Comparison of dns of compressible and incompressible turbulent droplet-laden heated channel flow with phase transition

In this paper a turbulent channel flow with dispersed droplets is examined. The dispersed phase is allowed to have phase transition, which leads to heat and mass transfer between the phases, and correspondingly modulates turbulent flow properties. As a point of reference we examine the flow of water droplets in air, containing also the vapor of water. The key element of this study concerns the treatment of the carrier phase as either a compressible or an incompressible fluid. We compare simulation results obtained with a pseudo-spectral discretization for the incompressible flow to those obtained with a finite volume approach for the compressible flow. The compressible formulation is not tailored for low Mach flow and we need to resort to a Mach number that is artificially high for simulation feasibility. We discuss differences in fluid flow, heat- and mass transfer and dispersed droplet properties. The main conclusion is that both formulations give a good general correspondence. Flow properties such as velocity fields agree very closely, while heat transfer as characterized by the Nusselt number differs by around 25%. Droplet sizes are shown to be slightly larger, particularly in the center of the channel, in case the compressible formulation is chosen. A low-Mach compressible formulation is required for a fully quantitative comparison

Quick calculation method for fluid flow through duct systems

Conditions for subsonic compressible flow through duct systems are quickly and easily calculated using compact series of curves showing dimensionless parametric functions of Mach number and specific heat ratio. Method is directly applicable to analysis and design of compressible flow systems in industrial fields or processes

Scalar transport in compressible flow

Transport of scalar fields in compressible flow is investigated. The effective equations governing the transport at scales large compared to those of the advecting flow are derived by using multi-scale techniques. Ballistic transport generally takes place when both the solenoidal and the potential components of the velocity do not vanish, despite of the fact that it has zero average value. The calculation of the effective ballistic velocity $V_b$ is reduced to the solution of one auxiliary equation. An analytic expression for $V_b$ is derived in some special instances, i.e. flows depending on a single coordinate, random with short correlation times and slightly compressible cellular flow. The effective mean velocity $V_b$ vanishes for velocity fields which are either incompressible or potential and time-independent. For generic compressible flow, the most general conditions ensuring the absence of ballistic transport are isotropy and/or parity invariance. When $V_b$ vanishes (or in the frame of reference moving with velocity $V_b$), standard diffusive transport takes place. It is known that diffusion is always enhanced by incompressible flow. On the contrary, we show that diffusion is depleted in the presence of time-independent potential flow. Trapping effects due to potential wells are responsible for this depletion. For time-dependent potential flow or generic compressible flow, transport rates are enhanced or depleted depending on the detailed structure of the velocity field.Comment: 27 pages, submitted to Physica

Smooth transonic flow in an array of counter-rotating vortices

Numerical solutions to the steady two-dimensional compressible Euler equations corresponding to a compressible analogue of the Mallier & Maslowe (Phys. Fluids, vol. A 5, 1993, p. 1074) vortex are presented. The steady compressible Euler equations are derived for homentropic flow and solved using a spectral method. A solution branch is parameterized by the inverse of the sound speed at infinity, $c_{\infty}^{-1}$, and the mass flow rate between adjacent vortex cores of the corresponding incompressible solution, $\epsilon$. For certain values of the mass flux, the solution branches followed numerically were found to terminate at a finite value of $c_{\infty}^{-1}$. Along these branches numerical evidence for the existence of extensive regions of smooth steady transonic flow, with local Mach numbers as large as 1.276, is presented

A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small value, $\mathrm{M}\approx 0.1$, in order to mimic incompressible flows. This strategy is widely used for high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations. The present work raises the question regarding the computational efficiency of compressible DG solvers as compared to a genuinely incompressible formulation. Our contributions to the state-of-the-art are twofold: Firstly, we present a high-performance discontinuous Galerkin solver for the compressible Navier-Stokes equations based on a highly efficient matrix-free implementation that targets modern cache-based multicore architectures. The performance results presented in this work focus on the node-level performance and our results suggest that there is great potential for further performance improvements for current state-of-the-art discontinuous Galerkin implementations of the compressible Navier-Stokes equations. Secondly, this compressible Navier-Stokes solver is put into perspective by comparing it to an incompressible DG solver that uses the same matrix-free implementation. We discuss algorithmic differences between both solution strategies and present an in-depth numerical investigation of the performance. The considered benchmark test cases are the three-dimensional Taylor-Green vortex problem as a representative of transitional flows and the turbulent channel flow problem as a representative of wall-bounded turbulent flows