Search Results (31)

This paper develops an analytical turbulence model for open-ended squeeze film damper (SFD) application. Prandtl’s mixing length theory is adopted to describe the momentum transfer within the damper for its thin-film turbulent flow. A novel turbulence coefficient function is developed to describe the effective fluid viscosity such that the classical Reynolds equation remains applicable. Model validation is presented by (i) comparing the damping coefficient obtained by several existing empirical formulas and (ii) correlating the rotor dynamic prediction with the experimental measurement of an integrated rotor-SFD test rig. This work provides a reduced form of turbulence coefficient for certain SFD implementations. It quantifies the turbulence effect under different operating conditions, which is valued as a practical tool to assess the significance of turbulence consequences in rotor dynamic applications. Full article

According to Prandtl’s boundary layer theory, the entrance length refers to the axial distance required for a flow to transition from its initial entry condition to a fully developed flow where the velocity profile stabilizes downstream. However, this theory remains applicable only under the assumption of Re ≫ 1, while its validity diminishes under low-Reynolds-number conditions. This study utilizes OpenFOAM based on the finite volume method to numerically examine Newtonian and viscoelastic fluids in a laminar circular pipe flow. The objective is to determine the range of Reynolds numbers for which the differential equations from within the Prandtl boundary layer theory are strictly valid. Additionally, the study explores the effects of Reynolds numbers (Re) ranging from 50 to 100, s solvent viscosity ratio (β) fixed at 0.3 and 0.7, and Weissenberg numbers (Wi) ranging from 0.2 to 5 on the entrance length and friction factor for the Oldroyd-B model. The results indicate the presence of a lower Reynolds number that impedes the attainment of the outcomes predicted by the Prandtl boundary layer theory for the entrance length. The inertia effect, the increase in solvent viscosity contribution, and the elastic effect exhibit a linear relationship with the entrance length and friction factor. Full article

The instability of the double-diffusive convection of an Oldroyd-B fluid in a vertical Brinkman porous layer caused by temperature and solute concentration differences with the Soret effect is studied. Based on perturbation theory, an Orr–Sommerfeld eigenvalue problem is derived and numerically solved using the Chebyshev collocation method. The effects of dimensionless parameters on the neutral stability curves and the growth rate curves are examined. It is found that Lewis number Le, Darcy–Prandtl number Pr_D, and normalized porosity η have critical values: When below these thresholds, the parameters promote instability, whereas exceeding them leads to suppression of instability. In addition, for Le < Le_c2 (a critical value of Le), S_r strengthens the instability of the flow, while for Le > Le_c2, S_r suppresses it. These results highlight the complex coupling of heat and mass transfer in Oldroyd-B fluids within porous media. Full article

This study investigates the three-dimensional, steady, laminar boundary-layer equations of a non-Newtonian fluid over a flat plate in the absence of body forces. The classical boundary-layer theory, introduced by Prandtl in 1904, suggests that fluid flows past a solid surface can be divided into two regions: a thin boundary layer near the surface, where steep velocity gradients and significant frictional effects dominate, and the outer region, where friction is negligible. Within the boundary layer, the velocity increases sharply from zero at the surface to the freestream value at the outer edge. The boundary-layer approximation significantly simplifies the Navier–Stokes equations within the boundary layer, while outside this layer, the flow is considered inviscid, resulting in even simpler equations. The viscoelastic properties of the fluid are modeled using the Rivlin–Ericksen tensors. Lie group analysis is applied to reduce the resulting third-order nonlinear system of partial differential equations to a system of ordinary differential equations. Finally, we determine the admissible forms of the freestream velocities in the x- and z-directions. Full article

In recent years, vibration control utilizing smart materials has garnered considerable attention. In this paper, we aim to achieve vibration suppression of a plate structure with a tail-fin shape by employing piezoelectric actuators—one of the smart materials. The plate structure is rigorously modeled based on the Kirchhoff–Love plate theory, while the piezoelectric actuators are formulated in accordance with the Prandtl–Ishlinskii model. This research proposed a control system that addresses the interference effects arising during vibration control by dividing multiple piezoelectric elements into two groups and implementing MIMO control. The efficacy of the proposed control method was validated through simulations and experiments. Full article

Aircraft propellers produce relatively large in-plane loads, called propeller 1P loads, during maneuvers such as turning, diving, and lifting, and these loads can negatively affect the flight and control of the aircraft. In order to study the change rule of 1P aerodynamic loads, in this paper, a mathematical model of the propeller 1P aerodynamic loads has been developed based on the blade element momentum theory. This mathematical model was then corrected using the Pitt–Peters incoming flow correction method, the Prandtl tip correction method, and the propeller root flow correction method. Based on this mathematical model, a calculation procedure for the propeller 1P aerodynamic loads was developed using MATLAB software, and the accuracy of the procedure was verified by comparing the results with CFD simulation results. Numerical simulations show that the results calculated based on the proposed mathematical model for the coefficients of thrust, power, bending moment, and the tangential force of the propeller have an error of less than ±6.00% compared to the CFD simulation results. For a small inflow angle, the coefficients of bending moment and tangential force of the whole propeller fluctuate in a small range. But, as the inflow angle increases, the fluctuation range of the aerodynamic characteristic parameters of the propeller increases and the fluctuation becomes more complicated. Through numerical calculations, it has been shown that the mathematical model presented herein is reliable and accurate. In addition, it greatly shortens the calculation time and improves the calculation efficiency. It is expected that the proposed model can provide a certain help for the strength design of the propeller structure and the study of the aerodynamic performance of the whole aircraft. Full article

The use of a diffuser in hydrokinetic turbines can improve the power coefficient. However, the risk of cavitation in the rotor blades increases. Studies suggest that backward-curved blades can reduce the axial load on the rotor and therefore prevent cavitation. Therefore, this work develops an optimization procedure applied to backward-curved blades in hydrokinetic turbines with diffusers based on the Blade Element Momentum Theory. The main contribution is to consider both the sweep effect and the presence of a diffuser in the optimization in an innovative way. We use a radial transformation function that adjusts the radial position considering the curvature of the blade during optimization under the effect of the diffuser. The results showed that the increase in blade curvature resulted in greater chord distributions and twist angles, especially at the blade tips. The Prandtl’s loss factor was not sensitive to sweep, but the linked circulation increased at the blade tips, suggesting an increased risk of cavitation. Depending on the sweep angle, the optimized blades were able to mitigate or avoid cavitation. In particular, a sweep angle of 30${}^{\circ }$ eliminated cavitation. This study indicated that the proposed optimization can effectively prevent cavitation, showing satisfactory results. Full article

Since the 1930s, theories of skin-friction drag from plates with rough surfaces have been based by analogy to turbulent flow in pipes with rough interiors. Failure of this analogy at small fluid velocities has frustrated attempts to create a comprehensive theory. Utilizing the concept of a self-similar roughness that disrupts the boundary layer at all scales, this investigation derives formulas for a rough or smooth plate’s skin-friction coefficient and forced convection heat transfer given its characteristic length, root-mean-squared (RMS) height-of-roughness, isotropic spatial period, Reynolds number, and the fluid’s Prandtl number. This novel theory was tested with 456 heat transfer and friction measurements in 32 data-sets from one book, six peer-reviewed studies, and the present apparatus. Compared with the present theory, the RMS relative error (RMSRE) values of the 32 data-sets span 0.75% through 8.2%, with only four data-sets exceeding 6%. Prior work formulas have smaller RMSRE on only four of the data-sets. Full article

Considering the factors affecting the surrounding rock stability of gob-side entry retaining, the applicability of a large-diameter, concrete-filled steel tube roadside support body in a top-coal caving fully mechanized face is discussed, and a new approach to gob-side entry retaining is proposed in this study. The mechanical model of the surrounding rock structure of gob-side entry retaining in a top-coal caving fully mechanized face was established, the critical state of column–roof contact shear slip instability was clarified through Prandtl foundation failure theory, and the deformation mechanism of the surrounding rock of the retained roadway was analyzed through numerical simulation. The results indicated that the range of the tensile stress zone and extreme tensile stress of the roof between columns are closely related to the spacing of columns, which is the key factor influencing the deformation of the retained roadway. In addition, besides uncontrollable factors, the stability of the contact interface between the roof and columns is directly related to the area of the contact interface between the concrete-filled steel tubes and the roof, and the size of the critical contact area is directly related to the properties of top-coal mass. Finally, a field test was carried out in 91–101 working panels in the Wang-Zhuang Coal Mine; the maximum convergence of the roof and floor was 510 mm, and the area of the retained roadway section reached 12.9 m², which is within a reasonable range. Full article

Within the framework of the theory of unsteady turbulent flows in a stratified fluid, a new parameterization of the turbulent Prandtl number is proposed. The parameterization is included in the k-ε-closure and used within the three-dimensional model of thermohydrodynamics of an enclosed water body where density distribution includes pycnocline. This allows us to describe turbulence in a stratified shear flow without the restrictions associated with the gradient Richardson number and justify the choice of closure constants. Numerical experiments, where the downward penetration of turbulence was considered, confirm the advantage of the developed approach in describing the effects neglected in the classical closures. Full article

In this paper, we propose and justify a spline-collocation method with first-order splines for approximate solution of nonlinear hypersingular integral equations of Prandtl’s type. We obtained the estimates of the convergence rate and the method error. The constructed computational scheme includes a continuous method for solving nonlinear operator equations, which is stable for perturbations of the coefficients and the right-hand sides of equations. Full article

The kinematic method of limit analysis theory was adopted in this paper to calculate the seismic bearing capacity of the shallow strip foundation on a rock mass obeying the non-linear modified Hoek-Brown failure criterion. The generalized Prandtl failure mechanism was chosen, which is different from the multi-wedge failure mechanism assumption commonly used in previous research. Three angle parameters were used to control the mechanism shapes, and the equivalent friction angle and equivalent cohesive were adopted to faithfully reflect the shape characteristics of the failure mechanism. The seismic action was considered using the pseudo-static method, which is simplified to the inertial force determined by the horizontal seismic coefficient. The validation of the present method was carried out by comparing with previous analytical results and the finite element model. Subsequently, the influences of the surface overload, the properties of the rock mass, and the seismic action on the shape and ultimate bearing capacity of the failure mechanism were investigated. For the convenience of practical engineering, this paper gives the ultimate bearing capacity of strip foundations on five representative rock foundations, and the variation trend of bearing capacity with the unit weight of rock mass, surface overload, and horizontal seismic coefficient. Full article

The hydrokinetic turbine is used worldwide for electrical generation purposes, as such a technology may strongly reduce environmental impact. Turbines designed using backward swept blades can significantly reduce the axial load, being relevant for hydro turbines. However, few works have been conducted in the literature in this regard. For the case of hydrokinetic rotors, backward swept blades are still a challenge, as the authors are unaware of any optimization procedures available, making this paper relevant for the current state of the art. Thus, the present work develops a new optimization procedure applied to hydrokinetic turbine swept blades, with the main objective being the design of blades with reduced axial load on the rotor and possibly a reduction in the cavitation. The proposed method consists of an extension of the blade element momentum theory (BEMT) to the case of backward swept blades through a radial transformation function. The method has low computational cost and easy implementation. Once it is based on the BEMT, it presents good agreement when compared to experimental data. As a result, the sweep heavily affects the chord and twist angle distributions along the blade, increasing the turbine torque and power coefficient. In the case of the torque, it can be increased by about 18%. Additionally, even though the bound circulation demonstrates a strong change for swept rotors, Prandtl’s tip loss seems to be not sensitive to the sweep effect, and alternative models are needed. Full article

On the basis of the Prandtl boundary layer theory and an improved perturbation method, the process of laminar flow bifurcating into the Southwest China vortex (SWV) in the Hengduan Mountains is studied. The results show that the formation of SWV is mainly determined by the speed of incoming airflow in the direction of the main axis of the Hengduan Mountains. The vortex is generated in the leeward area of the Hengduan Mountains when the speed of incoming airflow is greater than the critical velocity. Moreover, it means that the laminar flow bifurcates into a vortex. The formation position of the SWV is mainly determined by the relative position of the incoming airflow in the windward area of the Hengduan Mountains and the main axis of the Hengduan Mountains. The seasonal distribution of SWVs is determined by both the velocity of the incoming airflow and the relative position of the incoming airflow to the main axis of the Hengduan Mountains. These findings are consistent with the SWV observation facts, which not only adequately explain the physical formation mechanisms and processes of SWVs, but also present the formation location and seasonal distribution of SWVs. Meanwhile, a solution from laminar to vortex in circumflow motion is also presented. Full article

In our research work, we have developed a model describing the characteristics of the bio-convection and moving microorganisms in the flows of a magnetized generalized Burgers’ nanoliquid with Fourier’s and Fick’s laws in a stretchable sheet. Considerations have been made to Cattaneo–Christov mass and heat diffusion theory. According to the Cattaneo–Christov relation, the Buongiorno phenomenon for the motion of a nanoliquid in the generalized Burgers’ fluid has also been applied. Similarity transformations have been used to convert the control system of the regulating partial differential equations (PDEs) into ordinary differential equations (ODEs). The COMSOL software has been applied to obtain mathematical results of non-linear equations via the Galerkin finite element method (G-FEM). Logical and graphical measurements for temperature, velocity, and microorganisms analysis have also been examined. Moreover, nanoparticle concentrations have been achieved by examining different approximations of obvious physical parameters. Computations of this model show that there is a direct relationship among the temperature field and thermal Biot number and parameter of the generalized Burgers’ fluid. The temperature field is increased to grow the approximations of the thermal Biot number and parameter of generalized Burgers’ fluid. It is reasonable to deduce that raising the chemical reaction parameter and concentricity relaxation parameter or decreasing the Prandtl number, concentricity Biot quantity, and active energy parameter can significantly increase the nanoparticles concentration dispersion. Full article