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NASA NTRS2005

Navier-Stokes Computations With One-Equation Turbulence Model for Flows Along Concave Wall Surfaces

This report presents the use of a time-marching three-dimensional compressible Navier-Stokes equation numerical solver with a one-equation turbulence model to simulate the flow fields developed along concave wall surfaces without and with a downstream extension flat wall surface. The 3-D Navier- Stokes numerical solver came from the NASA Glenn-HT code. The one-equation turbulence model was derived from the Spalart and Allmaras model. The computational approach was first calibrated with the computations of the velocity and Reynolds shear stress profiles of a steady flat plate boundary layer flow. The computational approach was then used to simulate developing boundary layer flows along concave wall surfaces without and with a downstream extension wall. The author investigated the computational results of surface friction factors, near surface velocity components, near wall temperatures, and a turbulent shear stress component in terms of turbulence modeling, computational mesh configurations, inlet turbulence level, and time iteration step. The computational results were compared with existing measurements of skin friction factors, velocity components, and shear stresses of the developing boundary layer flows. With a fine computational mesh and a one-equation model, the computational approach could predict accurately the skin friction factors, near surface velocity and temperature, and shear stress within the flows. The computed velocity components and shear stresses also showed the vortices effect on the velocity variations over a concave wall. The computed eddy viscosities at the near wall locations were also compared with the results from a two equation turbulence modeling technique. The inlet turbulence length scale was found to have little effect on the eddy viscosities at locations near the concave wall surface. The eddy viscosities, from the one-equation and two-equation modeling, were comparable at most stream-wise stations. The present one-equation turbulence model is an effective approach for turbulence modeling in the near solid wall surface region of flow over a concave wall.

Wang, Chi R.↗

NASA NTRSDate not supplied

Comparison of Convective Heat Transfer Correlations and Their Application to NTP Reactors

This study analyzes various Nusselt number and friction factor correlations and applies them to a Small Nuclear Rocket Engine model with a Sinusoidal power distribution profile to understand their effects on the temperatures and pressures inside the reactor. A nodal thermal hydraulic solver was used to determine the fluid and channel surface temperatures while also incorporating variable fluid properties and channel roughness. The results showed that the considered friction factors could essentially be used interchangeably given that their difference affected the pressure by less than 1%. However, large variations in the tube surface temperature were obtained for the different Nusselt numbers while the fluid temperature distribution was forced to remain the same. Supersonic flow conditions presented by Maynard Taylor are investigated to serve as a baseline for how experimental errors can lead to uncertainties in the reported empirical correlations. Detailed experimental investigation is necessary to determine the Nusselt number correlation that will provide the best prediction of the thermal hydraulic performance inside the reactor fluid flow channels.

Nuclear Thermal Propulsion↗

NASA NTRS1971

Optimization of conical hydrostatic bearing for minimum friction.

Equations for the flow rate, load capacity, and friction torque for a conical hydrostatic bearing were developed. These equations were solved by a digital computer program to determine bearing configurations for minimum friction torque. Design curves are presented that show optimal bearing dimensions for minimum friction torque as a function of dimensionless flow rate for a range of dimensionless load capacity. Results are shown for both laminar and turbulent flow conditions. The results indicate that hydrostatic pocket friction is a significant portion of the total friction torque. However, the bearing dimensions for a minimum friction design are affected very little by inclusion of pocket friction in the analysis. For laminar flow the values of the outer-land radius ratio X3 and outer bearing radius ratio X4 did not change significantly with increasing friction factor. For turbulent flow, the outer bearing radius ratio X4 did not change with increasing friction factor; therefore the value determined for X4 in the laminar flow case is valid for all turbulent flows.

Nypan, L. J.↗

NASA NTRS1993

Oscillating flow and heat transfer in a channel with sudden cross section change

We have computationally examined oscillating flow (zero mean) between two parallel plates with a sudden change in cross section. The flow was assumed to be laminar incompressible with the inflow velocity uniform over the channel cross section but varying sinusoidally with time. The cases studied cover wide ranges of Re(sub max) (from 187.5 to 2000), Va (from 1 to 10.66), the expansion ratio (1:2 and 1:4) and A(sub r) (2 and 4). Also, three different geometric cases were discussed: (1) asymmetric expansion/contraction; (2) symmetric expansion/contraction; and (3) symmetric blunt body. For these oscillating flow conditions, the fluid undergoes sudden expansion in one-half of the cycle and sudden contraction inthe other half. The instantaneous friction factor, for some ranges of Re(sub max) and Va, deviated substantially from the steady-state friction factor for the same flow parameters. A region has been identified below which the flow is laminar quasi-steady. A videotape showing computer simulations of the oscillating flow demonstrates the usefulness of the current analyses in providing information on the transient hydraulic phenomena.

Ibrahim, Mounir↗

NASA NTRS1995

Numerical thermal analyses of heat exchangers for the stirling engine application

The Regenerator, Cooler and Heater for the NASA Space Power Research Engine (SPRE) have been analyzed in detail for laminar, incompressible and oscillatory flow conditions. Each component has been analyzed independently and in detail with the regenerator being modeled as two-parallel-plates channel with a solid wall. The ends of the channel are exposed to two reservoir maintained at different temperature thus providing an axial temperature gradient along the channel. The cooler and heater components have been modeled as circular pipes with isothermal walls. Two different types of thermal boundary conditions have been investigated for the cooler and heater, namely, symmetric and asymmetric temperature inflow. In symmetric temperature inflow the flow enters the channel with the same temperature in throughout the velocity cycle whereas, in asymmetric temperature inflow the flow enters with a different temperature in each half cycle. The study was conducted over a wide range of Maximum Reynolds number (RE(max) varying from 75 to 60000, Valensi number (Va) from 2.5 to 800, and relative amplitude of fluid displacement (A(sub r) from 0.357 to 1.34. A two dimensional Finite volume method based on the SIMPLE algorithm was used to solve the governing partial differential equations. Post processing programs were developed to effectively describe the heat transfer mechanism under oscillatory flows. The computer code was validated by comparing with existing analytical solutions for oscillating flows. The thermal field have been studied with the help of temperature contour and three dimensional plots. The instantaneous friction factor, wall heat flux and heat transfer coefficient have been examined. It has been concluded that in general, the frictional factor and heat transfer coefficient are higher under oscillatory flow conditions when the Valensi number is high. Also, the thermal efficiency decreases for lower A(r) values. Further, the usual steady state definition for the heat transfer coefficient does not seem to be valid.

Kannapareddy, Mohan Raj↗

NASA NTRS1993

Supersonic boundary-layer flow turbulence modeling

Baldwin-Lomax and kappa-epsilon turbulence models were modified for use in Navier-Stokes numerical computations of Mach 2.9 supersonic turbulent boundary layer flows along compression ramps. The computational results of Reynolds shear stress profiles were compared with experimental data. The Baldwin-Lomax model was modified to account for the Reynolds shear stress amplification within the flow field. A hybrid kappa-epsilon model with viscous sublayer turbulence treatment was constructed to predict the Reynolds shear stress profiles within the entire flow field. These modified turbulence models were effective for the computations of the surface pressure and the skin friction factor variations along an 8 deg ramp surface. The hybrid kappa-epsilon model could improve the predictions of the Reynolds shear stress profile and the skin friction factor near the corner of a 16 deg ramp.

Wang, Chi-Rong↗

NASA NTRS1987

SSME seal test program: Test results for smooth, hole-pattern and helically-grooved stators

All of the listed seals were tested in a liquid Halon test facility at high Reynolds numbers. In addition, a helically-grooved-stator seal was tested in an air seal facility. An analysis of the test results with comparisons to theoretical predictions supports the following conclusions: (1) For small seals, the Hirs' friction-factor model is more restricted than had been thought; (2) For smooth seals, predictions of stiffness and damping improve markedly as the radical clearance is reduced; (3) Friction-factor data for hole-pattern-seal stators frequently deviates from the Hirs model; (4) Predictions of stiffness and damping coefficients for hole-pattern-stator seals is generally reasonable; (5) Tests for the hole-pattern stators at reduced clearances show no clear optimum for hole-pattern seals with respect to either hole-area ratio or hole depth to minimum clearance ratios; (6) Tests of these hole-pattern stators show no significant advantage in net damping over smooth seals; (7) Tests of helically-grooved seal stators in Halon show reasonable agreement between theory and prediction for leakage and direct stiffness but poor agreement for the net damping coefficient.

Childs, Dara W.↗

NASA NTRS2001

Development of Flow and Heat Transfer Models for the Carbon Fiber Rope in Nozzle Joints of the Space Shuttle Reusable Solid Rocket Motor

Methodologies have been developed for modeling both gas dynamics and heat transfer inside the carbon fiber rope (CFR) for applications in the space shuttle reusable solid rocket motor joints. Specifically, the CFR is modeled using an equivalent rectangular duct with a cross-section area, friction factor and heat transfer coefficient such that this duct has the same amount of mass flow rate, pressure drop, and heat transfer rate as the CFR. An equation for the friction factor is derived based on the Darcy-Forschheimer law and the heat transfer coefficient is obtained from pipe flow correlations. The pressure, temperature and velocity of the gas inside the CFR are calculated using the one-dimensional Navier-Stokes equations. Various subscale tests, both cold flow and hot flow, have been carried out to validate and refine this CFR model. In particular, the following three types of testing were used: (1) cold flow in a RSRM nozzle-to-case joint geometry, (2) cold flow in a RSRM nozzle joint No. 2 geometry, and (3) hot flow in a RSRM nozzle joint environment simulator. The predicted pressure and temperature history are compared with experimental measurements. The effects of various input parameters for the model are discussed in detail.

Wang, Q.↗

NASA NTRS1959

Experimental Investigation of Gas-Side Performance of a Compact Finned-Tube Heat Exchanger

Heat-transfer and pressure-drop data were obtained experimentally for the gas side of a liquid-metal to air, compact finned-tube heat exchanger. The heat exchanger was fabricated from 0.185-inch Inconel tubing in an inline array. The fins were made of 310 stainless-steel- clad copper with a total thickness of 0.010 inch, and the fin pitch was 15.3 fins per inch. The liquid used as the heating medium was sodium. The heat-exchanger inlet gas temperature was varied from 5100 to 1260 R by burning JP fuel for airflow rates of 0.4 to 10.5 pounds per second corresponding to an approximate Reynolds number range of 300 to 9000. The sodium inlet temperature was held at 1400 R with the exception of a few runs taken at 1700 and 1960 R. The maximum ratio of surface temperature to air bulk temperature was 1.45. Friction-factor data with heat transfer were best represented by a single line when the density and viscosity of Reynolds number were evaluated at the average film temperature. At the lower Reynolds numbers reported, the friction data with heat transfer plotted slightly above the friction data without heat transfer. The density of the friction factor was calculated at the average bulk temperature. Heat-transfer results of this investigation were correlated by evaluating the physical properties of air (specific heat, viscosity, and thermal conductivity) at the film temperature.

Gedeon, Louis↗

NASA NTRS1994

Turbulence models and Reynolds analogy for two-dimensional supersonic compression ramp flow

Results of the application of turbulence models and the Reynolds analogy to the Navier-Stokes computations of Mach 2.9 two-dimensional compression ramp flows are presented. The Baldwin-Lomax eddy viscosity model and the kappa-epsilon turbulence transport equations for the turbulent momentum flux modeling in the Navier-Stokes equations are studied. The Reynolds analogy for the turbulent heat flux modeling in the energy equation was also studied. The Navier-Stokes equations and the energy equation were numerically solved for the flow properties. The Reynolds shear stress, the skin friction factor, and the surface heat transfer rate were calculated and compared with their measurements. It was concluded that with a hybrid kappa-epsilon turbulence model for turbulence modeling, the present computations predicted the skin friction factors of the 8 deg and 16 deg compression ramp flows and with the turbulent Prandtl number Pr(sub t) = 0.93 and the ratio of the turbulent thermal and momentum transport coefficients mu(sub q)/mu(sub t) = 2/Prt, the present computations also predicted the surface heat transfer rates beneath the boundary layer flow of the 16 compression ramp.

Wang, Chi R.↗

NASA NTRS1992

Dynamic light scattering analysis of solutions from which lysozyme crystals grow

The variation of the friction factor was measured by photon correlation spectroscopy during isothermal growth of chicken egg white lysozyme crystals. It was observed to initially increase to a maximum as crystals formed, and then to decrease to a constant value. The change in the friction factors was measured as a function of temperature at concentrations of lysozyme varying from one sufficiently low that molecular interactions were undetectable to concentrations near those at which crystals grow in solutions, in all cases the ionic strength was below that required for crystallization.

Bishop, J. B.↗

NASA NTRS1999

Predicting Turbulent Convective Heat Transfer in Three-Dimensional Duct Flows

The performance of an explicit algebraic stress model is assessed in predicting the turbulent flow and forced heat transfer in straight ducts, with square, rectangular, trapezoidal and triangular cross-sections, under fully developed conditions over a range of Reynolds numbers. Iso-thermal conditions are imposed on the duct walls and the turbulent heat fluxes are modeled by gradient-diffusion type models. At high Reynolds numbers (>/= 10(exp 5)), wall functions are used for the velocity and temperature fields; while at low Reynolds numbers damping functions are introduced into the models. Hydraulic parameters such as friction factor and Nusselt number are well predicted even when damping functions are used, and the present formulation imposes minimal demand on the number of grid points without any convergence or stability problems. Comparison between the models is presented in terms of the hydraulic parameters, friction factor and Nusselt number, as well as in terms of the secondary flow patterns occurring within the ducts.

Rokni, M.↗

NASA NTRSDate not supplied

Comparison of Convective Heat Transfer Correlations and Their Application to Nuclear Thermal Propulsion Reactors

Experiment↗

NASA NTRS1981

Characterization of superfluid helium transfer

The friction factor and steady state flow rate of superfluid helium (He II) are measured, with the driving pressure difference generated by the saturated vapor pressure and a small hydrostatic pressure head. The temperature ranged from 1.5 K to the transition temperature of 2.17 K. Three different lengths and two different internal diameters were used for the stainless steel transfer tubes, and the transfer of liquid helium (He I) was investigated with the same apparatus for comparison. It was found that the friction factor of He II is greater than that of He I for pressure differences greater than 20 mm Hg, and smaller below that magnitude.

Yang, L. C.↗

NASA NTRS1991

Linearized force representations for turbopump liquid annular seals

The analysis and the accompanying FORTRAN code, SEALPAL1, to simulate liquid annular seals with axial taper, Moody friction factors, and pre-swirl, are discussed. The output of the code includes all dynamic coefficients (stiffness, dampings, and inertias), leakage rate, torque, and horsepower loss. The computer code results were compared with five cases from the literature. The agreement was very good in almost all instances, except several predicted cross coupled stiffnesses were significantly lower than those appearing in the literature. This disagreement could reflect a theoretical or a programming error by the researcher or in the literature, or it could be a result of the difference in friction factor models or other assumptions employed.

Palazzolo, Alan B.↗

NASA NTRS2001

Predicting Turbulent Convective Heat Transfer in Fully Developed Duct Flows

The performance of an explicit algebraic stress model (EASM) is assessed in predicting the turbulent flow and forced heat transfer in both straight and wavy ducts, with rectangular, trapezoidal and triangular cross-sections, under fully developed conditions. A comparison of secondary flow patterns. including velocity vectors and velocity and temperature contours, are shown in order to study the effect of waviness on flow dynamics, and comparisons between the hydraulic parameters. Fanning friction factor and Nusselt number, are also presented. In all cases. isothermal conditions are imposed on the duct walls, and the turbulent heat fluxes are modeled using gradient-diffusion type models. The formulation is valid for Reynolds numbers up to 10(exp 5) and this minimizes the need for wall functions that have been used with mixed success in previous studies of complex duct flows. In addition, the present formulation imposes minimal demand on the number of grid points without any convergence or stability problems. Criteria in terms of heat transfer and friction factor needed to choose the optimal wavy duct cross-section for industrial applications among the ones considered are discussed.

Rokni, Masoud↗

NASA NTRS1992

Heat transfer in thin, compact heat exchangers with circular, rectangular, or pin-fin flow passages

Heat transfer and pressure drop have been measured of three thin, compact heat exchangers in helium gas at 3.5 MPa and higher, with Reynolds numbers of 450 to 36,000. The flow geometries for the three heat exchanger specimens were: circular tube, rectangular channel, and staggered pin fin with tapered pins. The specimens were heated radiatively at heat fluxes up to 77 W/sq cm. Correlations were developed for the isothermal friction factor as a function of Reynolds number, and for the Nusselt number as a function of Reynolds number and the ratio of wall temperature to fluid temperature. The specimen with the pin fin internal geometry had significantly better heat transfer than the other specimens, but it also had higher pressure drop. For certain conditions of helium flow and heating, the temperature more than doubled from the inlet to the outlet of the specimens, producing large changes in gas velocity, density, viscosity, and thermal conductivity. These changes in properties did not affect the correlations for friction factor and Nusselt number in turbulent flow.

Olson, D. A.↗

NASA NTRS1959

Analysis of Turbulent Flow and Heat Transfer in Noncircular Passages

Previous work on turbulent heat transfer and flow in tubes was generalized and applied to flow in non-circular passages of equilateral triangular and square cross section. Expressions for eddy diffusivity that had been verified for flow and heat transfer in tubes were assumed to apply in general along lines normal to a wall. Velocity distributions, wall shear-stress distributions, and friction factors, as well as wall heat-transfer distributions, wall temperature distributions, and average heat-transfer coefficients were calculated. In addition, results from a previous analysis for axial flow between rods were compared with new experimental data. For calculating wall temperature distributions, uniform heat generation in the passage wall and uniform heat transfer at the outer surface were assumed. The application of the results is restricted to moderately small peripheral wall temperature variations. Calculations were made for Reynolds numbers from 20,000 to 900,000 and Prandtl numbers from 0.73 to 300. Results show that velocities, shear stresses, and heat transfer in the region near the corner were lower than average values and were zero at the corner. Friction factors and average Nusselt numbers were lower than in a tube.

Taylor, Maynard F.↗