Velocity Exponent Research Articles

Heat transfer over a stretching surface with variable heat flux in micropolar fluids

Heat transfer over a stretching surface with uniform or variable heat flux in micropolar fluids is investigated in this Letter. The boundary layer equations are transformed into ordinary differential equations, and then they are solved numerically by a finite-difference method. The effects of the material parameter K, Prandtl number Pr, velocity exponent parameter m, and heat flux exponent parameter n on the heat transfer characteristics are studied. It is found that the local Nusselt number is higher for micropolar fluids compared to Newtonian fluids.

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet

An analysis is made for the steady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically conducting fluid over a stretching vertical sheet in its own plane. The stretching velocity, the surface temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The transformed boundary layer equations are solved numerically for some values of the involved parameters, namely the magnetic parameter M, the velocity exponent parameter m, the temperature exponent parameter n and the buoyancy parameter λ, while the Prandtl number Pr is fixed, namely Pr = 1, using a finite difference scheme known as the Keller-box method. Similarity solutions are obtained in the presence of the buoyancy force if n = 2m−1. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M increases for fixed λ and m. For m = 0.2 (i.e. n = −0.6), although the sheet and the fluid are at different temperatures, there is no local heat transfer at the surface of the sheet except at the singular point of the origin (fixed point).

Effects of magnetic field and suction/injection on convection heat transfer of non-Newtonian power-law fluids past a power-law stretched sheet with surface heat flux

The problem of magneto-hydrodynamic flow and heat transfer of an electrically conducting, non-Newtonian power-law fluid past a stretching sheet in the presence of a transverse magnetic field is analyzed. The surface of the stretching sheet is assumed to move with a power-law velocity and subject to uniform surface heat flux. The effects of suction or injection at the surface are considered. The resulting governing equations are transformed into nonlinear ordinary differential equations using appropriate transformations and then solved numerically based on central-difference approximations. The solution is found to be dependent on five governing parameters including the magnetic field parameter, the power-law fluid index, the sheet velocity exponent, the suction/blowing parameter, and the generalized Prandtl number. A systematical study is carried out to illustrate the effects of these major parameters on the sheet surface temperature, fluid temperature distributions in the boundary layer, the skin-friction coefficient and the local Nusselt number.

High pressure testing sand erosion in 3D flow channels and correlation with CFD

An experimental approach to accelerated laboratory testing sand erosion in high pressure flow channels of complicated 3D configurations was developed. The channels were designed for erosion-resistant valves in natural gas and oil severe service applications. An analysis of equations of the particle motion in turbulent flow defined a method for scaling the channel dimensions, the erodent size and fluid parameters in order to simulate erosion in the field by using an environmentally-friendly fluid at the laboratory conditions. A testing facility that operated at 40 bar of nitrogen pressure with silica sand as an erodent was built and calibrated. The flow channels were manufactured from organic glass (PMMA) in separate plates that facilitated weight loss measurements in different parts of the channels as well as erosion visualization. The particular grade of glass was selected after testing erosion in a range of materials in order to find close resemblance to stainless steel in terms of both the erosion rate angle function and the velocity exponent. The test results were used for validation of a CFD model of the particles motion and for understanding the reliability of the CFD predictions for the valve lifetime assessment. The CFD model was found to reproduce the complicated erosion patterns and actual weight losses on early stages of erosion very well. CFD predictions were reasonably accurate even as erosion progressed if integral values of the computed erosion rate over the erosion scars were used.

Sand erosion testing of novel compositions of hard ceramics

The sand erosion rates of novel compositions of hard ceramics such as tungsten carbide, silicon nitride, silicon carbide, and partially stabilized zirconia have been tested in air-sand erosion facilities. A new testing facility that ensured stable and reproducible erosion testing with sand velocities and concentrations up to 250 m/s and 5 wt% in air, respectively, was built at IMI. Special rig design features allowed accurate sand consumption monitoring during each test. High-speed photography was used to determine the sand velocity distribution at each test setting. Parallel testing of these materials in the benchmark facility at the University of Southampton elucidated the test parameters critical for reproducibility of the results in different test configurations. High-speed visualization of the sand impact on the material surface demonstrated fragmentation of almost every sand particle in the range of velocities of 60 m/s and higher. The evidence of extensive fragmentation contributed to understanding the origin of the erosion resistance of hard ceramics. The values of the velocity exponent ( n) were typical of those reported in literature. However, unlike the expected erosion behavior of a brittle material, an ultrafine grained binderless tungsten carbide was more erosive at low impact angle.

Depinning exponents of the driven long-range elastic string

We perform a high-precision calculation of the critical exponents for the long-range elasticstring driven through quenched disorder at the depinning transition, at zero temperature.Large-scale simulations avoid finite-size effects and improve accuracy. We explicitlydemonstrate the equivalence of fixed-velocity and fixed-driving-force simulations. Theroughness, growth, and velocity exponents are calculated independently, and thedynamic and correlation length exponents are derived. The critical exponents satisfy knownscaling relations and agree well with analytical predictions.

Effect of near‐fault ground motion and damper characteristics on the seismic performance of chevron braced steel frames

AbstractThis study is aimed at comparing the seismic performance of steel chevron braced frames (CBFs) with and without fluid viscous dampers (FVDs) as a function of the characteristics of the near‐fault (NF) ground motion and FVD parameters. For this purpose, comparative nonlinear time history (NLTH) analyses of single and multiple storey CBFs with and without FVDs are conducted using NF ground motions with various velocity pulse periods scaled to have small, moderate and large intensities. Additionally, NLTH analyses of single‐ and four‐storey CBFs with FVDs are conducted to study the effect of the damping ratio and velocity exponent of the FVD on the seismic performance of the frames. The analyses results revealed that the seismic performance of the CBFs without FVDs is very poor and sensitive to the velocity pulse period and the intensity of the NF ground motion due to brace‐buckling effects. Installing FVDs into the CBFs significantly improved their seismic performance by maintaining their elastic behaviour. Furthermore, FVDs with smaller velocity exponents and larger damping ratio are observed to be more effective in improving the seismic performance of the CBFs subjected to NF earthquakes. However, FVDs with damping ratios larger than 50% do not produce significant additional improvement in the seismic performance of the CBFs. Copyright © 2006 John Wiley & Sons, Ltd.

Analytical derivation of at-a-station hydraulic–geometry relations

This paper uses generalized expressions for both cross-section geometry and hydraulics (generalization of the Chezy and Manning relations) to derive explicit equations for the exponents and coefficients in the power-law at-a-station hydraulic-geometry relations. The exponents are shown to depend only on the depth exponent in the hydraulic relation (p) and the exponent that reflects the form of the cross-section (r). The coefficients depend on p and r, but also on the slope exponent in the generalized hydraulic relation and on the physical characteristics of the section: bankfull width, bankfull maximum depth, hydraulic conductance, and slope. The theoretical ranges of coefficient and exponent values derived herein are generally consistent with the averages and individual observed values reported in previous studies. However, observed values of the exponents at particular cross-sections commonly fall outside the theoretical ranges. In particular, the observed value of the velocity exponent m is commonly greater than the theoretical value, suggesting that hydraulic conductance often increases more strongly with discharge than predicted by the assumed hydraulic relations. The developments presented here provide new theoretical insight into the ways in which hydraulic and geometric factors determine hydraulic geometry. This insight should help to explain the variation of at-a-station hydraulic geometry and may facilitate prediction of hydraulic geometry at river reaches where detailed measurements are unavailable.

Seismic performance of chevron braced steel frames with and without viscous fluid dampers as a function of ground motion and damper characteristics

This study is aimed at comparing the seismic performance of steel chevron braced frames (CBFs) with and without viscous fluid dampers (VFDs) as a function of the intensity and frequency characteristics of the ground motion and VFD parameters. For this purpose, comparative nonlinear time history (NLTH) analyses of single and multiple story CBFs with and without VFDs are conducted using ground motions with various frequency characteristics scaled to represent small, moderate and large intensity earthquakes. Additionally, NLTH analyses of single and multiple story CBFs with VFDs are conducted to study the effect of the damping ratio and velocity exponent of the VFD on the seismic performance of the frames. The analysis results revealed that the seismic performance of the CBFs without VFDs is very poor and sensitive to the frequency characteristics and intensity of the ground motion due to brace buckling effects. Installing VFDs into the CBFs significantly improved their seismic performance by maintaining their elastic behavior. Furthermore, VFDs with smaller velocity exponents and larger damping ratio are observed to be more effective in improving the seismic performance of the CBFs. However, VFDs with damping ratios larger than 50% do not produce significant additional improvement in the seismic performance of the CBFs.

Scaling Laws and a Method for Identifying Components of Jet Noise

It is well established that there are three principal jet noise components for imperfectly expanded supersonic jets. However, to this date there has been no reliable and practical method for identifying the individual components. First, new scaling laws for the turbulent mixing noise component are developed from a comprehensive experimental database generated by the author. The scaling laws are based on the explicit recognition that a) the variation of the overall sound power level with jet velocity has a weak dependence on jet stagnation temperature ratio; b) the variation of the overall sound pressure level with velocity at every radiation angle is a function of jet stagnation temperature ratio. Therefore, the behavior of the turbulent mixing noise at each radiation angle can be characterized by the two independent parameters: the velocity ratio and the stagnation temperature ratio. These two findings set this study apart from past approaches and form the basis for the methodology developed here. It is demonstrated clearly that there is excellent collapse of the mixing noise spectra over the entire frequency range. Once the normalized or master spectra for the mixing noise are established, it is a trivial matter to subtract these from the total measured spectra to obtain the shock-associated noise. For moderately imperfectly expanded heated supersonic jets, the mixing noise component has the same spectral level as the shock-associated noise, over a wide range of higher frequencies. At the lower radiation angles in the forward quadrant, there is a substantial decrease in the values of the velocity exponents as the stagnation temperature ratio is increased. Proceeding aft, the values start to rise and in the peak sector of noise radiation, the velocity exponent becomes less sensitive to jet stagnation temperature ratio unlike at lower angles, and stays close to the values for the unheated jet.

R-410A and R-404A real gas thermodynamic relations and their application for predicting exergy efficiency in vapor compression heat pumps

Enthalpy and entropy equations, as these resulted from the Martin-Hou Equation of State, are presented for the promising mixtures R-404A and R-410A that replace the HCFC-22 in refrigerator and heat pump systems. Based on these equations, a model was developed to simulate the relevant thermodynamic heat pump cycle for vapour compression systems. The variation of exergy efficiency factor, COP and exergy flow is outlined. Moreover focusing on the partial derivatives of pressure, on the real gas heat capacity at constant volume and on real gas heat capacity at constant pressure, useful characteristics such as sound velocity and isentropic exponents are derived and plotted in charts, for a wide area of state conditions.

Passive hybrid systems for earthquake protection of cable-stayed bridge

The performance of passive hybrid control systems for the earthquake protection of a cable-stayed bridge under real earthquake ground motion is presented. A simplified lumped mass finite-element model of the Quincy Bay-view Bridge at Illinois is used for the investigation. A viscous fluid damper (VFD) is used as a passive supplemental energy dissipation device in association with elastomeric and sliding isolation systems to form a passive hybrid control system. The effects of non-linear viscous damping of the VFD on the seismic response of an isolated cable-stayed bridge are examined by taking different values of velocity exponent of the damper. Further, the influence of a variation in viscous damping on the response of the isolated bridge is also investigated. The seismic response of the bridge with passive hybrid systems is compared with the corresponding response of the bridge with only isolation systems, as well as with the uncontrolled bridge. The results of the investigation show that the addition of supplemental damping in the form of a viscous fluid damper significantly reduces the earthquake response of an isolated cable-stayed bridge. The non-linear viscous damping is found to be more effective in controlling the peak isolator displacement of the isolated bridge while simultaneously limiting the base shear in towers.

Dimensional Analysis of Jet Noise Data

*A formula for scaling laboratory model jet noise data to that of a full size jet engine is established. This is done by dimensional analysis and the Buckingham P theorem. It is well known that the noise intensity radiated by a jet varies as a high power of its velocity. This power law dependence is supported by theory and experiment. The most famous power law is the Lighthill U 8 law. In this work, a dimensionless form of the power law is sought and developed. Through the use of this nondimensional form power law, a “hot jet” limit is found at high jet temperature. In the hot jet limit, the velocity exponent and the proportionality constant of the power law are insensitive to further increase in jet temperature. This is a somewhat surprising result. Experimentally, it has been observed that seasonal temperature variation can lead to a 1.5 to 2.0 dB change in jet noise intensity. Here, environmental effects on jet noise such as seasonal and altitude variations are studied through results established by dimensional analysis. Finally, a way to scale jet mixing noise from perfectly expanded jets to shock containing jets is proposed.

Investigation of downstream and sideline subsonic jet noise using Large Eddy Simulation

The sound fields radiated by Mach number 0.6 and 0.9, circular jets with Reynolds numbers varying from 1.7×103 to 4×105 are investigated using Large Eddy Simulations. As the Reynolds number decreases, the properties of the sound radiation do not change significantly in the downstream direction, whereas they are modified in the sideline direction. At low Reynolds numbers, for large angles downstream from the jet axis, the acoustic levels are indeed remarkably lower and a large high-frequency part of the sound spectra vanishes. For all Reynolds numbers, the downstream and the sideline sound spectra both appear to scale in frequency with the Strouhal number. However their peak amplitudes vary following two different velocity exponents according to the radiation direction. The present observations suggest the presence of two sound sources: a Reynolds number-dependent source, predominant for large radiation angles, connected to the randomly-developing turbulence, and a deterministic source, radiating downstream, related to a mechanism intrinsic to the jet geometry, which is still to be comprehensively described. This view agrees well with the experimental results displaying two distinguishable components in turbulent mixing noise [1, 2].

A self-similar solution for forced convection boundary layer flow of a FENE-P fluid

Boundary layer flow of a viscoelastic fluid subjected to an external pressure gradient, surface mass flux and nonisothermal surface temperature is considered. We show that for a FENE-P fluid, the flow is governed by a generalized Falkner–Skan equation which admits a similarity solution only when the streamwise coordinate exponent of the inviscid velocity m = 1 / 3 (i.e. for axisymmetric stagnation point flow). We find that skin friction drag decreases while heat transfer at the plate increases as polymer extensibility decreases.

Delayed Fatigue of Hydroxy- and Fluorhydroxyapatite Ceramics in Simulated Body Fluid

Ultrafine hydroxyapatite (HA) and fluorhydroxyapatite (FHA) powders were synthesized and dense bioceramic samples were fabricated thereof. The samples were treepoint bend tested in different environments, i.e. in ambient air, distilled water and simulated human saliva, in the wide deformation rate range. Weibull’ statistics test was performed under standard testing conditions but in different media. The stress velocity exponent was evaluated from the dynamic fatigue testing data. The mean strength is shown to decrease when both ceramics are exposed to water or to simulated saliva. HA ceramics is more susceptible to the environment compared to FHA ceramics, due to the later is less subjected to the stress corrosion. Fracture surface observations revealed the crack propagation is of mixed trans- and intergranular mode. Strength distribution changes from uni-modal in air environment to bimodal in harsh conditions of water and saliva, indicating slow increment of flaw size in ceramics. Crack velocity exponent values correspond to transient region from dissociative chemisorption to ion solvation mechanisms of stress corrosion in both HA and FHA ceramics. Generally, FHA ceramics is considered to be much more reliable for application in bone defects replacement or dental reconstruction.

Critical exponents of the driven elastic string in a disordered medium

We analyze the harmonic elastic string driven through a continuous random potential above the depinning threshold. The velocity exponent beta = 0.33(2) is calculated. We observe a crossover in the roughness exponent zeta from the critical value 1.26 to the asymptotic (large force) value of 0.5. We calculate directly the velocity correlation function and the corresponding correlation length exponent nu = 1.29(5), which obeys the scaling relation nu = 1/(2 - zeta), and agrees with nu(FS), the finite-size-scaling exponent of fluctuations in the critical force. Surprisingly, the velocity correlation function is nonuniversal at short distances.

Explicit predictability and dispersion scaling exponents in fully developed turbulence

We apply a simple method to provide explicit expressions for different scaling exponents in intermittent fully developed turbulence, that before were only given through a Legendre transform. This includes predictability exponents for infinitesimal and noninfinitesimal perturbations, Lagrangian velocity exponents, and dispersion exponents. We obtain also new results concerning inverse statistics corresponding to exit-time moments.

Laminar Mixed Convection Adjacent to Vertical Continuously Stretching Sheets With Variable Viscosity and Variable Thermal Diffusivity

The paper presents a study of the laminar mixed convection adjacent to vertical continuously stretching sheets, taking into account the effects of variable viscosity and variable thermal diffusivity. The similarity solutions are reported for isothermal sheet moving with a velocity of the form uw=Bx0.5 and a continuous linearly stretching sheet with a linear surface temperature distribution. The equations of conservation of mass, momentum and energy, which govern the flow and heat transfer, are solved numerically by using the shooting method. The numerical results obtained for the flow and heat transfer characteristics reveal many interesting behaviors. The numerical results show that, variable viscosity, variable thermal diffusivity, the velocity exponent parameter, the temperature exponent parameter and the buoyancy force parameter have significant influences on the velocity and temperature profiles, shear stress and Nusselt number in two cases air and water.

Heat transfer correlations for open-cellular porous materials

A general correlation for volumetric heat transfer coefficient between stream of air and open-cellular porous materials was derived utilizing experimental data obtained by several researchers. The derived correlation is written in form of h v = ( A/ D s 2− n ) u n . Here, h v denotes the volumetric heat transfer coefficient, A is the constant, n is the velocity exponent, u is the mean fluid velocity and D s is the equivalent strut diameter of Dul'nev's unit cell for open-cell foam. The parameters, A and n, were determined by a least-square fit of the expression to the above-mentioned experimental data to give A = 13.0 and n = 0.791. Moreover, from the h v− u correlation thus determined, the following Nusselt vs. Reynolds number heat transfer correlation was proposed: Nu s = 0.124( Re s Pr) 0.791, where Nu s represents the Nusselt number defined by h v D s 2/ k f, Re s denotes the Reynolds number defined by uD s/ ν f, Pr is the Prandtl number, k f is the thermal conductivity of fluid and ν f is the kinetic viscosity of fluid. It is found that this correlation approximates 78.1% of the available experimental data with an error of less than ± 40%.