Characterizing and predicting bluff-body solid fuel ramjet performances via shape design and multi-objective optimization model

AN experimental investigation was conducted of the combustion behavior in solid fuel ramjets in order to determine the effects of configuration variables and operating conditions on combustion performance. Variables considered were fuel port flow rates, bypass dump momentum and geometry, and bypass ratio. Contents To be used in a tactical situation, the solid-fuel ramjet has to demonstrate combustion stability and high efficiency over the expected operating envelope of altitudes and Mach numbers. It must also show performance comparable to that of liquid-fuel ramjets and ducted rockets. Combustion studies on the solid-fuel ramjet have been underway at United Technologies—Chemical Systems Division since 1971.l The solid-fuel ramjet has two distinct combustion zones within the fuel grain: the recirculation zone behind the sudden expansion inlet, which provides flame stabiliation; and a diffusion flame in the developing boundary layer region after flow reattachment. Unburned gaseous fuel escapes from under the flame at the aft end of the fuel grain and results in decreased combustion efficiency. Aft mixing chambers and bypass air designs are being used to increase the efficiency. A schematic of the solid-fuel ramjet is shown in Fig. 1. The apparatus employed a polymethylmeth acrylate (PMM) fuel with a fuel port to dump inlet area ratio of 9.0 and a fuel port to nozzle throat area ratio of 4.0. The exit area of the grain was held fixed at the initial port area by using a thin orifice plate. The aft mixing chamber had a length to diameter ratio of 2.93. The aft mixing chamber consisted of three interchangeable sections such that the axial location and angular orientation of the bypass dumps could be varied. A summary of the test conditions is presented in Table 1. Figure 2 presents data obtained without bypass air. The regression rate expression indicates a weaker dependence on pressure than the earlier data of Boaz and Netzer.2 Figure 3 presents data obtained with bypass air. A slightly stronger dependence on pressure was shown while regression rate indicated very little or no dependence on air flux for the values tested. In the bypass situation, the mass flux through the grain is low but the pressure is maintained high, due to the total mass flux through the nozzle throat. These conditions minimize the convective heat flux to the fuel surface. For lower mass flux through the grain, the regression rate increases relative to the air flux; thus, more gas with radiative properties (fuel rich) is present. These results indicate that using bypass with PMM fuel changes the principal wall heat flux mechanism from convection to radiation.

Effects of new solid propellant configurations on the combustion characteristics of a ramjet

The interaction between grid refinement and features in design space is investigated for time dependent Navier-Stokes flows over a bluff body. A mixing measure and total pressure loss are calculated for a range of geometries and several grid refinements. In particular, 52 geometries are analyzed and a response surface surrogate-based outlier analysis revealed that as the grid is refined, three of these configurations stand out with off-trend mixing indices. Both grid refinement and multiple surrogate modeling exercises reveal that very high mixing indices are found in a very small island in design space. This important design region manifests itself only when the grid resolution is adequate. The high value of the mixing index is due to interaction between viscous flows and abrupt geometric variations of the bluff body . based on selected number of original CFD solutions 1-11 . In addition to offering a low-cost alternative for evaluating designs, surrogate models also offer advantages associated with the fact that they require a large number of designs to be evaluated together. Besides obvious advantages in terms of parallel computation, this can also reveal cases with significantly different behavior than others. Histogram and outlier analysis can identify and examine designs exhibiting unusual departure from the overall trend. The outliers can occur due to incomplete convergence or high errors due to inappropriate computational set-up such as grid distributions or boundary conditions. In that case, outlier analysis helps find and possibly correct these problems. However, outlier may also represent designs where the physical behavior changes significantly. In this study, the mixing problem associated with bluff body flows is investigated. Mixing is a process with many practical applications, including propulsion and power generation, homogenization of multiple materials and/or species, and various heat exchange and geophysical processes. In man-made devices, �

A research-scale solid-fuel ramjet test article has been developed to study the secondary combustion zone of solid fuel ramjets. Tests were performed at a constant core air mass flowrate of 0.77 kg/s with 0%, 15%, and 30% bypass ratios. The propulsive performance analysis results indicate that the 0% bypass case had the highest regression rate and fuel mass flowrate. The regression rate and fuel mass flowrate of fuel without carbon black was the lowest. The specific impulse with air mass flowrate included was highest for the 0% bypass case reaching 130 s and lowest for the 30% bypass case reaching 110 s. For specific impulse with air mass flowrate excluded, the 30% bypass case achieved 2,800 s while the 0% bypass case achieved 1,800 s. The characteristic velocity was greatest for 0% bypass reaching 1,025 m/s and lowest for 30% bypass reaching 900 m/s. The combustion efficiency was highest for the 15% bypass case with carbon black addition approaching 0.82. 50 kHz and 75 kHz CH* chemiluminescence imaging was performed. Analyzing thin slivers of the images over 40,001 frames with frequency-domain techniques showed that most of the high amplitude content occurred below 1-5kHz with small peaks near 20 kHz and 30 kHz. Dynamic mode decomposition (DMD) was performed on sets of 10,001 spatially-calibrated images and their corresponding uncalibrated, uncropped images. Most of the tests exhibited low-frequency axial pumping, transverse modes, and other mode shapes indicative of the secondary injection. The prominence of transverse and other jet-related modes over axial modes appeared to be related to increasing bypass ratio. High-frequency axial modes also appeared in a case thought to have high core-flow momentum that did not appear at these high frequencies for other cases. The DMD modes for 0% bypass were indiscernible due to high soot content. Most of the modes corresponding to the calibrated images also appeared in the uncalibrated images, however, with different mode amplitude rankings. PIV was performed at 5 kHz for one test at 15% bypass. The instantaneous vector fields for these tests displayed local velocities up to 600 m/s. The mean images showed velocities up to 250 m/s. The two-dimensional turbulent kinetic energies reached 200 m2/s2 in several regions throughout the flowfield. The turbulence intensity exceeded 0.20 near the bottom of the flowfield.

Investigation of the effect of geometry of combustor on combustion characteristics of solid-fuel ramjet with swirl flow

A series of reduced-order numerical simulations on a specific bluff body type (v-gutters) in a subsonic duct flow is performed to assess the unsteady wake dynamics. Two of the v-gutter's geometrical parameters are varied: the v-gutter's base angle (θ) and the size of a slit (ξ) at the leading-edge of the v-gutter. Turbulent flow kinematics and pressure field are analyzed to evaluate the unsteadiness at a freestream Mach number of M∞=0.25 and a freestream Reynolds number based on bluff body's transverse length (L = 17.8 mm) of ReL=0.1×106. Five v-gutter angles are considered (θ, rad=π/6,π/4,π/3,5π/12,π/2) and three slit sizes (ξ, mm =0,0.25,0.5) are considered only for a particular θ=[π/6]. In general, high fluctuations in velocity and pressure are seen for the bluffest body in consideration ( θ=π/2) with higher drag (cd) and total pressure loss ( Δp0). However, bluffer bodies produce periodic shedding structures that promote flow mixing. On the other hand, the presence of a slit on a streamlined body ( θ=π/6) tends to efficiently stabilize the wake and thus producing almost a periodic shedding structure with lower cd and Δp0. For θ=[π/6], broadened spectra in vortex shedding are seen with a peak at [fL/u∞]∼0.08. For θ≥[π/4], a dominant discrete shedding frequency is seen with a gradual spectral decay. Similarly, the effects of ξ on the θ=[π/6] case produce a discrete shedding frequency instead of a broadened one, as seen in the cases of θ≥[π/4]. The shedding frequency increases to a maximum of [fL/u∞]∼0.26 for the maximum slit size of ξ=0.5 mm. From the analysis of the x–t diagram and the modal analysis of vorticity and velocity magnitude in the wake, the peaks are indeed found to agree with the spectral analysis. More insights on the shedding vortices, momentum deficit in the wake, varying energy contents in the flow field, and the dominant spatiotemporal structures are also provided.

This paper presents a numerical investigation of ignition and combustion stabilization of a novel design of a solid-fuel ramjet (SFRJ) motor with and without swirl flow. The proposed design includes two solid fuels, retaining the simple design of the classic SFRJ. Numerical simulations of unsteady, turbulent, reactive, and swirling flow coupled with solid-fuel pyrolysis have been performed using an in-house CFD solver. Experiments on SFRJ were conducted via a connected-pipe test facility to validate the developed code. Furthermore, the code was validated for chemical reactions, heat diffusion, and swirl flow by using benchmark test cases of shock-induced, semi-infinite plate, and dump combustor with swirl flow, respectively. Then, the proposed and classic designs were simulated for the same inflow conditions and configurations, and the results were analyzed and discussed. It is found that the mixing degree, reactant residence time, mass flux, ignition delay time, and regression rate improve when using the proposed design. Moreover, the proposed design reveals interesting observations of a new flame being created and merged with the main flame.

Expandable Graphite, a Novel Regression Rate Enhancer in the Solid Fuel Ramjet

In this paper, the effect of sudden expansion ratio of solid fuel ramjet (SFRJ) combustor is numerically investigated with swirl flow. A computational fluid dynamics (CFD) code is written in FORTRAN to simulate the combustion and flow patterns in the combustion chamber. The connected-pipe facility is used to perform the experiment with swirl, and high-density Polyethylene (HDPE) is used as the solid fuel. The investigation is performed with different sudden expansion ratios, in which the port and inlet diameters are independently varied. The results indicated that the self-sustained combustion of the SFRJ occurs around the reattachment point at first, and then the heat released in reattachment point is used to achieve the self-sustained combustion in the redevelopment zone. The average regression rate is proportional to the sudden expansion ratio for the cases with a fixed port diameter, which is mainly dominated by the enhancement of heat transfer in backward-facing step. However, the average regression rate is inversely proportional to the sudden expansion ratio for the cases with fixed inlet diameter, which is influenced by the heat transfer mechanism of developed turbulent flow in the redevelopment zone.

Numerical investigation of bluff body for vortex induced vibration energy harvesting

Multi-objective Construction Site Layout Planning Using Genetic Algorithms

A multi-objective optimization model is established for the shape design of arch dams. In this model, the geometric parameters describing dam shape is taken as design variables; four objectives are considered of dam volume, maximal tensile stress, maximal pressure stress and relative depth of the zone with tensile stress that is larger than 1.0MPa; and the constraints include geometric constraints, dam volume constraint and mechanical property constrains, i.e., stress constraints, stability constraints, etc. Traditionally, multi-objective optimization schemes transform multiple objective functions into a single objective function in some manner, weighted sum method and Utopia point method for examples, and the resulting problem is solved as a single objective optimization problem. In this paper the cooperative game model analogy to the multi-objective optimization is proposed with each player correspond to one of the objective functions. After defining the utility of each player, the Nash arbitrary scheme is used to solve the cooperative game. The optimization of Baihetan arch dam, which is located in Sichuan province of China, is calculated as an engineering example. The results are compared to those obtained by weighted sum method and Utopia point method and indicate that the cooperative game method is superior to traditional methods. The optimal design saves 9.77×104m3 of dam volume, compared to initial design, along with the decrease of maximal tensile stress with 38.22%, the decrease of maximal pressure stress with 28.83%, and the decrease of relative depth of large tensile stress zone with 10.15%.

Reliable communication quality and reasonable cost control are two of important goals of Sink node location problem in modern communication. How to achieve an optimization solution by balancing both the two goals is a difficult tradeoff, especially in mobile wireless sensor networks. Therefore, with the maximum signal coverage as the communication quality goal, a constrained multi-objective optimization model is proposed by optimizing cost and communication quality at the same time. In order to deal with the constraints, we improve the classic multi-objective algorithm NSGA_II and adopt the strategy of binary tournament based on CV violation value to select the parent, so that the superior individuals have a greater probability to participate in the genetic operation. Finally, the problem model and algorithm proposed in this paper are applied to a set of Sink node location problems with different cost and network parameters. Compared with the NSGA_II algorithm, experimental results show that the new algorithm can improve the signal coverage better without much increase in cost. At the same time, the variances of the optimization results obtained in new algorithm are smaller, which means its optimization is more stable.

A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty

Ducted wind turbines are known to exceed the Betz limit for the power that may be extracted from free currents per unit cross‐sectional area of their rotors. The present study points to another advantage: the fact that the turbine rotor (and the associated subassemblies) need not be lifted up on the air and rotated to align with the wind. They can function just as effectively by installing them on the ground and sucking air inside it. The analysis evaluates the efficiency of a ducted wind turbine plant, exhausting into the wake of a bluff body, under both ideal and realistic component performance. The results indicate that there exists a strong need to develop diffusers with a very low loss coefficient (e.g. by employing suction or transpiration techniques). Under such conditions and by employing the above exhaust assist techniques, the ducted wind turbine concept may deliver efficiencies more than an order of magnitude larger than those of the conventional plants. Copyright © 2009 John Wiley & Sons, Ltd.