Wide range scaling laws for radiation driven shock speed, wall albedo and ablation parameters for high-Z materials

Accurate quantification of the blast load arising from detonation of a high explosive has applications in transport security, infrastructure assessment and defence. In order to design efficient and safe protective systems in such aggressive environments, it is of critical importance to understand the magnitude and distribution of loading on a structural component located close to an explosive charge. In particular, peak specific impulse is the primary parameter that governs structural deformation under short-duration loading. Within this so-called extreme near-field region, existing semi-empirical methods are known to be inaccurate, and high-fidelity numerical schemes are generally hampered by a lack of available experimental validation data. As such, the blast protection community is not currently equipped with a satisfactory fast-running tool for load prediction in the near-field. In this article, a validated computational model is used to develop a suite of numerical near-field blast load distributions, which are shown to follow a similar normalised shape. This forms the basis of the data-driven predictive model developed herein: a Gaussian function is fit to the normalised loading distributions, and a power law is used to calculate the magnitude of the curve according to established scaling laws. The predictive method is rigorously assessed against the existing numerical dataset, and is validated against new test models and available experimental data. High levels of agreement are demonstrated throughout, with typical variations of <5% between experiment/model and prediction. The new approach presented in this article allows the analyst to rapidly compute the distribution of specific impulse across the loaded face of a wide range of target sizes and near-field scaled distances and provides a benchmark for data-driven modelling approaches to capture blast loading phenomena in more complex scenarios.

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Aerodynamic Similarity Principles and Scaling Laws for Windmilling Fans

Volume 2A: Turbomachinery ◽

10.1115/gt2018-76640 ◽

2018 ◽

Author(s):

Dilip Prasad

Keyword(s):

Rotational Speed ◽

Pressure Loss ◽

Scaling Laws ◽

Dynamic Pressure ◽

Stagnation Pressure ◽

Design Parameters ◽

Similarity Parameter ◽

Wide Range ◽

Simulation Results ◽

Good Agreement

Windmilling requirements for aircraft engines often define propulsion and airframe design parameters. The present study is focused is on two key quantities of interest during windmill operation: fan rotational speed and stage losses. A model for the rotor exit flow is developed, that serves to bring out a similarity parameter for the fan rotational speed. Furthermore, the model shows that the spanwise flow profiles are independent of the throughflow, being determined solely by the configuration geometry. Interrogation of previous numerical simulations verifies the self-similar nature of the flow. The analysis also demonstrates that the vane inlet dynamic pressure is the appropriate scale for the stagnation pressure loss across the rotor and splitter. Examination of the simulation results for the stator reveals that the flow blockage resulting from the severely negative incidence that occurs at windmill remains constant across a wide range of mass flow rates. For a given throughflow rate, the velocity scale is then shown to be that associated with the unblocked vane exit area, leading naturally to the definition of a dynamic pressure scale for the stator stagnation pressure loss. The proposed scaling procedures for the component losses are applied to the flow configuration of Prasad and Lord (2010). Comparison of simulation results for the rotor-splitter and stator losses determined using these procedures indicates very good agreement. Analogous to the loss scaling, a procedure based on the fan speed similarity parameter is developed to determine the windmill rotational speed and is also found to be in good agreement with engine data. Thus, despite their simplicity, the methods developed here possess sufficient fidelity to be employed in design prediction models for aircraft propulsion systems.

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Aerodynamic Similarity Principles and Scaling Laws for Windmilling Fans

Journal of Turbomachinery ◽

10.1115/1.4041375 ◽

2018 ◽

Vol 140 (12) ◽

Author(s):

Dilip Prasad

Keyword(s):

Rotational Speed ◽

Pressure Loss ◽

Scaling Laws ◽

Dynamic Pressure ◽

Stagnation Pressure ◽

Design Parameters ◽

Similarity Parameter ◽

Wide Range ◽

Simulation Results ◽

Good Agreement

Windmilling requirements for aircraft engines often define propulsion and airframe design parameters. The present study is focused on two key quantities of interest during windmill operation: fan rotational speed and stage losses. A model for the rotor exit flow is developed that serves to bring out a similarity parameter for the fan rotational speed. Furthermore, the model shows that the spanwise flow profiles are independent of the throughflow, being determined solely by the configuration geometry. Interrogation of previous numerical simulations verifies the self-similar nature of the flow. The analysis also demonstrates that the vane inlet dynamic pressure is the appropriate scale for the stagnation pressure loss across the rotor and splitter. Examination of the simulation results for the stator reveals that the flow blockage resulting from the severely negative incidence that occurs at windmill remains constant across a wide range of mass flow rates. For a given throughflow rate, the velocity scale is then shown to be that associated with the unblocked vane exit area, leading naturally to the definition of a dynamic pressure scale for the stator stagnation pressure loss. The proposed scaling procedures for the component losses are applied to the flow configuration of Prasad and Lord (2010). Comparison of simulation results for the rotor-splitter and stator losses determined using these procedures indicates very good agreement. Analogous to the loss scaling, a procedure based on the fan speed similarity parameter is developed to determine the windmill rotational speed and is also found to be in good agreement with engine data. Thus, despite their simplicity, the methods developed here possess sufficient fidelity to be employed in design prediction models for aircraft propulsion systems.

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Fallacies of the Enthalpy Transfer Coefficient over the Ocean in High Winds

Journal of the Atmospheric Sciences ◽

10.1175/2011jas3714.1 ◽

2011 ◽

Vol 68 (7) ◽

pp. 1435-1445 ◽

Cited By ~ 34

Author(s):

Edgar L Andreas

Keyword(s):

Wind Speed ◽

Latent Heat ◽

Large Scale ◽

Scaling Laws ◽

Surface Fluxes ◽

Neutral Stability ◽

Transfer Coefficients ◽

Wide Range ◽

Interfacial Transfer ◽

High Winds

Abstract Mesoscale and large-scale atmospheric models use a bulk surface flux algorithm to compute the turbulent flux boundary conditions at the bottom of the atmosphere from modeled mean meteorological quantities such as wind speed, temperature, and humidity. This study, on the other hand, uses a state-of-the-art bulk air–sea flux algorithm in stand-alone mode to compute the surface fluxes of momentum, sensible and latent heat, and enthalpy for a wide range of typical (though randomly generated) meteorological conditions over the open ocean. The flux algorithm treats both interfacial transfer (controlled by molecular processes right at the air–sea interface) and transfer mediated by sea spray. Because these two transfer routes obey different scaling laws, neutral-stability, 10-m transfer coefficients for enthalpy CKN10, latent heat CEN10, and sensible heat CHN10 are quite varied when calculated from the artificial flux data under the assumption of only interfacial transfer—the assumption in almost all analyses of measured air–sea fluxes. That variability increases with wind speed because of increasing spray-mediated transfer and also depends on surface temperature and atmospheric stratification. The analysis thereby reveals as fallacious several assumptions that are common in air–sea interaction research—especially in high winds. For instance, CKN10, CEN10, and CHN10 are not constants; they are not even single-valued functions of wind speed, nor must they increase monotonically with wind speed if spray-mediated transfer is important. Moreover, the ratio CKN10/CDN10, where CDN10 is the neutral-stability, 10-m drag coefficient, does not need to be greater than 0.75 at all wind speeds, as many have inferred from Emanuel’s seminal paper in this journal. Data from the literature and from the Coupled Boundary Layers and Air–Sea Transfer (CBLAST) hurricane experiment tend to corroborate these results.

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Numerical Verification of Scaling Laws for Shock-Boundary Layer Interactions in Arbitrary Gases

Journal of Fluids Engineering ◽

10.1115/1.2819121 ◽

1997 ◽

Vol 119 (1) ◽

pp. 67-73 ◽

Cited By ~ 2

Author(s):

M. S. Cramer ◽

S. H. Park ◽

L. T. Watson

Keyword(s):

Boundary Layer ◽

Scaling Laws ◽

Plate Boundary ◽

Strong Support ◽

Ideal Gas ◽

Numerical Verification ◽

Dense Gases ◽

Ideal Gas Law ◽

Dimensional Interaction ◽

Wide Range

The steady, two-dimensional interaction of an oblique shock with a laminar flat-plate boundary layer has been examined through use of the Beam-Warming implicit scheme. A wide range of fluids is considered as are freestream pressures corresponding to dense gases, i.e., gases at pressures which are so large that the ideal gas law is no longer accurate. The results, when combined with the triple-deck theory of Kluwick (1994), provides strong support for the idea that the classical scaling laws can be extended to dense gases.

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NUMERICAL STUDIES ON THE VIBRATIONAL SPECTRUM OF FIBONACCI CHAIN: A MULTIFRACTAL ANALYSIS

International Journal of Modern Physics B ◽

10.1142/s0217979291000444 ◽

1991 ◽

Vol 05 (05) ◽

pp. 825-841 ◽

Cited By ~ 1

Author(s):

WLODZIMIERZ SALEJDA

Keyword(s):

Vibrational Spectrum ◽

Multifractal Analysis ◽

Scaling Laws ◽

Model Parameters ◽

Local Scaling ◽

One Dimensional ◽

Dynamic Matrix ◽

Numerical Studies ◽

Wide Range ◽

The One

A harmonic Hamiltonian modelling the lattice dynamics of the one-dimensional Fibonacci-type quasicrystal is studied numerically. The multifractal analysis of vibrational spectrum is performed. It is found that the integrated normalized density of states [Formula: see text], where x denotes the square of the eigenenergy of the dynamic matrix, exhibits a finite range of scaling indices α (i.e. α min ≤α≤ α max ) describing the local scaling laws of [Formula: see text]. The α-f spectra and the Renyi dimensions [Formula: see text] are calculated in a wide range of model parameters taking into account the next-nearest-neighbour (NNN) interactions of atoms. In particular, we have observed that: (1) The α-f spectra are smooth in the interval [Formula: see text]; (2) If the so-called parameter of quasi-periodicity Q increases, then αmin and the fractal dimension of vibrational spectra [Formula: see text] decrease; (3) If the strength of NNN interactions h grows then α min decreases but D increases.

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Creation and Maintenance of Cavities Under Horizontal Surfaces in Steady and Gust Flows

Journal of Fluids Engineering ◽

10.1115/1.4000241 ◽

2009 ◽

Vol 131 (11) ◽

Cited By ~ 29

Author(s):

R. E. A. Arndt ◽

W. T. Hambleton ◽

E. Kawakami ◽

E. L. Amromin

Keyword(s):

Experimental Data ◽

Scaling Laws ◽

Substantial Effect ◽

Low Flow ◽

Water Tunnel ◽

Sectional Area ◽

Cross Sectional ◽

Air Supply ◽

Wide Range ◽

Flow Speeds

An experimental study of air supply to bottom cavities stabilized within a recess under a horizontal surface has been carried out in a specially designed water tunnel. The air supply necessary for creating and maintaining an air cavity in steady and gust flows has been determined over a wide range of speed. Flux-free ventilated cavitation at low flow speeds has been observed. Stable multiwave cavity forms at subcritical values of Froude number were also observed. It was found that the cross-sectional area of the air supply ducting has a substantial effect on the air demand. Air supply scaling laws were deduced and verified with the experimental data obtained.

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A Simple Method for Estimating Velocity Distributions in Swirling Flows

Journal of Fluids Engineering ◽

10.1115/1.2911837 ◽

1994 ◽

Vol 116 (4) ◽

pp. 694-701

Author(s):

D. Kinnear ◽

P. A. Davidson

Keyword(s):

Scaling Laws ◽

Numerical Approach ◽

Structural Features ◽

Integral Approach ◽

Simple Method ◽

Numerical Solution Methods ◽

Wide Range ◽

Solution Methods ◽

High Reynolds ◽

Momentum Integral

We describe the important structural features of swirling recirculating flows induced by a rotating boundary. A knowledge of this structure has allowed us to match the core flow to the boundary layer using a momentum-integral technique. In particular, we derive a single integral-differential equation, valid for any shape of container, which predicts the distribution of swirl, secondary recirculation, and wall shear stress. This momentum-integral approach has been applied to three cases: flow between parallel disks; flow in a cone; and flow in a hemisphere. The results compare favorably with published experimental data, and with computed numerical results. Our momentum-integral approach complements numerical solution methods. For simple geometries all the important information can, in principle, be derived using the momentum-integral approach, and this is particularly useful for establishing the scaling laws. In more complex geometries a numerical approach may be more appropriate. However, even in such cases, the scaling laws derived using the momentum-integral analysis are still useful as they allow extrapolation of a single computation to a wide range of high Reynolds number flows.

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Fundamentals of fluid dynamics with an introduction to the importance of interfaces

10.1093/oso/9780198789352.003.0001 ◽

2017 ◽

Author(s):

H. A. Stone

Keyword(s):

Fluid Dynamics ◽

Differential Equations ◽

Fluid Mechanics ◽

Scaling Laws ◽

Fluid Flows ◽

Governing Equations ◽

Soft Interfaces ◽

Physical Intuition ◽

Basic Fluid ◽

Wide Range

The topics discussed are all related to basic fluid mechanics. In these introductory notes I highlight some of the main features of fluid flows and their mathematical characterization. There is much physical intuition encapsulated in the differential equations, and one of our goals is to gain more experience (i) understanding the governing equations and various related principles of kinematics, (ii) developing intuition with approximating the equations, (iii) applying the principles to a wide range of problems, which includes (iv) being able to rationalize scaling laws and quantitative trends, often without having a detailed solution in hand. Where possible we provide examples of the ideas with ‘soft interfaces’ in mind.

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Spectral analysis of the transition to turbulence from a dipole in stratified fluid

Journal of Fluid Mechanics ◽

10.1017/jfm.2012.437 ◽

2012 ◽

Vol 713 ◽

pp. 86-108 ◽

Cited By ~ 26

Author(s):

Pierre Augier ◽

Jean-Marc Chomaz ◽

Paul Billant

Keyword(s):

Reynolds Number ◽

Spectral Analysis ◽

Kinetic Energy ◽

Numerical Simulations ◽

Scaling Laws ◽

Stratified Fluid ◽

Shear Instability ◽

Transition To Turbulence ◽

Small Scale ◽

Wide Range

AbstractWe investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb–Chaplygin dipole in a stratified fluid for a high Reynolds number $Re= 28\hspace{0.167em} 000$ and a wide range of horizontal Froude number ${F}_{h} \in [0. 0225~0. 135] $ and buoyancy Reynolds number $\mathscr{R}= Re{{F}_{h} }^{2} \in [14~510] $. The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale ${L}_{b} = U/ N$, where $U$ is the characteristic horizontal velocity of the dipole and $N$ the Brunt–Väisälä frequency; second, the destabilization of the Kelvin–Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits a ${{\varepsilon }_{K} }^{2/ 3} { k}_{h}^{\ensuremath{-} 5/ 3} $ power law (where ${k}_{h} $ is the horizontal wavenumber and ${\varepsilon }_{K} $ is the dissipation rate of kinetic energy) from ${k}_{b} = 2\lrm{\pi} / {L}_{b} $ to the dissipative scales, with an energy deficit between the integral scale and ${k}_{b} $ and an excess around ${k}_{b} $. The vertical spectrum of kinetic energy can be expressed as $E({k}_{z} )= {C}_{N} {N}^{2} { k}_{z}^{\ensuremath{-} 3} + C{{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ where ${C}_{N} $ and $C$ are two constants of order unity and ${k}_{z} $ is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ shape and approaches the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum for ${k}_{z} \gt {k}_{o} $, ${k}_{o} $ being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ spectrum is associated with large horizontal scales $\vert {\mathbi{k}}_{h} \vert \lt {k}_{b} $ and the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum with the scales $\vert {\mathbi{k}}_{h} \vert \gt {k}_{b} $.

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