Flow Separation Point Research Articles

Shock Wave and Aeroelastic Coupling in Overexpanded Nozzle

The growing demand for increasing the engine power of a liquid rocket is driving the development of high-power De-Laval nozzles, which is primarily achieved by increasing the expansion ratio. A high-expansion-ratio for De-Laval nozzles can cause flow separation, resulting in unsteady, asymmetric forces that can limit nozzle life. To enhance nozzle performance, various separation control methods have been proposed, but no methods have been fully implemented thus far due to the uncertainties associated with simulating flow phenomena. A numerical study of a high-area-ratio rocket engine is performed to analyze the aeroelastic performance of its structure under flow separation conditions. Based on numerical methodology, the flow inside a rocket nozzle (the VOLVO S1) is analyzed, and different separation patterns are comprehensively discussed, including both free shock separation (FSS) and restricted shock separation (RSS). Since the location of the flow separation point strongly depends on the turbulence model, both the single transport equation and two-transport-equation turbulence models are simulated, and the findings are compared with the experimental results. Therefore, the Spalart–Allmaras (SA) turbulence model is the ideal choice for this rocket nozzle geometry. A wavelet is used to analyze the amplitude frequencies from 0 to 100 Hz under various pressure fluctuation conditions. Based on a clear understanding of the flow field, an aeroelastic coupling method is carried out with loosely coupled computational fluid dynamics (CFD)/computational structural dynamics (CSD). Some insights into the aeroelasticity of the nozzle under separated flow conditions are obtained. The simulation results show the significant impact of the structural response on the inherent pressure pulsation characteristics resulting from flow separation.

CFD investigation of supersonic two parallel expansions nozzles

This paper aims to validate the design contours and result parameters of the newly developed Dual Expansion Nozzle (DEN) using the Fastran software when it enters the non-adaptation regime with the increase in altitude and variation of the Nozzle Pressure Ratio (NPR). DEN design and Computational Fluid Dynamic (CFD) application utilize the High Temperature (HT) model defined by a calorically imperfect and thermally perfect gas, providing good accuracy compared to PG model. The computational domain is decomposed into subdivisions of structured grids using the algebraic grid generator software CFD-GEOM. The mesh convergence was analyzed using three mesh resolutions: coarse, medium, and fine. A comparison was made between the two conventional nozzles, MLN and the newly developed BPN, as both are currently used in aerospace propulsion to enhance aerodynamic performance. If a rocket engine operates under strongly over-expanded conditions with ambient pressure considerably higher than the nozzle exit pressure, and by increasing NPR value, the flow separates from the wall and can lead to high side loads. These loads are reduced in DEN. The flow separation point is observed close to the exit section for the DEN in comparison with Minimum Length Nozzle (MLN) and Best Performance Nozzle (BPN) for the same NPR, resulting in low flow separation and low side load effects for DEN. This result demonstrates a small loss in the exit Mach number, leading to less loss in the thrust coefficient and a small effect of boundary layer friction for DEN. Enhanced over-expanded aerodynamics is observed in DEN compared to MLN and BPN. The application is made for air with an exit Mach number equal to 3.00.

Investigation on the oblique water entry of the flared cavity

An experimental study of the oblique water entry of a flared cavity is reported in this paper. A numerical model is established that takes gas compressibility into account. This model effectively captures the additional flow phenomena that occur due to gas expansion and contraction within the cavity. There is a significant fluctuation phenomenon during the oblique water entry of the flared cavity, which is reflected not only in the movement of the water entry bubble but also in the slamming pressure. This fluctuation phenomenon is caused by the bottom cavity of the flared cavity, which adds the additional processes of external fluid inflow and internal fluid outflow compared with the closed-bottom structure, leading to additional flow due to conventional flow separation. When the external liquid flows into the cavity, the additional flow reduces the velocity potential of the fluid near the flow separation point, causing the bubble diameter near the flow separation point to contract. At the same time, the external liquid inflow causes the gas in the cavity to compress and the slamming pressure to increase. When the liquid flows out of the cavity, the additional flow increases the velocity potential of the fluid near the flow separation point, causing the bubble diameter near the flow separation point to expand. Meanwhile, the internal fluid outflow causes the gas in the cavity to expand and the slamming pressure to decrease.

Aerodynamic shape optimization using a physics-informed hot-start method combined with modified metric-based proper orthogonal decomposition

Aerodynamic shape optimization based on computational fluid dynamics still has a huge demand for improvement in the optimization effect and efficiency when optimizing the unstable flow of airfoils. This article presents a physics-informed hot-start method combined with modified metric-based proper orthogonal decomposition (MPOD-ML-Phys). The data-based filtering strategy is a core step in the original metric-based proper orthogonal decomposition method (MPOD), but existing filtering strategies generate a significant amount of additional computational consumption. Therefore, this article applies machine learning methods to data-based filtering strategy in MPOD and establishes a modified MPOD method (MPOD-ML). In addition, during the MPOD-ML process, a lot of hidden physical knowledge that is beneficial for optimization will also be generated. This article combines Bayesian optimization to construct an MPOD-ML-Phys method, which fully utilizes the flow physical knowledge in MPOD-ML. The efficiency and effect of MPOD-ML and MPOD-ML-Phys are validated by two typical cases: inverse and direct design for airfoils. The results indicate that both MPOD-ML and MPOD-ML-Phys methods can effectively improve the overall optimization efficiency. However, the intervention of machine learning models has significantly reduced the robustness of the MPOD-ML method, while the embedding of physical knowledge makes MPOD-ML-Phys more robust. Meanwhile, the optimized airfoil obtained by MPOD-ML-Phys has better drag divergence characteristics, a later flow separation point, and better flow stability.

Effect of synthetic jets actuator parameters on deep reinforcement learning-based flow control performance in a square cylinder

We conduct an active flow control study on the mass flow rate of synthetic jets on the upper and lower surfaces of a square cylinder using a deep reinforcement learning algorithm, with a focus on investigating the influence of the position and width of the synthetic jets on the flow control performance. At Reynolds numbers (Re) of 100 and 500, it is found that our proposed method significantly reduced the lift and drag coefficients of the square cylinder and completely suppressed vortex shedding in the wake. In particular, at Re = 100, placing the synthetic jets near the tail corner was beneficial for reducing drag, with a maximum drag reduction rate of 14.4%. When Re = 500, positioning the synthetic jets near the leading edge corner resulted in a maximum optimal drag reduction effect of 65.5%. This indicates that locating the synthetic jet at the main flow separation point can achieve optimal control. Furthermore, we notice that when the synthetic jets are positioned near the tail corner, vortex shedding can be completely suppressed. Additionally, a narrower width of the synthetic jets can enhance flow instability and increase the cost of flow control.

Comparison of Pressure-based and Skin Friction-based Methods for the Determination of Flow Separation of a Circular Cylinder with Roundness Imperfection

Introduction: A delayed detached eddy simulation in Open FOAM was performed to study flow separation of a circular cylinder with roundness imperfection up to 4% of its diameter at Reynolds numbers of 100, 3900, and 104 in normal flow. Methods: The flow was considered to be Newtonian and incompressible. The separation position was determined independently based on surface pressure distribution and skin friction. Results: Results show that the patterns of these distributions depend on both Reynolds number and roundness imperfection level, and flow separation in an imperfectly round cylinder may be induced by either an adverse pressure gradient or a Gentle Bend (GB) introduced by the roughness. For the separation point determined by the pressure-based method, its accuracy can be affected by the characteristic of pressure distribution near the separation point at low Reynolds numbers, and, thus, its physical validity needs to be verified by flow visualization at high Reynolds numbers. Conclusion: The skin friction-based method can accurately predict separation point for both perfectly and imperfectly round cylinders without additional information. When the roundness imperfection ratio reaches 2% and the Reynolds number reaches 3900, both approaches indicate that the flow separation point converges to the location of GB on the cylinder surface and the two sets of predicted separation points agree well.

Buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model

The aim of this study is to explore the buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model. The study includes the influence of turbulence integral length scale and wind yaw angle on the magnitude of buffeting force, spatial distribution of buffeting force, and buffeting displacement response. Under larger turbulence integral length scale, the buffeting force of the box beam and it’s spanwise correlation are larger, which verifies the three-dimensional effect of the buffeting force. It is worth mentioning that, unlike traditional section models, there are differences in the pressure values of the pressure strips in the aeroelastic model at the flow separation point, which may be influenced by the cables. The experimental results of different wind yaw angles show that there is little difference in the buffeting force of the box beam section under the condition of 0°∼15° wind yaw angle, indicating that the maximum buffeting response will occur in the range of 0°∼15° wind yaw angle, which is consistent with the displacement results measured by the aeroelastic model. In addition, by fixing the model with a steel wire, the static and vibration states of the model were achieved. However, due to the high stiffness of the model, it can only generate small buffeting displacement, and the self-excited force component can be almost ignored. There is no significant difference in the results between the static and vibration states.

An improved B-L model for dynamic stall prediction of rough-surface airfoils

The Beddoes-Leishman (B-L) semi-empirical model is a classical method for predicting the dynamic stall of wind turbine airfoils. However, the model performs poorly for rough-surface airfoils due to the premature entry of turbulence and stall condition under the roughness effect. In this study, an improved dynamic stall model is developed for rough-surface airfoils. Two corrections are involved in the modifications. First, the calculation of flow separation points is corrected considering the difference between the normal and tangential separation points, and then an attenuation coefficient is introduced for the effective angle of attack to account for the rough-surface effect. Subsequently, the proposed model is extensively verified by experimental data of S-series airfoils with rough surfaces. Results show that the proposed model can well predict the dynamic stall characteristics of rough-surface airfoils with a higher accuracy than that of the original B-L model under various mean angle of attacks, oscillating amplitudes and reduced frequencies. At last, the model is utilized to predict the operating loads of a wind turbine using the Blade-Element Momentum theory. Significant difference between the dynamic loads predicted by smooth and rough models is observed. This indicates that the roughness effect on the dynamic stall model as well as the prediction of the operating loads on wind turbines cannot be ignored.

Numerical study on the cavitation instability from the perspectives of pressure change and hydrodynamics evolution in the cavitating flow over a hydrofoil

The objective of this study is to investigate cavitation instability by analyzing the pressure change and hydrodynamics evolution in the cavitating flow over a hydrofoil. Two-dimensional (2D) simulation results indicate that the multi-peak pressure features are influenced by the position on the hydrofoil surface. The increased cavitation number in a certain range aggravates the oscillation of partial cavitation and promotes the cavity change, then leads to the occurrence of higher peak pressure and more complicated fluctuation frequency. The lift coefficient presents a near-linear increasing trend due to the extended low-pressure area on the suction surface and the suppression on the vortex generation in the stable development stage of sheet cavity. The interaction between the vortex with different directions on the trailing edge dominates the fluctuation of lift coefficient. The differences in three-dimensional (3D) cavitating flows with constant velocity inlet and sinusoidal velocity inlet are the flow separation point distribution and vortex changes. More separation points form in the downstream of the hydrofoil due to more cloud cavity reattachment behaviours for sinusoidal velocity inlet. Furthermore, the sinusoidal velocity inlet promotes a more violent cavity detachment and the large-scale vortex formation, which enhances the fluctuations of pressure change, lift and drag coefficient.

Wake of two tandem square cylinders

The wake of two tandem square cylinders of identical width (d) is experimentally studied, with a view to understanding the dependence of the flow structure, aerodynamics forces and Strouhal number on the centre-to-centre spacing ratio L/d and Reynolds number Re, where L is the distance between the cylinder centres. Extensive measurements are carried out, using hot-wire, particle imaging velocimetry, laser-induced fluorescence flow visualization, surface-oil-flow visualization and surface pressure scanning techniques, for L/d = 1.0 ~ 5.0 and Re ≡ U∞d/ν = 2.8 × (103 ~ 104), where U∞ is the free-stream velocity and ν is the kinematic viscosity of the fluid. The flow is classified into four regimes, i.e. the extended-body (L/d ≤ 1.5–2.0), reattachment (1.5–2.0 < L/d < 2.7–3.2), co-shedding (L/d ≥ 3.0–3.4) and transition (2.7 ≤ L/d ≤ 3.3) where both reattachment and co-shedding phenomena may take place. The mean drag and fluctuating drag and lift exhibit distinct features for different flow regimes, which is fully consistent with the proposed flow classification. Comparison is made between this flow and the wake of two tandem circular cylinders, which provides valuable insight into the profound effect of the flow separation point and the presence of sharp corners on the flow development and classification.

An Investigation on the Steady and Unsteady Wake Flow Regimes and Aerodynamic Characteristics of the Trapezoidal Cylinders Using Immersed Boundary-Lattice Boltzmann Method

Abstract In this study, the flow physics of the forward-facing (FF) and backward-facing (BF) trapezoidal cylinders (TC) subjected to two-dimensional, incompressible, and laminar flow is investigated using an in-house developed flexible forcing immersed boundary-lattice Boltzmann solver. The Reynolds number (Re) is defined based on the cylinder's characteristic length D. For the steady and unsteady flow regimes, Re is varied in the ranges of 10–40 and 75–125, respectively. The TCs shape is varied by modifying its nondimensional axial H/D and transverse Y/D length scales, between 0.5 to 2 and 0 to 1, respectively. Here, TCs horizontal central axis is always aligned along the incoming flow direction. It is observed that the flow separation points on the FF-TC and BF-TC are strongly influenced by the geometric (H/D and Y/D) and flow parameters (Re). Based on the boundary layer separation point, we have categorized the wake flow regimes behind the FF-TC and BF-TC into four types. In addition, the effect of the geometric and flow parameters on the drag coefficient (Cd), vortex shedding frequency, and steady and unsteady wake characteristics are thoroughly investigated here. Furthermore, by performing nonlinear regression analysis, we have proposed a set of correlation equations for the Cd and Strouhal number (St), using which the aerodynamic characteristics of differently shaped TC can be derived in the considered Re range without performing rigorous numerical simulations or experiments.

Study on Aerodynamic Drag Reduction by Plasma Jets for 600 km/h Vacuum Tube Train Sets

In order to break through the speed bottleneck, researchers envision using tubes to cover high-speed maglev trains and extract some of the air inside the tubes, creating a low-density environment on the ground, greatly reducing the aerodynamic drag of the trains, and in a relatively economical and feasible way, making high subsonic (600 km/h and above) and even supersonic ground transportation possible. The faster the running speed of high-speed trains, the greater the impact of aerodynamic drag on their energy consumption. Studying the aerodynamic characteristics of trains with a speed of 600 km/h can help optimize the aerodynamic shape of the train, reduce aerodynamic drag, and reduce energy consumption. This has positive implications for improving train energy efficiency, reducing energy consumption, and environmental impact. This paper adopts the numerical simulation method to study the drag reduction effect of the plasma arrangement and different excitation speeds on the train set in four positions when the incoming wind speed is 600 km/h, to analyze the mechanism of drag reduction, and then to analyze the combination of working conditions in order to investigate the drag reduction effect of plasma on the vacuum tube train set with an ambient pressure of 10,000 Pa. The findings demonstrate that the plasma induces the directional flow of the gas close to the wall to move the flow separation point backward and delay the separation of the flow, thereby reducing the front and rear differential pressure drag of the train set and lowering the aerodynamic drag coefficient of the entire train. The plasma arrangement is located at the rear of the flow separation point and in close proximity to the flow separation point. The pneumatic drag reduction effect peaks when the excitation speed reaches 0.2 times the train speed and the pneumatic drag reduction ratio is around 0.88%; the pneumatic drag reduction ratio of the rear car peaks when the excitation speed reaches 0.25 times the train speed and the pneumatic drag reduction ratio is 1.62%. The SDBD (Surface Dielectric Barrier Discharge) device is installed at the flow separation point around the nose tip of the rear car.

Towards the integration of distributed renewables: Operation analysis of pumped storage system under off-design condition based on CFD

Pumped storage plants are increasingly developing to cope with the rapid growth of renewable energy production. Micro-pumped storage (MPS) system is a new storage strategy for distributed energy integration. Centrifugal pump or axial pump replaces conventional pump turbines in this pumped storage system to ensure economic convenience and system flexibility. However, when MPS works in the generating operation mode, the limited high-efficiency range will result in complex hydrodynamic behavior and stability issues under off-design conditions due to renewable integration. At present, the instability mechanism of MPS under off-design conditions is not clear enough, and there is a lack of excellent research methods to analyze this problem. Therefore, this paper firstly introduces the entropy production theory considering the wall effect for visualizing the energy loss. Then the relationship between hydraulic performance and unsteady flow characteristics is established based on the loss characteristics. The results show that the entropy production theory with customized wall functions has higher accuracy and advantages in energy loss analysis compared to the default wall functions. Under partial loading conditions, the spatial-temporal instability of the flow separation point causes a rotating stall within the impeller, which in turn leads to destabilization and a significant reduction in hydraulic performance. Under overload conditions, despite slight changes in hydraulic performance, the most significant pressure fluctuation is six times stronger than the best efficiency point.

The influence of the lobed ejector on the horizontal axial tidal turbine and flow characteristic analysis

The power coefficient of the horizontal axis tidal turbine (HATT) is limited to 0.593 by the Betz limitation, however, the turbine's efficiency can be improved by incorporating a diffuser or lobe ejector. In this study. In this paper, water tunnel experiments were conducted to obtain the power and thrust coefficients of the original turbine and the turbine with a lobe ejector at different tip speed ratios (TSR). The accuracy of the numerical simulation was then verified by comparing it with the experimental results. The results reveal that the power coefficient of the turbine with a lobe ejector is up to 623% higher than that of the original turbine; however, it also leads to a negative thrust coefficient higher than the original turbine by 94.64%. To determine the optimal position of the lobe ejector, a numerical simulation of the turbine with a diffuser, which consists of a single inner lobe channel, was conducted under the same conditions. The findings demonstrate that the power coefficient of the diffuser is 123% higher than that of the original turbine, and the negative thrust is higher at 26.64%, significantly less than that of the lobe ejector. This indicates that the effect of the lobe ejector largely depends on the ejector effect of the outflow channel. Subsequently, to investigate the ejection effect of the lobe ejector, various aspects, including the vortex structure of the flow field, pressure coefficient of the blade section, velocity vector field of the rotor's center plane, and wake velocity curve, were analyzed. Moreover, the changes in the position of flow separation points along different sections of the blade from the blade root to the blade tip, the variation of the spiral structure of the blade root vortex, the evolution of the velocity vector field in the low-velocity region of the turbine's wake flow field and the alteration of the velocity curve of the wake flow field were further examined.

Dual solutions of aqueous Ti-alloy & MWCNT hybrid nanofluid: A stability test

The flow and heat transfer induced by an exponentially shrinking sheet with Ti-alloy & MWCNT hybrid nanofluid are investigated in this paper. Additionally, this investigation focuses on the flow separation of hybrid nanofluid with an inclined magnetic field, thermal buoyancy force, and Joule heating effect. The Tiwari and Das model is used to formulate the hybrid nanofluid mathematical model. Suitable similarity transformations convert partial differential equations (PDEs) into a system of ordinary differential equations (ODEs). The resultant system is numerically solved by implementing the shooting approach along with the RK-4 technique. Multiple solutions are found for this current problem, and intriguingly, the velocity and temperature profiles of these two solution branches exhibit opposing characteristics. In conclusion, conducting a stability study on these two alternative solutions is worthwhile to determine which solution is more realistic and stable. The temporal stability test reveals that only the first solution is stable or physically valid. The important outcomes of this study, based on the stable solutions, are as follows: (i) velocity (temperature) is found to be higher (lower) when thermal buoyancy is absent and it is found to be lower (higher) for opposing thermal buoyancy; (ii) the skin friction coefficient and rate of heat transfer are found to be better for aiding thermal buoyancy and lower for opposing thermal buoyancy; and (iii) the thickness of momentum and thermal boundary layers is thinner for the first solution than the second solution. Furthermore, in this work, the flow patterns (streamlines) are investigated. The flow separation point is finally located. This current study revealed strong consistency with previous research. These types of studies are very useful in the areas of medical and aerodynamic science.

Effects of horizontal-to-vertical stiffness ratio on the vibration characteristics of a two-mass vocal fold model

In order to evaluate the effects of stiffness ratio of vocal fold on three-dimensional behavior of vocal fold vibration, numerical simulations were performed by using a two-mass vocal fold model with different stiffness ratio of the horizontal and vertical direction. A ratio of the spring constants for the same direction were fixed, while it for the orthogonal directions was changed. To simulate the airflow through the glottis, the one-dimensional Bernoulli’s equation was solved with an equivalent circuit for the compressible flow propagation. The vocal fold shape was represented by a smooth shape with cylindrical masses and tangential faces. The flow separation point was estimated using the boundary layer theory. The results showed that overall fundamental frequency of the vocal folds increased with increasing horizontal stiffness, whereas the vertical stiffness changes had few effects on it. We also found that there were topical conditions in which fundamental frequency rapidly changed with a few changes in stiffness ratio. The stiffness ratio at that time was from 0.80 to 1.08. Before and after the change, there was difference whether the motion trajectory of mass was circular or linear. These results indicate that the vertical stiffness largely affects the oscillation modes of vocal folds.

A novel wake flow control method for drag reduction of a high-speed train with vortex generators installing on streamlined tail nose

The head/tail of a high-speed train has been designed in a streamlined way to achieve good aerodynamic performance, which leads to the flow separation point moving close to the tail nose tip. Therefore, the conventional way with some add-ons, i.e., the passive flow control, to suppress the flow separation in advance is not a good choice for this train wake flow improvement. Also, with the increase of the train speed, it is urgent to study new methods for the aerodynamic drag reduction of the train. The wake of the high-speed train is characterized by a pair of counter-rotating vortices, contributing to low surface pressure on the streamlined tail and posing a risk to the train operation. Thus, lowering the intensity of counter-rotating vortices and enhancing the surface pressure become a significantly potential drag reduction method. In the current study, a novel wake flow control method, named the vortex intensity reduction theory (VIRT), for the drag reduction of a high-speed train with vortex generators installing on the streamlined tail nose, was proposed to generate a pair of vortices with opposite rotating directions, expecting to weaken the wake vortices and have a higher-pressure distribution on the tail, as compared to the base case. The results show that with the installation of vortex generators (VGs), the train wake flow intensity is suppressed, and the influence region is reduced, resulting in the better train wake flow structures, as compared to the train without VGs. The VGs have significant impact on the aerodynamic performance of the tail car, while this effect is not evidently observed on the head and middle cars. The VGs contribute to the surface pressure increase on the streamlined tail, resulting into a reduction of pressure difference between the head and tail cars. As a result, a reduction of 5.11% in the aerodynamic drag and a reduction of 14.93% in the aerodynamic lift of the tail car are obtained, while for a three-car grouping train model, the reductions are about 2.23% and 72.66%, respectively. Therefore, the VIRT based on VGs proposed in this paper can effectively reduce the aerodynamic force of the tail car and alleviate the intensity of wake flow of the high-speed train, which will provide a newly potential drag reduction method of the next generation high-speed train.

Flow reversal for hybrid nanofluid with heat generation and slip effect in Darcy porous medium: The stability analysis

This investigation focuses on the flow reversal and separation of hybrid nanofluid, with heat generation and first-order velocity slip, in a Darcy porous medium. The Choi–Eastman nanofluid model is used to formulate the hybrid nanofluid mathematical model. Suitable similarity transformations convert partial differential equations into a system of ordinary differential equations. The resultant systems are numerically solved by implementing the shooting approach. Multiple solutions are found for this current problem, and intriguingly, the velocity and temperature profiles of these two solution branches exhibit opposing characteristics. In conclusion, conducting a stability study on these two alternative solutions is worthwhile to determine which solution is more realistic and stable. The temporal stability test reveals that only the first solution is stable or physically valid. The important outcomes of this study, based on the stable solutions, are as follows: (i) the hybrid nanofluid’s Nusselt number, skin friction, and velocity rise when the inclined magnetic parameter rises, (ii) the value of the smallest eigenvalue increases with higher values of the inclined magnetic parameter, and (iii) the thickness of momentum and thermal boundary layers is thinner for the first solution than the second solution. Additionally, the identification of flow separation and reversal points is valuable for aerospace technology, following the Prandtl theory. Finally, this study provides streamlined patterns to enhance the understanding of fluid flow behavior.

Flow-induced vibration of an elliptic cylinder with a splitter-plate attachment at low-Reynolds number: Self-limited oscillations

Flow-induced vibrations (FIV) of a rigid, elastically-mounted elliptical cylinder-plate assembly which is free to move in the cross-flow (transverse) direction is studied using numerical simulations. These simulations were conducted for a laminar flow at a Reynolds number of Re=100 over a reduced velocity range of Ur= 2–30, with a low mass ratio (m∗=10) and zero structural damping, for various values of the aspect ratio AR of the elliptical cylinder; namely, AR= 0.5, 0.67, 0.75, 1, 1.5 and 2. It is shown that the characteristics of the FIV response of an elliptical cylinder-plate assembly that occurs over a limited velocity range (viz., self-limited FIV) such as the vibration amplitude, the reduced-velocity range with vibrations, the nature of the branching behaviour (e.g., synchronization and non-synchronization branches in the amplitude response), and the vortex-shedding (wake) modes are strongly dependent on the aspect ratio. The self-limited FIV response of the assembly is enhanced for AR increasing from 0.75 to 1.5. However, it is found that for AR=2, the reduced-velocity range over which the FIV response occurs is significantly shortened owing to the absence of a non-synchronization branch in the amplitude response for this case. There is a critical value (AR)cri of the aspect ratio below which oscillations in an elliptical cylinder-plate assembly cannot be induced. This critical value occurs in the range 0.67<(AR)cri<0.75 for an assembly in a laminar flow at Re=100 for a fixed splitter-plate length LSP/D=0.5 (D is the equivalent diameter of the ellipsoidal cylinder). A careful analysis shows that there is close relationship between the presence of structural oscillations in the assembly and the location of flow separation points on the windward surface of the elliptical cylinder.

Theoretical and numerical investigation of the carreau fluid model during a non-isothermal roll coating process: A comparative study

BackgroundThe roll-coating process plays an important role in many industries for its practical applications, such as paint, PVC-coated fabrics and plastic industries. Roll coating is commonly used to put thin coating films over continuous substrates such as foils and papers. There are several roll-to-roll coating methods, including forward and roll over web. However, the reverse roll coating study of the non-Newtonian fluid model is presented in this paper. The constitutive equation for the viscoelastic Carreau fluid model as the non-Newtonian fluid is derived using the momentum and energy equations. To simplify the nonlinear systems of partial differential equations, appropriate non-dimensional parameters are employed to convert them into systems of ordinary differential equations. MethodBy taking the Weissenberg number as a small parameter, a series solution is obtained for considerable quantities like pressure gradient, axial velocity, flow rate, pressure distribution, and temperature distribution using the perturbation method. In contrast, the numeric outcome of some quantities of engineering interest, like flow rate, coating thickness, share stresses, and separation points, are calculated. Streamlines in 2D and 3D are also drawn to observe the flow pattern. To validate the solution, the problem is also solved numerically with the BVP Midrich method. The analysis of the results demonstrates a satisfactory agreement between the analytical and numerical solutions. ResultsThe graphical investigation examines the influence of different fluid parameters on velocity profile, shear stress, pressure profile, temperature profile, and pressure gradient. A comprehensive mechanism behind these outcomes is deliberated. It has been observed that velocity rises on increasing the Weissenberg number; however, velocity decreases in the case of the velocities ratio. Further, the Brickman number has a significant influence on the temperature profile and has increased with the increase in the Brickman number. Moreover, the separation point and coating thickness decrease with the velocities ratio increase. The results accuracy is checked against papers that have already been published. The comparison reveals good agreement; therefore, the resultant analytical model gives new ways to forecast film thickness and explain influence parameters. Hence, these factors may help in an efficient coating process and improve the substrate life.