A new turbulence model for two-dimensional, steady and unsteady boundary layers in strong adverse pressure gradients is described. The model is developed in a rational way based on understanding of the flow physics obtained from experiments. The turbulent shear stress is given by a mixing length model, but the mixing length in the outer region is not a constant times the boundary layer thickness; it varies according to an integral form of the turbulence kinetic energy equation. This approach accounts for the history effects of the turbulence. The form of the near-wall mixing length model is derived based on the distribution of the shear stress near the wall, and it takes into account the pressure and convection terms which become important in strong adverse pressure gradients. Since the significance of the normal stresses in turbulent kinetic energy production increases as separation is approached, a model accounting for this contribution is incorporated. Experimental data indicate a change in turbulence structure near and through separation. Such a change can be significant and is accounted for here using an empirical function. The complete model was tested against steady and unsteady, two-dimensional experimental cases with adverse pressure gradients up to separation. Improved predictions compared to those obtained with other turbulence models were demonstrated.

High-pressure-ratio turbines have flows dominated by shock structures that pass downstream into the next blade row in an unsteady fashion. Recent numerical results have indicated that these unsteady shocks may significantly affect the aerodynamic and mechanical performance of turbine blading. High cost and limited accessibility of turbine rotating equipment severely restrict the quantitative evaluation of the unsteady flowfield in that environment. Recently published results of the Virginia Tech transonic cascade facility indicate high integrity in simulation of the steady-state flow phenomena. The facility has recently been modified to study the unsteady effects of passing shock waves. Shock waves are generated by a shotgun blast upstream of the blade row. Shadowgraph photos and high-response pressure data are compared to previously published experimental and numerically predicted results. Plots are included that indicate large fluctuations in estimated blade lift and cascade loss.

An experimental investigation was conducted to measure skin friction along the chamber walls of supersonic combustors. A direct force measurement device was used to measure simultaneously an axial and a transverse component of the small tangential shear force passing over a nonintrusive floating element. This measurement was made possible with a sensitive piezoresistive deflection sensing unit. The floating head is mounted to a stiff cantilever beam arrangement with deflection due to the flow on the order of 0.00254 mm (0.0001 in). This allowed the instrument to be a nonnulling type. A second gage was designed with active cooling of the floating sensor head to eliminate nonuniform temperature effects between the sensor head and the surrounding wall. The key to this device is the use of a quartz tube cantilever with piezoresistive strain gages bonded directly to its surface. A symmetric fluid flow was developed inside the quartz tube to provide cooling to the backside of the floating head. Tests showed that this flow did not influence the tangential force measurement. Measurements were made in three separate combustor test facilities. Tests at NASA Langley Research center consisted of a Mach 3.0 vitiated air flow with hydrogen fuel injection at P t = 500 psia (3466 kPa) and T t = 3000 R (1667 K). Two separate sets of tests were conducted at the General Applied Science Laboratory (GASL) in a scramjet combustor model with hydrogen fuel injection in vitiated air at Mach = 3.3, P t = 800 psia (5510 kPa), and T t = 4000 R (2222 K). Skin friction coefficients between 0.001–0.005 were measured dependent on the facility and measurement location. Analysis of the measurement uncertainties indicate an accuracy to within ± 10–15 percent of the streamwise component.

A new approach to the solution of the two-dimensional, incompressible, boundary-layer equations based on the Finite Element Method in both directions is investigated. Earlier Finite Element Method treatments of parabolic boundary-layer problems used finite differences in the streamwise direction, thus sacrificing some of the possible advantages of the Finite Element Method. The accuracy and computational efficiency of different interpolation functions for the velocity field are evaluated. A new element especially designed for boundary layer flows is introduced. The effect that the treatment of the continuity equation has on the stability and accuracy of the numerical results is also discussed. The parabolic nature of the equations is exploited in order to reduce the memory requirements. The solution is obtained for one line at a time, thus only two levels are required to be stored at any time. Efficient solvers for tridiagonal and pentadiagonal forms are used for solving the resulting matrix problem. Numerical predictions are compared to analytical and experimental results for laminar and turbulent flows, with and without pressure gradients. The comparisons show very good agreement. Although most of the cases were tested on a mainframe, the low requirements in CPU time and memory storage allows the implementation of the method on a conventional PC.

A complete numerical calculation procedure for predicting the effects of mass loading and particle diameter on laminar slurry jet breakup in a low velocity, coaxial gas stream has been developed. The method is based on the Volume of Fluid technique for the Navier-Stokes equations. The severe restrictions involved in earlier treatments have been relaxed. The influence of particle loading on liquid phase density and the influence of particle spacing on drag are included. The particular case considered is a slurry with a methanol liquid phase with aluminum oxide beads in order to compare with some related experimental results. The methanol liquid in the slurry is vaporized due to mass transfer in the gas stream. The variation of the instantaneous jet shape of the methanol slurry jet at low loadings is generally similar to that of an all-liquid methanol jet, but the final shapes at breakup are different. In the region of low mass loading (up to 20 percent), the effects of mass loading are to stabilize the interface and increase the breakup time of the slurry jet with increasing mass loading. Above that region of mass loading (more than 20 percent), the effects of mass loading are to destabilize the interface and decrease the breakup time of the slurry jet with increased mass loading. At the same mass loading condition, a slurry jet with large diameter particles has a more stabilizing effect than one with small diameter particles. Therefore, a slurry jet with higher mass loading and smaller diameter particles breaks up faster.

The steady, three-dimensional, incompressible Navier-Stokes equations written in terms of velocity, vorticity, and temperature are solved numerically for channel flows and a jet in a cross flow. Upwind differencing of the convection term was used in the computation for convergence and simplicity. Comparisons were made with experimental results for laminar flow in the entrance region of a square channel, and good agreement was obtained. The method was also applied to a turbulent, buoyant jet in a cross-flow problem with the Boussinesq approximation and a constant Prandtl eddy viscosity model. Good agreement with experiment was obtained in this case also.

The results of an experimental investigation of the free turbulent mixing of wakes and jets in axial pressure gradients are presented. The data include static pressure and velocity profiles and the turbulent intensity which is presented in terms of the parameter u ′ cL 2 ¯ ( Δ u ) max 2 . It is hypothesized that the representation of the Reynolds stress by a generalized Clauser eddy viscosity model is scaled by this parameter. The experimentally observed dependence of this turbulence quantity on flow field dimensionality and the imposed pressure gradient places more stringent demands on the form of the eddy viscosity than has been shown before. However, the experimental data reveal some fortuitous behavior which aids in the specification of the spatial dependence of the turbulence parameter, leaving the scaling to be determined primarily by the initial conditions, i.e., the state of the turbulence in the near field. Substantial lateral static pressure gradients were observed in all two-dimensional cases studied. It is shown that the boundary-layer form of the viscous flow equations are inadequate in such cases, and a numerical solution of a system of equations that includes an approximate form of the lateral momentum equation provides predictions in good agreement with the data for the mean flow field.

The interaction between a viscous mixing layer induced by tangential injection, and an external supersonic flow field is considered experimentally and analytically. Both subsonic and supersonic injection are investigated. The experiments were performed at freestream Mach numbers of 2.85 and 4.19 using air as the injectant. The principal observations are in the form of spark schlieren photographs, interferograms, and wall pressure distributions. The experiments were arranged to cross Lin’s neutral stability boundary for parallel streams. Transition occurred in all cases, but an increase in stability was noted with either a decrease in the injectant Mach number or an increase in the Mach number of the external flow. Both of these results follow the trends predicted by the stability theory. For the supersonic injection cases, it was found that simple inviscid theory is sufficient to predict the overall interaction pattern between streams, when the ratio of initial boundary layer thickness to the injection slot height is small. However, when the injection is subsonic, the injectant initial conditions in terms of either pressure or Mach number at the slot exit are determined by the downstream viscous-inviscid interaction with the external supersonic flow. A simple one-dimensional theory is applied to this problem to enable prediction of the initial conditions.