RANS Turbulence Models Research Articles

Turbulence Quantification in Supercritical Nitrogen Injection: An Analysis of Turbulence Models

In Liquid Rocket Engines, higher combustion efficiencies come at the cost of the propellants exceeding their critical point conditions and entering the supercritical domain. The term fluid is used because, under these conditions, there is no longer a clear distinction between a liquid and a gas phase. The non-conventional behavior of thermophysical properties makes the modeling of supercritical fluid flows a most challenging task. In the present work, a RANS computational method following an incompressible but variable density approach is devised on which the performance of several turbulence models is compared in conjunction with a high accuracy multi-parameter equation of state. Also, a suitable methodology to describe transport properties accounting for dense fluid corrections is applied. The results are validated against experimental data, becoming clear that there is no trend between turbulence model complexity and the quality of the produced results. For several instances, one- and two- equation turbulence models produce similar and better results than those of Large Eddy Simulation (LES). Finally, considerations about the applicability of the tested turbulence models in supercritical simulations are given based on the results and the structural nature of each model.
 Keywords: Supercritial fluids, RANS turbulence modeling, Liquid rocket engines

Numerical Simulation of Vacuum Leak Jet and Jet Noise

With the explosive growth of space debris, collisions among space debris and spacecrafts seem to be inevitable, which may greatly threaten the structure of on-orbit spacecrafts as well as astronauts’ safety. It is of crucial importance to locate the leak source and evaluate the corresponding damage quickly and accurately to ensure the safety of astronauts and spacecraft equipment. It is widely accepted that acoustic emission method can be used to detect on-orbit leak for space station; however, accurate prediction of vacuum leak noise in space station is difficult as jet and jet noise in vacuum environments are different from those in terrestrial environment. Therefore, this paper tries to investigate sound generations of vacuum leak jet by numerically analyzing dynamics of unsteady vacuum jet flow. Specifically, numerical simulation based on realizable k-ε model is adopted to study the aerodynamic properties and the aeroacoustic characteristics. Results show that RANS turbulent model can capture the pressure fluctuation with high computation efficiency and acceptable accuracy. Secondly, leak from 1 atm to vacuum forms a supersonic flow with Mach number ranging from 2 to 3, accompanied by obvious gradients of steady density, pressure, and temperature. However, the terrestrial leak from 2 atm to 1 atm forms subsonic jet flow with gradually varying gradients of density, pressure, and temperature. Thirdly, obvious reflections of pressure perturbations at the surface, with the mean free path of air molecule being 0.6 mm, can be found and form cavity-like acoustic resonance. Such resonant mechanism contributes to harmonic acoustic properties of the vacuum jet noises besides the broadband turbulent mixing noises.

Experimental and Numerical Analysis of Gas/Powder Flow for Different LMD Nozzles

The Laser Metal Deposition (LMD) process is an additive manufacturing method, which generates 3D structures through the interaction of a laser beam and a gas/powder stream. The stream diameter, surface density and focal plan position affect the size, efficiency and regularity of the deposit tracks. Therefore, a precise knowledge of the gas/powder streams characteristics is essential to control the process and improve its reliability and reproducibly for industrial applications. This paper proposes multiple experimental techniques, such as gas pressure measurement, optical and weighting methods, to analyze the gas and particle velocity, the powder stream diameter, its focal plan position and density. This was carried out for three nozzle designs and multiple gas and powder flow rates conditions. The results reveal that (1) the particle stream follows a Gaussian distribution while the gas velocity field is closer to a top hat one; (2) axial, carrier and shaping gas flow significantly impact the powder stream’s focal plan position; (3) only shaping gas, powder flow rates and nozzle design impact the powder stream diameter. 2D axisymmetric models of the gas and powder streams with RANS turbulent model are then performed on each of the three nozzles and highlight good agreements with experimental results but an over-estimation of the gas velocity by pressure measurements.

A 3D-CFD methodology to investigate boundary layers and assess the applicability of wall functions in actual industrial problems: A focus on in-cylinder simulations

In the industrial practice, 3D-CFD in-cylinder simulations still largely rely on RANS turbulence models and high-Reynolds wall treatments, i.e. based on wall functions. However, the use of the latter represents a potential source of error, leading to poor estimations of shear stress and heat flux at the wall. In fact, universal laws of the wall can be claimed only under very restricted conditions, which are hardly (to say never) met in industrial applications. As a result, typical dimensionless profiles of velocity and temperature on the combustion chamber walls are far from standard wall functions.In the present paper, a methodology to investigate the presence of dimensionless profiles comparable to universal wall laws in boundary layers of actual industrial problems is presented. In particular, attention is focused on 3D-CFD in-cylinder simulations. While the existing literature deals with DNS or hybrid URANS/LES approaches applied to simplified geometries and low revving speed conditions (for computational cost reasons), in the present paper a RANS k-ε turbulence model with a low-Reynolds wall treatment is adopted. In addition, an alternative strategy to extract velocity and temperature dimensionless profiles from the computed fields is proposed. The methodology is preliminary tested on a 2D plane channel (where the existence of wall functions is a priori acknowledged), at both quasi-isothermal and highly non-isothermal conditions. Afterwards, it is applied to the well-known “GM Pancake” engine test case, showing that both u+ and T+ calculated on the combustion chamber walls remarkably differ from analytical standard wall functions. Finally, in order to demonstrate the importance of dimensionless profiles to properly predict heat transfer, two different high-Reynolds simulations of the “GM Pancake” engine are proposed, one with standard wall functions and one with u+ and T+ profiles provided by the low-Reynolds analysis. While the former underestimates heat fluxes, the latter provides results in good agreement with the experiments.

RANS and SRS simulations of the flow around a smooth cylinder

The paper focuses on the numerical simulation of the flow around circular cylinder with Reynolds number 2∙104. The 2D and 3D mesh is used for the computational domain. RANS turbulence model SST k-ω is used for the 2D task. The 3D task is solved using Scale-Resolving Simulation models LES, SAS, DES. Drag coefficient, lift coefficient, pressure coefficient and velocity field in the wake are evaluated.

CFD-Modeling of fluid domains with embedded monoliths with emphasis on automotive converters

A new approach for calculating flow domains with embedded monoliths is presented, focusing on a system suitable for an automotive converter. Using appropriate boundary conditions, the monolith itself can be excluded from the CFD computational domain, leaving two mapped computational domains upstream and downstream of the monolith. The resulting method enables more detailed results of the downstream flow profile than afforded by the commonly used porous body approach for simulating a monolith, but without the complexities of a full 3D calculation of the entire domain, including the monolith. The present approach was validated with experimental flow data from the literature collected with a prismatic (planar) monolith with approximately 4500 channels. Sensitivity studies were performed to check the influence of the downstream turbulence model, inlet turbulence boundary conditions, and spatial discretization schemes. RANS turbulence models (k-ω SST and k-ε) generally predict the experimentally measured flow profile downstream of the monolith although the transition to turbulence cannot be reproduced correctly. Currently, LES is the best approach for adequately describing the characteristics of flow downstream of monoliths.

Experimental and numerical analysis on the surge instability characteristics of the vortex flow produced large vapor cavity in u-shape notch spool valve

The u-shape notch, one of those representative types of throttling notch, is widely applied in the spools of hydraulic proportional directional valves. Because of its vacuum-suction nozzle-structural effect, the u-shape notch usually possesses relatively large flow capacity, while produces drastic cavitation as well. In this paper, the notch flow characteristics to form the large vapor cavity and its surge instability characteristics are discussed by experimental and numerical analysis. It is found that, instead of the vena contracta flow, but the notch vortex flow creates the more suitable low pressure condition for cavitation inception, with the helical-stream-trend to form the cavity spiral shape with clear vapor-liquid interface. Compared with the RANS turbulent model, the LES turbulent model associated with the multi-phase cavitation model reproduce the cavity volume and the spiral shape better, while the ISO surface of vapor volume fraction number equal to 0.6 is used to approximately represent the two-phase interface. In appropriate notch configurations, the vapor cavity shows surge instability, which couples the fluctuation of flow parameters with the mass transfer process. The notch flow resistance seems to play an important role on the surge behavior, since with the decrease of the notch depth, the harmonic oscillation turns into damped oscillation, while with the increase of the notch opening, the oscillation intensifies, and even gets disturbed from the downstream vapor shedding. The biggish notch flow resistance may suppress the surge instability, but reduce the flow capacity as well. It may be not easy to figure out an optimal notch structure only. However, using more number of larger flow resistance notches to replace few number of smaller flow resistance notches may be a positive suggestion.

Experimental and numerical investigation of heat transfer characteristics of jet impingement on a flat plate

In this present work, round jet impingement on a heated flat plate at constant heat flux is analysed experimentally and numerically. Experiments have been performed at various Reynolds numbers (Red = 10,000 to 25,000) and at four different nozzles to plate spacing (h/d = 4, 6, 8 and 10). Different RANS turbulence model namely, k-ω SST, Realizable k-e, RNG k-e and ν2f were used to validate the numerical results with experimental results. The results of various turbulence models were analysed for varying inlet turbulent intensities and eddy viscosity ratios. It has been observed that the inlet turbulent intensity and eddy viscosity ratio are significant for the accurate prediction of realistic results.

Comparative analysis of turbulence models in hydraulic jumps

A numerical simulation of the incompressible multiphase hydraulic jump flow was performed to compare the interface prediction through the use of the three RANS turbulence models: k–ɛ, RNGk– ɛ and SST k–w. A three dimensional no submerged hydraulic jump and a two dimensional submerged hydraulic jump were modeled. Both the geometry and the mesh were created using the open source Gmsh code. The project\'s geometry consists of a rectangular channel with length and height differences between the two dimensional and three dimensional simulations. Uniform hexahedral cells were used for the mesh. Three refining meshes were constructed to allow to verify simulation convergence. The Volume of Fluid (abbr. VOF) method was used for treatment of the air-water surface. The turbulence models were evaluated in three distinct set up configurations to provide a greater accuracy in the flow representation. In the two-dimensional analysis of a submerged hydraulic jump simulation, the turbulence model RNG RNG k– ɛ provided a better interface adjust with the experimental results than the model k– ɛ and SST k–w. In the three-dimensional simulation of a no-submerged hydraulic jump the k–# showed better results than the SST k–w and RNG k– ɛ capturing the height and length of the ledge with a better fit with the experimental results.

A stable, positivity-preserving scheme for cross-diffusion source term in RANS turbulence models: Application to k-ω turbulence models

Stabilization measures that are introduced to the numerical treatment of the cross-diffusion term in k-ω turbulence models are presented. Specifically, a new treatment of the full form of the cross-diffusion term that appears in near-wall k-ω turbulence models is presented. Preserving the positivity of the turbulent specific dissipation rate plays a pivotal role in the design of the new scheme. Results obtained from three-dimensional numerical simulations using an unstructured-grid-based flow solver demonstrate the significant improvement compared to conventional schemes.

Numerical assessment of miniaturized cold spray nozzle for additive manufacturing

Purpose Application of cold spray technology may exhibit significant benefits for the additive manufacturing process, particularly for producing intricate objects. To ascertain the feasibility of such an application, this paper aims to present a numerical investigation of the effect of scaling down a convergent-divergent (de Laval) nozzle, which is typically used in the cold spray industry, on the compressible flow parameters and thermal characteristics. Design/methodology/approach The Navier–Stokes equations and energy equation governing compressible flow are numerically solved using a finite volume method with a coupled solver. The conjugate heat transfer technique is used to couple fluid and solid heat transfer domains and predict the local heat transfer coefficient between the solid and fluid. The use of various RANS turbulence models has also been investigated to quantify the effect of the turbulence model on the simulation. Findings The numerical results reveal that the flow and thermal characteristics are altered as the convergent-divergent nozzle is scaled down. The static pressure and temperature profiles at any section in the nozzle are shifted toward higher values, while the Mach number profile at any section in the nozzle is shifted toward a lower Mach number. The turbulent kinetic energy at the nozzle exit increases with the scaling down of the nozzle geometry. This study also provides convincing evidence that the adiabatic approach is still suitable even though the temperature of the nozzle wall is extremely high, as required for industrial application. Results indicate that it is feasible to use the available capabilities of the cold spray technology for additive manufacturing after scaling down the nozzle. Originality/value The idea of adopting cold spray technology for additive manufacturing is new and innovative. To develop this idea into a viable commercial product, a thorough understanding of the flow physics within a cold spray nozzle is required. The simulation results discussed in this paper demonstrate the effect that scaling down of a convergent-divergent nozzle has on the flow characteristics in the nozzle.

Numerical investigation of methanol bluff-body flame using variants of RANS turbulence models with conditional moment closure model

In this article, conditional moment closure model (CMC) along with four variants of RANS turbulence models is used for investigating a methanol bluff-body flame. This work attempts to establish the accuracy of turbulence models in predicting the mixing fields, which results in improved predictions of the mean and variance of mixture fraction. This ensures an accurate probability density function (pdf) of the mixture fraction field which is used to obtain unconditional quantities from the conditional quantities calculated from CMC closure. The flow and mixing field are calculated using ANSYS Fluent software by incorporating four different turbulence models viz. standard k-ε (SKE), modified k-ε (MKE), RNG k-ε and Reynolds stress turbulence models. Flow field simulations have been coupled with an in-house CMC solver to obtain the mean flame structure. Profiles of mixture fraction showed an excellent agreement with the experimental data when Reynolds stress turbulence model was used. The unconditional mean temperature and species mass fraction obtained from the CMC model shows improved predictions when coupled with the Reynolds stress turbulence models. Because of inaccurate mixing field and hence the pdf predicted from SKE, MKE and RNG k-ε models, the unconditional quantities showed significant deviations from the experimental results.

Wind field simulation over complex terrain under different inflow wind directions

Accurate numerical simulation of wind field over complex terrain is an important prerequisite for wind resource assessment. In this study, numerical simulation of wind field over complex terrain was further carried out by taking the complex terrain around Siu Ho Wan station in Hong Kong as an example. By artificially expanding the original digital model data, Gambit and ICEM CFD software were used to create high-precision complex terrain model with high-quality meshing. The equilibrium atmospheric boundary layer simulation based on RANS turbulence model was carried out in a flat terrain domain, and the approximate inflow boundary conditions for the wind field simulation over complex terrain were established. Based on this, numerical simulations of wind field over complex terrain under different inflow wind directions were carried out. The numerical results were compared with the wind tunnel test and field measurement data for land and sea fetches. The results show that the numerical results are in good agreement with the wind tunnel data and the field measurement data which can verify the accuracy and reliability of the numerical simulation. The near ground wind field over complex terrain is complex and affected obviously by the terrain, and the wind field characteristics should be fully understood by numerical simulation when carrying out engineering application on it.

Minimising flow losses within the pulse tube of a Stirling pulse tube cryocooler

Successful operation of Stirling pulse tube cryocoolers relies on minimising flow mixing within the pulse tube. Hence, the pulse tube and the flow straighteners at either end must be designed with great care. In this study, the flow within the pulse tube of an existing Stirling pulse tube cryocooler is numerically analysed and alternative flow straightener designs are suggested. The numerical simulation have been carried out using CONVERGE CFD, a finite volume Navier-Stokes solver. The standard k-ε RANS turbulence model has been used to account for the effects of turbulence within the pulse tube.

A computationally derived heat transfer correlation for in-tube cooling turbulent supercritical CO2

This paper computationally investigates the turbulent heat transfer of sCO2 flows cooled in large horizontal tubes with diameter of 15.75 mm, 20 mm and 24.36 mm using RANS turbulence models. The numerical models were validated against experimental data published in literature to demonstrate the reliability of CFD simulations on the heat transfer coefficient prediction and buoyancy effect capture to turbulent sCO2. Based on the validated model, a number of computations, involving a wide range of operating conditions, have been carried out. The effect of mass flux (200–800 kg/m2s), pressure (8–10 MPa), heat flux (5–36 kW/m2) and tube diameter has been analysed. Results demonstrate that the AKN model shows the best consistencies with the experimental measurements and is also able to well reproduce the heat transfer characteristics under various conditions. As the mass flux increases, the heat transfer coefficients go up due to the enhanced turbulence diffusion. Pressure has a significant effect on the distribution of heat transfer coefficient, and its peak drops sharply with rising pressure. At Tb > Tpc, with the heat flux and tube diameter increasing, sCO2 heat transfer performance is improved; whereas at Tb < Tpc, the heat flux and tube diameter almost have no effects on the heat transfer performance. Considerable deviations with the existing heat transfer correlations necessitate the development of a new correlation to predict the heat transfer coefficients of cooling turbulent sCO2 in large horizontal pipes. Based on the reliable computational datasets, a Nusselt number equation based on the Gnielinski form with the ratio of density incorporated is formulated.

CFD-modelling of free surface flows in closed conduits

Computational fluid dynamics (CFD) is gaining an increasing importance in the field of hydraulic engineering. This publication presents different application examples of a two-phase approach as implemented in the open source software OpenFOAM. The chosen approach is based on the volume of fluid method focusing on the simulation of flow in closed conduits. Three examples are presented: single-phase flow over a ground sill and free surface flow over a hill as well as complex free surface flow in a sewer model. The first example compares the results of different RANS turbulence models with experimental results. The results of the second example are compared with an analytical solution. In the last example the behaviour of the free surface flow is compared with the results of a model test and existing simulations using a simplified, open channel geometry for the closed conduit. For the examples analysed, the two-phase approach provides stable and reliable results.

CFD-modelling of free surface flows in closed conduits

Computational fluid dynamics (CFD) is gaining an increasing importance in the field of hydraulic engineering. This publication presents different application examples of a two-phase approach as implemented in the open source software OpenFOAM. The chosen approach is based on the volume of fluid method focusing on the simulation of flow in closed conduits. Three examples are presented: single-phase flow over a ground sill and free surface flow over a hill as well as complex free surface flow in a sewer model. The first example compares the results of different RANS turbulence models with experimental results. The results of the second example are compared with an analytical solution. In the last example the behaviour of the free surface flow is compared with the results of a model test and existing simulations using a simplified, open channel geometry for the closed conduit. For the examples analysed, the two-phase approach provides stable and reliable results.

Comparative RANS turbulence modelling of lost salt core viability in high pressure die casting

In this work, the implementation of three turbulence models inside the open source C++ computational fluid dynamics (CFD) library OpenFOAM were tested in 2D and 3D to determine the viability of salt cores in high pressure die casting. A finite-volume and volume of fluid approach was used to model the two-phase flow of molten metal and air, with the latter being treated as compressible. Encouragingly, it is found that, although the choice of turbulence model seems to affect the dispersion of the two-phase interface, the force acting at the surface of the salt core depends only very weakly on the turbulence model used. The results were also compared against those obtained using the commercially available and widely-used casting software MAGMA5.

Influence of molten salt-(FLiNaK) thermophysical properties on a heated tube using CFD RANS turbulence modeling of an experimental testbed

In a liquid fuel molten salt reactor (MSR) a key factor to consider upon its design is the strong coupling between different physics present such as neutronics, thermo-mechanics and thermal-hydraulics. Focusing in the thermal-hydraulics aspect, it is required that the heat transfer is well characterized. For this purpose, turbulent models used for FLiNaK flow must be valid, and its thermophysical properties must be accurately described. In the literature, there are several expressions for each material property, with differences that can be significant. The goal of this study is to demonstrate and quantify the impact that the uncertainty in thermophysical properties has on key metrics of thermal hydraulic importance for MSRs, in particular on the heat transfer coefficient. In order to achieve this, computational fluid dynamics (CFD) simulations using the RANS k-ω SST model were compared to published experiment data on molten salt. Various correlations for FLiNaK’s material properties were used. It was observed that the uncertainty in FLiNaK’s thermophysical properties lead to a significant variance in the heat coefficient. Motivated by this, additional CFD simulations were done to obtain sensitivity coefficients for each thermophysical property. With this information, the effect of the variation of each one of the material properties on the heat transfer coefficient was quantified performing a one factor at a time approach (OAT). The results of this sensitivity analysis showed that the most critical thermophysical properties of FLiNaK towards the determination of the heat transfer coefficient are the viscosity and the thermal conductivity. More specifically the dimensionless sensitivity coefficient, which is defined as the percent variation of the heat transfer with respect to the percent variation of the respective property, was −0.51 and 0.67 respectively. According to the different correlations, the maximum percent variations for these properties is 18% and 26% respectively, which yields a variation in the predicted heat transfer coefficient as high as 9% and 17% for the viscosity and thermal conductivity, respectively. It was also demonstrated that the Nusselt number trends found from the simulations were captured much better using the Sieder Tate correlation than the Dittus Boelter correlation. Future work accommodating additional turbulence models and higher fidelity physics will help to determine whether the Sieder Tate expression truly captures the physics of interest or whether the agreement seen in the current work is simply reflective of the single turbulence model employed.

Numerical simulation of a viscoelastic RANS turbulence model in a diffuser

One of the newest viscoelastic RANS turbulence models for drag reducing flows with polymer additives is studied considering different rheological properties. A finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model is used to describe the viscoelastic effect of the polymer solutions and the $$k - \varepsilon - \overline {{v^2}} - f$$ turbulence framework is applied for turbulence modelling. The geometry in this study is a twodimensional diffuser. The finite volume method (FVM) with a non-uniform collocated mesh is used to solve the momentum and constitutive equations. In order to evaluate the turbulence model, the flow is simulated with different parameters such as the Weissenberg number and the maximum polymer extensibility and compared with the experimental results qualitatively. The velocity profiles, pressure distribution, reattachment length, and the amount of the drag reduction predicted by the turbulence model are in line with the experimental results.