The desire to improve gas turbines has led to a significant body of research concerning film cooling optimization. The open literature contains many studies considering the impact on film cooling performance of both geometrical factors (hole shape, hole separation, hole inclination, row separation, etc.) and physical influences (effect of density ratio (DR), momentum flux ratio, etc.). Film cooling performance (typically film effectiveness, under either adiabatic or diabatic conditions) is almost universally presented as a function of one or more of three commonly used non-dimensional groups: blowing—or local mass flux—ratio, density ratio, and momentum flux ratio. Despite the abundance of papers in this field, there is some confusion in the literature about the best way of presenting such data. Indeed, the very existence of a discussion on this topic points to lack of clarity. In fact, the three non-dimensional groups in common use (blowing ratio (BR), density ratio, and momentum flux ratio) are not entirely independent of each other making aspects of this discussion rather meaningless, and there is at least one further independent group of significance that is rarely discussed in the literature (specific heat capacity flux ratio). The purpose of this paper is to bring clarity to this issue of correct scaling of film cooling data. We show that the film effectiveness is a function of 11 (additional) non-dimensional groups. Of these, seven can be regarded as boundary conditions for the main flow path and should be matched where complete similarity is required. The remaining four non-dimensional groups relate specifically to the introduction of film cooling. These can be cast in numerous ways, but we show that the following forms allow clear physical interpretation: the momentum flux ratio, the blowing ratio, the temperature ratio (TR), and the heat capacity flux ratio. Two of these parameters are in common use, a third is rarely discussed, and the fourth is not discussed in the literature. To understand the physical mechanisms that lead to each of these groups being independently important for scaling, we isolate the contribution of each to the overall thermal field with a parametric numerical study using 3D Reynolds-averaged Navier–Stokes (RANS) and large eddy simulations (LES). The results and physical interpretation are discussed.

High-pressure (HP) nozzle guide vane (NGV) endwalls are often characterized by highly three-dimensional (3D) flows. The flow structure depends on the incoming boundary layer state (inlet total pressure profile) and the (static) pressure gradients within the vane passage. In many engine applications, this can lead to strong secondary flows. The prediction and design of optimized endwall film cooling systems is therefore challenging and is a topic of current research interest. A detailed experimental investigation of the film effectiveness distribution on an engine-realistic endwall geometry is presented in this paper. The film cooling system was a fairly conventional axisymmetric double-row configuration. The study was performed on a large-scale, low-speed wind tunnel using infrared (IR) thermography. Adiabatic film effectiveness distributions were measured using IR cameras, and tests were performed across a wide range of coolant-to-mainstream momentum-flux and mass flow ratios (MFRs). Complex interactions between coolant film and vane secondary flows are presented and discussed. A particular feature of interest is the suppression of secondary flows (and associated improved adiabatic film effectiveness) beyond a critical momentum flux ratio. Jet liftoff effects are also observed and discussed in the context of sensitivity to local momentum flux ratio. Full coverage experimental results are also compared to 3D, steady-state computational fluid dynamics (CFD) simulations. This paper provides insights into the effects of momentum flux ratio in establishing similarity between cascade conditions and engine conditions and gives design guidelines for engine designers in relation to minimum endwall cooling momentum flux requirements to suppress endwall secondary flows.

The computational and experimental assessment of a lean-burn low-NOx combustor simulator for an engine component test facility is presented. The Engine Component Aero-Thermal (ECAT) facility is a full-scale engine-parts facility, designed for the study of the aero-thermal performance of fully cooled high-pressure nozzle guide vanes (NGVs). The facility operates with non-dimensionally matched engine conditions in terms of Reynolds number, Mach number and coolant-to-mainstream pressure ratio. The combustor simulator is designed to replicate lean-burn conditions of swirl and temperature distortion upstream of the nozzle guide vanes. The purpose is to allow the study of flow capacity, aerodynamic performance (with film cooling), and thermal performance (overall effectiveness) in the presence of engine-realistic inlet distortions. Detailed experimental measurements with multi-hole probes and thermocouples are presented and compared to results from RANS Simulations. Additional simulations were performed to understand how the elevated back pressure and vane potential field affect the non-dimensional profiles of pressure loss, residual swirl and temperature at the combustor-turbine interface. This is perhaps the most comprehensive study to date of a combustor simulator in an engine-scale research facility, providing unique insight into the known challenges of simulator design, scaling issues when moving from low to high Reynolds number, and limitations of CFD in this flow environment.

Thermal engines based on pressure gain combustion offer new opportunities to generate thrust with enhanced efficiency and relatively simple machinery. The sudden expansion of detonation products from a single-opening tube yields thrust, although this is suboptimal. In this article, we present the complete design optimization strategy for nozzles exposed to detonation pulses, combining unsteady Reynolds-averaged Navier-Stokes solvers with the accurate modeling of the combustion process. The parameterized shape of the nozzle is optimized using a differential evolution algorithm to maximize the force at the nozzle exhaust. The design of experiments begins with a first optimization considering steady-flow conditions, subsequently followed by a refined optimization for transient supersonic flow pulse. Finally, the optimized nozzle performance is assessed in three dimensions with unsteady Reynolds-averaged Navier-Stokes capturing the deflagration-to-detonation transition of a stoichiometric, premixed hydrogen-air mixture. The optimized nozzle can deliver 80% more thrust than a standard detonation tube and about 2% more than the optimized results assuming steady-flow operation. This study proposes a new multi-fidelity approach to optimize the design of nozzles exposed to transient operation, instead of the traditional methods proposed for steady-flow operation.

This paper presents a method to significantly accelerate optimization of film cooling systems. The method combines high-fidelity computational fluid dynamics with scalar tracking implemented, a proxy model (linear superposition model) initialized with the computational fluid dynamics solution, and a multi-objective evolutionary algorithm approach. The proposed method is structured as follows: the computational fluid dynamics solution is used to predict the (generally complex) flow domain for the film cooling system; the scalar tracking method identifies the contributions of individual holes to an overall cooling effectiveness distribution by associating a unique passive scalar variable to the flow associated with each hole, and solving an additional advection–diffusion (scalar transport) equation; the proxy model is a (generally linear) superposition model implemented – for example – in Matlab, which inherits the scalar values from the computational fluid dynamics solution, and allows extrapolation of solutions to new design points as part of an optimization process; the optimization process is handled with a multi-objective evolutionary algorithm approach which iterates the proxy model to optimize for a defined objective function. The process works with inner and outer convergence loops. The inner convergence loop is the multi-objective evolutionary algorithm interfacing with the proxy model, which achieves convergence against a design target. At the end of each inner loop cycle, a high-fidelity computational fluid dynamics simulation is run, and this is used to recalibrate the proxy model. Convergence for a given objective function is typically achieved with six outer-loop iterations (high-fidelity computational fluid dynamics runs) and 10,000 inner-loop iterations per outer-loop iteration. The significant advantage of the proposed method is that for certain optimization problems, the computational cost can be reduced by several orders of magnitude, replacing thousands of high-fidelity computational fluid dynamics runs with approximately six computational fluid dynamics runs. The process is demonstrated by applying the optimization method to the film cooling of a flat plate. In our example we have an objective function which maximizes the component life (related to the difference from an arbitrary target temperature distribution) and minimizes the mixing loss introduced by the films. The flow environment was moderately compressible. The optimization converged after six computational fluid dynamics runs. A 30% reduction in mixing loss, a 11% increase in component life, and a 30% reduction in cooling mass flow rate were achieved. The advantages and limitations of the proposed method are also discussed in detail.