Assumption Of Velocity Research Articles

Large-eddy simulations of velocity and temperature fluctuations in hot and cold fluids mixing in a tee junction with an upstream straight or elbow main pipe

Thermal striping resulting in thermal fatigue is an important safety issue for nuclear power plants. In this work, temperature and velocity fluctuations in hot and cold fluids mixing in a tee junction with the main pipe connected either to an upstream straight or elbow pipe have been numerically predicted using large-eddy simulations (LES) on the FLUENT platform with the assumption of fully-developed velocity at both main and branch pipe inlets. The numerical results for the case with an upstream straight pipe were found to be in reasonable agreement with the available experimental data. The reason for the small discrepancy between the numerical results and experimental data can be attributed to the turbulence velocity being 10% of the fully-developed velocity at the main and branch pipe inlets in the LES calculations, while in the experiments the turbulence velocity was about 10% of the average velocity upstream of the tee junction. The simulated normalized mean and root-mean square (RMS) temperatures and the velocities at both straight and elbow tees were then compared, as well as the power spectrum densities (PSD) of the temperature fluctuations. The elbow pipe upstream of the main pipe has a significant influence on the mixing, resulting in increased temperature and velocity fluctuations. The flow pattern of the elbow tee deviates from the wall jet due to the secondary flow in the upstream elbow pipe.

Dynamics of a spacecraft with large flexible appendage constrained by multi-strut passive damper

This paper is concerned with the dynamics of a spacecraft with multi-strut passive damper for large flexible appendage. The damper platform is connected to the spacecraft by a spheric hinge, multiple damping struts and a rigid strut. The damping struts provide damping forces while the rigid strut produces a motion constraint of the multibody system. The exact nonlinear dynamical equations in reducedorder form are firstly derived by using Kane’s equation in matrix form. Based on the assumptions of small velocity and small displacement, the nonlinear equations are reduced to a set of linear second-order differential equations in terms of independent generalized displacements with constant stiffness matrix and damping matrix related to the damping strut parameters. Numerical simulation results demonstrate the damping effectiveness of the damper for both the motion of the spacecraft and the vibration of the flexible appendage, and verify the accuracy of the linear equations against the exact nonlinear ones.

The variance of convection velocity in the turbulent boundary layer and its effect on coherence length

The Efimtsov model of coherence length and the Corcos cross spectrum model are commonly used to define the power spectra of the turbulent boundary layer near the wall. The models are useful for defining the pressure fields acting on structures such as aircraft fuselage and ship hulls as they move through fluid. In an effort to establish the validity of the models, the spectral definitions were used to synthesize time series data whose properties could then be compared to the actual data from which the model parameters were derived. Analysis of the synthesized time data indicated that the data contained coherence lengths longer than those specified in the models. The longer coherence lengths are shown to be related to the assumption of constant convection velocity that is fundamental to the Corcos model. A time domain technique is introduced by which the instantaneous convection velocity can be measured. Using this technique, statistics on the convection velocity for wall pressure data acquired during flight tests are shown to be normally distributed. Time data produced using a normally distributed convection velocity contains the specified coherence length, confirming that the assumption of constant convection velocity in the Corcos model was the source of the error. The coherence decay caused by convection velocity variance is shown to be Gaussian. A model is derived which divides the coherence decay into an exponential structural decay term and a Gaussian phase decay term. This is shown to be a good model for the coherence decay, except for frequencies around the peak in the power spectrum. The structural decay term is further divided into exponential and rectangular terms to represent inner layer and outer layer processes, respectively. The partitioned model is shown to correctly describe the coherence decay for the entire frequency band and provides a measure of the allocation of power between the inner and outer layer processes. It is concluded that the variance in the convection velocity has a significant effect on the decay of coherent power in the wall pressure of the turbulent boundary layer.

Experimental and Numerical Study on Slamming Impact

This paper presents the results of experimental and numerical research on the slamming phenomenon. Two experimental techniques were proposed in this study. The traditional free drop tests were carried out. However, the free drop tests done in this study using an LM guide showed excellent repeatability, unlike those of other researchers. The coefficients of variation for the drop test done in this experiment were less than 0.1. The other experimental technique proposed in this study was a novel concept that used a pneumatic cylinder. The pneumatic cylinder could accelerate the specimen over a very short distance from the free surface. As a result, high rates of repeatability were achieved. In the numerical study, the development of in-house code and utilization of commercial code were carried out. The in-house code developed was based on the boundary element method. It is a potential code. This was mostly applied to the computation of the wedge entry problem. The commercial code utilized was FLUENT. Most of the previous slamming research was done under the assumption of a constant body velocity all through the impact process, which is not realistic at all. However, the interaction of a fluid and body were taken into account by employing a user-defined function in this study. The experimental and numerical results were compared. The in-house code based on BEM showed better agreement than that of the FLUENT computation when it cames to the wedge computation. However, the FLUENT proved that it could deal with a very complex geometry while BEM could not. The proposed experimental and numerical procedures were shown to be very promising tools for dealing with slamming problems.

Error analysis of the converted wave deduced by equivalent velocity assumption

Based on the assumption of the equivalent velocity and offset, the converted wave travel-time equation, which has a double square root due to the asymmetric ray-path of the down-going P-wave and the up-coming S-wave, can be transformed into a single square root equation if the common scatterpoint (CSP) gathers are binned. This method simplifies the equation and decreases the errors of converted wave migration transferred by P-wave velocity error, compared to the equivalent offset method (EOM) migration proposed by Bancroft, Geiger and Foltinek . In this paper, the errors caused by the introduction of equivalent velocity for the PS-wave are analysed in detail. The discrete errors and effects introduced by discretization of the equivalent offset are presented, and finally the conditions for applying CSP gathers for PS-wave processing under the control of reasonable error limits are derived.

Multi-material pressure relaxation methods for Lagrangian hydrodynamics

In Arbitrary Lagrangian–Eulerian (ALE) methods for hydrodynamics with several materials, multiple-material Lagrangian cells invariably arise when the flow field is remapped onto a new mesh. One must close the system of equations for multi-material cells; this, in effect, constitutes a model—either explicit or implicit—for the sub-scale dynamics. We discuss several different multi-material closure model algorithms for Lagrangian hydrodynamics under the assumption of a single velocity for 1D, multiple-material cells. Russian researchers at the All-Russian Research Institute of Experimental Physics (VNIIEF) have developed several models, which we describe in some detail; recent work by US researchers was developed independent of the details of these models. This work contains a comparison of these different approaches, which we believe is unique in the literature. We compare these methods on two standard test problems and discuss the results.

ON THE LOCAL DARK MATTER DENSITY

An analysis of the kinematics of 412 stars at 1-4 kpc from the Galactic mid-plane by Moni Bidin et al. (2012) has claimed to derive a local density of dark matter that is an order of magnitude below standard expectations. We show that this result is incorrect and that it arises from the assumption that the mean azimuthal velocity of the stellar tracers is independent of Galactocentric radius at all heights. We substitute the assumption, supported by data, that the circular speed is independent of radius in the mid-plane. We demonstrate that the assumption of constant mean azimuthal velocity is implausible by showing that it requires the circular velocity to drop more steeply than allowed by any plausible mass model, with or without dark matter, at large heights above the mid-plane. Using the approximation that the circular velocity curve is flat in the mid-plane, we find that the data imply a local dark-matter density of 0.008 +/- 0.003 Msun/pc^3 = 0.3 +/- 0.1 GeV/cm3, fully consistent with standard estimates of this quantity. This is the most robust direct measurement of the local dark-matter density to date.

Investigation of Pressure Pulse Distribution in Porous Media

Diffusivity equation commonly used for pressure distribution prediction in porous media results from substituting equation of state and continuity equation in Navier-Stokes momentum equation. From mathematical point of view this equation format shows infinite propagation speed for pressure pulse through porous media, which is physically impossible. This issue may caused by numerous assumptions that has been implemented for developing diffusivity equation. However, if we omit two main assumptions of steady state condition and constant velocity and consider linear approximation for velocity field, the pressure propagation differential equation would be hyperbolic which is called Telegraph Equation. The propagation speed is limited for this equation. In this work, these equations are compared in prediction of pressure pulse propagation in Cartesian coordination with different parameters. The results show that the telegraph equation has minor correction in some cases as: far distances from pressure pulse source, when the fluid has high viscosity and for the rocks with low porosity and permeability; so considering common parameters in hydrocarbon reservoirs, the diffusivity equation has sufficient accuracy for reservoir engineering applications.

Improving the time‐machine: estimating date of birth of grade II gliomas

Here we present a model aiming to provide an estimate of time from tumour genesis, for grade II gliomas. The model is based on a differential equation describing the diffusion-proliferation process. We have applied our model to situations where tumour diameter was shown to increase linearly with time, with characteristic diametric velocity. We have performed numerical simulations to analyse data, on patients with grade II gliomas and to extract information concerning time of tumour biological onset, as well as radiology and distribution of model parameters. We show that the estimate of tumour onset obtained from extrapolation using a constant velocity assumption, always underestimates biological tumour age, and that the correction one should add to this estimate is given roughly by 20/v (year), where v is the diametric velocity of expansion of the tumour (expressed in mm/year). Within the assumptions of the model, we have identified two types of tumour: the first corresponds to very slowly growing tumours that appear during adolescence, and the second type corresponds to slowly growing tumours that appear later, during early adulthood. That all these tumours become detectable around a mean patient age of 30 years could be interesting for formulation of strategies for early detection of tumours.

ARRIVAL TIME CALCULATION FOR INTERPLANETARY CORONAL MASS EJECTIONS WITH CIRCULAR FRONTS AND APPLICATION TOSTEREOOBSERVATIONS OF THE 2009 FEBRUARY 13 ERUPTION

A goal of the NASA STEREO mission is to study the feasibility of forecasting the direction, arrival time and internal structure of solar coronal mass ejections (CMEs) from a vantage point outside the Sun-Earth line. Through a case study, we discuss the arrival time calculation of interplanetary CMEs (ICMEs) in the ecliptic plane using data from STEREO/SECCHI at large elongations from the Sun in combination with different geometric assumptions about the ICME front shape (Fixed-\Phi (FP): a point and harmonic Mean (HM): a circle). These forecasting techniques use single-spacecraft imaging data and are based on the assumptions of constant velocity and direction. We show that for the slow (350 km/s) ICME on 2009 February 13-18, observed at quadrature by the two STEREO spacecraft, the results for the arrival time given by the HM approximation are more accurate by 12 hours than those for FP in comparison to in situ observations of solar wind plasma and magnetic field parameters by STEREO/IMPACT/PLASTIC, and by 6 hours for the arrival time at Venus Express (MAG). We propose that the improvement is directly related to the ICME front shape being more accurately described by HM for an ICME with a low inclination of its symmetry axis to the ecliptic. In this case the ICME has to be tracked to > 30{\deg} elongation to get arrival time errors < 5 hours. A newly derived formula for calculating arrival times with the HM method is also useful for a triangulation technique assuming the same geometry.

Scaling of peak flows with constant flow velocity in random self-similar networks

Abstract. A methodology is presented to understand the role of the statistical self-similar topology of real river networks on scaling, or power law, in peak flows for rainfall-runoff events. We created Monte Carlo generated sets of ensembles of 1000 random self-similar networks (RSNs) with geometrically distributed interior and exterior generators having parameters pi and pe, respectively. The parameter values were chosen to replicate the observed topology of real river networks. We calculated flow hydrographs in each of these networks by numerically solving the link-based mass and momentum conservation equation under the assumption of constant flow velocity. From these simulated RSNs and hydrographs, the scaling exponents β and φ characterizing power laws with respect to drainage area, and corresponding to the width functions and flow hydrographs respectively, were estimated. We found that, in general, φ &gt; β, which supports a similar finding first reported for simulations in the river network of the Walnut Gulch basin, Arizona. Theoretical estimation of β and φ in RSNs is a complex open problem. Therefore, using results for a simpler problem associated with the expected width function and expected hydrograph for an ensemble of RSNs, we give heuristic arguments for theoretical derivations of the scaling exponents β(E) and φ(E) that depend on the Horton ratios for stream lengths and areas. These ratios in turn have a known dependence on the parameters of the geometric distributions of RSN generators. Good agreement was found between the analytically conjectured values of β(E) and φ(E) and the values estimated by the simulated ensembles of RSNs and hydrographs. The independence of the scaling exponents φ(E) and φ with respect to the value of flow velocity and runoff intensity implies an interesting connection between unit hydrograph theory and flow dynamics. Our results provide a reference framework to study scaling exponents under more complex scenarios of flow dynamics and runoff generation processes using ensembles of RSNs.

Wave motions in non-uniform one-dimensional waveguides

Wave approach is used in the analysis of wave motions in one-dimensional non-uniform waveguides. Under assumptions of constant wave velocity and no wave conversion, one class of non-uniform rods including four different profiles results. The obtained results indicate kinetic energy is preserved as constant and wave amplitude is inversely proportional to square root of the cross-section area of the rod. The obtained spectrograms and dispersion relations indicate that under certain conditions there exists a cut-off frequency, below which waves do not propagate along the non-uniform waveguides. The conclusions are similar for high frequency longitudinal wave motions of arbitrary non-uniform rods. For a Euler-Bernoulli beam with exponent variation in geometry and material variation, the bending wave motion is also analyzed including its cut-off frequencies.

A covering theory of special relativity

Under the assumption of closed-path velocity of light invariant, we show both the general expression of velocity of light in an ordinary inertial reference frame and the generalized Lorentz transformation between the ordinary inertial reference frame and the absolute (privileged) reference frame. Although such assumption can not determine theory ambiguously, some significant results can still be obtained by the assumption. Furthermore, the study shows that the relativity of simultaneity is not a universal concept.

Experimental investigation of the decay from a ship’s propeller

In the present study, an experimental investigation of the decay of the maximum velocity and its turbulent characteristics behind a ship propeller, in “bollard pull” condition (zero speed of advance), is reported. Velocity measurements were performed in laboratory by use of a Laser Doppler Anemometry (LDA) measurement system. Earlier researchers described that the maximum axial velocity is constant at the initial stage of a ship’s propeller jet (Fuehrer and Romisch, 1977; Blaauw and van de Kaa, 1978; Berger et al., 1981; Verhey, 1983) as reported in a pure water jet (Albertson et al., 1950; Lee et al., 2002; Dai, 2005), but a number of researchers disagreed with the constant velocity assumption. The present study found that the maximum axial velocity decays in the zone of flow establishment and the zone of established flow with different rates. The investigation provides an insight into the decays of both the maximum velocity and the maximum turbulent fluctuation in axial, tangential and radial components and the decay of the maximum turbulent kinetic energy. Empirical equations are proposed to allow coastal engineers to estimate the jet characteristics from a ship’s propeller.

Depth-dependent intrinsic and scattering seismic attenuation in north central Italy

SUMMARY In this study the attenuation mechanism of seismic wave energy in north central Italy is estimated using low-magnitude earthquake local data recorded at six stations managed by INGV. Most of the analysed events are located along the Alpine chain in the zone of Iseo and Garda lakes, while a minor part in the Po valley. The zone investigated is characterized by the occurrence of significantly intense earthquakes (magnitude up to 6.6) the most recent occurred in 2004 close to the city of Salo on the coast of the Garda lake (Mw= 5.0). Due to the high population density and presence of industrial activity the investigated area is characterized by a high seismic risk. First, the ordinary Multiple Lapse Time Window Analysis (MLTWA) method is applied in the assumption of uniform velocity and scattering and the couple of B0, the seismic albedo and Le−1, the extinction length inverse (corresponding to the total attenuation coefficient) is calculated in the frequency bands of 1.5, 3, 6 and 12 Hz. To retrieve more realistic estimates, the obtained values of B0 and Le−1 are corrected taking into account the effects of a depth-dependent earth model, consisting of an earth structure characterized by a transparent upper mantle and a heterogeneous crust. We find that the corrected intrinsic and scattering attenuation parameters (which are proportional to the inverse of the intrinsic/scattering quality factors, Q−1I and Q−1S) are strongly frequency dependent, with a prevalence of scattering attenuation over the intrinsic dissipation. The corrected and uncorrected values of total Q are in agreement with the total Q values obtained with different approaches for the same area.

Estimation of stride length in level walking using an inertial measurement unit attached to the foot: A validation of the zero velocity assumption during stance

In a variety of applications, inertial sensors are used to estimate spatial parameters by double integrating over time their coordinate acceleration components. In human movement applications, the drift inherent to the accelerometer signals is often reduced by exploiting the cyclical nature of gait and under the hypothesis that the velocity of the sensor is zero at some point in stance. In this study, the validity of the latter hypothesis was investigated by determining the minimum velocity of progression of selected points of the foot and shank during the stance phase of the gait cycle while walking at three different speeds on level ground. The errors affecting the accuracy of the stride length estimation resulting from assuming a zero velocity at the beginning of the integration interval were evaluated on twenty healthy subjects. Results showed that the minimum velocity of the selected points on the foot and shank increased as gait speed increased. Whereas the average minimum velocity of the foot locations was lower than 0.011 m/s, the velocity of the shank locations were up to 0.049 m/s corresponding to a percent error of the stride length equal to 3.3%. The preferable foot locations for an inertial sensor resulted to be the calcaneus and the lateral aspect of the rearfoot. In estimating the stride length, the hypothesis that the velocity of the sensor can be set to zero sometimes during stance is acceptable only if the sensor is attached to the foot.

A simplified approach for solving coagulation–diffusion equation to estimate atmospheric background particle number loading factors contributed by emissions from localized sources

Abstract Coagulation and condensation/evaporation combined with atmospheric dispersion are the main processes responsible for the evolution of aerosol particle size distributions and number concentrations emitted from localized sources. A crucial question is: what fraction of freshly emitted particles survive intra-coagulation effect to persist in the atmosphere and become available for further interaction with background aerosols?. The difficulty in estimating this quantity, designated as the number survival fraction, arises due chiefly to the joint action of atmospheric diffusion with nonlinear coagulation effects which are computationally intensive to handle. We provide a simplified approach to evaluate this quantity in the context of instantaneous (puff) and continuous (plume) releases based on a reduction of the respective coagulation–diffusion equations under the assumption of a constant coagulation kernel (K). The condensation/evaporation processes, being number conserving, are not included in the study. The approach consists of constructing moment equations for the evolution of number concentration and variance of the spatial extension of puff or plume in terms of either time or downstream distance. The puff model, applicable to instantaneous releases is solved within a 3-D, spherically symmetric framework, under an additional assumption of a constant diffusion coefficient (D) which renders itself amenable to a closed form solution that provides a benchmark for developing the solution to the plume model. The latter case, corresponding to continuous releases, is discussed within a 2-D framework under the assumptions of constant advection velocity (U) and space dependent diffusion coefficient expressed in terms of turbulent energy dissipation rate (ɛ). The study brings out the special effect of the coagulation-induced flattening of the spatial concentration profiles because of which particle sizes will be larger at the centre of a Gaussian puff. For a puff of initial width b0 consisting of N0 particles, we obtain a formula for the number survival fraction as ψ puff ( ∞ ) = ( 1 + 5 A / 4 ) − 4 / 5 where, A = K N 0 / { 4 ( 2 π ) 3 / 2 D b 0 } . For plume of initial width σ0 emitting S0 particles per unit time, the formula for the survival fraction obtained by fitting the numerical solutions is obtained as ψ plume ( ∞ ) = ( 1 + 1.32 μ ) − 0.76 where, μ = K S 0 / { 6 3 U σ 0 4 / 3 ( C ɛ ) 1 / 3 } and C is a constant (∼0.8). The implication of these results such as robustness with respect to uncertainties in the choice of the initial data and applications for a few practically important problems such as vehicular emissions, forest fires, etc are discussed.

The force–time profile of elite front crawl swimmers

In this study, we used recently developed technology to determine the force–time profile of elite swimmers, which enabled coaches to make informed decisions on technique modifications. Eight elite male swimmers with a FINA (Federation Internationale de Natation) rank of 900+ completed five passive (streamline tow) and five net force (arms and leg swimming) trials. Three 50-Hz cameras were used to video each trial and were synchronized to the kinetic data output from a force-platform, upon which a motorized towing device was mounted. Passive and net force trials were completed at the participant's maximal front crawl swimming velocity. For the constant tow velocity, the net force profile was presented as a force–time graph, and the limitation of a constant velocity assumption was acknowledged. This allowed minimum and maximum net forces and arm symmetry to be identified. At a mean velocity of 1.92 ± 0.06 m · s−1, the mean passive drag for the swimmers was 80.3 ± 4.0 N, and the mean net force was 262.4 ± 33.4 N. The mean location in the stroke cycle for minimum and maximum net force production was at 45% (insweep phase) and 75% (upsweep phase) of the stroke, respectively. This force–time profile also identified any stroke asymmetry.

An investigation into the feasibility of internal strain measurement in solids by correlation of ultrasonic images

This paper investigates the feasibility of an ultrasonic method for measuring internal displacements and strains in engineering components at depths of tens of millimetres. The principle is to use an ultrasonic array to generate images of the speckle pattern produced by the material microstructure before and after the application of load. Under the assumption of constant ultrasonic velocity, a block-matching method is used to find the relative displacement of small portions of the images between the two loading states, and hence the strain. Experiments performed using a 5 MHz ultrasonic array show that good displacement measurement results are obtained from the speckle directly below the array at depths of up to 45 mm. The results demonstrate that the technique can be used to identify the onset of plasticity and non-uniformity in strain across the field of view. However, while the actual values of strain obtained are correct in some directions, they are systematically incorrect in other directions by a factor between five and six. It is shown that this is because the change in ultrasonic velocity owing to load (the acousto-elastic effect) has, in some cases, a more significant effect on ultrasonic propagation time than the change in distance owing to strain.

Enhancing particle image tracking performance with a sequential Monte Carlo method: The bootstrap filter

One of the common problems of current pattern match and particle image tracking algorithms is the deployment of constant velocity assumption for particle motion between two frames, which would result in serious errors when high velocity gradient flows are measured. To address this issue, a new particle image tracking method—bootstrap filter tracking is proposed. In this new method, a simple nonlinear dynamic model which takes particle acceleration into account is employed and a sequential Monte Carlo method—bootstrap filter is used in conjunction with pattern match algorithm to strengthen the particle image tracking performance. By using the nonlinear system model and bootstrap filter, particle location at next time step can be predicted accurately and the new method is able to measure high velocity gradient flows with better performance than the traditional particle image tracking algorithms. This new method is validated by using numerically generated particle images. Its accuracy in terms of particle image density, out-of-plane displacement and displacement gradient is compared with the Kalman filter tracking (Takehara et al., 2000 [34]) and the Super-PIV (Keane et al., 1995 [30]) methods. The three algorithms are also compared by using a set of real turbulent jet images. The test results demonstrate that the bootstrap filter tracking method is superior than the Kalman filter tracking and the Super-PIV methods for measuring low density, high velocity gradient flows.