Radiating-Conducting Thick-Transparent Normal Shock Solution

1972 ◽  
Vol 15 (12) ◽  
pp. 2150 ◽  
Author(s):  
Leland A. Carlson
Keyword(s):  
Normal Shock ◽  
Shock Solution

A Correction to the Barotropic Model of Gaseous Cavitation in Choked Converging-Diverging Nozzle Flows

2020 ◽  
Author(s):  
Michael Waldrop ◽  
Flint Thomas
Keyword(s):  
Static Pressure ◽  
Pressure Ratio ◽  
Normal Shock ◽  
Inlet Pressure ◽  
Maximum Pressure ◽  
Prediction Errors ◽  
Cavitation Model ◽  
Static Pressure Distribution ◽  
Shock Solution ◽  
Nozzle Inlet

Abstract The Barotropic Cavitation Model describes the behavior of a homogeneous mixture of liquid and gas bubbles (gaseous cavitation) as it traverses a converging-diverging (CD) nozzle. Its normal shock formulation makes reliable and accurate predictions of streamwise static pressure distribution from the nozzle inlet to just downstream of the throat and in the diverging section as the flow approaches the nozzle outlet. It fails in the intermediate portion of the divergence with maximum pressure prediction errors (as a fraction of nozzle inlet pressure) roughly equivalent to the back pressure ratio (as high as 0.46). A correction to the streamwise static pressure distributions predicted by the normal shock solution of the Barotropic Cavitation Model is proposed, applied and compared to experiments with aerated and non-aerated cavitation in several fluids. When used to simulate aerated cavitation of dodecane in a CD nozzle it predicts the location of first disagreement between the normal shock solution and experimental static pressure measurements within 4% of nozzle length. A polynomial curve fit between this predicted point (xcorr) and the normal shock location (xshock) then reduces maximum prediction error for static pressure in the correction region to no more than 0.11 (as a fraction of inlet pressure) for the aerated dodecane cases examined. For non-aerated gaseous cavitation in dodecane, water or JP8 jet fuel this error ratio does not exceed 0.13 and typical values are less than 0.07.

scholarly journals Aerodynamic Inverse Design of Transonic Compressor Cascades with Stabilizing Elastic Surface Algorithm

2021 ◽  
Vol 11 (11) ◽  
pp. 4845
Author(s):  
Mohammad Hossein Noorsalehi ◽  
Mahdi Nili-Ahmadabadi ◽  
Seyed Hossein Nasrazadani ◽  
Kyung Chun Kim
Keyword(s):  
Design Method ◽  
Inverse Design ◽  
Normal Shock ◽  
Compressor Cascade ◽  
Elastic Surface ◽  
Transonic Compressor ◽  
Pressure Distributions ◽  
The Difference ◽  
Inverse Design Method ◽  
Transonic Cascade

The upgraded elastic surface algorithm (UESA) is a physical inverse design method that was recently developed for a compressor cascade with double-circular-arc blades. In this method, the blade walls are modeled as elastic Timoshenko beams that smoothly deform because of the difference between the target and current pressure distributions. Nevertheless, the UESA is completely unstable for a compressor cascade with an intense normal shock, which causes a divergence due to the high pressure difference near the shock and the displacement of shock during the geometry corrections. In this study, the UESA was stabilized for the inverse design of a compressor cascade with normal shock, with no geometrical filtration. In the new version of this method, a distribution for the elastic modulus along the Timoshenko beam was chosen to increase its stiffness near the normal shock and to control the high deformations and oscillations in this region. Furthermore, to prevent surface oscillations, nodes need to be constrained to move perpendicularly to the chord line. With these modifications, the instability and oscillation were removed through the shape modification process. Two design cases were examined to evaluate the method for a transonic cascade with normal shock. The method was also capable of finding a physical pressure distribution that was nearest to the target one.

Normal shock-wave properties in imperfect air and nitrogen

AIAA Journal ◽  
1965 ◽  
Vol 3 (3) ◽  
pp. 554-556 ◽  
Author(s):  
CLARK H. LEWIS ◽  
E. G. BURGESS
Keyword(s):  
Shock Wave ◽  
Normal Shock ◽  
Normal Shock Wave ◽  
Wave Properties

A shock solution for the nonlinear shallow water equations

2010 ◽  
Vol 658 ◽  
pp. 166-187 ◽  
Author(s):  
MATTEO ANTUONO
Keyword(s):  
Shock Wave ◽  
General Solution ◽  
Theoretical Analysis ◽  
Asymptotic Behaviour ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Boundary Data ◽  
Depth Analysis ◽  
Nonlinear Shallow Water Equations ◽  
Shock Solution

A global shock solution for the nonlinear shallow water equations (NSWEs) is found by assigning proper seaward boundary data that preserve a constant incoming Riemann invariant during the shock wave evolution. The correct shock relations, entropy conditions and asymptotic behaviour near the shoreline are provided along with an in-depth analysis of the main quantities along and behind the bore. The theoretical analysis is then applied to the specific case in which the water at the front of the shock wave is still. A comparison with the Shen & Meyer (J. Fluid Mech., vol. 16, 1963, p. 113) solution reveals that such a solution can be regarded as a specific case of the more general solution proposed here. The results obtained can be regarded as a useful benchmark for numerical solvers based on the NSWEs.

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