A Coupled FDM/Bem Solution for the Conjugate Heat Transfer Problem

He, Mengyuan; Bishop, P J; Kassab, Alain J.; Minardi, A.

doi:10.1080/10407799508928826

Cited by 22 publications

(8 citation statements)

References 4 publications

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“…This is in sharp contrast to the domain meshing methods, such as FVM and FEM where heat fluxes are computed by the numerical differentiation in a post‐processing stage. He et al (1995a, b) adopted the BEM/FVM approach in the further studies of CHT in incompressible flow in ducts subjected to a constant wall temperature and constant heat flux boundary conditions. Kontinos (1997) also adopted the BEM/FVM coupling algorithm to solve the CHT over metallic thermal protection panels at the leading edge of the X‐33 in a Mach 15 hypersonic flow regime.…”

Section: Introductionmentioning

confidence: 99%

BEM/FVM conjugate heat transfer analysis of a three‐dimensional film cooled turbine blade

Kassab

Divo

Heidmann

et al. 2003

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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We report on the progress in the development and application of a coupled boundary element/finite volume method temperature‐forward/flux‐back algorithm developed to solve conjugate heat transfer arising in 3D film‐cooled turbine blades. We adopt a loosely coupled strategy where each set of field equations is solved to provide boundary conditions for the other. Iteration is carried out until interfacial continuity of temperature and heat flux is enforced. The NASA‐Glenn explicit finite volume Navier‐Stokes code Glenn‐HT is coupled to a 3D BEM steady‐state heat conduction solver. Results from a CHT simulation of a 3D film‐cooled blade section are compared with those obtained from the standard two temperature model, revealing that a significant difference in the level and distribution of metal temperatures is found between the two. Finally, current developments of an iterative strategy accommodating large numbers of unknowns by a domain decomposition approach is presented. An iterative scheme is developed along with a physically‐based initial guess and a coarse grid solution to provide a good starting point for the iteration. Results from a 3D simulation show the process that converges efficiently and offers substantial computational and storage savings.

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Section: Introductionmentioning

confidence: 99%

BEM/FVM conjugate heat transfer analysis of a three‐dimensional film cooled turbine blade

Kassab

Divo

Heidmann

et al. 2003

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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“…5 indicates that this value is within 16% of the measured value. Comparison of the measured wall static pressure (11,997 Pa) with the wind-tunnel console gauges (12,273 Pa) determined that the data acquisitionsystem and console gauge had a margin of error less than 2%. By using the Mach number value of 3.03 and by knowing the total pressure and temperature, the wind-tunnel ow characteristics can be summarized as given in Table 1.…”

Section: Methodsmentioning

confidence: 99%

“…Consequently, solid/ uid interfacial heat uxes that are required to enforce continuity in the CHT problem are naturally provided by the BEM conduction analysis, unlike FVM and FEM where heat uxes are computed in a postprocessing stage by numerical differentiation. He et al 10,11 adopted this approach in further studies of CHT in incompressible ow in ducts subjected to constant wall temperature and constantheat ux boundaryconditions.Kontinos 12 also adopted the BEM/FVM coupling algorithm to solve the CHT over metallic thermal protection panels at the leading edge of the of the X-33 in a Mach 15 hypersonic ow regime.…”

mentioning

confidence: 99%

Coupled Dual Reciprocity Boundary Element/Finite Volume Method for Transient Conjugate Heat Transfer

Rahaim

Kassab

Cavalleri

2000

Journal of Thermophysics and Heat Transfer

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A coupled nite volume/dual reciprocity boundary element method is developed to solve the transient conjugate heat transfer problem of convective heat transfer over and conduction heat transfer within a solid body. In this approach, the ow eld and forced convection heat transfer external to the body is resolved by numerically solving the time-dependent Navier-Stokes equations using a nite volume method, whereas the temperature eld within the body is resolved by numerically solving the heat conduction equation using a dual reciprocity boundary element method. The boundary discretization utilized to generate the computational grid for the external ow eld provides the boundary discretization required for the boundary element method. Coupling of the two elds is accomplished by enforcing interface continuity of heat ux and temperature. Transient heat transfer data needed to verify the code were obtained in a series of experiments that are reported. Details of the experimental setup and test conditions are provided. Numerical simulations of the experiments show good agreement with obtained experimental data. Nomenclature a = nonlinear diffusivity, function of w C(n ) = free term in boundary element method (BEM) equations c = speci c heat D = diagonal matrix E(x, n ) = negative of normal derivative of T ¤ multiplied by k e = speci c energy F = dual reciprocity BEM (DRBEM) interpolating matrix F c = x component of convective ux vector F d = x component of diffusive ux vector f = expansion function G = BEM in uence matrix multiplying vector of nodal uxes G c = y component of convective ux vector G d = y component of diffusive ux vector H = BEM in uence matrix multiplying vector of nodal temperatures h = speci c enthalpy h ¤ = half-channel height k = thermal conductivity k 0 = reference thermal conductivity L = number of additional DRBEM expansion points N = number of BEM nodes P = DRBEM interpolating matrix Pe = Peclet number Pr = Prandtl number p = pressure = negative of normal derivative of u k multiplied by k q(x) = heat ux vector r (x, n ) = Euclidean distance between source (n ) and eld point (x) T = temperature T B = bulk temperature T W = wall temperature T 0 = reference temperature T ¤ = Green's free space solution t = time u = x component of velocity v = y component of velocity W = vector of conserved variables x = location of eld point a = dual reciprocity method expansion coef cient C = boundary of domain X c = speci c heat ratio D t = time step h t , h q = weighting parameters in DRBEM time-marching scheme l = dynamic viscosity n = location of source point r = normal viscous stress s = viscous shear stress U = DRM interpolating matrix u = DRM expansion function w = Kirchhoff parameter w 0 = reference Kirchhoff parameter X = domain

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“…The BEM is used to solve solid heat conduction problem. He et al [13,14], M He et al [15], Kontinos [16], Rahaim and Kassab [17] and Rahaim et al [18] adopted this conjugate heat transfer analysis method to solve different coupled problems. Kassab et al [19] reported on the coupling of the BEM method with the Glenn-HT code.…”

Section: Introductionmentioning

confidence: 98%

BEM/FDM conjugate heat transfer analysis of a two-dimensional air-cooled turbine blade boundary layer

et al. 2008

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A coupled boundary element method (BEM) and finite difference method (FDM) are applied to solve conjugate heat transfer problem of a two-dimensional air-cooled turbine blade boundary layer. A loosely coupled strategy is adopted, in which each set of field equations is solved to provide boundary conditions for the other. The Navier-Stokes equations are solved by HIT-NS code. In this code, the FDM is adopted and is used to resolve the convective heat transfer in the fluid region. The BEM code is used to resolve the conduction heat transfer in the solid region. An iterated convergence criterion is the continuity of temperature and heat flux at the fluid-solid interface. The numerical results from the BEM adopted in this paper are in good agreement with the results of analytical solution and the results of commercial code, such as Fluent 6.2. The BEM avoids the complicated mesh needed in other computation method and saves the computation time. The results prove that the BEM adopted in this paper can give the same precision in numerical results with less boundary points. Comparing the conjugate results with the numerical results of an adiabatic wall flow solution, it reveals a significant difference in the distribution of metal temperatures. The results from conjugate heat transfer analysis are more accurate and they are closer to realistic thermal environment of turbines.

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A Coupled FDM/Bem Solution for the Conjugate Heat Transfer Problem

Cited by 22 publications

References 4 publications

BEM/FVM conjugate heat transfer analysis of a three‐dimensional film cooled turbine blade

BEM/FVM conjugate heat transfer analysis of a three‐dimensional film cooled turbine blade

Coupled Dual Reciprocity Boundary Element/Finite Volume Method for Transient Conjugate Heat Transfer

BEM/FDM conjugate heat transfer analysis of a two-dimensional air-cooled turbine blade boundary layer

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