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

1997 ◽  
Vol 119 (1) ◽  
pp. 67-73 ◽  
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.

The flat plate boundary layer. Part 1. Numerical integration of the Orr–-Sommerfeld equation

1970 ◽  
Vol 43 (4) ◽  
pp. 801-811 ◽  
Author(s):  
R. Jordinson
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Plate Boundary ◽  
Mean Flow ◽  
Comparison With Experiment ◽  
Wide Range ◽  
The Mean ◽  
Sommerfeld Equation ◽  
Range Of Values ◽  
Flat Plate Boundary Layer

Numerical space-amplified solutions of the Orr-Sommerfeld equation for the case of a boundary layer on a flat plate have been calculated for a wide range of values of frequency and Reynolds number. The mean flow is assumed to be parallel and given by the appropriate component of the Blasius solution. The results are presented in a form suitable for comparison with experiment and are also compared with calculations of earlier authors.

Estimation of Properties of Organic Compounds

2001 ◽  
Author(s):  
L. K. Doraiswamy
Keyword(s):  
Organic Compounds ◽  
Process Development ◽  
Ideal Gas ◽  
The Other ◽  
Ideal Gas Law ◽  
Wide Range ◽  
Law Of Corresponding States ◽  
Pvt Behavior ◽  
Reduced Temperature ◽  
Simple Ideal

A primary requirement of any reactor design or process development computation is knowledge of the major properties of the compounds involved. Although most of these can be obtained from the literature, there is still a need to estimate them from correlations. The main difficulty is the large number of correlations proposed for a given property and the need to select the best from among them. No single correlation works with equally high precision under all conditions. On the other hand, correlations that can be used with acceptable levels of precision over a wide range of conditions are also available for a number of properties. The slight sacrifice of accuracy is often more than compensated for by the ease and generality of application of these methods. Our emphasis here will be on such correlations. For a detailed treatment, reference should be made to books devoted exclusively to properties estimation. The book by Reid, Prausnitz, and Poling (1987), along with its earlier versions by Reid and Sherwood (1958, 1966) and Reid, Prausnitz, and Sherwood (1977), and the works of Janz (1958), Hansch and Leo (1979), and Lyman, Reehl, and Rosenblatt (1982) are noteworthy. The following methods selected for a few properties are based in part on the recommendations contained in these treatises. The two most important bases for formulating correlations for estimating the properties of organic compounds (indeed of any compound) are the law of corresponding states (LCS), and the method of group contributions (GC). LCS is based on the concept that all substances exhibit identical properties under conditions equally removed from their critical states. The “equally removed” state for any property is usually expressed as the ratio of its value at that state to the value at the critical state and is referred to as the reduced property. Thus Tr — T/TC, Pr = P/PC, Vr = V/Vc and ηr = η/ ηc are the reduced temperature, pressure, volume, and viscosity, respectively. If the simple ideal gas law PV/RgT — Z, where Z is the compressibility, can be recast in terms of reduced properties as PrVt/RgTr = Z/ZC, then the PVT behavior of all fluids can be represented as Pr versus Tr plots for different values of Zr.

Stokes Layers in Horizontal-Wave Outer Flows

1996 ◽  
Vol 118 (3) ◽  
pp. 537-545 ◽  
Author(s):  
J. E. Choi ◽  
M. K. Sreedhar ◽  
F. Stern
Keyword(s):  
Boundary Layer ◽  
Computational Study ◽  
Perturbation Expansion ◽  
Plate Boundary ◽  
Navier Stokes ◽  
Additional Parameter ◽  
Small Disturbance ◽  
Wave Speeds ◽  
Wide Range ◽  
Horizontal Wave

Results are reported of a computational study investigating the responses of flat plate boundary layers and wakes to horizontal wave outer flows. Solutions are obtained for temporal, spatial, and traveling waves using Navier Stokes, boundary layer, and perturbation expansion equations. A wide range of parameters are considered for all the three waves. The results are presented in terms of Stokes-layer overshoots, phase leads (lags), and streaming. The response to the temporal wave showed all the previously reported features. The magnitude and nature of the response are small and simple such that it is essentially a small disturbance on the steady solution. Results are explainable in terms of one parameter ξ (the frequency of oscillation). For the spatial wave, the magnitude and the nature of the response are significantly increased and complex such that it cannot be considered simply a small disturbance on the without-wave solution. The results are explainable in terms of the two parameters λ−1 and x/λ (where λ is the wavelength). A clear asymmetry is observed in the wake response for the spatial wave. An examination of components of the perturbation expansion equations indicates that the asymmetry is a first-order effect due to nonlinear interaction between the steady and first-harmonic velocity components. For the traveling wave, the responses are more complex and an additional parameter, c (the wave speed), is required to explain the results. In general, for small wave speeds the results are similar to a spatial wave, whereas for higher wave speeds the response approaches the temporal wave response. The boundary layer and perturbation expansion solutions compares well with the Navier Stokes solution in their range of validity.

Transonic and Boundary Layer Similarity Laws in Dense Gases

1996 ◽  
Vol 118 (3) ◽  
pp. 481-485 ◽  
Author(s):  
M. S. Cramer ◽  
S. T. Whitlock ◽  
G. M. Tarkenton
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Transonic Flow ◽  
Scaling Laws ◽  
Scaling Law ◽  
Small Disturbance ◽  
Physical Mechanisms ◽  
Dense Gases ◽  
Compressible Boundary Layers ◽  
Similarity Laws

We discuss the validity of similarity and scaling laws for transonic flow and compressible boundary layers when dense gas effects are important. The physical mechanisms for the failure of each class of scaling law are delineated. In the case of transonic flow, a new similitude based on a modified small disturbance equation is presented.

scholarly journals Predicting specific impulse distributions for spherical explosives in the extreme near-field using a Gaussian function

2021 ◽  
pp. 204141962199349
Author(s):  
Jordan J Pannell ◽  
George Panoutsos ◽  
Sam B Cooke ◽  
Dan J Pope ◽  
Sam E Rigby
Keyword(s):  
Scaling Laws ◽  
Near Field ◽  
Specific Impulse ◽  
Gaussian Function ◽  
Data Driven ◽  
Blast Load ◽  
Structural Deformation ◽  
Load Prediction ◽  
Validation Data ◽  
Wide Range

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.

Making sense of sensemaking: using the sensemaking epistemic game to investigate student discourse during a collaborative gas law activity

2021 ◽  
Author(s):  
Kevin H. Hunter ◽  
Jon-Marc G. Rodriguez ◽  
Nicole M. Becker
Keyword(s):  
Problem Solving ◽  
Conceptual Understanding ◽  
Ideal Gas ◽  
Interactive Simulation ◽  
Structural Components ◽  
Student Discourse ◽  
Coding Scheme ◽  
Making Sense ◽  
Ideal Gas Law ◽  
The Ideal

Beyond students’ ability to manipulate variables and solve problems, chemistry instructors are also interested in students developing a deeper conceptual understanding of chemistry, that is, engaging in the process of sensemaking. The concept of sensemaking transcends problem-solving and focuses on students recognizing a gap in knowledge and working to construct an explanation that resolves this gap, leading them to “make sense” of a concept. Here, we focus on adapting and applying sensemaking as a framework to analyze three groups of students working through a collaborative gas law activity. The activity was designed around the learning cycle to aid students in constructing the ideal gas law using an interactive simulation. For this analysis, we characterized student discourse using the structural components of the sensemaking epistemic game using a deductive coding scheme. Next, we further analyzed students’ epistemic form by assessing features of the activity and student discourse related to sensemaking: whether the question was framed in a real-world context, the extent of student engagement in robust explanation building, and analysis of written scientific explanations. Our work provides further insight regarding the application and use of the sensemaking framework for analyzing students’ problem solving by providing a framework for inferring the depth with which students engage in the process of sensemaking.

Observations of Small-Scale Turbulence and Energy Dissipation Rates in the Cloudy Boundary Layer

2006 ◽  
Vol 63 (5) ◽  
pp. 1451-1466 ◽  
Author(s):  
Holger Siebert ◽  
Katrin Lehmann ◽  
Manfred Wendisch
Keyword(s):  
Boundary Layer ◽  
Energy Dissipation ◽  
Wind Velocity ◽  
Turbulence Theory ◽  
Horizontal Wind ◽  
Inertial Subrange ◽  
Intermittent Flow ◽  
Small Scale ◽  
Dissipation Rates ◽  
Wide Range

Abstract Tethered balloon–borne measurements with a resolution in the order of 10 cm in a cloudy boundary layer are presented. Two examples sampled under different conditions concerning the clouds' stage of life are discussed. The hypothesis tested here is that basic ideas of classical turbulence theory in boundary layer clouds are valid even to the decimeter scale. Power spectral densities S( f ) of air temperature, liquid water content, and wind velocity components show an inertial subrange behavior down to ≈20 cm. The mean energy dissipation rates are ∼10−3 m2 s−3 for both datasets. Estimated Taylor Reynolds numbers (Reλ) are ∼104, which indicates the turbulence is fully developed. The ratios between longitudinal and transversal S( f ) converge to a value close to 4/3, which is predicted by classical turbulence theory for local isotropic conditions. Probability density functions (PDFs) of wind velocity increments Δu are derived. The PDFs show significant deviations from a Gaussian distribution with longer tails typical for an intermittent flow. Local energy dissipation rates ɛτ are derived from subsequences with a duration of τ = 1 s. With a mean horizontal wind velocity of 8 m s−1, τ corresponds to a spatial scale of 8 m. The PDFs of ɛτ can be well approximated with a lognormal distribution that agrees with classical theory. Maximum values of ɛτ ≈ 10−1 m2 s−3 are found in the analyzed clouds. The consequences of this wide range of ɛτ values for particle–turbulence interaction are discussed.

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