Semi-empirical Friction Research Articles

Frictional resistance investigation of sCO2 and a semi-empirical friction factor correlation based on wall-of-the-law

The flow resistance characteristics of variable property fluids, particularly supercritical fluids, such as supercritical CO2 (sCO2), play a crucial role in the design, operation control, and simulation of energy systems. However, drastic changes in thermophysical properties near the pseudo-critical regime under various boundary conditions make it challenging to find suitable theoretical and correlation models that can accurately predict their friction factors.In this study, the experimental investigations on the frictional resistance characteristics of upward sCO2 flow under different heat flux and tube wall roughness is conducted. The results show that as the heat flux increases, sCO2′s friction factor decreases under the same reference temperature, and the decrease becomes less significant with increasing tube wall roughness. The SST k-ω simulation attributes this phenomenon to the suppressed sensitivity of turbulence velocity fluctuations to thermal boundary conditions in high roughness pipes. Additionally, the experiment shows that near the pseudo-critical point, sCO2′s friction factor abnormally increases, which can be reasonably explained by the density fluctuation theory. A new semi-empirical expression for the variable property fluid's friction factor by combining the law-of-the-wall is derived for the first time, and the correlation is regressed based on the experimental and literature results. The new correlation exhibits good predicting performance, with 94% of predictions falling within ±20% absolute deviation from the original experimental results. This result confirms consistent flow resistance characteristics between supercritical flow and subcritical single-phase flow.

A Semi-empirical correlation for stratified two-phase flow friction factors

The optimal design of two-phase flow pipes depends on various variables. Pressure drop and liquid hold-up are essential parameters in the appropriate design of pipes. These parameters can be estimated by numerical simulation of pipes. However, the simulation strongly depends on both phase frictions. Frictions are commonly calculated using friction factors, and various empirical correlations have been proposed to calculate friction factors, but most of these correlations are dependent on the experimental conditions.The present study proposes a semi-empirical friction factor model by modifying an existing model in the literature for stratified two-phase flows. Experimental data from various laboratories are taken to validate the interface shear stress, velocity profile and pressure gradient. Compared with previous models, the predicted velocity profiles and shear stresses are in better agreement with the experimental data.

A Novel Semiemperical Friction Coefficient Model Between Needle and Polyvinyl Alcohol Tissue Phantom and Its Validation by Using Computational Inverse Technique

Abstract Needle–tissue interactive force is vital for developing a virtual simulation and planning system (SPS) and optimizing needle control strategy, wherein the friction coefficient is an important parameter but difficult to pre-determine. The existing studies on friction coefficient estimation were lack of qualitative analysis and did not consider the effect of normal pressure and interactive velocity, which may lead to the inaccuracy of the friction calculation. In this paper, we proposed a novel semiempirical friction coefficient model based on the modified classical elastic friction theory that constructs the relationship between the friction coefficient and parameters such as the normal pressure and velocity. The proposed friction coefficient model is validated by using the computational inverse technique based on coupled finite element material point (CFEMP) contact algorithm. The results show that the friction coefficient between the needle and polyvinyl alcohol (PVA) tissue phantom varies from 0.091 to 0.242 with different normal pressure (7.95–17.80 kPa) and insertion velocity (1–9 mm/s), which agrees well with the experimental data. The results of the paper can help to better understand the intrinsic characteristics of the needle–tissue interactions and optimal needle actuation strategies.

Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

An improved semi-empirical friction model for gas-liquid two-phase flow in horizontal and near horizontal pipes

ABSTRACT Pressure drop and liquid hold-up are two very important fluid flow parameters in design and control of multiphase flow pipelines. Friction factors play an important role in the accurate calculation of pressure drop. Various empirical and semi-empirical closure relations exist in the literature to calculate the liquid-wall, gas-wall and interfacial friction in two-phase pipe flow. However most of them are empirical correlations found under special experimental conditions. In this paper by modification of a friction model available in the literature, an improved semi-empirical model is proposed. The proposed model is incorporated in the two-fluid correlations under equilibrium conditions and solved. Pressure gradient and velocity profiles are validated against experimental data. Using the improved model, the pressure gradient deviation from experiments diminishes by about 3%; the no-slip condition at the interface is satisfied and the velocity profile is predicted in better agreement with the experimental data.

IMEX_SfloW2D 1.0: a depth-averaged numerical flow model for pyroclastic avalanches

Abstract. Pyroclastic avalanches are a type of granular flow generated at active volcanoes by different mechanisms, including the collapse of steep pyroclastic deposits (e.g., scoria and ash cones), fountaining during moderately explosive eruptions, and crumbling and gravitational collapse of lava domes. They represent end-members of gravity-driven pyroclastic flows characterized by relatively small volumes (less than about 1 Mm3) and relatively thin (1–10 m) layers at high particle concentration (10–50 vol %), manifesting strong topographic control. The simulation of their dynamics and mapping of their hazards pose several different problems to researchers and practitioners, mostly due to the complex and still poorly understood rheology of the polydisperse granular mixture and to the interaction with the complex natural three-dimensional topography, which often causes rapid rheological changes. In this paper, we present IMEX_SfloW2D, a depth-averaged flow model describing the granular mixture as a single-phase granular fluid. The model is formulated in absolute Cartesian coordinates (whereby the fluid flow equations are integrated along the direction of gravity) and can be solved over a topography described by a digital elevation model. The numerical discretization and solution algorithms are formulated to allow for a robust description of wet–dry conditions (thus allowing us to accurately track the front propagation) and an implicit solution to the nonlinear friction terms. Owing to these features, the model is able to reproduce steady solutions, such as the triggering and stopping phases of the flow, without the need for empirical conditions. Benchmark cases are discussed to verify the numerical code implementation and to demonstrate the main features of the new model. A preliminary application to the simulation of the 11 February pyroclastic avalanche at the Etna volcano (Italy) is finally presented. In the present formulation, a simple semi-empirical friction model (Voellmy–Salm rheology) is implemented. However, the modular structure of the code facilitates the implementation of more specific and calibrated rheological models for pyroclastic avalanches.

Effect of roughness on water flow through a synthetic single rough fracture

A single fracture is usually idealized theoretically as smooth parallel plates, but the real fractures are rough-walled with points of contact. Though relative roughness is considered in quantifying the flow through a single rough fracture (SRF) previously, additional factors such as the distribution of rough elements and bending degree of streamlines should be considered in order to obtain more accurate results. Semiempirical friction factor (f) and discharge per unit width (q) equations are first deduced taking relative roughness, roughness elements distribution and streamline reattachment length into consideration. A horizontal SRF model was then set up and a series of experiments and simulations were performed. Main conclusions are drawn: Recirculation of streamlines arises in the rough element and the intensity of the recirculation increases with the angle from which the streamlines enter into the rough elements and Reynolds number (Re); streamlines are discontinuously distributed when asperity height is large and nonlinear flow occurs; the nonlinearity of the flow increases with the increasing the asperity height and Re; the critical value of related roughness used to judge whether the influence of roughness on water flow through a SRF can be ignored or not should be much lower than 0.033; the revised f and q equations under laminar flow through a SRF are proved to be better when calculating the f and q values.

Development of a semi-empirical friction model in automotive driveshaft joints

High speed and sport utility vehicles with large joint articulation angle demand lower friction in automotive driveshaft joints to meet noise and vibration comfort levels. Thus a more thorough understanding of internal friction characteristics and mechanisms is required. In this paper, a friction model in automotive driveshaft joints was developed through the use of test data from an instrumented Constant Velocity (CV) joint friction apparatus with actual driveshaft assemblies. Experiments were conducted under different realistic operating conditions of oscillatory speeds, CV joint articulation angles, lubrication, and torque. The experimental data was used to develop a physics-based semi-empirical CV joint internal friction model as a function of different CV joint operating parameters. It was found that the proposed friction model captures the experimental results well. Also the friction model estimates the generated axial force (GAF) in tripod CV joints well, which is the main source of force that causes vehicle vibration problems.

A model for simulating the instantaneous crank kinematics and total mechanical losses in a multicylinder in-line engine

A two-degree-of-freedom dynamic model is constructed to simulate the instantaneous crank kinematics and total mechanical losses arising in a multicylinder gasoline engine coupled to a dynamometer. The simulation model is driven using specified cylinder gas pressures, and loaded by nominal brake torque and total friction losses. Existing semi-empirical torque loss models (based on calibrated single-cylinder diesel engine data) are used to account for the instantaneous friction losses in the piston-ring assembly, in bearings, and in auxiliaries. The model is specialized to the simulation of crank kinematics and matched brake torque for a three-cylinder in-line direct injection spark ignition (DISI) engine, without a gearbox. This allows the total friction loss to be separated from the brake torque for an engine not fitted with the very large number of sensors otherwise needed to calibrate analytical friction models. An equivalent simulation model is also constructed using GT-Crank, which excludes explicit reference to friction. In using both models to simulate steady state operation at a specified mean engine speed, the output torque is matched by iteration. The GT-Crank model necessarily compensates for internal losses by exaggerating the total output torque. Both simulation models are compared with measured crank kinematics and brake torque obtained from a dynamometer-loaded I3 DISI engine. The paper shows that by comparing the matched output torque from simulation with the measured output torque from the engine, the proposed model gives a very good high-speed prediction of the total mechanical losses. At low speed, the instantaneous model is still not accurate. It is also shown, however, that apart from the no-load condition, use of an average torque to compensate for friction (as in GT-Crank) is wholly acceptable for simulating instantaneous crank kinematics. This is the first reported instance of a simulation model (which includes the particular form of semi-empirical friction loading) being comprehensively compared and verified using multicylinder DISI engine data.

Augmented heat transfer in triangular ducts with full and partial ribbed walls

Fully developed heat transfer coefficients and friction factors in triangular ducts with full and partial ribbed walls were experimentally obtained for Reynolds numbers between 10-10. The vertex corners of the triangular ducts were 90, 55, and 35 deg. Five rib configurations were tested: full and partial 90-deg transverse ribs, full and partial 45-deg crossed ribs on three-wall, and partial 45-deg crossed ribs on two-wall of the triangular duct. The results show that heat transfer coefficients were higher on the ribbed walls and the 90-deg vertex corner of the triangular duct than on the 55-deg vertex corner, and subsequently higher than those on the 35-deg vertex corner. The heat transfer coefficients and friction factors in triangular ducts with partial ribbed walls (90or 45-deg ribs) were 10% higher than those with full ribbed walls. The results also show that heat transfer coefficients and friction factors were higher in triangular ducts with 90-deg transverse ribs (full or partial) than those with 45-deg crossed ribs. The semi-empirical friction and heat transfer correlations in ribbed triangular ducts were obtained.

Heat Transfer and Friction in Rectangular Channels With Ribbed or Ribbed-Grooved Walls

The effect of compound turbulators on friction factors and heat transfer coefficients in rectangular channels with two opposite ribbed-grooved walls was determined for a Reynolds number range of 10,000 to 50,000. The channel width-to-height ratio was 10. The fully developed heat transfer coefficients and friction factors on the ribbed-grooved and smooth side walls of each test channel were measured for six rib-groove spacings (p/e = 8, 10, 15, 20, 25, and 30). The fully developed friction and heat transfer in similar aspect ratio rectangular channels with two opposite ribbed walls with two rib spacings (p/e = 8.5 and 11.5) was also measured for comparison. The results show that the heat transfer performance of the rib-groove roughened duct is much better than the rib roughened duct. The rib-groove roughened wall enhances the heat transfer 3.4 times and pays 6 times the pressure drop penalty, whereas the rib roughened wall, with similar rib height and rib spacing, enhances the heat transfer 2.4 times and pays about the same pressure drop penalty. Semi-empirical friction and heat transfer correlations were obtained. Flow measurements show that the roughened ducts have flatter velocity profiles than the smooth duct and rib-groove roughened duct produces higher turbulence intensity than the rib roughened duct. The flatter velocity profile and higher turbulence intensity are responsible for producing higher heat transfer.

Experimental Study of Friction in a Pneumatic Actuator at Constant Velocity

This paper describes an experimental method of determining sliding friction forces in a pneumatic actuator. Several empirical and semi-empirical friction models are evaluated using measured friction force data. A repeatability study is also performed to qualitatively assess friction randomness and a change in friction regimes.

Augmented heat transfer in rectangular channels of narrow aspect ratios with rib turbulators

The effects of the rib angle-of-attack on the distributions of the local heat transfer coefficient and on the friction factors in short rectangular channels of narrow aspect ratios with a pair of opposite rib-roughened walls are determined for Reynolds numbers from 10 000 to 60 000. The channel width-to-height ratios are 2 4 and 1 4 ; the corresponding rib angles-of-attack are 90°, 60°, 45°, and 30°, respectively. The results indicate that the narrow-aspect-ratio channels give better heat transfer performance than the wide-aspect-ratio channels for a constant pumping power. Semi-empirical friction and heat transfer correlations are obtained. The results can be used in the design of turbine cooling channels of narrow aspect ratios.

A Graphical Representation of Tribological Properties in Polymer-Graphite/Epoxy Sliding

Ultrahigh-molecular-weight polyethylene (UHMWPE) and polycarbonate were slid dry against continuous graphite fiber/epoxy plates in reciprocating multiple-pass tests for different values of fiber orientation, virgin surface roughness, and normal load. Regression equations were developed from the data relating the coefficient of friction and wear rate to fiber orientation and virgin surface roughness. The wear rate and coefficient of friction were plotted versus fiber orientation and virgin surface roughness to form three-dimensional friction and wear “surfaces.” Semiempirical friction and wear “surfaces” were found to be a convenient and compact method of presenting the complex data. Local maximum and minimum points could be easily identified and differences in the tribological properties of different materials became readily apparent. Presented as an American Society of Lubrication Engineers paper at the ASLE/ASME Lubrication Conference in Hartford, Connecticut, October 18–20, 1983