Critical Mach Numbers of Flow around Two-Dimensional and Axisymmetric Bodies

The paper presents the calculated results obtained by the author for critical Mach numbers of the flow around two-dimensional and axisymmetric bodies. Although the previously proposed method was applied by the author for two media, air and water, this chapter is devoted only to air. The main goal of the work is to show the high accuracy of the method. For this purpose, the work presents numerous comparisons with the data of other authors. This method showed acceptable accuracy in comparison with the Dorodnitsyn method of integral relations and other methods. In the method under consideration, the parameters of the compressible flow are calculated from the parameters of the flow of an incompressible fluid up to the Mach number of the incoming flow equal to the critical Mach number. This method does not depend on the means determination parameters of the incompressible flow. The calculation in software Flow Simulation was shown that the viscosity factor does not affect the value critical Mach number. It was found that with an increase in the relative thickness of the body, the value of the critical Mach number decreases. It was also found that the value of the critical Mach number for the two-dimensional case is always less than for the axisymmetric case for bodies with the same cross-section.

Taper stacking for the aerodynamic performance of wings

Purpose The critical Mach number, lift-to-drag ratio and drag force play important role in the performance of the wings. This paper aims to investigate the effect of taper stacking, which has been used to generalize wing sweeping, on those parameters. Design/methodology/approach The results obtained are based on steady-state turbulent flowfields computations. The baseline wing is ONERA M6. Various wing planforms are generated by linearly or parabolically varying the spanwise stacking location. The critical Mach number is determined by changing the freestream Mach number for a fixed angle of attack. On the other hand, the analysis of the drag force is carried out by changing the angle of attack to keep the lift force constant. Findings By changing the stacking location, the critical Mach number and the corresponding lift-to-drag ratio have increased by around 7 and 3%, respectively. A reduction of 12.8% in total drag force has been observed in one of the analyzed cases. Moreover, there exist some cases in which the values of drag reduce significantly while the lift is the same. Practical implications The results of this new stacking approach have implied that the drag force can be decreased without decreasing the lift. This outcome is valuable for increasing the range and endurance of an aircraft. Originality/value This work generalizes wing sweeping by modifying the taper stacking along the span. In literature, wing sweep is enhanced using segmented stacking of taper distribution. The present study is further enhancing this concept by introducing continuous stacking (infinite number of stacking segments) for the first time.

Assessment of Compressible RANS and LES Methods for Organic Vapor Flows Past a NACA4412 Airfoil

In this contribution, an assessment of compressible Reynolds Averaged Navier Stokes equations (RANS) and Large Eddy Simulation (LES) is presented using transonic organic vapor flow past a NACA4412 airfoil as a case study. The NACA4412 represents a canonical geometry, which, in case of air, has been well investigated numerically and experimentally. The results of the real gas simulations are compared with those of air simulations. For the real gas, the organic vapor Novec 649® is chosen as a representative fluid. The thermodynamic behavior of Novec 649® is modeled with the Peng-Robinson equation of state. Different inlet Mach numbers are applied, namely, a sub-critical, the critical, and a super-critical Mach number. It turns out, that the critical Mach number of the NACA4412 airfoil increases when Novec 649® is used as working fluid. Furthermore, it is shown that real gas flow simulations cause additional difficulties for the computational fluid dynamics (CFD) analysis. Although the speed of sound of Novec 649® is lower than the speed of sound of air, a finer grid resolution is required for the real gas simulations due to its high density. Based on an extensive simulation study, an assessment of different numerical modelling strategies and methods is given.

Increase of Critical Mach Number by Local Linearization Method and Airfoil Construction at Subsonic and Transonic Regimes

A symmetrical airfoil has been constructed by local linearization method. A single-point objective function is defined to check the convergence of the method. As an example, the nose and tail zone of supercritical airfoil is fixed and a flat line is placed between them. The optimizable element of the airfoil contour was conjoined with the nose and tail elements of fixed shape at the sections with coordinates xs1= 0.11 and xs2= 0.66, respectively. The optimizable part of airfoil (the fixed chord line) is divided into N=55 segments. The convergence of this method has been shown with the airfoil constructed with higher critical Mach number rather than the initial airfoil. Finally, this airfoil has been compared with the supercritical airfoil NASA SC (2)-0012 at M∞=0.76. At the second part, several airfoils have been constructed and simulated over different Subsonic and Transonic Mach numbers. Finally, the drag coefficient on constructed airfoils have been compared with supercritical airfoil.