In this work, forced convection in the laminar outflow between two disks is predicted. The disks can be corotating or contrarotating with equal or with different angular velocities. A published closed form solution is used to model the forced convection. The simplified energy equation is discretized using a finite difference method. The discretized equation is solved using the tridiagnal matrix algorithm (TDMA). Results are obtained for a heat flux as well as a specified temperature boundary condition and are presented for various flow parameters such as throughflow Reynolds number, rotational Reynolds number, gap ratio and speed ratio. The parameters except the speed ratio affect the temperature field strongly. The computed Nusselt number is in good agreement with the published experimental data. The coupling of closed form solution and energy equation predicts temperature field accurately. Additionally, the solution procedure is simplified considerably and the solution is obtained with lesser computational resources.

The Marangoni propulsion of spheres and elliptical disks floating on the air–water interface were studied to understand the effect of particle shape on its motion and its stability at moderate Reynolds numbers. Self-propulsion of the Marangoni surfer was achieved by coating half of the spheres and the elliptical disks with either a solution of soap or isopropyl alcohol (IPA). The presence of the soap or IPA resulted in a surface tension gradient across the particles which propelled the particles in the direction of increasing surface tension. Beyond a critical velocity, a transition was observed from a straight-line motion to a rotational motion. These vortices were observed to shed above a critical Reynolds number resulting in an unbalanced torque that caused the particles to rotate. Increasing the aspect ratio between the major and minor axes of the elliptical disks was found to decrease their stability and greatly enhance their rate of rotation. This was especially true for elliptical disks traveling in a direction parallel to their major axis. The interactions between the particles and the wall of a Petri dish were also studied. Repulsive, concave curvature was found to decrease stability and enhance rotational motion, while attractive, convex curvature was shown to stabilize the straight-line motion of the spheres. For the neutrally buoyant elliptical disks, the presence of the bounding wall was found to greatly stabilize the straight-line motion of the elliptical disks when they were traveling in a direction parallel to their minor axis.

In this study, computational fluid dynamics ( cfd ) software and detached eddy simulation turbulence model were used to simulate butterfly valves with different designs. The effects of shaft diameters on the value and the fluctuation of valve disk torque were studied, and the physical reason was discussed. The simulation results were verified by comparing with the experimental data. The findings revealed that with the closing of the valve, the hydraulic torque of the valve disk first increases and then decreases. Meanwhile, the torque decreases gradually with the increase of the shaft diameter. The variation of torque is caused by the change of pressure on both sides of the valve disk. The result also indicates that the fluctuation of torque is induced by the flow separation phenomenon occurs on the valve disk. The fluctuation is significant for the valve opening from 20% to 60%. The strength of the torque fluctuation is greater for the smaller shaft diameter. This study provides a theoretical basis for the design and optimization of butterfly valves.

The stagnation flow and heat transfer from the blunt surface of a finite circular disk subjected to a uniform stream of an incompressible fluid is revisited in this paper. A laminar boundary layer analyses were carried out employing the method developed by Frössling. The involved auxiliary functions were calculated for several Prandtl numbers. It was found that the exact knowledge of the velocity at the outer edge of the boundary layer was essential to achieve an accurate velocity solution. In addition to the analytical work, computational fluid dynamics (CFD) simulations and a detailed experimental study were conducted including heat transfer measurements in a wind tunnel and a large water towing tank. The analytical treatment enabled a clear discussion of the effect of the Prandtl number on convective heat transfer from a blunt disk. A primary effect and a secondary effect were distinguished based on the analytical treatment. The boundary layer theory offered a rather efficient calculation method, and its results were in an excellent agreement with experimental data.

The parasitic drag losses incurred by wet clutches, used in transmission systems, can significantly affect vehicular powertrain efficiency. This paper presents a novel implicit solution for hydrodynamic parasitic drag losses of disengaged clutches. These are generated by conjunctional friction, taking into account lubricant film separation during codirectional and counter-directional disk pair rotations. Lubricant film rupture is considered through application of incipient reverse flow boundary condition, which is representative of lubricant film separation. The results point to the operating conditions at which significant power losses occur. In particular, the time efficient model is able to represent the small losses incurred during codirectional rotation of disk pairs.

Computational fluid dynamics (CFD) has been unable to reliably predict aeration and drag torque in clutches. In this study, a CFD method was developed to reliably predict the onset of aeration and drag torque as a function of the clutch's rotational speed. This study showed that though the oil and air behave as if they are incompressible at steady-state, the formulation must account for the compressible nature of the gas and the unsteady processes that occur before reaching steady-state. This study also showed that the dynamic nature of the contact angle between the oil and the stationary disk must be accounted for to predict drag torque and aeration as a function of rotational speed, and a model of the dynamic-contact angle was developed.

When a liquid is forced to flow radially outward in the gap between two coaxial, parallel annular disks—one rotating and one stationary—the liquid occupies the entire gap until the speed of the rotating disk reaches a critical value. Beyond that critical speed, gas from the outer radius starts to enter into the gap, a process referred to as aeration. The higher the rotational speed, the greater is the extent of penetration by the gas into the gap. The extent of gas penetration strongly affects the torque exerted between the two disks because of the large difference in the gas and liquid viscosities. In this study, a reduced-order model is developed to predict the onset of aeration, extent of gas penetration into the gap, and drag torque as a function of the disk's rotational speed, gap between disks, properties of the liquid, and mass flow rate of the liquid forced through the gap. The model developed was validated by comparing predictions with experimental data.

This paper presents a smoothed particle hydrodynamics (SPH) modeling technique based on the cylindrical coordinates for axisymmetrical hydrodynamic applications, thus to avoid a full three-dimensional (3D) numerical scheme as required in the Cartesian coordinates. In this model, the governing equations are solved in an axisymmetric form and the SPH approximations are modified into a two-dimensional cylindrical space. The proposed SPH model is first validated by a dam-break flow induced by the collapse of a cylindrical column of water with different water height to semi-base ratios. Then, the model is used to two benchmark water entry problems, i.e., cylindrical disk and circular sphere entry. In both cases, the model results are favorably compared with the experimental data. The convergence of model is demonstrated by comparing with the different particle resolutions. Besides, the accuracy and efficiency of the present cylindrical SPH are also compared with a fully 3D SPH computation. Extensive discussions are made on the water surface, velocity, and pressure fields to demonstrate the robust modeling results of the cylindrical SPH.

The flow behavior through the vented channel of a brake disk determines its thermal performance, viz. its resistance to brake fade, brake wear, thermal distortion, and thermal cracking. We present experimental results of the flow characteristics inside the vented channel of a radial vane brake rotor with a selected number of vanes (i.e., 18, 36, and 72) but constant porosity ( ε ∼ 0.8) at low rotational speeds (i.e., 25 rpm ≤ N ≤ 400 rpm). Using bulk flow and velocity field mapping measurement techniques, we observed that increasing the number of vanes for a given rotational speed results in (i) the increase in the mass flow rate of the air pumped by the rotor, (ii) the reduction of inflow angle ( β ) becoming more closely aligned with the vanes, (iii) more uniformly distributed passage velocity profiles, and (iv) increased Rossby number. In addition, for a certain range of rotational speeds (i.e., 100 rpm ≤ N ≤ 400 rpm), we identified the biased development of streamwise secondary flow structures in the vented passages that only form on the inboard side of the rotor. This is due to the entry conditions where the incoming flow must transition sharply from the axial to the radial direction as air is drawn into the rotating channel. The biased secondary flow is likely to cause uneven cooling of the brake rotor, leading to thermal distortion. At lower rotational speeds (i.e., N < 100 rpm), the biased secondary flows transitions into a symmetric structure.

Porous disks are commonly encountered in experimental studies dealing with flow through objects such as wind turbines, parachutes, and fluidic devices to regulate pressure and/or downstream turbulence. Perforations are typically staggered and only porosity is altered to attain the required disk drag coefficient, despite a documented influence of topology. Few works have reported, however, to which extent the spatial distribution of the circular perforations affect the mean flow pertaining freestanding disks, and for this reason, this work presents a first, more systematic study focused on the effect of azimuthally varying hole topology and porosity on disk drag and near-wake characteristics. An experimental study performed in airflows of negligible freestream turbulence at Reynolds numbers in the order of 10 5 is reported and related to the existing literature to ensure reliability. Complementary to drag measurements, near-wake surveys have been performed on a variety of perforation layouts using two-component laser Doppler velocimetry and two-component particle image velocimetry. It is shown that minor changes in perforations can cause drastic changes in near-wake flow topology and no perforation layout can be consistently associated with highest drag. Explicit empirical expressions for drag coefficient linked with the simplified topologies considered have been derived.

The larger objective of this research comes from the fact that optimization studies in “pumps operated as turbines” have concentrated only within flow zones without any physical perception regarding the influence of nonflow zones such as back-cavities in standard end-suction pumps. Four pumps of different designs are selected and their back cavities are reduced by inserting solid material, leaving a very small axial clearance. The effects are investigated on an experimental platform, which reveal unique phenomena taking place. The first is associated with the reduction of expected disk friction (hence improvement in shaft torque), while the second is more intricate considering the effect on fluid momentum through reorganization of tangential velocities, based on the mixing zone theory proposed in the paper. The net effect of reducing the volume of nonflow zones (i.e., filling of cavity) is the enhancement of efficiency in the range of 1.3% to 3.6% (±0.4%) in turbine mode. The experimental disk friction coefficient as a function of blade Reynolds number is corroborated with the established theory proposed by different researchers. A significant phenomenon observed was the elimination of vibration and noise at overload operating conditions with the minimal axial clearance.

Mathematical relations are obtained for velocities and pressure distribution for a fluid entering the peripheral clearance of a pair of rotating concentric disks that converges and discharges through an opening at the center. Both, the flows in the gap of corotating disks and in the gap of contrarotating disks can be predicted using the present analytical solutions. The prediction of instability of radial velocity for corotating disks at the speed ratio of unity is very important for practical applications. The radial velocity profile is similar to a parabolic profile exactly at speed ratio of unity. The profile drastically changes with the small difference of ± 1 % in the disks’ rotation. The radial convection was observed in the tangential velocity at a low radius. Centrifugal force caused by disk rotation highly influences the flow resulting in backflow on the disks. The pressure consists of friction losses and convective inertia. Therefore, the pressure decrease is high for increased speed ratio, throughflow Reynolds number, and rotational Reynolds number. The pressure decrease for the flow between contrarotating disks is lesser than that for the flow between corotating disks due to decreased viscous losses in the tangential direction. This study provides valuable guidance for the design of devices where disks are rotated independently by highlighting the instabilities in the radial velocity at the speed ratio of unity.

A new approach based on the open source tool OpenFOAM is presented for the numerical simulation of a mini gerotor pump working at low pressure. The work is principally focused on the estimation of leakage flow in the clearance disk between pump case and gears. Two main contributions are presented for the performance of the numerical simulation. On one hand, a contact point viscosity model is used for the simulation of solid–solid contact between gears in order to avoid the teeth tip leakage. On the other hand, a new boundary condition has been implemented for the gear mesh points motion in order to keep the mesh quality while moving gears with relative velocity. Arbitrary coupled mesh interface (ACMI) has been used both in the interface between clearance disk in inlet/outlet ports and between clearance disk and interteeth fluid domain. Although the main goal of the work is the development of the numerical method rather than the study of the physical analysis of the pump, results have been compared with experimental measurement and a good agreement in volumetric efficiency and pressure fluctuations has been found. Finally, the leakage flow in the clearance disk has been analyzed.

Computations of pulsating supercavity flows behind axisymmetric disk cavitators are presented. The method of computation is a finite volume discretization of the equations of mixture fluid motion. The gas phase is treated as compressible, the liquid phase as incompressible, and the interface accuracy enhanced using a volume of fluid (VOF) approach. The re-entrant, pulsating, and twin vortex modes of cavity closure are delineated and computationally resolved, including the expected hysteresis. A phase diagram of cavitation number versus ventilation rate at three Froude conditions is computationally constructed. Sample re-entrant, pulsation, and twin vortex snapshots are presented. Pulsation results are compared with stability criterion from the literature as well as examined for their expected character. Computations appear to capture the complete spectrum of cavity closure conditions. A detailed comparison of computational simulation and physical experiment at similar conditions is also included as a means to validate the computational results.

The present contribution addresses the analysis of the leakage behavior of a small hydro Francis turbine using an analytical approach, which was validated based on the results of computational fluid dynamics (CFD). For a custom-designed Francis turbine with a specific speed of n q = 41.9 rpm, the flow chambers resulting from the labyrinth geometry were added to a traditional full CFD model of the turbine and numerical simulations were performed for several operation points ranging from part load (Q min = 0.5 × Q opt ) to over load (Q max = 1.3 × Q opt ). Consequently, the single losses occurring in the runner seals on crown and band side as well as the pressure distribution within the runner side spaces could be evaluated and compared to the results gained with an analytical approach, which was originally developed to calculate the leakage flow of centrifugal pumps. The comparison of the pressure distribution achieved with the numerical simulation and the analytical calculation shows that both approaches match well if the angular velocity of the fluid ω Fluid trapped in the runner side spaces is calculated in an appropriate way. Furthermore, the achieved results demonstrate that the use of the analytical model enables the calculation of the disk friction and leakage losses with sufficient accuracy. This paper contributes to the improvement of the performance prediction of Francis turbines based on combined numerical and analytical calculations.

Within the present investigation, a miniature viscous disk pump (VDP) is utilized to characterize and quantify non-Newtonian fluid elastic turbulence effects, relative to Newtonian flow behavior. Such deviations from Newtonian behavior are induced by adding polyacrylamide to purified water. The VDP consists of a 10.16 mm diameter disk that rotates above a C-shaped channel with inner and outer radii of 1.19 mm and 2.38 mm, respectively. A channel depth of 230 μ m is employed. Fluid inlet and outlet ports are located at the ends of the C-shaped channel. Experimental data are given for rotational speeds of 126 1/s, 188 1/s, 262 1/s, and 366 1/s, pressure rises as high as 700 Pa, and flow rates up to approximately 0.00000005 m 3 /s. Reynolds number ranges from 2.9 to 6.5 for the non-Newtonian polyacrylamide solution flows and from 51.6 to 149.8 for the Newtonian pure water flows. To characterize deviations due to non-Newtonian elastic turbulence phenomena, two new parameters are introduced, PrR and HCR, where HCR is the ratio of head coefficient (HC) for the polyacrylamide solution and head coefficient for the water solution, and PrR is the ratio of pump power for the polyacrylamide solution and pump power for the water solution. Relative to Newtonian, pure water flows, the polyacrylamide solution flows give pump head coefficient data, dimensional pressure rise data, slip coefficients (SCs), specific speed (SS) values, and dimensional power data, which show significant variations and differences as they vary with flow coefficient (FC) or dimensional volumetric flow rate. Also important are different ranges of specific speed (SS) for the pure water and polyacrylamide solutions, and a lower range of SC or slip coefficient values for the polyacrylamide solution flows, compared to the pure water flows. These variations are due to increased elastic turbulence losses, which occur as viscosity magnitudes increase and the elastic polymers are excited by mechanical stress, which causes them to extend, deform, stretch, and intertwine.

Mathematical expressions are derived for flow velocities and pressure distributions for a laminar flow in the gap between two rotating concentric disks. Fluid enters the gap between disks at the center and diverges to the outer periphery. The Navier–Stokes equations are linearized in order to get closed-form solution. The present solution is applicable to the flow between corotating as well as contrarotating disks. The present results are in agreement with the published data of other investigators. The tangential velocity is less for contrarotating disks than for corotating disks in core region of the radial channel. The flow is influenced by rotational inertia and convective inertia both. Dominance of rotational inertia over convective inertia causes backflow. Pressure depends on viscous losses, convective inertia, and rotational inertias. Effect of viscous losses on pressure is high at small throughflow Reynolds number. The convective and rotational inertia influence pressure significantly at high throughflow and rotational Reynolds numbers. Both favorable and unfavorable pressure gradients can be found simultaneously depending on a combination of parameters.

In this work, an exact solution to the steady-state Navier–Stokes (NS) equations is presented for viscous flows between two stretchable disks with mass transpiration effects. The governing momentum equations were converted into an ordinary differential equation by a similarity transformation technique. The similarity equation was solved numerically and the effects of Reynolds number and the mass transpiration parameter were investigated. At very low Reynolds numbers (i.e., R → 0), a creeping flow was observed with a parabolic radial velocity profile and a cubic function profile for the vertical velocity. With the increase of the Reynolds number, the flow shows a boundary layer behavior near the wall with a constant velocity core flow in the centerline region between the two disks for mass suction or lower mass injection. The effects of the mass transpiration on the flow are quite different and interesting. With strong suction, the radial profiles also show boundary layer type characteristics with a core flow. But for large mass injection, the radial velocity approaches to a linear profile under higher Reynolds number. These results are a rare case of an exact solution to the NS equations and are useful as a benchmark problem for the validation of three-dimensional (3D) numerical computation code.

Although the flow between parallel and inclined disks is a simple representation of many complex flow situations, this class of flow poses significant problems for experimental and numerical study. This paper presents experimental results of the pressure distribution for turbulent radial flow between parallel and inclined disks, considering different ratios between the diameters of the frontal disk and feeding orifice. The experimental results bolster the lack of data for both flow situations in the turbulent regime and demonstrate differences between them. The results presented have high accuracy and known uncertainty, making them useful for comparison to analytical and numerical results.

The characteristic flow behavior, time-averaged velocity distributions, phase-resolved ensemble-averaged velocity profiles, and turbulence properties of the flow in the interdisk midplane between shrouded two corotating disks at the interdisk spacing to disk radius aspect ratio 0.2 and rotation Reynolds number 3.01 × 105 were experimentally studied by flow visualization method and particle image velocimetry (PIV). An oval core flow structure rotating at a frequency 60% of the disks rotating frequency was observed. Based on the analysis of relative velocities, the flow in the region outside the oval core flow structure consisted of two large vortex rings, which move circumferentially with the rotation motion of the oval flow core. Four characteristic flow regions—solid-body-rotation-like region, buffer region, vortex region, and shroud-influenced region—were identified in the flow field. The solid-body-rotation-like region, which was featured by its linear distribution of circumferential velocity and negligibly small radial velocity, was located within the inscribing radius of the oval flow core. The vortex region was located outside the circumscribing radius of the oval flow core. The buffer region existed between the solid-body-rotation-like region and the vortex region. In the buffer region, there existed a “node” point that the propagating circumferential velocity waves diminished. The circumferential random fluctuation intensity presented minimum values at the node point and high values in the solid-body-rotation-like region and shroud-influenced region due to the shear effect induced by the wall.