On the breakdown of characteristics solutions in flows with vibrational relaxation

1967 ◽  
Vol 27 (1) ◽  
pp. 49-57 ◽  
Author(s):  
B. S. H. Rarity
Keyword(s):  
Relaxation Time ◽  
Mach Number ◽  
Supersonic Flow ◽  
Steady Flow ◽  
Speed Of Sound ◽  
Vibrational Relaxation ◽  
Precise Measure ◽  
Derivatives Of ◽  
Relaxing Gas ◽  
Flow Case

The breakdown of the characteristics solution in the neighbourhood of the leading frozen characteristic is investigated for the flow induced by a piston advancing with finite acceleration into a relaxing gas and for the steady supersonic flow of a relaxing gas into a smooth compressive corner. It is found that the point of breakdown moves outwards along the leading characteristic as the relaxation time decreases and that there is no breakdown of the solution on the leading characteristic if the gas has a sufficiently small, but non-zero, relaxation time. A precise measure of this relaxation time is derived. The paper deals only with points of breakdown determined by initial derivatives of the piston path or wall shape. In the steady-flow case, the Mach number based on the frozen speed of sound must be greater than unity.

Transonic Buffeting on Aerofoils

1960 ◽  
Vol 64 (599) ◽  
pp. 683-686 ◽  
Author(s):  
C. J. Wood
Keyword(s):  
Mach Number ◽  
Supersonic Flow ◽  
Speed Of Sound ◽  
Sudden Increase ◽  
Loss Of Control ◽  
Mixed Flow ◽  
Critical Mach Number ◽  
Control Effectiveness

There are many problems to be solved when it is required to fly an aircraft at speeds approaching the speed of sound. When the speed of the aeroplane exceeds its critical Mach number, regions of supersonic flow appear at points on its surface, where the velocity of the displaced air is greatest. These regions of supersonic flow increase in size with increasing speed until the flow is wholly supersonic. The range of speed in which this mixed flow occurs is called the transonic range. In this range an aircraft will experience a sudden increase in drag, trim changes, loss of control effectiveness and possibly instability, or buffeting.

The flow of a jet from a body opposing a supersonic free stream

1966 ◽  
Vol 26 (2) ◽  
pp. 337-368 ◽  
Author(s):  
P. J. Finley
Keyword(s):  
Mach Number ◽  
Supersonic Flow ◽  
Steady Flow ◽  
Flow Model ◽  
Free Stream ◽  
Sufficient Condition ◽  
Exit Plane ◽  
Force Coefficient ◽  
Short Account ◽  
Series Of Experiments

A series of experiments is described in which a jet issues from an orifice at the nose of a body in supersonic flow to oppose the mainstream. An analytical model of the flow is developed which suggests that the aerodynamic features of a steady flow depend primarily on a jet flow-force coefficient, and the Mach number of the jet in its exit plane. A sufficient condition for steady flow is developed. The experiments are found to agree well with predictions based on the flow model. A short account is presented of some previous investigations, and some of their conclusions are re-examined in the light of the present study.

Monitoring the encapsulation of chlorin e6 derivatives into polymer carriers by NMR spectroscopy

2019 ◽  
Vol 23 (11n12) ◽  
pp. 1576-1586 ◽  
Author(s):  
Sara Pfister ◽  
Luca Sauser ◽  
Ilche Gjuroski ◽  
Julien Furrer ◽  
Martina Vermathen
Keyword(s):  
Relaxation Time ◽  
Nmr Spectroscopy ◽  
Core Region ◽  
Chlorin E6 ◽  
Polypropylene Glycol ◽  
Polymer Carriers ◽  
H Nmr ◽  
Line Shape Analysis ◽  
Dynamic Methods ◽  
Derivatives Of

The encapsulation of five derivatives of chlorin e6 with different hydrophobicity and aggregation properties into a series of five poloxamer-type triblock copolymer micelles (BCMs) with varying numbers of polyethylene and polypropylene glycol (PEG, PPG) units was monitored using 1H NMR spectroscopy. NMR chemical shift and line shape analysis, as well as dynamic methods including diffusion ordered spectroscopy (DOSY) and T1 and T2 relaxation time measurements of the chlorin and the polymer resonances, proved useful to assess the chlorin–BCM compatibility. The poloxamers had high capability to break up aggregates formed by chlorins up to intermediate hydrophobicity. Physically entrapped chlorins were always localized in the BCM core region. The loading capacity correlated with chlorin polarity for all poloxamers among which those with the lowest number of PPG units were most efficient. DOSY data revealed that relatively weakly aggregating chlorins partition between the aqueous bulk and micellar environment whereas more hydrophobic chlorins are well retained in the BCM core region, rendering these systems more stable. T1 and T2 relaxation time measurements indicated that motional freedom in the BCM core region contributes to encapsulation efficiency. The BCM corona dynamics were rather insensitive towards chlorin entrapment except for the poloxamers with short PEG chains. The presented data demonstrate that 1H NMR spectroscopy is a powerful complementary tool for probing the compatibility of porphyrinic compounds with polymeric carriers such as poloxamer BCMs, which is a prerequisite in the development of stable and highly efficient drug delivery systems suitable for medical applications like photodynamic therapy of tumors.

Mach Number Influence on Reduced-Order Models of Inviscid Potential Flows in Turbomachinery

2002 ◽  
Vol 124 (4) ◽  
pp. 977-987 ◽  
Author(s):  
Bogdan I. Epureanu ◽  
Earl H. Dowell ◽  
Kenneth C. Hall
Keyword(s):  
Mach Number ◽  
Steady Flow ◽  
Inviscid Flow ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Spatial Gradients ◽  
Potential Flows ◽  
Proper Orthogonal Decomposition Technique ◽  
Flow Through ◽  
Phase Angles

An unsteady inviscid flow through a cascade of oscillating airfoils is investigated. An inviscid nonlinear subsonic and transonic model is used to compute the steady flow solution. Then a small amplitude motion of the airfoils about their steady flow configuration is considered. The unsteady flow is linearized about the nonlinear steady response based on the observation that in many practical cases the unsteadiness in the flow has a substantially smaller magnitude than the steady component. Several reduced-order modal models are constructed in the frequency domain using the proper orthogonal decomposition technique. The dependency of the required number of aerodynamic modes in a reduced-order model on the far-field upstream Mach number is investigated. It is shown that the transonic reduced-order models require a larger number of modes than the subsonic models for a similar geometry, range of reduced frequencies and interblade phase angles. The increased number of modes may be due to the increased Mach number per se, or the presence of the strong spatial gradients in the region of the shock. These two possible causes are investigated. Also, the geometry of the cascade is shown to influence strongly the shape of the aerodynamic modes, but only weakly the required dimension of the reduced-order models.

scholarly journals Звуковой удар от тонкого тела и локальных областей нагрева сверхзвукового набегающего потока

2021 ◽  
Vol 91 (4) ◽  
pp. 558
Author(s):  
А.В. Потапкин ◽  
Д.Ю. Москвичев
Keyword(s):  
Mach Number ◽  
Supersonic Flow ◽  
Free Stream ◽  
Local Heating ◽  
Air Flow ◽  
Sonic Boom ◽  
Incoming Flow ◽  
Combined Method ◽  
Cold Flow ◽  
Free Stream Mach Number

The problem of a sonic boom generated by a slender body and local regions of supersonic flow heating is solved numerically. The free-stream Mach number of the air flow is 2. The calculations are performed by a combined method of phantom bodies. The results show that local heating of the incoming flow can ensure sonic boom mitigation. The sonic boom level depends on the number of local regions of incoming flow heating. One region of flow heating can reduce the sonic boom by 20% as compared to the sonic boom level in the cold flow. Moreover, consecutive heating of the incoming flow in two regions provides sonic boom reduction by more than 30%.

A Theory for the High-Speed Flow of Gas-Solids Mixtures under Conditions of Equilibrium and Constant Fractional Lag

1969 ◽  
Vol 184 (3) ◽  
pp. 59-66 ◽  
Author(s):  
B. N. Cole ◽  
H. M. Bowers ◽  
F. R. Mobbs
Keyword(s):  
Mach Number ◽  
Speed Of Sound ◽  
Gas Dynamics ◽  
High Speed ◽  
Solid Particles ◽  
High Speed Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Speed Flow ◽  
Constant Area

A theory is presented for the high-speed, one-dimensional flow of a gas-solids mixture, assuming constant fractional lags of temperature and velocity between the solid particles and the gas. A mixture speed of sound is is derived and used as the basis of a mixture Mach number. Expressions are deduced which are parallel to many well-known relationships in orthodox one-dimensional gas dynamics. The investigation covers frictionless flow in a variable area duct and flow with friction in a constant area duct. The effect of solids volume is also taken into account.

Rapid computation of rotary derivatives for subsonic and low transonic flows

2019 ◽  
Vol 36 (9) ◽  
pp. 3108-3121
Author(s):  
Jian-Ming Fu ◽  
Hai-Min Tang ◽  
Hong-Quan Chen
Keyword(s):  
Mach Number ◽  
Normal Velocity ◽  
New Approach ◽  
Content Type ◽  
Strip Theory ◽  
Model Aircraft ◽  
Computational Fluid Dynamics Cfd ◽  
Steady Solutions ◽  
State Pressure ◽  
Derivatives Of

Purpose The purpose of this paper is to develop a new approach for rapid computation of subsonic and low-transonic rotary derivatives with the available steady solutions obtained by Euler computational fluid dynamics (CFD) codes. Design/methodology/approach The approach is achieved by the perturbation on the steady-state pressure of Euler CFD codes. The resulting perturbation relation is established at a reference Mach number between rotary derivatives and normal velocity on surface due to angular velocity. The solution of the reference Mach number is generated technically by Prandtl–Glauert compressibility correction based on any Mach number of interest under the assumption of simple strip theory. Rotary derivatives of any Mach number of interest are then inversely predicted by the Prandtl–Glauert rule based on the reference Mach number aforementioned. Findings The resulting method has been verified for three typical different cases of the Basic Finner Reference Projectile, the Standard Dynamics Model Aircraft and the Orion Crew Module. In comparison with the original perturbation method, the performance at subsonic and low-transonic Mach numbers has significantly improved with satisfactory accuracy for most design efforts. Originality/value The approach presented is verified to be an efficient way for computation of subsonic and low-transonic rotary derivatives, which are performed almost at the same time as an accounting solution of steady Euler equations.

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