Engineering topics

Chen, C. F.

Publications and source records attributed to Chen, C. F..

At least 19 records

NASA NTRS1993

Double-diffusive fingering convection in a porous medium

The characteristics of nonlinear two-dimensional horizontally periodic double-diffusive fingering convection in a saturated porous medium is investigated, using the Darcy equation including Brinkman and Forchheimer terms for the momentum equation. To solve the equations and the corresponding initial and boundary conditions, a Galerkin method is applied in the horizontal direction, and a hybrid finite difference method is used in the vertical direction. The developed computer code was used to compute the thermal convection case, and the results were found to be in good agreement with existing results.

Chen, Falin↗

NASA NTRS1992

Effect of surface tension on the onset of convection in a double-diffusive layer

The effect of surface tension on the stability of a double-diffusive layer is considered using linear stability analysis. The surface tension is assumed to vary linearly with temperature and solute concentration. The eigenvalue problem is solved by the Galerkin method. Results show that the predicted stability boundary based on Marangoni effects alone is completely altered in the presence of buoyancy effects induced by low gravity levels (about 10 exp -5 g). At reduced gravity levels, salt-finger instability may onset in the overstable mode due to the stabilizing effect of surface tension. Fluid properties in terms of the Prandtl and the Lewis numbers have a profound effect on the stability conditions; opposite stability characteristics are found in salt solutions and in molten metals.

Chen, C. F.↗

NASA NTRS1992

Onset of salt finger convection in a gravity gradient

The effects of gravity level elevation in a centrifuge on the onset of salt finger convection in a double-diffusive system are examined. It is shown that the steady onset of salt finger convection in a double-diffusive layer is exactly analogous to the small-gap Taylor-Couette problem. The results presented by Chandrasekhar (1961) for the Taylor-Couette problem are extended to cover a wider range of application in the present case.

Chen, C. F.↗

NASA NTRS1992

Fluid mechanics of directional solidification at reduced gravity

The primary objective of the proposed research is to provide additional groundbased support for the flight experiment 'Casting and Solidification Technology' (CAST). This experiment is to be performed in the International Microgravity Laboratory-1 (IML-1) scheduled to be flown on a space shuttle mission scheduled for 1992. In particular, we will provide data on the convective motion and freckle formation during directional solidification of NH4Cl from its aqueous solution at simulated parameter ranges equivalent to reducing the gravity from the sea-level value down to 0.1 g or lower. The secondary objectives of the proposed research are to examine the stability phenomena associated with the onset of freckles and the mechanisms for their subsequent growth and decline (to eventual demise of some) by state-of-the-art imaging techniques and to formulate mathematical models for the prediction of the observed phenomena.

Chen, C. F.↗

NASA NTRS1992

Convection in superposed fluid and porous layers

Thermal convection due to heating from below in a porous layer underlying a fluid layer has been analyzed using the Navier-Stokes equations for the fluid layers and the extended Darcy equation (including Brinkman and Forchheimer terms) for the porous layer. The flow is assumed to be two-dimensional and periodic in the horizontal direction. The numerical scheme used is a combined Galerkin and finite-difference method, and appropriate boundary conditions are applied at the interface. Results have been obtained for depth ratios of 0, 0.1, 0.2, 0.5, and 1.0, where this ratio is defined as the ratio of the thickness of the fluid layer to that of the porous layer. For the depth ratio of 0.1, the convection is dominated by the porous layer, similar to the situation at onset, even though the Rayleigh number for the fluid layer is well into the supercritical regime.

Chen, Falin↗

NASA NTRS1992

Effects of g-jitter and cross-diffusion on the onset of convection in doubly diffusive systems

The effects of a modulated gravity field in doubly diffusive layers with and without cross-diffusion are studied. Attention is focused on the determination of linear stability criteria for such systems. Floquet theory is used to establish the stability criteria by a systematic analysis of the topology of the neutral curves from which stability boundaries can be constructed. Convective stability boundaries for gravity-modulated doubly cross-diffusive systems are presented for the cases of dynamically free and rigid boundaries. Two physically different forms of layer stratification are considered: (1) imposed independent gradients of two components and (2) a solute gradient induced by a fixed temperature gradient.

Terrones, Guillermo↗

NASA NTRS1992

Stability analysis of surface tension effects on a double-diffusive layer

The linear stability characteristics of a fluid layer with simultaneous temperature and concentration gradients in a reduced gravity field are examined. The surface tension of the fluid is assumed to be a linear function of temperature and concentration. It is concluded that a small amount of gravity may damp out oscillatory instability or may alter its dynamics so that instability appears as steady convection. The onset of salt-finger instability may be in the overstable mode due to the surface tension method. The Lewis and Prandtl numbers of the material have a strong influence on the stability boundaries and onset characteristics of the system.

Chen, C. F.↗

NASA NTRS1992

Surface tension effects on the onset of double-diffusive convection

Experiments have been carried out to determine the critical thermal Rayleigh number for onset of convection in a horizontal layer of density-stratified fluid with a free surface when heated from below. Three different aqueous solutions were used: salt, glycerol, and acetic acid. The rates of change in surface tension with concentration for these three solutions are positive, nearly zero, and negative, respectively. Compared to the rigid-rigid boundaries, the critical thermal Rayleigh number was found to be larger by 11.2 percent for the salt solution and smaller by 10.0 percent for the glycerol solution. With the acetic acid solution, however, the effect of the free surface was found to be negligible.

Chen, C. F.↗

NASA NTRS1991

Experimental study of directional solidification of aqueous ammonium chloride solution

Directional solidification experiments have been carried out using the analog casting system of NH4Cl-H2O solution by cooling it from below with a constant-temperature surface ranging from -31.5 C to +11.9 C. The NH4Cl concentration was 26 percent in all solutions, with a liquidus temperature of 15 C. It was found that finger convection occurred in the fluid region just above the mushy layer in all experiments. Plume convection with associated chimneys in the mush occurred in experiments with bottom temperatures as high as +11.0 C. However, when the bottom temperature was raised to +11.9 C, no plume convection was observed, although finger convection continued as usual. A method has been devised to determine the porosity of the mush by computed tomography. Using the mean value of the porosity across the mush layer and the permeability calculated by the Kozeny-Carman relationship, the critical solute Rayleigh number across the mush layer for onset of plume convection was estimated to be between 200 and 250.

Chen, C. F.↗

NASA NTRS1991

Convective instability in superposed fluid and anisotropic porous layers

The onset of thermal convection due to heating from below in a system consisting of a fluid layer overlying a porous layer with anisotropic permeability and thermal diffusivity is studied. The linear perturbation equations are solved numerically. It is found that the effects of anisotropy on the onset of thermal convection are most profound for small values of the depth ratio xi (ratio of fluid layer thickness to porous layer thickness), since in that case, the onset of convection corresponds to significant motion in both layers. For fixed vlues of the vertical permeability in the porous medium, decreasing the value of zeta (ratio of horizontal to vertical permeability) leads to stabilization of the superposed layer configuration because of increased resistance to motion in the porous medium. For larger values of xi, the onset of motion is increasingly confined to the fluid layer, with the transport of heat through the porous layer occurring primarily by conduction. Accordingly, the influence of zeta on the stability characteristics for larger xi is less significant than the effects of an anisotropic thermal conductivity.

Chen, Falin↗

NASA NTRS1991

The role of gravity on macrosegregation in alloys

During dendritic solidification liquid flow is induced both by buoyancy forces and solidification shrinkage. There is strong evidence that the major reason for the liquid flow is the former, i.e., thermosolutal convection. In the microgravity environment, it is thought that the thermosolutal convection will be greatly diminished so that convection will be confined mainly to the flow of interdendritic liquid required to satisfy the solidification shrinkage. An attempt is made to provide improved models of dendritic solidification with emphasis on convection and macrosegregation. Macrosegregation is an extremely important subject to the commercial casting community. The simulation of thermosolutal convection in directionally solidified (DS) alloys is described. A linear stability analysis was used to predict marginal stability curves for a system that comprises a mushy zone underlying an all-liquid zone. The supercritical thermosolutal convection in directionally solidified dendritic alloys was also modeled. The model assumes a nonconvective initial state with planar and horizontal isotherms and isoconcentration that move upward at a constant solidification velocity. Results are presented for systems involving lead-tin alloys and show significant differences with results of plane-front solidification.

Poirier, D. R.↗

NASA NTRS1990

Salt-finger convection under reduced gravity

Salt-finger convection in a double-diffusive system is a motion driven by the release of gravitational potential due to differential diffusion rates. Because of the fact that the destabilizing effect of the concentration gradient is amplified by the Lewis number (the ratio of thermal diffusivity to solute diffusivity) salt-finger convection can be generated at very much reduced gravity levels. This effect may be of importance in the directional solidification of binary alloys carried out in space. The transport of solute and heat by salt-finger convection at microgravity conditions is considered; instability arising from surface tension gradients, the Marangoni instability, is discussed, and the possible consequences of combined salt-finger and Marangoni instability are considered.

Chen, C. F.↗

NASA NTRS1990

Double-diffusive convection and its effect under reduced gravity

This paper reviews recent results on three aspects of double-diffusive convection under reduced gravity: diffusive instability caused by sideways heating, diffusive instability caused by bottom heating, and the salt-finger convection case. Some of the processes that are likely to occur during solidification are highlighted. Using property values of lead-tin alloy, it is concluded that diffusive instabilities are unlikely to occur at steady reduced gravity levels of 0.01 and 0.0001 g(0). Salt finger convection is likely to be generated, however.

Chen, C. F.↗

NASA NTRS1989

Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below

Experiments have been carried out in a horizontal superposed fluid and porous layer contained in a test box 24 cm x 12 cm x 4 cm high. The porous layer consisted of 3 mm diameter glass beads, and the fluids used were water, 60 and 90 percent glycerin-water solutions, and 100 percent glycerin. The depth ratio d, which is the ratio of the thickness of the fluid layer to that of the porous layer, varied from 0 to 1.0. Fluids of increasingly higher viscosity were used for cases with larger d in order to keep the temperature difference across the tank within reasonable limits. The size of the convection cells was inferred from temperature measurements made with embedded thermocouples and from temperature distributions at the top of the layer by use of liquid crystal film. The experimental results showed: (1) a precipitous decrease in the critical Rayleigh number as the depth of the fluid layer was increased from zero, and (2) an eightfold decrease in the critical wavelength between d = 0.1 and 0.2. Both of these results were predicted by the linear stability theory reported earlier (Chen and Chen, 1988).

Chen, Falin↗

NASA NTRS1988

Onset of finger convection in a horizontal porous layer underlying a fluid layer

The problem of the onset of finger convection in a porous layer underlying a fluid layer is considered using linear stability analysis. The linear stability equations for the porous layer are formulated for temperature and salinity gradients existing in both layers. The eigenvalue problem is solved by a shooting method. The solution method and associated computer program are validated by comparison with the results of Sun (1973) for the thermal convection case. Results are also presented for the onset of salt-finger convection.

Chen, F.↗

NASA NTRS1987

Double-diffusive effects during solidification

When a fluid contains two diffusing components with different molecular diffusivities, such as heat and solute concentration, convective motion may be generated when potential energy is released owing to differential diffusion. In the solidification of binary alloys and doped semiconductors, temperature and concentration gradients do exist simultaneously. If these gradients are aligned in a suitable manner, convection may ensue. In the case of the binary alloy, such convection may extend through the mushy zone and may be the cause of macrosegregations. In the case of doped semiconductors, the convective motion may cause the nonuniform distribution of dopant in the product. In this paper, the fundamentals of double-diffusive convection will be reviewed, and its effect on solidification will be discussed.

Chen, C. F.↗

NASA NTRS1973

State space approach to mixed boundary value problems.

A state-space procedure for the formulation and solution of mixed boundary value problems is established. This procedure is a natural extension of the method used in initial value problems; however, certain special theorems and rules must be developed. The scope of the applications of the approach includes beam, arch, and axisymmetric shell problems in structural analysis, boundary layer problems in fluid mechanics, and eigenvalue problems for deformable bodies. Many classical methods in these fields developed by Holzer, Prohl, Myklestad, Thomson, Love-Meissner, and others can be either simplified or unified under new light shed by the state-variable approach. A beam problem is included as an illustration.

Chen, C. F.↗

NASA NTRS1972

On identifying transfer functions and state equations for linear systems.

Two methods are established for identifying constant-coefficient, C to the 2n power type of noise-free linear systems if the time response data of the input-output or of all states are known. 2n response data are required to identify an nth-order transfer function or state equation for an unknown linear system. The order of the unknown system can be identified by checking a sequence of determinants. The Z transform and its inversion are mainly used.

Shieh, L. S.↗