A New High Resolution TVD Scheme for Unsteady Flows with Shock Waves

Turbines used in upper stage engine for a rocket are sometimes designed as a supersonic turbine with partial admission. This study deals with numerical investigation of supersonic partial admission turbine in order to understand influences on the unsteady flow pattern, turbine losses and aerodynamic forces on rotor blades due to partial admission configuration. Two-dimensional CFD analysis is conducted using “Numerical Turbine” code. Its governing equation is URANS (Unsteady Reynolds Averaged Navier-Stokes Simulation) and fourth-order MUSCL TVD scheme is used for advection scheme. The unsteady simulation indicates that strongly non-uniform circumferential flow field is created due to the partial admission configuration and it especially becomes complex at 1st stage because of shock waves. Some very high or low flow velocity regions are created around the blockage sector. Nozzle exit flow is rapidly accelerated at the inlet of blockage sector and strong rotor LE shock waves are created. In contrast, at rotor blade passages and Stator2 blade passages existing behind the blockage sector, working gas almost stagnates. Large flow separations and flow mixings occur because of the partial admission configuration. As a result, additional strong dissipations are caused and the magnitude of entropy at the turbine exit is approximately 1.5 times higher than that of the full admission. Rotor1 blades experience strong unsteady aerodynamic force variations. The aerodynamic forces greatly vary when the Rotor1 blade passes through the blockage inlet region. The unsteady force in frequency domain indicates that many unsteady force components exist in wide frequency region and the blockage passing frequency component becomes pronounced in the circumferential direction force. Unsteady forces on Rotor2 blades are characterized by a low frequency fluctuation due to the blockage passing.

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A high resolution cell vertex TVD scheme for the solution of the two and three dimensional Euler equations

Twelfth International Conference on Numerical Methods in Fluid Dynamics - Lecture Notes in Physics ◽

10.1007/3-540-53619-1_232 ◽

1990 ◽

pp. 442-446 ◽

Cited By ~ 6

Author(s):

N. Kroll ◽

C. Rossow

Keyword(s):

High Resolution ◽

Euler Equations ◽

Three Dimensional ◽

Tvd Scheme ◽

Resolution Cell

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Inverse Energy Cascade of Fast Magnetosonic Turbulence in the Heliosheath

10.5194/egusphere-egu2020-12219 ◽

2020 ◽

Author(s):

Bertalan Zieger

Keyword(s):

Solar Wind ◽

High Resolution ◽

Shock Waves ◽

High Frequency ◽

Collisionless Plasma ◽

Energy Cascade ◽

Fast Mode ◽

Turbulence Spectrum ◽

Inverse Energy Cascade ◽

Voyager 2

The solar wind in the heliosheath beyond the termination shock (TS) is a non-equilibrium collisionless plasma consisting of thermal solar wind ions, suprathermal pickup ions (PUI) and electrons. In such multi-ion plasma, two fast magnetosonic wave modes exist: the low-frequency fast mode that propagates in the thermal ion component and the high-frequency fast mode that propagates in the suprathermal PUI component [Zieger et al., 2015]. Both fast modes are dispersive on fluid and ion scales, which results in nonlinear dispersive shock waves. In this talk, we briefly review the theory of dispersive shock waves in multi-ion collisionless plasma. We present high-resolution three-fluid simulations of the TS and the heliosheath up to 2.2 AU downstream of the TS. We show that downstream propagating nonlinear magnetosonic waves grow until they steepen into shocklets (thin current sheets), overturn, and start to propagate backward in the frame of the downstream propagating wave, as predicted by theory [McKenzie et al., 1993; Dubinin et al., 2006]. The counter-propagating nonlinear waves result in fast magnetosonic turbulence far downstream of the shock. Since the high-frequency fast mode is positive dispersive on fluid scale, energy is transferred from small scales to large scales (inverse energy cascade). Thermal solar wind ions are preferentially heated by the turbulence. Forward and reverse shocklets in the heliosheath can efficiently accelerate both ions and electrons to high energies through the shock drift acceleration mechanism. We validate our three-fluid simulations with in-situ high-resolution Voyager 2 magnetic field and plasma observations at the TS and in the heliosheath. Our simulations reproduce the magnetic turbulence spectrum with a spectral slope of -5/3 observed by Voyager 2 in frequency domain [Fraternale et al., 2019]. However, since Taylor&#8217;s hypothesis is not true for fast magnetosonic perturbations in the heliosheath, the inertial range of the turbulence spectrum is not a Kolmogorov spectrum in wave number domain.&#160;

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Gridless Adaptive Method for Simulating Unsteady Flows with Moving Shocks

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.271-272.948 ◽

2012 ◽

Vol 271-272 ◽

pp. 948-952

Author(s):

Sai Hu Pu

Keyword(s):

High Resolution ◽

Numerical Test ◽

Unsteady Flows ◽

Adaptive Method ◽

Test Cases ◽

Computational Domain ◽

Local Pressure ◽

Time Step ◽

Physical Features ◽

Cloud Of Points

In this paper, the gridless adaptive method is extended to simulate unsteady flows with moving shocks. In order to capture physical features like moving shocks with local high resolution, a technique of dynamic cloud of points is achieved by adopting clouds refinement and clouds coarsening procedures during the evolution of the unsteady flows. The regions for clouds refinement and clouds coarsening are determined at every time step by an indicator, which is defined as a function of the local pressure gradient. Once the regions of cloud of points to be adjusted are located by the indicator, the clouds refinement is carried out by introducing new points based on the existing structure of cloud of points, and the clouds coarsening procedure is also implemented simultaneously in order to control the size of the points distributed in the whole computational domain. The numerical test cases show that the gridless adaptive method presented can capture moving shocks with high resolution successfully in both inviscid and viscous test cases.

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