Surface pressure distribution

Figure 5.10 shows the surface pressure distribution at different values of Re. The distribution changes remarkably little between Re = 400 and 1.6 x 10. Since form drag now predominates as noted above, is also insensitive to Re. For 750 < Re < 3.5 x 10, the Newton s law range, Cq varies by only +13%... 

Actual shapes of fluid particles deviate from the idealized shape which leads to Eqs. (8-15) and (8-16). Surface pressure distributions derived from observed shapes (W2) are shown in Fig. 8.3 for spherical-cap bubbles at high Re. It is seen that the pressure variation is well described by Eq. (8-15) for 0 < 0 < while the potential flow pressure distribution, Eq. (1-32), gives good agreement up to about 30° from the nose. 

Surface pressure distribution measurement is of fundamental importance in the experimental study of aerodynamic problems in the fields of avionics, car, rocket, aerospace, and aircraft design [1]. The conventional methods based on pressure taps or transducers have a number of limitations. The most serious problem is that their very nature limits them to providing information only at discrete points on the surface of a substrate. A new approach to surface pressure distribution measurement, the use of pressure-sensitive paint (PSP), has recently developed that offers the potential of revolutionizing the nature of such measurements in the field of aerodynamics. This method employs the oxygen sensitivity of fluorescent materials in the form of a paint, in conjunction with image processing techniques, to map the pressure field over... 

Fig. 4. Phosphorescent image of a section of a model aircraft wing showing the surface pressure distribution as a function of tilt angle (a) during a wind tunnel experiment. (The colors, whilst artificial, reflect the pressure at different points on the surface. In this case, the polymer matrix was composed of poly(aminothionylphosphazene)-b-poly[THF] (31) and the dye was [Ru(phenPh2)3]Cl2. The images were obtained from a series of tests run at the National Research Council Wind Tunnel in Ottawa)...

Here = icR , or 2Rj is the midsection of a sphere or a cylinder of Rj in ength is the surface pressure distribution and P, is the pressure after nomal reflection of SW in a homogeneous medium ... 

Figure 3 Predictions of Elastic Deformation Amplitude for a Sinusoidal Surface Pressure Distribution...

Surface pressure distribution for an oblate particle ( = 0.5) in creeping regime = 0.01). 

A thorough description of the internal flow stmcture inside a swid atomizer requires information on velocity and pressure distributions. Unfortunately, this information is still not completely available as of this writing (1996). Useful iasights on the boundary layer flow through the swid chamber are available (9—11). Because of the existence of an air core, the flow stmcture iaside a swid atomizer is difficult to analyze because it iavolves the solution of a free-surface problem. If the location and surface pressure of the Hquid boundary are known, however, the equations of motion of the Hquid phase can be appHed to reveal the detailed distributions of the pressure and velocity. 

For a building with sharp corners, Cp is almost independent of the wind speed (i.e., Reynolds number) because the flow separation points normally occur at the sharp edges. This may not be the case for round buildings, w here the position of the separation point can be affected by the wind speed. For the most common case of the building with a rectangular shape, Cp values are normally between 0.6 and 0.8 for the upwind wall, and for the leeward wall 0,6 < C, < —0.4. Figure 7.99 and Table 7.32 show an example of the distribution of surface pressure coefficient values on the typical industrial building envelope. 

The pressure distribution across the mold is a function of both the mold surface and the platen flatness. The larger the mold size and the platen, the more difficult it is to maintain the high degree of flatness required. The mold and platen flatness is also critical in the area of heat transfer from the platen to the mold itself. 

The systems of Eqs. (8.56-8.58), (8.64-8.66), and (8.77-8.79) allow us to find the density, velocity, temperature and pressure distributions along the capillary axis, as well as the interface surface shape. 

The main task of head-disk gas lubrication analysis is to calculate the air pressure distributions for various known slider surface structures and given working conditions. In the following calculation examples, the modified Reynolds equation derived by Fukui and Kaneko was used, and the flow rate coefficient Qp was calculated by using the Eq (10). 

Let us compare the magnitude of the van der Waals pressure with that of air bearing pressure. In Section 3.2, we have shown the numerical solution of gas pressure distribution for a two-rail slider and a O t pe slider. By simply summing up the contributions of gas pressure and van der Waals pressure and integrating over the whole slider surface area, the total dimensionless load carrying capacity becomes... 

The model has been applied successfully to predicting the performances of bearings, gears, seals, and engines [10-12]. A fundamental limitation of the statistic models is their inability to provide detailed information about local pressure distribution, film thickness fluctuation, and asperity deformation, which are crucial for understanding the mechanisms of lubrication, friction, and surface failure. As an alternative, researchers paid a great interest to the deterministic ML model. 

The word deterministic" means that the model employs a specific surface geometry or prescribed roughness data as an input of the numerical procedure for solving the governing equations. The method was originally adopted in micro-EHL to predict local film thickness and pressure distributions over individual asperities, and it can be used to solve the mixed lubrication problems when properly combined with the solutions of asperity contacts. 

Consider a distributed pressure acting on an elastic halfspace, and let the pressure distribution and the normal surface deformation be denoted hy p(x) and v x) for line contacts, or hypix, y) and v(x, y) for point contacts, respectively. According to the theory of contact mechanics [18], the normal surface deformation v(x) or v x,y) caused by a distributed pressure may be written in the forms of... 

In numerical analysis, both functions of normal surface deformation and pressure distribution have to be discretized in a space domain over U grid points for a line load, or grid points for two-dimensional distributed load. As an example, the deformation for line loading can be rewritten in discrete form as follows ... 

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