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Finite elements and finite differences for transonic flow calculations

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Hafez, M. M.↗

Results of the SPAS-01 RCS plume impingement test

The Orbiter RCS flowfield is modeled in the free molecular region and an impingement analysis is performed to characterize on-orbit plume interactions with nearby bodies, such as the SPAS-01 satellite. The flow in the far field is treated with a source flow model at any point 40 ft from the nozzle. Impingement is calculated according to Newtonian impact theory. The flow density in the far field is expressed in terms of a conservation of energy equation, with account taken of the expansion of the gas, cooling, and the angular distribution. The SPAS-01 platform gathered data at eight different positions around the Orbiter to test the model predictions. Excellent agreement was obtained in predictions of the torque and rotation rate induced on the SPAS by firing the thrusters.

Lazaron, M. P.↗

A nonoscillatory shock capturing scheme using flux limited dissipation

A method for modifying the third order dissipative terms by the introduction of flux limiters is proposed. The first order dissipative terms can then be eliminated entirely, and in the case of a scalar conservation law the scheme is converted into a total variation diminishing scheme provided that an appropriate value is chosen for the dissipative coefficient. Particular attention is given to: (1) the treatment of the scalar conservation law; (2) the treatment of the Euler equations for inviscid compressible flow; (3) the boundary conditions; and (4) multistage time stepping and multigrid schemes. Numerical results for transonic flows suggest that a central difference scheme augmented by flux limited dissipative terms can lead to an effective nonoscillatory shock capturing method.

Jameson, A.↗

Construction of explicit and implicit symmetric TVD schemes and their applications

A one-parameter family of explicit and implicit total variation diminishing (TVD) schemes is developed which permits incorporation of an expanded group of slope and flux limiters. The numerical technique is intended for use in calculations which include a time-differencing scheme and an optional Lax-Wendroff scheme. Methods of extending the TVD models to nonlinear scalar equations and systems of hyperbolic conservation equations are described. Sample results are presented from calculations of shocked flows around NACA 0012 and NACA 0018 airfoils.

Yee, H. C.↗

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Woods, Claudia M.↗

The dc power control for a liquid-fed resistojet

A simple breadboard power controller was designed and demonstrated for a new liquid-fed water resistojet. The 1-piece laboratory model thruster has an integrated vaporizer/superheater using a single heating element. Heater temperature was maintained at or near a preset reference value with the closed loop controller providing pulse width modulated (PWM) dc power into the thruster heater. A combined thruster, temperature readout, PWM transfer function was experimentally determined. This transfer function was used to design a proportional plus integral controller that demonstrated zero steady state error, conservative stability margins and adequate transient response to step changes in propellant flow rate, input voltage and temperature reference. Initial turn-on temperature overshoot from room temperature to a 650 C setpoint was 80 C. In addition, EMI was alleviated by reducing heater dI/dt and dV/dt using a simple diode-inductor-capacitor network. Based on limited initial tests, thruster preheat with no propellant flow was necessary to achieve stable system operation during startup. Breadboard power efficiency was 99 percent at 1 kW, and component mass was 0.4 kg excluding the power loss and mass of an input filter required for spacecraft integration.

Gruber, Robert P.↗

The solution of the Elrod algorithm for a dynamically loaded journal bearing using multigrid techniques

A numerical solution to a theoretical model of vapor cavitation in a dynamically loaded journal bearing is developed utilizing a multigrid iteration technique. The method is compared with a noniterative approach in terms of computational time and accuracy. The computational model is based on the Elrod algorithm, a control volume approach to the Reynolds equation which mimics the Jakobsson-Floberg and Olsson cavitation theory. Besides accounting for a moving cavitation boundary and conservation of mass at the boundary, it also conserves mass within the cavitated region via a smeared mass or striated flow extending to both surfaces in the film gap. The mixed nature of the equations (parabolic in the full film zone and hyperbolic in the cavitated zone) coupled with the dynamic aspects of the problem create interesting difficulties for the present solution approach. Emphasis is placed on the methods found to eliminate solution instabilities. Excellent results are obtained for both accuracy and reduction of computational time.

Woods, C. M.↗

dc power control for a liquid-fed resistojet

A simple breadboard power controller was designed and demonstrated for a new liquid-fed water resistojet. The 1-piece laboratory model thruster has an integrated vaporizer/superheater using a single heating element. Heater temperature was maintained at or near a preset reference value with the closed loop controller providing pulse width modulated (PWM) dc power into the thruster heater. A combined thruster, temperature readout, PWM transfer function was experimentally determined. This transfer function was used to design a proportional plus integral controller that demonstrated zero steady state error, conservative stability margins and adequate transient response to step changes in propellant flow rate, input voltage and temperature reference. Initial turn-on temperature overshoot from room temperature to a 650 C setpoint was 80 C. In addition, EMI was alleviated by reducing heater dI/dt and dV/dt using a simple diode-inductor-capacitor network. Based on limited initial tests, thruster preheat with no propellant flow was necessary to achieve stable system operation during startup. Breadboard power efficiency was 99 percent at 1 kW, and component mass was 0.4 kg excluding the power loss and mass of an input filter required for spacecraft integration.

Gruber, Robert P.↗

Integration of Biological, Physical/Chemical and Energy Efficient Systems in the CELSS Antarctic Analog: Performance of Prototype Systems and Issues for Life Support

The Controlled Ecological Life Support System (CELSS) Antarctic Analog Project (CAAP) is a joint endeavor between the National Science Foundation, Office of Polar Programs (NSF-OPP), and the National Aeronautics and Space Administration (NASA). The fundamental objective is to develop, deploy, and operate a testbed of advanced life support technologies at the Amundsen-Scott South Pole Station that enable the objectives of both the NSF and NASA. The functions of food production, water purification, and waste treatment, recycle, and reduction provided by CAAP will improve the quality of life for the South Pole inhabitants, reduce logistics dependence, enhance safety, and minimize environmental impacts associated with human presence on the polar plateau. Because of the analogous technical, scientific, and mission features with Planetary missions, such as a mission to Mars, CAAP provides NASA with a method for validating technologies and overall approaches to supporting humans. Prototype systems for waste treatment, water recycle, resource recovery and crop production are being evaluated in a testbed at Ames Research Center. The combined performance of these biological and physical/chemical systems as an integrated function in support of the human habitat will be discussed. Overall system performance will be emphasized. The effectiveness and efficiency of component technologies will be discussed in the context of energy and mass flow within the system and contribution to achieving a mass and energy conservative system. Critical to the discussion are interfaces with habitat functions outside of the closed-loop life support: the ability of the system to satisfy the life support requirements of the habitat and the ability to define input requirements. The significance of analog functions in relation to future Mars habitats will be discussed.

Bubenheim, David L.↗

Development of A Maximum Anti-Slosh Baffle Pressure Load Model

The sloshing of propellants can affect the stability of a spacecraft and the integrity of the tank structure. Undesirable sloshing can be controlled by the addition of anti-slosh baffles, and the spacing and configuration of baffles are driven by damping requirements. The structural design of the baffle is determined after consideration of many factors, such as the strength and rigidity needed to support the baffle for its lifetime. Therefore, knowledge of distributed pressure loading is important for detailed structural design. In addition, the resultant force and moment produced by the distributed pressure are of direct importance to the design of a vehicle’s control system. Previous experimental investigations have been conducted to determine the liquid pressure loads and slosh damping associated with a rigid ring baffle. The results suggested that when the nondimensional velocity parameter is larger than 1.0, the theories agree with the test. However, when the velocity parameter is less than 1.0, all theories are nonconservative and under-predict the pressure loads. The present study has derived a maximum pressure load on the slosh baffle based on the energy conservation principle. It is verified from CFD that pressure in the slosh flow field can be decomposed into static and transient components. The CFD results confirm that there is a phase shift in pressure across the baffle, which depends on the fluid damping. Higher damping leads to a higher phase shift. The CFD investigation further verifies the proposed theory: the maximum pressure load occurs when the phase shift is 90 degrees. A comparison of the present computational results to the previous comprehensive experimental data validates the maximum pressure theory. When the baffle is submerged, the maximum pressure theory envelopes all the experimental data points.

CFD↗

Tracking Radioactive Isotopes in HVAC and Application for Hot Cell Analyses - 20155

In recent years, the surge in the number of isotope production facilities under design has increased the need to analyze isotope migration in facility Heating, Ventilation, and Air Conditioning (HVAC) during normal operations and accident scenarios. These facilities are used to produce isotopes for medical, security, and industrial applications and as such are subject to license and regulatory requirements 10CFR20, 10CFR30, 10CFR50, and 10CFR70. GOTHIC, a general-purpose thermal-hydraulics software package, includes the ability to model isotopic tracers, radioactive decay and isotope migration as well as HEPA and charcoal filters for isotope retention. A GOTHIC model was developed by Zachry Nuclear Engineering (ZNE) to examine the effect of negative room pressure, HEPA filtration, and HVAC fluctuations on radiation areas, hot cells and gloveboxes. Radioactive tracers were used to simulate the concentration of spills within contaminated areas, track the migration of isotopes of interest, and determine the isotopic retention and buildup on facility HEPA filters. A variety of isotopes with concern to dose (e.g., Kr-85, Sr-90, I-131, etc.), including their decay and progeny, are included in the analysis. Negative pressures are maintained in the regions of interest by a representative central HVAC system equipped with a volumetric fan that exhausts to the environment after a series of isolation valves and HEPA filters. GOTHIC is an industry trusted tool for providing engineering solutions for a variety of applications, including fission product tracking, aerosol and particulate transport and ventilation assessments. The software provides an integrated analysis environment that includes a graphical user interface (GUI) for constructing analysis models, a numerical solver that includes parallel processing capabilities and a post-processor for evaluating simulation results. It solves the conservation equations for mass, momentum and energy for multicomponent, multi-phase flow in lumped parameter and multi-dimensional geometries (1, 2, or full 3D), including the effects of turbulence, diffusion and buoyancy. It has been developed and maintained under a Quality Assurance program in compliance with the requirements of 10CFR50 Appendix B and applicable portions of ASME NQA-1 since 1995. GOTHIC has been used for assessing both forced and natural convection conditions for a wide range of applications, including: - Tracking concentration of hazardous gases and chemicals for habitability and safety assessments - Determining ventilation and filtration requirements and optimizing location and arrangement of these systems - Room heat-up, including diverse and Flexible coping strategies for Extended Loss of AC Power (FLEX/ELAP) - Equipment Qualification (EQ) A distinctive feature of GOTHIC is the ability to track many different fields/substances in a simulation, including user defined tracer elements, in the liquid, vapor and droplet fields as well as surfaces and filters. This capability allows GOTHIC to model fission product transport and release or the removal of particulates or harmful toxins from exhaust gases using a spray scrubber or other types of filtration systems. GOTHIC also includes models for engineered equipment, such as fans, filters, charcoal filters, dryers/demisters, dampers, etc. The aerosols and other filtered material are removed or accumulated in these components. The range of aerosol and radiological applications that GOTHIC has been used for includes: - Source Term: Primary Coolant (Equilibrium) Activity; Non-Water Coolant Source/Leakage. - Conditions for Iodine Re-evolution: Sump/Suppression Pool Conditions and pH; - RWST Conditions and pH. - Isotope Removal Mechanisms: Containment Sprayed and Unsprayed Region Mixing; Charcoal Filter Heating due to Iodine decay. - Radionuclide Transport and Decay: Post-LOCA Release in containment; Transport between connected Compartments and vent systems; Groundwater transport of radionuclides. - Non-Newtonian Fluid modeling for sludge, waste tanks, etc. ADAMS ML071581053 (titled 'Best Practice Guidelines for the use of CFD in Nuclear Reactor Safety Applications') poses guidelines for applying single phase CFD codes in nuclear reactor safety problems and GOTHIC is listed as a 'tool for 3D flows' and 'dispersal and deposition of radionuclides.' The Nuclear Quality Assurance (NQA) pedigree of GOTHIC is an important aspect for applications in the nuclear industry. The fundamental tracer models (convective transport, molecular and turbulent diffusion, removal mechanisms, etc.) have been verified using analytical solutions and validated against applicable separate effects tests. Also, GOTHIC has been benchmarked to many integrated effects tests, including Phebus FP (Fission Product). GOTHIC gives good agreement for the buildup and decay of fission products in Phebus Test 3. The model developed by ZNE demonstrates GOTHIC's applicability and acceptability for use in analyzing the migration and retention of radioactive isotopes and their progeny in normal operation and accident scenario analyses for isotope production facilities, hot cells, and gloveboxes. The tracer activities calculated by GOTHIC can then be used in downstream radiation transport and shielding codes like RADTRAD-NAI{sup C}, MCNP{sup R}, and MicroShield{sup R} to determine on-site and of-site doses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Investigation of Extreme Leading-Edge Roughness on Thick Low-Drag Airfoils to Indicate Those Critical to Separation

Several airfoils, Including a conventional NACA 23021 and some low-drag airfoils for which the thickness had been increased to the point that they were considered doubtfully conservative with respect to separation, were investigated as smooth airfoils and after the application of a standard roughness. The results show some of the airfoils to be critical to separation resulting from such flow disturbances. It is concluded, pending the further investigation of separation difficulties, that airfoil sections falling definitely within the conservative range should be used.

AIRFOILS - NACA 65,3-418 - CHAR & MOMENTS - LOW-DR↗

Calculation of flow about two-dimensional bodies by means of the velocity-vorticity formulation on a staggered grid

A method for calculating the incompressible viscous flow about two-dimensional bodies, utilizing the velocity-vorticity form of the Navier-Stokes equations using a staggered-grid formulation is presented. The solution is obtained by employing an alternative-direction implicit method for the solution of the block tridiagonal matrix resulting from the finite-difference representation of the governing equations. The boundary vorticity and the conservation of mass are calculated implicitly as a part of the solution. The mass conservation is calculated to machine zero for the duration of the computation. Calculations for the flow about a circular cylinder, a 2-pct thick flat plate at 90-deg incidence, an elliptic cylinder at 45-deg incidence, and a NACA 0012, with and without a deflected flap, at - 90-deg incidence are performed and compared with the results of other numerical investigations.

Stremel, Paul M.↗

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

Imlay, Scott T.↗

Three dimensional hypersonic flow simulations with the CSCM implicit upwind Navier-Stokes method

The Bardina and Lombard (1985) three-dimensional CSCM Navier-Stokes method is presently extended to the simulation of complex hypersonic reentry vehicle external flows at angle of attack. The robust stability of the method derives from the combination of conservative implicit upwind flux difference splitting with a three-dimensional diagonally-dominant approximate factorization and relaxation scheme and characteristic-based implicit boundary approximations. The method's efficiency derives from an implicit symmetric Gauss-Seidel 'method of planes' relaxation scheme with alternating directional space marching sweeps along the flow coordinate direction.

Bardina, Jorge↗

A New Test Method for Material Flammability Assessment in Microgravity and Extraterrestrial Environments

The standard oxygen consumption (cone) calorimeter (described in ASTM E 1354 and NASA STD 6001 Test 2) is modified to provide a bench-scale test environment that simulates the low velocity buoyant or ventilation flow generated by or around a burning surface in a spacecraft or extraterrestrial gravity level. The Equivalent Low Stretch Apparatus (ELSA) uses an inverted cone geometry with the sample burning in a ceiling fire (stagnation flow) configuration. For a fixed radiant flux, ignition delay times for characterization material PMMA are shown to decrease by a factor of three at low stretch, demonstrating that ignition delay times determined from normal cone tests significantly underestimate the risk in microgravity. The critical heat flux for ignition is found to be lowered at low stretch as the convective cooling is reduced. At the limit of no stretch, any heat flux that exceeds the surface radiative loss at the surface ignition temperature is sufficient for ignition. Regression rates for PMMA increase with heat flux and stretch rate, but regression rates are much more sensitive to heat flux at the low stretch rates, where a modest increase in heat flux of 25 kW/m2 increases the burning rates by an order of magnitude. The global equivalence ratio of these flames is very fuel rich, and the quantity of CO produced in this configuration is significantly higher than standard cone tests. These results [2] demonstrate the ELSA apparatus allows us to conduct normal gravity experiments that accurately and quantifiably evaluate a material s flammability characteristics in the real-use environment of spacecraft or extra-terrestrial gravitational acceleration. These results also demonstrate that current NASA STD 6001 Test 2 (standard cone) is not conservative since it evaluates materials flammability with a much higher inherent buoyant convective flow.

Olson, S. L.↗

nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. Here, in this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.

42 ENGINEERING↗

Surrogate-equation technique for simulation of steady inviscid flow

A numerical procedure for the iterative solution of inviscid flow problems is described, and its utility for the calculation of steady subsonic and transonic flow fields is demonstrated. Application of the surrogate equation technique defined herein allows the formulation of stable, fully conservative, type dependent finite difference equations for use in obtaining numerical solutions to systems of first order partial differential equations, such as the steady state Euler equations. Steady, two dimensional solutions to the Euler equations for both subsonic, rotational flow and supersonic flow and to the small disturbance equations for transonic flow are presented.

Johnson, G. M.↗