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Compressible turbulent accelerating boundary layer flow model for convective heat transfer from rocket combustion gases, noting heat flux
Detailed three-dimensional compressible transitional/turbulent boundary-layer profiles are presented for use as test cases in numerical and integral calculation procedures. The profiles were obtained from tests conducted in the Mach 20 leg of the Langley High Reynolds Number Helium Facility. The presented data represent an arduous test case for analytical prediction methods, since 'low Reynolds number' and precursor transition effects should probably be accounted for to accurately predict the boundary-layer growth and development.
The glushko one equation model of turbulence is extended to compressible flows without boundary layer approximations.
An existing three-dimensional compressible integral boundary-layer method was modified to account for mean dilatation effects, to model transition properly, and to provide better numerical stability near computational boundaries. Results of this method were compared against those from a three-dimensional finite-difference boundary-layer method on a difficult test case. An interaction procedure was developed to couple this integral method with a number of wing-alone and wing-body transonic potential codes to account for viscous effects. A strip wake model, including thickness and curvature effects, was developed and incorporated into this interaction procedure. Results from this procedure were compared against experimental data and results from previous procedures, on test cases where viscous effects were large.
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 three-dimensional, forward-swept sidewall-compression inlet has been tested in the Mach 4 Blowdown Facility at the NASA Langley Research Center to examine parameters that affect inlet starting, operability, and performance. The inlet was designed to simultaneously provide good starting and mass capture characteristics through the combination of forward-swept sidewalls and the aft placement of the downstream cowl. Parametrics examined included top surface compression, geometric contraction ratio, sidewall compression angle, boundary-layer thickness on the vehicle undersurface, and cowl position. To simulate combustion effects on inlet operation, the inlet was mechanically back pressured to determine maximum achievable combustor-to-inlet pressure ratio prior to inlet unstart. Inlet operability and performance are shown in terms of inlet starting (pulsed and self-starting) and unstarting characteristics, inlet static pressure distributions, combustor back pressure limits, mass capture, and flow uniformity.
Baldwin-Lomax and kappa-epsilon turbulence models were modified for use in Navier-Stokes numerical computations of Mach 2.9 supersonic turbulent boundary layer flows along compression ramps. The computational results of Reynolds shear stress profiles were compared with experimental data. The Baldwin-Lomax model was modified to account for the Reynolds shear stress amplification within the flow field. A hybrid kappa-epsilon model with viscous sublayer turbulence treatment was constructed to predict the Reynolds shear stress profiles within the entire flow field. These modified turbulence models were effective for the computations of the surface pressure and the skin friction factor variations along an 8 deg ramp surface. The hybrid kappa-epsilon model could improve the predictions of the Reynolds shear stress profile and the skin friction factor near the corner of a 16 deg ramp.
The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.
An analytical/numerical method has been developed to predict the static thrust performance of non-axisymmetric, two-dimensional convergent-divergent exhaust nozzles. Thermodynamic nozzle performance effects due to over- and underexpansion are modeled using one-dimensional compressible flow theory. Boundary layer development and skin friction losses are calculated using an approximate integral momentum method based on the classic karman-Polhausen solution. Angularity effects are included with these two models in a computational Nozzle Performance Analysis Code, NPAC. In four different case studies, results from NPAC are compared to experimental data obtained from subscale nozzle testing to demonstrate the capabilities and limitations of the NPAC method. In several cases, the NPAC prediction matched experimental gross thrust efficiency data to within 0.1 percent at a design NPR, and to within 0.5 percent at off-design conditions.
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.