New time-marching methods for compressible Navier-Stokes equations with applications to aeroacoustics problems

2022 ◽  
Vol 419 ◽  
pp. 126863
Vivek S. Yadav ◽  
Naveen Ganta ◽  
Bikash Mahato ◽  
Manoj K. Rajpoot ◽  
Yogesh G. Bhumkar
T. Tanuma ◽  
N. Shibukawa ◽  
S. Yamamoto

An implicit time-marching higher-order accurate finite-difference method for solving the two-dimensional compressible Navier-Stokes equations was applied to the numerical analyses of steady and unsteady, subsonic and transonic viscous flows through gas turbine cascades with trailing edge coolant ejection. Annular cascade tests were carried out to verify the accuracy of the present analysis. The unsteady aerodynamic mechanisms associated with the interaction between the trailing edge vortices and shock waves and the effect of coolant ejection were evaluated with the present analysis.

2020 ◽  
Vol 67 ◽  
pp. 100-119 ◽  
Laurent Boudin ◽  
Céline Grandmont ◽  
Bérénice Grec ◽  
Sébastien Martin ◽  
Amina Mecherbet ◽  

In this paper, we propose a coupled fluid-kinetic model taking into account the radius growth of aerosol particles due to humidity in the respiratory system. We aim to numerically investigate the impact of hygroscopic effects on the particle behaviour. The air flow is described by the incompressible Navier-Stokes equations, and the aerosol by a Vlasov-type equation involving the air humidity and temperature, both quantities satisfying a convection-diffusion equation with a source term. Conservations properties are checked and an explicit time-marching scheme is proposed. Twodimensional numerical simulations in a branched structure show the influence of the particle size variations on the aerosol dynamics.

Vaclav Slama ◽  
Bartolomej Rudas ◽  
Ales Macalka ◽  
Jiri Ira ◽  
Antonin Zivny

Abstract An advanced in-house procedure, which is based on a commercial numerical code, to predict a potential danger of unstalled flutter has been developed and validated. This procedure using a one way decoupled method and a full-scale time-marching 3D viscous model in order to obtain the solution of the Unsteady Reynolds-Averaged Navier-Stokes equations in the time domain thus calculate an aerodynamic work and a damping ratio is used as an essential tool for developing ultra-long last stage rotor blades in low pressure turbine parts for modern steam turbines with a large operating range and an enhanced efficiency. An example is shown on a development of the last stage blade for high backpressures.

2017 ◽  
Vol 818 ◽  
pp. 344-365 ◽  
Dominik Dierkes ◽  
Martin Oberlack

The present contribution is a significant extension of the work by Kelbin et al. (J. Fluid Mech., vol. 721, 2013, pp. 340–366) as a new time-dependent helical coordinate system has been introduced. For this, Lie symmetry methods have been employed such that the spatial dependence of the originally three independent variables is reduced by one and the remaining variables are: the cylindrical radius $r$ and the time-dependent helical variable $\unicode[STIX]{x1D709}=(z/\unicode[STIX]{x1D6FC}(t))+b\unicode[STIX]{x1D711}$, $b=\text{const.}$ and time $t$. The variables $z$ and $\unicode[STIX]{x1D711}$ are the usual cylindrical coordinates and $\unicode[STIX]{x1D6FC}(t)$ is an arbitrary function of time $t$. Assuming $\unicode[STIX]{x1D6FC}=\text{const.}$, we retain the classical helically symmetric case. Using this, and imposing helical invariance onto the equation of motion, leads to a helically symmetric system of Euler and Navier–Stokes equations with a time-dependent pitch $\unicode[STIX]{x1D6FC}(t)$, which may be varied arbitrarily and which is explicitly contained in all of the latter equations. This has been conducted both for primitive variables as well as for the vorticity formulation. Hence a significantly extended set of helically invariant flows may be considered, which may be altered by an external time-dependent strain along the axis of the helix. Finally, we sought new conservation laws which can be found from the helically invariant Euler and Navier–Stokes equations derived herein. Most of these new conservation laws are considerable extensions of existing conservation laws for helical flows at a constant pitch. Interestingly enough, certain classical conservation laws do not admit extensions in the new time-dependent coordinate system.

2003 ◽  
Vol 125 (2) ◽  
pp. 308-314 ◽  
C. Cravero ◽  
A. Satta

Turbomachinery flows can nowadays be investigated using several numerical techniques to solve the full set of Navier-Stokes equations; nevertheless the accuracy in the computation of losses is still a challenging topic. The paper describes a time-marching method developed by the authors for the integration of the Reynolds averaged Navier-Stokes equations in turbomachinery cascades. The attention is focused on turbine sections and the computed aerodynamic performances (outlet flow angle, profile loss, etc.,) are compared to experimental data and/or correlations. The need for this kind of CFD analysis tools is stressed for the substitution of standard correlations when a new blade is designed.

2014 ◽  
Vol 610 ◽  
pp. 60-64
Rui Xi ◽  
Zhan Ling Ji ◽  
Hong Guang Jia ◽  
Qian Jin Xiao

A numerical method integrating computational fluid dynamics and computational structural dynamics for predicating wing flutter in time domain is described. A strong coupling employing the dual-time method is adopted. The Newmark algorithm is used to solve flutter equation in modal spaces while the finite-volume algorithm for the Navier-Stokes equations is used to solve the flow. The computed flutter boundaries of AGARD wing 445.6 for frees-tream Mach numbers ranging from 0.499 to 1.141 agree well with the experiment than using the DLM.

1988 ◽  
Vol 110 (3) ◽  
pp. 339-346 ◽  
O. K. Kwon

A robust, time-marching Navier–Stokes solution procedure based on the explicit hopscotch method is presented for solution of steady, two-dimensional, transonic turbine cascade flows. The method is applied to the strong conservation form of the unsteady Navier–Stokes equations written in arbitrary curvilinear coordinates. Cascade flow solutions are obtained on an orthogonal, body-conforming “O” grid with the standard k–ε turbulence model. Computed results are presented and compared with experimental data.

1999 ◽  
Vol 4 (1) ◽  
pp. 124-134
L. K. Lundin ◽  
V. A. Barker ◽  
J. N. Sørensen

This paper deals with the simulation of 3‐D rotating flows based on the velocity‐vorticity formulation of the Navier‐Stokes equations in cylindrical coordinates. The governing equations are discretized by a finite difference method. The solution is advanced to a new time level by a two‐step process. In the first step, the vorticity at the new time level is computed using the velocity at the previous time level. In the second step, the velocity at the new time level is computed using the new vorticity. We discuss here the second part which is by far the most time‐consuming. The numerical problem is that of solving a singular, large, sparse, over‐determined linear system of equations, and the iterative method CGLS is applied for this purpose. We discuss some of the mathematical and numerical aspects of this procedure and report on the performance of our software on a wide range of parallel computers.

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