor differences in the variation of mean streamwise velocity. The rough surfaces of a clustered arrangement can generate large-scale SMs, resulting in spanwise-alternating high-momentum pathways (HMPs) and low-momentum pathways (LMPs) in the time-averaged velocity. Because of SMs, the streamwise turbulence intensity is enhanced in the outer region and a larger-scale spectral peak occurs in the turbulence energy spectra. On the other hand, the outer-layer similarity is still satisfied for the homogeneous random arrangement. The wall-attached structures of streamwise velocity fluctuations in the presence of roughness are extracted through a three-dimensional clustering identification approach. The wall-attached structures retain their geometric self-similarity for both rough surfaces, whereas the length and width of these structures decreases and increases, respectively. The population density scales inversely with the height, reflecting the hierarchical nature of the structures. In addition, when the streamwise velocity fluctuations within the wall-attached structures are conditionally averaged, the profile exhibits logarithmic behavior in the logarithmic region for the homogeneous random arrangement; in the case of the clustered arrangement, the reconstructed profile is affected by the SMs. A new identification approach is applied to decompose the secondary flow structures into wall-detached structures, and the logarithmic behavior of the streamwise turbulence intensity is reconstructed on the basis of the new wall-attached structures. The present results provide evidence of the presence of the wall-attached structures in instantaneous flow fields of rough-wall turbulence, for both homogeneous and heterogeneous roughness arrangements.

Numerical investigation of flow and heat transfer of supercritical carbon dioxide in the vertical helically-coiled tube under half-side heating condition

ABSTRACT The supercritical boiler is one of the ways to enable sustainable energy development. Its revolution cannot be separated from the study of the characteristics of supercritical carbon dioxide in a spiral pipe. This research article provided an industrially compliant model of a water-cooled wall spiral pipe with one-side heating for heat transfer. The simulation was set for various parameters including P = 30.42 MPa, Tin = 578–643 K, q = 105–180 kW/m2, G = 1784–2348 kg/m2s. The article discussed in detail factors such as buoyancy and secondary flow for these cases. The results showed that in the range of high parameters, mass fluxes, heat fluxes, and inlet temperature all had a substantial influence on the temperature and velocity fields, with the mass flux showing a non-monotonic trend on the HTC and the heat flux having a more subtle influence on the HTC. The inhomogeneous heating pattern affected the buoyancy and secondary flow motion, changing the temperature field in the tube, and enhancing the velocity field at the bend and on the heating side. A new empirical correlation for supercritical CO2 with non-uniform heating was proposed.

Secondary Motion of Non-Spherical Particles in Gas Solid Flows

Objective of this study is to investigate the effect of secondary motion of particles in multiphase gas-solid flows parametrically and test the relative impacts of particle shape and orientation information on particle distribution. For that purpose, predictive accuracies of simplified drag coefficient models are assessed for the conditions relevant to a wood recovery plant operating at dilute flow regime. After demonstrating the strong impact of the shape and orientation information on the force balance for single particles, we compared the steady state Eulerian-Lagrangian simulation results for particle volume fractions, residence times and particle diameter distributions within the chamber for different (i) superficial gas velocities (5 m/s, 7.5 m/s), (ii) orientation tendencies and (iii) particle shapes. Transient simulations are performed until the system reaches steady state conditions by monitoring the mass flow rates of the particulate phases leaving the chamber. The secondary motion of non-spherical particles is represented by stochastic sampling from the available experimental data. Analysis of the force balance on single particles revealed log-scale variations if the orientation of the particles with respect to flow fluctuates. Variations in the single particle force balances are found to be still visible in the CFD analysis, where the secondary motion of particles drastically changed the particle distribution in the chamber. The native non-spherical model which only accounts for the shape correction was found to over-predict the entrainment, leading to a significantly different particle volume fraction and diameter distributions. Spherical particle assumption also caused significant errors in the particle distribution, which increases as aspect ratio of the cylindrical particle diverges from one. Results show that particle orientation statistics are extremely important to capture the particle mixing and segregation patterns at dilute regime, which cannot be captured with such simplifying assumptions.

Coated Piston Ring Pack and Cylinder Liner Elastodynamics in Correlation to Piston Subsystem Elastohydrodynamic: Through FEA Modelling

A finite element model is developed to assess the effects of the TiSiCN thin film coating of the piston ring on the structural strength of the piston subsystem. The complex, cyclically variable forces are considered in load and boundary conditions. The model included combustion dynamics, contact kinetics, piston subsystem primary and secondary motions, and lubricated contact conditions to evaluate the applied forces. A comparative analysis is performed for coated and uncoated cases. Four different crown geometries are tried for selecting the best case of crown design for coated piston subsystem components. The analysis predicts better strength in coated cases compared to uncoated ones. The type-A crown design develops less stress, while the compression ring suffers the most due to elastic deformation and is more prone to fatigue failure.

Penetrative convection in a bi‐disperse porous medium

The present paper investigates penetrative convection in a bi‐disperse porous medium. In particular, penetrative convection is modeled via a quadratic dependence on the temperature for the fluid density. For the problem under examination, convection can occur only through a secondary stationary motion since the validity of the principle of exchange of stabilities is proved. Via linear instability analysis of the conduction solution, the critical Rayleigh number for the onset of penetrative convection is determined. Moreover, the nonlinear stability is investigated via weighted energy method. In order to analyze the behavior of the stability and instability thresholds, numerical simulations are performed through Chebyshev‐ method, proving the stabilizing effect of the upper boundary layer temperature on the onset of convective motion.

Simulation Analysis and Experimental Verification of Tribodynamics of Reciprocating Friction Pairs in Low-Speed Marine Engines

The performance of reciprocating friction pairs in low-speed marine diesel engines has an important impact on the economy, stability, and safety of the ship operation, which deserves special attention. However, the available research is very limited. In this article, a new tribodynamics modeling method and an online measurement method for friction force are proposed. The friction force is simulated and verified by experiments. Based on the principle of multibody dynamics and mixed lubrication theory, a tribodynamic model coupling the reciprocating friction pairs (piston assembly–cylinder liner, piston rod–stuffing box, and crosshead slipper–guide) is first established. The friction force and dynamics are theoretically analyzed. Then a friction measurement method, which can measure the friction force of reciprocating friction pairs under engine firing conditions, is developed and used to verify the simulation. By comparison, it is found that the simulated friction is in good agreement with the experimental one. The results show that the crosshead slipper and piston assembly have obvious secondary motion, which will affect the vibration and noise of the engine. The friction force of the piston assembly is much higher than that of other reciprocating friction pairs. Improving the lubrication state near the top dead center of the piston assembly is of great significance to reduce the friction loss of the low-speed marine engines.

Intensification of Solid–Liquid Suspension Performance in an Elliptical Uncovered Unbaffled Stirred Tank

The combination of an elliptical uncovered unbaffled stirred tank with a rigid-flexible impeller is a creative effort to improve the performance of solid–liquid suspensions. In this work, we proposed a new mixer combining an elliptical uncovered unbaffled stirred tank (E-UUST) with a rigid-flexible impeller. The just suspended speed (Njs), just suspended power consumption (Pjs), local axial solid concentration, and the largest Lyapunov exponent (LLE) in the E-UUST and the circular uncovered unbaffled stirred tank (C-UUST) were compared under the conditions of equal liquid height and volume. In addition, development of a secondary vortex structure was discussed based on the secondary flow theory by visualization. The results demonstrate that Njs and Pjs, in the E-UUST system, can be reduced significantly by 17 and 37.4%, respectively. The degree of homogeneity of the solids can be effectively increased using the E-UUST. Moreover, the E-UUST with a rigid-flexible impeller can achieve more chaotic mixing and reach a state of just suspension at lower power consumption. Finally, secondary motions in the E-UUST were observed, which may be the reason solid suspension in the E-UUST is better than in the C-UUST. This study shows that the E-UUST can be effectively used to intensify solid–liquid suspension performance and help understand the chaotic mixing of solid–liquid two-phase flows in stirred tanks.

An improved passive tuned mass damper assisted by dual stiffness

A tuned mass damper (TMD) is one of the oldest and most commonly used passive control devices attached to structures to absorb lateral loads of energy from main systems. In the last decades, several novel tuned mass dampers have been designed to increase the performance of TMDs in decreasing the structural responses during excitation vibrations. Moreover, several formulations and numerical optimization methods have been developed to optimize the TMDs parameters. This paper proposes a novel passive tuned mass damper with dual stiffness (DSTMD). The DSTMD includes mass, primary and secondary springs, dashpot, and motion limiting chamber. The performance of DSTMDs depends on their properties such as mass, primary and secondary stiffness, damping coefficient, and the length of the motion limiting chamber. Thus, a metaheuristic optimization algorithm, called the Mouth Brooding Fish algorithm, was used to optimize the DSTMDs parameters. The effectiveness of the optimum DSTMD on two different linear ten-story structures under several earthquakes has been studied and compared with the effectiveness of classical optimum TMDs. According to the study, optimum DSTMDs generally show better effects for certain excitations, and as an average performance, they are superior compared to the classical optimum TMDs in reducing maximum displacement of the buildings. At last, structural yielding is considered, and the performance analysis on this structure shows that the DSTMD has a superior effect in reducing the maximum displacement and is among the best methods for the calculated absolute yielding amount.

Influence of thermal effect in piston skirt lubrication considering thermal deformation of piston and cylinder liner

With the development of high-strength marine diesel engines, piston skirt lubrication plays an increasingly important role. In this study, to ensure that the mixed lubrication can be applied, the contact of the PS corner and CL is simplified to a spring–damper system. A coupled dynamical–tribological numerical model of a piston skirt is proposed by combining mixed lubrication and the secondary motion of the piston. The model is then used to study how the thermal effect of the piston skirt-cylinder liner friction pair affects (i) the secondary motion of the piston, (ii) the contact force of the piston-skirt corner points, and (iii) the lubrication characteristics, while considering ring friction, friction moment of piston pin and three-dimensional thermal deformation of the piston and cylinder liner. The results show that the secondary motion under the thermal condition is less than that under the cold condition, and the reverse rotation of the piston under the thermal condition occurs earlier. Asperity contact and corner points contact appear under the thermal condition, and the friction mean effective pressure under the cold condition is 47.7% greater than that under the thermal condition. Overall, it is necessary to consider the thermal effect of the piston skirt-cylinder liner friction pair.

Three-Dimensional Performance Evaluation of Hemispherical Coriolis Vibratory Gyroscopes

In this paper, the oscillation patterns and characteristics of gyroscopic reaction to rotation-induced Coriolis force and phase relations are reviewed by examining the main principles of operation of Coriolis vibratory gyroscopes based on the dynamic relations and proposed improvements in performance using parameter changes. Coriolis vibratory gyroscopes (CVGs) are among the most modern applicable gyroscopes in position detection that have replaced traditional gyroscopes due to some great features of the design of vibrating proof mass and elastic suspension. Given the key characteristics of capacitive versus piezoelectric excitation technologies for determining the vibration type in sensors, their operating principles and equations have completely changed. Therefore, two-dimensional finite element analysis is required to evaluate their optimal performance. Since the sensor space is constantly vibrating, a general equation is presented in this paper to explain the impact of parameters on the frequency of different operating modes. The main purposes of building vibrating gyroscopes are replacing the constant spinning of the rotor with a vibrating structure and utilizing the Coriolis effect, based on which the secondary motion of the sensitive object is generated according to the external angular velocity.

Decay of secondary motion downstream bends in turbulent pipe flows

Decay of secondary motion downstream 180° pipe bends is investigated using large-eddy simulations for the bend radii of 1≤rB/dh≤3.375 at a Reynolds number of Reh=10 000. The velocity and turbulence characteristics are validated against experimental data for a straight pipe section as well as against experimental and direct numerical simulations data for a 90° pipe bend. As the bend radius decreases, a larger magnitude of turbulence intensity is induced immediately downstream of the bend, and for the largest magnitude, the highest gradient of the decay turbulence intensity is observed. As a result, the recovery length needed to reestablish the velocity profile downstream of the pipe bend decreases. Turbulence is transported at a higher rate, indicating that the recovery of the velocity profile is driven by turbulence transport. Secondary motions are induced by the curvature of the pipe bend, and as the bend radius decreases, the magnitude of the secondary motion increases. The results show how the secondary motion decay in magnitude as the flow moves downstream the pipe bend. At the outlet of the bend, secondary motions are dominating at the walls and within the bulk flow. As the fluid moves further downstream, the secondary flows dominate close to the walls, and at a length of x/dh=5, a negligible difference in secondary motion is observed for the different bend radii.

Effect of Radial Clearance on the Secondary Motion and Tribological Performance of Stirling Engine Piston-Crosshead

The cylinder radial clearance is a significant influencing factor for secondary motion and frictional power consumption of Stirling engine piston-crosshead structure. In this paper, a piston-crosshead dynamical model of the Stirling engine considering the surface tribological characteristics is established, and the correctness of the model is verified on the piston rod sealing test bench. The influence of the clearance on the dynamics and the tribology of the Stirling engine piston-crosshead is analysed based on this model, and it is shown that the crosshead knocking force and the frictional force reach equilibrium when the clearance is 0.06 mm.

Parametric Analysis of Gas Leakage in the Piston–Cylinder Clearance of Reciprocating Compressors

Gas leakage is one of the main sources of inefficiencies in low-capacity reciprocating compressors, undermining the compressor performance by reducing the mass flow rate and increasing the energy consumption. In reciprocating compressors, leakage in the piston–cylinder clearance is driven by the piston motion and pressure difference between the compression chamber and the internal environment of the shell. This paper reports a parametric numerical analysis of leakage in the piston–cylinder clearance of a low-capacity reciprocating compressor. A simulation model based on the Reynolds equation is applied throughout the compression cycle to assess the effect of the compressor operating conditions, clearance geometry, piston velocity and piston secondary motion on the leakage and compressor performance. A 3D CFD model is also developed to validate the Reynolds leakage model and to evaluate the effect of the piston secondary motion on leakage, assuming the piston is fixed with predetermined eccentricities. The results show that the compressibility effects are very relevant to estimate the gas leakage. The simulations also revealed that leakage is more detrimental to the compressor performance when it is operating in low back-pressure conditions. Additionally, the piston secondary motion can intensify the gas leakage in the piston–cylinder clearance by up to 90%. On the other hand, the piston velocity only plays a minor role in assessing the leakage.

Assessment of RANS turbulence model performance in tight lattice LWR fuel subchannels

Reynolds-averaged Navier–Stokes simulations have been performed of the turbulent flow (Re=48000) through a tight lattice (P/D=1.194) subchannel typical of those found in nuclear thermal–hydraulic applications. A wide range of turbulence models (linear eddy-viscosity, non-linear eddy-viscosity and stress-transport) and the use of different near-wall treatments, including low-Re models, standard wall-functions and the more advanced analytical wall-function, have been considered. Results indicate that only those models capable of reproducing some degree of stress anisotropy are able to correctly predict the presence of secondary motion and only the low-Re near-wall treatment was able to reproduce the correct qualitative behaviour of the wall shear stress along the rod surface, in agreement with experimental results by Hooper (1980). They also demonstrate both the failure of the standard wall-function approach in reproducing flows with significant near-wall convection and pressure-gradient effects, and the limitations of using linear eddy-viscosity approaches in flows with even moderate anisotropic effects. Although models utilizing a low-Re near-wall approach demonstrated superior overall performance, the analytical wall-function tested offers improvements over the standard ‘log-law’ based formulation.

Primary atomization of liquid jets: Identification and investigation of droplets at the instant of their formation using direct numerical simulation

A detailed investigation of droplet characteristics for the primary atomization of a round liquid jet injected into stagnant gas is performed using direct numerical simulation. The material properties correspond to a Diesel injection, and the numerical framework is based on the volume-of-fluid method. The study is carried out in the statistically steady state, which allows to collect time-averaged droplet formation statistics. A novel algorithm continuously detects droplets at the instant they detach from the liquid core jet, which are referred to as primary droplets. The main droplet characteristics, such as volume, velocity and sphericity, are captured for newly formed primary droplets as well as all other droplets in the domain. This allows a detailed comparison between droplet characteristics during and after their formation. In addition, the droplet Weber, Reynolds and Stokes numbers are computed. These dimensionless numbers govern important physical processes occurring subsequent to the droplet formation, such as potential secondary breakup and droplet motion. One central goal is to provide information relevant for large eddy simulation of sprays in the Eulerian–Lagrangian framework, where the formation of small droplets from the liquid core jet cannot be resolved, and therefore potentially needs to be modeled. Moreover, the relative importance of primary and secondary atomization is estimated for this specific setup. It is found that the distribution of the droplet sizes is very similar for primary droplets and the entire droplet collective. Furthermore, the droplet Weber numbers are significantly below the critical Weber number required for secondary droplet breakup. Together, these two observations indicate that, for the investigated configuration, primary atomization is the dominating process, while secondary atomization only plays a minor role. Moreover, the high droplet volume fraction observed shows that droplet–droplet collisions and coalescence can be expected to influence the spray behavior. To put the obtained results into perspective, empirical correlations for the Sauter Mean Diameter are used to discuss potential trends for higher Reynolds and Weber numbers.

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent riblets

Direct numerical simulations of a turbulent channel flow developing over convergent–divergent (C–D) riblets at a Reynolds number of Reb=2800 are presented. It is found that, with a fixed normalized riblet height of h+=5, as the ratio of the riblet spacing and the height, s/h, increases from 2 to 10, the strength of the large-scale secondary flow motion Γ generated by the C–D riblets peaks around s/h=4 when the C–D riblets behavior lies between d- and k-type roughness. Compared to the baseline case with smooth walls, the turbulent activities and energy level increase significantly and peak at s/h=4 when Γ is the highest. It is shown that while the intense local turbulent kinetic energy (TKE) production occurring in the diverging region is caused by the high local velocity gradient due to the downwelling of the secondary flow, the strong local TKE production occurring in the converging region is caused by the high turbulent shear stress associated with upwelling. Furthermore, the TKE transport characteristics are significantly altered by the secondary flow motion, especially over the converging and diverging regions. The secondary flow is not caused by the local imbalance between turbulent kinetic energy production and dissipation but by the yawed riblets. It is then more appropriate to classify this flow as a Prandtl’s secondary flow of the first kind, also known as the geometry-driven secondary flow. Finally, in comparison with the baseline case, the drag increases for all the riblet cases examined, and a direct correlation between the amount of drag and intensity of the secondary flow exists, both peaking at s/h=4.

Analysis of circulating tumour cells separation in a curved microchannel under a high gravitational field

Cancer cells can detach from their original place and travel through tiny blood vessels or lymphatic capillaries in nearby tissues, forming a new tumour in other places of the body. While these circulating tumour cells (CTCs) are usually few in relation to the native blood cells, they provide crucial information about the characteristics of the primary tumour. Therefore, detecting and separating such cells from the bloodstream is an essential step in terms of diagnosis, treatment and prognosis of cancer patients. Perhaps, one of the well-known methods of separating CTCs is inertial focusing using a curved microchannel. This approach leaves CTCs separation strongly dependant on the channel design and Reynolds number for a given sample’s properties. Thus, the design suitable for a certain sample does not necessarily suit others. Here, a novel micro-analytical device is proposed and analysed. The device is based on using a spiral microchannel spinning around its axis at low rotation speed. The rotation generates Corilois secondary motions, focusing the separation of CTCs. The strength and structure of these Corilois motions can be adjusted easily by changing the rotation rate, which is under external control. This opens up the possibility of handling samples with different properties, achieving both higher throughput and complete separation of CTCs. The present work demonstrates the separation of human breast cancer cells using this approach over a wide range of volume flow rates (100–1000 ml/h) at different rotation rates (0–200 rpm), operating at relatively moderate Reynolds number. A model is developed, giving a quantitative prediction of flow and cells separation. It is shown that, for a single design, the cancer cells can be sorted completely with 100 % purity over a wide range of flow rates (400–700 ml/h) with a small adjustment of the rotation rate.

The effect of spanwise heterogeneous surfaces on mixed convection in turbulent channels

Turbulent mixed convection in channel flows with heterogeneous surfaces is studied using direct numerical simulations. The relative importance of buoyancy and shear effects, characterised by the bulk Richardson number $Ri_b$ , is varied in order to cover the flow regimes of forced, mixed and natural convection, which are associated with different large-scale flow organisations. The heterogeneous surface consists of streamwise-aligned ridges, which are known to induce secondary motion in the case of forced convection. The large-scale streamwise rolls emerging under smooth-wall mixed convection conditions are significantly affected by the heterogeneous surfaces and their appearance is considerably reduced for dense ridge spacings. It is found that the formation of these rolls requires larger buoyancy forces than over smooth walls due to the additional drag induced by the ridges. Therefore, the transition from forced convection structures to rolls is delayed towards larger $Ri_b$ for spanwise heterogeneous surfaces. The influence of the heterogeneous surface on the flow organisation of mixed convection is particularly pronounced in the roll-to-cell transition range, where ridges favour the transition to convective cells at significantly lower $Ri_b$ . In addition, the convective cells are observed to align perpendicular to the ridges with decreasing ridge spacing. We attribute this reorganisation to the fact that flow parallel to the ridges experience less drag than flow across the ridges, which is energetically more beneficial. Furthermore, we find that streamwise rolls exhibit a very slow dynamics for $Ri_b=1$ and $Ri_b=3.2$ when the ridge spacing is of the order of the rolls’ width. For these cases the up- and downdrafts of the rolls move slowly across the entire channel instead of being fixed in space, as observed for the smooth-wall cases.