Solutions for supersonic rotational flow around a corner using a new co-ordinate system

1968 ◽  
Vol 34 (4) ◽  
pp. 735-758 ◽  
Author(s):  
T. C. Adamson
Keyword(s):  
Similarity Solution ◽  
Inviscid Flow ◽  
Numerical Results ◽  
Rotational Flow ◽  
Incoming Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
Perfect Gas ◽  
Convex Corner

A co-ordinate system consisting of the left-running characteristics (α = const.) and the streamlines (ϕ = const.) is used. The governing equations are derived in terms of α and ϕ for a two-dimensional steady supersonic rotational inviscid flow of a perfect gas. The equations are applied to the problem of an initially parallel supersonic rotational flow which expands around a convex corner. The velocity of the incoming flow at the wall is considered to be either supersonic (case 1) or sonic (case 2). For each case, solutions uniformly valid in the region near the leading characteristic and in the region near the corner, are found for the Mach angle and flow deflexion angle in terms of their values on the leading characteristic and at the corner. In case 2, a transonic similarity solution is found and composite solutions are constructed for each region. Comparisons are made with existing exact numerical results.

LIFT AND DRAG OF A TWO-DIMENSIONAL PAD SLIDING UPON A POROUS SURFACE

1996 ◽  
Vol 20 (4) ◽  
pp. 349-363
Author(s):  
André Desseaux ◽  
Jean-Luc Menet
Keyword(s):  
Approximate Solution ◽  
Vertical Velocity ◽  
Similarity Solution ◽  
Numerical Results ◽  
Porous Surface ◽  
Quasilinearization Method ◽  
Two Dimensional ◽  
Governing Equations ◽  
Lift And Drag ◽  
Asymptotic Formulation

We consider the influence of withdrawal or injection of a fluid through a porous surface on the flow limited by a long parallel slider. Due to the no-slip conditions, the flow lacks of symmetry. But, a choice for a vertical velocity independent on the gap between the two surfaces is equivalent to a classical similarity solution. Then, the governing equations are reduced to a set of three ordinary differential equations. The quasilinearization method is a powerful tool to resolve these equations as soon as a first approximate solution is known. In both cases of small and large values for Re, we present an asymptotic formulation and use these first solutions for the scheme. A comparison with our numerical results shows that, respectively, these two approximations can be used until Re<5 for the first one and if Re>25 for the second. The different numerical results (velocity profiles, pressure, lift and drag) as functions of Re are analysed and compared with other published values.

Unsteady transonic flows in two-dimensional channels

1972 ◽  
Vol 52 (3) ◽  
pp. 437-449 ◽  
Author(s):  
T. C. Adamson
Keyword(s):  
Inviscid Flow ◽  
Time Varying ◽  
Two Dimensional ◽  
Perfect Gas ◽  
Flow Disturbance ◽  
Specific Heats ◽  
Isentropic Flow ◽  
Perturbation Potential ◽  
Temporal Flow ◽  
Nozzle Flows

A two-dimensional, unsteady, transonic, irrotational, inviscid flow of a perfect gas with constant specific heats is considered. The analysis involves perturbations from a uniform sonic isentropic flow. The governing perturbation potential equations are derived for various orders of the ratio of the characteristic time associated with a temporal flow disturbance to the time taken by a sonic disturbance to traverse the transonicregime. The case where this ratio is large compared to one is studied in detail. A similarity solution involving an arbitrary function of time is found and it is shown that this solution corresponds to unsteady chimel flows with either stationary or time-varying wall shapes. Numerical computations are presented showing the temporal changes in flow structure as a disturbance dies out exponentially for the following typical nozzle flows: simple accelerating (Meyer) flow and flow with supersonic pockets (Taylor and limiting Taylor flow).

Efficiency Comparison Between Circular and Semicircular Fins Circumscribing Circular Pipes

2011 ◽  
Vol 133 (4) ◽  
Author(s):  
R. Chakraborty ◽  
A. Sirkar
Keyword(s):  
Temperature Distribution ◽  
Thermal Performance ◽  
Numerical Results ◽  
Circular Pipe ◽  
Two Dimensional ◽  
Governing Equations ◽  
Degree Polynomial ◽  
Circular Pipes ◽  
Efficiency Comparison ◽  
Detailed Derivation

A new design of fin has been conceived, which is in the shape of a semicircular strip. A step-by-step straightforward detailed derivation of the governing equations for two-dimensional temperature distribution in a semicircular fin has been presented, assuming a third degree polynomial. Numerical results are presented to illustrate the effects of pipe size and the number of semicircular fins on the thermal performance of the fin. It has been shown mathematically that the efficiency of a semicircular fin can be greater than that of a circular fin, having same total volume of fin material when employed over the circumference of a circular pipe.

scholarly journals A Numerical Simulation of the Inviscid Flow Through a Counterrotating Propeller

1986 ◽  
Vol 108 (2) ◽  
pp. 187-193 ◽  
Author(s):  
M. L. Celestina ◽  
R. A. Mulac ◽  
J. J. Adamczyk
Keyword(s):  
Numerical Simulation ◽  
Flow Field ◽  
High Speed ◽  
Inviscid Flow ◽  
Solution Procedure ◽  
Numerical Results ◽  
Governing Equations ◽  
Flow Through ◽  
Coding Strategy

This paper presents the results of a numerical simulation of the time-averaged inviscid flow field through the blade rows of a multiblade row turboprop configuration. The governing equations are outlined along with a discussion of the solution procedure and coding strategy. Numerical results obtained from a simulation of the flow field through a modern high-speed turboprop will be shown.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

scholarly journals Influence of a Standing Wave Flow-Field on the Dynamics of a Spray Diffusion Flame

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 27
Author(s):  
J. Barry Greenberg ◽  
David Katoshevski
Keyword(s):  
Liquid Phase ◽  
Flow Field ◽  
Standing Wave ◽  
Diffusion Flame ◽  
Stokes Number ◽  
Flame Height ◽  
Wave Flow ◽  
Two Dimensional ◽  
Governing Equations ◽  
First Time

A theoretical investigation of the influence of a standing wave flow-field on the dynamics of a laminar two-dimensional spray diffusion flame is presented for the first time. The mathematical analysis permits mild slip between the droplets and their host surroundings. For the liquid phase, the use of a small Stokes number as the perturbation parameater enables a solution of the governing equations to be developed. Influence of the standing wave flow-field on droplet grouping is described by a specially constructed modification of the vaporization Damkohler number. Instantaneous flame front shapes are found via a solution for the usual Schwab–Zeldovitch parameter. Numerical results obtained from the analytical solution uncover the strong bearing that droplet grouping, induced by the standing wave flow-field, can have on flame height, shape, and type (over- or under-ventilated) and on the existence of multiple flame fronts.

Numerical Analysis of Two-Phase Pipe Flow of Liquid Helium Using Multi-Fluid Model

2001 ◽  
Vol 123 (4) ◽  
pp. 811-818 ◽  
Author(s):  
Jun Ishimoto ◽  
Mamoru Oike ◽  
Kenjiro Kamijo
Keyword(s):  
Phase Transition ◽  
Gas Phase ◽  
Liquid Helium ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Numerical Results ◽  
Phase Flow ◽  
Two Dimensional ◽  
Two Phase ◽  
Normal Fluid

The two-dimensional characteristics of the vapor-liquid two-phase flow of liquid helium in a pipe are numerically investigated to realize the further development and high performance of new cryogenic engineering applications. First, the governing equations of the two-phase flow of liquid helium based on the unsteady thermal nonequilibrium multi-fluid model are presented and several flow characteristics are numerically calculated, taking into account the effect of superfluidity. Based on the numerical results, the two-dimensional structure of the two-phase flow of liquid helium is shown in detail, and it is also found that the phase transition of the normal fluid to the superfluid and the generation of superfluid counterflow against normal fluid flow are conspicuous in the large gas phase volume fraction region where the liquid to gas phase change actively occurs. Furthermore, it is clarified that the mechanism of the He I to He II phase transition caused by the temperature decrease is due to the deprivation of latent heat for vaporization from the liquid phase. According to these theoretical results, the fundamental characteristics of the cryogenic two-phase flow are predicted. The numerical results obtained should contribute to the realization of advanced cryogenic industrial applications.

Internal waves in a viscous atmosphere

1975 ◽  
Vol 72 (4) ◽  
pp. 773-786 ◽  
Author(s):  
W. L. Chang ◽  
T. N. Stevenson
Keyword(s):  
Energy Source ◽  
Incompressible Fluid ◽  
Internal Waves ◽  
Infinite Number ◽  
Similarity Solution ◽  
Small Amplitude ◽  
Horizontal Plane ◽  
Two Dimensional ◽  
The Waves ◽  
Isothermal Atmosphere

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

Analytical Study of the Convection Heat Transfer From an Isothermal Wedge Surface to Fluids

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. Bachiri ◽  
A. Bouabdallah
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Ad Hoc ◽  
Convection Heat Transfer ◽  
Analytical Approximation ◽  
Numerical Results ◽  
Convection Heat ◽  
Governing Equations ◽  
Wedge Surface ◽  
Prandtl Numbers

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.

GAP-LABELING PROPERTIES OF THE ENERGY SPECTRUM FOR TWO-DIMENSIONAL FIBONACCI QUASILATTICES

1995 ◽  
Vol 09 (01) ◽  
pp. 55-66
Author(s):  
YOUYAN LIU ◽  
WICHIT SRITRAKOOL ◽  
XIUJUN FU
Keyword(s):  
Energy Spectrum ◽  
Density Of States ◽  
Energy Gap ◽  
Fractional Part ◽  
Numerical Results ◽  
Step Height ◽  
Integrated Density Of States ◽  
Two Dimensional

We have analytically obtained the occupation probabilities on subbands of the hierarchical energy spectrum and the step heights of the integrated density of states for two-dimensional Fibonacci quasilattices. Based on the above results, the gap-labeling properties of the energy spectrum are found, which claim that the step height is equal to {mτ}, where the braces denote the fractional part, and m is an integer that can be used to label the corresponding energy gap. Numerical results confirm these results very well.

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