Citation
Zung, Laurence BeiYu (1967) Particle fluid mechanics in shear flows, acoustic waves, and shock waves. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:11302015140521884
Abstract
Three different categories of flow problems of a fluid containing small particles are being considered here. They are: (i) a fluid containing small, nonreacting particles (Parts I and II); (ii) a fluid containing reacting particles (Parts III and IV); and (iii) a fluid containing particles of two distinct sizes with collisions between two groups of particles (Part V).
Part I
A numerical solution is obtained for a fluid containing small particles flowing over an infinite disc rotating at a constant angular velocity. It is a boundary layer type flow, and the boundary layer thickness for the mixture is estimated. For large Reynolds number, the solution suggests the boundary layer approximation of a fluidparticle mixture by assuming W = W_{p}. The error introduced is consistent with the Prandtl’s boundary layer approximation. Outside the boundary layer, the flow field has to satisfy the “inviscid equation” in which the viscous stress terms are absent while the drag force between the particle cloud and the fluid is still important. Increase of particle concentration reduces the boundary layer thickness and the amount of mixture being transported outwardly is reduced. A new parameter, β = 1/Ω τ_{v}, is introduced which is also proportional to μ. The secondary flow of the particle cloud depends very much on β. For small values of β, the particle cloud velocity attains its maximum value on the surface of the disc, and for infinitely large values of β, both the radial and axial particle velocity components vanish on the surface of the disc.
Part II
The “inviscid” equation for a gasparticle mixture is linearized to describe the flow over a wavy wall. Corresponding to the PrandtlGlauert equation for pure gas, a fourth order partial differential equation in terms of the velocity potential ϕ is obtained for the mixture. The solution is obtained for the flow over a periodic wavy wall. For equilibrium flows where λ_{v} and λ_{T} approach zero and frozen flows in which λ_{v} and λ_{T} become infinitely large, the flow problem is basically similar to that obtained by Ackeret for a pure gas. For finite values of λ_{v} and λ_{T}, all quantities except v are not in phase with the wavy wall. Thus the drag coefficient C_{D} is present even in the subsonic case, and similarly, all quantities decay exponentially for supersonic flows. The phase shift and the attenuation factor increase for increasing particle concentration.
Part III
Using the boundary layer approximation, the initial development of the combustion zone between the laminar mixing of two parallel streams of oxidizing agent and small, solid, combustible particles suspended in an inert gas is investigated. For the special case when the two streams are moving at the same speed, a Green’s function exists for the differential equations describing first order gas temperature and oxidizer concentration. Solutions in terms of error functions and exponential integrals are obtained. Reactions occur within a relatively thin region of the order of λ_{D}. Thus, it seems advantageous in the general study of twodimensional laminar flame problems to introduce a chemical boundary layer of thickness λ_{D} within which reactions take place. Outside this chemical boundary layer, the flow field corresponds to the ordinary fluid dynamics without chemical reaction.
Part IV
The shock wave structure in a condensing medium of small liquid droplets suspended in a homogeneous gasvapor mixture consists of the conventional compressive wave followed by a relaxation region in which the particle cloud and gas mixture attain momentum and thermal equilibrium. Immediately following the compressive wave, the partial pressure corresponding to the vapor concentration in the gas mixture is higher than the vapor pressure of the liquid droplets and condensation sets in. Farther downstream of the shock, evaporation appears when the particle temperature is raised by the hot surrounding gas mixture. The thickness of the condensation region depends very much on the latent heat. For relatively high latent heat, the condensation zone is small compared with Ʌ_{D}.
For solid particles suspended initially in an inert gas, the relaxation zone immediately following the compression wave consists of a region where the particle temperature is first being raised to its melting point. When the particles are totally melted as the particle temperature is further increased, evaporation of the particles also plays a role.
The equilibrium condition downstream of the shock can be calculated and is independent of the model of the particlegas mixture interaction.
Part V
For a gas containing particles of two distinct sizes and satisfying certain conditions, momentum transfer due to collisions between the two groups of particles can be taken into consideration using the classical elastic spherical ball model. Both in the relatively simple problem of normal shock wave and the perturbation solutions for the nozzle flow, the transfer of momentum due to collisions which decreases the velocity difference between the two groups of particles is clearly demonstrated. The difference in temperature as compared with the collisionless case is quite negligible.
Item Type:  Thesis (Dissertation (Ph.D.))  

Subject Keywords:  Engineering  
Degree Grantor:  California Institute of Technology  
Division:  Engineering and Applied Science  
Major Option:  Engineering and Applied Science  
Thesis Availability:  Public (worldwide access)  
Research Advisor(s): 
 
Thesis Committee: 
 
Defense Date:  10 May 1967  
Funders: 
 
Record Number:  CaltechTHESIS:11302015140521884  
Persistent URL:  http://resolver.caltech.edu/CaltechTHESIS:11302015140521884  
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided.  
ID Code:  9297  
Collection:  CaltechTHESIS  
Deposited By:  Leslie Granillo  
Deposited On:  02 Dec 2015 16:19  
Last Modified:  02 Dec 2015 16:19 
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