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This paper presents the elaborated hydrodynamics studies of three types of air nozzles of CFBC boilers, types of air nozzles are bubble cap, arrow head and modified arrow head nozzles, and all these air nozzles are arranged in a 3 × 3 array and manufactured using FDM 3D print. The array of air nozzle is mounted onto the 200 × 200 × 2000-mm-transparent full-loop CFBC test rig. The different fluidization regimes for three types of air nozzles are studied. This research study is the sequel of the previous experiments where we had experimented different particle sizes, different bed heights and different velocities for a bubble cap nozzle, to avoid complication and number of experiments involving various velocities, bed heights, particle sizes and nozzles, and in this experiment we had kept bed height, particle size and velocity as fixed and nozzle geometry as variables. The bed height is kept as 200 mm from the distributor plate, particle size is taken as 200 μm and velocity as 1 m/s. The parameters considered for this include the velocity, pressure drop and the regimes of fluidization. The hydrodynamic study is conducted both experimentally and computationally; the results are then compared to find out the most optimal design of nozzle among the three. Based on experimental and computation results, the modified arrow head nozzle is a good hydrodynamic stable air nozzle to be used in the CFBC boiler, though its pressure drop is more.

Numerical analyses, validation and geometric optimization of a converging-diverging nozzle flows has been established in the present work. The optimal nozzle contour for a given nozzle pressure ratio and length yields the largest obtainable thrust for the conditions and thus minimises the losses. Application of such methods reduces the entry cost to the market, promote innovation and accelerate the development processes. A parametric geometry, numerical mesh and simulation model is constructed first to solve the problem. The simulation model is then validated by using experimental and computational data. The optimizations are completed for conical and bell shaped nozzles also to find the suitable nozzle geometries for the given conditions. Results are in good agreement with existing nozzle flow fields. The optimization loop described and implemented here can be used in the all similar situations and can be the basis of an improved nozzle geometry optimization procedure by means of using a multiphysics system to generate the final model with reduced number sampling phases.

Purpose The purpose of this paper is to design a double parabolic nozzle and to compare the performance with conventional nozzle designs. Design/methodology/approach The throat diameter and divergent length for Conical, Bell and Double Parabolic nozzles were kept same for the sake of comparison. The double parabolic nozzle has been designed in such a way that the maximum slope of the divergent curve is taken as one-third of the Prandtl Meyer (PM) angle. The studies were carried out at Nozzle Pressure Ratio (NPR) of 5 and also at design conditions (NPR = 3.7). Experimental measurements were carried out for all the three nozzle configurations and the performance parameters compared. Numerical simulations were also carried out in a two-dimensional computational domain incorporating density-based solver with RANS equations and SST k-ω turbulence model. Findings The numerical predictions were found to be in reasonable agreement with the measured experimental values. An enhancement in thrust was observed for double parabolic nozzle when compared with that of conical and bell nozzles. Research limitations/implications Even though the present numerical simulations were capable of predicting shock cell parameters reasonably well, shock oscillations were not captured. Practical implications The double parabolic nozzle design has enormous practical importance as a small increase in thrust can result in a significant gain in pay load. Social implications The thrust developed by the double parabolic nozzle is seen to be on the higher side than that of conventional nozzles with better fuel economy. Originality/value The overall performance of the double parabolic nozzle is better than conical and bell nozzles for the same throat diameter and length.

Viscous effects on an ideal gas flow in a supersonic convergent–divergent nozzle are a well-studied subject in classical gas dynamics. However, the ideal assumption fails on fluids that exhibit complex behaviours such as near-critical-region and non-ideal dense vapours. Under those conditions, a realistic equation of state (EOS) plays a vital role for a precise and realistic computation. This work examines the problem for solving the quasi-one-dimensional viscous compressible flow using a realistic EOS. The governing equations are discretised and solved using the fourth-order Runge–Kutta method coupled with a state-of-the-art EOS to calculate the thermodynamic properties. The role of the Grüneisen parameter along with viscous and real gas effects and their influence on the sonic point formation are discussed. The study shows that the flow may not achieve the supersonic regime for any pressure ratio depending on the combination of that parameter and the normalised friction factor. In addition, the analysis yields the discharge coefficient and the isentropic nozzle efficiency, which may achieve maximum values as a function of the stagnation conditions. Finally, the study also evaluates the formation and intensity of normal shock waves by using the Rankine–Hugoniot relations, which now depend on the real gas and viscous effects in opposition to the inviscid solution. Moreover, the methodology used captures the sonic point and shock wave position by a space marching algorithm using the Brent method for scalar minimisation. Experimental data available in the open literature corroborate the approach.

Critical flow Venturi nozzles (toroidal, cylindrical, convergent–divergent, or C–D) nozzles) have discharge coefficients predicted through numerical and experimental investigations. Unfortunately, the imprecision of the critical-flow Venturi nozzle design makes it impossible to study the influence of inlet curvature Rc on the discharge coefficient in the laminar boundary layer area. This study examines how the inlet curvature affects the discharge coefficient, or Cd, in the laminar boundary layer area of a critical-flow Venturi nozzle with a cylindrical throat and toroidal shape. The inlet curvature has a range from one throat diameter to three and a half throat diameters. This range of inlet curvatures was obtained by throat the inlet of a high-precision nozzle that was primarily compliant with ISO 9300. The C-D nozzle showed the impact of the convergence angle on the discharge coefficient. The results showed that the highest discharge coefficient occurs at Rc= 2dth for a throat diameter of 0.5588 mm, whereas for dth= 3.175 mm, it occurs at Rc= 2.5dth for toroidal nozzle. For this C-D nozzle, the highest discharge coefficient was observed to occur at a curvature of angle of 10°. Moreover, Cd increases significantly with increase of inlet stagnation pressure but with a small throat diameter.

In this study, a method for designing supersonic nozzles with axisymmetric plugs at high temperature has been proposed. The approach is based on the theory of Prandtl-Mayer expansion at high temperatures using the method of characteristics. For this purpose, a code in FORTRAN language was developed in order to obtain the nozzle design. Once the latter was obtained, we were interested in the evolution of the thermodynamic parameters of the flow such as pressure, temperature, and Mach number. The results achieved were confronted with those obtained for a perfect gas model. Regarding the design parameters (length, section ratio, thrust coefficient and mass coefficient), we found that the PG model gives very satisfactory results for values of and 0 below 2.00 and 1000 , respectively. As and 0 increase, this affects performance, requiring the use of our HT model to correct the calculations. In order to minimize the weight of this nozzle, this research is investigating the truncation of the Plug nozzle to increase its performances. All calculations were performed for air.

In cold spray applications, optimum process conditions to accelerate particles may vary with different densities of the feedstock. These conditions could depend on the geometry of the spray nozzle, suggesting possible benefits of material-specific nozzle designs. The present study developed a nozzle geometry optimization concept based on three-dimensional computational fluid dynamics (3D-CFD) simulations to provide a specific nozzle design. Applying a design of experiments (DoE) approach, the proposed model seeks an optimal nozzle geometry, using aluminum Al6061 and pure copper with mean particle diameters of 40 µm as examples. Different geometry parameters were varied to reach the highest particle velocities before impact on the substrate, such as the nozzle’s divergent section length, throat cross section, and expansion ratio. The process gas was nitrogen with set stagnation pressure and temperature of 5 MPa and 500 °C, respectively. For high particle impact velocities, the simulation identified the divergent section length as the most influential parameter, followed by the throat cross section. In addition, the results show that the expansion ratio must be carefully tuned to avoid over-expansion of the gas already inside the nozzle, which is detrimental to the particle acceleration.

Informed by large-eddy simulation (LES) data and resolvent analysis of the mean flow, we examine the structure of turbulence in jets in the subsonic, transonic and supersonic regimes. Spectral (frequency-space) proper orthogonal decomposition is used to extract energy spectra and decompose the flow into energy-ranked coherent structures. The educed structures are generally well predicted by the resolvent analysis. Over a range of low frequencies and the first few azimuthal mode numbers, these jets exhibit a low-rank response characterized by Kelvin–Helmholtz (KH) type wavepackets associated with the annular shear layer up to the end of the potential core and that are excited by forcing in the very-near-nozzle shear layer. These modes too have been experimentally observed before and predicted by quasi-parallel stability theory and other approximations – they comprise a considerable portion of the total turbulent energy. At still lower frequencies, particularly for the axisymmetric mode, and again at high frequencies for all azimuthal wavenumbers, the response is not low-rank, but consists of a family of similarly amplified modes. These modes, which are primarily active downstream of the potential core, are associated with the Orr mechanism. They occur also as subdominant modes in the range of frequencies dominated by the KH response. Our global analysis helps tie together previous observations based on local spatial stability theory, and explains why quasi-parallel predictions were successful at some frequencies and azimuthal wavenumbers, but failed at others.

Altitude-adapted nozzles are designed to facilitate flow adaptation during rocket ascent in the atmosphere, without requiring mechanical activation. As a consequence, the performance of the nozzle is significantly improved. The aim of this study is to develop a new profile of axisymmetric supersonic nozzles adapted at altitude (Dual Bell Nozzle with Central Body), which is characterized by an E-D nozzle as a basic profile. The performances obtained for this nozzle (E-D Nozzle) are then compared to those of a Plug nozzle. The E-D nozzle shows significant performance advantages over the Plug nozzle, including a 13.02% increase in thrust, knowing that the length of the E-D nozzle is half that of the Plug nozzle under the same design conditions. Finally, viscous calculations using the k-ω SST turbulence model were conducted to compare the performance of the dual bell nozzle with central body (DBNCB) and the E-D nozzle with the same cross-sectional ratio, and to assess the impact of nozzle pressure ratio (NPR) variations on the operation mode of the DBNCB. The results obtained show that the DBNCB offers the best performance in most phases of flight.

Rocket nozzles are often cooled by passing liquid propellants through channels in the nozzle walls. Estimating heat transfer to the wall from the hot gases in the nozzle is essential in deciding on the coolant flow requirements. The present work examines the computational estimation of convection heat transfer to the nozzle walls for compressible turbulent flows. Computations were performed using the rhoPimpleFoam solver in OpenFOAM® with two different turbulence models. We simulate the supersonic flow over a flat plate and validate the heat flux calculation method and turbulence model characteristics. We compare two methods of calculating convection heat transfer in the context of the nozzle flow case presented by Back & Massier. We find that the realizablek-ε turbulence model works well in estimating the heat transfer coefficient.