Judson R. Baron

A new adaptive algorithm for turbulent flows

Abstract A novel adaptive algorithm for turbulent flows introduces a combination of grid embedding and grid redistribution techniques, as appears to be necessary for efficient resolution of the small scales involved in viscous flows. A method for implementing an algebraic (Baldwin-Lomax) turbulence model with unstructured embedded meshes is developed also. The adaptive algorithm is applied to airfoil flow fields at relatively high Re values of order 10 6 , and comparisons are made with experimental data. Two airfoil geometries are considered: a single-element NACA 0012 section in both subsonic and transonic flow; and a two-element NLR section in subsonic flow for two distinct flap deflection settings. The latter simulations appear to be the first Navier-Stokes computations presented. Essential flow physics, such as shock-boundary layer interactions and small separation bubbles, are “captured” by the new adaptive algorithm with considerable detail. In addition, the algorithm appears to provide flexibility in generating a mesh around relatively complicated geometries, such as multi-element airfoils.

Thermal diffusion effects in mass transfer

Abstract Recent interest in the influence of thermodynamic coupling on mixture boundary layers has prompted the presentation of exact solutions with and without such coupling. Results are presented for stagnation point injection of helium and Freon-13 into an airstream layer. Significant heat transfer rate and recovery temperature effects are discussed in terms of the sign of the thermal diffusion ratio which formed the basis for the injectant choices.

An experimental investigation of a two-layer inviscid shock cap due to blunt-body nose injection

Blunt-body solutions for suspersonic flow usually concern closed body surfaces. This paper reports on an experimental investigation of a two-layer shock cap and indicates the existence of a predictable contact surface separating the layers. The inner layer was generated by injecting air through a contoured axisymmetric channel on a blunt body so as to simulate a hemispherical contact surface in a Mach number 4.8 flow. Results show the existence of the contact surface and the influence of a range of mass-injection rates upon the displacement of the bow shock and contact surface from the body.

Spatiotemporal Adaptation Algorithm for Two-Dimensional Reacting Flows

A spatio-temporal adaptive algorithm for solving the unsteady Euler equations with chemical source terms is presented. Quadrilateral cells are used in two spatial dimensions which allow for embedded meshes tracking moving flow features with spatially varying time-steps which are multiples of global minimum time-steps. Blast wave interactions corresponding to a perfect gas (frozen) and a Lighthill dissociating gas (nonequilibrium) are considered for circular arc cascade and 90 degree bend duct geometries.

EXPERIMENTAL INVESTIGATION OF THERMAL DIFFUSION EFFECTS IN LAMINAR AND TURBULENT SHEAR FLOW

Abstract An experimental investigation was conducted to determine the order of magnitude of thermal diffusion across a laminar and a turbulent shear layer. A short length of a cooled free jet was passed through stationary gas and subsequently recaptured into a continuous circulating system. Various mixtures of helium and nitrogen were investigated. With temperatures of 78°K in the jet and 310°K in the surrounding chamber, steady-state helium concentrations in the laminar jet were as much as 7 per cent smaller than in the surroundings. The experimental results are in good agreement with a simplified analysis. With a turbulent sheat layer between the jet and surroundings, the helium concentration inside the jet increases to within 0.1 per cent higher than the chamber level. The thermal diffusion ratio (i.e. thermal to mass concentration diffusion coefficients) in the turbulent shear layer was thus at least two orders of magnitude smaller than in the laminar case and of opposite sign. It is suggested that similar separation effects are to be expected for other steady flows with closed streamlines, such as base flows and flows past cavities.

Minimum radiative transfer geometries

Abstract Optimal control methods are applied to minimize the radiative energy transfer to a two-dimensional body with imposed isoperimetric constraints on base height and surface arc-length. Primary emphasis is on the effect of changes in body geometry on the radiative energy transfer to the surface. The radiation field is specified by the differential approximation and simultaneous evaluation of the coupled flow and radiation fields is necessary. The fields are based on a one-strip integral method with a radiation closure condition applied at the base to circumvent the considerable difficulty associated with the attainment of radiative equilibrium in the large. A first-order gradient algorithm is applied to the system describing the state of the shock layer gas using body surface curvature as the control variable. A major problem proves to be numerical instabilities associated with the approximate, stiff system of ordinary differential equations. Some evidence indicates that the one-strip formulation leads to unrealistic behavior in the influence functions (adjoint variables) for the optimization procedure. Optimal solutions, obtained for a sequence of nose angles, demonstrate that nose angle has a crucial effect on the total radiative transfer to the surface for the assumed geometric constraints and flight conditions ( M∞≈ 30 ). Physically, the reduced transfer is related to the shock layer volume control achieved with optimal shapes; however, average temperature also tends to decrease for the optimal sequence. An overall minimum radiative transfer geometry requires a cusped nose; nevertheless, the total energy transfer rates are less by an order of magnitude relative to a reference wedge level for nose angles as large as 25 per cent of the wedge angle.

A variable closure differential approximation for anisotropic radiation

Abstract Spatially varying closure based on ellipsoidal intensity modeling is used to describe the anisotropic radiation field by means of a modified differential approximation. Singular behavior in region corners is identified and accounted for, and a self-consistent boundary condition suggested for the ratio of lowest order moments of intensity. Completed examples indicate removal of virtually the entire differences between Milne-Eddington and exact results.