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NASA NTRS1975

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

Cooke, C. H.↗

NASA NTRS1980

Numerical analysis of complex fluid-flow systems

Very flexible computer-assisted numerical analysis is used to solve dynamic fluid-flow equations characterizing computer-controlled heat dissipation system developed for Space lab. Losses caused by bends, ties, fittings, valves, and like are easily included, and analysis can solve both steady-state and transient cases. It can also interact with parallel thermal analysis.

Holland, R. L.↗

NASA NTRS1981

Ultrasonic frequency analysis

Technique is used for evaluation and characterization of materials, fluids, and biological tissue. Method eliminates problem of electrical drive pulse shape by slaving tracking generator to local oscillator of spectrum analyzer. Logic/timing generator is used to control pulse transmission and receiving sequence, pulse width, and pulse repetition rate.

Cantrell, J. H.↗

NASA NTRS1980

Low cost cryostat

A cryostat for use in a low or a substantially gravity-free environment adapted to cool an experiment through the use of helium 2, or helium in its super fluid state is characterized by a number of interchangeable daughter dewars and helium supply or mother dewar. A low pressure venting system is provided for converting helium contained in the mother dewar to a superfluid state for use as a primary cryogen. Each daughter dewar is adapted to be removably mounted in mated relation on the mother dewar and is characterized by support for an experiment package, a source of helium to be employed as a secondary cryogen. A heat pipe is suspended from each daughter dewar and adapted to be extended into the mother dewar for facilitating cooling of the secondary cryogen. A transfer of heat from the package to the primary cryogen, via the secondary cryogen, is accommodated as a film flow of helium 2 progresses from the heat pipe to the experiment dewar.

Stephens, J. B.↗

NASA NTRS1992

U-Th-Pb, Rb-Sr, and Sm-Nd isotopic systematics of lunar troctolitic cumulate 76535 - Implications on the age and origin of this early lunar, deep-seated cumulate

The U-Th-Pb, Rb-Sr, and Sm-Nd isotopic systematics of four lightly leached residues of pristine, high-Mg, troctolitic cumulate 76535 were analyzed in order to determine their ages and magma sources. The data indicate that the cumulate was in isotopic equilibrium with a fluid or magma characterized by a high U-238/Pb-204 (mu) value of 600 at 4.236 Ga. Two and three stage Pb evolution calculations define even greater source mu values of about 1000, assuming low lunar initial mu values between 5 and 40 prior to about 4.43 Ga. These results are similar to mu values for KREEP sources and are also consistent with values from 78235, suggesting that at least some high-Mg suite rocks were derived from magma sources with high-mu values similar to KREEP, and support that idea that these rocks postdate primary lunar differentiation and formation of ferroan anorthosites.

Premo, Wayne R.↗

NASA NTRS1998

Investigations in Martian Sedimentology

The purpose of this report is to investigate and discuss the Martian surface. This report was done in specific tasks. The tasks were: characterization of Martian fluids and chemical sediments; mass wasting and ground collapse in terrains of volatile-rich deposits; Mars Rover terrestrial field investigations; Mars Pathfinder operations support; and Martian subsurface water instrument.

Moore, Jeffrey M.↗

NASA NTRS2000

Novel Optical Diagnostic Techniques for Studying Particle Deposition Upon Large Cylinders in a Sheared Suspension

On a twelve-month voyage to Mars, one astronaut will require at least two tons of potable water and two tons of pure oxygen. Efficient, reliable fluid reclamation is therefore necessary for manned space exploration. Space habitats require a compact, flexible, and robust apparatus capable of solid-fluid mechanical separation over a wide range of fluid and particle densities and particle sizes. In space, centrifugal filtration, where particles suspended in fluid are captured by rotating fixed-fiber mat filters, is a logical candidate for mechanical separation. Non-colloidal particles are deposited on the fibers due to inertial impaction or direct interception. Since rotation rates are easily adjustable, inertial effects are the most practical way to control separation rates for a wide variety of multiphase mixtures in variable gravity environments. Understanding how fluid inertia and differential fluid-particle inertia, characterized by the Reynolds and Stokes numbers, respectively, affect deposition is critical in optimizing filtration in a microgravity environment. This work will develop non-intrusive optical diagnostic techniques for directly visualizing where and when non-colloidal particles deposit upon, or contact, solid surfaces: 'particle proximity sensors'. To model particle deposition upon a single filter fiber, these sensors will be used in ground-based experiments to study particle dynamics as in the vicinity of a large (compared with the particles) cylinder in a simply sheared (i.e., linearly-varying, zero-mean velocity profile) neutrally-buoyant, refractive-index matched solid-liquid suspension.

Yoda, M.↗

NASA NTRS1995

Numerical Simulations of High Enthalpy Pulse Facilities

Axisymmetric flows within shock tubes and expansion tubes are simulated including the effects of finite rate chemistry and both laminar and turbulent boundary layers. The simulations demonstrate the usefulness of computational fluid dynamics for characterizing the flows in high enthalpy pulse facilities. The modeling and numerical requirements necessary to simulate these flows accurately are also discussed. Although there is a large body of analysis which explains and quantifies the boundary layer growth between the shock and the interface in a shock tube, there is a need for more detailed solutions. Phenomena such as thermochemical nonequilibrium. or turbulent transition behind the shock are excluded in the assumptions of Mirels' analysis. Additionally there is inadequate capability to predict the influence of the boundary layer on the expanded gas behind the interface. Quantifying the gas in this region is particularly important in expansion tubes because it is the location of the test gas. Unsteady simulations of the viscous flow in shock tubes are computationally expensive because they must follow features such as a shock wave over the length of the facility and simultaneously resolve the small length scales within the boundary layer. As a result, efficient numerical algorithms are required. The numerical approach of the present work is to solve the axisymmetric gas dynamic equations using an finite-volume formulation where the inviscid fluxes are computed with a upwind TVD scheme. Multiple species equations are included in the formulation so that finite-rate chemistry can be modeled. The simulations cluster grid points at the shock and interface and translate this clustered grid with these features to minimize numerical errors. The solutions are advanced at a CFL number of less than one based on the inviscid gas dynamics. To avoid limitations on the time step due to the viscous terms, these terms are treated implicitly. This requires a block tri-diagonal matrix inversion along each line of cells normal to the wall. The cost of this inversion is more than offset by the larger allowable time step. The source terms representing the finite-rate chemical kinetics are also treated implicitly. An algebraic turbulence model for compressible flow is used. The flow in a low pressure shock tube is computed and the results are compared with Mirels'analysis. The driven gas is nitrogen at 70 Pa, and the incident shock speed is approximately 2.9 km/sec so that there is little dissociation. The simulations include a laminar boundary layer and are run until the limiting flow regime is achieved. At this limit, the shock and interface travel at the same velocity because the amount of driven gas between these two features remains the same: the mass flow across the shock is equal to the mass of gas being entrained at the interface by the boundary layer. Simulations with several grids are presented to establish the grid independence of the solution, Good agreement is achieved between Mirels' correlations and the computations. This is expected since the flow conditions are chosen to be consistent with the assumptions used in Mirels' analysis. This comparison adds credibility to the numerical approach and highlights some of the differences between the theory and the detailed simulations. In addition, simulations of the HYPULSE expansion tube are presented for two operating conditions and the computations are compared to experimental data. The operating gas for both cases is nitrogen. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium. in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a pressure of 38 kPa and is characterized by a turbulent boundary layer. The simulations compare well with experiment and reveal that the nonuniformity in pressure observed during the test time is related to variations in the boundary layer displacement thickness.

Wilson, Gregory J.↗

NASA NTRS2004

Probe for Sampling of Interstitial Fluid From Bone

An apparatus characterized as both a membrane probe and a bone ultrafiltration probe has been developed to enable in vivo sampling of interstitial fluid in bone. The probe makes it possible to measure the concentration of calcium and other constituents of the fluid that may be relevant to bone physiology. The probe could be especially helpful in experimental studies of microgravitational bone loss and of terrestrial bone-loss disease states, including osteoporosis. The probe can be implanted in the bone tissue of a living animal and can be used to extract samples of the interstitial bone fluid from time to time during a long-term study. The probe includes three 12-cm-long polyacrylonitrile fibers configured in a loop form and attached to polyurethane tubing [inside diameter 0.025 in. (0.64 mm), outside diameter 0.040 in. (1 mm)]; the attachment is made by use of a 1-cm-long connecting piece of polyurethane tubing [inside diameter 0.035 0.003 in. (0.89 0.08 mm), outside diameter 0.060 0.003 in. (1.52 0.08 mm)]. At the distal end, a 2-cm-long piece of polyurethane tubing of the same inner and outer diameters serves as a connector to a hub. A 1-cm long piece of expanded poly (tetrafluoroethylene) tubing over the joint between the fibers and the connecting tubing serves as a tissue-in-growth site.

Janle, Elsa M.↗

NASA NTRS2011

A Data Mining Project to Identify Cardiovascular Related Factors That May Contribute to Changes in Visual Acuity Within the US Astronaut Corps

Many of the cardiovascular-related adaptations that occur in the microgravity environment are due, in part, to a well-characterized cephalad-fluid shift that is evidenced by facial edema and decreased lower limb circumference. It is believed that most of these alterations occur as a compensatory response necessary to maintain a "normal" blood pressure and cardiac output while in space. However, data from both flight and analog research suggest that in some instances these microgravity-induced alterations may contribute to cardiovascular-related pathologies. Most concerning is the potential relation between the vision disturbances experienced by some long duration crewmembers and changes in cerebral blood flow and intra-ocular pressure. The purpose of this project was to identify cardiovascular measures that may potentially distinguish individuals at risk for visual disturbances after long duration space flight. Toward this goal, we constructed a dataset from Medical Operation tilt/stand test evaluations pre- (days L-15-L-5) and immediate post-flight (day R+0) on 20 (3 females, 17 males). We restricted our evaluation to only crewmembers who participated in both shuttle and space station missions. Data analysis was performed using both descriptive and analytical methods (Stata 11.2, College Station, TX) and are presented as means +/- 95% CI. Crewmembers averaged 5207 (3447 - 8934) flight hours across both long (MIR-23 through Expedition16) and short (STS-27 through STS-101) duration missions between 1988 and 2008. The mean age of the crew at the time of their most recent shuttle flight was 41 (34-44) compared to 47 (40-54) years during their time on station. In order to focus our analysis (we did not have codes to separate out subjects by symptomotology) , we performed a visual inspection of each cardiovascular measures captured during testing and plotted them against stand time, pre- to post-flight, and between mission duration. It was found that pulse pressure most clearly differentiated the two mission types. Statistical analysis confirmed that pulse pressure was significantly higher before [45.6; (42.1 to 49.1)] and after [50.7; (46.9 to 54.6)] time on station compared with their most recent shuttle flight [31.6 (27.8 to 35.4), and 32.2 (28.3 to 36.0) respectively] even after correcting differences in age and cumulative number of mission hours. Without knowing the identity of which long duration crewmembers demonstrated visual changes, we were limited to examining whether certain crew regulate components of pulse pressure, systolic and diastolic blood pressure, differently due to microgravity exposure. To that end, we stratified crew into tertiles based on either their pre-flight measure of systolic or diastolic blood pressure. Those crew in the highest tertile for both systolic (lower tertile (n=8; 103-111), middle tertile (n=7; 113-121), and upper tertile (n=5; 125-136) and diastolic blood pressure (lower tertile (n=8; 58-64), middle tertile (n=7; 67-73), and upper tertile (n=5; 75-81) demonstrated less variability in pulse pressure between R+0 and L-10 (Figure 2). Interestingly, those crewmembers with the highest resting systolic blood pressure demonstrated either no change or in some instances an increase in total peripheral resistance, where those in the lower tertiles had lower values of total peripheral resistance compared to pre-flight levels. In this study, it was found that crewmembers in the highest tertile for both systolic and diastolic blood pressure demonstrated less variability in pulse pressure and that the decrease in variability was due in part to lower levels of compliance as indicated by similar or higher levels of total peripheral resistance after compared with before flight levels. Whether there is a relation between blood pressure regulation and total peripheral resistance in crew presenting with negative changes in visual acuity remains unknown.

Westby, Christian M.↗

NASA NTRS2013

LADEE Propulsion System Cold Flow Test

Lunar Atmosphere and Dust Environment Explorer (LADEE) is a NASA mission that will orbit the Moon. Its main objective is to characterize the atmosphere and lunar dust environment. The spacecraft development is being led by NASA Ames Research Center and scheduled for launch in 2013. The LADEE spacecraft will be operated with a bi-propellant hypergolic propulsion system using MMH and NTO as the fuel and oxidizer, respectively. The propulsion system utilizes flight-proven hardware on major components. The propulsion layout is composed of one 100-lbf main thruster and four 5-lbf RCS thrusters. The propellants are stored in four tanks (two parallel-connected tanks per propellant component). The propellants will be pressurized by regulated helium. A simulated propulsion system has been built for conducting cold flow test series to characterize the transient fluid flow of the propulsion system feed lines and to verify the critical operation modes, such as system priming, waterhammer, and crucial mission duty cycles. Propellant drainage differential between propellant tanks will also be assessed. Since the oxidizer feed line system has a higher flow demand than the fuel system does, the cold flow test focuses on the oxidizer system. The objective of the cold flow test is to simulate the LADEE propulsion fluid flow operation through water cold flow test and to obtain data for anchoring analytical models. The models will be used to predict the transient and steady state flow behaviors in the actual flight operations. The test activities, including the simulated propulsion test article, cold flow test, and analytical modeling, are being performed at NASA Marshall Space Flight Center. At the time of the abstract submission, the test article checkout is being performed. The test series will be completed by November, 2012

Williams, Jonathan Hunter↗

NASA NTRS2015

Resource Prospector Propulsion System Cold Flow Testing

Resource Prospector (RP) is a NASA mission being led by NASA Ames Research Center with current plans to deliver a scientific payload package aboard a rover to the lunar surface. As part of an early risk reduction activity, Marshall Space Flight Center (MSFC) and Johnson Space Flight Center (JSC) have jointly developed a government-version concept of a lunar lander for the mission. The spacecraft consists of two parts, the lander and the rover which carries the scientific instruments. The lander holds the rover during launch, cruise, and landing on the surface. Following terminal descent and landing the lander portion of the spacecraft become dormant after the rover embarks on the science mission. The lander will be equipped with a propulsion system for lunar descent and landing, as well as trajectory correction and attitude control maneuvers during transit to the moon. Hypergolic propellants monomethyl hydrazine and nitrogen tetroxide will be used to fuel sixteen 70-lbf descent thrusters and twelve 5-lbf attitude control thrusters. A total of four metal-diaphragm tanks, two per propellant, will be used along with a high-pressure composite-overwrapped pressure vessel for the helium pressurant gas. Many of the major propulsion system components are heritage missile hardware obtained by NASA from the Air Force. In parallel with the flight system design activities, a simulated propulsion system based on flight drawings was built for conducting a series of water flow tests to characterize the transient fluid flow of the propulsion system feed lines and to verify the critical operation modes such as system priming, waterhammer, and crucial mission duty cycles. The primary objective of the cold flow testing was to simulate the RP propulsion system fluid flow operation through water flow testing and to obtain data for anchoring analytical models. The models will be used to predict the transient and steady state flow behaviors in the actual flight operations. All design and build efforts, including the analytical modeling, have been performed. The cold flow testing of the propulsion system was set up and conducted at a NASA MSFC test facility. All testing was completed in the summer of 2014, and this paper documents the results of that testing and the associated fluid system modeling efforts.

Williams, Hunter↗

NASA NTRS2001

Optimized suspension culture: the rotating-wall vessel

Suspension culture remains a popular modality, which manipulates mechanical culture conditions to maintain the specialized features of cultured cells. The rotating-wall vessel is a suspension culture vessel optimized to produce laminar flow and minimize the mechanical stresses on cell aggregates in culture. This review summarizes the engineering principles, which allow optimal suspension culture conditions to be established, and the boundary conditions, which limit this process. We suggest that to minimize mechanical damage and optimize differentiation of cultured cells, suspension culture should be performed in a solid-body rotation Couette-flow, zero-headspace culture vessel such as the rotating-wall vessel. This provides fluid dynamic operating principles characterized by 1) solid body rotation about a horizontal axis, characterized by colocalization of cells and aggregates of different sedimentation rates, optimally reduced fluid shear and turbulence, and three-dimensional spatial freedom; and 2) oxygenation by diffusion. Optimization of suspension culture is achieved by applying three tradeoffs. First, terminal velocity should be minimized by choosing microcarrier beads and culture media as close in density as possible. Next, rotation in the rotating-wall vessel induces both Coriolis and centrifugal forces, directly dependent on terminal velocity and minimized as terminal velocity is minimized. Last, mass transport of nutrients to a cell in suspension culture depends on both terminal velocity and diffusion of nutrients. In the transduction of mechanical culture conditions into cellular effects, several lines of evidence support a role for multiple molecular mechanisms. These include effects of shear stress, changes in cell cycle and cell death pathways, and upstream regulation of secondary messengers such as protein kinase C. The discipline of suspension culture needs a systematic analysis of the relationship between mechanical culture conditions and biological effects, emphasizing cellular processes important for the industrial production of biological pharmaceuticals and devices.

Non-NASA Center↗

NASA NTRS2010

Freezable Radiator Model Correlation and Full Scale Design

Freezable radiators offer an attractive solution to the issue of thermal control system scalability. As thermal environments change, a freezable radiator will effectively scale the total heat rejection it is capable of as a function of the thermal environment and flow rate through the radiator. Scalable thermal control systems are a critical technology for spacecraft that will endure missions with widely varying thermal requirements. These changing requirements are a result of the space craft s surroundings and because of different thermal loads during different mission phases. However, freezing and thawing (recovering) a radiator is a process that has historically proven very difficult to predict through modeling, resulting in highly inaccurate predictions of recovery time. This paper summarizes efforts made to correlate a Thermal Desktop (TM) model with empirical testing data from two test articles. A 50-50 mixture of DowFrost HD and water is used as the working fluid. Efforts to scale this model to a full scale design, as well as efforts to characterize various thermal control fluids at low temperatures are also discussed.

Lillibridge, Sean T.↗

NASA NTRS2011

Freezable Radiator Model Correlation Improvements and Fluids Study

Freezable radiators offer an attractive solution to the issue of thermal control system scalability. As thermal environments change, a freezable radiator will effectively scale the total heat rejection it is capable of as a function of the thermal environment and flow rate through the radiator. Scalable thermal control systems are a critical technology for spacecraft that will endure missions with widely varying thermal requirements. These changing requirements are a result of the space craft s surroundings and because of different thermal rejection requirements during different mission phases. However, freezing and thawing (recovering) a radiator is a process that has historically proven very difficult to predict through modeling, resulting in highly inaccurate predictions of recovery time. To attempt to improve this, tests were conducted in 2009 to determine whether the behavior of a simple stagnating radiator could be predicted or emulated in a Thermal Desktop(trademark) numerical model. A 50-50 mixture of DowFrost HD and water was used as the working fluid. Efforts to scale this model to a full scale design, as well as efforts to characterize various thermal control fluids at low temperatures are also discussed. Previous testing and modeling efforts showed that freezable radiators could be operated as intended, and be fairly, if not perfectly predicted by numerical models. This paper documents the improvements made to the numerical model, and outcomes of fluid studies that were determined necessary to go forward with further radiator testing.

Lillibridge, Sean↗

NASA NTRS2012

Supercritical CO2 Cleaning System for Planetary Protection and Contamination Control Applications

Current spacecraft-compatible cleaning protocols involve a vapor degreaser, liquid sonication, and alcohol wiping. These methods are not very effective in removing live and dead microbes from spacecraft piece parts of slightly complicated geometry, such as tubing and loosely fitted nuts and bolts. Contamination control practices are traditionally focused on cleaning and monitoring of particulate and oily residual. Vapor degreaser and outgassing bakeout have not been proven to be effective in removing some less volatile, hydrophilic biomolecules of significant relevance to life detection. A precision cleaning technology was developed using supercritical CO2 (SCC). SCC is used as both solvent and carrier for removing organic and particulate contaminants. Supercritical fluid, like SCC, is characterized by physical and thermal properties that are between those of the pure liquid and gas phases. The fluid density is a function of the temperature and pressure. Its solvating power can be adjusted by changing the pressure or temperature, or adding a secondary solvent such as alcohol or water. Unlike a regular organic solvent, SCC has higher diffusivities, lower viscosity, and lower surface tension. It readily penetrates porous and fibrous solids and can reach hard-to-reach surfaces of the parts with complex geometry. Importantly, the CO2 solvent does not leave any residue. The results using this new cleaning device demonstrated that both supercritical CO2 with 5% water as a co-solvent can achieve cleanliness levels of 0.01 mg/cm2 or less for contaminants of a wide range of hydrophobicities. Experiments under the same conditions using compressed Martian air mix, which consists of 95% CO2, produced similar cleaning effectiveness on the hydrophobic compounds. The main components of the SCC cleaning system are a high-pressure cleaning vessel, a boil-off vessel located downstream from the cleaning vessel, a syringe-type high-pressure pump, a heat exchanger, and a back pressure regulator (BPR). After soaking the parts to be cleaned in the clean vessel for a period, the CO2 with contaminants is flushed out of the cleaning vessel using fresh CO2 in a first-in-first-out (FIFO) method. The contaminants are either precipitating out in the boil-off container or being trapped in a filter subsystem. The parts to be cleaned are secured in a basket inside and can be rotated up to 1,400 rpm by a magnetic drive. The fluid flows within the vessel generate tangential forces on the parts surfaces, enhancing the cleaning effectiveness and shortening the soaking time. During the FIFO flushing, the pump subsystem pushes fresh CO2 into the cleaning vessel at a constant flow rate between 0.01 and 200 mL/min, while the BPR regulates the pressure in the cleaning vessel to within 0.1 bar by controlling the needle position in an outlet valve. The fresh CO2 gas flows through the heat exchanger at a given temperature before entering the cleaning vessel. A platinum resistance thermometer (PRT) reads the cleaning vessel interior temperature that can be controlled to within 0.1 K. As a result, cleaning vessel temperature remains constant during the FIFO flushing. There is no change in solvent power during FIFO flushing since both temperature and pressure inside the cleaning vessel remain unchanged, thus minimizing contaminants left behind. During decompression, both temperature and pressure are strictly controlled to prevent bubbles from generating in the cleaning vessel that could stir up the contaminants that sank to the bottom by gravity.

Lin, Ying↗

NASA NTRS1987

The coupled dynamics of fluids and spacecraft in low gravity and low gravity fluid measurement

The very large mass fraction of liquids stored on broad current and future generation spacecraft has made critical the technologies of describing the fluid-spacecraft dynamics and measuring or gauging the fluid. Combined efforts in these areas are described, and preliminary results are presented. The coupled dynamics of fluids and spacecraft in low gravity study is characterizing the parametric behavior of fluid-spacecraft systems in which interaction between the fluid and spacecraft dynamics is encountered. Particular emphasis is given to the importance of nonlinear fluid free surface phenomena to the coupled dynamics. An experimental apparatus has been developed for demonstrating a coupled fluid-spacecraft system. In these experiments, slosh force signals are fed back to a model tank actuator through a tunable analog second order integration circuit. In this manner, the tank motion is coupled to the resulting slosh force. Results are being obtained in 1-g and in low-g (on the NASA KC-135) using dynamic systems nondimensionally identical except for the Bond numbers.

Hansman, R. John↗

NASA NTRS1991

Characterizing He II flow through porous materials using counterflow data

An empirical extension of the two-fluid model is used to characterize He II flow through porous materials. It is shown that four empirical parameters are necessary to describe the pressure and temperature differences induced by He II flow through a porous sample. The three parameters required to determine pressure differences are measured in counterflow and found to compare favorably with those for isothermal flow. The fourth parameter, the Gorter-Mellink constant, differs substantially from smooth tube values. It is concluded that parameter values determined from counterflow can be used to predict pressure and temperature differences in a variety of flows to an accuracy of about +/- 20 percent.

Maddocks, J. R.↗