Flat Plate Boundary Layer Flow Research Articles

Production terms in chemically reacting equilibrium flows, discussed for a binary mixture laminar boundary layer flow

For a continuously changing flow field of a binary mixture assumed to be in local chemical equilibrium, the concentration of species is uniquely determined by the law of mass-action as a function of any two independent thermodynamic variables such as temperature and pressure. This implies infinite large reaction rates leading to indefinite production rates of species. The partial continuity equation is superfluous being replaced by the law of mass-action. This partial continuity equation on the other hand can be used in connection with the other flow equations as well as the law of mass-action to determine this production rate in equilibrium state. Further on, it is shown that for a flat plate boundary layer flow under certain assumptions the profile m ∗ Aδ 2/μ is a similar profile which can be put into a nearly closed analytical form. In this expression, m ∗ A is the production rate of species A, δ the boundary layer thickness and μ the viscosity. This equilibrium profile as well as the equilibrium profiles of concentration and temperature are compared with corresponding nonequilibrium profiles. The equilibrium profiles appear to be limiting profiles approached asymptotically at infinite distances.

Stability of Parallel Flows of Second-Order Liquids

The Orr-Sommerfeld equation, modified to include viscoelastic terms, is solved using a finite-difference method. Combined Couette-Poiseuille flow and flat-plate boundary-layer flow are considered, and it is shown that, for second-order liquids, the influence of the viscoelasticity is always stabilizing. The present numerical scheme, which is based on central differences, does not involve a filtering or a suppressing process and, consequently, is thought to be an improvement over the previously used methods, all of which are based on forward differences.

An exact periodic solution of the energy equation

An exact periodic solution of the unsteady energy equation for an incompressible fluid with constant properties is derived to illustrate the effect of an oscillation through the viscous dissipation on a temperature field. The flow field used here is a generalization of the well-known Couette flow solution of steady flow, in which one wall is at rest and the other wall oscillates in its own plane about a constant mean velocity. The solution is subject to two boundary conditions that correspond to the heat-transfer and thermometer problems. In order to have some suggestions about the approximate solutions, the solution is compared with its own approximate form. The temperature field consists of a time-mean, first and second harmonic fluctuation. The time-mean temperature profiles show the large influence of oscillation. The time-mean heat flux into or the time-mean temperature of the oscillating wall increases with frequency, and is ultimately proportional to the square root of the frequency. In § 4 the present exact solution of the Couette flow is compared with the formerly obtained approximate solution of the flat plate boundary-layer flow in terms of the wall characteristic values at high frequencies.

Flat Plate Boundary-Layer Studies in a Partially Ionized Gas

A combined experimental and numerical investigation was conducted on the flat plate boundary-layer flow of a partially ionized gas. Free molecule cylindrical Langmuir probes were used to measure charged particle density, electron temperature and plasma potential distributions in the boundary layer. The ambipolar diffusion flux to the plate surface was determined by an array of flush-mounted surface electrodes. A probe size-study was carried out and an empirical formula was obtained to make correction for the sheath-fringing field effect on ion current collection to small flush probes. Numerical integrations were made of the charged species conservation and electron energy equations in the quasi-neutral region of the boundary layer for a thin plasma sheath. Mechanisms leading to the cooling of the electrons were investigated. Numerical profiles of charged particle density, electron temperature and plasma potential compared favorably with experimental results. Ambipolar diffusion fluxes predicted theoretically agreed very well with the measured flush probe ion saturation current. The validity of employing such a flush-mounted surface electrode in determination of the free stream charged particle density was then established.

Numerical solutions for radiating hypervelocity boundary-layer flow on a flat plate.

Abstract : The effects of thermal radiation on laminar, flat plate boundary layer flow have been investigated. Non-similar velocity and temperature profiles were obtained as numerical solutions of an appropriate set of finite difference equations. Simplified expressions for the thermodynamic and transport properties were used together with a mean radiation absorption coefficient approximating that of air. On the basis of the results of a previous approximate analysis, it was assumed that the boundary layer would be optically thin; for the velocity range considered (10 to 40 km/s) the numerical results confirmed this hypothesis. It was found that the maximum temperatures in the radiating boundary layers were much lower than in the corresponding non-radiating cases and that the radiating boundary layers were much thinner. Changing the exponent in the temperature-viscosity relationship mu proportional to T to the omega power from 1.0 to .75 had a negligible effect on the maximum temperature in the boundary layer but caused a significant reduction in its thickness and thus in the radiative heat flux to the wall. The predictions of the approximate analysis were compared with the numerical results and found to give useful engineering estimates of the properties of radiating boundary layers. (Author)

Radiative cooling of a uniform gas flow.

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