FIGURE 17 - available via license: Creative Commons Attribution 4.0 International
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Convection of coherent structures in the separated shear layer, shown by means of contours of ∂ρ/∂x. Instantaneous snapshots t = 1.3 × 10 −5 s apart from left to right.
Source publication
Flow dynamics and wall-pressure signatures in a high-Reynolds-number overexpanded nozzle with free shock separation - Volume 895 - E. Martelli, L. Saccoccio, P. P. Ciottoli, C. E. Tinney, W. J. Baars, M. Bernardini
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Citations
... Despite the fact such issues may become even more critical during landing, where the jet may impinge on a flat surface, comprehensive and quantitative models for predicting unsteady pressure forces are still to be developed. Resonances in jet flows originating from "truncated ideal contour" (TIC) nozzles, and operating within the free separation regime, have been observed within very narrow over-expansion ratio ranges (Baars et al. 2012a;Jaunet et al. 2017;Martelli et al. 2020). Recent investigations have demonstrated that the associated pressure disturbances are likely to generate significant lateral forces that could lead to structural damage or even flight control problems (Bakulu et al. 2021). ...
... The linear dynamics of inviscid annular supersonic jets, similar to those that are encountered in the exhaust a converging diverging nozzle, was explored in this article. The aim was to provide insights on the physical origins of tonal dynamics, observed in very limited expansion regimes in experiments Baars et al. 2012b), and possibly responsible of unsteady side-loads (Bakulu et al. 2021;Martelli et al. 2020). The focus was therefore put to the first azimuthal Fourier mode of flow fluctuations, the only ones responsible for off-axis loads in axisymmetric nozzles. ...
This article delves into the dynamics of inviscid annular supersonic jets, akin to those exiting converging-diverging nozzles in over-expanded regimes. It focuses on the first azimuthal Fourier mode of flow fluctuations and examines their behavior with varying mixing layer parameters and expansion regimes. The study reveals that two unstable Kelvin-Helmholtz waves exist in all cases, with the outer layer wave being more unstable due to velocity gradient differences. The inner layer wave is more sensitive to base flow changes and extends beyond the jet, potentially contributing to nozzle resonances. The article also investigates guided-jet modes, which are found to be robust and not highly sensitive to base flow parameters, making them essential for understanding jet dynamics. A simplified model is used to obtain ideal base flows with realistic shape to study varying nozzle pressure ratios (NPR) effects on the dynamics of the waves supported by the jet.
... Large-expansion-area nozzles have been extensively studied [1][2][3][4] for enhancing propulsion performance in high-temperature environments. These studies specifically investigate their performance and effects in such extreme thermal conditions. ...
This paper presents a numerical study on regenerative cooling in supersonic nozzles, with the aim of identifying the optimal RANS turbulence model for accurately predicting conjugate heat transfer. Three turbulence models, SST, RSM-ω, and RSM-ω with shear flow corrections (SFC), were tested through comparative analysis and simulations to evaluate their accuracy in predicting the heat flux rate and temperature on the nozzle wall. The results indicate that the RSM-ω turbulence model with shear flow corrections provides the best thermal prediction, achieving an improvement of 28% compared with the next best model. The coolant pressure can be very useful in the case of a very hot gas flow, owing to the increase in its saturation temperature. The height of the slot was found to be less important, which means that another factor can be considered a priority when constructing film-cooling systems. The influence of the hydrogen coolant on the gas temperature was also investigated, and it was found that hydrogen was effective in reducing the wall gas temperature, thus preventing the hot sidewall from reaching temperatures that could melt the wall material. The transient results show that the temperature of the side gas increased rapidly as the coolant side after the start-up process, and the time required for cooling the walls was found to be much higher than that of the hot gas flowing in the nozzle. Good agreement was found between the simulation and available experimental data.
... 21 highlighted the capacity of delayed detached eddy simulations (DDESs) in capturing RSS self-sustained unsteadiness in an axisymmetric TOC nozzle. Recently, Martelli et al. 22 and Bakulu et al. 23 performed a DDES calculation of an over-expanded TIC nozzle experiencing an FSS regime. Simulations, validated with experimental measurements, confirmed for a prescribed NPR the existence of a low-frequency breathing mode as well a higher frequency contribution. ...
... The insight that nozzle low-frequency shock oscillations were due to a standing wave produced by an upstream and a downstream propagating traveling wave 25 is now the commonly accepted theory 22,26,27 and known as transonic resonance. On the contrary, the nature of the high frequency unsteadiness is not yet clear, and it is often associated with the screech, which is an acoustic instability prevalent in underexpanded jets. ...
... At present, the unsteady dynamics at moderate values of NPR is poorly known. The only notable works on this subject are those attributed to Jaunet et al. 9 and Martelli et al., 22 who showed the emergence of a tonal high-frequency dynamics. The mechanism at stake in this condition is poorly known and the most accepted hypothesis conjectures about the existence of a feedback loop between the Mach disks. ...
When rocket engine nozzles operate at a high degree of over-expansion, an internal flow separation occurs with a strong unsteady shock–wave boundary layer interaction. The global dynamics results in a low-frequency mode, which is associated with the shock displacement, and a high-frequency mode, which is correlated with the shear layer–boundary layer interaction. While the mechanism responsible for the low-frequency oscillation is known, the one in charge of the high-frequency unsteadiness is not yet clear. The scope of this paper is to provide a physical explanation for this mechanism. To do that, a delayed detached eddy simulation is used to numerically reproduce the flow in the case of a sub-scale cold-gas truncated ideal contour nozzle. The obtained results are successfully compared to the experiments and confirm the presence of two non-axisymmetric wall pressure signatures at Strouhal numbers St=fDj/Uj≃0.2 and 0.3 with different azimuthal selections. To reveal the origin of such modes, a power spectral density analysis is performed in the separated region. The analysis shows that both modes originate from the external shear layer and behave as “twins” in the separated region. The reason is that both modes are two sides of the same impinging shear layer instability: the acoustic mode propagates with the sound velocity, while the hydrodynamic one propagates with the supersonic shear layer velocity. In this context, the resulting self-sustained dynamics may be due to an acoustic–hydrodynamic feedback loop involving the impinging shear layer instability of the external supersonic shear layer and the separated region.
... As can be seen in Fig. 16b, although the local grid refinement decreased slightly the curvature of the Mach disk, the recirculating region did not break. More recently, Martelli et al. [60], performed an experimentally validated Delayed Detached Eddy Simulation (DDES), on a highly over-expanded, sub-scale TIC nozzle. The unsteady numerical results revealed a counter-rotating vortex pair, immediately downstream of the Mach disk, in line with what Nasuti and Onofri described in [17] and with the results shown in Fig. 16. ...
A key requirement to achieve sustainable high-speed flight and efficiency improvements in space access, lies in the advanced performance of future propulsive architectures. Such concepts often feature high-speed nozzles, similar to rocket engines, but employ different configurations tailored to their mission. This paper presents a numerical investigation on the aerodynamic performance of a representative novel exhaust system, which employs a high-speed, truncated, ideal contoured nozzle and a complex-shaped cavity region at the base. Reynolds-Averaged Navier-Stokes computations are performed for a number of Nozzle Pressure Ratios (NPRs) and free stream Mach numbers in the range of 2.7 < NPR < 24 and 0.7 < M∞ < 1.2 respectively. The corresponding Reynolds number lies within the range of 1.06 · 106 < Red < 1.28 · 106 based on the maximum diameter of the configuration. The impact of the cavity on the aerodynamic characteristics is revealed by direct comparison to an identical non-cavity configuration. Results show a consistent trend of increasing base drag with increasing NPR for all examined M∞ for both configurations, owing to the jet entrainment effect. Cavity is found to have no impact on the incipient separation location of the nozzle flow. At conditions of M∞ = 1.2 and high NPRs, the cavity has a significant effect on the aerodynamic performance, transitioning nozzle operation to under-expanded conditions. This results in approximately 12% higher drag coefficient compared to the non-cavity case and shifts the minimum NPR for which the system produces positive gross propulsive force to higher values.
... Nomenclature C f = wall shear-stress coefficient E = total energy per unit mass H = total enthalpy per unit mass h = height or enthalpy per unit mass k = turbulence kinetic energy L = interaction length or cone longitudinal length M = Mach number N = grid points p = pressure Q i = turbulent heat flux vector q w = heat transfer at the wall Re = Reynolds number S ij = strain-rate tensor St = Stanton number t = time u i = velocity vector u vd = Van Driest transformed mean streamwise velocity u τ = friction velocity x; y; z = Cartesian coordinates γ = specific-heat ratio δ 0 = boundary-layer thickness at the reference location ε = turbulence dissipation θ = momentum boundary-layer thickness θ c = half cone angle κ = thermal conductivity μ = viscosity ρ = density σ ij = viscous stress tensor τ ij = Reynolds stress tensor τ w = wall shear stress S HOCK-WAVE/TURBULENT-BOUNDARY-LAYER interaction (SBLI) is one of the most important issues in aeronautics and aerospace engineering; see, e.g., the representative review papers of Dolling [1], Smits and Dussauge [2], Babinsky and Harvey [3], Clemens and Narayanaswamy [4], and Gaitonde and Adler [5]. SBLI always happens whenever a shock sweeps across the boundary layer developing on a solid wall, such as supersonic airfoil [1], supersonic/ hypersonic intake [6,7], and overexpanded nozzle [8,9], in a variety of aeronautical flows of practical interest. The shock wave imposes an adverse pressure gradient on the incoming boundary layer. ...
A parametric study of hypersonic impinging conical-shock-wave/turbulent-boundary-layer interaction (CSBLI) is carried out at hypersonic high-Reynolds-number conditions (Mach number 6.0, [Formula: see text], based on the freestream momentum boundary-layer thickness and wall viscosity) by means of numerical simulation of the Reynolds-averaged Navier–Stokes (RANS) equations, with the eventual goal of establishing wall temperature effects. Comparison with available experimental data shows that RANS is capable of predicting the main features of hypersonic oblique shock-wave/turbulent-boundary-layer interaction, namely, typical size and distribution of the wall properties. A large number of flow cases, especially at high Reynolds number, were computed to examine the scaling of the heat transfer over a wide range of wall temperatures. As expected, the interaction zone of hypersonic CSBLI is reduced as the wall is cooled. A simple power of heat transfer originally introduced by Back and Cuffel (“Changes in Heat Transfer from Turbulent Boundary Layers Interacting with Shock Waves and Expansion Waves,” AIAA Journal, Vol. 8, No. 10, 1970, pp. 1871–1873) for planar shock-induced interactions is here considered to account for hypersonic CSBLIs, which is found to successfully collapse the data to the distributions obtained for supersonic/hypersonic, cold/hot interactions. The value range of the power exponent [Formula: see text] is within 0.75–0.95.
... In such a situation, the corner region of a backward facing step near the nozzle exit, as shown in Fig. 1, acts as a "test cell" or "vacuum cell". The approach of using the backward-facing step as a test cell instead of a large vacuum chamber was employed by many researchers in the past for quick evaluation of the ejection characteristics of the diffuser [7,8,9,10,11,12]. The exhaust diffuser system is said to be "started" if there is no flow separation in the nozzle resulting in a series of reflected oblique shocks that seals the test cell and the nozzle exit from any backflow and helps to maintain the low vacuum level in the test cell during the testing of the nozzle. ...
... To validate numerical results, an experimental set up has been developed to perform coldflow testing of the nozzle with the present STED configuration with and without vacuum chamber. The earlier investigations were done at Jet Propulsion Lab (JPL) in order to find a best diffuser configuration for use in ground-level testing of a full-scale nozzle (Ae/At ~20.3) with a 6000 lb thrust [5,7,8]. For this purpose, several experiments at JPL were conducted on various one-tenth scale nozzle-diffuser systems [5,7,8]. ...
... The earlier investigations were done at Jet Propulsion Lab (JPL) in order to find a best diffuser configuration for use in ground-level testing of a full-scale nozzle (Ae/At ~20.3) with a 6000 lb thrust [5,7,8]. For this purpose, several experiments at JPL were conducted on various one-tenth scale nozzle-diffuser systems [5,7,8]. The nozzle-diffuser system used in this paper for numerical investigation is one of the one-tenth small scale nozzlediffuser systems on which a cold-flow (Ȗ=1.4) ...
Large area ratio nozzles that are employed for space propulsion applications are not meant to be tested at the ground-level conditions because of the flow conditions that occurs in their divergent section due to their low exhaust pressures. Therefore, it is desired to perform the experimental evaluation at high-altitude to evaluate the performance of the said nozzles. Generally, a high-altitude test facility, consisting of a supersonic exhaust diffuser, is generally employed. In thispaper, a second-throat exhaust diffuser has been numerically investigated to predict its minimum starting pressure, and to understand the flow physics in the diffuser using Computational Fluid Dynamics (CFD). Numerical computation of the flow field in the diffuser system is done for the two cases: 1) when the nozzle and the diffuser system are initially evacuated to a low pressure, and 2) when the nozzle and the diffuser system are initially at ambient pressure (1 bar). Simulations have been carried out for cold flow situation (Ȗ=1.4) over a range of nozzle inlet stagnation pressures. Numerical results compare favorably with the theoretical and experimental results and provide adequate insight to the flow physics and internal shock structures formed in thediffuser in addition to minimum starting pressure, diffuser wall pressure and vacuum thrust.
... A crucial part of the enhanced wall-pressure perturbations through the emergence of a separation shock structure is its consequent generation of aeroacoustical resonance. One of these prominent discrete tones recorded in low area ratio nozzles is the so-called transonic resonance 46 , associated with a feedback loop between upstream and downstream propagating waves from the shear layer that is approximately equal to frequencies one quarter of an acoustic standing wave in an open pipe of length L 12,36 . Another type of sound generation, through possibly broadband-shock associated noise (BBSAN) or screech 47 , follows a similar pathway where a feedback loop is always maintained between waves originating from the initial separation zone, to the downstream acoustic waves that radiate back upstream 48 . ...
... where k is the von Kármán constant and U i, j is the velocity gradient tensor. Note that these constants differ from the original DDES, and are based on calibration tests done by Martelli et al. 5,11,12 . f d acts as a shielding function that enforces RANS treatment at the wall even if one performs a wall-resolved simulation. ...
... The overall qualitative features of the wall-pressure spectra are also very similar to those obtained in prior works 5,12,13,34,36 , where the salient features of the wallpressure PSD shares many qualitative similarities with the canonical OSWBLI configurations (e.g., Dupont, Haddad, and Debieve 23 ), even though the flow boundaries here are fundamentally very different in nature with measurements from compression ramps, blunt fins etc. ...
We perform a combined numerical and experimental study to investigate the transonic shock-wave/turbulent-boundary-layer interactions (STBLI) in a shock-induced separated subscale planar nozzle with fully-expanded Mach number,$M_j = 1.05$ and jet Reynolds number $Re \sim 10^5$. The nozzle configuration is tested via time-resolved schlieren visualisation. While numerous studies have been conducted on the high Reynolds number separated flowfields, little is known on the weak shock wave unsteadiness present in low nozzle pressure ratio (NPR) transonic nozzles. Therefore, numerical simulations are carried out with high resolution three-dimensional delayed detached eddy simulation (DDES), to study the spatiotemporal dynamics of wall pressure signals and unsteady shock interactions. The transient statistics considered include spectral Fourier and wavelet-based analysis and dynamic mode decomposition (DMD). The spectral analyses reveal energetic low frequency modes corresponding to the staging behaviour of shock unsteadiness, and high frequencies linked to the characteristics of the Kelvin-Helmholtz instabilities in the downstream turbulent mixing layer. The mechanisms for the low frequency unsteadiness is educed through modal decomposition and spectral analysis, wherein it is found that the downstream perturbations within the separation bubble play a major role in not only closing the aeroacoustic feedback loop, but allowing the continual evolution and sustainment of low frequency unsteadiness. An analysis via the vortex sheet method is also carried out to characterise the screech production, by assuming an upstream propagating guided jet mode
... In viscous flows, vortex generation, boundary layer detachment, flow separation, and recirculation are present [4][5][6]; the sensitivity of the Mach disk shape to radial pressure gradients [7]. As well as the flow separation modes present characteristics defined in truncated ideal contour (TIC), thrust optimized contour (TOC), thrust optimized parabolic (TOP), conical nozzle types [8][9][10], planar nozzles [11,12] and diffusers [13,14]. ...
... The empirical equation (17) facilitated the calculations by connecting with the analytical equations involved (1), (2), (4), (5), (6), and (18) to obtain the curves shown in Fig. 8. Table 15 presents the magnitudes of the parameters at the shock position A x /A * , for rp = 0.4, rp = 0.5, rp = 0.6 and rp = 0.7. In convergent-divergent nozzles for the overexpanded flow condition, and according to the designs of the aerodynamic profiles of the walls, the shock wave can reach values close to Mach 5. Therefore, the empirical equation (17) and the data from Tables 7, 8, and 9, for the range of 1 ≤ Mx ≤ 5 and 1.1 ≤ k ≤ 1.67, is an appropriate and relevant option to be applied. ...
In the present work for a quasi-one-dimensional isentropic compressible flow model, an empirical equation of the Mach number is constructed as a function of the stagnation pressure ratio for an analytical equation that algebraic procedures cannot invert. The Excel 2019 Solver tool was applied to calibrate the coefficients and exponents of the empirical equation during its construction for the Mach number range from 1 to 10 and 1 to 5. A specific heat ratio from 1.1 to 1.67 and the generalized reduced gradient iterative method were used to minimize the sum of squared error, which was set as the objective function. The results show that for Mach 1 to 10, an error of less than 0.063% is obtained, and for Mach 1 to 5, an error of less than 0.00988% is obtained. It is concluded that the empirical equation obtained is a mathematical model that reproduces the trajectories of the inverted curves of the analytical equation studied.
... Still, not every flow can be captured. The experiment requires robust sensors and well-fabricated nozzles, and the most common approach is to measure the wall pressure distribution [2][3][4][5][6]. Detailed descriptions of the nozzle contour and experimental data are not easily found. ...
Capturing elaborated flow structures and phenomena is required for well-solved numerical flows. The finite difference methods allow simple discretization of mesh and model equations. However, they need simpler meshes, e.g., rectangular. The inverse Lax-Wendroff (ILW) procedure can handle complex geometries for rectangular meshes. High-resolution and high-order methods can capture elaborated flow structures and phenomena. They also have strong mathematical and physical backgrounds, such as positivity-preserving, jump conditions, and wave propagation concepts. We perceive an effort toward direct numerical simulation, for instance, regarding weighted essentially non-oscillatory (WENO) schemes. Thus, we propose to solve a challenging engineering application without turbulence models. We aim to verify and validate recent high-resolution and high-order methods. To check the solver accuracy, we solved vortex and Couette flows. Then, we solved inviscid and viscous nozzle flows for a conical profile. We employed the finite difference method, positivity-preserving Lax-Friedrichs splitting, high-resolution viscous terms discretization, fifth-order multi-resolution WENO, ILW, and third-order strong stability preserving Runge-Kutta. We showed the solver is high-order and captured elaborated flow structures and phenomena. One can see oblique shocks in both nozzle flows. In the viscous flow, we also captured a free-shock separation, recirculation, entrainment region, Mach disk, and the diamond-shaped pattern of nozzle flows.
... The area of spatial propulsion is specifically potential since the nozzle is among the vital components of a launcher. Indeed, for nozzles with high area ratio, the specific impulse is improved, allowing therefore for payload enhancement and launching cost reduction [4][5]. However, the internal supersonic flow is subjected to several instabilities as it operates under overexpanding conditions for almost all the mission steps [5]. ...
... However, the internal supersonic flow is subjected to several instabilities as it operates under overexpanding conditions for almost all the mission steps [5]. As the flow develops within the divergent part of the nozzle, local free (FSS) or restricted (RSS) separation may occur inducing side loads, that can alter the structural integrity of the nozzle as well as launcher performances reduction [4,6]. ...
The purpose of this work is to perform a CFD study of the free shock separation (FSS) in an overexpanded nozzle. The original contraction profile of the nozzle was numerically replaced by a set of curves, where the overall length was identical with the test-rig. For the baseline case, the static pressure and the separation location exhibited a good agreement with the experimental measurements, provided by the DLR. The Error-function contraction profile has revealed a relative displacement of 1.38% on the separation location in the core flow direction. In this case, there was an increase in the thrust coefficient, that has been improved up to 1.7% in comparison with the baseline nozzle design.
