Centered simple waves for the two-dimensional pseudo-steady isothermal flow around a convex corner

2019 ◽  
Vol 40 (5) ◽  
pp. 705-718
Author(s):  
Wancheng Sheng ◽  
Aidi Yao
Keyword(s):  
Isothermal Flow ◽  
Two Dimensional ◽  
Convex Corner ◽  
Simple Waves

The two-dimensional unsteady supersonic flow around a convex corner

2018 ◽  
Vol 15 (03) ◽  
pp. 443-461 ◽  
Author(s):  
Wancheng Sheng ◽  
Shouke You
Keyword(s):  
Supersonic Flow ◽  
Euler Equations ◽  
Compression Wave ◽  
The Self ◽  
Two Dimensional ◽  
Convex Corner ◽  
Simple Waves ◽  
Unsteady Supersonic Flow ◽  
Self Similar Solution ◽  
Self Similar

The flow around a convex corner is one of the most important elementary flows. In this paper, we are concerned with the two-dimensional (2D) unsteady supersonic flow turning a convex corner. We firstly give the properties of general centered simple for the two-dimensional isentropic irrotational pesudo-steady Euler equations. Then, by using the properties of general centered simple waves, we construct the self-similar solution for the two-dimensional isentropic irrotational supersonic flow around a convex corner and prove that the supersonic flow turns the convex corner by a centered expansion wave or a centered compression wave under appropriate conditions on the downstream state.

Effects of horizontally two-dimensional bodies on the mass transport near the sea bottom

1977 ◽  
Vol 83 (3) ◽  
pp. 415-431 ◽  
Author(s):  
Jacques Lamoure ◽  
Chiang C. Mei
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Experimental Evidence ◽  
Coriolis Force ◽  
Gravity Waves ◽  
Harmonic Waves ◽  
Two Dimensional ◽  
Convex Corner ◽  
Horizontal Dimension ◽  
Sea Bottom

Mass transport close to the sea bottom is investigated for simple harmonic waves around a body with a small horizontal dimension. For gravity waves it is shown that the mass transport very near the bottom points towards a convex corner, but near the top of the boundary layer its direction reverses. Possible implications for silting near a pile and a harbour entrance are discussed and some experimental evidence given. For tides, the Coriolis force introduces a spiralling variation within the boundary layer, and possible inferences for coastline modification are drawn.

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.

Supersonic Flow Past a Wedge with a Flame at its Apex

1968 ◽  
Vol 19 (1) ◽  
pp. 80-90 ◽  
Author(s):  
R. Foster ◽  
J. F. Clarke
Keyword(s):  
Supersonic Flow ◽  
Flame Front ◽  
Flow Patterns ◽  
Chemical Energy ◽  
Two Dimensional ◽  
Pressure Flow ◽  
Simple Waves ◽  
Flow Past ◽  
Flow Deflection ◽  
Plane Flame

SummaryThe wholly supersonic flow past a two-dimensional wedge is analysed on the assumption that release of chemical energy into the stream can be accomplished across a thin discontinuous plane flame front attached to the apex. Forces experienced by the wedge are calculated and representative flow patterns exhibited. Some typical interactions between the flame and shocks or centred simple waves are discussed, with emphasis on the use of pressure-flow-deflection diagrams to obtain results.

Interaction of fan–jump–fan composite waves in a two-dimensional steady jet for van der Waals gases

2017 ◽  
Vol 14 (01) ◽  
pp. 73-134 ◽  
Author(s):  
Geng Lai
Keyword(s):  
Supersonic Flow ◽  
Van Der Waals ◽  
Wave Interaction ◽  
Goursat Problem ◽  
Two Dimensional ◽  
Interaction Zone ◽  
Simple Waves ◽  
Discontinuous Boundary ◽  
Type Boundary ◽  
Discontinuous Boundary Data

We consider a two-dimensional (2D) steady jet generated by gas streaming in parallel supersonic flow out of a duct and into the atmosphere. When the gas is a van der Waals gas, at the corners at the exit of the duct, the parallel supersonic flow expands symmetrically into centered simple waves, jump–fan (JF) composite waves, fan–jump composite waves, or fan–jump–fan (FJF) composite waves. This paper studies the interaction of the symmetric centered FJF composite waves in the jet. The interaction of the FJF composite waves is more involved in comparison to our earlier work on the interaction of the symmetric centered JF composite waves, since the flow in the FJF composite wave interaction zone is rotational. To construct the flow in the interaction zone, we consider a Goursat-type boundary value problem with discontinuous boundary data associated with the 2D and isentropic steady Euler equations. The existence of a global piecewise smooth solution to this Goursat problem is obtained by a new method based on characteristics.

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