Hybrid Analytical/Numerical Computation of Heat Transfer in a Gas-Driven Fracture

1986 ◽  
Vol 108 (3) ◽  
pp. 585-590 ◽  
Author(s):  
S. K. Griffiths ◽  
R. H. Nilson ◽  
F. A. Morrison
Keyword(s):  
Heat Transfer ◽  
Surrounding Medium ◽  
Numerical Procedure ◽  
Early Time ◽  
Similarity Solutions ◽  
Fixed Number ◽  
Coupled Processes ◽  
Hydraulic Fractures ◽  
Rock Blasting ◽  
Fracture Growth

In gas-driven hydraulic fractures, as occur in rock blasting and underground nuclear testing, the high-temperature gases (1000 to 30,000 K) are radically cooled by heat transfer to the host material. This significantly reduces both the maximum extent and rate of fracture growth. The coupled processes of fluid flow, heat transfer, and rock deformation governing fracture growth are calculated here by a hybrid analytical/numerical procedure. The gas motion along a fracture of increasing length and aperture is described by a finite-difference form of the one-dimensional transport equations; fluid friction, advective heat transfer, and heat loss to the walls of the fracture are considered. Lateral heat losses are evaluated in a quasi-analytical fashion, based on an integral method that accounts for the convective film resistance between the fluid and fracture wall, as well as the conductive resistance within the surrounding medium. The calculations are performed on a difference grid that expands to maintain a fixed number of points uniformly distributed along the fracture. The present numerical results agree, within appropriate limits, with known similarity solutions. Beyond this, new nonsimilar solutions for early-time fracture growth are presented.

Effects of Insulated and Isothermal Baffles on Pseudosteady-State Natural Convection Inside Spherical Containers

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Yuping Duan ◽  
S. F. Hosseinizadeh ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Enhancement ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Transfer Enhancement ◽  
Nusselt Numbers ◽  
Extended Surface ◽  
Parametric Studies ◽  
Thermal Layer

The effects of insulated and isothermal thin baffles on pseudosteady-state natural convection within spherical containers were studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106, and 107, baffles with three lengths positioned at five different locations were investigated (120 cases). The fluid that is heated adjacent to the sphere rises replacing the colder fluid, which sinks downward through the stratified stable thermal layer. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid, thus causing oscillations in the temperature and flow fields. Due to flow obstruction (blockage or confinement) effect of baffles and also because of the extra heating afforded by the isothermal baffle, multi-cell recirculating vortices are observed. This additional heat is directly linked to creation of another recirculating vortex next to the baffle. In effect, hot fluid is directed into the center of the sphere disrupting thermal stratified layers. For the majority of the baffles investigated, the Nusselt numbers were generally lower than the reference cases with no baffle. The extent of heat transfer modification depends on Ra, length, and location of the extended surface. With an insulated baffle, the lowest amount of absorbed heat corresponds to a baffle positioned horizontally. Placing a baffle near the top of the sphere for high Ra number cases can lead to heat transfer enhancement that is linked to disturbance of the thermal boundary layer. With isothermal baffles, heat transfer enhancement is achieved for a baffle placed near the bottom of the sphere due to interaction of the counterclockwise rotating vortex and the stratified layer. For some high Ra cases, strong fluctuations of the flow and thermal fields indicating departure from the pseudosteady-state were observed.

Full-Coverage Film Cooling—Part II: Heat Transfer Data and Numerical Simulation

1980 ◽  
Vol 102 (4) ◽  
pp. 1006-1012 ◽  
Author(s):  
M. E. Crawford ◽  
W. M. Kays ◽  
R. J. Moffat
Keyword(s):  
Heat Transfer ◽  
Film Cooling ◽  
Numerical Procedure ◽  
Stanton Number ◽  
Data Sets ◽  
Blowing Ratio ◽  
Diameter Hole ◽  
Full Coverage ◽  
Sample Data ◽  
Length Data

Experimental research into heat transfer from full-coverage film-cooled surfaces with three injection geometries was described in Part I. This part has two objectives. The first is to present a simple numerical procedure for simulation of heat transfer with full-coverage film cooling. The second objective is to present some of the Stanton number data that was used in Part I of the paper. The data chosen for presentation are the low-Reynolds number, heated-starting-length data for the three injection geometries with five-diameter hole spacing. Sample data sets with high blowing ratio and with ten-diameter hole spacing are also presented. The numerical procedure has been successfully applied to the Stanton number data sets.

Multi-Objective Optimization of a Microturbine Compact Recuperator

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Diego Micheli ◽  
Valentino Pediroda ◽  
Stefano Pieri
Keyword(s):  
Heat Transfer ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Design Procedure ◽  
Domain Size ◽  
Multidisciplinary Optimization ◽  
Computational Domain ◽  
Surface Geometry ◽  
Multi Objective ◽  
Flux Boundary Conditions

An automatic approach for the multi-objective shape optimization of microgas turbine heat exchangers is presented. According to the concept of multidisciplinary optimization, the methodology integrates a CAD parametric model of the heat transfer surfaces, a three-dimensional meshing tool, and a CFD solver, all managed by a design optimization platform. The repetitive pattern of the surface geometry has been exploited to reduce the computational domain size, and the constant flux boundary conditions have been imposed to better suit the real operative conditions. A new approach that couples cold and warm fluids in a periodic unitary cell is introduced. The effectiveness of the numerical procedure was verified comparing the numerical results with available literature data. The optimization objectives are maximizing the heat transfer rate and minimizing both friction factor and heat transfer surface. The paper presents the results of the optimization of a 50kWMGT recuperator. The design procedure can be effectively extended and applied to any industrial heat exchanger application.

Scalable Heat Transfer Characterization on Film Cooled Geometries Based on Discrete Green’s Functions

2020 ◽  
Author(s):  
Jorge Saavedra ◽  
Venkat Athmanathan ◽  
Guillermo Paniagua ◽  
Terrence Meyer ◽  
Doug Straub ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Flat Plate ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Green's Functions ◽  
Green’S Functions ◽  
Numerical Procedure ◽  
Local Heat Transfer ◽  
Sensitivity Matrix

Abstract The aerothermal characterization of film cooled geometries is traditionally performed at reduced temperature conditions, which then requires a debatable procedure to scale the convective heat transfer performance to engine conditions. This paper describes an alternative engine-scalable approach, based on Discrete Green’s Functions (DGF) to evaluate the convective heat flux along film cooled geometries. The DGF method relies on the determination of a sensitivity matrix that accounts for the convective heat transfer propagation across the different elements in the domain. To characterize a given test article, the surface is discretized in multiple elements that are independently exposed to perturbations in heat flux to retrieve the sensitivity of adjacent elements, exploiting the linearized superposition. The local heat transfer augmentation on each segment of the domain is normalized by the exposed thermal conditions and the given heat input. The resulting DGF matrix becomes independent from the thermal boundary conditions, and the heat flux measurements can be scaled to any conditions given that Reynolds number, Mach number, and temperature ratios are maintained. The procedure is applied to two different geometries, a cantilever flat plate and a film cooled flat plate with a 30 degree 0.125” cylindrical injection orifice with length-to-diameter ratio of 6. First, a numerical procedure is applied based on conjugate 3D Unsteady Reynolds Averaged Navier Stokes simulations to assess the applicability and accuracy of this approach. Finally, experiments performed on a flat plate geometry are described to validate the method and its applicability. Wall-mounted thermocouples are used to monitor the surface temperature evolution, while a 10 kHz burst-mode laser is used to generate heat flux addition on each of the discretized elements of the DGF sensitivity matrix.

scholarly journals Morphological evolution of microscopic dewetting droplets with slip

2017 ◽  
Vol 828 ◽  
pp. 271-288 ◽  
Author(s):  
Tak Shing Chan ◽  
Joshua D. McGraw ◽  
Thomas Salez ◽  
Ralf Seemann ◽  
Martin Brinkmann
Keyword(s):  
Slip Length ◽  
Morphological Evolution ◽  
Early Time ◽  
Slip Boundary Condition ◽  
Similarity Solutions ◽  
Contact Angles ◽  
Equilibrium Contact Angle ◽  
Navier Slip ◽  
Slip Boundary ◽  
Quasistatic Regime

We investigate the dewetting of a droplet on a smooth horizontal solid surface for different slip lengths and equilibrium contact angles. Specifically, we solve for the axisymmetric Stokes flow using the boundary element method with (i) the Navier-slip boundary condition at the solid/liquid boundary and (ii) a time-independent equilibrium contact angle at the contact line. When decreasing the rescaled slip length $\tilde{b}$ with respect to the initial central height of the droplet, the typical non-sphericity of a droplet first increases, reaches a maximum at a characteristic rescaled slip length $\tilde{b}_{m}\approx O(0.1{-}1)$ and then decreases. Regarding different equilibrium contact angles, two universal rescalings are proposed to describe the behaviour of the non-sphericity for rescaled slip lengths larger or smaller than $\tilde{b}_{m}$. Around $\tilde{b}_{m}$, the early time evolution of the profiles at the rim can be described by similarity solutions. The results are explained in terms of the structure of the flow field governed by different dissipation channels: elongational flows for $\tilde{b}\gg \tilde{b}_{m}$, friction at the substrate for $\tilde{b}\approx \tilde{b}_{m}$ and shear flows for $\tilde{b}\ll \tilde{b}_{m}$. Following the changes between these dominant dissipation mechanisms, our study indicates a crossover to the quasistatic regime when $\tilde{b}$ is many orders of magnitude smaller than $\tilde{b}_{m}$.

Melting Heat Transfer in Squeezed Nanofluid Flow Through Darcy Forchheimer Medium

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
M. Farooq ◽  
S. Ahmad ◽  
M. Javed ◽  
Aisha Anjum
Keyword(s):  
Heat Transfer ◽  
Flow Behavior ◽  
Transfer Characteristic ◽  
Skin Friction Coefficient ◽  
Similarity Solutions ◽  
Brownian Diffusion ◽  
Physical Parameters ◽  
Melting Heat ◽  
Melting Heat Transfer ◽  
Melting Parameter

In this attempt, melting heat transfer characteristic of unsteady squeezed nanofluid flows in non-Darcy porous medium is interrogated. The nanofluid model incorporates Brownian diffusion and thermophoresis to characterize the heat and mass transport in the presence of thermal and solutal stratification. Similarity solutions are implemented to acquire nonlinear system of ordinary differential equations which are then evaluated using Homotopic technique. Flow behavior of involved physical parameters is examined and explanations are stated through graphs. We determine and analyze skin friction coefficient, Nusselt and Sherwood numbers through graphs. It is evident that larger melting parameter results in decrement in temperature field, while horizontal velocity enhances for higher melting parameter. Moreover, temperature and concentration fields are dominant for higher Brownian diffusion parameter.

Some Reflections On Sparrow's Work On Similarity Solutions for Laminar Film Condensation On a Vertical Plate

2021 ◽  
Author(s):  
Vijay K. Dhir
Keyword(s):  
Heat Transfer ◽  
Vertical Plate ◽  
Generalized Solution ◽  
Similarity Solutions ◽  
Film Condensation ◽  
Gravitational Acceleration ◽  
Curved Surfaces ◽  
Laminar Film ◽  
Laminar Film Condensation ◽  
Variable Gravity

Abstract In this contribution in honor of Late Prof. E. M. Sparrow, we reflect on the pioneering work of Sparrow and Gregg on the development of similarity solutions for laminar film condensation on a vertical plate. Dhir and Lienhard using this work as a basis developed a generalized solution for isothermal curved surfaces on which gravitational acceleration varied along the surface and for variable gravity situations. Subsequently non-isothermal surfaces were also considered. These studies were publisher earlier in the J. Heat Transfer.

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