Residual‐based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics

The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non‐uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual‐based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared‐solenoidal mean flow, and for the aeolian tone generated by flow past a two‐dimensional cylinder. Copyright © 2016 John Wiley & Sons, Ltd.     

Stability and Existence of Multidimensional Subsonic Phase Transitions

The purpose of this paper is to prove the uniform stability of multidimensional subsonic phase transitions satisfying the viscosity-capillarity criterion in a van der Waals fluid, and further to establish the local existence of phase transition solutions.     

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.     

A computational study of gas flow in a De‐Laval micronozzle at different throat diameters

A numerical study has been carried out to investigate the gas flows in a micronozzle using a continuum model under both slip and no‐slip boundary conditions. The governing equations were solved with a finite volume method. The numerical model was validated with available experimental data. Numerical results of exit thrust showed good agreement with experimental data except at very low Reynolds numbers. For parametric studies on the effect of geometric scaling, the nozzle throat diameter was varied from 10 to 0.1 mm, whereas throat Reynolds number was varied from 5 to 2000. A correlation has also been developed to calculate the specific impulse at specified throat diameter and Reynolds number. The effect of different gases on the specific impulse of the nozzle, such as helium, nitrogen, argon and carbon dioxide, was also examined. Copyright © 2008 John Wiley & Sons, Ltd.     

On the choice of approximations in direct problems of nozzle design

Two problems are considered: the design of a supersonic nozzle with a uniform exit characteristic and the design of a subsonic nozzle part with a plane (straight) sonic line in the minimum cross section. It is shown how the choice of a nozzle profile approximation affects the direct solutions to variational gas dynamics problems. The nozzle profile is described by polynomials or splines (quadratic, cubic, rational). The varied variables are the profile’s expansion coefficients in terms of basis functions or the parameters to be interpolated. It is shown that a priori information on the monotonicity of the desired profile improves the efficiency of the solution.     

Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.     

Inviscid flow modelling using asymmetric implicit finite difference schemes

Asymmetric spatial implicit high‐order schemes are introduced and, based on Fourier analysis, the dispersion and damping are calculated depending on the asymmetry parameter. The derived schemes are then applied to a number of inviscid problems. For incompressible convection problems the proposed asymmetric schemes (applied as upwind schemes) lead to stable and accurate results. To extend the applicability of the proposed schemes to compressible problems acoustic upwinding is used. In a two‐dimensional compressible flow example acoustic and conventional upwinding are combined. Evaluation of all presented results leads to the conclusion that, of the studied schemes, the implicit fifth order upwinding scheme with an asymmetry parameter of about 0.5 leads to the optimal results. Copyright © 2005 John Wiley & Sons, Ltd.     

An experimental study of the effect of the blow-in rate on the size of the flow separation region

Experimental results are presented concerning the effect of the air blow-in rate on the size of the flow separation region downstream of a rearward-facing step at different step heights. The stream function is found from the experimental velocity profiles, the streamline = 0 being taken as the boundary line. It is shown that the separation region increases as the blow-in rate is increased. Generalization of the experimental results for different blow-in rates and step heights has made it possible to obtain an analytical expression describing the location of some characteristic lines in the separation region (boundary streamline, reverse-flow boundary, line of reverse-flow maximum velocity, line of variable-velocity layer thickness, and the displacement thickness line). Velocity profiles are obtained by means of a hot-wire anemometer. Analytical expressions are written as polynomials with unknown coefficients. The results obtained may be helpful in developing techniques for the treatment of heat transfer under flow separation conditions.     

THE UNIQUENESS OF A TRANSONIC SHOCK IN A NOZZLE FOR THE 2-D COMPLETE EULER SYSTEM WITH THE VARIABLE END PRESSURE

In this paper, by use of the methods in [1-3], we establish the uniqueness of a 2-D transonic shock solution in a nozzle when the end pressure in the diverging part of the nozzle lies in an appropriate scope. Especially, we remove the crucial but unnatural assumption in recent references which the transonic shock must be assumed to go through a fixed point in advance.     

Numerical simulations of sloshing and suppressing sloshing using the optimization technology method

Sloshing is a common phenomenon in nature and industry, and it is important in many fields, such as marine engineering and aerospace engineering. To reduce the sloshing load on the side walls, the topology optimization and optimal control methods are used to design the shape of the board, which is fixed in the middle of the tank. The results show that the new board shape, which is designed via topology optimization, can significantly reduce the sloshing load on the side wall.