Properties of the compressibility and transport motion in wall-bounded turbulent flows at Mach 8

The compressibility effect and transport motion in highspeed turbulent boundary layer (TBL) is a fundamental problem because they dominate the average and statistical characteristics. Using the statistical methods and flow visualization technology, flat-plate TBLs at [Formula: see text] with high- and low-wall temperatures, [Formula: see text] and 1.9, are investigated based on the direct numerical simulation (DNS) datasets. Compared with previous studies, this study considers relative higher Mach number and strong cold wall temperature condition at the same time. First, the turbulent Mach number and turbulent intensity show that the compressibility effects are enhanced by the cooling process. Second, the high-order statistical moments and structure parameters confirm cold wall that causes stronger compressibility and the corresponding increased intensities of local streamwise and wall-normal transport motions. Finally, for uncovering the relationship between the compressibility effect and turbulent transport, more in-depth visualization analyses of velocity streaks are performed. It is found that ‘knot-like’ structures are generated when cooling the wall, and they lead to stronger intermittent, which results in the rapid increase of local compressibility effect and the wall-normal transport motion. Our research sheds light on providing a theoretical basis for further understanding the compressibility effects of TBL at high Mach number.

Effect of wall temperature on the kinetic energy transfer in a hypersonic turbulent boundary layer

The effect of wall temperature on the transfer of kinetic energy in a hypersonic turbulent boundary layer for different Mach numbers and wall temperature ratios is studied by direct numerical simulation. A cold wall temperature can enhance the compressibility effect in the near-wall region through increasing the temperature gradient and wall heat flux. It is shown that the cold wall temperature enhances the local reverse transfer of kinetic energy from small scales to large scales, and suppresses the local direct transfer of kinetic energy from large scales to small scales. The average filtered spatial convection and average filtered viscous dissipation are dominant in the near-wall region, while the average subgrid-scale flux of kinetic energy achieves its peak value in the buffer layer. It is found that the wall can suppress the inter-scale transfer of kinetic energy, especially for the situation of a cold wall. A strong local reverse transfer of fluctuating kinetic energy is identified in the buffer layer in the inertial range. Helmholtz decomposition is applied to analyse the compressibility effect on the subgrid-scale flux of kinetic energy. A strong transfer of the solenoidal component of fluctuating kinetic energy is identified in the buffer layer, while a significant transfer of the dilatational component of fluctuating kinetic energy is observed in the near-wall region. It is also shown that compression motions have a major contribution to the direct transfer of fluctuating kinetic energy, while expansion motions play a marked role in the reverse transfer of fluctuating kinetic energy.

Effect of Compressibility on Velocity Profile and Friction Factor of Gaseous Laminar Flows in a Microtube

Laminar flow of nitrogen gas in a microtube was simulated numerically to obtain velocity profile and Fanning friction factor in a quasi-fully developed region. The numerical procedure based on Arbitrary-Lagrangian-Eulerian method solved two-dimensional compressible momentum and energy equations. The computations were performed for a wide range of Reynolds number in laminar flow regime with adiabatic wall condition. It was found that the velocity profile deviates from the parabola as Mach number increases, and the product of Fanning friction factor and Reynolds number is not a constant but a function of only Mach number. To explain the compressibility effect, a new theoretical flow model which gives the velocity profile of gaseous laminar flows in a microtube was proposed under the assumption of purely axial flow. The theoretical velocity profile is taking radial-direction density change into account, and coincides with the numerically obtained velocity profile. The proposed flow model also shows that the Fanning friction factor of a compressible flow in a microtube is expressed by a quadratic function of Mach number. The coefficient of the Mach squared term is 40% of the numerically obtained correlation. The compressibility effect on friction factor of gaseous laminar flows in a microtube partly results from velocity profile change which must occur to keep the mass velocity profile when density changes in radial direction. The remainder of the compressibility effect can be considered to result from actual mass transfer in the radial direction whose existence was demonstrated by the numerical results.

Unsteady nonlinear panel method with mixed boundary conditions

A new panel method had been developed to account for unsteady nonlinear subsonic flow. Two boundary conditions were used to solve the potential flow about complex configurations of airplanes. Dirichlet boundary condition and Neumann formulation are frequently applied to the configurations that have thick and thin surfaces respectively. Mixed boundary conditions were used in the present work to simulate the connection between thick fuselage and thin wing surfaces. The matrix of linear equations was solved every time step in a marching technique with Kelvin's theorem for the unsteady wake modeling. To make the method closer to the experimental data, a Nonlinear stripe theory which is based on a two-dimensional viscous-inviscid interaction method for each station along the wing spanwise direction and Prandtle-Glauert rule for compressibility effect were used to enhance the potential results of the method. The fast turnaround time and the ability to model arbitrary geometries is the goal of the present work. Different airplanes configurations were simulated (DLR-F4, light jet, cargo and four engine commercial airplanes). The results of pressure and forces coefficients were compared with the DLR-F4 airplane. The comparisons showed a satisfying agreement with the experimental data. The method is simple and fast as compared with other singularity methods, which may be dependent as a preliminary method to design aircrafts.

Volume of Fluid Based Model of Heavy Fuel Oil Droplet Evaporation and Combustion

Modern CFD simulations of combustion resolve simplified sub-models for droplet evaporation and combustion within a Lagrangian framework. Break-up effects like puffing and micro-explosions are usually neglected but, they eventually influence the evaporation and combustion behaviour of heavy fuel sprays. We are developing a Volume of Fluid (VoF)-based CFD solver that allows us to model single droplet differential evaporation with the break-up effects. Puffing/micro-explosion and droplet ejection proceed in three steps: nucleation of a bubble of a light component within the droplet, expansion/coalescence of the bubbles and finally eruption with sub-droplets formation. Our goal is to individually model each event and then combine them in a composite simulation. Henceforth we can get data in realistic conditions to be used in Lagrangian spray simulations. We identified three relevant features that are necessary to create a reliable representation: interface tracking, differential evaporation, and compressibility effect. The solver is based on the Volume of Fluid (VoF) technique and coded within the open-source OpenFOAM framework. VoF technique consists of transporting the volume fraction of one of the two phases (liquid or gas). The Navier-Stokes equations are solved for a single-phase but adapting the physical properties to the volume fraction value. A state-of-the-art method called iso-Advector was adopted to reconstruct the interface from the volume fraction field. The evaporation was implemented as a source term in the volume fraction equation, and the conservation equations were modified accordingly. In order to calculate the vapour and liquid physical properties, RKS equation of state (EOS) was implemented. The droplet was assumed to have 2 phases: light and heavy, having physical properties comparable to water and heavy fuel oil (HFO), respectively. The pressure closure equation was modified to handle large pressure differences during the internal evaporation of light components. The validation of the solver was performed through benchmark cases as multiphase shock-tube, droplet oscillation and boiling interface either with experimental works and analytical solutions. A single suspended droplet experiment was performed to measure the velocity of an ejected micro-droplet during puffing using a shadowgraphy technique. The code is able to predict ejection velocity within a 15% error, which seems to be promising. The present article documents part of the algorithm development and its validation. In particular, the step describing the ejection of the inner vapours is described.