On an Approximate Method of Calculating Pressures on Non-lifting Head Shapes at Supersonic Speeds

1955 ◽  
Vol 6 (1) ◽  
pp. 31-45
Author(s):  
H. K. Zienkiewicz
Keyword(s):  
Method Of Characteristics ◽  
Order Theory ◽  
Stagnation Pressure ◽  
Slender Body Theory ◽  
Pressure Losses ◽  
The Method Of Characteristics ◽  
Curvature Approximation ◽  
Body Theory ◽  
Theory And Experiment ◽  
Good Agreement

SummarySlender-body theory is used to derive the ogive of curvature approximation for very slender, pointed, convex head shapes at supersonic speeds. Results of application of this approximation, together with the λ-method for circular arc ogives, to a variety of non-slender head shapes show very good agreement with the method of characteristics, van Dyke's second-order theory and experiment. Good agreement with the method of characteristics and with experiment is obtained even in cases when the stagnation pressure losses across the nose shock wave are not negligible.

Slender-body theory for steady sheared plumes in very viscous fluid

2008 ◽  
Vol 612 ◽  
pp. 21-44 ◽  
Author(s):  
ROBERT J. WHITTAKER ◽  
JOHN R. LISTER
Keyword(s):  
Simple Model ◽  
Shear Flow ◽  
Viscous Fluid ◽  
Experimental Studies ◽  
Slender Body ◽  
Slender Body Theory ◽  
Dimensionless Parameters ◽  
Dynamical Regimes ◽  
Body Theory ◽  
Good Agreement

A simple model based on slender-body theory is developed to describe the deflection of a steady plume by shear flow in very viscous fluid of the same viscosity. The key dimensionless parameters measuring the relative strengths of the shear, diffusion and source flux are identified, which allows a number of different dynamical regimes to be distinguished. The predictions of the model show good agreement with many, but not all, observations from previous experimental studies. Possible reasons for the discrepancies are discussed.

scholarly journals Study of Unsteady Flow in a Heat Exchanger by the Method of Characteristics

1992 ◽  
Vol 114 (4) ◽  
pp. 459-463 ◽  
Author(s):  
Yuan Mao Huang
Keyword(s):  
Heat Exchanger ◽  
Unsteady Flow ◽  
Transfer Rate ◽  
Method Of Characteristics ◽  
Governing Equations ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Improvement Factor ◽  
The One ◽  
Good Agreement

The one-dimensional, unsteady flow in an air-to-air heat exchanger is studied. The governing equations are derived and the method of characteristics with the uniform interval scheme is used in the analysis. The effect of the fin improvement factor on the air temperature in the heat exchanger and the heat transfer rate of the heat exchanger, and air properties in the heat exchanger are analyzed. The numerical results are compared and show good agreement with the available data.

Inhomogeneous distribution of a rigid fibre undergoing rectilinear flow between parallel walls at high Péclet numbers

2009 ◽  
Vol 630 ◽  
pp. 267-298 ◽  
Author(s):  
JOONTAEK PARK ◽  
JASON E. BUTLER
Keyword(s):  
Simple Shear Flow ◽  
Inhomogeneous Distribution ◽  
Slender Body Theory ◽  
Shear Rates ◽  
Net Migration ◽  
High Shear Rates ◽  
Fibre Suspensions ◽  
Parabolic Flow ◽  
Body Theory ◽  
Good Agreement

We use slender-body theory to simulate a rigid fibre within simple shear flow and parabolic flow at zero Reynolds number and high Péclet numbers (weak Brownian motion). Hydrodynamic interactions of bulk fibres with the bounding walls are included using previously developed methods (Harlen, Sundararajakumar & Koch, J. Fluid Mech., vol. 388, 1999, pp. 355–388; Butler & Shaqfeh, J. Fluid Mech., vol. 468, 2002, pp. 205–237). We also extend a previous analytic theory (Park, Bricker & Butler, Phys. Rev. E, vol. 76, 2007, 04081) predicting the centre-of-mass distribution of rigid fibre suspensions undergoing rectilinear flow near a wall to compare the steady and transient distributions. The distributions obtained by the simulation and theory are in good agreement at sufficiently high shear rates, validating approximations made in the theory which predicts a net migration of the rigid fibres away from the walls due to a hydrodynamic lift force. The effect of the inhomogeneous distribution on the effective stress is also investigated.

scholarly journals Pulse Propagation in a Helix—Theory and Experiment

1974 ◽  
Vol 41 (4) ◽  
pp. 1047-1051 ◽  
Author(s):  
J. W. Phillips
Keyword(s):  
Experimental Model ◽  
Strain Gage ◽  
Method Of Characteristics ◽  
Pulse Propagation ◽  
Numerical Results ◽  
Interface Problem ◽  
One Dimensional ◽  
The Method Of Characteristics ◽  
Theory And Experiment

Wittrick’s general one-dimensional equations governing the propagation of small elastic disturbances in a helical waveguide are solved by the method of characteristics, and numerical results for a particular interface problem are compared with strain gage records from an impacted experimental model. The agreement between theory and experiment is found to be excellent for the type of pulse considered, namely, an initially longitudinal compressive pulse approximately seventy rod-diameters in length.

Effect of a Continuous Area Convergence on the Motion of a Shock Wave

1969 ◽  
Vol 20 (3) ◽  
pp. 248-258 ◽  
Author(s):  
P. L. Wilcox
Keyword(s):  
Shock Wave ◽  
Shock Tube ◽  
Experimental Work ◽  
Method Of Characteristics ◽  
Unsteady Motion ◽  
Experimental Results ◽  
Area Change ◽  
Transient Motion ◽  
The Method Of Characteristics ◽  
Good Agreement

SummaryThe transient motion of a shock wave is investigated during its passage through ducts containing various area convergences. The method of characteristics has been used to follow the unsteady motion of the shock wave in an inviscid, non-conducting gas. The strength of the shock is taken to be large enough so that initially both sets of characteristics face downstream. The results are found to be in good agreement with unsteady and quasi-steady theories. A comparison is made between the characteristics results and experimental results obtained in a 1 ft (0·305 m) diameter shock tube. This shock tube incorporates a 3·75:1 linear area change in the low pressure section length. Good agreement is found between experiment and theory. A comparison is also made with other experimental work.

A hydrodynamical analysis of fish turning manoeuvres

1972 ◽  
Vol 182 (1066) ◽  
pp. 59-72 ◽  
Keyword(s):  
Present Theory ◽  
Inviscid Fluid ◽  
Centre Of Mass ◽  
Turning Process ◽  
Slender Body Theory ◽  
Turning Mechanism ◽  
Three Stages ◽  
Straight Lines ◽  
Body Theory ◽  
Good Agreement

Slender body theory, adapted here to the study of unsteady, curvilinear large amplitude movements in an inviscid fluid, is applied to the study of the turning mechanism in fishes. The vortex wake is represented by the circulation shed from the fins in the present theory. Examination of filmed sequences of turning fish show that the turning process includes three stages, distinguished by different movements of the centre of mass. In the first and third stages the centre of mass moves in straight lines in the initial and final directions of swimming while in the middle period it moves along an approximately circular connecting arc. The forces and moments acting on the fish, calculated by the present method are found to be in good agreement with these experimental observations.

A Calculation Procedure for Three-Dimensional, Viscous, Compressible Duct Flow. Part II—Stagnation Pressure Losses in a Rectangular Elbow

1979 ◽  
Vol 101 (4) ◽  
pp. 423-428 ◽  
Author(s):  
John Moore ◽  
Joan G. Moore
Keyword(s):  
Three Dimensional ◽  
Inviscid Flow ◽  
Stagnation Pressure ◽  
Calculation Procedure ◽  
Duct Flow ◽  
Pressure Losses ◽  
Pressure Distributions ◽  
Starting Point ◽  
Flow Part ◽  
Good Agreement

Three-dimensional, turbulent flow is calculated in an elbow used by Stanitz for an experimental investigation of secondary flow. Calculated wall-static pressure distributions and distributions of stagnation-pressure loss, both spatial and as a function of mass-flow ratio, are in good agreement with Stanitz’ measurements, justifying the use of a relatively simple mixing-length viscosity model. The calculation procedure and the results of two-dimensional “inviscid” flow calculations used as the starting point for the present calculations are described in Part I of this paper. The computed flow field shows clearly the development of the passage vortices.

Study of the Fluid Flow in the Elliptical Duct by the Method of Characteristics

1993 ◽  
Vol 115 (1) ◽  
pp. 80-84 ◽  
Author(s):  
Yuan Mao Huang ◽  
C. H. Ho
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Method Of Characteristics ◽  
Numerical Results ◽  
Hyperbolic Type ◽  
Governing Equations ◽  
The Method Of Characteristics ◽  
The Finite Difference Method ◽  
The Heat Transfer Coefficient ◽  
Good Agreement

This study develops a mathematical model to determine the properties of laminar flow in the elliptical duct. With some assumptions, the nonlinear governing equations of the air in the elliptical duct are transformed into the hyperbolic type. The method of characteristics is then applied. Numerical results are obtained by using the finite difference method and the uniform interval scheme. The air properties in the elliptical duct are analyzed. The local Nusselt number and the heat transfer coefficient along the duct are studied. The numerical results are compared and show good agreement with the available data.

scholarly journals Software development for subsonic aircraft’s unsteady longitudinal stability derivatives calculation

2005 ◽  
Vol 32 (4) ◽  
pp. 319-340 ◽  
Author(s):  
Nikola Maricic
Keyword(s):  
Method Of Images ◽  
Lattice Method ◽  
Aerodynamic Stability ◽  
Slender Body Theory ◽  
Stability Derivatives ◽  
Doublet Lattice Method ◽  
Body Theory ◽  
General Configuration ◽  
Finite Element Methodology ◽  
Good Agreement

Subsonic general configuration aircrafts? unsteady longitudinal aerodynamic stability derivatives can be estimated using finite element methodology based on the Doublet Lattice Method (DLM), the Slender Body Theory (SBT) and the Method of Images (MI). Applying this methodology, software DERIV is developed. The obtained results from DERIV are compared to NASTRAN examples HA21A and HA75H. A good agreement is achieved.

Pulse Propagation in Straight and Curved Beams—Theory and Experiment

1974 ◽  
Vol 41 (1) ◽  
pp. 71-76 ◽  
Author(s):  
F. B. Crowley ◽  
J. W. Phillips ◽  
C. E. Taylor
Keyword(s):  
Method Of Characteristics ◽  
Pulse Propagation ◽  
Curved Beam ◽  
Curved Beams ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Isochromatic Fringe ◽  
Fringe Patterns ◽  
Theory And Experiment ◽  
Good Agreement

The equations from Morley’s one-dimensional theory governing the motion of a curved beam subjected to an arbitrary pulse are solved numerically using the method of characteristics. Propagation of initially longitudinal pulses in beam assemblages with both straight and curved sections is investigated. Simulated isochromatic fringe patterns are constructed by a Calcomp plotter and are compared with actual photoelastic patterns. Remarkably good agreement is found between theory and experiment in all the cases investigated. It is concluded that Morley’s theory can be applied to pulse propagation problems of the type investigated.

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