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NASA NTRS1995

Unsteady Aerodynamic Models for Turbomachinery Aeroelastic and Aeroacoustic Applications

Theoretical analyses and computer codes are being developed for predicting compressible unsteady inviscid and viscous flows through blade rows of axial-flow turbomachines. Such analyses are needed to determine the impact of unsteady flow phenomena on the structural durability and noise generation characteristics of the blading. The emphasis has been placed on developing analyses based on asymptotic representations of unsteady flow phenomena. Thus, high Reynolds number flows driven by small amplitude unsteady excitations have been considered. The resulting analyses should apply in many practical situations and lead to a better understanding of the relevant flow physics. In addition, they will be efficient computationally, and therefore, appropriate for use in aeroelastic and aeroacoustic design studies. Under the present effort, inviscid interaction and linearized inviscid unsteady flow models have been formulated, and inviscid and viscid prediction capabilities for subsonic steady and unsteady cascade flows have been developed. In this report, we describe the linearized inviscid unsteady analysis, LINFLO, the steady inviscid/viscid interaction analysis, SFLOW-IVI, and the unsteady viscous layer analysis, UNSVIS. These analyses are demonstrated via application to unsteady flows through compressor and turbine cascades that are excited by prescribed vortical and acoustic excitations and by prescribed blade vibrations. Recommendations are also given for the future research needed for extending and improving the foregoing asymptotic analyses, and to meet the goal of providing efficient inviscid/viscid interaction capabilities for subsonic and transonic unsteady cascade flows.

Verdon, Joseph M.↗

NASA NTRS2001

A High-Lift Building Block Flow: Turbulent Boundary Layer Relaminarization

A working wind tunnel test facility has been constructed at the University of Notre Dame's Hessert Center. The relaminarization test facility has been constructed in the 1.5m x 1.5m (5ft x 5 ft) atmospheric wind tunnel and generates a Re(theta)=4694 turbulent boundary layer in nominally zero-pressure gradient before it is exposed to the Case #1 pressure gradient (K approximately equal to 4.2 x 10(exp -6), which is believed to be sufficient to achieve relaminarization. Future work to be conducted will include measuring the response of the turbulent boundary layer to the favorable pressure gradients created in the test facility and documenting this response in order to understand the underlying flow physics responsible for relaminarization. It is the goal of this research to have a better understanding of accelerated turbulent boundary layers which will aid in the development of future flow diagnostic utilities to be implemented in applied aerodynamic research.

Bourassa, Corey↗

NASA NTRS2004

Numerical Simulations of Buoyancy Effects in low Density Gas Jets

This paper deals with the computational analysis of buoyancy effects in the near field of an isothermal helium jet injected into quiescent ambient air environment. The transport equations of helium mass fraction coupled with the conservation equations of mixture mass and momentum were solved using a staggered grid finite volume method. Laminar, axisymmetric, unsteady flow conditions were considered for the analysis. An orthogonal system with non-uniform grids was used to capture the instability phenomena. Computations were performed for Earth gravity and during transition from Earth to different gravitational levels. The flow physics was described by simultaneous visualizations of velocity and concentration fields at Earth and microgravity conditions. Computed results were validated by comparing with experimental data substantiating that buoyancy induced global flow oscillations present in Earth gravity are absent in microgravity. The dependence of oscillation frequency and amplitude on gravitational forcing was presented to further quantify the buoyancy effects.

Satti, R. P.↗

NASA NTRS1996

Local and Global Bifurcations of Flow Fields During Physical Vapor Transport: Application to a Microgravity Experiment

The local bifurcation of the flow field, during physical vapor transport for a parametric range of experimental interest, shows that its dynamical state ranges from steady to aperiodic. Comparison of computationally predicted velocity profiles with laser doppler velocimetry measurements shows reasonable agreement in both magnitude and planform. Correlation of experimentally measured crystal quality with the predicted dynamical state of the flow field shows a degradation of quality with an increase in Rayleigh number. The global bifurcation of the flow field corresponding to low crystal quality indicates the presence of a traveling wave for Ra = 1.09 x 10(exp 5). For this Rayleigh number threshold a chaotic transport state occurs. However, a microgravity environment for this case effectively stabilizes the flow to diffusive-advective and provides the setting to grow crystals with optimal quality.

Duval, W. M. B.↗

NASA NTRS2004

Summary of the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control

A CFD validation workshop for synthetic jets and turbulent separation control (CFDVAL2004) was held in Williamsburg, Virginia in March 2004. Three cases were investigated: synthetic jet into quiescent air, synthetic jet into a turbulent boundary layer crossflow, and flow over a hump model with no-flow-control, steady suction, and oscillatory control. This paper is a summary of the CFD results from the workshop. Although some detailed results are shown, mostly a broad viewpoint is taken, and the CFD state-of-the-art for predicting these types of flows is evaluated from a general point of view. Overall, for synthetic jets, CFD can only qualitatively predict the flow physics, but there is some uncertainty regarding how to best model the unsteady boundary conditions from the experiment consistently. As a result. there is wide variation among CFD results. For the hump flow, CFD as a whole is capable of predicting many of the particulars of this flow provided that tunnel blockage is accounted for, but the length of the separated region compared to experimental results is consistently overpredicted.

Rumsey, C. L.↗

NASA NTRS2006

Summary of the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control

A computational fluid dynamics (CFD) validation workshop for synthetic jets and turbulent separation control (CFDVAL2004) was held in Williamsburg, Virginia in March 2004. Three cases were investigated: synthetic jet into quiescent air, synthetic jet into a turbulent boundary layer crossflow, and flow over a hump model with no-flow-control, steady suction, and oscillatory control. This paper is a summary of the CFD results from the workshop. Although some detailed results are shown, mostly a broad viewpoint is taken, and the CFD state-of-the-art for predicting these types of flows is evaluated from a general point of view. Overall, for synthetic jets, CFD can only qualitatively predict the flow physics, but there is some uncertainty regarding how to best model the unsteady boundary conditions from the experiment consistently. As a result, there is wide variation among CFD results. For the hump flow, CFD as a whole is capable of predicting many of the particulars of this flow provided that tunnel blockage is accounted for, but the length of the separated region compared to experimental results is consistently overpredicted.

Rumsey, C. L.↗

DOE OSTI2023

Grand challenges in the design, manufacture, and operation of future wind turbine systems

Abstract. Wind energy is foundational for achieving 100 % renewable electricity production, and significant innovation is required as the grid expands and accommodates hybrid plant systems, energy-intensive products such as fuels, and a transitioning transportation sector. The sizable investments required for wind power plant development and integration make the financial and operational risks of change very high in all applications but especially offshore. Dependence on a high level of modeling and simulation accuracy to mitigate risk and ensure operational performance is essential. Therefore, the modeling chain from the large-scale inflow down to the material microstructure, and all the steps in between, needs to predict how the wind turbine system will respond and perform to allow innovative solutions to enter commercial application. Critical unknowns in the design, manufacturing, and operability of future turbine and plant systems are articulated, and recommendations for research action are laid out. This article focuses on the many unknowns that affect the ability to push the frontiers in the design of turbine and plant systems. Modern turbine rotors operate through the entire atmospheric boundary layer, outside the bounds of historic design assumptions, which requires reassessing design processes and approaches. Traditional aerodynamics and aeroelastic modeling approaches are pressing against the limits of applicability for the size and flexibility of future architectures and flow physics fundamentals. Offshore wind turbines have additional motion and hydrodynamic load drivers that are formidable modeling challenges. Uncertainty in turbine wakes complicates structural loading and energy production estimates, both around a single plant and for downstream plants, which requires innovation in plant operations and flow control to achieve full energy capture and load alleviation potential. Opportunities in co-design can bring controls upstream into design optimization if captured in design-level models of the physical phenomena. It is a research challenge to integrate improved materials into the manufacture of ever-larger components while maintaining quality and reducing cost. High-performance computing used in high-fidelity, physics-resolving simulations offer opportunities to improve design tools through artificial intelligence and machine learning, but even the high-fidelity tools are yet to be fully validated. Finally, key actions needed to continue the progress of wind energy technology toward even lower cost and greater functionality are recommended.

17 WIND ENERGY↗

NASA NTRS1997

Enhanced Control Effector Designs for Airbreathing Transatmospheric Vehicles

A study was conducted to evaluate the potential effectiveness of a moveable cowl-trailing-edge design for airbreathing hypersonic single-stage-to-orbit (SSTO) configurations, which can be extended or deflected from the nominal position in order to provide additional pitching moment capability. This additional pitching moment capability may reduce the necessary deflection angle from conventional control surfaces and the associated trim drag penalty. Calculations for a generic SSTO configuration with baseline and modified cowl trailing edge geometries were performed at Mach 6 and 10 initially with an engineering analysis code in order to examine several design parametrics. In order to more accurately model geometries and flow physics, 2-D viscous computational fluid dynamics (CFD) predictions were obtained. FInally, a limited set of 3D CFD predictions were obtained at Mach 6 in order to show the effects of modeling 3D flow fields as well as the full 3D vehicle geometry. Comparisons of aftbody surface pressures and force and moment predictions show differences between initial predictions and 2-D CFD solutions due to geometry modeling and calculation method differences. The 3-D CFD predictions confirm the trends observed in the 2-D solutions and provide additional information on 3D effects. These analyses shows that cowl-trailing-edge extensions were effective in providing additional (nose-down) pitching moment increments as well as increased thrust compared to the baseline geometry. These effects reduce the control surface deflection angle required to trim the vehicle and the associated trim drag. Cowl-trailingedge deflections were not as effective, generating more nose-up pitching moment and decreased thrust compared to non-deflected cases.

Cockrell, Charles E.↗

NASA NTRS1991

The aerodynamic characteristics of vortex ingestion for the F/A-18 inlet duct

A Reduced Navier-Stokes (RNS) solution technique was successfully combined with the concept of partitioned geometry and mesh generation to form a very efficient 3D RNS code aimed at the analysis-design engineering environment. Partitioned geometry and mesh generation is a pre-processor to augment existing geometry and grid generation programs which allows the solver to (1) recluster an existing gridlife mesh lattice, and (2) perturb an existing gridfile definition to alter the cross-sectional shape and inlet duct centerline distribution without returning to the external geometry and grid generator. The present results provide a quantitative validation of the initial value space marching 3D RNS procedure and demonstrates accurate predictions of the engine face flow field, with a separation present in the inlet duct as well as when vortex generators are installed to supress flow separation. The present results also demonstrate the ability of the 3D RNS procedure to analyze the flow physics associated with vortex ingestion in general geometry ducts such as the F/A-18 inlet. At the conditions investigated, these interactions are basically inviscid like, i.e., the dominant aerodynamic characteristics have their origin in inviscid flow theory.

Anderson, Bernhard H.↗

NASA NTRS1991

The aerodynamic characteristics of vortex ingestion for the F/A-18 inlet duct

A Reduced Navier-Stokes (RNS) solution technique was successfully combined with the concept of partitioned geometry and mesh generation to form a very efficient 3-D RNS code aimed at the analysis-design engineering environment. Partitioned geometry and mesh generation is a pre-processor to augment existing geometry and grid generation programs which allows the solver to (1) recluster an existing gridlife mesh lattice, and (2) perturb an existing gridfile definition to alter the cross-sectional shape and inlet duct centerline distribution without returning to the external geometry and grid generator. The present results provide a quantitative validation of the initial value space marching 3-D RNS procedure and demonstrates accurate predictions of the engine face flow field, with a separation present in the inlet duct as well as when vortex generators are installed to suppress flow separation. The present results also demonstrate the ability of the 3-D RNS procedure to analyze the flow physics associated with vortex ingestion in general geometry ducts such as the F/A-18 inlet. At the conditions investigated, these interactions are basically inviscid like, i.e., the dominant aerodynamic characteristics have their origin in inviscid flow theory.

Anderson, Bernhard H.↗

NASA NTRS1994

Passive porosity with free and fixed separation on a tangent-ogive forebody

Despite the extensive experimental and computational data base in the literature on passive porosity, no clear explanation of the governing flow physics exists. It is theorized that the positive porosity concept modifies the external pressure loading by allowing communication between high- and low-pressure regions on the external surface. This study determines the dominant flow phenomena that govern the effectiveness of passive porosity. It aims to assess the contribution of each phenomenon as related to a porous slender axisymmetric forebody. To assess the influence of the mass transfer and pressure equalization phenomena on the effectiveness of passive porosity on slender axisymmetric forebodies, strakes were attached to the 5.0-caliber solid and porous forebodies to force crossflow separation. Longitudinal force and moment data were obtained at a Mach number of 0.1 over an angle-of-attack range of 0 to 55 deg.

PRESSURE EQUALIZATION↗

NASA NTRS1996

Three-Dimensional Simulations of Marangoni-Benard Convection in Small Containers by the Least-Squares Finite Element Method

This paper reports a numerical study of the Marangoni-Benard (MB) convection in a planar fluid layer. The least-squares finite element method (LSFEM) is employed to solve the three-dimensional Stokes equations and the energy equation. First, the governing equations are reduced to be first-order by introducing variables such as vorticity and heat fluxes. The resultant first-order system is then cast into a div-curl-grad formulation, and its ellipticity and permissible boundary conditions are readily proved. This numerical approach provides an equal-order discretization for velocity, pressure, vorticity, temperature, and heat conduction fluxes, and therefore can provide high fidelity solutions for the complex flow physics of the MB convection. Numerical results reported include the critical Marangoni numbers (M(sub ac)) for the onset of the convection in containers with various aspect ratios, and the planforms of supercritical MB flows. The numerical solutions compared favorably with the experimental results reported by Koschmieder et al..

Yu, Sheng-Tao↗

NASA NTRS2013

Time-Accurate Local Time Stepping and High-Order Time CESE Methods for Multi-Dimensional Flows Using Unstructured Meshes

With the wide availability of affordable multiple-core parallel supercomputers, next generation numerical simulations of flow physics are being focused on unsteady computations for problems involving multiple time scales and multiple physics. These simulations require higher solution accuracy than most algorithms and computational fluid dynamics codes currently available. This paper focuses on the developmental effort for high-fidelity multi-dimensional, unstructured-mesh flow solvers using the space-time conservation element, solution element (CESE) framework. Two approaches have been investigated in this research in order to provide high-accuracy, cross-cutting numerical simulations for a variety of flow regimes: 1) time-accurate local time stepping and 2) highorder CESE method. The first approach utilizes consistent numerical formulations in the space-time flux integration to preserve temporal conservation across the cells with different marching time steps. Such approach relieves the stringent time step constraint associated with the smallest time step in the computational domain while preserving temporal accuracy for all the cells. For flows involving multiple scales, both numerical accuracy and efficiency can be significantly enhanced. The second approach extends the current CESE solver to higher-order accuracy. Unlike other existing explicit high-order methods for unstructured meshes, the CESE framework maintains a CFL condition of one for arbitrarily high-order formulations while retaining the same compact stencil as its second-order counterpart. For large-scale unsteady computations, this feature substantially enhances numerical efficiency. Numerical formulations and validations using benchmark problems are discussed in this paper along with realistic examples.

Chang, Chau-Lyan↗

DOE OSTI2018

Advanced Ultrasupercritical (AUSC) Materials Thick-Walled Cycling Header Development for ComTest-AUSC (Final Report)

Alstom Power Inc., a wholly owned subsidiary of the General Electric Company (GE) recently completed “Advanced Ultrasupercritical (AUSC) Materials Thick-Walled Cycling Header Development for ComTest-AUSC” under Award No. DE-FE0026183 for the U.S. Department of Energy National Energy Technology Laboratory (DOE NETL). This project developed a design for testing of a high temperature nickel-based superalloy thick-walled header to simulate cycling and flexible plant operation in new and existing plants. The objective was to simulate the expected thermal stresses of a new AUSC plant or a retrofit header in an existing plant to improve flexible dynamic operation while maintaining component integrity and overall power plant reliability. The high performance superalloy materials that enable higher operating temperatures and pressures can support future transformational power technologies including new AUSC plants at 4250-5000 psi, 730°C/760°C or will serve as a replacement component in a repowered or retrofit USC coal powered cycling plant at 3600 psi, 600°C. These alloys can also enable supercritical CO2 cycles, nuclear power, solar power and more efficient natural gas combined cycle units as targeted by the U.S. DOE/NETL Cross-Cutting Research Technology Program Plan. Recently developed advanced nickel alloys such as Inconel 740H (740H) and Haynes 282 (H282) have been successfully tested on a pilot scale for fireside corrosion using steam loop tubing at AUSC temperatures of 760°C in actual operating coal fired boiler. These high strength materials have been demonstrated their adequacy for use in other high temperature boiler components such as superheater tubes. Thick-walled superheater outlet headers which operate at high temperatures and pressure under severe cycling condition are considered as one of the most critical component in the AUSC coal fired boiler. Over the design life of a plant, these headers are exposed to the most severe fatigue and creep damage accumulation and need to be properly designed for the expected cycling in an AUSC plant with flexible operation. These materials need to demonstrate adequate design life of 20 to 30 years for creep and fatigue conditions. The following tasks were performed: 1. A conceptual design was developed of a thick-walled component representative of typical headers with several tube connections and proper flow rates (~100,000 lbs/hr) suitable for Phase II test at 760°C operation. This was based on a process analysis of expected full scale new and component retrofit designs for AUSC; 2. A multi-physics flow and heat transfer computational fluid dynamics (CFD) analysis of the component for proper layout of the header configuration, number and geometry (size) of tubes required for bypass flow, flow rates through the tubing, and sectional pressure drops was performed. Steam to header metal heat transfer film coefficients in the header section and the tubes during the two stages (half load and full load) of the cycling operation were evaluated and used in the stress analysis; 3. Detailed analytical evaluation of the thick-walled pipe and tube connections for mechanical integrity under cycling conditions was performed. This included transient thermal stress analysis and fatigue usage estimation including the tube-to-pipe weld geometries and weld materials; 4. A layout and design of the thick-walled test component was developed and instrumentation required for a test was identified; 5. Continuum Damage Mechanics (CDM) creep prediction models were extended to 740H and H282 and validated with public data on 740H and H282 for use in creep analysis. In addition, detailed creep analyses were performed separately for the design life of the conceptual AUSC superheater outlet header using these General Electric (GE) creep constitutive models. GE was the prime contractor for the project, which was directed by Principal Investigator Robert Schrecengost and Lead Scientist Dr. B. Reddy Ganta. Other collaborative participants in this project included GE Global Research, GE Boiler Engineering, and a Technical Consultant from EPRI.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS2009

CFD Analysis of Nozzle Jet Plume Effects on Sonic Boom Signature

An axisymmetric full Navier-Stokes computational fluid dynamics study is conducted to examine nozzle exhaust jet plume effects on the sonic boom signature of a supersonic aircraft. A simplified axisymmetric nozzle geometry, representative of the nozzle on the NASA Dryden NF-15B Lift and Nozzle Change Effects on Tail Shock research airplane, is considered. The computational fluid dynamics code is validated using available wind-tunnel sonic boom experimental data. The effects of grid size, spatial order of accuracy, grid type, and flow viscosity on the accuracy of the predicted sonic boom pressure signature are quantified. Grid lines parallel to the Mach wave direction are found to give the best results. Second-order accurate upwind methods are required as a minimum for accurate sonic boom simulations. The highly underexpanded nozzle flow is found to provide significantly more reduction in the tail shock strength in the sonic boom N-wave pressure signature than perfectly expanded and overexpanded nozzle flows. A tail shock train in the sonic boom signature is observed for the highly underexpanded nozzle flow. Axisymmetric computational fluid dynamics simulations show the flow physics inside the F-15 nozzle to be nonisentropic and complex. Although the one-dimensional isentropic nozzle plume results look reasonable, they fail to capture the sonic boom shock train in the highly underexpanded nozzle flow.

Bui, Trong T.↗

NASA NTRSDate not supplied

Multi-Objective Optimization of a Diodic Profile

The present paper investigates the flow physics of Tesla valves and studies how various geometric parameters affect their performance. The performance of the valve is measured by its diodicity, evaluated by comparing pressure drops and discharge coefficients in the forward and reverse flow directions. First, only the flow return angle of a baseline geometry was varied to understand the impact of return angle on valve performance. These baseline geometries are first analyzed with CFD, and then fabricated and installed in a steady-state experimental test rig equipped with pressure transducers, to measure forward and reverse discharge coefficients. Seven additional geometries are also tested in cold flow to identify the impact of diode count, diode volume, and orifice size on valve performance. Next, a multi-objective optimizer is allowed to vary 12 geometric parameters to produce an optimum geometry.

Propulsion↗

DOE OSTI2022

Interactions between molecular-scale processes and hyporheic exchange for understanding Fe-S-C cycling in riparian wetlands (Final Report)

Wetlands represent some of the most productive ecosystems on the planet and critically influence global environmental health. Specifically, wetlands promote water quality by transforming nutrients and organic compounds and sequestering metals and contaminants. Riparian wetland hyporheic zones, where toxic surface water and anoxic groundwater mix, exhibit dynamic conditions that drive steep redox gradients and promote hotspots of diverse and fluctuating microbial activity. Changes in climate, water quality, and water quantity can disturb hydrologic flow and biogeochemical processing in these environments. Understanding how sulfate loading, impacted by hydrologic flux and anthropogenic inputs, influences iron and carbon cycling in wetlands will be crucial for predicting water quality issues driven by iron mineral precipitation and sorption, such as the release of heavy metals and other toxic elements. We used a fully integrated multi-scale and multi-method approach to develop a mechanistic understanding of how hydrologic flow influences coupled iron and sulfur cycles in riparian wetlands. This entailed hydrological, geochemical, and microbial observations at two locations: an anthropogenic sulfate-impacted riparian wetland in northern Minnesota, and a low-sulfate Fe-rich riparian wetland in Tims Branch at the Savannah River Site (SRS). These sites were characterized by hydrologically dynamic conditions where the stream and wetland systems oscillated between gaining (upward flow) and losing (downward flow) conditions that recharged the system occasionally with oxidants that fueled a variety of biogeochemical reactions. Aqueous geochemical measurements of surface water, groundwater, and porewater samples were made alongside solid-phase geochemical analyses of sediment gravity cores. Bulk X-ray absorption spectroscopy at the Advanced Photon Source (APS; Argonne) interrogated the speciation and distribution of Fe and S mineral phases of the sediments. Interestingly, it was discovered that, despite strongly reducing conditions, Fe(III) compounds and a variety of intermediate valence S compounds were stable in the subsurface. Indeed, compounds like thiosulfate, S(0), and intermediate valence organosulfur compounds were more prevalent than FeS and pyrite. The composition of the sediments did change with changes in hydrologic flow, showing their reactivity in changing redox conditions. The abundance of these intermediate S compounds was likely formed as a result of anaerobic oxidation by aqueous and solid-phase Fe(III) compounds, fueling a cryptic S cycle that is driving the breakdown of organic matter in the hyporheic zone. Microbiome surveys showed a core community that seemed stable across the landscape, but changed with increasing depth into the sediment. The community composition did not seem to change dramatically with changes in season or hydrologic flow, except for some organisms that have the potential to contribute to S cycling. More work is needed to confirm their functional activity. These fine process-scale analyses were placed within a dynamic field context using physical flow parameters from surface water and groundwater level measurements. These data helped shed light on sulfur-driven biogeochemical processes in hydrologically dynamic riparian wetlands, addressing a gap in our understanding about the impacts of pollution and other anthropogenic changes on ecologically sensitive environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Integrating geophysical monitoring data into multiphase fluid flow reservoir simulation

Simulation of multiphase flow systems are of critical importance in managing hydrological systems. Flow simulations are affected by a number of factors including structure and flow properties including porosity and permeability as well as the anisotropy and heterogeneity of these properties. In many cases traditional hydrological and reservoir data are highly affected by these parameters, but are not directly sensitive to them. As such modellers often adjust these parameters in an ad hoc manner until solutions numerically converge. Simulation models are generally based on structural data from reflection seismics whose physical flow properties are then populated using geostatistical extrapolation techniques utilizing a sparse number of borehole logs and core analysis. In multiphase systems including enhanced oil recovery and carbon capture and sequestration uncertainties regarding phase-dependent physical properties confounds this challenge further. Geophysical methods provide a means by which to gain an improved understanding of phase distributions in the subsurface. In this paper we will look at applications from active carbon capture and sequestration and enhanced oil recovery applications, as well as synthetic examples. Geophysical data including electromagnetic and gravity are inverted using structural constraints from the reservoir model. Inversions are then mapped into flow properties using calibrated relations such as Archie’s Equation. The coupled models can then be used to both verify and improve on the reservoir flow model which improves it’s predictive power and utility as a management tool.

02 PETROLEUM↗