A Force Estimation Method for Viscous Separated Flow Over Slender Axisymmetric Bodies With Tapered Tails

A new impulse method for modeling the normal force distributions along slender axisymmetric bodies with tapered tails is presented. This method is based on a decomposition of the hydrodynamic impulse along the body into an inviscid, profile-dependent component and a viscous, profile-independent component. It is applicable to separated flows up to 30 deg of incidence. Model results for the normal force distributions, total normal force, and total moment on axisymmetric streamlined bodies with tapered tails are compared with computational fluid dynamics (CFD) simulations and experimental data up to a Reynolds number of 23 × 106 with good agreement. The model was also tested on a missile-shaped body and was found to be in excellent agreement with experimental results.

VISCOUS SHOCK PROFILES FOR 2 × 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH AN UMBILIC POINT

This article analyzes the existence of viscous shock profiles joining two states satisfying the Rankine–Hugoniot condition that comes from hyperbolic 2 × 2 systems of conservation laws having quadratic flux functions with an isolated umbilic point: the point where the characteristic speeds coincide and the Jacobian matrix of the flux functions is diagonalizable. The systems studied in this note are particularly in Schaeffer and Shearer's cases I and II which are relevant to the three-phase Buckley–Leverett model for oil reservoir flow. It is shown that any compressive and overcompressive shocks have a viscous shock profile provided that there are no undercompressive shock with viscous profile having the same propagation speed. The idea of the proof is a generalization of the first theorem of Morse to noncompact level sets. It is also shown that there exists a shock satisfying the Liu–Oleĭnik condition but having no viscous shock profile. In this case, there is an undercompressive shock with viscous shock profile.

Optimization of Wind Turbines Using Helicoidal Vortex Model

The problem of the design of a wind turbine for maximum output is addressed from an aerodynamical point of view. It is shown that the optimum inviscid design, based on the Goldstein model, satisfies the minimum energy condition of Betz only in the limit of light loading. The more general equation governing the optimum is derived and an integral relation is obtained, stating that the optimum solution satisfies the minimum energy condition of Betz in the Trefftz plane “in the average.” The discretization of the problem is detailed, including the viscous correction based on the 2-D viscous profile data. A constraint is added to account for the thrust on the tower. The minimization problem is solved very efficiently by relaxation. Several optimized solutions are calculated and compared with the National Renewable Energy Laboratory (NREL) rotor, using the same profile, but different chord and twist distributions. In all cases, the optimization produces a more efficient design.

Optimization of Wind Turbines Using Helicoidal Vortex Model

The problem of the design of a wind turbine for maximum output is addressed from an aerodynamical point of view. It is shown that the optimum inviscid design, based on the Goldstein model, satifies the minimum energy condition of Betz only for light loading. The more general equation governing the optimum is derived and an integral relation is obtained, stating that the optimum solution satisfies the minimum energy condition of Betz in the Trefftz plane “in the average”. The discretization of the problem is detailed, including the viscous correction based on the 2-D viscous profile data. A constraint is added to account for the force on the tower. The minimization problem is solved very efficiently by relaxation. Several optimized solutions are calculated and compared with the NREL rotor, using the same profile, but different chord and twist distributions. In all cases, the optimization produces a more efficient design.

A Shock Loss Model for Supersonic Compressor Cascades

Loss models used in compression system performance prediction codes are often developed from the study of two-dimensional cascades. In this paper, compressible fluid mechanics has been applied to the changes in shock geometry that are known to occur with back pressure for unstarted operation of supersonic compressor cascades. This physics-based engineering shock loss model is applicable to cascades with arbitrary airfoil shapes. Predictions from the present method have been compared to measurements and Navier–Stokes analyses of the LO30-4 and L030-6 cascades, and very good agreement was demonstrated for unstarted operation. A clear improvement has been demonstrated over previously published shock loss models for unstarted operation, both in the accuracy of the predictions and in the range of applicability. The dramatic increase in overall loss with increasing inlet flow angle is shown to be primarily the result of increased shock loss, and much of this increase is caused by the detached bow shock. For a given Mach number, the viscous profile loss is nearly constant over the entire unstarted operating range of the cascade, unless a shock-induced boundary layer separation occurs near stall. Shock loss is much more sensitive to inlet Mach number than is viscous profile loss.

A Shock Loss Model for Supersonic Compressor Cascades

Loss models used in compression system performance prediction codes are often developed from the study of two-dimensional cascades. In this paper, compressible fluid mechanics has been applied to the changes in shock geometry that are known to occur with back pressure for unstarted operation of supersonic compressor cascades. This physics-based engineering shock loss model is applicable to cascades with arbitrary airfoil shapes. Predictions from the present method have been compared to measurements and Navier-Stokes analyses of the L030-4 and L030-6 cascades, and very good agreement was demonstrated for unstarted operation. A clear improvement has been demonstrated over previously published shock loss models for unstarted operation, both in the accuracy of the predictions and in the range of applicability. The dramatic increase in overall loss with increasing inlet flow angle is shown to be primarily the result of increased shock loss, and much of this increase is caused by the detached bow shock. For a given Mach number, the viscous profile loss is nearly constant over the entire unstarted operating range of the cascade, unless a shock-induced boundary layer separation occurs near stall. Shock loss is much more sensitive to inlet Mach number than is viscous profile loss.