Pressure field

Continuum theory has also been applied to analyse tire dynamics of flow of nematics [77, 80, 81 and 82]. The equations provide tire time-dependent velocity, director and pressure fields. These can be detennined from equations for tire fluid acceleration (in tenns of tire total stress tensor split into reversible and viscous parts), tire rate of change of director in tenns of tire velocity gradients and tire molecular field and tire incompressibility condition [20]. 

In this element the velocity and pressure fields are approximated using biquadratic and bi-linear shape functions, respectively, this corresponds to a total of 22 degrees of freedom consisting of 18 nodal velocity components (corner, mid-side and centre nodes) and four nodal pressures (corner nodes). 

Fluid statics, discussed in Sec. 10 of the Handbook in reference to pressure measurement, is the branch of fluid mechanics in which the fluid velocity is either zero or is uniform and constant relative to an inertial reference frame. With velocity gradients equal to zero, the momentum equation reduces to a simple expression for the pressure field, Vp = pg. Letting z be directed vertically upward, so that g, = —g where g is the gravitational acceleration (9.806 mVs), the pressure field is given by... 

Tsuchiya, M., S. Murakami, A. Nochida, K. Kondo, and Y. Ishida. 1997. Development of a new i-e model for flow and pressure fields around bluff body. /. Witid Engineering and Industrial Aerodynamics, vols. 67-68, pp. 169-182. 

The major mechanism of a vapor cloud explosion, the feedback in the interaction of combustion, flow, and turbulence, can be readily found in this mathematical model. The combustion rate, which is primarily determined by the turbulence properties, is a source term in the conservation equation for the fuel-mass fraction. The attendant energy release results in a distribution of internal energy which is described by the equation for conservation of energy. This internal energy distribution is translated into a pressure field which drives the flow field through momentum equations. The flow field acts as source term in the turbulence model, which results in a turbulent-flow structure. Finally, the turbulence properties, together with the composition, determine the rate of combustion. This completes the circle, the feedback in the process of turbulent, premixed combustion in gas explosions. The set of equations has been solved with various numerical methods e.g., SIMPLE (Patankar 1980) SOLA-ICE (Cloutman et al. 1976). 

Leyer, J. C. 1982. An experimental study of pressure fields by exploding cylindrical clouds. Combustion and Flame. 48 251-263. 

Considering the case of premixed flames, it is noted by Thomas and Williams [26] that sound radiation can be related to the rate of change of the flame surface area by assuming that the burning velocity is constant. Similarly, Ref. [35] and later Ref. [36] indicate that in the wrinkled flame regime, the rate of chemical conversion is directly linked to the flame surface area A(t). For a mixture of fresh reactants at a constant equivalence ratio, the pressure field is directly linked to the instantaneous flame surface ... 

The first item is easily treated by considering the eigen-modes of the system and expanding the pressure field on a basis formed by these modes. The second item is less well documented but is clearly important. The presence of boundaries not only modifies the structure of the mean flow but also influences the flame dynamics. This is demonstrated in a set of recent experiments in which the lateral confinement was varied systematically [45]. 

The situation is different for incompressible flow. In that case, no equation of motion for the pressure field exists and via the mass conservation equation Eq. (17) a dynamic constraint on the velocity field is defined. The pressure field entering the incompressible Navier-Stokes equation can be regarded as a parameter field to be adjusted such that the divergence of the velocity field vanishes. 

At that stage, the approximation obtained for the velocity field does generally not fulfil the mass conservation equation. In order to ensure mass conservation, corrections to the velocity and pressure field are introduced via... 

A passive system is much the same as an active system with the exception of the fan. A passive system relies only on stack and wind effects to produce the pressure field. As can be seen in Table 31.1, passive systems do not always reduce radon concentrations to acceptable levels, but careful design and installation may improve the effectiveness of a passive system. 

Theofanous, T., L. Biasi, H. S. Isbin, and H. K. Fauske, 1969, A Theoretical Study on Bubble Growth in Constant and Time-Dependent Pressure Fields, Chem. Eng. Sci. 24 885. (2)... 

Prediction of cavitational activity distribution based on theoretical analysis of the bubble dynamics equations can be used to identify the regions with maximum pressure fields in a large scale reactor and then may be small reactors can... 

Keil F, Dahnke S (1996) Numerical calculation of pressure field in sonochemical reactor. Chem Ing Tech 68 419 -22... 

Dahnke S, Keil F (1998) Modeling of three dimension linear pressure field in sonochemical reactores with homogenous and inhomogenous density distribution of cavity bubbles. Ind Eng Chem Res 37 848-864... 

Dahnke S, Keil F (1999) Modeling of linear pressure fields in sonochemical reactor considering an inhomogeneous density distribution of cavitation bubble. Chem Eng Sci 54 2865-2872... 

Moholkar VS, Rekveld S, Warmoeskerken MMCG (2000) Modeling of the acoustic pressure fields and the distribution of the cavitation phenomena in a dual frequency sonic processor. Ultrasonics 38 666-670... 

One of the simplest approaches to quantify the pressure field downstream of the constriction used to generate cavitation is to assume linear pressure recovery profile. Yan et al. [8] have used similar approach also considering a single bubble to be existing independent of the other bubbles. Such an approach may be adequate when the intensity of turbulence is quite low i.e. for a venturi type constriction or any other constriction with a smooth variation in the cross-sectional flow area. The pressure recovery from the point at which cavitation starts to any downstream pipe position can be approximated by a linear expression with respect to the distance downstream of the constriction. In such a case, the local pressure at any downstream position can be estimated as ... 

A more realistic approach to quantify the pressure field is to consider the effect of turbulence [6]. For a pipe flow, the turbulent pressure fluctuations are due to velocity perturbations as a result of the formation of eddies. The instantaneous turbulent velocity can be calculated by assuming a sinusoidal velocity variation in... 

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