Low Speed Compressible Flow Research Articles

Vortex dynamics over a dihedral plane in a transitional slightly compressible flow: a computational study

In this paper, three different vortex diagnostic methods are compared to obtain a better understanding of boundary layer influence on the transport of vortical structures involving a complete analysis of vorticity, the Vorticity Threshold Criterion (VTC), and the Weiss Criterion (WC). These three techniques are basically confronted to find a suitable understanding of all flow characteristics (the swirling dynamics produced downstream of the discontinuity point of the dihedral) for a range of laminar to transitional Reynolds numbers. The computations on this dihedral plane are made using a 2D DNS method. The Weiss criterion, coming from the analysis of the incompressible Euler equations is validated and applied to low speed compressible flows ( M=0.2). A detailed analysis of the swirling procedure is performed for Reynolds numbers 242, 400 (laminar), 565 and 800 (transitional). Finally, different averaged or instantaneous, local or global quantities are used to analyse and characterize Concentrated Structures as a function of the Reynolds number evolution.

Identification of concentrated structures in slightly compressible two-dimensional flows

In this paper, different vortex diagnostic methods are compared to obtain a better understanding of boundary layer influence on the transport of vortical structures involving a complete analysis of vorticity, the Vorticity Threshold Criterion (VTC), and the Weiss Criterion (WC). These three techniques are basically confronted to find a suitable understanding of all flow characteristics for a range of laminar to transitional Reynolds numbers. The computations on this dihedral plane are done using a 2D DNS method. The Weiss criterion, coming from the analysis of the incompressible Euler equations is validated and applied to low speed compressible flows (Mach number=0.2).

Finite element analysis of low-speed compressible flows within convectively cooled structures

A Galerkin-based finite element algorithm is used to solve the transient compressible Navier-Stokes equations for low-speed flows within convectively cooled structures. This algorithm solves simultaneously for the temperature distribution in the structure and coolant. While most flows for which the algorithm is intended have low Mach numbers, the compressible equations are used to represent gradients of density and other flow quantities that accompany significant temperature variations. The algorithm is first applied to flows with small Mach numbers with little or no temperature variation for validation against incompressible flow solutions. The algorithm is then used to analyze an experimental model of a convectively cooled structure.

Kinetic Theory of Turbulent Flow

A new and analytical approach is proposed for resolving the closure problem and for achieving the desired analytical treatment of turbulent flow. The kinetic theory is utilized and the molecular distribution function in the time-averaged-flow-velocity frame is approximated. This new distribution is explicitly related to turbulence. It can be considered as a further approximation of the usual Chapman-Enskog and Grad distributions, since the turbulent energy number is small even in strong turbulence; thus, the theory is valid for strong turbulence. Only one-point correlations and perfect gases are studied. Navier-Stokes equations are kept intact, but new moment equations obtained directly from the Boltzmann equation in the above frame will be employed to approximate and to replace the Navier-Stokes moments. In particular, the Reynolds stress equation is exactly imbedded within and fully recovered via the new total stress equation. Fourth- and higher-order velocity correlations are analytically eliminated via the approximation of the molecular distribution. For low-speed compressible flow, 40 component-equations for 40 unknowns are obtained. A closed hierarchy of equations governing the turbulent correlations is analytically derived for the first time, without any phenomenological hypotheses. For high-speed flows, more moments are required. Detailed analyses are needed to ascertain whether a unique and closed hierarchy can be found for such flows.

The Laminar Boundary Layer on a Hot Cylinder Fixed in a Fluctuating Stream

The equations for nonsteady, two-dimensional low-speed compressible flow in the laminar boundary layer are solved approximately by use of the Pohlhausen technique with the assumption of quartic profiles for the velocity and temperature. The external flow considered is of the form of a steady basic velocity with a superimposed small amplitude oscillation such as may arise, for example, when a sound wave is present in a uniform incident stream. The analysis is then applicable to the case of a hot cylinder fixed in such a stream. Terms of the order of the incident stream Mach number are neglected in the expressions for external flow quantities (whereas the low-speed boundary-layer equations involve errors of the order of only the square of this Mach number). Two special cases are worked out—the flow over a flat plate for which there is fair agreement with available exact calculations, and the flow over a circular cylinder.

Laminar Boundary Layer with Suction and Injection

With the assumptions of a heat insulated body, a Prandtl number of unity and a linear temperature-viscosity relation the axisymmetric equations governing a given high-speed compressible flow are reduced to the equations describing an incompressible two-dimensional flow past a flat plate with a determinable main stream and normal wall velocity distribution. The results are applied to the supersonic flows over a cone with wall velocities proportional (i) to the first power and (ii) to the inverse-half-power of distance along a generator when the resulting incompressible flows are known. Also the flow near the tip of a general slender body of revolution in supersonic flow with constant wall velocity is obtained by solving numerically the equations of the correlated incompressible flow. It is also shown that, if the assumption of an insulated body is discarded, a given high-speed compressible flow may still be correlated with a determinable low-speed compressible flow.