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![Based on a schematic of a supersonic nozzle designed by the method of characteristics [3]](profile/Beric-Skews-2/publication/324440055/figure/fig1/AS:720665699176449@1548831500917/Based-on-a-schematic-of-a-supersonic-nozzle-designed-by-the-method-of-characteristics-3.png)
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The existing nozzle contour profiles of the CSIR's supersonic or High Speed Wind Tunnel (HSWT) produce weak waves in the test section region, which effectively degrades the air flow quality in the test section. This paper describes a calculation method developed to improve the flow quality in the test section region subject to the HSWT's limitation...
Contexts in source publication
Context 1
... the case of a converging-diverging supersonic wind tunnel nozzle, presented in the schematic in figure 3, the subsonic flow in the convergent portion of the nozzle is accelerated to sonic conditions at the nozzle throat region. A sonic "line" exists which is marginally curved, but for most applications it is assumed to be straight. ...
Context 2
... region is referred to as the straightening section which is designed to cancel the expansion waves originating in the expansion section. Figure 3 illustrates the manner in which the expansion wave at í µí±í µí±, originating in the expansion section is reflected at ℎ, on the opposite side of the nozzle wall and cancels at í µí±í µí±, in the straightening section of the profile. Downstream of points í µí±í µí±, í µí±í µí± and í µí±í µí±, lies the test section wall where the flow is uniform and parallel at the desired Mach number [3]. ...
Context 3
... 21 highlights that the flow Mach number becomes uniform and figure 22 portrays the density gradients becoming negligible as the flow expands towards the test section, implying that the straightening section is effectively cancelling expansion waves generated in the expansion section. The viscous solutions are presented in figure 23, which shows Mach number contours, and figure 24, which shows density gradient contours. Except for the distinct boundary layer, the flow trends are comparable to the inviscid solutions, in that the Mach number becomes uniform and the density gradients detect no irregularities in the test section region. ...
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Citations
... The limits on the yaw angles studied here were informed by reports on flow angularity in various supersonic wind tunnels, which tended to range from ±0.2 to 0.5 • (e.g. Jackson, Corlett & Monta 1981;Vallabh & Skews 2017). For this reason, one fully three-dimensional simulation is conducted with 0.5 • yaw introduced for Re = 11 × 10 6 m −1 . ...
The growth and characteristics of linear, oblique instabilities on a highly swept fin on a straight cone in Mach 6 flow are examined. Large streamwise pressure gradients cause doubly inflected cross-flow profiles and reversed flow near the wall, which necessitates using the harmonic linearized Navier–Stokes equations. The cross-flow instability is responsible for the most-amplified disturbances, however, not all disturbances show typical cross-flow characteristics. Distinct differences in perturbation structure are shown between small ( $\sim$ 3–5 mm) and large ( $\sim$ 10 mm) wavelength disturbances at the unit Reynolds number $Re' = 11 \times 10^6$ m $^{-1}$ . As a result, amplification measurements based solely on wall quantities bias a most-amplified disturbance assessment towards larger wavelengths and lower frequencies than would otherwise be determined by an off-wall total-energy approach. A spatial-amplification energy-budget analysis demonstrates (i) that wall-normal Reynolds-flux terms dictate the local growth rate, despite other terms having a locally larger magnitude and (ii) that the Reynolds-stress terms are responsible for large-wavelength disturbances propagating closer to the wall compared with small-wavelength disturbances. Additionally, the effect of free-stream unit Reynolds number and small yaw angles on the perturbation amplification and energy budget is considered. At a higher Reynolds number ( $Re' = 22 \times 10^6$ m $^{-1}$ ), the most-amplified wavelength shrinks. Perturbations do not behave self-similarly in the thinner boundary layer, and the shift in most-amplified wavelength is due to decreased dissipation relative to the lower-Reynolds-number case. Small yaw angles produce a streamwise shift in the boundary layer and disturbance amplification. The yaw results quantify a potential uncertainty source in experiments and flight.
... BLC is employed to modify the optimum geometry from inviscid analysis to reproduce the same flow characteristics in the presence of boundary layer in the viscous regime [29]. In the present study, BLC is applied to the results from the inviscid optimization. ...
For high-precision measurement in supersonic wind tunnel experiments, it is of crucial importance to produce a uniform flow in the measurement section downstream of the nozzle. This paper proposes and verifies a new design methodology for supersonic wind tunnel nozzles that can generate highly uniform airstream at a design Mach number at the nozzle exit. Shape design optimization has been conducted by employing surrogate-assisted evolutionary algorithms coupled with computational fluid dynamics. This approach has yielded higher flow uniformity than that of the nozzle designed by using the method of characteristics in the inviscid regime. By applying boundary layer correction to the nozzle contour obtained from the inviscid optimization, nearly uniform core flow of Mach 2.5 has been achieved at the nozzle exit in the presence of viscosity. In the viscous optimization, nozzle shape optimization has been performed by incorporating viscous simulations without using boundary layer correction to evaluate its efficacy in comparison with the former approach. It has been found that the deviation from the design Mach number and the flow deflection from the horizontal direction cannot be minimized simultaneously. This has been attributed to the constraint associated with the nozzle length. It has also been found that the result of the former approach combining the inviscid optimization and boundary layer correction can be regarded as one of the results of the viscous optimization.
... This demands for a study on proper contour designs of nozzles. Extensive research has been carried out on the accurate design of shock-free nozzles for a number of applications (supersonic wind tunnels, rocket propulsive nozzles, etc) [10][11][12][13][14][15]. In this study, we assess the importance of a proper nozzle contour design for plasma-assisted CO 2 pooling in supersonic nozzles. ...
Plasma assisted CO2 dissociation has recently been the topic of many studies. The production of chemical fuels from environmentally unfriendly CO2 through supersonic nozzles is one of the most prominent approaches under investigation. However, the experiments show that the theoretical conversion rates are far away from being achieved. In this study, two-dimensional fully coupled cases are investigated. This brings insights about how the CO2 dissociation can be improved; mainly by a correct design of nozzles. The proper shape of a nozzle is a fundamental aspect to be taken into account numerically and in experiments to avoid undesirable phenomena such as the occurrence of shocks. The proper design of the nozzle shape leads to a shock-free flow being uniform at the nozzle outlet. A high degree of cooling can be achieved in a shock-free nozzle. Moreover it is shown that there is no optimal value for Mach number provided that the nozzles are sized properly. If the sizing is done correctly, it is found that higher Mach numbers lead to higher degree of non-equilibrium and thereby to higher dissociation rate. The sizing of the nozzle to maximize the departure from equilibrium in the nozzle is the final key of an efficient CO2 dissociation. Finally, the results are compared with those of a semi-analytical method to conclude that if the nozzle is conceived in a proper way, simpler approaches can also give satisfactory results.
... High-speed wind tunnels are commonly classified as blowdown and indraft tunnels. In most of the previous studies especially in [3][4][5][6][7], it is noticed that the initial design parameters for the educational supersonic wind tunnels are based on the existing/available facilities such as power sources, pressure vessels, or suction equipment, etc. Therefore, the intention and main objective of this project are to propose a design methodology that can be adopted for the design of any high-speed (supersonic) wind tunnel irrespective of its type. ...
Commission (ERDF) project. This study was carried out after the inlet section of the supersonic wind tunnel prototype had been designed in Part-I [1] by introducing a simplified design approach of “Table of Inclination”. The design optimization of the exhaust section i.e. diffuser of the wind tunnel is the main objective of the current study. Diffuser design optimization was carried out in three steps; at first, the selection of the diffuser type was carried out and the initial estimated design was created. In the next step, 2D optimization of the wind tunnel design was carried out, and finally, 3D optimization of the complete wind tunnel model was performed. The main geometric parameters of diffuser design were optimized using CFD analysis. Due to the proposed design optimization strategy, the conventionally long diffuser length was successfully reduced. Additionally, 3D optimization further improved the design and helped to resolve the problem of higher operating power. This compact wind tunnel duct will have relatively lower manufacturing costs as well as the overall testing facility will occupy a smaller space. The optimized design of the diffuser and its integration with the inlet section of the wind tunnel marked the completion of the design of the full wind tunnel duct.
... In several studies especially in Refs. [3][4][5][6][7], it is observed that the initial design parameters for most of the educational high-speed wind tunnels were based on the existi-ng/available facilities such as power sources, pressure vessels, or suction equipment, etc. ...
... Additionally, studies such as Refs. [7,18,25] discussed different methods of MOC calculations while several studies [11,12,14] discussed various types of C-D nozzles that can be used in supersonic wind tunnels. In the earlier stages, divergent nozzle design using MOC was based on the manual calculations and hand-drawn sheets which were lengthy and extremely sensitive to errors. ...
... The conventional method of characteristics (MOC) is utilized with the region-to-region solving approach to design a shockfree inlet nozzle. In this approach, the flow properties are computed inside each region bounded by the characteristics-mesh involving additional approximations [7]. Although region-toregion is an excellent approach of MOC, it is comparatively less used due to its lengthy procedure. ...
This study aims to develop a simplified approach for the design of high-speed wind tunnels, operating within the range of Mach 1-4. The study is conducted in two stages; design stage-I consists of the basic parts of a high-speed wind tunnel, i.e. test section and nozzle throat sizes along with the calculations of the minimum pressure ratios necessary for the starting and running of the wind tunnel. Design stage-II is the aerodynamic design of the inlet nozzle contour with the focus on the divergent nozzle section only. In this stage, the fundamental method of characteristics (MOC) is employed by using region-to-region solution approach. Due to the long and complicated procedure of classical MOC, a simpler approach of “table of inclination” is proposed. This inclination table approach is simple in use, highly precise, and efficient which reduces more than 75 % of the calculation time of the MOC. Validation of the nozzle contour design is performed with the Area-Mach ratio relation followed by the results verification obtained from the MATLAB programming. The contour design results of the study are highly accurate (less than 1 % error) which manifests the future possible significance of the inclination table approach for supersonic wind tunnel designs.
One of the essential requirements in Cold Spray Additive Manufacturing (CSAM) is the control over the profile of the deposited materials. This paper introduces a workflow for designing contoured axisymmetric nozzles, which aims to improve on the metal particle delivery and the deposit profile of current commercial cold spray nozzles. The workflow uses two aerospace design codes based on the Method of Characteristics (MOC). By using coupled Eulerian-Lagrangian Computational Fluid Dynamics (CFD) simulations, the performance of a current commercial cold spray nozzle is compared with that of a redesigned nozzle. The new nozzle is obtained by performing a multi-objective optimization of the nozzle inner wall profile. This is done by varying the nozzle inlet convergent angle, the throat radius of curvature, and the inflection angle in the divergent section. The design performance is then assessed by evaluating a penalty function for each nozzle shape. The penalty function combines some of the most desirable characteristics in CSAM, namely a high particle impact velocity, a good spatial uniformity in this velocity and a good uniformity of the radial distribution of the particles. The numerical predictions show that the optimized nozzle shape delivers a more radially uniform deposit. A higher particle velocity is obtained at the same operating conditions/costs used by the industry standard nozzle. This study suggests that this integrated, multi-objective, parametric design approach can be built up in complexity to further improve the deposition performance of cold spray nozzles in additive manufacturing.
This study presents part-II of the work-in-progress for the development of a high-speed wind tunnel under the EU Commission (ERDF) project. This study was carried out after the inlet section of the supersonic wind tunnel prototype had been designed in part-I [1] by introducing a simplified design approach of “table of inclination”. The design optimization of the exhaust section, i.e., diffuser of the wind tunnel is the main objective of the current study. Diffuser design optimization was carried out in three steps; at first, the selection of the diffuser type was carried out and the initial estimated design was created. In the next step, 2D optimization of the wind tunnel design was carried out, and finally, 3D optimization of the complete wind tunnel model was performed. The main geometric parameters of diffuser design were optimized using CFD analysis. Due to the proposed design optimization strategy, the conventionally long diffuser length was successfully reduced. Additionally, 3D optimization further improved the design and helped to resolve the problem of higher operating power. This compact wind tunnel duct will have relatively lower manufacturing costs as well as the overall testing facility will occupy a smaller space. The optimized design of the diffuser and its integration with the inlet section of the wind tunnel marked the completion of the design of the full wind tunnel duct.
This paper aims to design a small-scale, compact supersonic wind tunnel nozzle using the method of characteristics and perform computational fluid dynamics (CFD) simulations to validate the design. The wind tunnel is designed to have a test section of 7cm × 7cm and a test section Mach number of 2.0. Simulations were performed for both 3D inviscid and viscous cases and it shows that for both cases, the obtained Mach number conforms with the design requirements. A further study on the effects of different pressure ratios, towards the position of shock waves, shows that an increase in the ratio would result the shock waves to shift downstream.
