The application of lasers in industrial drilling processes is rapidly increasing. Consequently there is a great need to understand the fundamental physics of the laser drilling process. Recent experiments have shown that material removal occurs via the combined action of vaporization and melt expulsion due to the vaporization-induced recoil pressure. The authors (Batteh et al., 1998) developed a quasi-steady stagnation flow analysis to study the physical mechanisms of laser drilling by examining the heat transfer and fluid flow in the molten metal. This paper presents an extension of that analysis by including the effects of nonequilibrium vaporization. A Knudsen layer analysis is used to model the nonequilibrium evaporation at the liquid-vapor interface and the compressible flow outside the Knudsen layer. The analysis gives the pressure, temperature, and density jumps across the Knudsen layer. Numerical results for the combined stagnation flow and Knudsen layer analysis are shown for several different materials over a range of laser intensities commonly used in laser drilling. Drilling trends are shown as functions of the laser energy and beam radius. The results show that a significant portion of the material removed occurs through melt expulsion due to the vaporization-induced recoil pressure. The results from both the equilibrium and Knudsen layer models for vaporization are compared, and the validity of equilibrium vaporization models are discussed.
{"title":"A Coupled Stagnation Flow and Knudsen Layer Analysis for Laser Drilling","authors":"J. Batteh, M. M. Chen, J. Mazumder","doi":"10.1115/imece1999-1077","DOIUrl":"https://doi.org/10.1115/imece1999-1077","url":null,"abstract":"\u0000 The application of lasers in industrial drilling processes is rapidly increasing. Consequently there is a great need to understand the fundamental physics of the laser drilling process. Recent experiments have shown that material removal occurs via the combined action of vaporization and melt expulsion due to the vaporization-induced recoil pressure. The authors (Batteh et al., 1998) developed a quasi-steady stagnation flow analysis to study the physical mechanisms of laser drilling by examining the heat transfer and fluid flow in the molten metal. This paper presents an extension of that analysis by including the effects of nonequilibrium vaporization. A Knudsen layer analysis is used to model the nonequilibrium evaporation at the liquid-vapor interface and the compressible flow outside the Knudsen layer. The analysis gives the pressure, temperature, and density jumps across the Knudsen layer. Numerical results for the combined stagnation flow and Knudsen layer analysis are shown for several different materials over a range of laser intensities commonly used in laser drilling. Drilling trends are shown as functions of the laser energy and beam radius. The results show that a significant portion of the material removed occurs through melt expulsion due to the vaporization-induced recoil pressure. The results from both the equilibrium and Knudsen layer models for vaporization are compared, and the validity of equilibrium vaporization models are discussed.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129876724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is an extension of our previous work on simulation of complex phase front evolution in the diffusion-dominated situation. The Navier-Stokes equations are solved using a finite-volume method based on a second-order accurate central-difference scheme in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second-order spatial accuracy of the underlying solver. The presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations. The convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh. The accuracy and fidelity of the solver is validated and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated. The method will be useful in studying the effects of fluid flow on the evolution of complex solid-liquid phase boundaries.
{"title":"Simulation of Flow and Heat Transfer With Phase Boundaries and Complex Geometries on Cartesian Grids","authors":"H. Udaykumar, R. Mittal, W. Shyy","doi":"10.1115/imece1999-1093","DOIUrl":"https://doi.org/10.1115/imece1999-1093","url":null,"abstract":"\u0000 This paper is an extension of our previous work on simulation of complex phase front evolution in the diffusion-dominated situation. The Navier-Stokes equations are solved using a finite-volume method based on a second-order accurate central-difference scheme in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second-order spatial accuracy of the underlying solver. The presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations. The convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh. The accuracy and fidelity of the solver is validated and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated. The method will be useful in studying the effects of fluid flow on the evolution of complex solid-liquid phase boundaries.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133314915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Kumar, Vladimir A. Boychev, Zhuomin M. Zhang, D. Tanner
Fabry-Perot (F-P) resonators were built from two superconductive YBa2Cu3O7-δ (YBCO) films separated by a spacer. Each film of 35 nm thickness was deposited on a Si substrate ≈0.2 mm thick. A slow-scan Michelson interferometer was employed to measure the transmittance of the resonator in the far-infrared frequency region from 10 to 90 cm−1 at temperatures between 10 and 300 K. Measurements showed that in the normal state the peak (or resonant) transmittance decreases with temperature, whereas in the superconducting state it can increase with decreasing temperature. The transmittance of the resonator was calculated using properties of individual reflectors obtained previously. When the effect of partial coherence is taken into consideration, the calculated transmittance is in good agreement with the experiments. Furthermore, the maximum possible resonant transmittance was predicted based on an optimization analysis considering the interference effects. The effect of the YBCO film thickness on the transmittance peaks was also studied, showing that the resonant transmittance decreases but the finesse increases as the film thickness is increased. This study should help improve the future design of F-P resonators based on HTSC thin films.
{"title":"Fabry-Perot Resonators Built With YBa2Cu3O7-δ Films on Si Substrates","authors":"A. Kumar, Vladimir A. Boychev, Zhuomin M. Zhang, D. Tanner","doi":"10.1115/imece1999-1058","DOIUrl":"https://doi.org/10.1115/imece1999-1058","url":null,"abstract":"\u0000 Fabry-Perot (F-P) resonators were built from two superconductive YBa2Cu3O7-δ (YBCO) films separated by a spacer. Each film of 35 nm thickness was deposited on a Si substrate ≈0.2 mm thick. A slow-scan Michelson interferometer was employed to measure the transmittance of the resonator in the far-infrared frequency region from 10 to 90 cm−1 at temperatures between 10 and 300 K. Measurements showed that in the normal state the peak (or resonant) transmittance decreases with temperature, whereas in the superconducting state it can increase with decreasing temperature. The transmittance of the resonator was calculated using properties of individual reflectors obtained previously. When the effect of partial coherence is taken into consideration, the calculated transmittance is in good agreement with the experiments. Furthermore, the maximum possible resonant transmittance was predicted based on an optimization analysis considering the interference effects. The effect of the YBCO film thickness on the transmittance peaks was also studied, showing that the resonant transmittance decreases but the finesse increases as the film thickness is increased. This study should help improve the future design of F-P resonators based on HTSC thin films.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122692350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Hoelke, H. T. Henderson, F. Gerner, M. Kazmierczak
For on-chip electronic cooling, a micromachined silicon LHP (Loop Heat Pipe) is being developed, with a Coherent Porous Silicon (CPS) wick as the central part. The present work is a lumped-element network analysis of the overall heat removal performance of such a device. A heat flux of more than 100 W/cm2 is predicted for a micromachined baseline LHP. Moreover, this system-level model shows that a higher performance could be achieved by optimizing the vapor-removing duct. This would be possible without severe microfabrication challenges. The predicted performance of an optimized LHP with reduced turbulent flow losses in the evaporator exceeds 1000 W/cm2.
{"title":"Analysis of the Heat Transfer Capacity of a Micromachined Loop Heat Pipe","authors":"A. Hoelke, H. T. Henderson, F. Gerner, M. Kazmierczak","doi":"10.1115/imece1999-1062","DOIUrl":"https://doi.org/10.1115/imece1999-1062","url":null,"abstract":"\u0000 For on-chip electronic cooling, a micromachined silicon LHP (Loop Heat Pipe) is being developed, with a Coherent Porous Silicon (CPS) wick as the central part. The present work is a lumped-element network analysis of the overall heat removal performance of such a device. A heat flux of more than 100 W/cm2 is predicted for a micromachined baseline LHP. Moreover, this system-level model shows that a higher performance could be achieved by optimizing the vapor-removing duct. This would be possible without severe microfabrication challenges. The predicted performance of an optimized LHP with reduced turbulent flow losses in the evaporator exceeds 1000 W/cm2.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121357329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents experimental and numerical results for the quench of a gear blank in agitated and stagnant oil. Temperatures within the gear blank are determined with a whole domain-optimizer technique inverse solution method, to calculate the time history at every point in the gear blank. The development of this procedure represents the first stage in an overall analysis of the quench process that will later include material phase transformations and deformation. The paper presents ten variations in setting up the inverse problem, to analyze which combination of independent variables and decision variables results in the best match between experimental and numerical results. The results indicate that dividing the boundary of the gear blank into four zones and assigning a fixed heat transfer coefficient or heat flux to each zone yields an average RMS error (average difference between experimental and numerical results) of the order of 40 K. This error can be reduced by either increasing the number of zones, by reducing the number of thermocouples being matched, or by allowing the heat transfer or heat flux to vary within the zones. Of these possibilities, variation of heat transfer within the zones gives the best improvement in the quality of the match for the amount of extra computational effort required to run the problem.
{"title":"Analysis of Heat Transfer During Quenching of a Gear Blank","authors":"S. Aceves, Sahai","doi":"10.1115/imece1999-1073","DOIUrl":"https://doi.org/10.1115/imece1999-1073","url":null,"abstract":"\u0000 This paper presents experimental and numerical results for the quench of a gear blank in agitated and stagnant oil. Temperatures within the gear blank are determined with a whole domain-optimizer technique inverse solution method, to calculate the time history at every point in the gear blank. The development of this procedure represents the first stage in an overall analysis of the quench process that will later include material phase transformations and deformation.\u0000 The paper presents ten variations in setting up the inverse problem, to analyze which combination of independent variables and decision variables results in the best match between experimental and numerical results. The results indicate that dividing the boundary of the gear blank into four zones and assigning a fixed heat transfer coefficient or heat flux to each zone yields an average RMS error (average difference between experimental and numerical results) of the order of 40 K. This error can be reduced by either increasing the number of zones, by reducing the number of thermocouples being matched, or by allowing the heat transfer or heat flux to vary within the zones. Of these possibilities, variation of heat transfer within the zones gives the best improvement in the quality of the match for the amount of extra computational effort required to run the problem.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1999-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129716427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The grid partial analytical solution method is a newly developed unconditionally stable explicit numerical solution method for solving parabolic partial differential equations. This method discretizes only the spatial domain and predicts a continuous time dependent function at each spatial nodal point. As such, instead of conventionally predicting the solution from a number set, this method predicts from a functional domain. The typical properties of the grid partial analytical solution method can be summarized as the following: (1) It predicts a continuous nodal time dependent function rather than a discrete nodal value. (2) The prediction is unconditionally stable. And unlike any other unconditionally stable finite difference schemes which will lose accuracy when Fourier number becomes large, the proposed method allows single step time marching and unlimited reduction in the spatial step size Δx. (3) For a fixed time step, the higher value of the grid Fourier number resulting from decreasing Δx, the higher the accuracy is achieved in the predicted solution. (4) The grid partial analytical solution converges uniformly to the full analytical solution as the spatial truncation error is infinitely decreased by reducing the spatial step size Δx. This unique characteristic of the analytical treatment of time also makes it possible to treat other time dependent nonhomogeneities involved in heat conduction problem analytically. In this paper, a moving source heat conduction problem is posed and its grid partial analytical solution method developed.
{"title":"Development of a Grid Partial Analytical Solution Method for Solving the Moving Source Heat Conduction Problem","authors":"Xing Ouyang, P. Bishop","doi":"10.1115/imece1997-0924","DOIUrl":"https://doi.org/10.1115/imece1997-0924","url":null,"abstract":"\u0000 The grid partial analytical solution method is a newly developed unconditionally stable explicit numerical solution method for solving parabolic partial differential equations. This method discretizes only the spatial domain and predicts a continuous time dependent function at each spatial nodal point. As such, instead of conventionally predicting the solution from a number set, this method predicts from a functional domain. The typical properties of the grid partial analytical solution method can be summarized as the following:\u0000 (1) It predicts a continuous nodal time dependent function rather than a discrete nodal value.\u0000 (2) The prediction is unconditionally stable. And unlike any other unconditionally stable finite difference schemes which will lose accuracy when Fourier number becomes large, the proposed method allows single step time marching and unlimited reduction in the spatial step size Δx.\u0000 (3) For a fixed time step, the higher value of the grid Fourier number resulting from decreasing Δx, the higher the accuracy is achieved in the predicted solution.\u0000 (4) The grid partial analytical solution converges uniformly to the full analytical solution as the spatial truncation error is infinitely decreased by reducing the spatial step size Δx.\u0000 This unique characteristic of the analytical treatment of time also makes it possible to treat other time dependent nonhomogeneities involved in heat conduction problem analytically. In this paper, a moving source heat conduction problem is posed and its grid partial analytical solution method developed.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"101 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114426963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new conduction calibration apparatus has been designed to deliver heat fluxes up to a maximum of 100 kW/m2 with an established goal of ± 5 % precision. This system will provide a close to purely diffusive (as opposed to radiative) heat flux boundary condition and, when compared to the gauge’s response in the National Institute of Standards and Technology (NIST) radiative calibration facility, act as a check on the sensitivity of a heat flux gauge to the mode of heat transfer. A platinum-plated copper block heated electrically with 2 kW power is designed to produce uniform temperatures up to 750 K across its face. A cold plate will be maintained around 290 K through pool boiling using a liquid refrigerant and a remote condenser. A 1 mm wide helium filled gap between the hot plate and the sensing surface of a cooled heat flux gauge will provide the high conductive fluxes desired (while limiting radiation to a few per cent and avoiding the uncertainties associated with contact resistance). Detailed numerical modeling of the device is being used to identify limitations and evaluate alternatives in the design, and to analyze the level of uncertainty associated with the facility. A description of the apparatus and the results of preliminary modeling are reported.
{"title":"Development of a High Flux Conduction Calibration Apparatus","authors":"W. Grosshandler, D. Blackburn","doi":"10.1115/imece1997-0904","DOIUrl":"https://doi.org/10.1115/imece1997-0904","url":null,"abstract":"A new conduction calibration apparatus has been designed to deliver heat fluxes up to a maximum of 100 kW/m2 with an established goal of ± 5 % precision. This system will provide a close to purely diffusive (as opposed to radiative) heat flux boundary condition and, when compared to the gauge’s response in the National Institute of Standards and Technology (NIST) radiative calibration facility, act as a check on the sensitivity of a heat flux gauge to the mode of heat transfer. A platinum-plated copper block heated electrically with 2 kW power is designed to produce uniform temperatures up to 750 K across its face. A cold plate will be maintained around 290 K through pool boiling using a liquid refrigerant and a remote condenser. A 1 mm wide helium filled gap between the hot plate and the sensing surface of a cooled heat flux gauge will provide the high conductive fluxes desired (while limiting radiation to a few per cent and avoiding the uncertainties associated with contact resistance). Detailed numerical modeling of the device is being used to identify limitations and evaluate alternatives in the design, and to analyze the level of uncertainty associated with the facility. A description of the apparatus and the results of preliminary modeling are reported.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129499835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A numerical study is performed to investigate thermal transport phenomena in turbulent gas flow through a tube with high uniform wall temperature. A k-ε turbulence model is employed to determine the turbulent viscosity and the turbulent kinetic energy. The turbulent heat flux is expressed by Boussinesq approximation in which the eddy diffusivity of heat is determined by a t2¯-εt heat-transfer model. The governing boundary-layer equations are discretized by means of a control volume finite-difference technique and numerically solved using a marching procedure. It is disclosed from the study that: (i) Like in a pipe with high uniform wall heat flux, laminarization takes place in a turbulent gas flow through a pipe with high uniform wall temperature, (ii) Once laminarization occurs, both velocity and temperature gradients at the wall diminish along the flow, resulting in a substantial reduction in both the turbulent kinetic energy and temperature variance across the whole tube cross section, and (iii) these attenuations cause a deterioration in heat transfer performance.
{"title":"Thermal Transport Phenomena in Turbulent Gas Flows Through a Tube With High Constant Wall Temperature","authors":"S. Torii, Wen‐Jei Yang","doi":"10.1115/imece1997-0913","DOIUrl":"https://doi.org/10.1115/imece1997-0913","url":null,"abstract":"\u0000 A numerical study is performed to investigate thermal transport phenomena in turbulent gas flow through a tube with high uniform wall temperature. A k-ε turbulence model is employed to determine the turbulent viscosity and the turbulent kinetic energy. The turbulent heat flux is expressed by Boussinesq approximation in which the eddy diffusivity of heat is determined by a t2¯-εt heat-transfer model. The governing boundary-layer equations are discretized by means of a control volume finite-difference technique and numerically solved using a marching procedure. It is disclosed from the study that: (i) Like in a pipe with high uniform wall heat flux, laminarization takes place in a turbulent gas flow through a pipe with high uniform wall temperature, (ii) Once laminarization occurs, both velocity and temperature gradients at the wall diminish along the flow, resulting in a substantial reduction in both the turbulent kinetic energy and temperature variance across the whole tube cross section, and (iii) these attenuations cause a deterioration in heat transfer performance.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133699104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper presents some sample computations that employ three different schemes for the discretization of the incompressible Navier-Stokes equations: colocated mesh (CM) with basic second order finite difference approximations for the interior nodes, with two different implementations of the pressure boundary condition, and the conventional staggered mesh (SM). The specific goal is to better appreciate the well known spatial oscillation, or “pressure wiggle”, phenomenon usually attributed to the use of colocated mesh. A modified artificial compressibility method (ACM) and the MAC method were used for the colocated and staggered mesh calculations, respectively, but the focus of our findings is on the converged steady state results which pertain more to the asymptotic steady state discretization scheme (i.e. SM or CM) than the pseudo-time iteration method for obtaining these asymptotic solutions. Two different implementations of the pressure boundary condition were employed in conjunction with the ACM: 1) the requirement that the boundary pressure acts so that the continuity equation is satisfied at the boundary or 2) the requirement that the normal pressure gradient on the boundary satisfies the Navier-Stokes equation. Sample 2D and 3D calculations are performed on the driven cavity problem using these three techniques for a Reynolds number of 100. The results of these sample calculations are analyzed based on solutions available in the literature, and a comparison is made between the various methods and boundary condition implementations. The colocated mesh results indicate that the spatial oscillations, when present, were never greater than the overall accuracy, which is judged to be consistent with expected truncation errors of the various methods. The major objections of the oscillations are thus cosmetic rather than substantive. Furthermore, when the normal pressure gradient condition from the Navier-Stokes equation is used in conjunction with a colocated mesh, the spatial oscillations in the computations are significantly reduced for the pressure and are essentially non-existent for the velocities. These results suggest that the colocated mesh, with artificial compressibility or with other methods of computation, is a viable discretization scheme without the use of complex interpolation schemes to simulate a staggered mesh.
{"title":"A Comparison Between Colocated Mesh and Staggered Mesh Solutions for the Steady State Simple Driven Cavity Problem","authors":"J. Batteh, M. M. Chen","doi":"10.1115/imece1997-0925","DOIUrl":"https://doi.org/10.1115/imece1997-0925","url":null,"abstract":"\u0000 This paper presents some sample computations that employ three different schemes for the discretization of the incompressible Navier-Stokes equations: colocated mesh (CM) with basic second order finite difference approximations for the interior nodes, with two different implementations of the pressure boundary condition, and the conventional staggered mesh (SM). The specific goal is to better appreciate the well known spatial oscillation, or “pressure wiggle”, phenomenon usually attributed to the use of colocated mesh. A modified artificial compressibility method (ACM) and the MAC method were used for the colocated and staggered mesh calculations, respectively, but the focus of our findings is on the converged steady state results which pertain more to the asymptotic steady state discretization scheme (i.e. SM or CM) than the pseudo-time iteration method for obtaining these asymptotic solutions. Two different implementations of the pressure boundary condition were employed in conjunction with the ACM: 1) the requirement that the boundary pressure acts so that the continuity equation is satisfied at the boundary or 2) the requirement that the normal pressure gradient on the boundary satisfies the Navier-Stokes equation. Sample 2D and 3D calculations are performed on the driven cavity problem using these three techniques for a Reynolds number of 100. The results of these sample calculations are analyzed based on solutions available in the literature, and a comparison is made between the various methods and boundary condition implementations. The colocated mesh results indicate that the spatial oscillations, when present, were never greater than the overall accuracy, which is judged to be consistent with expected truncation errors of the various methods. The major objections of the oscillations are thus cosmetic rather than substantive. Furthermore, when the normal pressure gradient condition from the Navier-Stokes equation is used in conjunction with a colocated mesh, the spatial oscillations in the computations are significantly reduced for the pressure and are essentially non-existent for the velocities. These results suggest that the colocated mesh, with artificial compressibility or with other methods of computation, is a viable discretization scheme without the use of complex interpolation schemes to simulate a staggered mesh.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114772915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
By means of weakly nonlinear analysis, we investigate the interaction between two physically distinct instability modes arising in the non-Boussinesq convection flow in a differentially heated tall vertical air-filled cavity. It is shown that in the neighborhood of the codimention-2 point the primary parallel flow becomes unstable due to both shear and buoyant disturbances. The flow dynamics is modeled by a system of the two coupled Landau equations. Different possible instability wave patterns are found, and the parameter regions of their existence are discussed. Energy analysis of the interacting instability modes is also presented.
{"title":"Non-Boussinesq Convection in a Tall Cavity Near the Codimension-2 Point","authors":"S. Suslov, S. Paolucci","doi":"10.1115/imece1997-0915","DOIUrl":"https://doi.org/10.1115/imece1997-0915","url":null,"abstract":"\u0000 By means of weakly nonlinear analysis, we investigate the interaction between two physically distinct instability modes arising in the non-Boussinesq convection flow in a differentially heated tall vertical air-filled cavity. It is shown that in the neighborhood of the codimention-2 point the primary parallel flow becomes unstable due to both shear and buoyant disturbances. The flow dynamics is modeled by a system of the two coupled Landau equations. Different possible instability wave patterns are found, and the parameter regions of their existence are discussed. Energy analysis of the interacting instability modes is also presented.","PeriodicalId":306962,"journal":{"name":"Heat Transfer: Volume 3","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1997-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126140087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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