Solution Of Laminar Boundary Layer Equations Research Articles

A numerical method for solution of the discharge coefficients in externally pressurized gas bearings with inherent orifice restrictors

To study the discharge coefficients of aerostatic bearings, a new numerical method which combines the method of “separation of variables” for solution of laminar boundary-layer equations and analytical solution of Reynolds equation is proposed. The discharge coefficients are suitable for solution of Reynolds equation. The influences of flow and geometry parameters on discharge coefficients are investigated and the results indicate that there exists parameters insensitive and sensitive regions in discharge coefficient analysis. Further research shows that flow and geometry parameters affect discharge coefficient by influencing the pressure ratio (pr/ps) and discharge coefficient tends to be constant when pressure ratio is approximately less than 0.6, which is the reason that there exists the parameters insensitive and sensitive regions.

Numerical research of pressure depression in aerostatic thrust bearing with inherent orifice

Abstract The undesirable pressure depression in aerostatic bearing will cause the loss of aerostatic bearing load capacity. Therefore, the method of “separation of variables” (MSV) for solution of laminar boundary-layer equations is utilized to investigate the pressure depression. The influences of supply pressure, orifice diameter, film thickness and pressure ratio on the pressure depression are studied. The results manifest that pressure depression is weakened with decreasing supply pressure and film thickness and increasing orifice diameter. The increase of pressure ratio which is determined by the flow and geometry parameters will weaken the inertial effect and then results in weakening the pressure depression. What's more, when pressure ratio is larger than the critical value 0.9409, the pressure depression will disappear.

A Method of “Separation of Variables” for the Solution of Laminar Boundary-Layer Equations of Narrow-Channel Flows

A method of solution for laminar channel flow is established using the von Mises transformation followed by the “separation” of the main flow velocity into amplitude and profile functions. The known boundary conditions on the latter enable a generalized solution that yields, through a parametric relation between auxiliary parameters (the characteristics), a system of ordinary differential equations for the velocity amplitude and the pressure. The result is a powerful semi-analytical method which is very easy to implement for a variety of internal flow configurations. The method is, in essence, a downstream general solution which may be extended upstream to the singular limit of a uniform main flow velocity distribution at the channel entrance. The regular solution for uniform initial velocity distribution cannot thus be obtained. Comparisons with other solutions show only qualitative agreement, for reasons which are discussed, whereas agreement with experimental results, made in a separate publication, is remarkably good.

On the accuracy of Merk's method for solution of laminar boundary-layer equations

On the accuracy of Merk's method for solution of laminar boundary-layer equations

Solutions of Laminar Boundary-Layer Equations Involving Separations

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