Unsplit Schemes for Hyperbolic Conservation Laws with Source Terms in One Space Dimension

The present work is concerned with the extension of the theory of characteristics to conservation laws with source terms in one space dimension, such as the Euler equations for reacting flows. New spacetime curves are introduced on which the equations decouple to the characteristic set of O.D.E's for the corresponding homogeneous laws, thus allowing the introduction of functions analogous to the Riemann Invariants. The geometry of these curves depends on the spatial gradients for the solution. This particular decomposition can be used in the design of efficient unsplit algorithms for the numerical integration of the equations. As a first step, these ideas are implemented for the case of a scalar conservation law with a nonlinear source term. The resulting algorithm belongs to the class of MUSCL-type, shock-capturing schemes. Its accuracy and robustness are checked through a series of tests. The aspect of the stiffness of the source term is also studied. Then, the algorithm is generalized for a system of hyperbolic equations, namely the Euler equations for reacting flows. An extensive numerical study of unstable detonations is performed

The effect of electrostatic charges on particle-laden duct flows

We report on direct numerical simulations of the effect of electrostatic charges on particle-laden duct flows. The corresponding electrostatic forces are known to affect particle dynamics at small scales and the associated turbophoretic drift. Our simulations, however, predicted that electrostatic forces also dominate the vortical motion of the particles, induced by the secondary flows of Prandtl's second kind of the carrier fluid. Herein we treated flows at two frictional Reynolds numbers ($Re_\mathrm{\tau}=$ 300 and~600), two particle-to-gas density ratios ($\rho_\mathrm{p}/\rho=$ 1000 and 7500), and three Coulombic-to-gravitational force ratios ($F_\mathrm{el}/F_\mathrm{g}=$ 0, 0.004, and 0.026). In flows with a high density ratio at $Re_\mathrm{\tau}=$ 600 and $F_\mathrm{el}/F_\mathrm{g}=$ 0.004, the particles tend to accumulate at the walls. On the other hand, at a lower density ratio, respectively a higher $F_\mathrm{el}/F_\mathrm{g}$ of 0.026, the charged particles still follow the secondary flow structures that are developed in the duct. However, even in this case, the electrostatic forces counteract the particles' inward flux from the wall and, as a result, their vortical motion in these secondary structures is significantly attenuated. This change in the flow pattern results in an increase of the particle number density at the bisectors of the walls by a factor of five compared to the corresponding flow with uncharged particles. Finally, at $Re_\mathrm{\tau}=$ 300, $\rho_\mathrm{p}/\rho=$ 1000, and $F_\mathrm{el}/F_\mathrm{g}=$ 0.026 the electrostatic forces dominate over the aerodynamic forces and gravity and, consequently the particles no longer follow the streamlines of the carrier gas

Influence of the helicopter configuration on its electrostatic charging

A helicopter flying through an atmosphere containing particulates may accumulate high electrostatic charges which can challenge its operational safety. In this paper we report on the in uence of the helicopter configuration on its electrification. Our study is based on a recently developed numerical approach according to which the turbulent air flow around the rotorcraft is estimated via large eddy simulations while the particulate flow is computed via Lagrangian particle tracking. Also, this approach incorporates a model for the triboelectric charge transfer during particle-helicopter collisions that is brie y described herein. The configurations that we examined in our study include rotor systems of two different sizes equipped with two, three or four blades. Our results reveal that a helicopter with fewer blades accumulates less electric current even though the charge on each individual blade is higher. Further, the location of the charge build-up on the rotor disk depends strongly on the number of blades. Also, according to our computations, a reduction of the rotor size leads to a reduction of its electrification, if all other parameters are kept constant

Influence of the rotor configuration on the electrostatic charging of helicopters

A helicopter flying through an atmosphere containing particulates may accumulate high electrostatic charges that can challenge its operational safety. In this paper the influence of the helicopter configuration on its electrification is reported. The current study is based on a recently developed numerical approach in which the turbulent airflow around the rotorcraft is estimated via large-eddy simulations, whereas the particulate flow is computed via Lagrangian particle tracking. Also, this approach incorporates a model for the triboelectric charge transfer during particle-helicopter collisions that is briefly described herein. The configurations examined in the study include rotor systems equipped with two, three, or four blades. Also investigated are the effects of the rotor size and its rotational frequency. The current results predict that a helicopter with fewer blades accumulates less electric current, even though the charge on each individual blade is higher. Furthermore, the location of the charge buildup on the rotor disk depends strongly on the number of blades. Also, according to current computations, a reduction of the rotor size leads to a reduction of its electrification, even if the blade tip velocity is kept constant