scholarly journals Mathematical Model and Experimental Evaluation of Drag Torque in Disengaged Wet Clutches

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Shoaib Iqbal ◽  
Farid Al-Bender ◽  
Bert Pluymers ◽  
Wim Desmet
Keyword(s):  
Flow Rate ◽  
Stokes Equations ◽  
Automatic Transmission ◽  
Experimental Results ◽  
Navier Stokes ◽  
Drag Torque ◽  
Navier Stokes Equations ◽  
Rotational States ◽  
Disk Size ◽  
Transmission Fluid

When the clutch is in disengaged condition, ideally no torque should be transmitted. However, in reality, the relative motion between the disks causes viscous shearing of fluids in the gap. This results in a drag torque which is considered as a loss. The objective of the present study is to formulate a drag torque model as well as to experimentally evaluate the effect of several parameters on the drag torque. A model based on continuity and Navier-Stokes equations, considering laminar flow, is deduced. The drag torque estimated by the model is the sum of drag torque due to shearing of the automatic transmission fluid (ATF) and mist (suspension of ATF in air) film. In order to validate the model and characterize the drag torque, experiments are performed using an SAE no. 2 test setup under real conditions of variable ATF flow rate and disks' rotational states for higher clutch speed range. The drag torque predicted by the model is in good agreement with the experimental results obtained by varying the flow properties and disks' rotational states. By analyzing the experimental results, a factor by which, the variation in parameters such as ATF flow rate, ATF temperature, disk size, and disk rotational state influencing the drag torque is determined.

Model for Predicting Drag Torque in Open Multi-Disks Wet Clutches

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Shoaib Iqbal ◽  
Farid Al-Bender ◽  
Bert Pluymers ◽  
Wim Desmet
Keyword(s):  
Stokes Equations ◽  
Volume Fraction ◽  
Automatic Transmission ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Drag Torque ◽  
Navier Stokes Equations ◽  
Transmission Fluid ◽  
Flow Pressure ◽  
Air Film

A mathematical model based on continuity and Navier-Stokes equations, considering laminar flow in the gap between the disks, is presented to estimate the drag torque in open multidisks wet clutches. By taking into account the effects of Poiseuille and centrifugal forces, the flow pressure and velocity fields are investigated. The model quantifies the volume fraction of fluids and predicts the evolution of film shape. The drag torque estimated by the model is the sum of drag torque due to shearing of automatic transmission fluid (ATF) and the mist (suspension of ATF in air) film. In order to validate the model, experiments are performed on SAE# 2 test-setup under actual operating conditions of clutches. The model is capable of predicting the drag torque under conditions of variable flow rate and different disks rotational state for higher clutch speed range.

Perturbation Procedures for Nonlinear Viscous Flows

1983 ◽  
Vol 50 (2) ◽  
pp. 265-269
Author(s):  
D. Nixon
Keyword(s):  
Perturbation Theory ◽  
Shock Waves ◽  
Transonic Flow ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Two Dimensions ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations

The perturbation theory for transonic flow is further developed for solutions of the Navier-Stokes equations in two dimensions or for experimental results. The strained coordinate technique is used to treat changes in location of any shock waves or large gradients.

Oscillatory forcing of flow through porous media. Part 1. Steady flow

2002 ◽  
Vol 465 ◽  
pp. 213-235 ◽  
Author(s):  
D. R. GRAHAM ◽  
J. J. L. HIGDON
Keyword(s):  
Porous Media ◽  
Flow Rate ◽  
Stokes Equations ◽  
Nonlinear Flow ◽  
Navier Stokes ◽  
Full Time ◽  
Inertial Effects ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean

Oscillatory forcing of a porous medium may have a dramatic effect on the mean flow rate produced by a steady applied pressure gradient. The oscillatory forcing may excite nonlinear inertial effects leading to either enhancement or retardation of the mean flow. Here, in Part 1, we consider the effects of non-zero inertial forces on steady flows in porous media, and investigate the changes in the flow character arising from changes in both the strength of the inertial terms and the geometry of the medium. The steady-state Navier–Stokes equations are solved via a Galerkin finite element method to determine the velocity fields for simple two-dimensional models of porous media. Two geometric models are considered based on constricted channels and periodic arrays of circular cylinders. For both geometries, we observe solution multiplicity yielding both symmetric and asymmetric flow patterns. For the cylinder arrays, we demonstrate that inertial effects lead to anisotropy in the effective permeability, with the direction of minimum resistance dependent on the solid volume fraction. We identify nonlinear flow phenomena which might be exploited by oscillatory forcing to yield a net increase in the mean flow rate. In Part 2, we take up the subject of unsteady flows governed by the full time-dependent Navier–Stokes equations.

Study of Flow and Thrust in Nozzle-Flapper Valves

1975 ◽  
Vol 97 (1) ◽  
pp. 39-50 ◽  
Author(s):  
S. Hayashi ◽  
T. Matsui ◽  
T. Ito
Keyword(s):  
Approximate Formula ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Relaxation Method ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vena Contracta ◽  
Radial Gap ◽  
Good Agreement

The Navier-Stokes equations and the equation of continuity describing the flow in the flat-faced nozzle-flapper valve are numerically solved by the iterative relaxation method and the effect of the flow contraction (vena contracta) occurring in the radial gap in the valve is investigated. Furthermore, an approximate formula for the flow force acting on the flapper is derived on the basis of the numerical solutions. The formula for the flow force is in good agreement with experimental results.

Steady streaming in a turbulent oscillating boundary layer

2007 ◽  
Vol 571 ◽  
pp. 265-280 ◽  
Author(s):  
PIETRO SCANDURA
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Stokes Equations ◽  
Infinite Plate ◽  
Harmonic Component ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Steady Streaming ◽  
Time Average

The turbulent flow generated by an oscillating pressure gradient close to an infinite plate is studied by means of numerical simulations of the Navier–Stokes equations to analyse the characteristics of the steady streaming generated within the boundary layer. When the pressure gradient that drives the flow is given by a single harmonic component, the time average over a cycle of the flow rate in the boundary layer takes both positive and negative values and the steady streaming computed by averaging the flow over n cycles tends to zero as n tends to infinity. On the other hand, when the pressure gradient is given by the sum of two harmonic components, with angular frequencies ω1 and ω2 = 2ω1, the time average over a cycle of the flow rate does not change sign. In this case steady streaming is generated within the boundary layer and it persists in the irrotational region. It is shown both theoretically and numerically that in spite of the presence of steady streaming, the time average over n cycles of the hydrodynamic force, acting per unit area of the plate, vanishes as n tends to infinity.

An analytically predictive model for moderately rarefied gas flow

2012 ◽  
Vol 698 ◽  
pp. 406-422 ◽  
Author(s):  
Thomas Veltzke ◽  
Jorg Thöming
Keyword(s):  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Knudsen Diffusion ◽  
Convective Transport ◽  
Surface Topology ◽  
Fickian Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations

AbstractIn microducts deviation from continuum flow behaviour of a gas increases with rarefaction. When using Navier–Stokes equations to calculate a flow under slightly and moderately rarefied conditions, slip boundary conditions are used which in turn refer to the tangential momentum accommodation coefficient (TMAC). Here we demonstrate that, in the so-called slip and transition regime, the flow in microducts can be reliably described by a consistently non-empirical model without considering the TMAC. We obtain this equation by superposition of convective transport and Fickian diffusion using two-dimensional solutions of Navier–Stokes equations and a description for the Knudsen diffusion coefficient as derived from kinetic theory respectively. For a wide variety of measurement series found in the literature the calculation predicts the data accurately. Surprisingly only size of the duct, temperature, gas properties and inlet and outlet pressure are necessary to calculate the resulting mass flow by means of a single algebraic equation. From this, and taking the discrepancies of the TMAC concerning surface roughness and nature of the gases into account, we could conclude that neither the diffusive proportions nor the total mass flow rates are influenced by surface topology and chemistry at Knudsen numbers below unity. Compared to the tube geometry, the model slightly underestimates the flow rate in rectangular channels when rarefaction increases. Likewise, the dimensionless mass flow rate and the diffusive proportion of the total flow are distinctly higher in a tube. Thus the cross-sectional geometry has a significant influence on the transport mechanisms under rarefied conditions.

scholarly journals Comparing fluid mechanics models with experimental data

2003 ◽  
Vol 358 (1437) ◽  
pp. 1567-1576 ◽  
Author(s):  
G. R. Spedding
Keyword(s):  
Fluid Mechanics ◽  
Stokes Equations ◽  
Physical World ◽  
Experimental Models ◽  
Experimental Results ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Dimensionless Groups ◽  
Model Predictions ◽  
Provided Examples

The art of modelling the physical world lies in the appropriate simplification and abstraction of the complete problem. In fluid mechanics, the Navier–Stokes equations provide a model that is valid under most circumstances germane to animal locomotion, but the complexity of solutions provides strong incentive for the development of further, more simplified practical models. When the flow organizes itself so that all shearing motions are collected into localized patches, then various mathematical vortex models have been very successful in predicting and furthering the physical understanding of many flows, particularly in aerodynamics. Experimental models have the significant added convenience that the fluid mechanics can be generated by a real fluid, not a model, provided the appropriate dimensionless groups have similar values. Then, analogous problems can be encountered in making intelligible but independent descriptions of the experimental results. Finally, model predictions and experimental results may be compared if, and only if, numerical estimates of the likely variations in the tested quantities are provided. Examples from recent experimental measurements of wakes behind a fixed wing and behind a bird in free flight are used to illustrate these principles.

Simulation-Based Analysis of 3D Flow Inside a Micropump With Passive Valves

2007 ◽  
Author(s):  
A. F. Tabak ◽  
A. Solak ◽  
E. Y. Erdem ◽  
C. Akcan ◽  
S. Yesilyurt
Keyword(s):  
Flow Rate ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Driving Frequency ◽  
Arbitrary Lagrangian Eulerian ◽  
Navier Stokes Equations ◽  
New Developments ◽  
Arbitrary Lagrangian Eulerian Method ◽  
Simulation Based

It is expected that chemical, biological and environmental applications of microdevices will increase with new developments in micromachining techniques. In this work, a micropump design that utilizes passive valves and an actuated diaphragm is presented. The flow rate is controlled by the deflection and the frequency of the diaphragm’s displacement. Passive valves are used for directing the flow. Poiseuille flow analogy is used to generate the equivalent pressure drop and flow rate via modifying the viscosity in the valve-channel in order to replace the variation of the channel width due to valve movement. Overall flow in the micropump is governed by three-dimensional time-dependent Navier Stokes equations. Deformation of the domain due to moving boundaries that coincide with the diaphragm motion is handled with the arbitrary Lagrangian-Eulerian method. Flow rate, hydraulic power and the efficiency of the micropump are obtained with respect to driving frequency and displacement of the diaphragm.

Modeling the Effect of Stability Bleed on Back-Pressure in Mixed-Compression Supersonic Inlets

2015 ◽  
Vol 137 (12) ◽  
Author(s):  
Lv Yongzhao ◽  
Li Qiushi ◽  
Li Shaobin
Keyword(s):  
Mach Number ◽  
Flow Rate ◽  
Stokes Equations ◽  
Functional Relation ◽  
Back Pressure ◽  
Normal Shock ◽  
Navier Stokes ◽  
Correction Coefficient ◽  
Navier Stokes Equations ◽  
Plenum Pressure

To stabilize the terminal normal shock on high-static pressure at outlet, called back-pressure pout, stability bleed slots are used in the throat of mixed-compression supersonic inlets. In this paper, a model for the functional relation between the bleed flow rate mbl and back-pressure pout is established based on a bleed flow rate model (BFRM) in order to study the effect of stability bleed on the back-pressure in mixed-compression supersonic inlets. Given the inlet flow parameters Min, pin*, and Tin*, the plenum pressure ppl at slots' outlet, the terminal normal shock position xs in this model, the bleed flow rate mbl, Mach number M¯out, and back-pressure pout were derived one by one from the basic laws of conservation. To study the effect of plenum pressure ppl on subsonic flow of the divergent section behind the terminal normal shock, a correction coefficient κ is introduced to modify the Mach number M¯out. Furthermore, numerical simulations based on Reynolds-Averaged Navier–Stokes equations were performed to analyze the functional relation between the bleed flow rate mbl and back-pressure pout. Computational fluid dynamics (CFD) results show that the present model agrees with the data.

The effects of surface roughness on the flow in multiple connected fractures

2022 ◽  
Author(s):  
Pouria Aghajannezhad ◽  
Mathieu Sellier
Keyword(s):  
Surface Roughness ◽  
Hydraulic Resistance ◽  
Flow Rate ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Roughness Coefficient ◽  
Computationally Efficient ◽  
Navier Stokes Equations ◽  
Discrete Fracture Networks ◽  
The Impact

Abstract We present a novel computationally efficient approach for investigating the effect of surface roughness on the fluid flow in discrete fracture networks at low Reynolds number. The effect of parallel and series fracture arrangements on the flow rate and hydraulic resistance was studied numerically by patching Hele-Shaw (HS) cells to represent the network. In this analysis, the impact of surface roughness was studied in different arrangements of the network. For this aim, four models with different sequences of fracture connections were studied. The validity of the models was assessed by comparing the results with solutions of the full Navier-Stokes equations (NSE). The approximate hydraulic resistance and flow rate calculated by the HS method were found to be in good agreement with the NSE (less than 7% deviation). Results suggest a quadratic relationship between the network hydraulic resistance and the joint roughness coefficient (JRC). Notably, an increase in surface roughness caused a growth in hydraulic resistance and a fall in flow rate. Further insight was provided by drawing an analogy between resistors in electrical circuits and fractures in networks.

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