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At least 145 records · Page 8

Grid-generated isotropic homogeneous turbulence at high Reynolds numbers

Consideration is given to an empirical formula for the longitudinal correlation function for grid-generated incompressible fluid turbulence at Reynolds numbers above 12,800. The formula, which relates the longitudinal correlation function to the inverse cube of a dimensionless geometrical ratio, is shown to minimize the global correlation integrals into which the two-point velocity correlation tensor has been substituted subject to a global constraint on the Sobolev concomitent of the longitudinal correlation function. Furthermore, the energy spectrum function associated with the empirical formula is shown to satisfy a tertiary Helmholtz-type linear condition throughout the initial period of decay.

Rosen, G.↗

Development of thermal stratification and destratification scaling concepts. Volume 1: Definition of thermal stratification scaling parameters and experimental investigations

The dimensionless parameters associated with the thermal stratification and pressure history of a heated container of liquid and its vapor were examined. The Modified Grashof number, the Fourier number, and an Interface number were parameterized using a single test liquid, Freon 113. Cylindrical test tanks with spherical dome end caps were built. Blanket heaters covered the tanks and thermocouples monitored the temperatures of the liquid, the ullage, the tank walls, and the foam insulation encapsulating the tank. A centrifuge was used for the 6 inch tank to preserve the same scaling parameter values between it and the larger tanks. Tests were conducted over a range of Gr* values and the degree of scaling was checked by comparing the dimensionless pressures and temperatures for each scaled pair of tests. Results indicate that the bulk liquid temperature, the surface temperature of the liquid, and the tank pressure can be scaled with the three dimensionless parameters. Some deviation was, however, found in the detailed temperature profiles between the scaled pairs of tests.

Lovrich, T. N.↗

Numerical investigation of the thermal stratification in cryogenic tanks subjected to wall heat flux

The flow pattern and thermal stratification of a cryogenic cylindrical tank are numerically studied. The tank sidewall is subjected to either a uniform heat-flux or two discrete levels of uniform heat-flux at the upper and lower halves of the tank wall. The tank bottom is kept at a constant temperature controlled by the heat exchanger of a thermodynamic vent system. The tank pressure is also assumed constant resulting in a constant saturation temperature at the interface which is higher than the tank bottom temperature. The effects of vapor motion and vapor superheat on the mass and heat transfer processes at the interface are assumed negligible such that the calculations of liquid region can be decoupled from the vapor region. Dimensionless steady-state conservation equations are solved by a finite-difference method. The effects of modified Rayleigh number, Prandtl number, tank aspect ratio, wall heat-flux parameter, and wall heat-flux distribution on the liquid velocity and temperature fields are investigated. Also, their effects on the rate of heat transfer through the interface and the tank bottom are examined.

Lin, Chin-Shun↗

Numerical investigation of the thermal stratification in cryogenic tanks subjected to wall heat flux

The flow pattern and thermal stratification of a cryogenic cylindrical tank are numerically studied. The tank sidewall is subjected to either a uniform heat-flux or two discrete levels of uniform heat-flux at the upper and lower halves of the tank wall. The tank bottom is kept at a constant temperature controlled by the heat exchanger of a thermodynamic vent system. The tank pressure is also assumed constant resulting in a constant saturation temperature at the interface which is higher than the tank bottom temperature. The effects of vapor motion and vapor superheat on the mass and heat transfer processes at the interface are assumed negligible such that the calculations of liquid region can be decoupled from the vapor region. Dimensionless steady-state conservation equations are solved by a finite-difference method. The effects of modified Rayleigh number, Prandtl number, tank aspect ratio, wall heat-flux parameter, and wall heat-flux distribution on the liquid velocity and temperature fields are investigated. Also, their effects on the rate of heat transfer through the interface and the tank bottom are examined.

Lin, Chin-Shun↗

Further Experiments on the Flow and Heat Transfer in a Heated Turbulent Air Jet

Measurements have been made of the mean total-head and temperature fields in a round turbulent jet with various initial temperatures. The results show that the jet spreads more rapidly as its density becomes lower than that of the receiving medium, even when the difference is not sufficiently great to cause measurable deviations from the constant-density, dimensionless, dynamic-pressure profile function. Rough analytical considerations have given the same relative spread. The effective "turbulent Prandtl number" for a section of the fully developed jet was found to be equal to the true (laminar) Prandtl number within the accuracy of measurement. (author)

FLOW - JETS↗

Heat Transfer from Cylinders in Transition From Slip Flow to Free-Molecule Flow

Over 600 measured heat-transfer coefficients in the transition from slip to free-molecule flow have been correlated by using the Nusselt number Nu as a function of the Knudsen Kn and Reynolds Re (or Mach M) numbers. The experimental range for these heat-transfer data from transverse cylinders in air corresponds to the following dimensionless groups: M, 0.10 to 0.90; Re, 0.03 to 11.5; Kn, 0.10 to 5.0. The total air temperature T(sub t) was maintained constant at 80 F, but wire temperature was Varied from 150 to 580 F. At Kn=0.10, Nu extrapolates smoothly into slip-flow empirical curves that show Nu as a function of Re and M or Kn. The correlation gradually changes from the square root of Re(sub t) dependence characteristic of continuum flow to first-power Re dependence as Kn increases (decreasing Re). At the experimental limit Kn ft 5.0, the Nu data correlate with a mean fractional error of 413 percent by the prediction of free-molecule-flow theory. In comparing experimental results with theory, an accommodation coefficient of 0.57+/-0.07 was inferred from the heat-transfer data, which were obtained with etched tungsten wire in air. The wire recovery temperature T(sub e) was measured and compared with existing data and theory in terms of a ratio eta(equivalent to T(sub e)/T(sub t). The results can be divided into three groups by Kn criteria: For Kn less than 2.01, eta is independent of Kn, and eta decreases from 1.0 to 0.97 as M increases from 0 to 0.90; for 2.0 less than Kn less than 5.0, eta is a function of both Kn and M in this transition region to fully developed free-molecule flow; and for Kn greater than 5.0, eta predicted by free-molecule-flow theory is observed and increases from 1.0 to 1.08 as M increases from 0 to 0.90, again independent of Kn. Therefore, these T(sub e) data provide a guide to the boundary of fully developed free-molecule flow, which is.inferred from this research to exist for Kn greater than 5.0. This boundary criterion is substantiated by other published data on T(sub e) at supersonic speeds.

Cybulski, Ronald J.↗

The Dynamics of Miscible Interfaces: A Space Flight Experiment

This report presents experiments of a less viscous liquid displaced by a more viscous, miscible liquid in a vertical tube of small diameter. The liquids used are silicone oils of various viscosities. The more viscous fluid has a higher density than the less viscous fluid. The experiments showed that the interface between the liquids can be unstable and exhibits an asymmetric, sinuous shape for downward displacement. The Reynolds number is negligibly small in these experiments and the Peclet number for mass transfer is O(50)-0(l0(exp 5)). The influence of gravity is characterized by the dimensionless parameter F=g(Delta)(rho)d(sup 2)/(mu)U where g is the acceleration due to gravity, Delta(rho) is the density difference between the fluids, d is the tube diameter, mu is the viscosity of the more viscous fluid, and U is the displacement speed. Visualization and PIV measurement of the unstable linger are reported. Experiments were also conducted to study immiscible displacements in tubes in order to compare with previously obtained results for miscible fluids.

Maxworthy, Tony↗

Stagnation region gas film cooling: Effects of dimensionless coolant temperature

An experimental investigation was conducted to mode the film cooling performance for a turbine vane leading edge using the stagnation region of a cylinder in cross flow. Experiments were conducted with a single row of spanwise angled (25 deg) coolant holes for a range of the coolant blowing ratio and dimensionless coolant temperature with free stream-to-wall temperature ratio approximately 1.7 and Re sub D = 90000. the cylindrical test surface was instrumented with miniature heat flux gages and wall thermocouples to determine the percentage reduction in the Stanton number as a function of the distance downstream from injection (x/d sub 0) and the location between adjacent holes (z/S). Data from local heat flux measurements are presented for injection from a single row located at 5 deg, 22.9 deg, 40.8 deg, from stagnation using a hole spacing ratio of S/d = 5. The film coolant was injected with T sub c T sub w with a dimensionless coolant temperature in the range 1.18 or equal to theta sub c or equal to 1.56. The data for local Stanton Number Reduction (SNR) showed a significant increase in SNR as theta sub c was increased above 1.0.

Bonnice, M. A.↗

Pressure loss modulus correlation for Delta p across uniformly distributed-loss devices

A dimensionless group, called a pressure loss modulus (N(sub PL)), is introduced that, in conjunction with an appropriately defined Reynolds number, is of considerable engineering utility in correlating steady-state Delta p vs flow calibration data and subsequently as a predictor, using the same or a different fluid, in uniformly distributed pressure loss devices. It is particularly useful under operation in the transition regime. Applications of this simple bivariate correlation to three diverse devices of particular interest for small liquid rocket engine fluid systems are discussed: large L/D capillary tube restrictors, packed granular catalyst beds, and stacked vortex-loss disk restrictors.

Nunz, Gregory J.↗

Spray measurements of aerothermodynamic effect on disintegrating liquid jets

An experimental investigation was made to determine the effect of atomizing gas mass flux and temperature on liquid jet breakup in sonic velocity gas flow. Characteristic drop size data were obtained by using the following atomizing gases: nitrogen, argon, and helium to breakup water jets in high velocity gas flow. A scattered light scanning instrument developed at Lewis Research Center was used to measure Sauter mean diameter (SMD). The three gases gave a molecular weight range of 4 to 40 and atomizing gas mass flux and temperature were varied from 6 to 50 g/sq cm and 275-400 K, respectively. The ratio of liquid jet diameter to SMD, D(sub 0)/D(sub 32), was correlated with aerodynamic and liquid-surface force ratios, i.e., the product of the Weber and Reynolds number, We Re, the gas to liquid density ratio, rho(sub g)/rho(sub 1) g and also the molecular scale dimensionless group, rho(sub 1)(Vm exp 3)/ mu(sub 1) g, to give the following expression: D(sub 0)/D(sub 32) = 0.90 x 10(exp -8) x (We Re rho sub g/rho sub 1)exp 0.44 x (rho sub 1 Vm exp 3/mu sub 1 g)exp 0.67 where We Re = ((rho sub g)exp 2(D sub 0)exp 2(V sub C)exp3))/ mu sub 1 sigma, mu sub 1 is liquid viscosity, sigma is surface tension, V sub C is the acoustic gas velocity, V sub m is the RMS velocity of gas molecules, and g is the acceleration of gas molecules due to gravity. Good agreement was obtained with atomization theory for liquid-jet breakup in the regime of aerodynamic stripping. Also, due to its low molecular weight and high acoustic velocity, helium was considerably more effective than nitrogen or argon in producing small-droplet sprays with values of D(sub 32) on the order of 5 microns.

Ingebo, Robert D.↗

A turbulence module for the NPARC code

A turbulence module is developed for the 2D version of the NPARC code which is currently restricted to planar or axisymmetric flows without swirling. Four turbulence models have been built into the module: Baldwin-Lomax, Chien, Shih-Lumley and CMOTT models. The first is a mixing-length eddy-viscosity model which is mainly used for initialization of computational fields and the last three are the low Reynolds number two-equation models. Unlike chien's model, both the Shih-Lumley and CMOTT models do not involve the dimensionless wall distance y(sup +), an advantage for separated flow calculations. Contrary to the NPARC and most other compressible codes, the non-delta form of transport equations is used which leads to a simpler linearization and is more effective than using the delta form in ensuring the positiveness of the turbulent kinetic energy and its dissipation rate. To reduce numerical diffusion while maintaining necessary stability, a second-order accurate and bounded scheme is used for the convective terms of the turbulent transport equations. This scheme is implemented in a deferred correction manner so that the main coefficients of the resulting difference equations are always positive, thus making the numerical solutions process unconditionally stable. The system of equations is solved via a decoupled method and by the alternating direction TDMA of Thomas. The module can be easily linked to the NPARC code for turbulent flow calculations.

Zhu, J.↗

High Reynolds number and turbulence effects on aerodynamics and heat transfer in a turbine cascade

Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.5 x 10 exp 6 and a range of turbulence intensities from 1.8 to about 15 percent. The purpose of this study was to obtain fundamental heat transfer and pressure distribution data over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range of Reynolds numbers encountered in the Space Shuttle main engine (SSME) turbopump turbines. Specifically, the study aimed to determine (1) the effect of Reynolds number on heat transfer, (2) the effect of upstream turbulence on heat transfer and pressure distribution, and (3) the relationship between heat transfer at high Reynolds numbers and the current data base. The results of this study indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparison of the experimental results were also made with a numerical solution from a two-dimensional Navier-Stokes code.

Yeh, Frederick C.↗

High Reynolds number and turbulence effects on aerodynamics and heat transfer in a turbine cascade

Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.5 million and a range of turbulence intensities from 1.8 to about 15 percent. Fundamental heat transfer and pressure distribution data are obtained over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range of Reynolds numbers encountered in the SSME turbopump turbines. The results obtained indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparison of the experimental results were also made with a numerical solution from a 2D Navier-Stokes code.

Yeh, Frederick C.↗

Exact solutions of laminar-boundary-layer equations with constant property values for porous wall with variable temperature

Exact solution of the laminar-boundary-layer equations for wedge-type flow with constant property values are presented for transpiration-cooled surfaces with variable wall temperatures. The difference between wall and stream temperature is assumed proportional to a power of the distance from the leading edge. Solutions are given for a Prandtl number of 0.7 and ranges of pressure-gradient, cooling-air-flow, and wall-temperature-gradient parameters. Boundary-layer profiles, dimensionless boundary-layer thicknesses, and convective heat-transfer coefficients are given in both tabular and graphical form. Corresponding results for constant wall temperature and for impermeable surfaces are included for comparison purposes.

Donoughe, Patrick L↗

High Reynolds Number and Turbulence Effects on Turbine Heat Transfer

Experimental data on pressure distribution and heat transfer on a turbine airfoil were obtained over a range of Reynolds numbers from 0.75 to 7.0 x 10(exp 6) and a range of turbulence intensities from 1.8 to about 15%. The purpose of this study was to obtain fundamental heat transfer and pressure distribution data over a wide range of high Reynolds numbers and to extend the heat transfer data base to include the range or Reynolds numbers encountered in the Space Shuttle main engine turbopump turbines. The results of this study indicated that Reynolds number and turbulence intensity have a large effect on both the transition from laminar to turbulent flow and the resulting heat transfer. For a given turbulence intensity, heat transfer for all Reynolds numbers at the leading edge can generally be correlated with the Frossling number developed for lower Reynolds numbers. For a given turbulence intensity, heat transfer for the airfoil surfaces downstream of the leading edge can be approximately correlated with a dimensionless parameter. Comparisons of the experimental results were also made with a numerical solution from a two-dimensional Navier-Stokes code.

Yeh, Frederick C.↗

Influence of Small Steps on Wall Pressure Fluctuation Spectra Measured on Tu-144LL Flying Laboratory

Results of analyzing flight-test data of pressure-fluctuation fields in front of forward-facing steps and behind backward-facing steps are presented. The range of dimensionless step heights (normalized by boundary-layer displacement thickness) in the flight test was 0.042-0.236. The flight tests covered a mach-number range from 0.57 to 1.97. In the mach-number ranges covered by wind-tunnel tests (0.57 to 0.78 and 1.5 to 2) data agree very well with the flight data. Very importantly, the flight-test data fill in the gap previously existing for small-step pressure-fluctuations in the range of mach 0.78 to 1.5. Increased pressure-fluctuations were observed in the transonic region.

Efimtsov, B. M.↗

Turbulent transport model of wind shear in thunderstorm gust fronts and warm fronts

A model of turbulent flow in the atmospheric boundary layer was used to simulate the low-level wind and turbulence profiles associated with both local thunderstorm gust fronts and synoptic-scale warm fronts. Dimensional analyses of both type fronts provided the physical scaling necessary to permit normalized simulations to represent fronts for any temperature jump. The sensitivity of the thunderstorm gust front to five different dimensionless parameters as well as a change from axisymmetric to planar geometry was examined. The sensitivity of the warm front to variations in the Rossby number was examined. Results of the simulations are discussed in terms of the conditions which lead to wind shears which are likely to be most hazardous for aircraft operations.

Lewellen, W. S.↗

The onset of electrohydrodynamic instability in isoelectric focusing

The onset of electrohydrodynamic motion associated with the imposition of an electric field across a thin layer of liquid has been investigated for the case in which the electrical conductivity varies linearly over the depth of the layer. The variation of the conductivity is due to concentration gradients in the charge-carrying solutes and its spatio-temporal evolution is represented by a convective-diffusion equation. When the viscous relaxation time is long compared to the time for charge relaxation, the analysis reveals that the neutral stability curves for the layer can be characterized by three dimensionless parameters: Ra(sub e) is equivalent to d(epsilon)E(sup 2, sub 0) Delta sigma/mu K(sub eff) sigma(sub 0), an electrical Rayleigh number; delta sigma/sigma(sub 0), the relative conductivity increment; and alpha, the transverse wave number of the disturbance. Here d is the thickness, epsilon is the dielectric constant, and mu is the viscosity of layer, E(sub 0) is the applied field strength at the lower conductivity boundary, and K(sub eff) is an effective diffusivity associated with the Brownian motion of the charge-carrying solutes. With viscous-stress-free boundaries, at which the electrical conductivity and the normal component of the electric field are prescribed, the critical Ra(sub e) is 1.504 x 10(exp 4) at a critical transverse wave number of 1.97 when Delta sigma/sigma(sub 0) is 10. As Delta sigma/sigma(sub 0) increases, the critical Ra(sub e) increases and shifts to shorter wavelength disturbances; the critical imposed field strength, however, passes through a minimum because the lower-conductivity boundary exerts a considerable stabilizing influence in the presence of steep conductivity gradients. Similar trends were obtained for liquid layers with rigid boundaries.

Baygents, James C.↗