Reynolds-averaged Navier-Stokes Solutions Research Articles

Non-equilibrium turbulent boundary layers in high reynolds number flow at incompressible conditions: effects of streamline curvature and three dimensionality

The physics and computational prediction of turbulent boundary layer flow over axisymmetric and three-dimensional bodies are examined. Three cases were considered for which extensive experimental results and companion Reynolds-averaged Navier Stokes (RANS) solutions were obtained and/or available in the open literature. These cases all have Reynolds numbers based upon the freestream velocity and body geometric scale on the order of 10 5 to 10 6 , which is large for laboratory scales but small compared to the maximum scales observed for full-scale vehicles. Despite significant differences in approach flow fields and geometries for these three cases, some common themes emerged in the findings. All cases involved complications due to pressure gradients combined with streamwise curvature, and all exhibited regions of turbulence reduction due to accelerated flow. These complications led to discrepancies in computed results even in attached flow regions where it is often assumed that RANS models provide reliable predictions. The authors recommend further work on modelling approaches that can capture rapid distortion effects on turbulence transport that can be incorporated into industry-useful frameworks. Two cases involving laterally symmetric, three-dimensional wall-mounted hills with aft-body separation revealed that asymmetric mean flow fields are likely to result. This finding has been observed in experiments conducted in multiple facilities and in computations using multiple solvers and turbulence models. It is concluded that non-unique and asymmetric global flow solutions are fundamental to flow cases with lateral geometric symmetry involving turbulent boundary layer separation. Further work is also needed to accurately predict low-frequency unsteadiness due to geometries that produce non-unique mean flow fields. For such flows, it remains to be definitively determined whether experimentally observed modes of the mean flow are equivalent, or nearly equivalent, to asymmetric mean flow solutions obtained using RANS approaches.

Addressing performance improvement of a neural network model for Reynolds-averaged Navier–Stokes solutions with high wake formation

PurposeDeep-learning techniques are recently gaining a lot of importance in the field of turbulence. This study focuses on addressing the problem of data imbalance to improve the performance of an existing deep learning neural network to infer the Reynolds-averaged Navier–Stokes solution, proposed by Thuerey et al. (2020), in the cases of airfoils with high wake formation behind them. The model is based on a U-Net architecture, which calculates pressure and velocity solutions for fluid flow around an airfoil.Design/methodology/approachIn this work, we propose various methods for training the model on selectively generated data with different distributions, which would be representative of the under-performing test samples. The property we chose for selectively generating data was the fraction of negative x-velocity in the domain. We have used Grad-CAM to compare the layer activations of different models trained using the proposed methods.FindingsWe observed that using our methods, the average performance on the samples with high wake formation (i.e. flow over airfoils at high angle of attack) has improved. Using one of the proposed methods, an average performance improvement of 15.65% was observed for samples of unknown airfoils compared to a similar model trained using the original method.Originality/valueThis work demonstrates the use of imbalanced learning in the field of fluid mechanics. The performance of the model is improved by giving significance to the distribution of the training data without changes to the model architecture.

Aeroacoustics computation for propellers based on harmonic balance solution

In this paper, a novel open-source framework is presented for the evaluation of noise emissions produced by aerodynamic bodies exhibiting dominant motion at specific frequencies. This behavior is frequently encountered in propellers used for urban air mobility applications. The reduced order model called harmonic balance is employed to compute the unsteady flow solution, reducing the computational cost. The approach tackles K different frequencies by capturing the flow solution at N discrete time instances within a single period, where N is defined as 2K+1. The time history of the conservative variables on the solid surfaces is reconstructed through a Fourier interpolation. The Kirchhoff Ffowcs Williams Hawkings integral formulation, integrated into SU2, is used to compute the sound pressure level perceived by farfield observers. The integral formulation propagates the acoustic solution with a computational cost independent of observer distance. The noise emission of a pitching wing and a propeller is computed with the proposed framework. Regarding a small, isolated propeller operating at low Reynolds numbers in forward flight, we conducted a comparison of the aerodynamic and aeroacoustic results between a fully time-accurate solution and a steady-state Reynolds Averaged Navier-Stokes solution within a rotating reference frame. The harmonic balance results demonstrated improved agreement with the fully unsteady solution across the first three blade-pass frequencies and exhibited this consistency over a broader range of propagation angles.

Control-Volume-Based Exergy Method of Truncated Busemann Inlets in Off-Design Conditions

A scramjet engine consisting of several components is a highly coupled system that urgently needs a universal performance metric. Exergy is considered as a potential universal currency to assess the performance of scramjet engines. In this paper, a control-volume-based exergy method for the Reynolds-averaged Navier–Stokes solution of truncated and corrected Busemann inlets was proposed. An exergy postprocessing code was developed to achieve this method. Qualitative and quantitative analyses of exergies in the Busemann inlets were performed. A complete understanding of the evolution process of anergy and the location where anergy occurs in the inlet at various operation conditions was also obtained. The results show that the exergy destroyed in the Busemann inlet can be decomposed into shock wave anergy, viscous anergy and thermal anergy. Shock wave anergy accounts for less than 4% of the total exergy destroyed while thermal anergy and viscous anergy, in a roughly equivalent magnitude, contribute to almost all the remaining. The vast majority of inflow exergy is converted into boundary pressure work and thermal exergy. Some of the thermal exergy excluded by the computation of the total pressure recovery coefficient belongs to the available energy, as this partial energy will be further converted into useful work in combustion chambers.

Propeller-Wing Interaction: A Simplified Method for Coupling BEM and CFD

This paper presents a numerical procedure for studying the interaction between the wake generated by a propeller and the wing, considering a tiltrotor model framed within the T-TECH Italian project, which has the scope to develop innovative technologies for a flight demonstrator. A tiltrotor is an aircraft that generates lift and propulsion by way of powered rotors mounted on rotating shafts or nacelles at the ends of a fixed wing; in which, in contrast with conventional aircraft, the dimension of the propeller is comparable with the vehicle one. The procedure proposes to couple a 3D low-order unsteady Boundary Element Method (BEM) approach, to evaluate the performance of the isolated propeller, and a Reynolds-Averaged Navier-Stokes (RANS) solution for the analysis of the flow field interaction between the propeller (simulated as actuator disk) and the wing.

Characteristics Investigations of Ducted Ka4-70 Series Propeller with Boss Cap Fins Using Numerical and Experimental Method

Unconventional system that are generally adopted for ship propulsion are Ducted Propellers. These devices have recently been studied with medium-fidelity computational fluid dynamics code (based on the potential flow hypothesis) with promising results. Numerical and experimental comparison of ducted propeller with PBCF, case studies with Propeller Ka4-70 used combination ducted and PBCF Divergent. The study was done numerically using computational fluid dynamics (CFD) approach. The solver is based on the Reynolds-Averaged Navier-Stokes (RANS) solutions and turbulence modelling explicit algebraic stress model (EASM). The test data was obtained from CFD simulations consisting of the open propeller and combination Nozzle plus PBCF, but the experiment was done to Nozzle and PBCF only. All measurements were carried out from J = 0 to J = 1.0 with speeds from 0 m/s to 2.445 m/s. The results of the comparative investigation cases between numerical and experiment analysis from Ka4-70 propellers with Nozzle 19A and PBCF Divergent appears that between CFD and experiments, several phenomena are seen. (i) the Ka4-70 propeller without Nozzle 19A and PBCF divergent experienced large pressure at low-speed J = 0.1 to high-speed J = 0.7, but Ka4-70 propeller with Nozzle and PBCF divergent reach highest pressure at J = 0.1 to J = 0.5; (ii) the Ka4-70 propeller without 19A nozzle and PBCF divergent increases the flow velocity at the boss cap fins but does not increase the axial induce velocity, while Ka4-70 propeller using nozzle and PBCF divergent increases the axial induce velocity of the blade, but does not increase the flow velocity of the boss cap fins; (iii) Ka4-70 propeller without Nozzle and PBCF value increase of propeller η0 to 12% when ESD added in the form of Nozzle and PBCF when J is high, from J = 0.7 to J = 1.0. ; (iv) Ka4-70 propellers with Nozzle 19A and PBCF Divergent has very similar η0 from J=0 to J=1.0. CFD approach are still appropriate to be relied upon for the overall simulation.

Global Stability Analysis of Full-Aircraft Transonic Buffet at Flight Reynolds Numbers

Fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. The framework here proposed is based on a Jacobian-free approach that enables GSA on large 3D grids, making this the first stability study on a full-aircraft at typical flight Reynolds numbers. The Reynolds-averaged Navier–Stokes solutions compare reasonably well with the available experiments and are used as base flows for the stability analyses. GSA is first performed at wind tunnel Reynolds number conditions, and a buffet-cell mode localized in the wing outboard region is found to be responsible for the onset. When the side-of-body (SOB) separation becomes larger at higher angles of attack, two additional modes are detected: a high-frequency mode localized in the SOB region and a low-frequency long-wavelength buffet-cell mode that may represent the link with the shock-oscillation instability found in two-dimensional airfoils. The existence of the buffet-cell mode is confirmed at flight Reynolds numbers. However, due to the presence of large SOB separation at the onset angle of attack, this mode is distributed along the whole wing and an SOB separation mode also appears. As well as characterizing buffet on industry-relevant geometries and flow conditions, this study proves that the proposed GSA framework is feasible for large 3D numerical grids and can represent a useful tool for buffet onset prediction during design and certification phases of commercial aircraft.

From shear to veer: theory, statistics, and practical application

Abstract. In the past several years, wind veer – sometimes called “directional shear” – has begun to attract attention due to its effects on wind turbines and their production, particularly as the length of manufactured turbine blades has increased. Meanwhile, applicable meteorological theory has not progressed significantly beyond idealized cases for decades, though veer's effect on the wind speed profile has been recently revisited. On the other hand the shear exponent (α) is commonly used in wind energy for vertical extrapolation of mean wind speeds, as well as being a key parameter for wind turbine load calculations and design standards. In this work we connect the oft-used shear exponent with veer, both theoretically and for practical use. We derive relations for wind veer from the equations of motion, finding the veer to be composed of separate contributions from shear and vertical gradients of crosswind stress. Following from the theoretical derivations, which are neither limited to the surface layer nor constrained by assumptions about mixing length or turbulent diffusivities, we establish simplified relations between the wind veer and shear exponent for practical use in wind energy. We also elucidate the source of commonly observed stress–shear misalignment and its contribution to veer, noting that our new forms allow for such misalignment. The connection between shear and veer is further explored through analysis of one-dimensional (single-column) Reynolds-averaged Navier–Stokes solutions, where we confirm our theoretical derivations as well as the dependence of mean shear and veer on surface roughness and atmospheric boundary layer depth in terms of respective Rossby numbers. Finally we investigate the observed behavior of shear and veer across different sites and flow regimes (including forested, offshore, and hilly terrain cases) over heights corresponding to multi-megawatt wind turbine rotors, also considering the effects of atmospheric stability. From this we find empirical forms for the probability distribution of veer during high-veer (stable) conditions and for the variability in veer conditioned on wind speed. Analyzing observed joint probability distributions of α and veer, we compare the two simplified forms we derived earlier and adapt them to ultimately arrive at more universally applicable equations to predict the mean veer in terms of observed (i.e., conditioned on) shear exponent; lastly, the limitations, applicability, and behavior of these forms are discussed along with their use and further developments for both meteorology and wind energy.

A study into the effect of tip clearance on the performance of b-series and kaplan-series ducted propellers

A study into the effect of tip clearance on ducted propellers was carried out. Two series of propellers, namely B-series and Kaplan-series, were used. The gap between tip of propeller and ducted was varied from 2mm to 5mm. The study was conducted numerically using computational fluid dynamics (CFD) approach. The solver is based on the Reynolds-Averaged Navier-Stokes (RANS) solutions and two turbulence modelling, i.e. k-ω SST by Menter and explicit algebraic stress model (EASM), were applied in order to find out the optimum results. This paper objective to discuss energy efficiency on ships by investigating variations of propeller tip clearances. Overall results showed that EASM demonstrated better score (particularly in term of thrust and efficiency) than the k-ω SST. The highest thrust, torque and efficiency were achieved at 3mm tip clearance for both series. Moreover, Kaplan-series showed better results than the B-series propeller indicating that the use of ducted propeller using Kaplan-series is more appropriate.

Towards high-accuracy deep learning inference of compressible flows over aerofoils

The present study investigates the accurate inference of Reynolds-averaged Navier–Stokes solutions for the two-dimensional compressible flow over aerofoils with a deep neural network. Our approach yields networks that learn to generate precise flow fields for varying body-fitted, structured grids by providing them with an encoding of the corresponding mapping to a canonical space for the solutions. We apply the deep neural network model to a benchmark case of incompressible flow at randomly given angles of attack and Reynolds numbers and achieve an improvement of more than an order of magnitude compared to previous work. Further, for transonic flow cases, the deep neural network model accurately predicts complex flow behavior at high Reynolds numbers, such as shock wave/boundary layer interaction, and quantitative distributions like pressure coefficient, skin friction coefficient as well as wake total pressure profiles downstream of aerofoils. The proposed deep learning method significantly speeds up the predictions of flow fields and shows promise for enabling fast aerodynamic designs.

Penalized Wall Function Method for Turbulent Flow Modeling

A novel penalized wall function method for simulations of wall-bounded compressible turbulent flows is proposed. The new approach is based on the Reynolds-averaged Navier–Stokes (RANS) equations to model the outer region of the turbulent boundary layer, while the inner part is approximated by the equilibrium wall function model. The differential formulation to match the external and the wall function solutions is reformulated in a form of the generalized characteristic-based volume penalization method to model the transfer of the shear stress from the outer region of the boundary layer to the wall and to impose the wall-stress boundary conditions on the RANS solution. The exchange location is specified implicitly through a localized source term in the boundary layer equation, written as a function of the normalized distance from the wall. The wall-stress condition is determined by solving an auxiliary equation for the wall-stress, ensuring the correct matching of the RANS and the wall function solutions at the exchange layer. The proposed method noticeably reduces the near-wall mesh resolution requirements without significant modification of the RANS solver and removes the ill-defined explicit matching procedure, commonly used by traditional wall function-based methods. The penalized wall function approach is implemented using the vertex-centered control volume method on unstructured computational grids. The effectiveness of the developed penalized wall function method is demonstrated for twodimensional bump-in-channel flow for the Spalart–Allmaras turbulence model.

Robustness of Reduced-Order Jet Noise Models

Three statistical jet noise prediction models are compared for a representative set of single-stream jet cases, which include cold and hot jets of the Strategic Investment in Low-Carbon Engine Technology experiment at an acoustic Mach number of 0.875 as well as the cold jets of the NASA small hot jet acoustic rig experiment at acoustic Mach numbers of 0.5 and 0.9. The implemented models are those proposed by Tam and Auriault (Jet Mixing Noise from Fine-Scale Turbulence,” AIAA Journal, Vol. 37, No. 2, 1999, pp. 145–153), Khavaran and Bridges (“An Empirical Temperature Variance Source Model in Heated Jets,” NASA TM 2012-217743, 2012), and the Goldstein’s “A Generalized Acoustic Analogy,” Journal of Fluid Mechanics, Vol. 488, July 2003, pp. 315–333) generalized acoustic analogy (GAA) model. By virtue of reduced-order modeling, which is based on the single-point mean flow and turbulence statistics, all of these implementations use a number of empirical dimensionless source parameters for far-field noise spectra predictions. In comparison with the Tam and Auriault model, the Khavaran and GAA model implementations use several dimensionless parameters, which are available from previous literature and assumed to be more or less universal for a class of single-stream jets. These parameters include the fluctuating enthalpy function and the dimensionless amplitudes of autocovariances of turbulent fluctuating stresses and velocities available from the literature. The comparison of the three models is aimed at not only assessing their accuracy for a range of jet conditions, observer angles, and frequencies but also to examine their robustness outside of a reference jet experiment for which their source models were calibrated. For the input to each model, the mean flow, turbulence kinetic energy, and dissipation rate extracted from Large Eddy Simulations and Reynolds-averaged Navier–Stokes solutions are considered.

Using a three-dimensional tube bundle model to investigate the leakage flow characteristics of the rotating brush seal

In comparison to the traditional brush seal, the rotating brush seal installed on a rotating shaft eliminates the influence of friction heat effects and improves the operational stability of the rotating shaft system. Relevant investigations give sparse detailed parameters and experimental data for the rotating brush seal providing insufficient data support and prompting further investigation for the sealing characteristics of the rotating brush seal. In this article, the three-dimensional tube bundle model was regarded as the computational fluid domain of the rotating brush seal. The multi-block structured mesh was applied to discrete the computational domain. The effect of the pressure ratio and rotational speed on the leakage flow and aerodynamic characteristics of the brush seal were numerically investigated using three-dimensional Reynolds-Averaged Navier-Stokes solutions and [Formula: see text] turbulence model. Similar to the traditional brush seal, the leakage flow rate of the rotating brush seal increases linearly with the pressure ratio. The effect of the pressure ratio on the flow coefficient is more significant at low pressure ratio. When the pressure ratio increases from 1.5 to 2.5, the flow coefficient increases by 44.40%. However, when the pressure ratio increases from 3.5 to 4.5, the flow coefficient just increases by 4.12%. It means that the flow coefficient shows a trend independent of the pressure ratio at higher pressure ratio. The flow coefficient obtained by computational fluid dynamics model is found to increase lightly as the rotational speed increases. The rear bristles are subjected to large axial aerodynamic force and are prone to axial deformation. The investigation provides the reference for the performance analysis and design of rotating brush seal.

Coherent fundamental-harmonic interactions in a compressible shear layer via integral nonlinear instability approach

A physics-based integral approach is adopted here to develop a theory for studying bi-modal excitation of the shear layer of a Mach 1.5 planar jet. The transverse shapes of the mean flow quantities are given by analytical functions modeling the corresponding jet experiment and Reynolds-averaged Navier–Stokes solution. The transverse shapes of the frequency modes of the coherent large-scale structure are obtained as the eigenfunctions of the locally parallel linear stability theory. The Navier–Stokes equations are then reduced to a set of ordinary differential equations. The solution of this set, subject to the initial conditions, describes the nonlinear interaction among the excited frequency modes, as well as their interaction with the mean flow and the background turbulence. Our analysis shows that the time-averaged interaction among the modes is non-zero only if the two frequency modes are related to each other by the fundamental-harmonic frequency. We label the fundamental mode here, “f,” as the most amplified mode developing nonlinearly along the jet in the absence of other imposed modes. We then use the resulting theory to study the effect of bimodal excitation by harmonically related pairs (f, f/2) or (f, 2f) to see under which conditions this bimodal excitation can suppress the fundamental. We found that the combination of fundamental and harmonic (f, 2f) can effectively reduce the fundamental at an optimized phase lag. By viewing the fundamental as the most dominant sound source in the jet, it is, thus, possible to reduce the jet noise via bi-modal excitation.

Uncertainty quantification and sensitivity analysis of aerothermal performance for the turbine blade squealer tip

In this paper, an uncertainty quantification (UQ) method is proposed using the non-intrusive polynomial chaos expansion method and Smolyak sparse grids. Then coupled with three-dimensional Reynolds-Averaged Navier-Stokes (RANS) solutions, an uncertainty quantification procedure is carried out for aerodynamic and heat transfer performance of GE-E3 rotor blade squealer tip. A parameter sensitivity analysis using the Sobol Indice method is carried out to identify the key parameters for aerothermal performance of the squealer tip. Wherein, the inlet total pressure and the inlet flow angle are considered as flow condition uncertainty parameters and cavity depth is considered as geometrical uncertainty parameters. The uncertainty analysis results showed that under the influence of the uncertain geometry and operating conditions, the heat flux of squealer tip basically conforms to the normal distribution and the statistical mean value of it increased by 28.30% relative to the design value and the probability of it deviating from the design value by 10% is as high as 86.59%. The statistical average of the squealer tip film cooling effectiveness is reduced by 23.89% compared to the design value, and the probability of it deviating from the design value by 10% is as high as 85.08%. The result of sensitivity analysis reveals that the uncertainty of the aerodynamic characteristics of the squealer tip is almost entirely caused by the inlet flow angle which accounts for 94.01% of the variance of the leakage flow rate. And it is also the dominant variable for the uncertainty of the heat transfer performance considering that its variance indexes for tip heat flux QTip and film cooling effectiveness η are 67.71% and 54.42% respectively. Compared with the main effects, the influence of the interaction effects among the variables on the squealer tip aerothermal performance is almost negligible.

Generalized Acoustic Analogy Modeling of Hot Jet Noise

A generalized acoustic analogy model is implemented for the hot and cold static high-speed jet cases corresponding to conditions of the Strategic Investment in Low-carbon Engine Technology (SILOET) experiment performed by QinetiQ. The model is statistical and based on the covariance of fluctuating Reynolds stresses and enthalpy source terms in accordance with Goldstein’s theory. These quantities are obtained from a solution of the validated large-eddy simulation accelerated on graphics processing units. The covariance of fluctuating enthalpy terms is represented by the Khavaran and Bridges model, which involves the velocity autocorrelation function and temperature gradient in the jet. The velocity autocorrelation function and the covariance of fluctuating Reynolds stresses are approximated by an analytical Gaussian-exponential function. The input parameters of the acoustic model include single-point quantities such as the time-averaged local streamwise velocity, sound speed, temperature, vorticity magnitude, turbulent kinetic energy, and dissipation rate. Modeling choices for the acoustic length and time scales based on either the turbulent kinetic energy dissipation rate or mean flow vorticity are discussed. In each case, the model involves two dimensionless parameters associated with the acoustic correlation length and time scale. These two parameters are calibrated based on the far-field noise data at 90° observer angle. The sensitivity of the calibration coefficients to the jet type, cold versus hot, is investigated. Furthermore, the same acoustic model without recalibration is applied for far-field noise predictions of two NASA Small Hot Jet Acoustic Rig jets for acoustic Mach numbers 0.5 and 0.9. To probe the sensitivity of the acoustic model to the input flow data, Reynolds-averaged Navier–Stokes solutions of the same jet cases are considered along with the large-eddy-simulation solutions. The comparison of the predicted far-field noise spectra with the experiment is discussed in each case.

Aerodynamic Analysis and Optimization of Embedded Slot for Smooth Morphing Trailing Edge

Smooth morphing trailing edge (SMTE) has been receiving more attention as a new wing design concept in the past few years due to its high potential in reducing cruise drag, structural weight, aerodynamic noise, and fuel consumption. Apart from the necessity of using new flexible materials and compact actuation mechanisms, it is also faced with the challenge of providing sufficient lift as conventional high-lift devices did during low-speed flight phases. Insufficient low-speed aerodynamics could compromise aircraft takeoff and landing performance. In light of this, a concept of the embedded slot is proposed for use with SMTE. To study the full benefits of the embedded slot, constrained single-objective optimization is first conducted on a two-dimensional airfoil using kriging surrogate models built from Reynolds-averaged Navier–Stokes solutions. The final optimal results show that the maximum lift coefficient from SMTE with a slot is only slightly lower than that of a typical three-element Fowler flap. The parametric analysis showed the strong coupling effects on the aerodynamic performance of slot entry and exit geometry dimensions. Based on the optimal two-dimensional slot design, computer-aided design models of three-dimensional SMTE configurations are built and analyzed. Comparisons among High-Lift Common Research Model SMTEs with and without slot show that the embedded slot improved high-lift performance. After introducing the embedded slot, the maximum lift coefficient for SMTE is raised by 7.9% from 2.277 to 2.457, and the stall angle is increased by 2 deg. This is in comparison with the maximum lift coefficient of 2.572 for the conventional Common Research Model Fowler flap configuration. The results demonstrated the benefits of introducing embedded slot into SMTE for future high-lift designs.

Broadband shock-associated noise modelling for high-area-ratio under-expanded jets.

Broadband shock-associated noise (BBSAN) is an important component of supersonic jet noise for jets at off-design conditions when the pressure at the nozzle exit is different from the ambient. Two high-area-ratio under-expanded supersonic jets at nozzle pressure ratios (NPRs) 3.4 and 4.2 are considered. The jets correspond to conditions of the experiment in the Laboratory for Turbulence Research in Aerospace and Combustion (LTRAC) in the Supersonic Jet Facility of Monash University. Flow solutions are obtained by the large eddy simulation (LES) and Reynolds averaged Navier-Stokes (RANS) methods. The solutions are validated against the particle image velocimetry (PIV) data. For noise spectra predictions, the LES solution is combined with the time-domain Ffowcs Williams-Hawkings method. To probe the accuracy of the reduced-order method based on acoustic analogy, the RANS solutions are substituted in the Morris and Miller BBSAN method, where different options for modelling of the acoustic correlation scales are investigated. The noise spectra predictions are compared with the experimental data from the non-anechoic LTRAC facility and the NASA empirical sJet model. Apart from the low frequencies influenced by the jet mixing noise, the RANS-based acoustic predictions align with those from LES for most frequencies in the range of Strouhal numbers (St) 0.4 < St < 2 within 1-2 dB.

Effect of turbulence model uncertainty on scramjet strut injector flow field analysis

The effect of turbulence model closure coefficient uncertainty on the Reynolds-averaged Navier–Stokes solution of a scramjet strut fuel injector flow field is investigated with an uncertainty quantification and sensitivity analysis study for the Menter-BSL and Wilcox-2006 k-ω turbulence models. Simulations were performed using the VULCAN flow solver. Nonintrusive polynomial chaos theory was used for efficient propagation of uncertainty, and Sobol indices were utilized to quantify the sensitivity of various solution metrics to the variation of each closure coefficient. The output metrics of interest were evaluated at three crossflow planes, and included the integrated quantities of mixing efficiency, circulation, total pressure recovery, and one-dimensional Mach number, as well as the pointwise vorticity and eddy viscosity distributions. Influential sets of closure coefficients were identified for each turbulence model, with the Kármán and diffusion constants being the most prominent. These results are expected to assist future efforts aimed at reducing the uncertainty in the numerical design of scramjet fuel injectors through the identification of closure coefficients and physical aspects of the flow that warrant further investigation.

Gas-Kinetic Scheme Coupled with Turbulent Kinetic Energy Equation for Computing Hypersonic Turbulent and Transitional Flows

ABSTRACT For simulation of hypersonic turbulent and transitional flows at high Reynolds numbers, a gas-kinetic scheme (GKS) strongly coupled with the turbulent kinetic energy equation in shear stress transport (SST) k−ω turbulence model is developed. To extend the current method to transitional flows, Langtry-Menter transition model is added together with SST k−ω turbulence model. Comparisons among the numerical solutions from current GKS method coupled with turbulent kinetic energy equation, GKS method uncoupled with turbulent kinetic energy equation, Reynolds-Averaged Navier-Stokes (RANS) solutions with turbulence/transition models, and experimental data are conducted. It is concluded that the current method can significantly improve the accuracy of numerical results.