Engineering topics

Siegel, R.

Publications and source records attributed to Siegel, R..

At least 37 records · Page 2

NASA NTRS1986

Free boundary shape of a convectively cooled solidified region

The two-dimensional steady-state shape of a solidified region, such as a frost layer, was determined analytically for formation on a plate that is convectively cooled. The nonuniform shape of the layer is produced by exposure to a spatially nonuniform distribution of radiant energy. For high convective cooling the cooled wall approaches a uniform temperature, and an exact solution is obtained for the free boundary shape. For a lesser amount of convective cooling, the variation in temperature along the cooled boundary is treated by a boundary perturbation method. Some illustrative examples are given that show the effects of nonuniform heating and the magnitude of convective heat transfer at the cooled wall. Only one boundary condition is approximated by the perturbation solution; all of the other boundary conditions are satisfied exactly. The calculated results given here were found to satisfy the approximate boundary condition within a very small error.

Siegel, R.↗

NASA NTRS1985

Analysis of buoyancy effect on fully developed laminar heat transfer in a rotating tube

Laminar heat transfer is analyzed in a tube rotating about an axis perpendicular to the tube axis. The solution applies for flow that is either radially outward from the axis of rotation, or radially inward toward the axis of rotation. The conditions are fully developed, and there is uniform heat addition at the tube wall. The analysis is performed by expanding velocities and temperature in power series using the Taylor number as a perturbation parameter. Coriolis and buoyancy forces caused by tube rotation are included, and the solution is calculated through second-order terms. The secondary flow induced by the Coriolis terms always tends to increase the heat transfer coefficient; this effect can dominate for small wall heating. For radial inflow, buoyancy also tends to improve heat transfer. For radial outflow, however, buoyancy tends to reduce heat transfer; for large wall heating this effect can dominate, and there is a net reduction in heat transfer coefficient.

Siegel, R.↗

NASA NTRS1985

Analysis of three-dimensional solidification interface shape

The determination of the shape of the solidification interface in a cooling melt by the thermal boundary conditions is investigated analytically, extending the analysis of Siegel (1982) and Siegel and Sosoka (1982) to the three-dimensional case. The solutions are generated by continuation into the solid region from conditions at the cooled wall, and some numerical results are presented in tables and graphs. These findings and the analytical approach employed are applicable to crystallization and metal-forming processes.

Siegel, R.↗

NASA NTRS1985

Control of solidification boundary in continuous casting by asymmetric cooling and mold offset

A solution, developed to obtain solidification-interface shapes for complex situations in which both the ingot cooling and mold geometry are asymmetric, is analyzed. The effect of mold offsett and of unequal ingot side temperatures on the interface shapes is illustrated in graphs. The results of the analysis show how the solidification interface in continuous casting can be controlled by asymmetries in both mold geometry and cooling of the ingot sides.

Siegel, R.↗

NASA NTRS1984

Two-region analysis of interface shape in continuous casting with superheated liquid

A slab ingot is being formed as a continuous casting by withdrawal from a mold with parallel walls. The sides of the ingot below the mold are cooled to remove heat of fusion and energy transferred to the solidification interface by superheated liquid metal in the mold. A two-region analysis is made to determine the non-uniform heat conduction from the liquid metal to the interface, and then from the interface to the cooled ingot sides. The solidification interface shape is found that is compatible with the removal of fusion energy and nonuniform heating from the liquid. The solution is obtained by two applications of a Cauchy boundary value method.

Siegel, R.↗

NASA NTRS1984

Shape of porous region to control cooling along curved exit boundary

A cooled porous insert in a curved wall has a specified spatially varying heat flux applied to one side. It is desired to control the distribution of coolant flow out through this curved surface so that the surface will be kept at a desired uniform temperature. The flow regulation is accomplished by shaping the surface through which the coolant enters the region to obtain the required variation of flow resistance within the region. The proper surface shape is found by solving a Cauchy boundary value problem. Analytical solutions are given in two dimensions for various shapes of the heated boundary subjected to different heating distributions.

Siegel, R.↗

NASA NTRS1984

Solidification interface shape for continuous casting in an offset mold - Two analytical methods

A solution method for finding the unknown solidification interface in manufacturing slab ingots as a continuous casting is presented, which involves a product solution in the potential plane and the use of conjugate harmonic functions. It is argued that the method may be more direct for some geometries than the Cauchy boundary value method. Moreover, the usefulness of the Cauchy boundary value method is demonstrated through the example of a nonsymmetric horizontal mold where the walls are offset to support the lower ingot boundary.

Siegel, R.↗

NASA NTRS1983

Analysis of coolant entrance boundary shape of porous region to control cooling along exit boundary

A cooled porous region has a plane surface exposed to a specified spatially varying heat flux. The coolant leaves the region through this surface, and it is desired to control the flow distribution to maintain a specified uniform surface temperature. This is accomplished by having the coolant entrance surface shaped to provide in the region the necessary variation of path length and, hence, flow resistance. The surface shape at the coolant entrance is found by solving a Cauchy boundary value problem. An exact solution is obtained that will deal with a wide variety of heating distributions for both two- and three-dimensional shapes.

Siegel, R.↗

NASA NTRS1982

Determination of boundary shape of cooled porous region

The shape of a cooled porous wall section is found that will provide a uniform surface temperature, as dictated by material limitations, when the surface is subjected to spatially nonuniform heating. In the analysis, local temperatures and pressures in the porous material are expressed in terms of a potential function. From the imposed thermal conditions, this potential function is governed by the dual constraints of both its value and its normal derivative being specified along the heated surface. The unknown shape of this surface is obtained by meeting these dual conditions. The analytical method uses a generalized conformal mapping procedure that includes a curved boundary. The coolant flow can be compressible or incompressible, and its viscosity can depend on temperature.

Snyder, A.↗

NASA NTRS1982

Cauchy integral method for two-dimensional solidification interface shapes

A method is developed to determine the shape of steady state solidification interfaces formed when liquid above its freezing point circulates over a cold surface. The solidification interface, which is at uniform temperature, will form in a shape such that the non-uniform energy convected to it is locally balanced by conduction into the solid. The interface shape is of interest relative to the crystal structure formed during solidification; regulating the crystal structure has application in casting naturally strengthened metallic composites. The results also pertain to phase-change energy storage devices, where the solidified configuration and overall heat transfer are needed. The analysis uses a conformal mapping technique to relate the desired interface coordinates to the components of the temperature gradient at the interface. These components are unknown because the interface shape is unknown. A Cauchy integral formulation provides a second relation involving the components, and a simultaneous solution yields the interface shape.

Siegel, R.↗

NASA NTRS1982

Analysis of solidification interface shape resulting from applied sinusoidal heating

Maintaining a flat solidification interface is important for forming desired crystal structures in certain types of metal casting processes. This has application in new manufacturing techniques for naturally strengthened composite components such as turbine blades. The solidification interface shape will adjust to be compatible with the spatial distribution of energy being transferred to it. The interface shape must be found that satisfies conditions of simultaneously being at the fusion temperature and having an imposed spatially varying heat flux. Specific results are obtained for the heat transfer from the liquid phase varying along the interface in a cosine fashion. Interface shapes are found as a function of the amplitude and wavelength of the imposed heat transfer variations, and the sensitivity of the interface shape to these variations is examined.

Siegel, R.↗

NASA NTRS1981

Heat transfer in cooled porous region with curved boundary

Heat transfer characteristics are analyzed for a cooled two-dimensional porous medium having a curved boundary. A general analytical procedure is given in combination with a numerical conformal mapping method used to transform the porous region into an upper half plane. To illustrate the method, results are evaluated for a cosine shaped boundary subjected to uniform external heating. The results show the effects of coolant starvation in the thick regions of the medium, and the extent that internal heat conduction causes the heated surface to have a more uniform temperature.

Siegel, R.↗

NASA NTRS1978

Analysis of solidification interface shape during continuous casting of a slab

An analysis was made of the two-dimensional interface shape of a slab ingot being cast continuously by withdrawing it from a mold. The sides of the ingot are being cooled and the upper boundary of the ingot is in contact with a pool of molten metal. The solidification interface shape was determined from the analysis of the heat flow, utilizing the condition that the solidification interface is at constant temperature and must be normal to the lines of heat flow carrying away latent heat of fusion from the interface. The analysis includes the effect of interface curvature which, for a constant rate of withdrawing the cast ingot from the mold, causes the solidification to be nonuniform along the interface. The analysis was carried out by a conformal mapping procedure.

Siegel, R.↗

NASA NTRS1978

Shape of two-dimensional solidification interface during directional solidification by continuous casting

An analysis was made of the two-dimensional solidification of an ingot being cooled and withdrawn vertically downward from a mold consisting of parallel walls of finite length. Heat transfer analysis shows how the flatness of the interface is related to the ingot thickness, the withdrawal rate, the heat addition from the superheated liquid metal, and the temperature difference available for cooling. This provides an understanding of the conditions that will yield a maximum rate of casting while achieving the desired flatness of the interface. The results are interpreted with respect to the conditions for obtaining an aligned eutectic structure by directional solidification. In this process an additional constraint must be included that relates the ingot withdrawal rate and the heat transfer rate from the liquid metal to the solidification interface.

Siegel, R.↗

NASA NTRS1977

Effect of Fin Passage Length on Optimization of Cylinder Head Cooling Fins

The heat transfer performance of baffled cooling fins on cylinder heads of small, air-cooled, general-aviation aircraft engines was analyzed to determine the potential for improving cooling fin design. Flow baffles were assumed to be installed tightly against the fin end edges, an ideal baffle configuration for guiding all flow between the fins. A rectangular flow passage is thereby formed between each set of two adjacent fins, the fin base surface, and the baffle. These passages extend around each side of the cylinder head, and the cooling air absorbs heat as it flows within them. For each flow passage length, the analysis was concerned with optimizing fin spacing and thickness to achieve the best heat transfer for each fin width. Previous literature has been concerned mainly with maximizing the local fin conductance and has not considered the heating of the gas in the flow direction, which leads to higher wall temperatures at the fin passage exits. If the fins are close together, there is a large surface area, but the airflow is restricted.

Siegel, R.↗

NASA NTRS1976

Three-dimensional potential flow over hills and oval mounds

An analysis was made of the potential flow behavior for an initially uniform flow passing over a single axisymmetric hill, an oval mound, and a combination of two hills. Small perturbation theory was used, and the resulting Laplace equation for the perturbation velocity potential was solved by using either a product solution or a Green's function. The three dimensional solution is of interest in calculating the pressure distribution around obstacles, the flow of pollutants carried by the wind, and the augmentation of wind velocity for windmill siting. The augmentation in velocity at the top of a hill was found to be proportional to the hill height relative to a characteristic width dimension of the hill. An axisymmetric hill produced about 20 percent less velocity increase than a two dimensional ridge having the same cross-sectional profile.

Siegel, R.↗

NASA NTRS1976

Radiative behavior of a gas layer seeded with soot

Gaseous film or transpiration cooling may be used to reduce the heat flux reaching the wall of a container or other structures. Such a protective film, however, is usually not effective for reducing radiative heat transfer as most gases are transparent in the temperature range for which solid walls can exist. Therefore, heat transfer was examined for a gaseous layer seeded with radiation-absorbing carbon particles (soot) and flowing along a surface. The layer was subjected to an external high temperature source of blackbody radiation. The radiative behavior was found to depend on a parameter containing particle concentration, layer thickness and source temperature. Only a very small particle volume concentration, in the range of .0001, was required to obtain high absorption in a 1-cm-thick layer for typical conditions. The results provide the distance along the surface for which the heat transfer to the wall remains within an acceptable limit and the particles remain below a temperature at which they will melt or vaporize. The wall protection by the layer lasts only until the particles vaporize or the layer becomes so hot that it reradiates substantially to the wall. Depending on the layer mass velocity the protection may be effective for a distance along the wall of only a few layer thickness. Hence, to protect greater wall lengths, it will be necessary to introduce the suspension through multiple slots or holes along the wall.

Siegel, R.↗

NASA NTRS1975

Analysis of liquid-metal-jet impingement cooling in a corner region and for a row of jets

A conformal mapping method was used to analyze liquid-metal-jet impingement heat transfer. The jet flow region and energy equation are transformed to correspond to uniform flow in a parallel plate channel with nonuniform heat addition along a portion of one wall. The exact solution for the wall-temperature distribution was obtained in the transformed channel, and the results are mapped back into the physical plane. Two geometries are analyzed. One is for a single slot jet directed either into an interior corner formed by two flat plates, or over the external sides of the corner; the flat plates are uniformly heated, and the corner can have various included angles. The heat-transfer coefficient at the stagnation point at the apex of the plates is obtained as a function of the corner angle, and temperature distributions are calculated along the heated walls. The second geometry is an infinite row of uniformly spaced parallel slot jets impinging normally against a uniformly heated plate. The heat-transfer behavior is obtained as a function of the spacing between the jets. Results are given for several jet Peclet numbers from 5 to 50.

Siegel, R.↗