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A calculation was made for the flow and heat transfer in the turbulent free-convection boundary layer on a vertical flat plate. Formulas for the heat-transfer coefficient, boundary layer thickness, and the maximum velocity in the boundary layer were obtained.
A computer model of the combustion-gas-side heat transfer was developed to predict the effects of a jet impingement system and the possible range of improvements available. Using low temperature (315 C (600 F)) pretest data in an updated model, a high temperature silicon carbide jet impingement heat transfer system was designed and fabricated. The system model predicted that at the theoretical maximum limit, jet impingement enhanced heat transfer can: (1) reduce the flame temperature by 275 C (500 F); (2) reduce the exhaust temperature by 110 C (200 F); and (3) increase the overall heat into the working fluid by 10%, all for an increase in required pumping power of less than 0.5% of the engine power output. Initial tests on the GPU-3 Stirling engine at NASA-Lewis demonstrated that the jet impingement system increased the engine output power and efficiency by 5% - 8% with no measurable increase in pumping power. The overall heat transfer coefficient was increased by 65% for the maximum power point of the tests.
The heat-transfer coefficients have been determined for five steel cylinders having fins 1.22 inches wide and the spacing between the fins ranging from 0.022 to 0.131 inch. The cylinders were tested with and without baffles in a wind tunnel; they were also tested enclosed in jackets with the cooling air supplied by a blower. A maximum heat transfer was reached at a fin space of about 0.45 inch for the cylinders tested with each of the three methods of cooling investigated. The rise in temperature of the air passing between the fins and the change in flow pattern were found to be important factors limiting the heat transfer that may be obtained by decreasing the fin space. The use of baffles for directing the air around the cylinders with closely spaced fins proved very effective in increasing the over-all heat-transfer coefficient, provided that the spacing was not appreciably less than that for maximum heat transfer.
Convective heat-transfer coefficients in dry air were obtained for an ellipsoidal spinner of 30-inch maximum diameter for both stationary and rotating operation over a range of conditions including airspeeds up to 275 miles per hour, rotational speeds up to 1200 rpm, and angles of attack of zero and 40 The results are presented in terms of Nusselt numbers, Reynolds numbers, and convective heat-transfer coefficients. The studies included both uniform heating densities over the spinner and uniform surface temperatures.. In general, the results showed that rotation will increase the convective heat transfer from a spinner, especially in the turbulent-flow regions. Rotation of the spinner at 1200 rpm and at a free-stream velocity of 275 miles per hour increased the Nusselt number parameter in the turbulent-flow region by 32 percent over that obtained with a stationary spinner; whereas in the nose region, where the flow was laminar, an increase of only 18 percent was observed. Transition from laminar to turbulent flow occurred over a large range of Reynolds numbers primarily because of surface roughness of the spinner. Operation at an angle of attack of 40 had only small effects on the local convective heat transfer for the model studied.
An analysis of the single-blow transient testing technique for heat exchanger surfaces is made for perforated plate and similar discontinuous surfaces. The model assumes that there is no temperature variation across each plate, and allows for axial conduction in spacers: the resulting axial fluid temperature profile is discontinuous, rather than the usual continuous profile. Numerical solutions are obtained to the resulting set of coupled first-order differential equations for a step change in inlet fluid temperature. Results are presented in tabular form, which allow the heat transfer coefficients to be calculated from test data using the maximum slope technique.
A physics-based Nuclear Thermal Propulsion (NTP) Testing Reference Design (TRD) power balance model was coded in Simulink to investigate engine performance for various design and parameter modifications. Since the primary mode of heat transfer in NTP engines is convective, the convective heat transfer coefficient (HTC) is a key parameter that requires accurate representation. The industry standard Westinghouse correlation has an uncertainty of ±20% which was investigated in this study. The results showed that a 20% decrease in the HTC led to a 4.14% increase in maximum fuel temperature while a 20% decrease in the HTC led to a 1.81% decrease in maximum fuel temperature suggesting that narrowing the uncertainty of this correlation through experimental work would be a critical step in the development of NTP engines. Furthermore, a maximum fuel temperature relationship with specific impulse was developed for the TRD engine which showed potential engine operation between specific impulse values of 715 and 900 seconds with minimal changes to the engine design. This graph could be useful for high level vehicle performance estimations for fuel types with different maximum operating temperatures.
A physics-based Nuclear Thermal Propulsion (NTP) Testing Reference Design (TRD) power balance model was coded in Simulink to investigate engine performance for various design and parameter modifications. Since the primary mode of heat transfer in NTP engines is convective, the convective heat transfer coefficient (HTC) is a key parameter that requires accurate representation. The industry standard Westinghouse correlation has an uncertainty of ±20% which was investigated in this study. The results showed that a 20% decrease in the HTC led to a 4.14% increase in maximum fuel temperature while a 20% decrease in the HTC led to a 1.81% decrease in maximum fuel temperature suggesting that narrowing the uncertainty of this correlation through experimental work would be a critical step in the development of NTP engines. Furthermore, a maximum fuel temperature relationship with specific impulse was developed for the TRD engine which showed potential engine operation between specific impulse values of 715 and 900 seconds with minimal changes to the engine design. This graph could be useful for high level vehicle performance estimations for fuel types with different maximum operating temperatures.
This paper presents details of the methodology and numerical procedures developed at NASA Ames for full-body TEXAS sizing and optimization for Access to Space vehicle concepts. The core of the procedures is a robust implicit solver for one dimensional transient heat conduction in reusable multilayer TEXAS stackups. The solver includes an arbitrary number of material layers, contact resistances between materials, temperature and pressure dependent material and surface properties, numerous boundary-condition options, and self-adaptive time stepping. The solver is coupled with the Access-to-Space material database of 23 candidate TPS and structural materials and a thermal-environment database obtained from trajectory-based fullbody Navier-Stokes computations of the external flowfield. The thermal environment and material response are coupled through the use of T-type heat transfer coefficients. TIPS sizing and weight optimization are performed at every surface point on the vehicle based on sizing constraints which include material temperature limits, maximum backwall temperature, and cumulative interior heat flux. Typical results are presented for a lifting body concept with 10000 surface points, which required 35 minutes to compute on an SGI Indigo 2.
An air-launched cone-cylinder test vehicle designed to obtain data at Mach numbers above 4.0 was rocket boosted from a release Mach number of 5.18. The vehicle was launched at an altitude of 35,000 feet and reached peak velocity of 5150 feet per second at 28,500 feet. The total-drag coefficient (based on maximum cross-sectional area) decreased gradually from 0.31 at a Mach number of 1.75 to 0.145 at a Mach number of 5.18, while the Reynold's number (based on body length) increased from 31 x 10 to the 6th power to 107 x 10 to the 6th power. The skin friction coefficients, in general, were slightly lower than Van Driest's theoretical values for similar wall-temperature conditions. Convective heat-transfer coefficients were obtained from a single skin-thermocouple measurement. The maximum wall temperature recorded was 1240 degrees r.
Boiling heat transfer is governed by a complex interplay between surface conditions and gravitational acceleration. To isolate the sole effects of gravity, we investigated the pool boiling characteristics of liquid nitrogen on atomically smooth silicon dioxide (SiO 2 ) surfaces under terrestrial (1-g) and reduced gravity (0±0.02 g) conditions achieved via parabolic flight. Our results quantify a drastic reduction in the critical heat flux (CHF) in reduced gravity, decreasing from 16.15 W/cm 2 at 1-g to 5−6 W/cm 2 at μ-g due to the suppression of buoyancy. Conversely, we observed a distinct increase in the heat transfer coefficient (HTC) in the reduced gravity condition prior to CHF. By utilizing a surface with a maximum peak-to-valley height of ≈36.7 nm and low contact angle hysteresis (<10°), we confirm this HTC enhancement is an intrinsic response to the gravitational environment, decoupled from surface-defect-induced nucleation. These findings demonstrate that the influence of surface topography is significantly more prominent in reduced gravity than in terrestrial conditions, providing a critical baseline for rationalizing the design of cryogenic thermal management systems in space and quantum applications.
A gaseous H2/O2 rocket engine was constructed at the NASA-Lewis to provide a high heat flux source representative of the heat flux to the blades in the high pressure fuel turbopump (HPFTP) during startup of the space shuttle main engines. The high heat flux source was required to evaluate the durability of thermal barrier coatings being investigated for use on these blades. The heat transfer, and specifically, the heat flux to tubes located at the throat of the test rocket engine was evaluated and compared to the heat flux to the blades in the HPFTP during engine startup. Gas temperatures, pressures and heat transfer coefficients in the test rocket engine were measured. Near surface metal temperatures below thin thermal barrier coatings were also measured at various angular orientations around the throat tube to indicate the angular dependence of the heat transfer coefficients. A finite difference model for a throat tube was developed and a thermal analysis was performed using the measured gas temperatures and the derived heat transfer coefficients to predict metal temperatures in the tube. Near surface metal temperatures of an uncoated throat tube were measured at the stagnation point and showed good agreement with temperatures predicted by the thermal model. The maximum heat flux to the throat tube was calculated and compared to that predicted for the leading edge of an HPFTP blade. It is shown that the heat flux to an uncooled throat tube is slightly greater than the heat flux to an HPFTP blade during engine startup.
A description is given of some of the more significant thermal design considerations employed in the development and qualification of the monopropellant hydrazine terminal descent engines on the Viking Mars lander spacecraft. The terminal descent engine operates in a blowdown and throttling mode, which results in an operating thrust range of 638 to 90 lbf. Martian entry thermal design boundary conditions are described, along with resulting radiative and conductive engine thermal isolation hardware. Test results are presented, showing engine thermal design performance as compared with specified requirements. General engine materials of construction are described, along with Hastelloy B shell structural characteristics, which were extended to 2000 F by test and are compared with limited existing MIL-HDBK-5 data. Subscale test results are presented, showing the maximum catalyst bed cylinder design temperature of 1970 F. Test results also are presented, showing local reactor internal convective heat-transfer coefficients. Such data are unique, since the engine employs a completely radial flow catalyst bed design. This design approach is the first of its kind in the monopropellant hydrazine gas generator field to be flight qualified.
The fuel optimal control problem arising in coplanar orbital transfer employing aeroassisted technology is addressed. The mission involves the transfer from high energy orbit (HEO) to low energy orbit (LEO) without plane change. The basic approach here is to employ a combination of propulsive maneuvers in space and aerodynamic maneuvers in the atmosphere. The basic sequence of events for the coplanar aeroassisted HEO to LEO orbit transfer consists of three phases. In the first phase, the transfer begins with a deorbit impulse at HEO which injects the vehicle into a elliptic transfer orbit with perigee inside the atmosphere. In the second phase, the vehicle is optimally controlled by lift and drag modulation to satisfy heating constraints and to exit the atmosphere with the desired flight path angle and velocity so that the apogee of the exit orbit is the altitude of the desired LEO. Finally, the second impulse is required to circularize the orbit at LEO. The performance index is maximum final mass. Simulation results show that the coplanar aerocapture is quite different from the case where orbital plane changes are made inside the atmosphere. In the latter case, the vehicle has to penetrate deeper into the atmosphere to perform the desired orbital plane change. For the coplanar case, the vehicle needs only to penetrate the atmosphere deep enough to reduce the exit velocity so the vehicle can be captured at the desired LEO. The peak heating rates are lower and the entry corridor is wider. From the thermal protection point of view, the coplanar transfer may be desirable. Parametric studies also show the maximum peak heating rates and the entry corridor width are functions of maximum lift coefficient. The problem is solved using a direct optimization technique which uses piecewise polynomial representation for the states and controls and collocation to represent the differential equations. This converts the optimal control problem into a nonlinear programming problem which is solved numerically by using a modified version of NPSOL. Solutions were obtained for the described problem for cases with and without heating constraints. The method appears to be more robust than other optimization methods. In addition, the method can handle complex dynamical constraints.
Wind speed, ambient and surface temperatures from both Viking Landers have been used to compute bulk Richardson numbers and Monin-Obukhov lengths during the earliest phase of the Mars missions. These parameters are used to estimate drag and heat transfer coefficients, friction velocities and surface heat fluxes at the two sites. The principal uncertainty is in the specification of the roughness length. Maximum heat fluxes occur near local noon at both sites, and are estimated to be in the range 15-20 W/sq m at the Viking 1 site and 10-15 W/sq m at the Viking 2 site. Maximum values of friction velocity occur in late morning at Viking 1 and are estimated to be 0.4-0.6 m/s. They occur shortly after dawn at the Viking 2 site where peak values are estimated to be in the range 0.25-0.35 m/s. Extension of these calculations to later times during the mission will require allowance for dust opacity effects in the estimation of surface temperature and in the correction of radiation errors of the Viking 2 temperature sensor.
An embedded grid algorithm for the Euler and/or Navier-Stokes equations is developed and applied to delta wings at high angles of attack in low speed flow. The Navier-Stokes code is an implicit, finite volume algorithm, using flux difference splitting for the convective and pressure terms and central differencing for the viscous and heat transfer terms. Calculations are compared with detailed experimental results over an angle of attack range up to and beyond the maximum lift coefficient, corresponding to vortex breakdown at the trailing edge, for a delta wing nominally of unit aspect ratio. The results indicate that the overall flowfield, including surface pressures, surface streamlines, and vortex trajectories, can be simulated accurately with the global grid version of the present algorithm. However, comparison of computed velocities and vorticity with experimentally measured off-body values at an angle of attack of 20.5 deg indicates the core region is substantially more diffuse in the computations than that measured with either a five-hole probe or a laser velocimeter. Embedded grids, used to improve the numerical discretization in the core region, are formulated within the framework of the implicit, upwind-biased multi-grid algorithm. Structured levels of local nested refinements are made. Three-dimensional results for both Euler and Navier-Stokes calculations are shown, with up to 3 levels of embedded refinement. The embedding procedure was effective in eliminating a crossflow secondary separation produced in the Euler solutions on coarse grids.
Heat-transfer coefficients in the form of Stanton number and boundary-layer transition data were obtained from a free-flight test of a 100-inch-long 10 deg. total-angle cone with a 1/16-inch tip radius which penetrated deep into the region of infinite stability of laminar boundary layer over a range of wall-to-local-stream temperature radius and for local Mach numbers from 1.8 to 3.5. Experimental heat-transfer coefficients, obtained at Reynolds numbers up to 160 x 10(exp 6), were in general somewhat higher than theoretical values. A maximum Reynolds number of transition of only 33 x 10(exp 6) was obtained. Contrary to theoretical and some other experimental investigations, the transition Reynolds number initially increased while the wall temperature ratio increased at relatively constant Mach number. Further increases in wall temperature ratio were accompanied by a decrease in transition Reynolds number. Increasing transition Reynolds number with increasing Mach number was also indicated at a relatively constant wall temperature ratio.
Heat-transfer rates on the afterbody of the Apollo reentry configuration have been measured in a low-enthalpy wind tunnel at a Mach number of 8. The data have been presented as the ratio of the measured heat-transfer coefficient on the afterbody to the calculated heat-transfer coefficient at the stagnation point at zero angle of attack. This ratio was found to vary from a low of approximately 0.01 to a maximum of about 0.52 as the angle of attack varied from 0 to 55 deg.
In order to determine the effect of surface irregularities on local convective heat transfer, the variation in heat transfer coefficients on small (2-6 mm diam) hemispherical roughness elements on a flat plate has been studied in a wind funnel using IR techniques. Heat transfer enhancement was observed to vary over the roughness elements with the maximum heat transfer on the upstream face. This heat transfer enhancement increased strongly with roughness size and velocity when there was a laminar boundary layer on the plate. For a turbulent boundary layer, the heat transfer enhancement was relatively constant with velocity, but did increase with element size. When multiple roughness elements were studied, no influence of adjacent roughness elements on heat transfer was observed if the roughness separation was greater than approximately one roughness element radius. As roughness separation was reduced, less variation in heat transfer was observed on the downstream elements. Implications of the observed roughness enhanced heat transfer on ice accretion modeling are discussed.