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At least 1,621 records · Page 90

Computational Investigation of Nominally-Orthogonal Pneumatic Active Flow Control for High-Lift Systems

We explore the feasibility of using nominally-orthogonal jets as active aerodynamic load control for multi-element high-lift systems, and whether the nominally-orthogonal jets can offer a variety of performance improvements. These nominally-orthogonal jets inject momentum normal to the airfoil surface near the flap trailing edge, where they create a vortex that entrains flow from the opposing side and change the airfoil circulation. Lift-enhancement opportunities of trailing edge nominally-orthogonal jets have previously been studied by Malavard et al. and Blaylock et al. on single-element airfoils; however, their effect on drag was not thoroughly investigated. In this study, we investigate two- dimensional nominally-orthogonal jet effects on both lift and drag on a two-element airfoil, NLR7301. We utilize Chimera Grid Tools to generate structured curvilinear overset grids, and the Reynolds-averaged Navier-Stokes solver OVERFLOW-2 to solve for the flow field around the airfoil. We perform various computational sensitivity studies on the baseline airfoil without a jet to validate computational results against benchmark experimental data. Using a Chimera overset grid topology, we demonstrate a similar lift-enhancement effect between a nominally-orthogonal jet and a nominally-orthogonal physical tab employed at the same location on the studied airfoil. After we introduce the nominally-orthogonal jet concept, we investigate nominally-orthogonal jets with various momentum coefficient settings, C(sub µ) = 0.00 − 0.04 and present a lift-enhancement relationship ∆C(sub l) ≃ 3.59 (C(sub µ)) for this airfoil. We discuss that utilizing a nominally-orthogonal jet with C(sub µ) = 0.01 can shift the linear region of the lift curve by a ∆C(sub l) = 0.36 for the pressure side jet and by a ∆C(sub l) = −0.27 for the suction side jet. Employing a nominally-orthogonal jet is also shown effective in altering the drag. To study the impact, we carry out a drag decomposition study in the form of drag polars. We show for a given C(sub l) = 2.50, a nominally-orthogonal jet with C(sub µ) = 0.01 on the pressure and suction side of the airfoil results in 113 drag count decrements and 41 drag count increments, respectively, compared to the baseline airfoil with no jet. These results show that large and controllable changes in aerodynamic performance can be achieved by relatively small active flow control inputs using the nominally-orthogonal jets presented in this study.

Nominally-Orthogonal↗

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

Chattopadhyay, Aditi↗

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

The current work compares experimentally and computationally obtained nitric oxide (NO) planar laser induced fluorescence (PLIF) images of the mixing flowfields for three types of high-speed fuel injectors: a strut, a ramp, and a rectangular flushwall. These injection devices, which exhibited promising mixing performance at lower flight Mach numbers, are currently being studied as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. The EIMP aims to investigate scramjet fuel injection and mixing physics, and improve the understanding of underlying physical processes relevant to flight Mach numbers greater than eight. In the experiments, conducted in the NASA Langley Arc-Heated Scramjet Test Facility (AHSTF), the injectors are placed downstream of a Mach 6 facility nozzle, which simulates the high Mach number air flow at the entrance of a scramjet combustor. Helium is used as an inert substitute for hydrogen fuel. Both schlieren and PLIF techniques are applied to obtain mixing flowfield flow visualizations. The experimental PLIF is obtained by using a UV laser sheet to interrogate a plane of the flow by exciting fluorescence from the NO molecules, which are present in the AHSTF air. Consequently, the absence of signal in the resulting PLIF images is an indication of pure helium (fuel). The computational PLIF is obtained by applying a fluorescence model for NO to the results of the Reynolds-averaged simulations (RAS) of the mixing flow field carried out using the VULCAN-CFD solver. This approach is required because the PLIF signal is a nonlinear function of not only NO concentration, but also pressure, temperature, and the flow velocity. This complexity allows additional flow features to be identified and compared with those obtained from the computational fluid dynamics (CFD) simulations, however, such comparisons are only semiquantitative. Three-dimensional image reconstruction, similar to that used in magnetic resonance imaging, is also used to obtain images in the streamwise and spanwise planes from select cross-stream PLIF plane data. Synthetic schlieren is also computed from the RAS data. Good agreement between the experimental and computational results provides increased confidence in the CFD simulations for investigations of injector performance.

Drozda, Tomasz G.↗

High-Intensity Radiated Field Fault-Injection Experiment for a Fault-Tolerant Distributed Communication System

Safety-critical distributed flight control systems require robustness in the presence of faults. In general, these systems consist of a number of input/output (I/O) and computation nodes interacting through a fault-tolerant data communication system. The communication system transfers sensor data and control commands and can handle most faults under typical operating conditions. However, the performance of the closed-loop system can be adversely affected as a result of operating in harsh environments. In particular, High-Intensity Radiated Field (HIRF) environments have the potential to cause random fault manifestations in individual avionic components and to generate simultaneous system-wide communication faults that overwhelm existing fault management mechanisms. This paper presents the design of an experiment conducted at the NASA Langley Research Center's HIRF Laboratory to statistically characterize the faults that a HIRF environment can trigger on a single node of a distributed flight control system.

Yates, Amy M.↗

Computational Analysis of Powered Lift Augmentation for the LEAPTech Distributed Electric Propulsion Wing

A computational study of a distributed electric propulsion wing with a 40deg flap deflection has been completed using FUN3D. Two lift-augmentation power conditions were compared with the power-off configuration on the high-lift wing (40deg flap) at a 73 mph freestream flow and for a range of angles of attack from -5 degrees to 14 degrees. The computational study also included investigating the benefit of corotating versus counter-rotating propeller spin direction to powered-lift performance. The results indicate a large benefit in lift coefficient, over the entire range of angle of attack studied, by using corotating propellers that all spin counter to the wingtip vortex. For the landing condition, 73 mph, the unpowered 40deg flap configuration achieved a maximum lift coefficient of 2.3. With high-lift blowing the maximum lift coefficient increased to 5.61. Therefore, the lift augmentation is a factor of 2.4. Taking advantage of the fullspan lift augmentation at similar performance means that a wing powered with the distributed electric propulsion system requires only 42 percent of the wing area of the unpowered wing. This technology will allow wings to be 'cruise optimized', meaning that they will be able to fly closer to maximum lift over drag conditions at the design cruise speed of the aircraft.

Deere, Karen A.↗

Algorithm Performance Dataset from NASA Open-Source Software

NASA Langley Research Center has recently developed and released the open-source software Multi Model Monte Carlo with Python (MXMCPy- LAR-19756-1) as a general capability for computing the statistics of outputs from an expensive, high-fidelity model by leveraging faster, low-fidelity models for speedup. Given a fixed computational budget and a collection of models with varying cost/accuracy, multi model Monte Carlo (MC) seeks a sample allocation strategy across the models that results in an estimator with optimal variance reduction. MXMCPy is a versatile tool that enables convenient access to many existing multi-model MC approaches (over a dozen algorithms available) within one modular and extensible package [1]. With MXMCPy, users can easily compare existing methods to determine the best choice for their particular problem,while developers have a basis for implementing and sharing new variance reduction approaches. However,there is currently very little understanding about which algorithm will perform best for a given problem (defined by the correlation between and relative cost of the available models) without a brute force search.

Geoffrey F Bomarito↗

Comparison of Aerodynamic Analysis Tools Applied to a Propeller-Blown Wing

This paper describes initial results from an ongoing activity comparing two aerodynamic analysis tools: OVERFLOW, a Navier-Stokes flow solver, and FlightStream, a viscous surface-vorticity, unstructured panel method flow solver. Both tools are applied to analyses of an unblown wing and a propeller-blown wing, and then comparisons are performed between the predicted aerodynamic loads and moments from each tool. Computational performance and efficiencies of each tool and their usability in conceptual and preliminary air vehicle design are also discussed. A description of the workflow, underlying theoretical foundations, and best practices are provided. In comparing FlightStream and OVERFLOW, reasonable agreement between predicted performance is observed for flow regimes of interest at high angle of attack prior to stall, including blown wing aero-propulsive effects on lift augmentation and stall delay. In the post-stall regions, FlightStream appears to underestimate the effects of turbulent flow separation that contribute heavily to drag. However, as expected for a high-fidelity, time-accurate solver, the setup and computation time are substantially greater for OVERFLOW than for FlightStream.

Vivek Ahuja↗

Comparison of Aerodynamic Analysis Tools Applied to a Propeller-Blown Wing

This paper describes initial results from an ongoing activity comparing two aerodynamic analysis tools: OVERFLOW, a Navier-Stokes flow solver, and FlightStream, a viscous surface-vorticity, unstructured panel method flow solver. Both tools are applied to analyses of an unblown wing and a propeller-blown wing, and then comparisons are performed between the predicted aerodynamic loads and moments from each tool. Computational performance and efficiencies of each tool and their usability in conceptual and preliminary air vehicle design are also discussed. A description of the workflow, underlying theoretical foundations, and best practices are provided. In comparing FlightStream and OVERFLOW, reasonable agreement between predicted performance is observed for flow regimes of interest at high angle of attack prior to stall, including blown wing aero-propulsive effects on lift augmentation and stall delay. In the post-stall regions, FlightStream appears to underestimate the effects of turbulent flow separation that contribute heavily to drag. However, as expected for a high-fidelity, time-accurate solver, the setup and computation time are substantially greater for OVERFLOW than for FlightStream.

Vivek Ahuja↗

Influence of Computational Drop Representation in LES of a Droplet-Laden Mixing Layer

Multiphase turbulent flows are encountered in many practical applications including turbine engines or natural phenomena involving particle dispersion. Numerical computations of multiphase turbulent flows are important because they provide a cheaper alternative to performing experiments during an engine design process or because they can provide predictions of pollutant dispersion, etc. Two-phase flows contain millions and sometimes billions of particles. For flows with volumetrically dilute particle loading, the most accurate method of numerically simulating the flow is based on direct numerical simulation (DNS) of the governing equations in which all scales of the flow including the small scales that are responsible for the overwhelming amount of dissipation are resolved. DNS, however, requires high computational cost and cannot be used in engineering design applications where iterations among several design conditions are necessary. Because of high computational cost, numerical simulations of such flows cannot track all these drops. The objective of this work is to quantify the influence of the number of computational drops and grid spacing on the accuracy of predicted flow statistics, and to possibly identify the minimum number, or, if not possible, the optimal number of computational drops that provide minimal error in flow prediction. For this purpose, several Large Eddy Simulation (LES) of a mixing layer with evaporating drops have been performed by using coarse, medium, and fine grid spacings and computational drops, rather than physical drops. To define computational drops, an integer NR is introduced that represents the ratio of the number of existing physical drops to the desired number of computational drops; for example, if NR=8, this means that a computational drop represents 8 physical drops in the flow field. The desired number of computational drops is determined by the available computational resources; the larger NR is, the less computationally intensive is the simulation. A set of first order and second order flow statistics, and of drop statistics are extracted from LES predictions and are compared to results obtained by filtering a DNS database. First order statistics such as Favre averaged stream-wise velocity, Favre averaged vapor mass fraction, and the drop stream-wise velocity, are predicted accurately independent of the number of computational drops and grid spacing. Second order flow statistics depend both on the number of computational drops and on grid spacing. The scalar variance and turbulent vapor flux are predicted accurately by the fine mesh LES only when NR is less than 32, and by the coarse mesh LES reasonably accurately for all NR values. This is attributed to the fact that when the grid spacing is coarsened, the number of drops in a computational cell must not be significantly lower than that in the DNS.

Bellan, Josette↗

Internal Shock Interactions in Propulsion/Airframe Integrated Three-Dimensional Sidewall Compression Scramjet Inlets

The advantages and design requirements of propulsion/airframe integration for high Mach number flight have led to extensive study of the three-dimensional sidewall compression scramjet inlet in recent years. Recent research publications have indicated testing over a broad range of Mach number (2 to 18) in a variety of test gases, such as air, helium, and tetrafluoromethane. Multiple experimental techniques have been employed to obtain detailed internal shock interaction data, performance data, and inlet starting limits. Computational fluid dynamics has been effectively used for preliminary parametric studies as well as in parallel with experiments to aid in the explanation of unusual or unexpected flow phenomena. Inlets of this genre afford a relatively simple, generic geometry while producing a highly complex, three-dimensional flow field dominated by shock/shock and shock/boundary layer interactions. While the importance of the viscous effects in high speed inlet interactions is recognized, the present work addresses in a parametric fashion the inviscid effects of leading edge sweep, sidewall compression, and inflow Mach number on the internal shock structure in terms of inlet compression and mass capture. In the process, the source of the of the Mach number invariance with leading edge sweep for a constant sidewall compression class of inlet is identified, and a previously undocumented spillage phenomenon in a constant effective wedge angle class of inlets is discussed.

Holland, Scott D.↗

NCC Simulation Model: Simulating the operations of the network control center, phase 2

The simulation of the network control center (NCC) is in the second phase of development. This phase seeks to further develop the work performed in phase one. Phase one concentrated on the computer systems and interconnecting network. The focus of phase two will be the implementation of the network message dialogues and the resources controlled by the NCC. These resources are requested, initiated, monitored and analyzed via network messages. In the NCC network messages are presented in the form of packets that are routed across the network. These packets are generated, encoded, decoded and processed by the network host processors that generate and service the message traffic on the network that connects these hosts. As a result, the message traffic is used to characterize the work done by the NCC and the connected network. Phase one of the model development represented the NCC as a network of bi-directional single server queues and message generating sources. The generators represented the external segment processors. The served based queues represented the host processors. The NCC model consists of the internal and external processors which generate message traffic on the network that links these hosts. To fully realize the objective of phase two it is necessary to identify and model the processes in each internal processor. These processes live in the operating system of the internal host computers and handle tasks such as high speed message exchanging, ISN and NFE interface, event monitoring, network monitoring, and message logging. Inter process communication is achieved through the operating system facilities. The overall performance of the host is determined by its ability to service messages generated by both internal and external processors.

Benjamin, Norman M.↗

Computational Models of Human Performance: Validation of Memory and Procedural Representation in Advanced Air/Ground Simulation

The Man-Machine Interaction Design and Analysis System (MIDAS) under joint U.S. Army and NASA cooperative is intended to assist designers of complex human/automation systems in successfully incorporating human performance capabilities and limitations into decision and action support systems. MIDAS is a computational representation of multiple human operators, selected perceptual, cognitive, and physical functions of those operators, and the physical/functional representation of the equipment with which they operate. MIDAS has been used as an integrated predictive framework for the investigation of human/machine systems, particularly in situations with high demands on the operators. We have extended the human performance models to include representation of both human operators and intelligent aiding systems in flight management, and air traffic service. The focus of this development is to predict human performance in response to aiding system developed to identify aircraft conflict and to assist in the shared authority for resolution. The demands of this application requires representation of many intelligent agents sharing world-models, coordinating action/intention, and cooperative scheduling of goals and action in an somewhat unpredictable world of operations. In recent applications to airborne systems development, MIDAS has demonstrated an ability to predict flight crew decision-making and procedural behavior when interacting with automated flight management systems and Air Traffic Control. In this paper, we describe two enhancements to MIDAS. The first involves the addition of working memory in the form of an articulatory buffer for verbal communication protocols and a visuo-spatial buffer for communications via digital datalink. The second enhancement is a representation of multiple operators working as a team. This enhanced model was used to predict the performance of human flight crews and their level of compliance with commercial aviation communication procedures. We show how the data produced by MIDAS compares with flight crew performance data from full mission simulations. Finally, we discuss the use of these features to study communication issues connected with aircraft-based separation assurance.

Corker, Kevin M.↗

Photonics and other approaches to high speed communications

Our research group of 4 faculty and about 10-15 graduate students was actively involved (as a group) in the development of computer communication networks for the last five years. Many of its individuals have been involved in related research for a much longer period. The overall research goal is to extend network performance to higher data rates, to improve protocol performance at most ISO layers and to improve network operational performance. We briefly state our research goals, then discuss the research accomplishments and direct your attention to attached and/or published papers which cover the following topics: scalable parallel communications; high performance interconnection between high data rate networks; and a simple, effective media access protocol system for integrated, high data rate networks.

Maly, Kurt↗

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

The current work compares experimentally and computationally obtained nitric oxide (NO) planar laser-induced fluorescence (PLIF) images of the mixing flowfields for three types of high-speed fuel injectors: a strut, a ramp, and a rectangular flushwall. These injection devices, which exhibited promising mixing performance at lower flight Mach numbers, are currently being studied as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. The EIMP aims to investigate scramjet fuel injection and mixing physics, and improve the understanding of underlying physical processes relevant to flight Mach numbers greater than eight. In the experiments conducted in the NASA Langley Arc-Heated Scramjet Test Facility (AHSTF), the injectors are placed downstream of a Mach 6 facility nozzle, which simulates the high Mach number air flow at the entrance of a scramjet combustor. Helium is used as an inert substitute for hydrogen fuel. Both schlieren and PLIF techniques are applied to obtain mixing flowfield flow visualizations. The experimental PLIF is obtained by using a UV laser sheet to interrogate a plane of the flow by exciting fluorescence from the NO molecules that are present in the AHSTF air. Consequently, the absence of signal in the resulting PLIF images is an indication of pure helium (fuel). The computational PLIF is obtained by applying a fluorescence model for NO to the results of the Reynolds-averaged simulations (RAS) of the mixing flowfield carried out using the VULCAN-CFD solver. This approach is required because the PLIF signal is a nonlinear function of not only NO concentration, but also pressure, temperature, and the flow velocity. This complexity allows additional flow features to be identified and compared with those obtained from the computational fluid dynamics (CFD) simulations, however, such comparisons are only semiquantitative. Three-dimensional image reconstruction, similar to that used in magnetic resonance imaging, is also used to obtain images in the streamwise and spanwise planes from select cross-stream PLIF plane data. Synthetic schlieren is also computed from the RAS data. Good agreement between the experimental and computational results provides increased confidence in the CFD simulations for investigations of injector performance.

PLIF↗

Comparisons Between NO PLIF Imaging and CFD Simulations of Mixing Flowfields for High-Speed Fuel Injectors

The current work compares experimentally and computationally obtained nitric oxide (NO) planar laser-induced fluorescence (PLIF) images of the mixing flowfields for three types of high-speed fuel injectors: a strut, a ramp, and a rectangular flushwall. These injection devices, which exhibited promising mixing performance at lower flight Mach numbers, are currently being studied as a part of the Enhanced Injection and Mixing Project (EIMP) at the NASA Langley Research Center. The EIMP aims to investigate scramjet fuel injection and mixing physics, and improve the understanding of underlying physical processes relevant to flight Mach numbers greater than eight. In the experiments conducted in the NASA Langley Arc-Heated Scramjet Test Facility (AHSTF), the injectors are placed downstream of a Mach 6 facility nozzle, which simulates the high Mach number air flow at the entrance of a scramjet combustor. Helium is used as an inert substitute for hydrogen fuel. Both schlieren and PLIF techniques are applied to obtain mixing flowfield flow visualizations. The experimental PLIF is obtained by using a UV laser sheet to interrogate a plane of the flow by exciting fluorescence from the NO molecules that are present in the AHSTF air. Consequently, the absence of signal in the resulting PLIF images is an indication of pure helium (fuel). The computational PLIF is obtained by applying a fluorescence model for NO to the results of the Reynolds-averaged simulations (RAS) of the mixing flowfield carried out using the VULCAN-CFD solver. This approach is required because the PLIF signal is a nonlinear function of not only NO concentration, but also pressure, temperature, and the flow velocity. This complexity allows additional flow features to be identified and compared with those obtained from the computational fluid dynamics (CFD) simulations, however, such comparisons are only semiquantitative. Three-dimensional image reconstruction, similar to that used in magnetic resonance imaging, is also used to obtain images in the streamwise and spanwise planes from select cross-stream PLIF plane data. Synthetic schlieren is also computed from the RAS data. Good agreement between the experimental and computational results provides increased confidence in the CFD simulations for investigations of injector performance.

PLIF↗

Successes and Challenges of Incompressible Flow Simulation

During the past thirty years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of CFD discipline. Even though incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient, CFD tools become indispensable in fluid engineering for incompressible and low speed flow. This paper is intended to review some of the successes made possible by advances in computational technologies during the same period, and discuss some of the current challenges.

Kwak, Dochan↗

Experimental and Numerical Optimization of a High-Lift System to Improve Low-Speed Performance, Stability, and Control of an Arrow-Wing Supersonic Transport

An investigation was performed to evaluate leading-and trailing-edge flap deflections for optimal aerodynamic performance of a High-Speed Civil Transport concept during takeoff and approach-to-landing conditions. The configuration used for this study was designed by the Douglas Aircraft Company during the 1970's. A 0.1-scale model of this configuration was tested in the Langley 30- by 60-Foot Tunnel with both the original leading-edge flap system and a new leading-edge flap system, which was designed with modem computational flow analysis and optimization tools. Leading-and trailing-edge flap deflections were generated for the original and modified leading-edge flap systems with the computational flow analysis and optimization tools. Although wind tunnel data indicated improvements in aerodynamic performance for the analytically derived flap deflections for both leading-edge flap systems, perturbations of the analytically derived leading-edge flap deflections yielded significant additional improvements in aerodynamic performance. In addition to the aerodynamic performance optimization testing, stability and control data were also obtained. An evaluation of the crosswind landing capability of the aircraft configuration revealed that insufficient lateral control existed as a result of high levels of lateral stability. Deflection of the leading-and trailing-edge flaps improved the crosswind landing capability of the vehicle considerably; however, additional improvements are required.

Hahne, David E.↗

CFD analysis of jet mixing in low NO(x) flametube combustors

The Rich-burn/Quick-mix/Lean-burn (RQL) combustor has been identified as a potential gas turbine combustor concept to reduce NO(x) emissions in High Speed Civil Transport (HSCT) aircraft. To demonstrate reduced NO(x) levels, cylindrical flametube versions of RQL combustors are being tested at NASA Lewis Research Center. A critical technology needed for the RQL combustor is a method of quickly mixing by-pass combustion air with rich-burn gases. Jet mixing in a cylindrical quick-mix section was numerically analyzed. The quick-mix configuration was five inches in diameter and employed twelve radial-inflow slots. The numerical analyses were performed with an advanced, validated 3D Computational Fluid Dynamics (CFD) code named REFLEQS. Parametric variation of jet-to-mainstream momentum flux ratio (J) and slot aspect ratio was investigated. Both non-reacting and reacting analyses were performed. Results showed mixing and NO(x) emissions to be highly sensitive to J and slot aspect ratio. Lowest NO(x) emissions occurred when the dilution jet penetrated to approximately mid-radius. The viability of using 3D CFD analyses for optimizing jet mixing was demonstrated.

Talpallikar, M. V.↗