A one-equation model of turbulence for use with the compressible Navier-Stokes equations
The glushko one equation model of turbulence is extended to compressible flows without boundary layer approximations.
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The glushko one equation model of turbulence is extended to compressible flows without boundary layer approximations.
Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points.
Transonic viscous-inviscid interaction is considered using the Euler and inverse compressible turbulent boundary-layer equations. Certain improvements in the inverse boundary-layer method are mentioned, along with experiences in using various Runge-Kutta schemes to solve the Euler equations. Numerical conditions imposed on the Euler equations at a surface for viscous-inviscid interaction using the method of equivalent sources are developed, and numerical solutions are presented and compared with experimental data to illustrate essential points. Previously announced in STAR N83-17829
A boundary-layer transition study over a compression corner was conducted under a hypersonic flow condition. Due to the discontinuities in boundary layer flow, the full Navier-Stokes equations were solved to simulate the development of disturbance in the boundary layer. A linear stability analysis and PSE method were used to get the initial disturbance for parallel and non-parallel flow respectively. A 2-D code was developed to solve the full Navier-stokes by using WENO(weighted essentially non-oscillating) scheme. The given numerical results show the evolution of the linear disturbance for the most amplified disturbance in supersonic and hypersonic flow over a compression ramp. The nonlinear computations also determined the minimal amplitudes necessary to cause transition at a designed location.
An experimental investigation of the aerodynamic characteristics of a slender, square-based body of revolution was conducted at a Mach number of 3.12 for angles of attack from 0 degree to 10 degrees and for Reynolds numbers from 2 x 10(exp 6) to 15 x 10(exp 6). Boundary-layer measurements at zero angle of attack are compared with several compressible flow formulating for predicting boundary-layer characteristics. Comparison of experimental pressure and force values with theoretical values showed good agreement for low angles of attack. The measured mean skin-friction coefficients agreed well with those predicted by Mangler's transformation for laminar flow over cones.
The existence of streamwise vortices in nominally 2-dimensional boundary layers undergoing adverse pressure gradient was investigated. The free stream Mach number was 5.75, the wall to stagnation temperature ratio was 0.63 and the Reynolds number based on free stream conditions was 3.9 x 10 to the 7th power/ft. The model consisted of an axisymmetric compression flare preceded by a cylindrical axially symmetric body. A natural turbulent boundary layer was established well ahead of the compression region. Boundary layer profiles of static pressure, pitot pressure, and stagnation temperature were taken at a surface station with a local inclination of 20 deg. Profile measurements were obtained at various peripheral stations. The measurements revealed zero peripheral variations at the surface of the body and at the edge of the boundary layer. However, distinct wavy pressure variations were observed within the boundary layer profiles, indicating the existence of longitudinal vortex cells within the boundary layer.
New turbulence modeling options recently implemented for the 3-D version of Proteus, a Reynolds-averaged compressible Navier-Stokes code, are described. The implemented turbulence models include: the Baldwin-Lomax algebraic model, the Baldwin-Barth one-equation model, the Chien k-epsilon model, and the Launder-Sharma k-epsilon model. Features of this turbulence modeling package include: well documented and easy to use turbulence modeling options, uniform integration of turbulence models from different classes, automatic initialization of turbulence variables for calculations using one- or two-equation turbulence models, multiple solid boundaries treatment, and fully vectorized L-U solver for one- and two-equation models. Validation test cases include the incompressible and compressible flat plate turbulent boundary layers, turbulent developing S-duct flow, and glancing shock wave/turbulent boundary layer interaction. Good agreement is obtained between the computational results and experimental data. Sensitivity of the compressible turbulent solutions with the method of y(sup +) computation, the turbulent length scale correction, and some compressibility corrections are examined in detail. The test cases show that the highly optimized one-and two-equation turbulence models can be used in routine 3-D Navier-Stokes computations with no significant increase in CPU time as compared with the Baldwin-Lomax algebraic model.
Chemical reacting unsteady boundary layer analysis on vaporizing flat plate including compressibility, flame boundary and stagnation point behavior
An assessment was made of the applicability of a three dimensional boundary layer analysis of heat transfer, total pressure losses, and streamline flow patterns on the surfaces of both stationary and rotating turbine passages. In support of this effort, an analysis was developed to calculate a general nonorthogonal surface coordinate system for arbitrary three dimensional surfaces and also to calculate the boundary layer edge conditions for compressible flow using the surface Euler equations and experimental pressure distributions. Calculations are presented for the pressure, endwall, and suction surfaces of a stationary cascade and for the pressure surface of a rotating turbine blade. The results strongly indicate that the three dimensional boundary layer analysis can give good predictions of the flow field, loss, and heat transfer on the pressure, suction, and endwall surface of a gas turbine passage.
Bench testing of experimental jet pump using high energy compressed air and capable of boundary control in short takeoff and landing aircraft
Nonunique laminar boundary layer equation solutions in direct problem calculations are identified for the case of accelerating flow. As a separation or reattachment point is approached, the multiple solutions approach each other and become identical. The computer code used to generate these results was developed for the solution of compressible, laminar or turbulent boundary layer, and free wake problems, in either direct or inverse mode. Similarity solutions in either a primitive variable or a stream function form are possible, and the resulting equations are solved by means of a modified Keller's Box scheme in which the energy equation and turbulence modeling equations are solved simultaneously with the continuity and momentum equations. Examples illustrating the nature of the solutions at the separation and reattachment points are presented.
An assessment has been made of the applicability of a 3-D boundary layer analysis to the calculation of heat transfer, total pressure losses, and streamline flow patterns on the surface of both stationary and rotating turbine passages. In support of this effort, an analysis has been developed to calculate a general nonorthogonal surface coordinate system for arbitrary 3-D surfaces and also to calculate the boundary layer edge conditions for compressible flow using the surface Euler equations and experimental data to calibrate the method, calculations are presented for the pressure endwall, and suction surfaces of a stationary cascade and for the pressure surface of a rotating turbine blade. The results strongly indicate that the 3-D boundary layer analysis can give good predictions of the flow field, loss, and heat transfer on the pressure, suction, and endwall surface of a gas turbine passage.
An assessment has been made of the applicability of a three dimensional boundary layer analysis to the calculation of heat transfer and streamline flow patterns on the surfaces of both stationary and rotating turbine passages. In support of this effort, an analysis has been developed to calculate a general nonorthogonal surface coordinate system for arbitrary three dimensional surfaces and also to calculate the boundary layer edge conditions for compressible flow using the surface Euler equations and experimental pressure distributions. Using available experimental data to calibrate the method, calculations are presented for the endwall, and suction surfaces of a stationary cascade and for the pressure surface of a rotating turbine blade. The results strongly indicate that the three dimensional boundary layer analysis can give good predictions of the flow field and heat transfer on the pressure, suction, and endwall surfaces in a gas turbine passage.
An experimental investigation of the aerodynamics of a slender cone-cylinder body of revolution was conducted at a Mach number of 3.85 for angles of attack of 0 degree to 10 degrees and a Reynolds number of 3.85x10(exp 6). Boundary-layer measurements at zero angle of attack are compared with the compressible-flow formulations for predicting laminar boundary-layer characteristics. Comparison of experimental pressure and force values with theoretical values showed relatively good agreement for small angles of attack. The measured mean skin-friction coefficients agreed well with theoretical values obtained for laminar flow over cones.
Inlets having translatable centerbodies and provision for boundary layer removal
The analysis uses a compressibility transformation and utilizes higher order closure rules to complete the transformation. By requiring that the momentum equations in differential form be satisfied at the wall and at the sublayer edge, correspondence rules are obtained which relate the variable property (VP) flow to a constant property (CP) flow in which mass transfer and pressure gradient occur simultaneously. A new CP formulation is developed and numerical results for a variety of cases are presented. Comparisons with earlier forms of the transformation and with experiment are included. For the zero pressure gradient case some differences between the various predictions are observed. For the several pressure gradient cases examined, the results are found to be essentially identical to those given by first order closure rules; i.e., by a form of transformation which relates the VP flow to a CP flow with pressure gradient but zero mass transfer.
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A set of constitutive equations suitable for a priori computation of turbulent shear flows has been developed. Since no properties of a given turbulent flow need be known in advance in order to obtain a solution, the equations comprise a complete model of turbulence. Perturbation analysis shows that the model predicts a composite five-layer structure for an incompressible turbulent boundary layer, viz, a defect layer, a law-of-the-wall layer, a viscous sublayer, a near-surface roughness layer, and a viscous superlayer at the boundary-layer edge. Analysis of the defect layer demonstrates the key improvement of the model over its predecessor, the Saffman-Wilcox two-equation model of turbulence. Examination of model-predicted sublayer structure yields model-parameter boundary conditions appropriate for surfaces with roughness and mass injection. Results of numerical computations of compressible and incompressible equilibrium boundary layers show that, for such flows, the model is as accurate as mixing-length theory. Applications to transitional boundary layers and to nonequilibrium relaxation of a boundary layer passing from a rough to a smooth surface indicate that the model's applicability extends far beyond that of mixing-length theory's.