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NASA NTRS1993

Computation of confined coflow jets with three turbulence models

A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-epsilon model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-epsilon model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reattachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite-volume procedure. Numerical credibility of the solutions is ensured by using second-order accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-epsilon model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-epsilon model in capturing the essential flow features, while the RNG-based K-epsilon model does not seem to give improvements over the standard K-epsilon model under the flow conditions considered.

Zhu, J.↗

NASA NTRS1995

Effect of turbulence models on criticality conditions in swirling flows

The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.

Gatski, Thomas B.↗

NASA NTRS2000

Mathematical Modeling of an Oscillating Droplet

Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is performed by electromagnetic levitation. The natural oscillation frequency of the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the k-epsilon turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity.

Berry, S.↗

NASA NTRS2001

Modeling of Turbulent Flow in Electromagnetically Levitated Metal Droplets

This article details an effort to improve the understanding and prediction of turbulent flow inside a droplet of molten metal levitated in an electromagnetic field. It is shown that the flow field in a test case, a nickel droplet levitated under microgravity conditions, is in the transitional regime between laminar and turbulent flow. Past research efforts have used laminar, enhanced viscosity, and k-epsilon turbulence models to describe the flow. The method highlighted in our study is the renormalization group (RNG) algorithm. We show that an accurate description of the turbulent eddy viscosity is critical in order to obtain realistic velocity fields, and that the turbulent eddy viscosity cannot be uniform in levitated droplets. The RNG method does not impose isotropic length or time scales on the flow field, thus allowing such nonuniform features to be captured. A number of other materials processing applications exhibit similarly complex flow characteristics, such as highly recirculating, transitional, and free surface flows, for which this modeling approach may prove useful.

Berry, S.↗

NASA NTRS2002

Surface Oscillations of An Electromagnetically Levitated Droplet

Oscillating droplets are of interest in a number of disciplines. A practical application is the oscillating drop method, which is a technique for measuring surface tension and viscosity of liquid metals. It is especially suited to undercooled and highly reactive metals, because it is usually performed by electromagnetic levitation. The natural oscillation frequency a f the droplets is related to the surface tension of the material, and the decay of oscillations is related to its viscosity. The fluid flow inside the droplet must be laminar in order for this technique to yield good results. Because no experimental method has yet been developed to visualize flow in electromagnetically-levitated oscillating metal droplets, mathematical modeling is required to determine whether or not turbulence occurs. Three mathematical models of the flow: (1) assuming laminar conditions, (2) using the turbulence model, and (3) using the RNG turbulence model, respectively, are compared and contrasted to determine the physical characteristics of the flow. It is concluded that the RNG model is the best suited for describing this problem. The goal of the presented work was to characterize internal flow in an oscillating droplet of liquid metal, and to verify the accuracy of the characterization by comparing calculated surface tension and viscosity values to experimentally-obtained results.

Berry, S.↗

DOE OSTI2026

Design of Multi-Engine Freight Locomotive

This final report documents the completed engineering design of a modular, multi-engine renewable natural gas (RNG) hybrid freight locomotive. The project delivered a full systems design, component selection, and production and test plans for a near-zero-emission, Tier 5–capable line-haul locomotive, but did not proceed to fabrication or field testing due to withdrawal of the designated engine supplier.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

Develop an efficient and cost-effective novel anaerobic digestion system producing high purity of methane from diverse waste biomass

This project focuses on developing an advanced, intensified anaerobic digestion system aimed at transforming the treatment and conversion of organic wastes into valuable products, specifically renewable natural gas. The motivation for this research stems from the limitations of conventional anaerobic digestion technologies, which often face challenges such as long retention times, high operational costs, and incomplete organic material degradation. The new technology called Intensified Versatile Anaerobic Digestion (IVAD), is developed to address these challenges by incorporating innovative reactors and processes that enhance the overall efficiency and output of anaerobic digestion. The significance of this project lies in its potential to revolutionize waste management practices and waste biomass utilization. The IVAD system integrates a hyperthermophilic anaerobic acidification reactor, a hydrothermal treatment (HTT) unit, and both thermophilic and mesophilic methanogenic reactors. This combination enables a higher rate of organic breakdown and energy recovery, resulting in faster processing times, reduced reactor sizes, and lower operational costs compared to traditional systems. Key data include an increase in methane productivity to 1.18 m 3 /m 3 /day, a significant improvement compared to the baseline technology’s 0.64 m 3 /m 3 /day. Additionally, the IVAD system achieves a 45% reduction in levelized cost of energy (LCOE), down to $\$$10.04/MMBTU, and an energy return on investment (EROI) of 3.19, representing an 87% increase over baseline levels. Technical and economic analyses highlight that the IVAD system significantly reduces hydraulic retention time (HRT) and solid retention time (SRT). The HRT for the HTT reactor can be reduced from 1 hour to 0.5 hours, while decoupling SRT from HRT in the anaerobic acidification reactor (AAR) allows for further reductions. These design optimizations lead to smaller reactor volumes, cutting down equipment and construction costs. Despite these advancements, energy consumption remains comparable to conventional methods due to a novel heat recovery strategy, enhancing overall process productivity. The system also achieves in-situ CO 2 removal and ammonia stripping features, resulting in biogas with a methane purity level of 75%, and produces high-quality nitrogen fertilizer as an additional by-product. Public benefits of the IVAD system are substantial, contributing to sustainable waste management and renewable energy production. By providing a scalable solution that can be adopted by dairy farms and similar agricultural operations, the IVAD system helps reduce waste, produce renewable natural gas (RNG) suitable for transportation fuel, and generate fertilizer, supporting a circular economy. This project plays a role in achieving broader environmental objectives by mitigating greenhouse gas emissions and promoting energy independence. Additionally, it offers a pathway for farmers to lower operational costs while adopting practices that are both environmentally sustainable and economically advantageous.

03 NATURAL GAS↗

DOE OSTI2025

Updates to Anaerobic Digestion Pathways for Animal Manure in R&D GREET 2025

Livestock and poultry manure management in the U.S. is a greenhouse gas (GHG) intensive process, emitting 81.7 MMT CO 2 e in 2022 (1.5% of net U.S. GHG emissions). The primary GHG is methane (CH 4 ), with 2,312 kt released in 2022 (9% of U.S. CH 4 emissions). Manure management methods are commonly categorized by whether they are anaerobic (“wet”) or aerobic (“dry”) techniques. Although dry methods manage the largest share of manure, the majority of GHG emissions are generated during storage of manure in anaerobic conditions – typically in water-filled tanks, pits, or lagoons. There has been a 65% increase in emissions from 1990, primarily due to an increasing cattle population. Also, this rise in population has been coupled with a rise in animal confinement and density, which typically adopt wet manure management methods. Within wet methods, anaerobic bacteria proliferate and decompose volatile solids (VS) within the manure in a process called anaerobic digestion to produce roughly equal mixtures of CH 4 and carbon dioxide (CO 2 ). These GHGs are fugitive, in that they are assumed to be released to the atmosphere and contribute to GHGs within U.S. GHG inventories. If the methane is captured and purified (i.e., “upgraded”) this simultaneously mitigates GHGs that would have otherwise been released and produces a valuable energy product known colloquially as Renewable Natural Gas (RNG). Such processes are acknowledged by U.S. policy through programs such as the U.S. Renewable Fuels Standard (RFS), the federal Clean Fuel Production Credit (45Z), and state clean fuel standards (CFS). In the 45Z and CFS schemes, the GHG emissions of the business-as-usual (BAU) manure management system is taken as a baseline, and credits are received based on GHG reductions relative to this baseline. Thus, estimating the GHG emissions of the BAU scenario (also known as the “counterfactual”) is necessary.

09 BIOMASS FUELS↗

DOE OSTI2026

NREL's 1MW Water Electrolysis Stack Performance Validation to Pilot-Scale Renewable Natural Gas Production [Slides]

NREL has designed, built, and operates a 1MW water electrolyzer balance-of-plant to support industrial partners and the U.S. Department of Energy in developing next-generation PEM stacks to reduce the cost of hydrogen production. With that hydrogen, we are developing, innovating and de-risking a biomethanation process capable of megawatt-scale deployment that upgrades biogas waste streams to produce pipeline quality renewable natural gas (RNG). Biomethanation is a two-step process using a methanogenic microorganism to convert renewable hydrogen (H 2 ) and waste carbon dioxide (CO 2 ) to renewable methane (CH 4 ) - the primary component in natural gas. Using biogenic CO 2 from biogas sources like dairies, wastewater treatment plants, and landfills allows production of this drop-in direct replacement fuel. Research projects and future R&D topics are also discussed during the presentation.

08 HYDROGEN↗

DOE OSTI2025

Harvesting Energy from Wastewater by Converting Sewage

This project aims were to develop and demonstrate a scalable, integrated process to convert sewage sludge into renewable natural gas (RNG), enabling wastewater treatment plants (WWTPs) to become net energy producers. The system proposal integrates autothermal hydrothermal liquefaction (AT-HTL), supercritical salt precipitation (SCSP), and hydrothermal gasification (HTG), collectively forming the Supercritical Sludge-to-Gas (SC-S2G) platform. Initially, batch hydrothermal liquefaction reactions were used to screen sewage sludge using AT-HTL (later termed RI-HTL) conversion to biocrude, aqueous and char phases compared to hydrothermal liquefaction (HTL). Significant improvement in biocrude yield using peroxide addition at O:C ratio of 0.05 and under conditions of 300°C for 10 minutes gave 57% biocrude yield and 85% fluid carbon yield (biocrude plus aqueous), while minimizing the loss of carbon to char solids (~7%). Hence, RI-HTL was shown to be effective for conversion of real sewage sludge. The corrosion of the alloy reactor tubes or vessels is an important factor when developing a process that includes an oxidant and a chemically complex feed like sewage sludge. We investigated the corrosion rates on metal alloys at 350°C for 240 hours. Corrosion rates of 0.21 and 0.26 mpy for 304L and 316L stainless steel were measured respectively. The corrosion information obtained in this investigation was utilized by PNNL for design, materials sourcing and construction of the pilot scale continuous flow system.

09 BIOMASS FUELS↗

DOE OSTI2026

Updates to Anaerobic Digestion Pathways for Animal Manure in R&D GREET 2025 Rev.1

Renewable natural gas (RNG) produced from animal manure can significantly reduce greenhouse gas (GHG) emissions from the transportation sector, but accurate life cycle assessment (LCA) of this fuel depends on precise modeling of emissions from business-as-usual (BAU) manure manage ment. This report documents updates to the Research & Development version of the Greenhouse Gases, Regulated Emissions, and Energy Use in Technologies (R&D GREET) model that attempt to improve that precision.

09 BIOMASS FUELS↗

NASA NTRS1991

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗

NASA NTRS1991

Center for Modeling of Turbulence and Transition (CMOTT). Research briefs: 1990

Brief progress reports of the Center for Modeling of Turbulence and Transition (CMOTT) research staff from May 1990 to May 1991 are given. The objectives of the CMOTT are to develop, validate, and implement the models for turbulence and boundary layer transition in the practical engineering flows. The flows of interest are three dimensional, incompressible, and compressible flows with chemistry. The schemes being studied include the two-equation and algebraic Reynolds stress models, the full Reynolds stress (or second moment closure) models, the probability density function models, the Renormalization Group Theory (RNG) and Interaction Approximation (DIA), the Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Povinelli, Louis A.↗

NASA NTRS1992

Development of turbulence models for shear flows by a double expansion technique

Yakhot, V.↗

NASA NTRS1992

Center for Modeling of Turbulence and Transition (CMOTT): Research Briefs, 1992

The progress is reported of the Center for Modeling of Turbulence and Transition (CMOTT). The main objective of the CMOTT is to develop, validate and implement the turbulence and transition models for practical engineering flows. The flows of interest are three-dimensional, incompressible and compressible flows with chemical reaction. The research covers two-equation (e.g., k-e) and algebraic Reynolds-stress models, second moment closure models, probability density function (pdf) models, Renormalization Group Theory (RNG), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS).

Liou, William W.↗

NASA NTRS1993

Remarks on turbulent constitutive relations

The paper demonstrates that the concept of turbulent constitutive relations can be used to construct general models for various turbulent correlations. Some of the Generalized Cayley-Hamilton formulas for relating tensor products of higher extension to tensor products of lower extension are introduced. The combination of dimensional analysis and invariant theory can lead to 'turbulent constitutive relations' (or general turbulence models) for, in principle, any turbulent correlations. As examples, the constitutive relations for Reynolds stresses and scalar fluxes are derived. The results are consistent with ones from Renormalization Group (RNG) theory and two-scale Direct-Interaction Approximation (DIA) method, but with a more general form.

Shih, Tsan-Hsing↗

NASA NTRS1993

Calculations of turbulent separated flows

A numerical study of incompressible turbulent separated flows is carried out by using two-equation turbulence models of the K-epsilon type. On the basis of realizability analysis, a new formulation of the eddy-viscosity is proposed which ensures the positiveness of turbulent normal stresses - a realizability condition that most existing two-equation turbulence models are unable to satisfy. The present model is applied to calculate two backward-facing step flows. Calculations with the standard K-epsilon model and a recently developed RNG-based K-epsilon model are also made for comparison. The calculations are performed with a finite-volume method. A second-order accurate differencing scheme and sufficiently fine grids are used to ensure the numerical accuracy of solutions. The calculated results are compared with the experimental data for both mean and turbulent quantities. The comparison shows that the present model performs quite well for separated flows.

Zhu, J.↗

NASA NTRS1995

Evaluation of Turbulence Models for Unsteady Flows of an Oscillating Airfoil

Unsteady flowfields of a two-dimensional oscillating airfoil are calculated using an implicit, finite-difference, Navier Stokes numerical scheme. Five widely used turbulence models are used with the numerical scheme to assess the accuracy and suitability of the models for simulating the retreating blade stall of helicopter rotor in forward flight. Three unsteady flow conditions corresponding to an essentially attached flow, light-stall, and deep-stall cases of an oscillating NACA 0015 wing experiment were chosen as test cases for computations. Results of unsteady airloads hysteresis curves, harmonics of unsteady pressures, and instantaneous flowfield patterns are presented. Some effects of grid density, time-step size, and numerical dissipation on the unsteady solutions relevant to the evaluation of turbulence models are examined. Comparison of unsteady airloads with experimental data show that all models tested are deficient in some sense and no single model predicts airloads consistently and in agreement with experiment for the three flow regimes. The chief findings are that the simple algebraic model based on the renormalization group theory (RNG) offers some improvement over the Baldwin Lomax model in all flow regimes with nearly same computational cost. The one-equation models provide significant improvement over the algebraic and the half-equation models but have their own limitations. The Baldwin-Barth model overpredicts separation and underpredicts reattachment. In contrast, the Spalart-Allmaras model underpredicts separation and overpredicts reattachment.

Srinivasan, G. R.↗