Mathematical aspects of the theory of inviscid hypersonic flow

1991 ◽  
Vol 335 (1637) ◽  
pp. 121-138 ◽  
Keyword(s):  
Chemical Reactions ◽  
Mathematical Analysis ◽  
Solution Structure ◽  
Well Posedness ◽  
Two Dimensional ◽  
Open Problems ◽  
Real Gas ◽  
One Dimensional ◽  
Two Dimensional Flow ◽  
Real Gas Effects

This paper reviews some differential equations arising in the theory of inviscid hypersonic gasdynamics. The only real-gas effects that we have incorporated are simple models for chemical reactions. After describing what is known about the solution structure of these equations in unsteady one-dimensional and steady two- dimensional flow, we make some conjectures about the well-posedness and regularization of certain specific open problems which have not yet been susceptible to mathematical analysis.

An Evaluation of the Average Flow Model [1] for Surface Roughness Effects in Lubrication

1980 ◽  
Vol 102 (3) ◽  
pp. 360-366 ◽  
Author(s):  
J. L. Teale ◽  
A. O. Lebeck
Keyword(s):  
Surface Roughness ◽  
Flow Model ◽  
Two Dimensional ◽  
Roughness Effects ◽  
Important Conclusion ◽  
Average Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Two Dimensional Flow ◽  
Average Flow Model

The average flow model presented by Patir and Cheng [1] is evaluated. First, it is shown that the choice of grid used in the average flow model influences the results. The results presented are different from those given by Patir and Cheng. Second, it is shown that the introduction of two-dimensional flow greatly reduces the effect of roughness on flow. Results based on one-dimensional flow cannot be relied upon for two-dimensional problems. Finally, some average flow factors are given for truncated rough surfaces. These can be applied to partially worn surfaces. The most important conclusion reached is that an even closer examination of the average flow concept is needed before the results can be applied with confidence to lubrication problems.

Circulation Generation and Vortex Ring Formation by Conic Nozzles

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
Moshe Rosenfeld ◽  
Kakani Katija ◽  
John O. Dabiri
Keyword(s):  
Vortex Ring ◽  
Vortex Generator ◽  
Ring Formation ◽  
Vortex Rings ◽  
Two Dimensional ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Vortex Ring Formation ◽  
Exit Nozzle ◽  
Two Dimensional Flow

Vortex rings are one of the fundamental flow structures in nature. In this paper, the generation of circulation and vortex rings by a vortex generator with a static converging conic nozzle exit is studied numerically. Conic nozzles can manipulate circulation and other flow invariants by accelerating the flow, increasing the Reynolds number, and by establishing a two-dimensional flow at the exit. The increase in the circulation efflux is accompanied by an increase in the vortex circulation. A novel normalization method is suggested to differentiate between two contributions to the circulation generation: a one-dimensional slug-type flow contribution and an inherently two-dimensional flow contribution. The one-dimensional contribution to the circulation increases with the square of the centerline exit velocity, while the two-dimensional contribution increases linearly with the decrease in the exit diameter. The two-dimensional flow contribution to the circulation production is not limited to the impulsive initiation of the flow only (as in straight tube vortex generators), but it persists during the entire ejection. The two-dimensional contribution can reach as much as 44% of the total circulation (in the case of an orifice). The present study offers evidences on the importance of the vortex generator geometry, and in particular, the exit configuration on the emerging flow, circulation generation, and vortex ring formation. It is shown that both total and vortex ring circulations can be controlled to some extent by the shape of the exit nozzle.

scholarly journals MATHEMATICAL ANALYSIS OF A ONE-DIMENSIONAL MODEL FOR AN AGING FLUID

2013 ◽  
Vol 23 (09) ◽  
pp. 1561-1602
Author(s):  
DAVID BENOIT ◽  
LINGBING HE ◽  
CLAUDE LE BRIS ◽  
TONY LELIÈVRE
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Mathematical Analysis ◽  
Newtonian Fluids ◽  
Well Posedness ◽  
Dimensional Model ◽  
Partial Differential ◽  
One Dimensional ◽  
Longtime Behavior

We study mathematically a system of partial differential equations arising in the modeling of an aging fluid, a particular class of non-Newtonian fluids. We prove well-posedness of the equations in appropriate functional spaces and investigate the longtime behavior of the solutions.

scholarly journals Emergent order in rheoscopic swirls

2010 ◽  
Vol 667 ◽  
pp. 158-187 ◽  
Author(s):  
MICHAEL WILKINSON ◽  
VLAD BEZUGLYY ◽  
BERNHARD MEHLIG
Keyword(s):  
Order Parameter ◽  
Periodic Potential ◽  
Two Dimensional ◽  
One Dimensional ◽  
Emergent Order ◽  
Long Time ◽  
Parameter Field ◽  
Two Dimensional Flow ◽  
Reflection Of Light ◽  
Local Average

We consider the ordering of particles in a rheoscopic fluid (a suspension of microscopic rod-like particles) in a steady two-dimensional flow, and discuss its consequences for the reflection of light. The ordering is described by an order parameter which is a non-oriented vector, obtained by averaging solutions of a nonlinear equation containing the strain rate of the fluid flow. Exact solutions of this equation are obtained from solutions of a linear equation which are analogous to Bloch bands for a one-dimensional Schrödinger equation with a periodic potential. On some contours of the stream function, the order parameter approaches a limit, and on others it depends increasingly sensitively upon position. However, in the long-time limit a local average of the order parameter is a smooth function of position in both cases. We analyse the topology of the order parameter and the structure of the generic zeros of the order parameter field.

Aqueous solution structure of an intercalated actinomycin D-dATGCAT complex by two-dimensional and one-dimensional proton NMR

Biochemistry ◽  
1984 ◽  
Vol 23 (3) ◽  
pp. 403-408 ◽  
Author(s):  
Stephen C. Brown ◽  
Kary Mullis ◽  
Corey Levenson ◽  
Richard H. Shafer
Keyword(s):  
Aqueous Solution ◽  
Solution Structure ◽  
Actinomycin D ◽  
Proton Nmr ◽  
Two Dimensional ◽  
One Dimensional

An Assessment of Shock-Disturbances Interaction Considering Real Gas Effects

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
K. Hejranfar ◽  
S. Rahmani
Keyword(s):  
Theoretical Analysis ◽  
The Body ◽  
Mathematical Function ◽  
Perfect Gas ◽  
Real Gas ◽  
One Dimensional ◽  
Wide Range ◽  
Different Types ◽  
Real Gas Effects ◽  
Analytical Relations

In this study, a theoretical analysis is performed to assess the interaction of freestream disturbances with a plane normal shock considering real gas effects. Such effects are important in a field with high velocities and high temperatures. To perform the theoretical analysis, the downstream disturbances field is expressed as a mathematical function of the upstream one by incorporating real gas effects in the formulation. Here, the linearized one-dimensional perturbed unsteady Euler equations are used for the classification of the downstream/upstream disturbances field and the linearized one-dimensional perturbed Rankine–Hugoniot equations are applied to provide a relationship between the disturbances field of two sides of the shock. To incorporate real gas effects in the formulation, real gas relations and equilibrium air curve-fits are used in the resulting system of equations. The general formulation presented here may be simplified to derive Morkovin's formulation by the perfect gas assumption. The magnitudes of downstream disturbances field resulting from different types of upstream disturbances field (entropy wave and fast/slow acoustic waves) with the shock are expressed by appropriate analytical relations. Results for different disturbance variables are presented for a wide range of upstream Mach number considering real gas effects and compared with those of the perfect gas and some conclusions are made. The effects of the presence of body are also studied theoretically and the analytical relations for the magnitude of the pressure disturbance at the body for different types of upstream disturbances field considering real gas effects are provided and their results are presented and discussed.

Influence of suspended sediment on the transport processes of nonlinear reactive substances in turbulent streams

2002 ◽  
Vol 472 ◽  
pp. 307-331 ◽  
Author(s):  
R. REVELLI ◽  
L. RIDOLFI
Keyword(s):  
Suspended Sediment ◽  
Chemical Reactions ◽  
Fluid Dynamic ◽  
Suspended Particles ◽  
Transport Processes ◽  
Desorption Kinetics ◽  
Two Dimensional ◽  
Particle Sedimentation ◽  
Differential Model ◽  
One Dimensional

The fluid dynamic behaviour of a reactive chemical in a stream can be greatly influenced by the presence of sorbing suspended particles. In this case, a kinetically controlled mass transfer is established between sorbed and dissolved phases and complex interactions emerge between fluid dynamical transport processes, sorption–desorption kinetics and chemical reactions. These conditions often occur in rivers, where both suspended sediment and reactive substances are frequently present. This paper deals with the important case in which the chemical reactions are nonlinear decay phenomena that often affect chemical or biological substances. A vertical two-dimensional mathematical model is formulated to take into account advection, turbulent diffusion, particle sedimentation, exchange kinetics between sorbed and dissolved phases, and decay. The decay is modelled for the case in which two different nonlinear decay reactions affect the dissolved and sorbed phases. The main result of the work is to obtain analytically a one-dimensional differential model of the vertically averaged concentration of the dissolved phase, this being conceptually similar to the classical advection–dispersion–decay equation. However, in this case we include the effects of (i) the kinetics with the phase sorbed by suspended particles and (ii) the influence of the two different decay processes. For this purpose, the multiple-scale method of homogenization is applied to the two-dimensional model. The resultant one-dimensional differential model shows how suspended load and decay phenomena affect the pollutant transport mechanisms to a great extent in a non-intuitive way and that the links are nonlinear. Some quantitative results show that these influences are, in general, not negligible.

Sign in / Sign up

Export Citation Format

Share Document