Cartesian and contravariant formulations of the compressible Navier-Stokes equations applied to turbomachinery flows

Thesis/Dissertation · Sat Dec 31 23:00:00 EST 1988

OSTI ID:6376260

Sofronis, I J

The contravariant components of the full, two-dimensional, compressible Navier-Stokes (NS) equations are derived from Cartesian components and from tensor calculus. The Cartesian, full and thin-layer, components of the NS equations; in Chain Rule Conservation Law Form (CRCLF) are employed for solution of a variety of turbomachinery related problems. For numerical solution the Beam-Warming implicit scheme is employed. One-sided first and second-order accurate expressions are used for the streamwise convective derivatives. A modification of the FLARE approximation, consistent with the eigenvalues of the inviscid linearization Jacobians, is employed in regions of separated flows for the thin-layer equations. Results are presented for a variety of channel and cascade flows. Using the Cartesian CRCLF component, the contravariant decomposition is performed numerically within the code. The effect of Reynolds numbers, and different thickness/chord ratios for constricted channels and cascades are studied. Second-order accurate, one-sided differences show improved accuracy, compared with first-order accurate but require smaller time steps for stability. The total enthalpy variation, for Mach numbers ranging from 0.3 to 0.5, is small for the geometries considered. Results for circular cascades agree well with the results of other investigators. A comparison of the thin-layer approximation employing the Cartesian and contravariant components, shows lightly improved results when using the contravariant components. An analytical evaluation of the difference between Cartesian and contravariant thin-layer approximations is performed. Improved results using the body fitted NS equations are expected with closely spaced, thick cascade blades in low Reynolds number flows.

• Research Organization: Cincinnati Univ., OH (USA)
• OSTI ID: 6376260
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
420400* -- Engineering-- Heat Transfer & Fluid Flow
CALCULATION METHODS
CARTESIAN COORDINATES
COORDINATES
DIFFERENTIAL EQUATIONS
ENTHALPY
EQUATIONS
FLOW MODELS
MACHINERY
MATHEMATICAL MODELS
NAVIER-STOKES EQUATIONS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
REYNOLDS NUMBER
THERMODYNAMIC PROPERTIES
TURBOMACHINERY