A transformation of the hodograph equation and the determination of certain fluid motions

1953 ◽  
Vol 245 (904) ◽  
pp. 583-624 ◽  
Keyword(s):  
Harmonic Functions ◽  
Gas Dynamics ◽  
Free Stream ◽  
Nozzle Flow ◽  
Type Ii ◽  
Sonic Nozzle ◽  
Free Stream Mach Number ◽  
Particular Solution ◽  
Nozzle Flows

A transformation is given of the hodograph equation of two-dimensional gas dynamics, from the usual variables q, 6t to q and a new variable (J). The transformation, which suits any gas for which pp~y = const, with y> 1, is so chosen that certain solutions, which in terms of q, 6 are multi valued, become single-valued functions of q, <j). Such a solution is represented, over the whole domain which is of interest, by a single series in q, which is rapidly convergent; whereas in terms of q, 6 different series would be required for different branches of the function, and these would be but slowly convergent. By this method we can construct (i) the nozzle flow for which the axial velocity is a prescribed analytic function of position, in particular trans-sonic nozzle flows; and (ii) various cases of flow past aerofoil-shaped cylinders placed in a uniform stream. Taking y = T4, complete numerical results are given for one case of trans-sonic nozzle flow, and from these other such flows can be obtained by superposition, and a family of flows of type (ii) is investigated, in which the trailing edge of the aerofoil is cusped; the aerofoil shape has been calculated for two representative values of the free- stream Mach number. A limiting flow of this family is found to consist of a set of Prandtl-Meyer flows, analytically distinct but joining continuously where they abut. These flows are related to a particular solution of the hodograph equation which is of funda­ mental analytic importance; it stands in the same relation to the set of 'Chaplygin solutions’ as the generating function for Legendre polynomials does to the harmonic functions rnPn(cos 6).

Human Umbilical Cord Mesenchymal Stem Cells Induce into Chondrocytes in 3D Cultured System

2013 ◽  
Vol 749 ◽  
pp. 198-205
Author(s):  
Li Yu ◽  
Jing Liu ◽  
Chao Xu ◽  
Er Mei Luo ◽  
Ming Qiao Tang
Keyword(s):  
Real Time ◽  
Alcian Blue ◽  
Culture System ◽  
Type Ii Collagen ◽  
Human Umbilical Cord ◽  
Type Ii ◽  
Pellet Culture ◽  
Hla Dr

Objective: To investigate a better method of inducing hUC-MSCs into chondrocytes in different culture system in vitro. Method: hUC-MSCs were isolated and cultured by tissue block culture, and the cells surface antigens were identified by flow cytometry, hUC-MSCs were cultured with chondrogenic media and stained with Alcian Blue. The production of matrix was estimated from the determination of hydroxyproline content and Alcian Blue method. Expressions of glycosaminoglycan (GAG), type II collagen and Sox-9 were assayed by real-time fluorescence quantitative PCR. Results: The cultured hUC-MSCs phenotype was CD105+/CD29+/CD44+/ CD31-/CD34-/ CD40-/CD45-/HLA-DR-. hUC-MSCs weakly expressed chondrocyte marker, which strongly expressed GAG and type II collagen after chondrogenic induction, and the cells were incubated in pellet culture with higher expression. Real-time PCR results demonstrated that chondrogenic induction cells were expressed GAG, type II collagen and Sox-9, and the cells were incubated in pellet culture with higher expression. Conclusion: hUC-MSCs incubated in pellet culture is more conducive to differentiate into chondrocytes than those cultured in monolayer culture system.

A numerical study of the interaction between unsteay free-stream disturbances and localized variations in surface geometry

1989 ◽  
Vol 209 ◽  
pp. 285-308 ◽  
Author(s):  
R. J. Bodonyi ◽  
W. J. C. Welch ◽  
P. W. Duck ◽  
M. Tadjfar
Keyword(s):  
Numerical Solutions ◽  
Free Stream ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Surface Geometry ◽  
Navier Stokes Equations ◽  
S Waves ◽  
Tollmien Schlichting

A numerical study of the generation of Tollmien-Schlichting (T–S) waves due to the interaction between a small free-stream disturbance and a small localized variation of the surface geometry has been carried out using both finite–difference and spectral methods. The nonlinear steady flow is of the viscous–inviscid interactive type while the unsteady disturbed flow is assumed to be governed by the Navier–Stokes equations linearized about this flow. Numerical solutions illustrate the growth or decay of the T–S waves generated by the interaction between the free-stream disturbance and the surface distortion, depending on the value of the scaled Strouhal number. An important result of this receptivity problem is the numerical determination of the amplitude of the T–S waves.

scholarly journals Determination of free L-carnitine levels in type II diabetic women with and without complications

2007 ◽  
Vol 61 (7) ◽  
pp. 892-895 ◽  
Author(s):  
A Poorabbas ◽  
F Fallah ◽  
J Bagdadchi ◽  
R Mahdavi ◽  
A Aliasgarzadeh ◽  
...  
Keyword(s):  
Type Ii

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

Further Developments in the Aerodynamic Analysis of Unsteady Supersonic Cascades—Part 2: Aerodynamic Response Predictions

1977 ◽  
Vol 99 (4) ◽  
pp. 517-525 ◽  
Author(s):  
J. M. Verdon
Keyword(s):  
Free Stream ◽  
Narrow Range ◽  
Axial Flow ◽  
Stable Condition ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Numerical Predictions ◽  
Free Stream Mach Number ◽  
Parameter Values ◽  
Phase Angles

This paper is the second of a two-part report on a theoretical analysis of the aerodynamic response to an oscillating supersonic cascade in subsonic axial flow. Supersonic resonance criteria are discussed and lead to the distinction between subresonant and superresonant cascade motions. Numerical predictions, based on the unsteady solution reported in Part 1, are presented for two typical cascade configurations. These reveal the possibility of both subresonant and superresonant single-degree-of-freedom torsional instabilities. Subresonant instabilities occur over a broad range of frequencies and interblade phase angles, whereas superresonant instabilities occur only over a narrow range of such cascade parameter values. For a given blade motion frequency and free-stream Mach number, it appears that the least stable condition will usually lie in the subresonant region.

Direct numerical simulation of flow past a transversely rotating sphere up to a Reynolds number of 300 in compressible flow

2018 ◽  
Vol 857 ◽  
pp. 878-906 ◽  
Author(s):  
T. Nagata ◽  
T. Nonomura ◽  
S. Takahashi ◽  
Y. Mizuno ◽  
K. Fukuda
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Mach Number ◽  
Direct Numerical Simulation ◽  
Drag Coefficient ◽  
Rotation Rate ◽  
Free Stream ◽  
Rotating Sphere ◽  
Free Stream Mach Number ◽  
Low Reynolds

In this study, direct numerical simulation of the flow around a rotating sphere at high Mach and low Reynolds numbers is conducted to investigate the effects of rotation rate and Mach number upon aerodynamic force coefficients and wake structures. The simulation is carried out by solving the three-dimensional compressible Navier–Stokes equations. A free-stream Reynolds number (based on the free-stream velocity, density and viscosity coefficient and the diameter of the sphere) is set to be between 100 and 300, the free-stream Mach number is set to be between 0.2 and 2.0, and the dimensionless rotation rate defined by the ratio of the free-stream and surface velocities above the equator is set between 0.0 and 1.0. Thus, we have clarified the following points: (1) as free-stream Mach number increased, the increment of the lift coefficient due to rotation was reduced; (2) under subsonic conditions, the drag coefficient increased with increase of the rotation rate, whereas under supersonic conditions, the increment of the drag coefficient was reduced with increasing Mach number; and (3) the mode of the wake structure becomes low-Reynolds-number-like as the Mach number is increased.

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%.

Administration of a Mixture of Fungal Glucosidases to a Patient with Type II Glycogenosis (Pompe's Disease)

PEDIATRICS ◽  
1968 ◽  
Vol 42 (4) ◽  
pp. 672-676
Author(s):  
Ronald M. Lauer ◽  
Thelma Mascarinas ◽  
Antonio S. Racela ◽  
Antoni M. Diehl ◽  
Barbara Illingworth Brown
Keyword(s):  
Skeletal Muscle ◽  
Enzyme Assay ◽  
Glycogen Content ◽  
Hydrolytic Enzymes ◽  
Type Ii ◽  
Electron Microscopic ◽  
Pompe’S Disease ◽  
Pompe's Disease ◽  
Type Ii Glycogenosis

A case of Type II glycogenosis (Pompe's disease) has been studied by histochemical, electron microscopic, and biochemical techniques. These studies have been made prior to and after the intramuscular administration for 1 week of a mixture of hydrolytic enzymes containing both α-1,4- and α-1,6-glucosidase activities. Electron photomicrographs of the liver before enzyme administration showed glycogen to be located both within and outside of membrane-limited vacuoles. No change in this distribution could be detected in tissue removed by biopsy after enzyme administration. This impression was confirmed by the determination of glycogen content which was shown to be unchanged. Nevertheless, the liver was found by enzyme assay to contain the administered enzyme. Leucocytes isolated from blood taken 4 hours after the last enzyme injection were also shown to contain the parenterally administered glucosidases. In skeletal muscle glycogen was present chiefly as extrasaccular deposits which were unchanged in appearance by enzyme administration. No glucosidase activity was demonstrable in the skeletal muscle after such a treatment. Myocardium sectioned after autopsy had major deposits of glycogen in extrasaccular areas.

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