Longitudinal–transverse aerodynamic force in viscous compressible complex flow

Abstract

We report our systematic development of a general and exact theory for diagnosis of total force and moment exerted on a generic body moving and deforming in a calorically perfect gas. The total force and moment consist of a longitudinal part (L-force) due to compressibility and irreversible thermodynamics, and a transverse part (T-force) due to shearing. The latter exists in incompressible flow but is now modulated by the former. The theory represents a full extension of a unified incompressible diagnosis theory of the same type developed by J. Z. Wu and coworkers to compressible flow, with Mach number ranging from low-subsonic to moderate-supersonic flows. Combined with computational fluid dynamics (CFD) simulation, the theory permits quantitative identification of various complex flow structures and processes responsible for the forces, and thereby enables rational optimal configuration design and flow control. The theory is confirmed by a numerical simulation of circular-cylinder flow in the range of free-stream Mach number $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}M_{\infty }$ between 0.2 and 2.0. The L-drag and T-drag of the cylinder vary with $M_{\infty }$ in different ways, the underlying physical mechanisms of which are analysed. Moreover, each L-force and T-force integrand contains a universal factor of local Mach number $M$. Our preliminary tests suggest that the possibility of finding new similarity rules for each force constituent could be quite promising.

Lift and drag in two-dimensional steady viscous and compressible flow

“…For viscous compressible flow, this physical picture is consistent with a near-field force formula given by Wu & Wu (1993), see also Liu et al (2014b), where F is dominated by the domain integral of a moment of ∇ 2 (µω) for both two-and three-dimensional flows. However, if one traces the primary origin of the transversal vorticity field all the way to the body surface, then one again finds the longitudinal field, because it is the tangent pressure gradient that is the dynamic cause of the vorticity generation (Liu et al 2015).…”

“…Therefore, it is believed that a rational combination of the universal J-F formulae and aerodynamic force theories in terms of special near-field flows (e.g. Liu et al 2014b) can provide a powerful means for the development of modern high-speed aerodynamics at a fundamental level, especially for complex flows with coupled multiple dynamic and thermodynamic processes.…”

“…But it is these structures that determine the specific Mach-number dependence of lift and drag for each specific flow, and enable one to identify the detailed physical mechanisms responsible for the forces. These are evidently of crucial importance in engineering applications, and can be found only from detailed near-field flow data and explained by relevant diagnostic theories, such as that reported in Liu et al (2014b).…”

Lift and drag in three-dimensional steady viscous and compressible flow

“…Later progresses have led to a few different formulations on the aerodynamic force and moment for both steady and unsteady viscous flows, see the review of Wu, Ma & Zhou (2006, Chapter 11). In contrast, despite a few isolated efforts reviewed in Liu et al (2014a) and LZW, the modernization of high-speed near-field aerodynamic theory had long remained a nearly untouched subject till the longitudinaltransverse force theory of Liu et al (2014a,b), also based on the process splitting and coupling. We believe that this theory is just one of the possible formulations, and some more could be developed with no principle difficulty, for example the compressible force element theory of Chang and coworkers (Chang, Su & Lei 1998).…”

Aerodynamic force and Lamb vector field in compressible unsteady flows

“…A first extension of this theory to compressible flows was already proposed by Wu et al [13], and further developed by Liu et al [14], [15]. Mele and Tognaccini [16] retrieved the mid field property, proposing an alternative exact formula, with applications to two-dimensional transonic and supersonic flows.…”