Daniel J. Dorney

Shape optimization of supersonic turbines using global approximation methods

There is growing interest to adopt supersonic turbines for rocket propulsion. However, this technology has not been actively investigated in the United States for the last three decades. To aid design improvement, a global optimization framework combining the radial-basis neural network (NN) and the polynomial response surface (RS) method is constructed for shape optimization of a two-stage supersonic turbine, involving O(10) design variables. The design of the experiment approach is adopted to reduce the data size needed by the optimization task. The combined NN and RS techniques are employed. A major merit of the RS approach is that it enables one to revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a predefined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials consideration.

Simulations of the Unsteady Flow through the Fastrac Supersonic Turbine

Analysis of the unsteady aerodynamic environment in the Fastrac supersonic turbine is presented. Modal analysis of the turbine blades indicated possible resonance in crucial operating ranges of the turbopump. Unsteady computational fluid dynamics (CFD) analysis was conducted to support the aerodynamic and structural dynamic assessments of the turbine. Before beginning the analysis, two major problems with current unsteady analytical capabilities had to be addressed: modeling a straight centerline nozzle with the turbine blades and exit guide vanes (EGVs), and reducing run times significantly while maintaining physical accuracy. Modifications were made to the CFD code used in this study to allow the coupled nozzle/blade/EGV analysis and to incorporate Message Passing Interface (MPI) software. Because unsteadiness is a key issue for the Fastrac turbine [and future rocket engine turbines such as the Reusable Launch Vehicle (RLV)], calculations were performed for two nozzle-to-blade axial gaps. Calculations were also performed for the nozzle alone, and the results were imposed as an inlet boundary condition for a blade/EGV calculation for the large gap case. These results are compared to the nozzle/blade/EGV results.

Shape Optimization of Supersonic Turbines Using Response Surface and Neural Network Methods

Turbine performance directly affects engine specific impulse, thrust-to-weight ratio, and cost in a rocket propulsion system. A global optimization framework combining the radial basis neural network (RBNN) and the polynomial-based response surface method (RSM) is constructed for shape optimization of a supersonic turbine. Based on the optimized preliminary design, shape optimization is performed for the first vane and blade of a 2-stage supersonic turbine, involving O(10) design variables. The design of experiment approach is adopted to reduce the data size needed by the optimization task. It is demonstrated that a major merit of the global optimization approach is that it enables one to adaptively revise the design space to perform multiple optimization cycles. This benefit is realized when an optimal design approaches the boundary of a pre-defined design space. Furthermore, by inspecting the influence of each design variable, one can also gain insight into the existence of multiple design choices and select the optimum design based on other factors such as stress and materials considerations.

Simulation of Vortex Shedding in a Turbine Stage

Vortex shedding in a turbomachine blade row is affected by the passing of blades in the adjacent downstream blade row, but these effects have not been examined in the literature. A series of flow simulations has been performed to study vortex shedding in a turbine stage, and to quantify the blade interaction effects on the unsteady pressure response. The numerical issues of spatial order of accuracy and the use of Newton subiterations were investigated first. Second-order spatial accuracy was shown to be inadequate to model the shedding frequency response and time-averaged base pressure accurately. For the small time step employed for temporal accuracy, Newton iterations were shown to be unnecessary. The effects of the adjacent blade row were examined by comparing the shedding frequency response for the stage simulations to the response for isolated cascades. The vane shedding was shown to occur exactly on a series of harmonics of the blade passing frequency for the stage case, compared to a single predominant frequency for the isolated cascade. Losses were also examined in the wake region. It was shown that close to the trailing edge, losses were mainly due to wake mixing. Farther downstream of the trailing edge, losses were predominantly due to the trailing edge shock wave.

PARALLEL COMPUTATION OF TURBINE BLADE CLOCKING

This paper presents a numerical study of airfoil clocking of a six-row test turbine configuration with equal pitches. Since the rotor-stator interaction flow is highly unsteady, the numerical simulation of airfoil clocking requires the use of time marching methods, which can be computationally expensive. The large turnaround time and the associated cost for such simulations makes it unacceptable for the turbomachinery design process. To reduce the turnaround time and cost/MFLOP, a parallel code based on Message-Passing Interface libraries was developed. The relative circumferential positions of the three stator and three rotor rows in an industrial steam turbine were varied to increase turbine efficiency. A grid density study was performed to verify the grid independence of the computed solutions. The clocking of the second-stage airfoils gave approximately a 50% greater efficiency variation than the clocking of the third-stage airfoils. This was true for clocking both rotor and stator airfoils. Rotor clocking produces an efficiency variation which is approximately twice the efficiency variation produced by stator clocking. For both stator and rotor clocking, the maximum efficiency is obtained when the wake impinges on the leading edge of the clocked airfoil. NOMENCLATURE p Pressure T Temperature η Efficiency γ Ratio of specific heats of a gas

Simulation of Coupled Unsteady Flow and Heat Conduction in Turbine Stage

A three-dimensional, unsteady, compressible, e nite difference Navier ‐Stokes solver has been coupled with a three-dimensional, unsteady, e nite difference conduction heat-transfer solver to study conjugate heat-transfer problems in turbomachinery. The heat-transfer solver was validated by computing unsteady heat transfer in a cylinderandcomparingtheresultswithananalyticalsolution.Thecodewasthenappliedtoahigh-pressureturbine stage, typical of those found in modern high-bypassturbofan engines, with a nonuniform inlettemperatureproe le. The unsteady temperature e eld of a rotor blade, both at the surface and within the blade, has been examined in detail. The surface-temperature results have also been compared with those from a e ow simulation in which the blade surfaces were assumed to be adiabatic, demonstrating the need for the coupled approach.

A SURVEY OF HOT STREAK EXPERIMENTS AND SIMULATIONS

Experimental and computational data have shown that the flow exiting gas-turbine combustors can contain large circumferential and radial temperature non-uniformities. The temperature non-uniformities, or hot streaks, can have a significant impact on the performance and durability of first-stage turbine airfoils. This paper contains a survey of the hot streak experiments and simulations that have been performed during the last two decades, and the impact they have had on the design of high-pressure turbine stages.

A Study of the Effects of Tip Clearance in a Supersonic Turbine

Flow unsteadiness is a major factor in turbine performance and durability. This is especially true if the turbine is a high work design, compact, transonic, supersonic, counterrotating, or uses a dense drive gas. The vast majority of modern rocket turbine designs fall into these categories. In this study a parallelized unsteady three-dimensional Navier-Stokes analysis has been used to study the effects of tip clearance on the transient and time-averaged flow fields in a supersonic turbine. The predicted results indicate improved performance in the simulation including tip clearance. The main sources of the performance gains were: (1) a weakened shock system in the case with tip clearance, and (2) the fact that the reductions in the shock losses were greater than the losses introduced by tip clearance.

Experimental and Numerical Investigation of Losses in Low-Pressure Turbine Blade Rows

Experimental data and numerical simulations of low-pressure turbines have shown that unsteady blade row interactions and separation can have a significant impact on the turbine efficiency. Measured turbine efficiencies at takeoff can be as much as two points higher than those at cruise conditions. Several recent studies have revealed that the performance of low-pressure turbine blades is a strong function of the Reynolds number. In the current investigation, experiments and simulations have been performed to study the behavior of a low-pressure turbine blade at several Reynolds numbers. Both the predicted and experimental results indicate increased cascade losses as the Reynolds number is reduced to the values associated with aircraft cruise conditions. In addition, both sets of data show that tripping the boundary layer helps reduce the losses at lower Reynolds numbers. Overall, the predicted aerodynamic and performance results exhibit fair agreement with experimental data.

Evaluation of flow field approximations for transonic compressor stages

The flow through gas turbine compressors is often characterized by unsteady, transonic, and viscous phenomena. Accurately predicting the behavior of these complex multi-blade-raw flows with unsteady rotor-stator interacting Navier-Stokes analyses can require enormous computer resources. In this investigation, several methods for predicting the flow field, losses, and performance quantities associated with axial compressor stages are presented. The methods studied include: (1) the unsteady fully coupled blade row technique, (2) the steady coupled blade row method, (3) the steady single blade row technique, and (4) the loosely coupled blade row method. The analyses have been evaluated in tennis of accuracy and efficiency.