Navier-Stokes Code Research Articles

Cfd Tools as Applied to Indian Combat Aircraft Configuration-an Experience

Computational Fluid Dynamics (CFD) tools are extensively used by aircraft industries all over the world in design and development of airplanes, with emphasis on reducing both the cost and design cycle time. This paper deals with the use of CFD tools at Aeronautical Development Agency (ADA) in design and development of Indian combat aircraft. The applications include: (1) evaluation of incremental changes in aerodynamic configuration, (2) wave drag evaluation, (3) aerodynamic loads, (4) flow field around air data sensor locations, (5) Euler calculation for coupled internal and external flow field, and (6) viscous computation of high angles of attack flows. In the initial design phase, codes based on the potential theory were used for wing design and fuselage shape optimization. Later indigenously developed Euler and Navier-Stokes codes were employed for the various applications. This paper brings out the strength and weakness of CFD as experienced at ADA and its comparison with the Wind Tunnel and Flight Data.

Updated noise dose range of NASA’s X-59 aircraft estimated from propagation simulations

A follow-on study to Doebler and Loubeau [“The noise dose range of the X-59 estimated from propagation simulations,” JASA 150(4), A208 (2021)] is described. In the previous work, propagation simulations of NASA’s X-59 sonic thump were conducted using two near-field pressure solutions from NASA’s Cart3D computational fluid dynamics (CFD) code. The near-fields were propagated through realistic atmospheric profiles from the Climate Forecast System Version 2 database across the USA, and perceived level statistics of the thumps were presented. The current work repeats the previous analyses, instead using near-field CFD solutions from NASA’s Fully Unstructured Navier-Stokes (FUN3D) code for the same aircraft conditions (Mach 1.4 at 53 200 feet and Mach 1.3 at 43 000 feet), which achieve the minimum and maximum cruise loudness. NASA and contractors in the X-59 development and community noise testing project mutually agreed upon using FUN3D for generating near-field pressures. Sonic thump loudness statistics using the FUN3D near-fields are similar to those of Cart3D. The min loudness condition is about 1 dB (PL) greater when using the FUN3D solution, and the max loudness condition results are nearly identical. Understanding the X-59’s dose range for various flight and atmospheric conditions is important for planning X-59 community noise surveys.

Stable timestep formulas for high-order advection–diffusion and Navier–Stokes solvers

We derive three-dimensional stable timestep formulas for high-order explicit time integration of the advection–diffusion equation. The proposed formulas cover explicit first, second, third, and fourth-order Runge–Kutta integrators in time as well as upwind, central, second-order, high-order upwind (k-schemes), and flux-limiters for the advection term along with central discretization on the diffusion term. The stability rules are then compared to numerical computations of stable timesteps of the advection–diffusion equation and show excellent agreement. Finally, the formulas are implemented in a finite volume Navier–Stokes code and used to guide stable timestep selection to assess their suitability for Navier–Stokes solvers. All cases that were tested showed stable non-diverging solutions and significant improvement over common CFL-type stability specification. Despite its basis in the linear advection–diffusion equation, this work could be useful in providing a starting point for stable timestep selection for nonlinear evolutionary-type PDEs such as the Navier–Stokes equations.

A parallel stabilized quadratic equal-order finite element algorithm for the steady Navier–Stokes equations

This paper is concerned with a parallel stabilized quadratic equal-order finite element algorithm for the steady incompressible Navier–Stokes equations where a fully overlapping domain decomposition is used for parallelization. The basic idea of the studied algorithm is that each processor independently calculates a local stabilized solution in an interesting subdomain on a multiscale mesh that is fine around the subdomain and coarse on the rest of subdomain. The present algorithm can be solved simultaneously by the existing Navier–Stokes codes without substantial recoding. In the light of local a priori estimate for stabilized finite element solution, we analyse the error bound of the stabilized solution. Moreover, several parallel iterative stabilized quadratic equal-order finite element algorithms are presented, and three numerical examples which confirm the high efficiency of the parallel stabilized algorithms are provided.

Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models

Accurate prediction of the aerothermal environment is of great significance to space exploration and return missions. The canonical Fire II trajectory points are simulated to investigate the radiative transfer in the shock layer for Earth reentry at hypervelocity above 10 km/s using a developed radiation–flowfield uncoupling method. The thermochemical nonequilibrium flow is solved by an in-house PHAROS Navier–Stokes code, while the nongray radiation is integrated by the tangent slab approximation, respectively, combined with the two-, five-, and eight-step models. For the convective heating, the present results agree well with the data of Anderson’s relation. For the radiative heating, the two-step model predicts the closest values with the results of Tauber and Sutton’s relationship, while the five- and eight-step models predict far greater. The three-step models all present the same order of magnitude of radiative heating of 1 MW/m2 and show a consistent tendency with the engineering estimation. The Planck-mean absorption coefficient is calculated to show the radiative transfer significantly occurs in the shock layer. By performing the steady simulation at each flight trajectory point, the present algorithm using a nongray step model with moderate efficiency and reasonable accuracy is promising to solve the real-time problem in engineering for predicting both convective and radiative heating to the atmospheric reentry vehicle in the future.

Calibration of the Transitional Turbulence Model

In the present paper, the turbulent transition model from Langtry and Menter (“Correlation-Based Transition Modeling for Unstructured Parallelized Computational Fluid Dynamics Codes,” AIAA Journal, Vol. 47, No. 12, 2009, pp. 2894–2906) is implemented in the structured finite volume Reynolds-averaged Navier–Stokes code FANSC and coupled with the shear-stress transport turbulence model. The model is modified and recalibrated to better match experimental results. The local turbulent intensity is replaced with a more consistent turbulent fluctuation representation to avoid nonphysical solutions at the stagnation point that would contaminate the downstream boundary-layer predictions. A calibration is devised by customizing several constants involved in the equation for the intermittency and the destruction term for the turbulent kinetic energy . An optimization algorithm is thus employed to facilitate the calibration on well-known two-dimensional test cases, such as the flat plates of the T3 series and of Schubauer and Klebanoff (“Contributions on the Mechanics of Boundary-Layer Transition,” NACA TN 3489, 1955), as well as the NACA 0012 airfoil. The calibrated model is then validated on the NLF-0416 and S809 airfoil cases that have not been involved in the optimization process.

Preliminary Design and Dynamic Response of Multi-Purpose Floating Offshore Wind Turbine Platform: Part 1

Floating offshore wind turbine foundations are based on platforms operated by the oil and gas industry. However, they are designed and optimized to meet the wind turbines’ operating criteria. Although Malaysia is considered a low-wind-speed country, there are some locations facing the South China Sea that are found to be feasible for wind energy harnessing. The average daily wind speed may reach up to 15 m/s. Therefore, designing a cost-effective platform that can operate in Malaysian waters which has less severe environmental conditions compared to the North Sea would be a prudent undertaking. In this study, a new design of a multi-purpose floating offshore wind turbine platform (Mocha-TLP) is presented. In addition, the dynamic response of the platform to wave loads was investigated using the Navier–Stokes code STAR CCM+ developed by CD-adapco. Moreover, free-oscillation tests were performed to determine the natural periods of the platform. Three approaching wave cases and two wave conditions (WC) were considered. The results show that the natural periods of the platforms were within the recommended range for pitch, roll, yaw, heave, sway and surge motions. The platform was stable in rotational motion within the three cases. However, it experienced a noticeable surge motion which was more critical with wave condition one (WC1) since the wavelength equalled the length of the structure. The dynamic response of the platform to wave loads wase minimal and within the operational requirements for wind turbines.

Flow Nonuniformities Behind Accelerating and Decelerating Shock Waves in Shock Tubes

Shock tubes are used to investigate the chemical kinetics and radiative properties of gasses. Analyses of the flow conditions produced in shock tubes typically assume a single, constant shock speed even though the shock speed varies due to driver effects, boundary-layer growth, and diaphragm rupture effects. This paper will investigate the dependence of flow properties upon the entire shock speed history for a 100-mm-diam, 8-m-long shock tube using the FROSST axisymmetric shock tube Navier–Stokes code. A perfect gas is applied to remove the complexity of thermochemistry and allow a focus upon the flow details. Shock speed profiles ranging from accelerating to decelerating are simulated to qualitatively represent different experimental conditions, and the resulting test slugs compared. All shocks reach the test section at the same final shock Mach number of 6.53. Pressure variations caused by the accelerating shock are found to combine with entropy gradients introduced by the changing shock strength, yielding differences in maximum temperature of the test slug by as much as 56%, and differences in maximum pressure as high as 22% despite the shared tube-end Mach number. Local temperature and pressure around gas packets in the test slug are found to relax significantly through time in response to changing postshock conditions. Test slug variations due to boundary-layer effects are found to be present, but overwhelmed by the relaxation processes under many conditions.

A conservative multirate explicit time integration method for computation of compressible flows

In the context of high fidelity simulation of compressible flows (LES and DNS) at extreme scale (small time steps) on massively parallel supercomputers, explicit time integration methods are widely used since they both have a good computational cost trade-off at small time scales and require a small number of parallel communications, thus having little impact on the parallel strategy compared to their implicit counterpart. However, the synchronous nature of the time integration of the governing equations can be a severe constraint when the stability condition is applied globally since the time scales are related to the flow properties and the mesh resolution, which may show strong variations throughout the computational domain. We propose to further improve the efficiency (CPU wall-time reduction) of explicit Runge–Kutta methods by developing a multirate explicit time integration method, by means of flux interpolation at the boundary between cells evolving with different time-steps, which enforces the conservation properties. In terms of computational efficiency, the presented multirate time integration method is easy to implement in pre-existing Eulerian compressible Navier–Stokes codes, requires less additional memory storage, and provides a considerable speed-up while being robust and preserving the order of accuracy of the legacy explicit Runge–Kutta time integration method. The multirate time integration method is implemented in the massively parallel finite volume and high-order (spectral difference) IC3 code (Bodart et al., 2016) (fork of the solver CharLESX), but it can also be applied to any flux-based spatial method such as discontinuous Galerkin or others. For a targeted y+=0.2 on the developed turbulent channel flow test case at Reτ=392; a 2.48 effective speedup is obtained versus an expected theoretical speedup of 2.53.

Analysis and comparison of turbulence model coefficient uncertainty for canonical flow problems

The purpose of this paper is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-Averaged Navier–Stokes codes due to the epistemic uncertainty in closure coefficients for a set of turbulence model validation cases that represent the structure of several canonical flow problems. The study focuses on the analysis of a 2D Zero Pressure Gradient Flat Plate, a 2D NASA Wall Mounted Hump, and an Axisymmetric Shock Wave Boundary Layer Interaction, all of which are well documented on the NASA Langley Research Center Turbulence Modeling Resource website. The Spalart–Allmaras (SA), the Wilcox (2006) κ−ω (W2006), and the Menter Shear-Stress Transport (SST) turbulence models are considered in the stochastic analyses of these flow problems, and the FUN3D code was utilized as the flow solver. The uncertainty quantification approach involves stochastic expansions based on non-intrusive polynomial chaos to efficiently propagate the uncertainty. Sensitivity analysis is performed with Sobol indices to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results generalize a set of closure coefficients which have been identified as contributing most to the uncertainty in various output quantities of interest for the set of canonical flow problems considered in this study. Mainly, the SA turbulence model is most sensitive to the uncertainties in the diffusion constant (σ), the log layer calibration constant (κ), and the turbulent destruction constant (cw2). The predictive capability of the W2006 model is most sensitive to the uncertainties in a dissipation rate constant (σw), the shear stress limiter (Clim), and a turbulence-kinetic energy constant (β*). Likewise, the SST turbulence model was found to be most sensitive to the diffusion constants (σw1 and σw2), the log layer calibration constant (κ), and the shear stress limiter (a1).

Simulation of flow induced by single-dielectric-barrier-discharge plasma actuator using a high-order flux-reconstruction scheme

The starting vortex flow generated by a single-dielectric-barrier-discharge (SDBD) plasma actuator in still air is investigated numerically by direct numerical simulation (DNS) using a 4th order Navier–Stokes solver and Suzen's model for the plasma actuator. The Navier–Stokes equations and the equations for the electric field and the charge density distribution in the plasma body force model are solved by the same high-order method based on the flux reconstruction algorithm on arbitrary mixed grids, allowing easy extension to configurations of complex geometry. The computational method and its high orders of accuracy are verified for the problem of the translation of an isentropic vortex and validated for the vortex shedding problem behind a circular cylinder. The plasma body force model is then implemented in the Navier–Stokes code to perform highly resolved DNS of the starting vortex generated by an SDBD plasma actuator. The computed vortex pattern and its trajectory with time are compared with available experimental data. The computational results confirm similarity laws on the motion of the vortex.

Coarse grained simulations of shock-driven turbulent material mixing

We revisit coarse-grained simulation strategies for turbulent material mixing applications involving shock-driven turbulence in the context of the Radiation Adaptive Grid Eulerian (xRAGE) hydrodynamics and Besnard–Harlow–Rauenzahn (BHR) Reynolds-averaged Navier–Stokes codes, using newly available Low-Mach-Corrected (LMC) xRAGE hydrodynamics. Impact assessments are based on comparisons with a relevant shock-tube experiment for which turbulent mixing and velocity data are available. xRAGE Implicit Large-Eddy Simulation (ILES) and a recently proposed xRAGE-BHR bridging paradigm are tested. Bridging models turbulent stresses dynamically, based on decomposing the full stress into modeled and resolved components, using a differential filter as a secondary filtering operation to define the resolved part, and additionally requiring the resolved stress to approach the full stress with grid resolution refinement to ensure realizability of the bridging-based large-eddy simulation. Much improved scale-resolving with LMC-xRAGE ILES and with dynamic LMC-xRAGE/BHR bridging enables higher simulated mixing and turbulence levels on coarser grids. For the tested planar shock-tube case, the more-accurate models can achieve the same level of accuracy with less resolution than required with the highest-fidelity turbulence simulation models typically used at scale with default xRAGE hydrodynamics; two-levels of grid-coarsening savings can be thus achieved for the mixing prediction in these comparisons: one associated with the more-accurate LMC xRAGE hydrodynamics and an additional one from using the dynamic xRAGE-BHR bridging.

Flow around Ship Spoiler.(Dept.M)

To control the roll, pitch motion and speed of the ship, a proposed system of spoilers is mounted at the bottom of the ship. The bow spoilers consist of an even number of sections arranged port and starboard forward of the center of mass of me ship. The stem spoilers consist of an even number of sections arranged port and starboard attached to the ship's transom or transom plate. Injecting exhaust gas stabilizes cavities behind spoilers. The forces and moments acting on the ship's bottom depend on its inclination, spoiler extensions and positions of the spoilers relative to the ship's center of mass. To improve the understanding of the parameters affecting the flow field around such spoiler, we computed the flow field with different spoiler position, and inclination angle with air flow injection. We used a three-dimensional Navier-Stokes code (CFDRC, 2000) to model the two-phase (low field around a ship spoiler with the Free Surface simulation In Piecewise Linear Interface Construction (PUC) method. The governing equations are discretized on a structured grid using an upwind difference scheme. For different conditions, we detemline the bubbles shape, the two-dimensional flowfield around the spoiler body and the pressure variation on the wake of the spoiler body. Higher spoiler inclination angle gives higher pressure difference between front and back of the spoiler. Spoiler with injection at a distance L from ship spoiler gives higher pressure difference between front and back of the spoiler than injection just beside the spoiler In spoiler with 45o inclination angle the cavity has high stability with long bubble foot shape. The bubble shape depends on the spoiler position and inclination. These parameters affect the roll, pitch and speed of the ship.

Numerical and Experimental Analysis of Transient 2D Flow around Ship Spoiler.(Dept.M)

An experimental analysis and numerical computation were conducted for flow around ship spoiler mounted at the bottom of the ship and subjected to air injection The air was injected beside the spoiler and at a distance equals the spoiler length to stabilize cavities behind spoilers. This system was proposed to control the roll, pitch motion and speed of the ship, with injecting exhaust gas behind spoilers. The forces and moments acting on the ship's bottom depend on spoilers' inclination, extensions and positions relative to the ship's center of mass. To improve the understanding of the parameters affecting the flow field aroundsuch spoiler, experimental images of bubble formation are triggered and compared with the computed flow field at different spoiler inclination angle, and air injection position. Two dimensional Navier-Stokes code is used to model the two-phase flow field around a ship spoiler with the free surface simulation in Piecewise Linear Interface Construction (PLIC) method. The governing equations are discretized on a structured grid using an upwind difference scheme. For different conditions, the bubbles shape, the two-dimensional flow field around the spoiler body and the pressure variation on the wake of the spoiler body are computed, Flow field and bubble formation around the spoiler are recorded experimentally at different condition and time sequence with scientific video camera The Froude number was about 1.6 based on spoiler length. The computational and experimental results show that there is a good matching of bubble formation in the spoiler with 90', but in the condition of 45° the experimental images show that bubble filled the space between the bubble and the body of the ship. This is may be due to the two-dimension computational model consideration. So, a water layer was isolated between the bubble and the ship body. In the case of spoiler with 45° inclination angle, the flow is circulated inside the bubble. The bubble shape is longer which gives more negative pressure on larger area. The moment around the 450 spoiler fixationpoint is seven times of that around the 90° spoiler. In double injection condition beside and at a distance equal the horizontal spoiler length downstream the spoiler, the bubbles are more stable and the moment is higher by 7.9 and 17.8 times after 1.2 and 2 seconds, respectively, than that around the 90° spoiler. Thus, changing inclination spoiler angle and position relative to injection angle will give different bubble shapes which give different forces to control the roll, pitch motion and speed of the ship.

Influence of turbulence anisotropy on RANS predictions of wind-turbine wakes

Simulating wind-turbines in Reynolds-averaged Navier-Stokes (RANS) codes is highly challenging, at least partly due to the importance of turbulence anisotropy in the evolution of the wake. We present a preliminary investigation into the role of anisotropy in RANS simulations of vertical-axis turbines, by comparison with LES. Firstly an LES data-set serving as our ground-truth is generated, and verified against previously published works. This data-set provides raw turbulence anisotropy fields for several turbine configurations. This anisotropy is injected into RANS simulations of identical configurations to determine the extent to which it influences (i) the production of turbulence kinetic energy, (ii) the turbulence momentum forcing, and finally (iii) the mean-flow. In all these quantities we observe the anisotropy has a surprisingly limited effect, and is certainly not the leading-order error in Boussinesq RANS for these cases. Nevertheless we go on to show that it is feasible to predict anisotropy fields for unseen configurations based only on the mean-flow, by using a tensorized version of random-forest regression.

Analysis of Turbulence Model Uncertainty for Shock-Wave/Boundary-Layer Interaction Simulations

The purpose of this paper is to present results of an uncertainty and sensitivity analysis study of commonly used turbulence models in Reynolds-averaged Navier–Stokes codes due to the epistemic uncertainty in closure coefficients for shock-wave/turbulent boundary-layer interaction simulations. The study focuses on the analysis of an axisymmetric shock-wave/boundary-layer interaction (ASWBLI) turbulence model validation case including an axisymmetric cylindrical body with a trailing-edge flare of 20 deg at an upstream Mach number of 7.11. The Spalart–Allmaras, the Wilcox 2006 , and the Menter shear-stress transport turbulence models are considered in the stochastic analyses of the ASWBLI, which used the FUN3D flow solver. The uncertainty quantification approach involves stochastic expansions based on nonintrusive polynomial chaos to efficiently propagate the uncertainty. Sensitivity analysis is performed with Sobol indices to rank the relative contribution of each closure coefficient to the total uncertainty for several output flow quantities. The results of the current study identify a set of closure coefficients that contribute most to the uncertainty in various output quantities of interest, which are also consistent with the similar shock-induced separation studies.

Numerical Analysis of Self-Excited Combustion Instabilities in a Small MMH/NTO Liquid Rocket Engine

Combustion instabilities in a small MMH/NTO liquid rocket engine used for satellite attitude and course control are numerically investigated. A three-dimensional Navier-Stokes code is developed to simulate two-phase spray combustion for cases with five different droplet Sauter Mean Diameters. As the droplet size increases from 30 microns to 80 microns, pressure oscillations are stronger with larger amplitudes. But an increase of the droplet size in the range of 80 microns to 140 microns indicates a reduction in the amplitudes of pressure oscillations. This trend is the same as the Hewitt criterion. The first tangential (1T) mode and the first longitudinal (1L) mode self-excited combustion instabilities are captured in the 60-micron and 80-micron cases. Abrupt spikes occur in the mass fraction of MMH and coincide with abrupt spikes in the mass fraction of NTO at the downstream regions just adjacent to the impinging points. Thus, local combustible high-dense mixtures are formed, which result in quasiconstant volume combustion and abrupt pressure spikes. The propagation and reflection of pressure waves in the chamber stimulate the combustion instability. When the droplet size is too small or too large, it is difficult to form local high-dense premixtures and combustion is stable in the chamber.

Investigation of mooring damping effects on vortex-induced motion of a deep draft semi-submersible by coupled CFD-FEM analysis

The vortex-induced motion (VIM) of semi-submersible is gaining increasing attention from both industry and academia with the recent development of deep draft semi-submersible platforms. Field measurements of semi-submersibles reveal that the VIM responses are typically found to be smaller than those observed in model tests. The possible factors causing the VIM response reduction in the field measurements include Reynolds number, wave effects, mass ratios, and external damping from mooring lines. The objective of this study is to investigate the mooring-induced damping effects on VIM. The Finite Analytic Navier-Stokes (FANS) code is integrated with an in-house six degree-of-freedom (DoF) motion solver and an in-house nonlinear finite element (FEM) code MOORING3D, for the coupled CFD-FEM analysis of the VIM of a moored semi-submersible. The large eddy simulation (LES) turbulence model is used to provide accurate estimation of hydrodynamic loading. Simulations are performed for the 1:70 model of the platform under varying reduced velocities. Full-scale mooring systems with different water depths and mooring line numbers are designed to represent different levels of mooring damping effects. The simulated VIM response is compared with the experiments. The study reveals that mooring-induced damping is a critical factor contributing to the VIM response reduction in the field.

On the Influence of High Turbulence on the Convective Heat Flux on the High-Pressure Turbine Vane LS89

High-pressure turbine vanes and blades are subjected to a turbulent combustor flow affecting the heat transfer and boundary layer transition, hence, the temperature distribution. The accurate prediction of the temperature distribution is crucial for a reliable design and cooling implementation. Engine-representative measurements are hence mandatory for improving design tools. Recently, convective heat transfer measurements were conducted on a high-pressure turbine inlet guide vane (VKI LS89 airfoil) in the Isentropic Compression Tube (CT-2) facility at the von Karman Institute. This contribution focuses on the effect of high freestream turbulence generated by a new turbulence grid allowing a range of turbulence intensities in excess of 10% with representative length scales of the order of 1–2 cm. Three cases with varying turbulence levels are discussed in this paper. The different flow conditions are exit isentropic Mach numbers of 0.70–0.97, Reynolds numbers of 0.53 × 106 and 1.15 × 106 and a constant temperature ratio equal to 1.36. The heat transfer distributions along the vane suction side indicate a clear link between boundary layer transition and the stream-wise pressure gradients even at high levels of freestream turbulence intensity. Differences are put in evidence in the dynamics of the transition development. Future developments will focus also on the contribution of the other flow parameters under high turbulence. Heat transfer predictions from the boundary layer code TEXSTAN and Reynolds-Averaged Navier–Stokes code elsA (ensemble logiciel pour la simulation en Aérodynamique) are additionally compared to the experiments. Inherent difficulties associated with high turbulence modelling are clear from this early numerical work.

Starting flow in an impulse wind tunnel with a throttled prechamber

The unsteady axisymmetric flow forming in the process of starting an impulse wind tunnel equipped with a throttled prechamber was numerically simulated. A regime with the operating flow Mach number M = 8 was under consideration. Numerical simulation on the basis of Reynolds-averaged Navier–Stokes code and the k-ω SST turbulence model was performed. The starting process was simulated as a sudden rupture of a diaphragm separating the prechamber volume with high pressure and temperature from low pressure part of the facility including a nozzle, an operating section and an exhaust vacuum tank.. The diaphragm rupture initiates a gasdynamic process associated with the Riemann problem when the primary shock wave arises which moves through the nozzle to the operating section. Computed data show another “inverse” shock wave emerging in the nozzle. A starting “shock-wave package” forms between these shock waves, it includes a flow portion of high temperature and pressure. The specificity is discussed of identified the characteristics and flow patterns forming during the process of moving the shock-wave package.