Transonic flow of a fluid with positive and negative nonlinearity through a nozzle

  title={Transonic flow of a fluid with positive and negative nonlinearity through a nozzle},
  author={Devi Chandrasekar and Phoolan Prasad},
  journal={Physics of Fluids},
The one‐dimensional transonic flow of an inviscid fluid, which at large values of the specific heats exhibits both positive (Γ>0) and negative (Γ<0) nonlinearity regions {Γ=(1/ρ)[∂(ρa)/∂ρ]s} and which remains in a single phase, is studied. By assuming that Γ changes its sign in the small neighborhood of the throat of the nozzle where transonic flow exists and introducing a new scaling of the independent variables, an approximate first‐order partial differential equation (PDE) with a nonconvex… 

Unsteady transonic nozzle flow of dense gases

Vapours of retrograde fluids, i.e. media with large values of the specific heats, may have the remarkable property that sonic conditions are reached three times rather than once during isentropic

Transonic nozzle flow of dense gases

  • A. Kluwick
  • Engineering
    Journal of Fluid Mechanics
  • 1993
The paper deals with the flow properties of dense gases in the throat area of slender nozzles. Starting from the Navier–Stokes equations supplemented with realistic equations of state for gases which

Nozzle flows of dense gases

Numerical solutions for steady inviscid flows in conventional converging–diverging nozzles are obtained. The fluids considered are Bethe–Zel’dovich–Thompson fluids, i.e., those having specific heats

Shock regularization in dense gases by viscous–inviscid interactions

Transonic high-Reynolds-number flows through channels which are so narrow that the classical boundary-layer approach fails locally are considered in the presence of a weak stationary normal shock. As

Nonclassical effects in two‐dimensional transonic flows

The scientific interest and motivation for the investigation of Bethe–Zel’dovich–Thompson (BZT) fluids follows from the fact that all the nonclassical phenomena for these fluids occur for single

Exact solutions to non-classical steady nozzle flows of Bethe–Zel’dovich–Thompson fluids

Steady nozzle flows of Bethe–Zel’dovich–Thompson fluids – substances exhibiting non-classical gasdynamic behaviour in a finite vapour-phase thermodynamic region in close proximity to the

Real gas effects on the normal shock behavior near curved walls

The influence of dense gases on the curvature and the strength of a normal shock near curved walls is discussed. In classical gasdynamics there is a postshock expansion and the shock is curved

Transonic flows of Bethe—Zel'dovich—Thompson fluids

Bethe–Zel'dovich–Thompson fluids are ordinary, single-phase fluids in which the fundamental derivative of gasdynamics is negative over a finite range of temperatures and pressures. We examine the

Interacting laminar boundary layers of dense gases

The concept of triple deck theory is applied to study laminar interacting boundary layers of dense gases in external subsonic, supersonic and transonic flow. If the flow outside the boundary layer is



Shock formation in fluids having embedded regions of negative nonlinearity

The steepening of one‐dimensional finite‐amplitude waves in inviscid Van der Waals gases is described. The undisturbed medium is taken to be unbounded, at rest and uniform. The specific heat is taken

Nonlinear wave propagation on an arbitrary steady transonic flow

  • P. Prasad
  • Mathematics, Physics
    Journal of Fluid Mechanics
  • 1973
Here, we have studied the propagation of an arbitrary disturbance bounded in space on an arbitrary two- or three-dimensional transonic flow. First we have presented a general theory valid for an

Nonlinear stability and instability of transonic flows through a nozzle

We study transonic flows along a nozzle based on a one-dimensional model. It is shown that flows along the expanding portion of the nozzle are stable. On the other hand, flows with standing shock

Trapped waves in the neighbourhood of a sonic-type singularity

A model equation is derived to study trapped nonlinear waves with a turning effect, occurring in disturbances induced on a two-dimensional steady flow. Only unimodal disturbances under the short wave

Shock waves and phase changes in a large-heat-capacity fluid emerging from a tube

The emergence of a shockwave from the open end of a shock tube is studied, with special emphasis on test fluids of high molar heat capacity, i.e. retrograde fluids. A variety of wavelike

Regularity and large time behaviour of solutions of a conservation law without convexity

  • C. Dafermos
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1985
Synopsis Using the method of generalized characteristics, we discuss the regularity and large time behaviour of admissible weak solutions of a single conservation law, in one space variable, with one

A Fundamental Derivative in Gasdynamics

The quantity which is here called the fundamental derivative has been defined as the nondimensional form Γ≡12ρ3c4(∂2Υ/∂P2)s. The relation of Γ to other thermodynamic variables is discussed. It is

Negative shock waves

Negative or rarefaction shock waves may exist in single-phase fluids under certain conditions. It is necessary that a particular fluid thermodynamic quantity Γ ≡ −½δ In (δP/δν)s/δ In ν be negative:


The thermodynamics of a substance in the critical state has been exten­ sively studied, and a strong dependence of the thermodynamic parameters on the temperature and pressure near the critical point

Multiple Steady States for 1-D Transonic Flow

The existence of multiple steady states with the same farfield behavior is discussed for simple 1-D transonic model problems. These multiple solutions all have only entropy satisfying compressive