scholarly journals Modeling Turbulent Hydraulic Fracture Near a Free Surface

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Victor C. Tsai ◽  
James R. Rice
Keyword(s):  
Growth Rate ◽  
Fluid Flow ◽  
Free Surface ◽  
Hydraulic Fracture ◽  
Crack Opening ◽  
Pressure Profile ◽  
Numerical Approach ◽  
Chebyshev Series ◽  
Opening Displacement ◽  
Turbulent Fluid Flow

Motivated by observations of the subglacial drainage of water, we consider a hydraulic fracture problem in which the crack grows parallel to a free surface, subject to fully turbulent fluid flow. Using a hybrid Chebyshev/series-minimization numerical approach, we solve for the pressure profile, crack opening displacement, and crack growth rate for a crack that begins relatively short but eventually becomes long compared with the distance to the free surface. We plot nondimensionalized results for a variety of different times, corresponding with different fracture lengths, and find substantial differences when free-surface effects are important.

Oscillatory Incompressible Fluid Flow in a Tapered Tube With a Free Surface in an Inkjet Print Head

2005 ◽  
Vol 127 (1) ◽  
pp. 98-109 ◽  
Author(s):  
Dong-Youn Shin ◽  
Paul Grassia ◽  
Brian Derby
Keyword(s):  
Fluid Flow ◽  
Free Surface ◽  
Incompressible Fluid ◽  
Numerical Approach ◽  
Computational Time ◽  
Approximate Analytic Solution ◽  
Incompressible Fluid Flow ◽  
Print Head ◽  
Fluid Behavior ◽  
The Cost

Oscillatory incompressible fluid flow with a free surface occurs in an inkjet print head. Due to complex physical fluid behavior, numerical simulations have been a common approach to characterize the pressure and velocity development in time and space. However, the cost of a numerical approach is high in terms of computational time such that approximate analytic approaches have been developed. In this paper, an approximate analytic solution for a tapered nozzle section is described with a proper downstream boundary condition and the physical behavior of the meniscus deformation is modeled with a simple “window” theory.

Tip region of a hydraulic fracture driven by a laminar-to-turbulent fluid flow

2016 ◽  
Vol 797 ◽  
Author(s):  
E. V. Dontsov
Keyword(s):  
Fluid Flow ◽  
Turbulent Flow ◽  
Numerical Solution ◽  
Hydraulic Fracture ◽  
Asymptotic Solutions ◽  
Turbulent Regime ◽  
Zone Size ◽  
Turbulent Fluid Flow ◽  
Fully Developed Turbulent Flow ◽  
Steady Propagation

The focus of this study is to analyse the tip region of a hydraulic fracture, for which a fluid flow inside the crack transitions from the laminar to the turbulent regime away from the tip. To tackle the problem, a phenomenological formula for flow in pipes has been adapted to describe flow in a fracture through the concept of a hydraulic diameter. The selected model is able to capture laminar, turbulent and transition regimes of the flow. The near-tip region of a hydraulic fracture is analysed by focusing on steady propagation of a semi-infinite hydraulic fracture with leak-off, for which the aforementioned phenomenological formula for the fluid flow is utilized. First, the distance from the tip within which a laminar solution applies is estimated. Then, expressions for asymptotic solutions that are associated with fully developed turbulent flow inside the semi-infinite hydraulic fracture are derived. Finally, the laminar zone size and the asymptotic solutions are compared with the numerical solution, where the latter captures all regimes of the fluid flow.

Environmental crack and craze growth phenomena in polymers

1975 ◽  
Vol 342 (1628) ◽  
pp. 55-77 ◽  
Keyword(s):  
Fluid Flow ◽  
Crack Propagation ◽  
Crack Opening ◽  
Time Dependent ◽  
Relaxation Processes ◽  
Inorganic Glass ◽  
Opening Displacement ◽  
Crack Growth Behaviour ◽  
Craze Growth ◽  
Fluid Flow Control

The nature of slow crack and craze propagation in polymers and crack propagation in inorganic glass has been considered in terms of time dependent processes. By using a fracture mechanics analysis together with time dependent material parameters, equations have been derived to describe crack and craze propagation in both inert and active environments. Experimental data from a range of materials suggest that a crack opening displacement (c. o. d. ) criterion governs the crack propagation behaviour. Incorporation of a simple fluid flow model into the c. o. d. analysis has allowed the failure processes in liquid environments to be described. The data on organic polymers and inorganic glass suggest that when there are no problems of maintaining the environmental supply, the crack growth behaviour is controlled by relaxation processes in the material. At high crack speeds a transition from relaxation to fluid flow control occurs when the time scale is too short for the liquid flow to be maintained. The flow of an environment in long crazes can be shown to influence their behaviour in a similar manner, while under other conditions relaxation controlled craze growth can occur.

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